influences of microstructure and composition on the

Influence of composition and microstructure on the

electrical resistivity of binary magnesium alloys

vorgelegt von

M.-Ing.

Xiao Zhang

ORCID: 0000-0003-2719-3159

an der Fakultät III – Prozesswissenschaften der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

- Dr.-Ing. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Aleksander Gurlo

Gutachter: Priv.-Doz. Dr.-Ing. Sören Müller

Gutachter: Prof. Dr.-Ing. Norbert Hort

Tag der wissenschaftlichen Aussprache: 21. Juli 2021

Berlin 2021

Acknowledgement

I

Acknowledgement

First of all, I would like to acknowledge the financial support of the China Scholarship Council.

I sincerely thank Priv.-Doz. Dr.-Ing. Sören Müller for being my supervisor in Technische

Universität Berlin. His valuable suggestions and advice help me to complete my work. I also

gratefully thank Prof. Dr.-Ing. Norbert Hort as my supervisor in Helmholtz-Zentrum Hereon.

His support and guide me through the whole Ph.D duration. I especially thank Prof. Dr.

Aleksander Gurlo for being the chairman of my Ph.D defense committee.

I would like to express my gratitude to Dr. Yuanding Huang for his guidance and fruitful

discussions on my work. Many thanks also go to Dr. Serge Gavras for operating the TEM and

high resolution SEM. I also want to thank Dr. Veronika Kodetová for helping to measure

resistivity. Ms. Yuhui Zhang is acknowledged for offering the thermal database for

precipitation simulation.

Mr. Günter Meister helps prepare the materials; Mrs. Sabine Schubert and Mr. Daniel Strerath

help analyze the chemical composition. Many thanks to them.

Thank Dr. Weimin Gan and Dr. Xiaohu Li for their help with lab facilities and experiments

during my beam time in MLZ.

I would like to thank all the staffs of MBF department: Dr. Domonkos Tolnai, Dr. Hajo

Dieringa, Dr. Yiyi Lu, Dr. Yuling Xu, Dr. Sihang You, Dr. Hong Yang and Dr. Yaping Zhang,

etc. for their help. I would also like to thank all the colleagues and friends in MagIC for their

help and assistance during my Ph.D study.

Finally, I would like to thank my parents for their love and support. I would like to thank my

lovely wife Kerong Shi and daughter Sike Zhang for unreserved assistance. Only with the love

and support from my family I can finish my Ph.D.

Abstract

III

Abstract

Electrical resistivity is one characteristic and important physical property of a metal, and it is

sensitive to the composition and microstructure. The relationship between resistivity and

composition and microstructure makes resistivity a useful tool in materials research, such as

non-destructive evaluation and monitoring precipitation kinetics. However, this needs a good

understanding of how composition and microstructure influence resistivity, which is currently

lack in Mg alloys. Therefore, a systematic investigation of the resistivity of Mg alloys is

necessary.

Mg-Al, Mg-Gd, Mg-Sn and Mg-Zn series alloys with different solute content are prepared for

the current investigation. The resistivity of these alloys in the as-cast, solution treated, and aged

status are measured at different temperatures to study the influence of temperature, composition

and microstructure on the resistivity. In situ measurements are also conducted to study the

resistivity changes during isothermal ageing of Mg alloys.

The results show that Mg alloys have a positive temperature coefficient of resistivity (TCR).

The TCR varies from different solute content, which demonstrate the deviation from

Matthiessen’s rule in Mg alloys. When the alloys are solution treated, the following equation

can describe the relationship between resistivity and solute contents:

ρ(T)=ρMg(T)+δ(T)×c

ρ(T) is the resistivity of the alloy under a certain temperature, ρMg(T) is the resistivity of pure

Mg, δ(T) is the coefficient, and c is the concentration of the solute. δ(T) depends on both the

temperature and the type of solute. The reason for the increment is the lattice distortion caused

by the solute elements. When the alloys are aged, a phenomenological formula can describe

the relationship between the resistivity and the volume fraction of precipitates：

𝜌𝑒𝑓𝑓 = 𝜌𝛼1 +

12𝑉𝛽

1 − 𝑉𝛽

𝜌𝑒𝑓𝑓 is the effective resistivity, 𝑉𝛽 is the volume fraction of the precipitates, 𝜌𝛼 is the resistivity

of the 𝛼-Mg matrix. With the help of this formula, resistivity can be used to quantify the

precipitation kinetics of binary magnesium alloys.

Zusammenfassung

IV

Zusammenfassung

Der spezifische elektrische Widerstand ist eine charakteristische und wichtige physikalische

Eigenschaft eines Metalls und er ist empfindlich gegenüber Zusammensetzung und

Mikrostruktur. Die Beziehung zwischen spezifischem Widerstand, Zusammensetzung und

Mikrostruktur macht den spezifischen Widerstand zu einem nützlichen Werkzeug in der

Materialforschung, wie z. B. der zerstörungsfreien Bewertung und Überwachung der

Ausscheidungskinetik. Dies erfordert jedoch ein gutes Verständnis dafür, wie

Zusammensetzung und Mikrostruktur den spezifischen Widerstand beeinflussen. Dies fehlt

zurzeit jedoch bei Mg-Legierungen. Daher ist eine systematische Untersuchung des

spezifischen Widerstands von Mg-Legierungen erforderlich.

Für die aktuelle Untersuchung werden Legierungen der Mg-Al-, Mg-Gd-, Mg-Sn- und Mg-Zn-

Reihe mit unterschiedlichen Gehalten an Legierungselementen verwendet. Der spezifische

Widerstand dieser Legierungen im gegossenen, lösungsbehandelten und gealterten Zustand

wird bei verschiedenen Temperaturen gemessen, um den Einfluß von Temperatur,

Zusammensetzung und Mikrostruktur auf den spezifischen Widerstand zu untersuchen. In situ-

Messungen werden auch durchgeführt, um die spezifischen Widerstandsänderungen während

der isothermen Alterung von Mg-Legierungen zu bestimmen.

Die Ergebnisse zeigen, dass Mg-Legierungen einen positiven Temperaturkoeffizienten des

spezifischen Widerstands (TCR) aufweisen. Der TCR variiert mit verschiedenen Gehalten an

gelösten Legierungselement, was die Abweichung von der Matthiessen-Regel in Mg-

Legierungen zeigt. Wenn die Legierungen lösungsbehandelt werden, kann die folgende

Gleichung die Beziehung zwischen dem spezifischen Widerstand und dem Gehalt an gelösten

Stoffen beschreiben:


ρ(T) ist der spezifische Widerstand der Legierung bei einer bestimmten Temperatur, ρMg(T) ist

der spezifische Widerstand von reinem Mg, δ(T) ist der Koeffizient und c ist die Konzentration

des gelösten Stoffes. δ(T) hängt sowohl von der Temperatur als auch von der Art des gelösten

Stoffes ab. Der Grund für die Zunahme ist die durch die gelösten Elemente verursachte

Gitterverzerrung. Wenn die Legierungen gealtert werden, kann eine phänomenologische

Formel die Beziehung zwischen dem spezifischen Widerstand und dem Volumenanteil der

Ausscheidungen beschreiben:

Zusammenfassung

V


12𝑉𝛽

1 − 𝑉𝛽

𝜌𝑒𝑓𝑓 ist der effektive spezifische Widerstand, 𝑉𝛽 ist der Volumenanteil der Ausscheidungen,

𝜌𝛼 ist der spezifische Widerstand der α-Mg-Matrix. Mit Hilfe dieser Formel kann der

spezifische Widerstand verwendet werden, um die Ausscheidungskinetik binärer

Magnesiumlegierungen zu quantifizieren.

Table of contents

VI

Table of contents

Acknowledgement ..................................................................................................................... I

Abstract .................................................................................................................................... III

Zusammenfassung.................................................................................................................... IV

Table of contents ...................................................................................................................... VI

List of figures ............................................................................................................................ X

List of tables ........................................................................................................................... XII

List of abbreviations ............................................................................................................. XIII

List of symbols ...................................................................................................................... XIV

1 Introduction ........................................................................................................................ 1

2 Literature review................................................................................................................. 3

2.1 Magnesium and its alloys ........................................................................................... 3

2.1.1 Common alloying elements in magnesium alloys ............................................... 4

2.1.1.1 Aluminium .................................................................................................... 4

2.1.1.2 Zinc ............................................................................................................... 4

2.1.1.3 Manganese .................................................................................................... 4

2.1.1.4 Silver ............................................................................................................. 5

2.1.1.5 Zirconium ..................................................................................................... 5

2.1.1.6 Rare Earth Metals ......................................................................................... 5

2.1.1.7 Iron, Nickel and Copper ............................................................................... 5

2.1.2 Precipitation in magnesium alloys ....................................................................... 6

2.1.2.1 Mg-Al based alloys ....................................................................................... 7

2.1.2.2 Mg-Ca based alloys ...................................................................................... 8

2.1.2.3 Mg-Sn based alloys ...................................................................................... 8

2.1.2.4 Mg-Zn based alloys ...................................................................................... 9

2.1.2.5 Mg-RE based alloys.................................................................................... 10

2.1.2.5.1 Mg-Gd based alloys ............................................................................... 11

2.1.2.5.2 Mg-Nd based alloys ............................................................................... 12

2.2 Electrical resistivity of metals and its application ................................................... 13

2.2.1 Drude model....................................................................................................... 13

2.2.2 Matthiessen’s rule .............................................................................................. 17

2.2.2.1 Matthiessen’s rule ....................................................................................... 17

2.2.2.2 Deviations from Matthiessen’s Rule .......................................................... 19

2.2.3 Influencing Factors of electrical resistivity........................................................ 19

Table of contents

VII

2.2.3.1 Effect of lattice imperfection ...................................................................... 20

2.2.3.1.1 Vacancy .................................................................................................. 20

2.2.3.1.2 Dislocations and grain boundaries ......................................................... 20

2.2.3.2 Influence of solution element ..................................................................... 20

2.2.3.3 Effect of temperature .................................................................................. 22

2.2.4 Application of electrical resistivity .................................................................... 22

2.2.4.1 Non-destructive testing ............................................................................... 23

2.2.4.2 Phase transformation monitor ..................................................................... 23

2.2.4.3 Purity evaluation of metals ......................................................................... 24

3 Motivation ........................................................................................................................ 25

4 Materials and Experimental Details ................................................................................. 26

4.1 Materials .................................................................................................................. 26

4.1.1 Casting procedure .............................................................................................. 26

4.1.2 Solution treatment .............................................................................................. 27

4.1.3 Ageing treatment ................................................................................................ 28

4.2 Experimental Details ................................................................................................ 28

4.2.1 Microstructure characterizations ........................................................................ 28

4.2.1.1 Optical microscopy (OM) ........................................................................... 28

4.2.1.2 Scanning electron microscopy (SEM) ........................................................ 29

4.2.1.3 X-ray diffraction analysis ........................................................................... 29

4.2.1.4 Synchrotron radiation diffraction analysis ................................................. 30

4.2.2 Hardness test ...................................................................................................... 30

4.2.3 Electrical resistivity measurements.................................................................... 30

4.2.3.1 Resistivity measurement at low and room temperatures ............................ 30

4.2.3.2 Resistivity measurement at high temperature and in situ measurements ... 31

5 Results .............................................................................................................................. 32

5.1 Microstructure characterization ............................................................................... 32

5.1.1 As-cast alloys ..................................................................................................... 32

5.1.1.1 Mg-Al alloys ............................................................................................... 32

5.1.1.2 Mg-Gd alloys .............................................................................................. 35

5.1.1.3 Mg-Sn alloys............................................................................................... 37

5.1.1.4 Mg-Zn alloys .............................................................................................. 39

5.1.2 As-extruded alloy ............................................................................................... 41

5.1.3 Solution treated alloys........................................................................................ 42

5.1.3.1 Cast alloys................................................................................................... 42

5.1.3.2 Extruded alloy............................................................................................. 45

5.1.4 Aged alloys ........................................................................................................ 46

Table of contents

VIII

5.1.4.1 Mg-Al alloys ............................................................................................... 47

5.1.4.2 Mg-Gd alloys .............................................................................................. 49

5.1.4.3 Mg-Sn alloys............................................................................................... 51

5.1.4.4 Mg-Zn alloys .............................................................................................. 53

5.2 Age hardening behaviour ......................................................................................... 55

5.2.1 Mg-Al alloys ...................................................................................................... 55

5.2.2 Mg-Gd alloys ..................................................................................................... 56

5.2.3 Mg-Sn alloys ...................................................................................................... 58

5.2.4 Mg-Zn alloys ...................................................................................................... 59

5.3 Electrical resistivity ................................................................................................. 61

5.3.1 The resistivity of the as-cast alloys .................................................................... 61

5.3.1.1 Low and room temperatures ....................................................................... 61

5.3.1.2 Moderate temperatures ............................................................................... 61

5.3.2 The resistivity of the solution treated alloys ...................................................... 62

5.3.2.1 Cast alloys................................................................................................... 62

5.3.2.2 Extruded alloys ........................................................................................... 63

5.3.3 The resistivity of aged alloys ............................................................................. 64

5.3.4 In situ resistivity measurements during isothermal ageing ................................ 65

6 Discussion ......................................................................................................................... 67

6.1 Microstructure .......................................................................................................... 67

6.1.1 As-cast alloys ..................................................................................................... 67

6.1.1.1 Intermetallic phases .................................................................................... 67

6.1.1.2 Grain size .................................................................................................... 69

6.1.2 Solution treated alloys........................................................................................ 71

6.1.2.1 Cast alloys................................................................................................... 71

6.1.2.2 Extruded alloy............................................................................................. 73

6.1.3 Aged alloys ........................................................................................................ 73

6.2 Age hardening mechanism ....................................................................................... 74

6.2.1 Initial state .......................................................................................................... 74

6.2.2 Peak-aged condition ........................................................................................... 76

6.2.3 Over-aged condition........................................................................................... 77

6.3 Influencing factor of resistivity in binary magnesium alloys .................................. 78

6.3.1 Grain size ........................................................................................................... 78

6.3.2 Temperature ....................................................................................................... 79

6.3.3 Alloying elements and their contents ................................................................. 81

6.3.4 Heat treatment .................................................................................................... 83

Table of contents

IX

6.3.4.1 Solution treatment....................................................................................... 83

6.3.4.2 Ageing treatment ........................................................................................ 85

6.4 Precipitation kinetics quantified by resistivity ......................................................... 87

7 Conclusion ........................................................................................................................ 90

Reference ................................................................................................................................. 91

Table of figures

X

List of figures

Fig. 2-1 Unit cell and slip planes of magnesium [29]. ............................................................... 3

Fig. 2-2 Schematic diagrams of the Drude Model. .................................................................. 14

Fig. 2-3 Electrical resistivity of annealed and cold-worked (deformed) copper alloys. .......... 18

Fig. 2-4 Deviation from Matthiessen’s rule in SrRuO3 and CaRuO3 alloys. ........................... 19

Fig. 2-5 Resistivity of Cu-Au alloy in different states. ............................................................ 21

Fig. 2-6 Relationship between the resistivity and yield stress. ................................................ 24

Fig. 4-1 Casting system. (a) furnace, (b) direct chill casting system. ...................................... 27

Fig. 4-2 Resistivity sample and room temperature measurements apparatus. ......................... 31

Fig. 4-3 High-temperature resistivity measurement apparatus and schematic of the delta

method measurements. ............................................................................................................. 31

Fig. 5-1 OM and SEM (BSE) micrographs of as-cast Mg-Al alloys. ...................................... 33

Fig. 5-2 X-ray diffraction patterns of as-cast Mg-Al alloys. ................................................... 34

Fig. 5-3 OM and SEM (BSE) micrographs of as-cast Mg-Gd alloys. ..................................... 35

Fig. 5-4 Enlarged BSE micrograph of as-cast Mg-2.5Gd alloy. .............................................. 36

Fig. 5-5 X-ray diffraction patterns of as-cast Mg-Gd alloys. .................................................. 37

Fig. 5-6 OM and SEM (BSE) micrographs of as-cast Mg-Sn alloys....................................... 38

Fig. 5-7 BSE micrograph of as-cast Mg-2.5Sn alloy. .............................................................. 38

Fig. 5-8 X-ray diffraction patterns of as-cast Mg-Sn alloys. ................................................... 39

Fig. 5-9 OM and SEM (BSE) micrographs of as-cast Mg-Zn alloys. ..................................... 40

Fig. 5-10 X-ray diffraction patterns of as-cast Mg-Zn alloys. ................................................. 41

Fig. 5-11 OM and SEM (BSE) micrographs of as-extruded Mg-0.8Gd alloy. ........................ 42

Fig. 5-12 OM and SEM (BSE) micrographs of solution treated alloys. .................................. 43

Fig. 5-13 X-ray diffraction of solution treated alloys. ............................................................. 44

Fig. 5-14 Synchrotron diffraction pattern of the solution treated Mg-Gd alloy. ..................... 45

Fig. 5-15 Composition of the intermetallic phase in as-cast and solution treated Mg-Zn alloy.

.................................................................................................................................................. 45

Fig. 5-16 OM of extruded Mg-0.8Gd alloy with different solution times. .............................. 46

Fig. 5-17 Microstructures of Mg-8Al alloy aged at 175 °C. .................................................... 47



Fig. 5-20 X-Ray diffraction of Mg-8Al alloys aged at different conditions. ........................... 49

List of tables

XI

Fig. 5-21 Microstructures of Mg-2.5Gd alloys aged at 200 °C and 225 °C. ........................... 49

Fig. 5-22 Microstructures of Mg-2.5Gd alloys aged at 250 °C. .............................................. 50

Fig. 5-23 Synchrotron diffraction of Mg-2.5Gd alloys aged at different conditions. .............. 51

Fig. 5-24 Microstructures of Mg-2.5Sn alloy aged at 200 °C. ................................................ 51



Fig. 5-27 X-Ray diffraction of Mg-2.5Sn alloys aged at different conditions. ....................... 53

Fig. 5-28 Microstructures of Mg-2.5Zn alloy aged at 175 °C. ................................................ 53



Fig. 5-31 X-Ray diffraction of Mg-2.5Zn alloys aged at different conditions ........................ 55

Fig. 5-32 Age hardening curves of Mg-Al alloys. ................................................................... 56

Fig. 5-33 Age hardening curves of Mg-Gd alloys. .................................................................. 57

Fig. 5-34 Age hardening curves of Mg-Sn alloys. ................................................................... 59

Fig. 5-35 Age hardening curves of Mg-Zn alloys. (a) 175 °C; (b) 200 °C; (c) 225 °C. .......... 60

Fig. 5-36 The resistivity of as-cast alloys. ............................................................................... 61

Fig. 5-37 The resistivity of as-cast alloys. ............................................................................... 62

Fig. 5-38 The resistivity of solution treated alloys. ................................................................. 62

Fig. 5-39 The resistivity of solution treated alloys. ................................................................. 63

Fig. 5-40 Resistivity of Mg-0.8Gd alloy after solution treatment. .......................................... 64

Fig. 5-41 The resistivity of alloys aged at 225 °C. .................................................................. 65

Fig. 5-42 Resistivity changes during isothermal ageing. ......................................................... 66

Fig. 6-1 Phase diagrams of binary Mg alloys in the Mg-rich corner. ...................................... 68

Fig. 6-2 BSE micrographs of as-cast alloys. ............................................................................ 69

Fig. 6-3 Microstructure of solution treated Mg-1.5Zn alloy. ................................................... 72

Fig. 6-4 Hardness of alloys in the as-solution treated states. ................................................... 74

Fig. 6-5 Calculated diffusion rate of alloying elements in Mg matrix at 225 °C. ................... 77

Fig. 6-6 Resistivity of solution treated alloys. ......................................................................... 81

Fig. 6-7 Resistivity before and after solution treatment. ......................................................... 83

Fig. 6-8 Resistivity of alloys aged at 225 °C. .......................................................................... 86

Fig. 6-9 Volume fraction of the precipitates during isothermal aged at 225 °C. ..................... 88

List of tables

XII

List of tables

Table 2-1 The solubility data calculated by Pandat software (wt. %). ...................................... 6

Table 2-2 The conduction electron density, relaxation time and resistivity of selected elements

at 273 K [152]. ......................................................................................................................... 16

Table 4-1 Nominal chemical compositions of the alloys (at. %). ............................................ 26

Table 4-2 Solution treatment parameters of the as-cast alloys. ............................................... 27

Table 4-3 Ageing parameters of different alloys. .................................................................... 28

Table 5-1 Chemical compositions of the alloys (at. %). .......................................................... 32

Table 5-2 Grain sizes of as-cast Mg-Al alloys. ........................................................................ 33

Table 5-3 Amount of the Mg17Al12 in as-cast Mg-Al alloys and corresponding GOF. ........... 34

Table 5-4 Grain sizes of as-cast Mg-Gd alloys. ....................................................................... 36

Table 5-5 Amount of the Mg5Gd in as-cast Mg-Gd alloys and corresponding GOF. ............. 36

Table 5-6 Grain sizes of as-cast Mg-Sn alloys. ....................................................................... 37

Table 5-7 Amount of the Mg2Sn in as-cast Mg-Sn alloys and corresponding GOF. .............. 39

Table 5-8 Grain sizes of as-cast Mg-Zn alloys. ....................................................................... 39

Table 5-9 Amount of the Mg7Zn3 in as-cast Mg-Zn alloys and corresponding GOF. ............. 41

Table 5-10 Grain sizes of the as-extruded alloy in different directions. .................................. 42

Table 5-11 Grain sizes of the cast alloys after solution treated. .............................................. 43

Table 5-12 Grain sizes of the extruded Mg-0.8Gd alloy after solution treatment. .................. 46

Table 5-13 Age hardening data of Mg-8Al alloy. .................................................................... 56

Table 5-14 Age hardening data of Mg-Gd alloys. ................................................................... 58

Table 5-15 Age hardening data of Mg-Sn alloys. .................................................................... 58

Table 5-16 Age hardening data of Mg-Zn alloys. .................................................................... 60

Table 5-17 Resistivity of different alloys aged at 225 °C. ....................................................... 64

Table 6-1 Amount of alloying elements and intermetallic phases. .......................................... 68

Table 6-2 Parameters for calculating GRFs of different alloying elements ............................ 70

Table 6-3 Local strains of the nearest neighbouring Mg atoms from alloying elements [210].

.................................................................................................................................................. 75

Table 6-4 Alloys aged at 225 °C. ............................................................................................. 76

Table 6-5 TCR of different alloys. ........................................................................................... 80

Table 6-6 Specific resistivity increase and some physical properties of alloying elements. ... 82

Table 6-7 RRR values of the alloys. ........................................................................................ 84

List of abbreviations

XIII

List of abbreviations

AJ Mg-Al-Sr

AM Mg-Al-Mn

AS Mg-Al-Si

AZ Mg-Al-Zn

BCC Body centred cubic

BSE Backscattered electron

BF Bright field

DESY Deutsches Elektronen-Synchrotron

FCC Face centred cubic

Gd Gadolinium

G.P. Guinier–Preston

GRF Growth restriction factor

HAADF High-angle annular dark-field

HCP Hexagonal close packed

HV Vickers hardness

OM Optical microscopy

OPS Oxide polishing suspensions

RE Rare Earth metals

RRR Residual resistivity ratio

SEM Scanning electron microscopy

T4 Solution treatment

T6 Solution treatment and then artificially aged

TEM Transmission electron microscopy

TCR Temperature coefficient of resistivity

UTS Ultimate tensile strength

XRD X-Ray diffraction

List of symbols

XIV

List of symbols

R Resistance, see Eq.(2-1).

I Electrical current, see Eq.(2-1).

V Voltage, see Eq.(2-1),

Also, the unit of voltage: Volt.

E Electric field, see Eq.(2-2).

Electrical resistivity, see Eq.(2-2).

J Current density, see Eq.(2-2).

Unit of Resistance: Ohm.

A Unit of Electrical current: Ampere.

τ Relaxation time.

e Proton charge.

𝑚𝑒 Mass of the electron, see Eq.(2-3).

𝒗 Average electronic velocity, see Eq.(2-3).

𝒗𝐸 Average electronic velocity in an external electric field, see Eq.(2-4).

𝑁𝐴 Avogadro’s number, see Eq.(2-8).

𝜌𝑚 Mass density, see Eq.(2-8).

M Atomic mass of the clement, see Eq.(2-8).

𝜌𝑎 Electrical resistivity of an alloy, see Eq.(2-9).

𝜌𝑝 Electrical resistivity of pure metal, see Eq.(2-9).

𝜌0 Residual resistivity, see Eq.(2-10).

𝜌𝑇 Resistivity caused by thermal vibrations.

𝜌𝐼 Resistivity caused by impurity solute.

𝜌𝑐𝑤 Resistivity caused by cold-word.

α0 Temperature coefficient of resistivity, see Eq.(2-13).

1 Introduction

1

1 Introduction

Magnesium is a promising structural material due to its low density and high specific strength

[1-4]. In order to expand its application, current researches on magnesium are mainly focused

on improving the strength [5, 6], ductility [7, 8], creep resistance [9-11] and corrosion

resistance [12-14]. There are also investigations on the biomedical use of magnesium alloys

[15, 16]. However, studies lying on the physical properties of magnesium alloys are much less

compared to those on mechanical properties.

One of the most characteristic and important physical properties of a metal is the ability to

conduct electricity. Metals are good conductors because the valence electrons can move freely

through the whole metal and act as the charge carriers to conduct electricity. The free

movement of these electrons is affected by scatterers such as lattice imperfection, solution

elements and thermal vibration, so the conductivity is also affected by these factors [17-19].

The conductivity of a metal can also be characterized by its inverse, electrical resistivity.

Electrical resistivity, which is independent of the geometry of the sample, has shown sensitivity

to the microstructure changes. Therefore, it offers a possibility to study the microstructure

change of an alloy by monitoring the electrical resistivity changes.

Some investigations had been performed on electrical resistivity in magnesium alloys.

Salkovitz et al. [20, 21] investigated the resistivity of some dilute magnesium alloys. The

results showed that the resistivity increased linearly with alloying content. Pan et al. [22]

studied the electrical resistivity of some binary magnesium alloys and found that increment of

resistivity due to the solute element was in the sequence Zn<Al<Ca<Sn<Mn<Zr. Ying et al.

[23] discussed the influence of temperature on the resistivity of magnesium alloys range from

2 to 300 K. Their results indicated that the electrical resistivity of magnesium alloys was not

temperature-dependent in the temperature range 2 - 40 K. In the temperature range 40 - 300 K,

the electrical resistivity increased sharply due to the enhanced thermal vibration of the lattice.

Nevertheless, the materials used in these investigations are either in as-cast or T4 states; the

influence of microstructure change due to the heat treatment on the electrical resistivity has not

been well investigated.

Therefore, in order to have a full understanding of resistivity in magnesium, it is necessary to

investigate the influence of microstructure on resistivity. In this work Mg-Al, Mg-Gd, Mg-Sn and

Mg-Zn alloys had been chosen to study the influence of both the alloying elements and the

1 Introduction

2

microstructure on the resistivity. Resistivity in as-cast and T4 states was measured to study the

influence of alloying elements and their concentrations on resistivity. In situ measurements of the

resistivity during ageing were performed to investigate the influence of microstructure on resistivity.

The findings in the current work are expected to clarify the relationship between electrical

resistivity and the microstructure.

2 Literature review

3

2 Literature review

2.1 Magnesium and its alloys

Over the years, with the increasing demand for economical use of energy resources and ever-

stricter control over emissions to lower environmental impact, industries are constantly

searching for new, advanced materials as alternatives to “conventional” materials. Magnesium

is such a promising lightweight metal due to its low density and high specific strength [1-3].

Magnesium has a hexagonal close packed (hcp) crystallographic structure, and the lattice

parameters are a=0.31954 nm and c=0.51872 nm [24]. As shown in Fig. 2-1, there are four slip

planes in magnesium. At room temperature, slip mainly occurred in the basal plane (0001)

along the most occupied direction <11-20>. At high temperatures, non-basal prismatic and

pyramidal slip planes can be activated [25-28].

Fig. 2-1 Unit cell and slip planes of magnesium [29].

As a metal, magnesium is formed through the metallic bond. Each magnesium atom contributes

its valence electrons to form the electron cloud, known as the metallic bond. The metallic bond

makes magnesium a good conductor of electricity. The resistivity of pure magnesium is about

43 nΩ∙m at 295 K [30].

a1

c

a3

a2

Basal {0001}

Pyramidal I {01-11}

Prismatic {01-10}

Pyramidal II {11-22}

Unit cell

2 Literature review

4

2.1.1 Common alloying elements in magnesium alloys

Pure magnesium is rarely used for engineering applications due to its low mechanical

properties. Therefore, it is necessary to improve the properties of magnesium before its usage

in engineering applications. The strengthening mechanisms of magnesium include grain

boundary strengthening, solid solution strengthening and precipitation strengthening [31, 32].

The addition of alloying elements is a normal and effective way to improve the properties of

magnesium since the alloying elements can provide the solution strengthening and have the

potential to offer precipitation and grain boundary strengthening. Aluminium, zinc, manganese,

silver, zirconium and RE (Rear Earth) elements are commonly used in commercial Mg alloys.

2.1.1.1 Aluminium

Al is the most commonly used alloying element in magnesium. It is the major element in the

AZ, AM, AS and AE series alloys. Among them, AZ91 is the most widely used die casting

magnesium alloy [33].

When the content of aluminium is low, the alloy is strengthened by solid solution strengthening.

At a higher concentration of aluminium, the alloy can be strengthened by the precipitation of

the Mg17Al12 phase.

2.1.1.2 Zinc

Zn is another commonly used alloying element in commercial magnesium alloys. The ZK, ZE

and ZC series alloys are designed with the primary alloying element of Zn. It is the secondary

alloying element in the AZ series alloys.

Zn can effectively refine the grain size and provide the grain boundary strengthening [34];

Additionally, Zn contained alloys, such as ZK60 [35], ZE41 [36] and ZC63 [37], can always

be heat treated to obtain precipitation strengthening.

2.1.1.3 Manganese

M1A and M1C are alloys that contain Mn as the primary alloying element [38]. Instead of a

primary alloying element, Mn is more likely to be added as a subordinate alloying element in

Mg alloys. Such as in the Al contained AZ, AM and AS series alloys, and the Zn contained ZC

series alloys [38]. Mn can reduce iron content by formatting the Fe-Mn compound hence

improve the corrosion resistance of the alloys.

javascript:;

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5

2.1.1.4 Silver

Ag is the primary alloying element in the QE series alloys. The QE22 alloy has been employed

for several aerospace applications, including landing wheels, gearbox housings and rotor heads

for helicopters [39]. The QE22 alloy is heat treatable when it is in the peak-aged condition; it

has superior creep resistance over many other magnesium alloys [5].

2.1.1.5 Zirconium

Zr is the most effective grain refiner in magnesium alloys [46], a small amount of Zr can

significantly reduce the grain sizes of the cast alloys.

In many Mg alloys, such as the ZK, ZE, WE and QE series alloys, Zr is added [38]. However,

it is incompatible with Al or Mn containing alloys because these alloying elements will interact

with Zr and form stable compounds, which will eliminate the effect of grain refinement [47].

2.1.1.6 Rare Earth Metals

RE metals are a set of seventeen chemical elements grouped in the periodic table. The most

successful commercial Mg-RE alloys are the WE54 and WE43 alloys, which contain yttrium,

neodymium and heavy RE elements consist of Yb, Er, Dy and Gd [40]. RE elements are also

added as subordinate alloying elements in ZE, QE and AE series alloys [38].

Despite the commercial Mg alloys, high-performance Mg-RE alloys are also developed [41,

42]. One example is the Mg-RE-Zn alloys, with different compositions and appropriate heat

treatment; these alloys can have a high strength [43] or high ductility [44].

2.1.1.7 Iron, Nickel and Copper

Except for the above elements that can improve the performance of Mg alloys, there are also

impurities, mainly Fe, Ni and Cu, which are detrimental to the corrosion performance that

should be noted in Mg alloys [45, 46]. The corrosion rate of Mg alloys is usually insignificant

when the concentrations of impurities are under the tolerance limits, but it will substantially

increase when the impurity concentrations exceed the tolerance limits. Normally, the tolerance

limits of Fe, Ni and Cu are 170 weight ppm, 5 weight ppm and 1000 weight ppm [45].

The corrosion mechanism of these impurities is galvanic corrosion since Mg has the lowest

standard corrosion potential of all the engineering metals [47, 48]. Fe, Ni and Cu with a higher

standard corrosion potential and combined with low hydrogen overvoltage can constitute

efficient cathodes for magnesium and cause severe galvanic corrosion [47].

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2.1.2 Precipitation in magnesium alloys

Precipitation strengthening is an effective method to enhance the strength of Mg alloys and it

largely depends on the amount, morphology and distribution of the precipitates. Precipitation

strengthening of an alloy is normally achieved through three steps:

1) The alloy is heated up to a high temperature to get a supersaturated 𝛼-Mg phase;

2) Quench the alloy to room temperature to maintain the supersaturated 𝛼-Mg phase;

3) Subsequent ageing the alloy at a relatively low temperature to achieve a controlled

decomposition of the supersaturated solid solution into a fine distribution of precipitates

in the magnesium matrix [5, 49].

The supersaturated 𝛼-Mg single-phase is thermodynamically unstable; it tends to decompose

and reduces the internal energy of the system. Energy reduction is the driving force for

precipitation. In theory, the more exceeding solute, the higher the driving force and a larger

amount of the precipitates. Table 2-1 shows the maximum solubility and solubility at 200 °C

(common ageing temperature) of some alloying elements calculated by Pandat software.

Table 2-1 The solubility data calculated by Pandat software (wt. %).

Element Maximum solubility Solubility at 200 °C Solubility changes

Ag 13.78 0.01 13.77

Al 12.71 2.80 9.91

Ca 1.34 0.03 0.67

Ce 0.80 ~0 0.80

Dy 30.37 2.96 27.41

Gd 23.67 1.64 22.03

Li 5.37 5.72 -0.35

Mn 2.15 0.01 2.14

Nd 3.68 0.01 3.67

Sn 13.41 0.38 13.03

Y 13.91 1.76 12.15

Zn 5.94 2.65 3.29

Zr 2.13 0.01 2.12

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Despite the solubility changes, the precipitation process is another crucial factor that affects

the precipitation strengthening of magnesium alloys. Precipitation processes vary a lot with

different alloying elements. In some alloy systems, the only precipitates are the equilibrium

phase, some systems will precipitate the metastable phase during ageing, and in some systems,

there exist the G.P. zones [5]. In addition, precipitate shape and orientation also matter on the

precipitation strengthening in Mg alloys [50, 51]. Therefore, the investigations of the

precipitation process in Mg alloys have attracted researchers’ attention for a long time.

Alloying elements that can offer strong precipitation strengthening in magnesium alloys such

as Al [52, 53], Ca [54, 55], Sn [56, 57], Zn [58, 59] and RE [60-62] have been studied.

2.1.2.1 Mg-Al based alloys

Aluminium is the most widely used alloying element in magnesium alloys [63]. The

commercial AZ, AM and AJ series magnesium alloys are developed based on the binary Mg-

Al alloy with the addition of Zn and Manganese [64]. The maximum solubility of Al decreases

from 12.71 wt. % at eutectic temperature (437 °C) to about 2.8 wt. % at 200 °C.

The Mg17Al12 phase is believed to be the only precipitates formed during the ageing of Mg-Al

alloy [65]. It has a Burgers orientation relationship with the matrix, the growth habit plane is

(0001)Mg || (110)β with a coincident direction [1-210]Mg || [1-11]β [66]. The precipitation of the

Mg17Al12 phase during isothermal ageing is either continuous or discontinuous. Normally,

continuous and discontinuous precipitation can occur simultaneously. However, only

discontinuous or continuous precipitation can be observed at the end of the ageing under a

certain condition. Duly et al. [67] proposed a “Precipitation morphology map” to predict the

occurrence of discontinuous and continuous precipitation at different Al contents and ageing

temperatures. According to their results, continuous precipitation dominates at both high and

low temperatures. At intermediate temperatures, only discontinuous precipitation occurs

during isothermal ageing. However, the “Precipitation morphology map” is not consistent with

the results obtained by other experiments. A research of AZ91 alloy conducted by Malik [68]

reported that discontinuous precipitation is favoured at low temperatures and continuous

precipitation is favoured at high temperatures; at intermediate temperatures, discontinuous and

continuous precipitation can occur simultaneously. Robson [69] proposed a classical kinetic

theory based model to predict the continuous and discontinuous precipitation process in Mg-

Al alloy. The model took the competition between discontinuous and continuous precipitation

into account to predict the final microstructure. Their results demonstrated that continuous

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precipitation could effectively suppress the discontinuous precipitation by reducing the

supersaturation of Al in the matrix. In contrast, discontinuous precipitation had a weak

influence in suppressing continuous precipitation.

2.1.2.2 Mg-Ca based alloys

The maximum solubility of Ca in magnesium is about 1.34 wt. % and it is almost 0 wt. % at

200 °C. The binary Mg-Ca alloy shows moderate precipitation strengthening during isothermal

ageing at 200 °C [54]. The equilibrium precipitates in the Mg-Ca alloy is the Mg2Ca phase; it

has the same P63/mmc space group of magnesium matrix, this similarity may result in a higher

nucleation rate, therefore, a higher number density of precipitates [5]. However, due to the

sparse distribution and coarse morphology of the Mg2Ca phase, the precipitation strengthening

is quite weak in binary Mg-Ca alloy [70]. Therefore, efforts have been made in the past years

to enhance the precipitation strengthening of Mg-Ca alloy.

Mendis et al. reported the enhancement of age hardening response in Mg-Ca alloy due to the

microalloying with Al, In and Zn elements [71]. The addition of Al and Zn microalloying

elements could cause the formation of the uniformly dispersed metastable plate-like internally

ordered G.P. zones in the peak-aged condition. The addition of In could alter the habit plane of

plate-like G.P. zones from the basal plane to the prismatic plane, which was expected to be more

effective in hindering dislocation movement and hence enhanced the age response. Oh-ishi et

al. [70] confirmed the formation of the ordered G.P. zones in Mg-0.3Ca-xZn alloys and

considered the G.P. zones had excellent thermal stability since they remained even after

overaged conditions. Oh-ishi also concluded that the optimum amount of the Zn addition was

0.6 at. %. Excess addition of Zn would change the precipitation process and form a Ca2Mg6Zn3

ternary phase. The Ca2Mg6Zn3 phase would suppress the formation of the ordered G.P. zones

and reduce the peak hardness. Jayaraj et al. [72] verified that the peak-aged of Mg-0.5Ca-0.3Al

alloy was attributed to the ordered G.P. zones and the subsequent formation of the Al2Ca phase

caused the over-aged of Mg-0.5Ca-0.3Al.

2.1.2.3 Mg-Sn based alloys

The maximum solubility of Sn in Magnesium is 13.41 wt. % at eutectic temperature and 0.38

wt. % at 200 °C. The solubility varies over 13 wt. %, which makes the Mg-Sn alloy appropriate

to precipitation strengthening. The only precipitate in Mg-Sn alloy is the equilibrium FCC

Mg2Sn phase [5]. The characteristic property of the Mg2Sn phase is its high melting

2 Literature review

9

temperature of 770 °C. This makes the Mg-Sn alloy has the potential as a creep resistant alloy

[73, 74]. Nevertheless, the precipitation strengthening of binary Mg-Sn alloy is limited due to

the direct precipitation of Mg2Sn without any metastable precipitate phases during the

isothermal ageing [75]. Therefore, methods have been proposed to enhance its precipitation

strengthening. Like the Mg-Ca alloy, microalloying with other elements effectively enhances

the precipitation strengthening [76-79].

Microalloying with Zn had been proved to enhance the precipitation strengthening in Mg-Sn

alloy by making the Mg2Sn phase finer and dispersed more uniformly [80]. In addition to that,

the number density of the precipitates also increased compared to the non-Zn containing Mg-

Sn alloy [80]. The influence of the Ca addition on Mg-3Sn and Mg-5Sn alloys has also been

studied [81, 82]. The Ca addition would cause the formation of a high thermal stability phase,

the CaMgSn phase, which resulted in improved hardness, strength and creep resistance.

Schmid-Fetzer et al. investigated phase formation in Mg-Sn-Ca alloys by combining the

Calphad method with experimental investigations [83, 84]. They found that except for the

CaMgSn phase, the precipitation of the Mg2Ca or Mg2Sn phase would happen. The type of the

phase depends on the Sn/Ca weight ratio in the alloy.

For a long time, it is believed that the precipitation process of Mg-Sn alloy involves only the

precipitation of the FCC Mg2Sn phase. However, Fu et al. [85] introduced a high-pressure

ageing method and a novel hexagonal type Mg2Sn phase. This novel hexagonal Mg2Sn phase

had an average grain size of 25 nm; the uniformly distributed hexagonal Mg2Sn particles

significantly improved the strength and the ductility of Mg-Sn alloy. In addition, Kim et al.

[86] and Liu et al. [87, 88] found the metastable phase formation during the isothermal ageing

at low temperatures. Wang et al. [89] used first principle to study the precipitation process in

Mg-Sn alloy and proposed a new precipitation sequence: supersaturated solid solution (SSSS)

→ G.P. zones → HCP Mg3Sn → FCC Mg3Sn → 𝛽 Mg2Sn. However, the precipitation of G.P.

zones and metastable phase need to be confirmed by more experiments before they are formally

accepted in the precipitation sequence of Mg-Sn alloys [89].

2.1.2.4 Mg-Zn based alloys

Zn is another commonly used alloying element in commercial magnesium alloys. The ZK and

ZC series alloys are developed based on the binary Mg-Zn alloy [38]. The maximum solid

solubility of Zn in magnesium is 5.94 wt. % at eutectic temperature and decreases to 2.65 wt. %

2 Literature review

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at 200 °C. Compared to the Mg-Al alloy, the precipitation process of Mg-Zn alloy is quite

complex. The commonly accepted precipitation sequence is: SSSS → G.P. zones → 𝛽1′

Mg4Zn7 → 𝛽2′ MgZn2 → 𝛽 MgZn.

Murakami et al. [90] first found the formation in Mg-Zn alloy; however, it is then realized that

the formation of the G.P zones is restricted to the ageing temperature under 110 °C [91-93].

The precipitation of 𝛽1′ phase is also controversial. At the early stage, due to the limit of the

equipment, the 𝛽1′ phase is determined as a hexagonal structure and the composition is the same

as the 𝛽2′ phase MgZn2 [94, 95]. Later, a study conducted by Gao and Nie [96] claimed that the

𝛽1′ phase has a base-centred monoclinic structure and the composition is Mg4Zn7. Most

researchers now accept their results. Nevertheless, researchers in Japan [97-100] showed

different results to Gao and Nie, but coincident with the earlier study. They claimed the

difference was due to different ageing temperatures. They believed a higher ageing temperature

is favourable to the formation of the Mg4Zn7 type 𝛽1′ phase while a lower ageing temperature

results in the formation of the MgZn2 type 𝛽1′ phase.

In contrast to the argument of 𝛽1′ phase, 𝛽2

′ phase is widely accepted to be the hexagonal MgZn2

phase. Most 𝛽2′ phase has a basal plane plate morphology and provides much less of an

obstruction to the movement of dislocations [50, 101]. Therefore the over-aged of Mg-Zn alloy

is due to the formation of the 𝛽2′ phase. The formation of equilibrium 𝛽 phase needs longer

period of time [92].

2.1.2.5 Mg-RE based alloys

The RE elements can significantly improve the mechanical properties of magnesium alloys.

An Mg-RE based ultra-high alloy has been reported with the properties of 610 MPa in tensile

yield stress and 5 % in elongation [102]. Since the Mg-RE based alloys show the greater

potential for developing ultra-high strength magnesium alloys via precipitation strengthening,

many works have been conducted to study the Mg-RE based alloys [103-111].

The RE elements can be divided into two subgroups according to their atomic number, those

from La to Sm (lower atomic numbers and masses) being referred to as the light RE elements

and those from Gd to Lu (higher atomic numbers and masses) being referred to as the heavy

RE elements [112]. According to Rokhlin [113] and Hadorn et al. [114], the intermediate phase

formation amongst the Mg-RE alloy in the same sub-group shows great similarity.

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2.1.2.5.1 Mg-Gd based alloys

Gadolinium belongs to the heavy RE elements; its maximum solubility in Mg is 23.67 wt. %

and decreases to 1.64 wt. % at 200 °C. Many works have been devoted to investigating the

precipitation process of binary Mg-Gd alloy [115-118]. The precipitation sequence of binary

Mg-Gd alloy is considered as SSSS → 𝛽′′ Mg3Gd → 𝛽′ Mg7Gd → 𝛽1 Mg3Gd → 𝛽 Mg5Gd

[5].

Although both the 𝛽′′ and the 𝛽1 precipitates have the same Mg3Gd composition. Their lattice

structure is different, the 𝛽′′ phase has an HCP structure while the 𝛽1 phase has an FCC

structure. The 𝛽′′ phase precipitates at the early stage of ageing, according to Gao et al.[116],

it coexists in the matrix with the 𝛽′ phase after ageing at 250 °C for 0.5 hours. When the ageing

time is extended to 2 hours the only existing precipitates is the 𝛽′ phase. The 𝛽′ phase has a

base-centred orthorhombic structure and it is the key strengthening precipitate phase [119-121].

Recent studies revealed that the 𝛽′ phase includes two types of precipitates, the 𝛽𝑆′ and 𝛽𝐿

′

phase [122-124]. They have the same base-centered orthorhombic structure but different in the

lattice parameters, the lattice parameters of 𝛽𝐿′ phase are: a = 0.64 nm, b = 2.22 nm, c = 0.52

nm while a = 0.64 nm, b = 1.11 nm, c = 0.52 nm for 𝛽𝑆′ phase [123]. The precipitation of 𝛽1

phase is somehow under debate, Nie et al. [125] and Gao et al. [116] believed that the 𝛽1 phase

nucleates at the necks of the decomposed 𝛽′ precipitates and grows at the expense of 𝛽′, it is

supported by the fact that the 𝛽1 phase is always attached to two 𝛽′ particles; this is also

consistent to other Mg-RE alloys [126]. However, Apps et al. [127] disagreed with that; they

assumed that both 𝛽1 and 𝛽′ all nucleate on the 𝛽′′ phase and further ageing caused the two 𝛽′

particles attached to the 𝛽1 phase. Additionally, Meng et al. [128] even concluded that the

precipitation of 𝛽1 phase is impossible in binary Mg-Gd alloy due to its high formation energy

and low vibrational entropy according to their first-principles calculation. The formation of the

equilibrium 𝛽 phase caused the over-aged of Mg-Gd alloy. It is believed to be transformed in

situ from the 𝛽1 phase and the orientation relationship between the 𝛽 phase and matrix is the

same as that the orientation relationship between 𝛽1 phase and the matrix.

Recently, a study on the precipitation of binary Mg-Gd alloy associated with HAADF-STEM

(High-angle annular dark-field scanning transmission electron microscopy) was conducted by

Zhang et al. [129]. They proposed a very different precipitation sequence as follows: SSSS →

ordered solute clusters → G.P. zones → 𝛽′ → 𝛽𝑆′ + tail-like hybrid structures → 𝛽1 → 𝛽.

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Additionally, an unusual FCC-structured Gd platelets was found to precipitate when Mg-Gd

alloy was rapidly heated to 250 °C and held for 2 hours [130].

2.1.2.5.2 Mg-Nd based alloys

Nd is one of the light RE elements; its maximum solubility in Mg is 3.68 wt. % and decreases

to 0.01 wt. % at 200 °C. The precipitation sequence in the Mg‒Nd alloy is suggested to be:

SSSS → G.P. zones → 𝛽′′ Mg3Nd → 𝛽′ Mg7Nd → 𝛽1 Mg3Nd → 𝛽 Mg12Nd → 𝛽𝑒 Mg41Nd5

[5]. Compared to the precipitation in binary Mg-Gd, the difference in binary Mg-Nd is the

formation of G.P. zones.

The information on the precipitation of G.P. zones is limited due to the small size of these

features and instrumentation restrictions [131], Saito et al. [132] and Lefebvre et al. [133]

found that the G.P. zones were needle-shaped with long axes parallel to the [0001]Mg, but the

driving forces for G.P. zones remained a mystery. The 𝛽′′ phase was determined by Lefebvre

et al. [133], it had an FCC structure and the composition of Mg3Nd. It formed on the prismatic

planes and was fully coherent with the matrix [134]. Ma et al. [134] thought the formation of

the 𝛽′′ phase was mainly responsible for the precipitation strengthening in Mg-Nd alloy.

Nevertheless, Satio et al. [132] disagreed with that. They reported that 𝛽′′ phase was not

formed in Mg-Nd alloy was when ageing at temperatures ranging from 170 °C to 250 °C, the

peak-aged was due to the coexistence of G.P. zones and the 𝛽′ phase. They also concluded that

when the Mg-Nd alloy was over-aged, both the G.P. zones and the 𝛽′ phase disappeared and

coarse stable 𝛽1 phase was precipitated. Therefore, they assumed that the 𝛽1 phase was harmful

to the precipitation strengthening in Mg-Nd alloy. However, a study by Zhu et al. [135]

concluded that the 𝛽1 phase was the key strengthening phase in Mg-Nd alloy. They believed

that the 𝛽1 phase had six variants and formed on the {01-10} planes. They also found an

unreported phase designated as 𝛽2, the 𝛽2 phase always formed in connection points of two 𝛽1

particles of the same variant or different variants but having opposite shears directions. The 𝛽

phase coexisted with the 𝛽1 phase and was considered to be the equilibrium phase by Zaden et

al. [131]. However, it is confirmed that the equilibrium phase is in fact the 𝛽𝑒 phase, but it is

formed only at high heat treatment temperatures and sufficiently long durations [136].

The precipitation process in magnesium alloys has been extensively studied with the help of

TEM [95, 137], HAADF-STEM [138, 139], DSC (Differential scanning calorimetry) [140],

synchrotron radiation [141] and dilatometry [142]. Despite the traditional methods, electrical

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resistivity has been successfully introduced in investigating the precipitation process in steel

[143] and Al alloys [144, 145]. However, limited work has been performed to study electrical

resistivity in Mg alloys. Therefore, the current study targets understanding the electrical

resistivity changes in Mg alloys and exploring the possible use of the electrical resistivity in

Mg alloys.

2.2 Electrical resistivity of metals and its application

In 1827, Ohm published his work on resistance, the Ohm’s law:

𝐼 =𝑉

𝑅 (2-1)

Where I is the electrical current through the conductor, V is the voltage measured across the

conductor and R is the resistance of the conductor. The term of Ohm’s law could be changed

to [30, 146, 147]:

𝑬 = 𝜌𝐽 (2-2)

Where E is the electric field, J is current density, ρ is electrical resistivity. The electrical

resistivity is defined as the electrical resistance per unit length and unit of cross-sectional area.

It is an intrinsic property of metals independent of the shape of the sample and the applied

electric field. The resistivity is believed to be brought by the incoherent scattering of

conduction electrons [148-151]. Therefore, anything that increases the incoherent scattering,

such as impurity atoms, lattice defects and temperature, will raise the resistivity. Considerable

efforts have been devoted to understanding the electrical resistivity in metals since the early

nineteenth century.

2.2.1 Drude model

In 1897, Thomson discovered the electron and it was quickly realized that electrons contribute

to the electric currents. Three years later, Drude proposed a model based on the classic kinetic

theory of gases to calculate resistivity. In his model, he treated the free electrons as a classical

ideal gas; although the Drude model has many shortcomings, it is still used today as a quick

practical way to form simple pictures and rough estimates of the electrical properties of metals.

He made four basic assumptions in the model [152, 153]:

1) Free electron approximation. Drude assumed that when atoms of a metallic element are

brought together to form a metal, the valence electrons become detached and wander

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freely through the metal. They are the so-called free electrons and they are the charge

carriers. The positively charged ion cores remain intact and are immobile. The free

electrons can collide with the ion cores while they are moving. These collisions

instantaneously change their velocity. Besides the collisions, the electrons do not

interact with the ion cores.

2) Independent electron approximation. The free electrons do not interact with each other

at all: There is no coulomb interaction, and as opposed to a classical gas model, they

do not collide with each other either. Thus in the absence of externally electromagnetic

fields, each electron moves in a straight line until it collides with the ion cores. When

an external field is applied, each electron is taken to move as determined by Newton’s

laws of motion. Fig. 2-2 illustrates the free electron approximation and independent

electron approximation of the Drude Model.

Fig. 2-2 Schematic diagrams of the Drude Model.

a) without external electric field, b) with external electric field E.

3) Relaxation time and mean free path. Drude assumed that the probability that an electron

experiences a collision with the ion cores per unit time is 1/τ. It means that an electron

picked at random will, on average, travel for a time τ since its last collision. The time τ

is variously known as the relaxation time. It is assumed independent of the electron

position and is independent of time. In between collisions, the electrons move freely.

The mean length of this free movement is called the mean free path.

4) Electrons will achieve thermal equilibrium with their surroundings through collisions

with the ion cores. Drude presumed the electrons maintain local thermodynamic

equilibrium in a particularly simple way: immediately after each collision, an electron

obtains a velocity uncorrelated to its velocity before the collision, this velocity is

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

+++++

a) b)

+ Ion cores

Free electrons

𝒗𝐸 =− 𝑬

𝑚𝑒

v=0E

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15

randomly directed and its speed is related to the temperature where the collision

occurred.

With the basic assumptions of the Drude Model, we can now explain the resistivity of metals.

Consider the movement of an electron when an electric field E is applied. The equation of

motion, according to Newton’s law, is [152-154]:

𝑚𝑒

𝑑𝒗

𝑑𝑡= − 𝑬 (2-3)

𝑚𝑒 is the mass of the electron, 𝒗 is the average electronic velocity and is the proton charge.

According to the fourth assumption of Drude Model, the electrons are at thermal equilibrium

with their surroundings before the electric field is applied. Since there is no transfer of the

electrical current in the absence of externally applied electromagnetic fields, the average

electronic velocity 𝒗 equals zero. When an electric field E is applied, the electrons will achieve

a new thermal equilibrium with their surroundings in time τ. Therefore the average electronic

velocity in an external electric field E is:

𝒗𝐸 =− 𝑬

𝑚𝑒 (2-4)

With the average electronic velocity, we can calculate the current density J. Consider an area

A perpendicular to the electric field. The amount of charge passing through the area per unit

time is:

− 𝑛𝒗𝐸𝐴

n is the conduction electron density, that is, the number of conduction electrons per unit volume.

Therefore, the current density J is:

𝐽 = − 𝑛𝒗𝐸 (2-5)

Now with the Eq.(2-4) we can get:

𝐽 =𝑛 2

𝑚𝑒𝑬 (2-6)

Consider the Eq.(2-2) we know that:

𝜌 =𝑚𝑒

𝑛 2 (2-7)

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The Drude model thus explains the electrical resistivity quantitatively. In Eq.(2-7), 𝑚𝑒 and

are physical constants, so the electrical resistivity is determined by the conduction electron

density n and relaxation time . n is calculated by assuming that every atom contributes Z

conduction electrons (the valence electrons) [153] when atoms are brought together to form

metal. Then n is calculated:

𝑛 = 𝑁𝐴

𝑍𝜌𝑚𝑀

(2-8)

𝑁𝐴 is the Avogadro’s number, 𝜌𝑚 is the density of the solid in kg/m3, M is the atomic mass in

kilograms per atom. The relaxation time is calculated by applying the experimental data into

the Eq.(2-7). Table 2-2 gives the conduction electron density n, relaxation time and resistivity

𝝆 of selected elements. The Drude model does not seem to make any real predictions, because

it determines resistivity only at the expense of introducing another unknown parameter, the

relaxation time . It does, however, frame electrical resistivity in the terms that will be used

later for more detailed calculation, as a balance between the force -eE causing electrons to

accelerate, with the scattering events encoded in that causes them to decelerate [155].

Table 2-2 The conduction electron density, relaxation time and resistivity of selected

elements at 273 K [152].

Element n (1022/cm3) (10-14 s) 𝜌 (mΩ∙cm)

Li 4.70 0.88 8.55

Na 2.65 3.20 4.20

K 1.40 4.10 6.10

Rb 1.15 2.80 11.00

Cs 0.91 2.10 18.8

Cu 8.47 2.70 1.56

Ag 5.86 4.00 1.51

Au 5.90 3.00 2.04

Mg 8.61 1.10 3.90

Fe 17.00 0.24 8.90

Zn 13.20 0.49 5.50

Al 18.10 0.80 2.45

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The Drude Model was a great success at that time; it could explain Ohm’s law and the Hall

effect. Drude also “successfully” explained the Wiedemann–Franz law quantitatively using his

model. Despite its great success, it fails to explain the disparity between the expected heat

capacities of metals compared to insulators. In addition, the Drude model fails to explain the

existence of apparently positive charge carriers, as demonstrated by the positive Hall effect of

certain materials [153]. Sommerfeld put forth the free electron model by combining the Drude

model and quantum mechanical Fermi–Dirac statistics. It resolves the major problems of the

classical Drude model [156, 157]. Nevertheless, the successes of the Drude model were

considerable and it is still used today as a quick practical way to form simple pictures and rough

estimates of properties.

2.2.2 Matthiessen’s rule

2.2.2.1 Matthiessen’s rule

Before Drude proposed his model, studies on electrical resistivity were focused on the

influence of impurity concentration and temperature. Matthiessen and Vogt measured the

resistivity of a series of two-component mixtures of metals between 0 °C and 100 °C [158].

Based on the results, they concluded that the temperature derivative of the resistivity ρp(T) of

an ideally pure metal could be closely approximated using the relation:

𝑑𝜌𝑎(𝑐, 𝑇)

𝑑𝑇=

𝑑𝜌𝑝(𝑇)

𝑑𝑇 (2-9)

where 𝜌𝑎(𝑐, 𝑇) is the resistivity of a dilute alloy containing a concentration c of impurity.

Matthiessen and Vogt suggested that Eq.(2-9) can be applied at any temperature, then they

integrated it, starting at 0 K, to obtain:

𝜌𝑎(𝑐, 𝑇) = 𝜌𝑝(𝑇) + 𝜌0(𝑐) (2-10)

where 𝜌0(𝑐) is the impurity produced resistivity at 0 K. Eq.(2-10) is the so-called

“Matthiessen’s Rule”. According to Matthiessen’s Rule, the total resistivity of a dilute alloy is

divided into two parts. The first part, ρp(T) called the ideal resistivity, is temperature-dependent

and is independent of the impurity concentration. It is arising from the scattering of electrons

by lattice waves or phonons. The second part, 𝜌0(𝑐) called the residual resistivity, is a constant

that relies on the impurity concentration. It is caused by the scattering of electrons by impurity

atoms. Another way to express Matthiessen’s Rule is that the total resistivity is produced by

2 Literature review

18

the two scatters of electrons, lattice vibrations and impurities, independent and additive [151].

In fact, Matthiessen’s Rule is never exactly valid. There are always deviations from

Matthiessen’s Rule. However, in many cases, the deviations are small compared to either

𝜌𝑝(𝑇) or 𝜌0(𝑐) , so Matthiessen’s Rule represents quite a good approximation to the

experimental data [159, 160]. Fig. 2-3 is the resistivity of annealed and cold-worked (deformed)

copper-containing various amounts of Ni in atomic percentage. According to Matthiessen’s

rule, 𝜌𝐼 is caused by the concentration of Ni in the Cu matrix and is temperature-independent,

so it simply shifts up the 𝜌 versus T curve of pure Cu by an amount proportional to the Ni

content, 𝜌𝐼∝ NNi, where NNi is the Ni impurity concentration. 𝜌𝑇 is resistivity caused by

thermal vibrations and therefore is temperature-dependent, as shown in Fig. 2-3, from 80 K to

300 K, the resistivity increases with the temperature.

0 50 100 150 200 250 3000

10

20

30

40

50

60

1

0-9

Oh

mzm

CW

pure Cu (annealed)

pure Cu (deformed)

1.12 at.% Ni (annealed)

1.12 at.% Ni (deformed)



T / K

Fig. 2-3 Electrical resistivity of annealed and cold-worked (deformed) copper alloys.

𝜌𝑇 is resistivity caused by thermal vibrations, 𝜌𝐼 caused by Ni solute, 𝜌𝑐𝑤 caused by cold-

work [161, 162].

It should be noted that in Fig. 2-3, the deformed alloy, including pure Cu and Cu-1.12 % Ni,

has a higher resistivity compared to the annealed alloy with the same composition. This is due

to the higher concentration of dislocations in the deformed alloy. During the deformation, large

numbers of dislocations are introduced into the alloy and dislocations can also scatter the

conduction electrons and increase the resistivity, 𝜌𝑐𝑤 . Therefore, compared to the well-

annealed alloy, the deformed alloy has a higher resistivity. If we treat the dislocations as a type

of the “impurity” then the total residual resistivity, 𝜌0(𝑐), is the sum of 𝜌𝐼 and 𝜌𝑐𝑤 and the

Matthiessen’s rule is still correct in this term.

2 Literature review

19

2.2.2.2 Deviations from Matthiessen’s Rule

Despite the good approximation of Matthiessen’s rule to many experimental data, deviations

from Matthiessen’s Rule also exist in many alloys [163-167]. Fig. 2-4 shows the deviation of

Matthiessen’s Rule in SrRuO3 and CaRuO3 alloys [168]. ∆𝜌𝑖𝑟𝑟 is the resistivity caused by

electron irradiation introduced point defects. According to the Matthiessen’s Rule, the point

defects could be treated as some kind of “impurities” and the resistivity caused by them should

be temperature-independent. However, Fig. 2-4 shows a negative deviation from Matthiessen’s

rule in these two alloys. According to the author [168], this deviation from Matthiessen’s Rule

was due to the marked anisotropic scattering of the electrons together with their relatively short

mean free path. Deviation from Matthiessen’s Rule due to the interacting dislocations [169]

also has been observed. Generally, Matthiessen’s Rule is correct when assuming the electron-

impurity scattering is temperature-independent. However, this could be wrong for some

reasons [170]:

1) The addition of the impurities changed the phonon spectrum of the matrix;

2) The added impurities perturbed the phonon distribution;

3) The anisotropy of the relaxation times for phonon and impurities scattering.

Fig. 2-4 Deviation from Matthiessen’s rule in SrRuO3 and CaRuO3 alloys.

Reprinted from reference [168] with permission from EDP Science.

2.2.3 Influencing Factors of electrical resistivity

In Eq.(2-7), the parameters 𝑚𝑒 , and n are constants for a certain metal. Therefore, the

resistivity is mainly determined by the relaxation time. The relaxation time, which means the

average time between two collisions of an electron, is influenced by the lattice defects, impurity

atoms and temperature. Consequently, resistivity is also affected by these factors.

2 Literature review

20

2.2.3.1 Effect of lattice imperfection

Lattice imperfections are classified into point defects, linear defects and planar defects

according to the geometry or dimensionality of the defect [171]. In general, any kind of lattice

imperfection will destroy the periodicity of an ideal crystal and increase the scattering of the

electrons. Therefore, the resistivity is increased by any kind of lattice imperfection. Among all

the lattice imperfections, vacancy, dislocation and grain boundaries are the most common ones.

2.2.3.1.1 Vacancy

A vacancy is expected to cause a lattice relaxation in its immediate vicinity, which gives rise

to a change of the crystal lattice parameter [172]. This relaxation leads to the detriment of the

periodicity of the lattice and hence increases the scattering of the conduction electrons. The

resistivity is then increased due to the increased scattering. The influence of vacancies on the

resistivity is considered temperature-independent; however, the vacancy itself is temperature-

dependent, the number density of vacancies increases with temperature. Therefore, the total

contribution of vacancies to resistivity is temperature-dependent. The vacancy contribution to

the resistivity is negligibly small at room and cryogenic temperatures and becomes significant

at temperatures approaching the melting point [173].

2.2.3.1.2 Dislocations and grain boundaries

In contrast to vacancies, dislocations and grain boundaries are thought to be temperature-

independent factors. Dislocations, both the edge and screw dislocations, will introduce a strain

field due to the stretching or compressing of bonds [161]. This strain field destroys the

periodicity of the crystal and therefore increase the resistivity. Grain boundaries can be treated

as an aggregation of broken bonds, voids, vacancies, strained bonds and interstitial-type atoms

[161]. Therefore, the arrangement of atoms in the grain boundary region is disordered and the

disordered arrangement will increase the scattering probability of the electrons. Hence, the

resistivity is increased.

2.2.3.2 Influence of solution element

The effects of alloying elements on resistivity vary with the contents. In a dilute alloy, where

the content of the alloying element is restricted to less than 1 or 2 at. %, the increment of

resistivity is almost proportional to the atomic percentage. According to Linder’s rule, ∆ρ is

proportional to the square of the excess charge on the impurity,

2 Literature review

21

∆𝜌 = 𝑎 + 𝑏(∆𝑍)2 (2-11)

Where a and b are just constants for a given matrix metal and a given solute, according to the

period law, the coefficient a is zero if impurities and solvent are in the same row of the periodic

table [174]. Eq.(2-11) suggests that the intensity of impurity scattering is proportional to the

square of the excess impurity charge. This rule is quite reasonable in dilute alloys with small

size effects. When the content of the alloying element exceeds 2 at. %, the simple proportional

relationship between the increased resistivity and atomic percentage no longer fits all alloying

elements. Fig. 2-5 shows the influence of Au content on the electrical resistivity of Cu. As seen

in Fig. 2-5, the incremental increase of resistivity is proportional to the atomic percentage until

the Au reaches 15 at. %. After that, the resistivity depends on the status of the alloy. In the as-

quenched status, the alloy remains disordered as in the liquid state, the resistivity increases

with the Au content and reaches the maximum when the Au is approximately 50 at. %. When

the alloy is annealed, there are two decreases of the resistivity at 25 at. % and 50 at. %. This is

due to the formation of the intermetallic phase. This phenomenon indicates that the detriment

of the periodicity rather than the second phase causes more increase of resistivity.

Fig. 2-5 Resistivity of Cu-Au alloy in different states.

Data from Johansson and Linde [175].

0 20 40 60 80 100

Quenched

Au Cu

CuAuCu3Au

Annealed

Au / at. %

Res

isti

vit

y

2 Literature review

22

2.2.3.3 Effect of temperature

As described by Matthiessen’s Rule in Eq.(2-10), the ideal resistivity is temperature-dependent.

In a very rough approximation, the resistivity can be expressed as:

𝜌 ≈ 𝐴𝑇 + 𝐵 (2-12)

A and B are constants depending on the material; the first part of this equation’s right-hand side

represents the temperature-dependent ideal resistivity; the second part represents all the

temperature-independent resistivity caused by impurities and lattice imperfection. According

to Eq.(2-12), the resistivity varies almost linearly with the temperature. The temperature

coefficient of resistivity (TCR) 𝛼0 is then introduced to describe the fractional change in the

resistivity per unit temperature increase at the reference temperature T0:

𝛼0 = 1

𝜌0 [∆𝜌

∆𝑇]𝑇=𝑇0

(2-13)

where 𝜌0 is the resistivity at the reference temperature T0; ∆𝜌 is the resistivity change due to

the temperature; ∆𝑇 is the temperature change. 𝛼0 is a constant over a temperature range T0 to

T, if the 𝜌0 and 𝛼0 are determined, then the resistivity under different temperatures can be

calculated by:

𝜌 = 𝜌0[1 + 𝛼0(𝑇 − 𝑇0)] (2-14)

Eq.(2-14) is useful to predict the resistivity approximately. In fact, it is not a bad approximation

for some of the familiar pure metals such as Cu, Al, Au and Pt [161]. The linear approximation

of resistivity to the temperature is roughly obeyed above 50 K, as shown in Fig. 2-3. However,

at extremely low temperatures, the electrons are mainly scattered by impurities or defects in

the material and become almost constant with temperature. With sufficient purity, the

resistivity of metals is approximately equal to 0; this phenomenon is the so-called

superconductivity [176].

2.2.4 Application of electrical resistivity

Resistivity has been employed in both industry and academia as a useful tool to investigate

various microstructural and physical phenomena. It has been employed as a Non-Destructive

testing method in the industry [177-179]. It has also been adopted to study phase transformation

during ageing [143, 180-184] and evaluate the purity of high-purity metals [185-188] in

materials science.

2 Literature review

23

2.2.4.1 Non-destructive testing

Traditional methods for testing the welded joints, such as tensile testing and metallographic

observation, are destructive and time-consuming. In comparison, Eddy Current Testing (ECT)

provides a non-destructive way to examine the quality of welded joints, it is based on the

interaction between a magnetic field source and a test material [177].

If a coil is carrying an alternating current, an electromagnetic field is generated. When the test

sample is placed near the coil, eddy currents are induced in the sample. The induced eddy

currents, in turn, affect the electromagnetic field in the coil [178]. The eddy currents depend

on the electrical and magnetic properties of the test sample; therefore, the defects in the sample

are detectable because they change the resistivity of the sample.

Manesh [189] also reported that the resistivity could be directly used to assess surface bonding

strength in Al clad steel strip. A calibration diagram for evaluating the bonding quality using

the electrical resistivity test is plotted and a quality acceptance area was established in the plot.

2.2.4.2 Phase transformation monitor

Since the resistivity is sensitive to the microstructure change, it is reasonable to use resistivity

to investigate the phase transformation in materials.

Benrabah et al. [190] used in situ electrical resistivity measurements to study the dissolution

and the precipitation of the 𝛾′ phase in non-equilibrium conditions. It is found that the in situ

measurements can reveal the dissolution of the intragranular secondary 𝛾′ phase during the

heating and precipitation of secondary 𝛾′ phase during cooling. The results clearly showed the

advantage of electrical resistivity for tracking phase transformation during the heat treatments.

In situ electrical resistivity measurements have also been utilized to monitor the annealing

process of Al alloys [184]. The recovery, recrystallization and grain growth processes of the

cold-rolled Al sheet during annealing will decrease the resistivity. In addition to that, they

claimed that the resistivity could be used to predict the yield stress of the annealed sheet. As

shown in Fig. 2-6, the resistivity curve is almost equal to the yield stress curve at any post-

annealing time. This suggested that resistivity could be used to predict the mechanical

properties of materials.

The in situ resistivity measurements have also been used to study precipitation kinetics during

isothermal ageing [191, 192].

2 Literature review

24

Fig. 2-6 Relationship between the resistivity and yield stress.

Reprinted from reference [184] with permission from RightsLink / Elsevier.

2.2.4.3 Purity evaluation of metals

High-purity metals are required for applications in some advanced devices [188, 193],

especially for the semiconducting materials, which trace impurities influence their electrical

properties significantly. Despite the fabrication of a high-purity metal, the evaluation of the

purity remains a challenge since the accuracy of chemical analyses decrease when the trace

impurity levels become lower [185]. Therefore, the residual resistivity ratio (RRR) has been

adopted to evaluate the purity of metals. The RRR is defined as in Eq.(2-15).

𝑅𝑅𝑅 =𝜌298𝐾

𝜌4.2𝐾 (2-15)

It is the ratio of resistivity at room temperature to the residual resistivity at 4.2 K. The residual

resistivity is influenced by the lattice defects and the impurities. For a well-annealed metal, the

resistivity is predominated by the impurities. An improvement in the purity of the metal will

decrease the residual resistivity at 4.2 K and increase the RRR value. The RRR value is now a

commonly used method to evaluate the purity of a metal [185, 194].

3 Motivation

25

3 Motivation

Since the resistivity measurements have been shown to have the advantage for in situ phase

transformation monitoring in steel, Ti and Al alloys [143, 181, 191], it is reasonable to consider

resistivity as a tool to investigate the phase transformation process in Mg alloys. In order to use

resistivity to investigate the phase transformation, it is important to have a better understanding

of the influencing factors of resistivity in Mg alloys. Therefore, in the current work, Mg-Al,

Mg-Gd, Mg-Sn and Mg-Zn alloys were selected to investigate the influence of alloying

elements and microstructural changes on the electrical resistivity. These alloys were selected

based on the following facts:

1) Binary magnesium alloys were chosen to limit the variables when investigating the

influence of alloying elements on resistivity.

2) Al and Zn are selected because they are widely used in commercial magnesium alloys.

3) Gd is selected as a representative of the RE elements. Sn is selected because of its

potential in operating under high temperature.

4) These four elements possess significant differences in the maximum solubility and

solubility at typical ageing temperatures; this makes them excellent candidates to study

the influence of microstructure change on the electrical resistivity by performing

isothermal ageing on them.

The objectives of the current study are:

1) To understand how will composition influences the resistivity of Mg;

2) To understand how will microstructures influence the resistivity of Mg;

3) How can resistivity be used in material research?

4 Materials and Experimental Details

26


4.1 Materials

4.1.1 Casting procedure

Four series of binary Mg alloys were chosen to assess the influence of alloying elements and

their contents on the electrical resistivity in the current study. Pure Mg was used as a reference.

The designed chemical compositions of the alloys are given in Table 4-1.

Table 4-1 Nominal chemical compositions of the alloys (at. %).

Alloy Al Gd Sn Zn Mg

Mg-0.8Al 0.8 - - - Bal.

Mg-2.5Al 2.5 - - - Bal.

Mg-5Al 5 - - - Bal.

Mg-8Al 8 - - - Bal.

Mg-0.8Gd - 0.8 - - Bal.

Mg-1.5Gd - 1.5 - - Bal.

Mg-2.5Gd - 2.5 - - Bal.

Mg-0.8Sn - - 0.8 - Bal.

Mg-1.5Sn - - 1.5 - Bal.

Mg-2.5Sn - - 2.5 - Bal.

Mg-0.8Zn - - - 0.8 Bal.

Mg-1.5Zn - - - 1.5 Bal.

Mg-2.5Zn - - - 2.5 Bal.

Pure Mg - - - - Bal.

The alloys were prepared using commercial pure Mg (99.94%), Al (99.5%), Gd (99.5%), Sn

(99.5%) and Zn (99.5%). Pure Mg was first heated up to 750 °C under the protection of Ar +

2 % SF6, then the alloying elements (Al, Gd, Sn and Zn) were added to the Mg melt. The melt

was mechanically stirred at a rate of 200 rpm for 20 minutes to ensure a homogeneous

distribution of alloying elements. After that, the melt was poured into a pre-heated (700 °C)

permanent cylinder mould (1.0044, EU Grade) with a size of 70 mm in diameter and 230 mm

4 Materials and Experimental details

27

in height or a cube mould (1.0044, EU Grade) with a cross-section of 50 mm in width and 100

mm in length and the height of 230 mm. The wall thickness of both moulds is 5mm. The filled

mould was held at 670 °C for a few minutes with gas protection and then lowered into the

cooling water with a rate of 10 mm/s. The chemical contents of the alloys were determined

using Spark Optical Emission Spectrometer (Spectrolab M9, Ametek-Spectro), atomic

absorption spectroscopy (AAS, 240FS AA, Agilent) and X-ray fluorescence spectroscopy (M4

Tornado, Bruker).

Fig. 4-1 Casting system. (a) furnace, (b) direct chill casting system.

4.1.2 Solution treatment

The as-cast alloys were solution treated to dissolve the intermetallic phases into the matrix

before ageing treatment. Solution temperatures were selected according to the binary phase

diagrams as listed in Table 4-2. The solution treatment was performed under the protection of

Ar gas to avoid oxidation. Compared to commonly used heat treatments, the solution

temperatures in the current study are slightly higher in order to dissolve the intermetallic phases

completely. The specimens were water quenched to room temperature immediately after the

heat treatment.

Table 4-2 Solution treatment parameters of the as-cast alloys.

Alloy Solution treatment parameters

Mg-Al series 430±5 °C / 24 hrs

Mg-Gd series 530±5 °C / 24 hrs

Mg-Sn series 525±5 °C / 24 hrs

Mg-Zn series 340±5 °C / 8 hrs

20 cm

a) b)


28

Additionally, extruded Mg-0.8Gd alloys prepared in a former study [195] were used to study

the influence of grain size on resistivity. The extruded alloy was solution treated at 530 ± 5 °C;

different solution treatment times were performed to vary the grain size.

4.1.3 Ageing treatment

The solution treated materials were machined to a cubic sample of 10 mm3 and followed by

artificial ageing. For each series alloy, three temperatures were selected based on the phase

diagrams. The detailed parameters are shown in Table 4-3. The ageing treatment was conducted

in an oil bath with a limit of 250 °C to avoid oxidation.

Table 4-3 Ageing parameters of different alloys.

Alloy Ageing temperatures Max. ageing time

Mg-Al series 175 °C 336 hrs

200 °C 192 hrs

225 °C 192 hrs

Mg-Gd series 200 °C 600 hrs

225 °C 600 hrs

250 °C 360 hrs

Mg-Sn series 200 °C 600 hrs

225 °C 408 hrs

250 °C 264 hrs

Mg-Zn series 175 °C 336 hrs

200 °C 240 hrs

225 °C 240 hrs

4.2 Experimental Details

4.2.1 Microstructure characterizations

4.2.1.1 Optical microscopy (OM)

Metallographic samples of the as-cast alloys were sectioned from the same positions in

different casting ingots to avoid the influence of solidification on the microstructure. The

specimens for optical microscopy observations were mounted using Demotec 30 methyl


29

methacrylate embedding system. The specimens were placed in a mould and then the mixed

Demotec 30 was poured into it. After the Demotec 30 was cured, the mounted samples were

removed from the mould carefully. The mounted samples were ground with SiC abrasive paper

from 800 to 2500 grit. They were then carefully polished with water-free oxide polishing

suspensions (OPS) and 0.25 μm diamond suspension. The polished samples were etched in a

solution of 8 g picric acid, 5 ml acetic acid, 10 ml distilled water and 100 ml ethanol before

final observations. Optical microscopy observations were carried out on a Leica DMI5000

microscope with a digital camera attached. The average grain size of each alloy was measured

by the linear intercept method [196, 197] from the micrographs taken by polarized light using

the image analysis software AnalySIS Pro.

Figure 4-1 Schematic illustration of a sample depicting the approximate position.

4.2.1.2 Scanning electron microscopy (SEM)

The specimens for scanning electron microscopy (SEM) were prepared using the same

procedure as for OM before the chemical etching. After polishing, samples were directly

observed without chemical etching. Nevertheless, the aged Mg-Al series alloys were etched

before observation because of the low contrast of Mg and Al elements. The microstructure was

observed by a Vega 3 (TESCAN, Brno, Czech) and/or a Zeiss Ultra 55 (Carl Zeiss GmbH,

Oberkochen, Germany) SEM. The chemical composition of the secondary phases was

qualitatively analyzed using an energy dispersive X-ray spectrometer (EDS).

4.2.1.3 X-ray diffraction analysis

The as-cast intermetallic phases and precipitates after ageing treatment were identified using

X-ray diffractions. The X-ray diffractions were performed by the D8 ADVANCE


30

diffractometer (Brucker, Billerica, Massachusetts, US). The diffraction patterns were measured

with a step size of 0.02° and a step time of 0.5 s. For qualitative analysis, the bulk samples were

mechanically ground with SiC abrasive paper from 800 grit to 2500 grit. For quantitative

analysis, powder samples were used to obtain high-quality data for the full pattern simulation.

The weight of intermetallic phases was analyzed using TOPAS software with the Rietveld

method.

4.2.1.4 Synchrotron radiation diffraction analysis

Synchrotron radiation diffraction was used to determine the precipitates in binary Mg-Gd

alloys after aged. The experiment was conducted in DESY (Deutsches Elektronen-Synchrotron,

Hamburg) HEMS P07B. The synchrotron radiation beam has a wavelength of 0.014235 nm

and a cross-section of 700 μm2. The diffraction patterns (Debye-Scherrer rings) were recorded

by a detector and calibrated by a LaB6 standard powder sample. The Debye-Scherrer rings were

integrated into line profiles using the Fit2D [198] software and then analyzed.

4.2.2 Hardness test

The hardness measurements were performed on a standard microhardness tester (EMCOTEST

M1C010, Karl Frank GmbH, Germany) with a load of 5 kg and a dwell time of 30 s. The

samples for hardness measurements were mounted and ground with SiC abrasive paper from

800 grit to 2500 grit. For each selected point, 10 indentations were averaged to reduce random

errors.

4.2.3 Electrical resistivity measurements

4.2.3.1 Resistivity measurement at low and room temperatures

The resistivity at room temperature and low temperature (77 K) of the samples were tested with

a standard four-probe method connection. The samples’ dimensions were 80 mm in length and

a cross-section of 7 mm and 3 mm, as shown in Fig. 4-2. The resistivity was measured by a

Keithley device kit. A Keithley 228 Voltage/Current source supplies a fixed current and

Keithley 182 records the voltage on samples. The Keithley 7002 switch system enables the

change of current polarity during measurement in order to suppress the thermal electromotive

force. The room temperature measurements are conducted in an ethanol bath and low-

temperature measurements in a liquid nitrogen bath. A reference sample is also used to monitor

if the apparatus works properly.


31

Fig. 4-2 Resistivity sample and room temperature measurements apparatus.

4.2.3.2 Resistivity measurement at high temperature and in situ measurements

The high temperature and in situ electrical resistivity are measured by the Keithley 6220/2182A

kit with a standard four-probe method connection. The sample dimension is the same as the

room temperature sample. The temperature is controlled by an oil bath as in Fig. 4-3.

Fig. 4-3 High-temperature resistivity measurement apparatus and schematic of the delta

method measurements.

The in situ measurements are conducted at the same temperatures as the ageing temperature.

In order to eliminate the thermal electromotive force, a delta measuring method is introduced

in the measurement. As illustrated in Fig. 4-3, the Keithley 6220 supplies an alternating current

fixed at 105 mA. The Keithley 2182A measures the voltage on the samples. Since there needs

to be a delay time to stable the voltage when the current alters its direction, the measurement

by Keithley 2182A is two seconds after the current alters its direction. For each measurement,

it takes approximately 1/60 of a second; after the measurement, the current changes its direction

again. The recorded voltage is based on the following formula:

𝑉𝑛 = (𝑉𝑛−2𝑉𝑛+1+𝑉𝑛+2

4) 𝑛 𝑖𝑠 𝑜𝑑𝑑; 𝑉𝑛 = (

2𝑉𝑛+1−𝑉𝑛−𝑉𝑛+2

4) 𝑛 𝑖𝑠 𝑣 𝑛 (4-1)

a) b)

2182A

measured

V1

Delay

V2

V3 V5

V4 V6

6220

I-source

1st detla cycle

2nd detla cycle

3rd detla cycle

4th detla cycle

1st reading =[(V1-V2)+(V3-V2)]/4 4th reading =[(V5-V4)+(V5-V6)]/4

a) b)

5 Results

32

5 Results

The actual chemical compositions of the alloys are list in Table 5-1, where Gd was analyzed by

X-ray fluorescence spectroscopy, Fe and Ni were analyzed by atomic absorption spectroscopy

and the other elements were analyzed by spark optical emission spectroscopy. Despite the high Zn

contents alloys, the actual compositions are slightly lower than the designed composition due

to the burning loss during casting.

Table 5-1 Chemical compositions of the alloys (at. %).

Alloys Al

(at. %)

Gd

(at. %)

Sn

(at. %)

Zn

(at. %)

Fe

(at. %)

Si

(at. %)

Ni

(at. %)

Mg

(at. %)

Mg-0.8Al 0.77 - - - 0.00003 0.00002 0.00002 Bal.

Mg-2.5Al 2.47 - - - 0.00003 0.00001 0.00002 Bal.

Mg-5Al 5.01 - - - 0.00003 <0.00001 <0.00001 Bal.

Mg-8Al 7.97 - - - 0.00002 <0.00001 <0.00001 Bal.

Mg-0.8Gd - 0.80 - - 0.00003 0.00002 <0.00001 Bal.

Mg-1.5Gd - 1.45 - - 0.00003 0.00001 <0.00001 Bal.

Mg-2.5Gd - 2.32 - - 0.00003 0.00001 <0.00001 Bal.

Mg-0.8Sn - - 0.78 - 0.00003 0.00003 0.0004 Bal.

Mg-1.5Sn - - 1.42 - 0.00003 0.00001 <0.00001 Bal.

Mg-2.5Sn - - 2.40 - 0.00003 0.00002 <0.00001 Bal.

Mg-0.8Zn - - - 0.78 0.00003 0.00004 0.00003 Bal.

Mg-1.5Zn - - - 1.51 0.00004 0.00005 0.00002 Bal.

Mg-2.5Zn - - - 2.68 0.00003 0.00005 0.00002 Bal.

Pure Mg - - - - 0.00003 0.00005 <0.00001 Bal.

5.1 Microstructure characterization

5.1.1 As-cast alloys

5.1.1.1 Mg-Al alloys

The microstructures of as-cast Mg-Al alloys are shown in Fig. 5-1. At first glance, it is obvious

that the grain size decreases with increasing Al content and the amount of intermetallic phases

5 Results

33

increase with increasing Al contents. The microstructure also appears to be more homogeneous

with higher Al contents. The grain sizes of different Mg-Al alloys are listed in Table 5-2. It

shows that the addition of Al can significantly refine the grain. The grain size decreases from

841 μm in the Mg-0.8Al alloy to 187 μm in the Mg-8Al alloy.

Fig. 5-1 OM and SEM (BSE) micrographs of as-cast Mg-Al alloys.

(a), (e) Mg-0.8Al; (b), (f) Mg-2.5Al; (c), (g) Mg-5Al; (d), (h) Mg-8Al.

Table 5-2 Grain sizes of as-cast Mg-Al alloys.

Alloys Mg-0.8Al Mg-2.5Al Mg-5Al Mg-8Al

Grain size (μm) 841±513 384±215 218±155 187±105

50μm

50μm

50μm

50μm

2mm

2mm

2mm

b)

h)

f)

g)

e)

d)

c)

2mm

a)

5 Results

34

In Fig. 5-1, the BSE micrographs show that the as-cast alloys are mainly composed of 𝛼-Mg

matrix and intermetallic phases. The number of intermetallic phases increases with the Al

contents. According to the X-ray diffraction patterns, the intermetallic phase is confirmed to

be Mg17Al12 (space group: I-43m, a=b=c=1.0553 nm). As shown in Fig. 5-2, the Mg17Al12

peaks are obvious in Mg-8Al and Mg-5Al while it is negligible in Mg-0.8Al and Mg-2.5Al;

this is coincident to the BSE micrographs in Fig. 5-1 that the number of intermetallic phases in

Mg-0.8Al and Mg-2.5Al alloys are less. The amount of the Mg17Al12 phase in the as-cast alloys

was determined using the Rietveld method and listed in Table 5-3. The corresponding goodness

of fit (GOF) of the Rietveld refinement is also listed in the table. As in Table 5-3, the amount

of Mg17Al12 phase increases from 0 to 10.80 wt. % with the Al contents increasing from 0 to 8

at. %.

Fig. 5-2 X-ray diffraction patterns of as-cast Mg-Al alloys.

Table 5-3 Amount of the Mg17Al12 in as-cast Mg-Al alloys and corresponding GOF.

Alloys Mg-0.8Al Mg-2.5Al Mg-5Al Mg-8Al

Weight percent 0 2.52 % 7.67 % 10.80 %

Volume fraction 0 2.17 % 6.64 % 9.40 %

GOF 1.28 1.21 1.26 1.31

20 30 40 50 60 70 80 90

Mg17Al12

Mg

Mg-0.8Al

Mg-2.5Al

Mg-5Al

Mg-8Al

2

Inte

nsi

ty /

a.u

.

5 Results

35

5.1.1.2 Mg-Gd alloys

The microstructures of as-cast Mg-Gd alloys are shown in Fig. 5-3. The images of all alloys

are taken from the same position of the ingots of different alloys. From the OM micrographs

in Fig. 5-3, it can be seen that the as-cast Mg-Gd alloys show a typical dendritic structure due

to the large cooling rate and the contents of Gd seems to have a slight influence on the grain

size of Mg-Gd alloys. The specific grain size of different Mg-Gd alloys measured by the linear

intercept method are listed in Table 5-4. As shown in Table 5-4, the grain size decreases from

1426 μm to 1299 μm when the Gd content increases from 0.8 at. % to 2.5 at. %. Compared to

Al, the influence of Gd on grain refinement is negligible.

Fig. 5-3 OM and SEM (BSE) micrographs of as-cast Mg-Gd alloys.

(a), (d) Mg-0.8Gd; (b), (e) Mg-1.5Gd; (c), (f) Mg-2.5Gd.

The BSE micrographs in Fig. 5-3 show that the as-cast alloys are composed of 𝛼-Mg matrix

and intermetallic phases. An enlarged BSE micrograph in Fig. 5-4 indicates that segregation

areas also exist in the as-cast alloys. These segregations are located along grain boundaries and

100μm

d)

2mm

a)

100μm

e)

2mm

b)

2mm

c)

100μm

f)

5 Results

36

the interdendritic regions. The proportion of the segregation areas also increase with the Gd

contents.

Table 5-4 Grain sizes of as-cast Mg-Gd alloys.

Alloys Mg-0.8Gd Mg-1.5Gd Mg-2.5Gd

Grain size (μm) 1426±1116 1368±896 1299±791

Fig. 5-4 Enlarged BSE micrograph of as-cast Mg-2.5Gd alloy.

The intermetallic phases are identified using X-ray diffraction. As shown in Fig. 5-5, the

intermetallic phases are identified as Mg5Gd phase (space group F-43m, a=b=c=2.2344 nm) in

the Mg-2.5Gd alloy. In Mg-0.8Gd and Mg-1.5Gd alloys, the peak intensity of the Mg5Gd phase

is low, suggest that the formation of Mg5Gd phase is suppressed in Mg-0.8Gd and Mg-1.5Gd

alloys. The amount of the Mg5Gd phase in the as-cast Mg-Gd alloys are detected using the

Rietveld method and listed in Table 5-5. The corresponding GOF of the Rietveld refinement

suggests that the results are reliable. The weight fraction of the Mg5Gd phase increases from

0.35 wt. % in Mg-0.8Gd to 7.84 wt. % in Mg-2.5Gd.

Table 5-5 Amount of the Mg5Gd in as-cast Mg-Gd alloys and corresponding GOF.

Alloys Mg-0.8Gd Mg-1.5Gd Mg-2.5Gd

Weight percent 0.35 % 3.22 % 7.84 %

Volume fraction 0.22 % 1.95 % 4.85 %

GOF 1.33 1.61 1.43

50 μm

Intermetallic phase

Segregation

area

5 Results

37

Fig. 5-5 X-ray diffraction patterns of as-cast Mg-Gd alloys.

5.1.1.3 Mg-Sn alloys

The microstructures of as-cast Mg-Sn alloys are shown in Fig. 5-6. The OM graphics show the

as-cast Mg-Sn alloys have a typical dendritic structure and the contents of Sn seems to have

little effect on the grain size. The grain sizes of different Mg-Sn alloys are listed in Table 5-6.

With the increasing concentration of Sn from 0.8 at. % to 2.5 at. %, the grain size slightly

decreases from 1020 μm to 835 μm. The grain refinement of Sn is negligible in binary Mg-Sn

alloys.

Table 5-6 Grain sizes of as-cast Mg-Sn alloys.

Alloys Mg-0.8Sn Mg-1.5Sn Mg-2.5Sn

Grain size (μm) 1020±470 956±488 835±520

Like the Mg-Gd alloys, the as-cast Mg-Sn alloys are also composed of the 𝛼-Mg matrix,

intermetallic phases and segregation areas as illustrated in Fig. 5-7. The segregation areas are

distributed along grain boundaries and the interdendritic regions. In order to identify the

intermetallic phase, X-ray diffraction is performed on the as-cast Mg-Sn alloys. As shown in

Fig. 5-8, the intermetallic phase is identified as Mg2Sn (Space group: P63/mmc, a=b=0.3208

nm c=0.5217 nm). The amount of Mg2Sn in each alloy is determined using Rietveld method

and listed in Table 5-7. The weight percent of Mg2Sn increases from 0.85 wt. % in Mg-0.8Sn

alloy to 5.93 wt. % in Mg-2.5Sn alloy.

20 30 40 50 60 70 80 90

2

Mg-0.8Gd

Mg-1.5Gd

Mg-2.5Gd

Inte

nsi

ty /

a.u

.

Mg5Gd

Mg

5 Results

38

Fig. 5-6 OM and SEM (BSE) micrographs of as-cast Mg-Sn alloys.

(a), (d) Mg-0.8Sn; (b), (e) Mg-1.5Sn; (c), (f) Mg-2.5Sn.

Fig. 5-7 BSE micrograph of as-cast Mg-2.5Sn alloy.

100μm

d)

1mm

a)

100μm

e)

1mm

b)

1mm

c)

100μm

f)

10 μm

Intermetallic phase

Segregation

area

5 Results

39

Fig. 5-8 X-ray diffraction patterns of as-cast Mg-Sn alloys.

Table 5-7 Amount of the Mg2Sn in as-cast Mg-Sn alloys and corresponding GOF.

Alloys Mg-0.8Sn Mg-1.5Sn Mg-2.5Sn

Weight percent 0.85 % 1.77 % 5.93 %

Volume fraction 0.43 % 0.93 % 3.13%

GOF 1.28 1.34 1.34

5.1.1.4 Mg-Zn alloys

The microstructures of as-cast Mg-Zn alloys are shown in Fig. 5-9. As in the OM micrographs,

the microstructure of as-cast Mg-Zn alloys has an equiaxed grain structure, and the grain size

decreases with the increase in Zn content. The grain size of each alloy is listed in Table 5-8.

The average grain size decreases from 312 μm in Mg-0.8Zn to 166 μm in Mg-2.5Zn alloy.

Compared to the Gd and Sn, Zn shows a significant influence on refining the grain size even

with a small addition.

Table 5-8 Grain sizes of as-cast Mg-Zn alloys.

Alloys Mg-0.8Zn Mg-1.5Zn Mg-2.5Zn

Grain size (μm) 312±196 227±111 166±75

20 30 40 50 60 70 80 90

Inte

nsi

ty /

a.u

.

2

Mg-0.8Sn

Mg-1.5Sn

Mg-2.5Sn

Mg2Sn

Mg

5 Results

40

Fig. 5-9 OM and SEM (BSE) micrographs of as-cast Mg-Zn alloys.

(a), (d) Mg-0.8Zn; (b), (e) Mg-1.5Zn; (c), (f) Mg-2.5Zn.

The as-cast Mg-Zn alloys are composed of the 𝛼 -Mg matrix, intermetallic phases and

segregation areas as illustrated by the BSE graphics in Fig. 5-9. The morphology of the

intermetallic is dot-like in the Mg-0.8Zn alloy while it becomes larger and more irregular in

the Mg-2.5Zn alloy. The segregation areas are also distributed along grain boundaries and the

interdendritic regions.

In order to determine the intermetallic phase in as-cast Mg-Zn alloys, X-ray diffraction is

performed. According to the X-ray patterns in Fig. 5-10, the intermetallic phase in as-cast Mg-

Zn alloys is Mg7Zn3 phase (or Mg51Zn20, space group: Immm a=1.3962 nm b=1.4081 nm

c=1.4527 nm). The amount of the Mg7Zn3 is analyzed using the Rietveld method and listed in

Table 5-9. The amount of Mg7Zn3 phase increases from 1.50 wt. % in Mg-0.8Zn alloy to 9.51

wt. % in Mg-2.5Zn alloy.

2mm

a)

100μm

d)

2mm

b)

100μm

e)

2mm

c)

100μm

f)

5 Results

41

Fig. 5-10 X-ray diffraction patterns of as-cast Mg-Zn alloys.

Table 5-9 Amount of the Mg7Zn3 in as-cast Mg-Zn alloys and corresponding GOF.

Alloys Mg-0.8Zn Mg-1.5Zn Mg-2.5Zn

Weight percent 1.50 % 5.61 % 9.51 %

Volume fraction 0.92 % 3.50 % 5.98 %

GOF 1.46 1.42 1.19

5.1.2 As-extruded alloy

In order to study the influence of the grain size on the resistivity, various solution treatment

durations were performed on an extruded Mg-0.8Gd alloy to differ the grain size. The as-

extruded alloy was prepared in a previous study; the details about extrusion parameters can be

found elsewhere [199]. The micrographs of as-extruded alloy are illustrated in Fig. 5-11. As

shown in the OM graphics, the as-extruded alloy has equiaxial grains in parallel and

perpendicular directions. The grain sizes measured from different directions are listed in Table

5-10. The results show that different directions have the same grain size, which indicates that

the alloy was fully recrystallized during extrusion. It can be seen in the BSE graphics that there

exist fewer small bright particles in the sample parallel to the extrusion direction. These

particles are distributed along the extrusion direction. In the sample perpendicular to the

extrusion direction, no obvious intermetallic phases are observed.

20 30 40 50 60 70 80 90

Inte

nsi

ty /

a.u

.

2

Mg-0.8Zn

Mg-1.5Zn

Mg-2.5Zn

Mg7Zn3

Mg

5 Results

42

Fig. 5-11 OM and SEM (BSE) micrographs of as-extruded Mg-0.8Gd alloy.

(a), (c) Parallel to extrusion direction; (b), (d) Perpendicular to extrusion direction.

Table 5-10 Grain sizes of the as-extruded alloy in different directions.

Direction Parallel Perpendicular

Grain size (μm) 42±16 38±14

5.1.3 Solution treated alloys

5.1.3.1 Cast alloys

The as-cast alloys are solution treated to study the influence of the existing form of the alloying

elements on resistivity. The solution treated alloys are also prepared for the following

isothermal ageing treatment. The solution treatment temperatures are decided based on the

phase diagrams for different alloy series.

Fig. 5-12 shows the OM and SEM (BSE) micrographs of solution treated Mg-8Al, Mg-2.5Gd,

Mg-2.5Sn and Mg-2.5Zn alloys. These alloys are selected as representative for each series

because of the highest solute content. Their grain sizes are listed in Table 5-11. In the BSE

micrographs, Mg-8Al and Mg-2.5Sn alloys are shown to have a homogeneous microstructure

without any intermetallic phase, while in Mg-2.5Gd and Mg-2.5Zn alloys some particles are

observed.

200 μm

200 μm

a)

b)

50 μm

50 μm

c)

d)

5 Results

43

Fig. 5-12 OM and SEM (BSE) micrographs of solution treated alloys.

(a), (e) Mg-8Al; (b), (f) Mg-2.5Gd; (c), (g) Mg-2.5Sn; (d), (h) Mg-2.5Zn.

Table 5-11 Grain sizes of the cast alloys after solution treated.

Alloys Mg-8Al Mg-2.5Gd Mg-2.5Sn Mg-2.5Zn

Grain size (μm) 440±190 766±408 306±130 185±90

b)

d)

c)

a)

1mm

1mm

1mm

e)

f)

g)

h)

20μm

20μm

20μm

20μm

1mm

5 Results

44

In order to confirm the phase components, X-ray diffractions are performed on the solution

treated alloys, as illustrated in Fig. 5-13. The results show that in Mg-8Al and Mg-2.5Sn, only

the Mg phase peaks are present, indicating that the intermetallic phases are fully dissolved in

the matrix, which is coincident with the BSE micrographs. However, the X-ray pattern of Mg-

Zn also indicates that the intermetallic phase is fully dissolved into the matrix, but the BSE

micrograph shows some intermetallic phases still present. The reason why peaks of the

intermetallic phase cannot be detected may be due to the limited amount of the phase and the

low resolution of the laboratory X-ray apparatus. The pattern of solution treated Mg-Gd alloy

shows that except for the Mg phase, other phases in the solution treated Mg-Gd exist.

It should also be noted in Fig. 5-13, the position of the Mg peaks of the solution treated alloys

are slightly different. Compared to the standard Mg peaks (PDF#35-0821), the peaks in Mg-

Zn and Mg-Al alloys shift to the large 2θ angle direction while in Mg-Gd alloy the peaks shift

to the small 2θ angle direction.

Fig. 5-13 X-ray diffraction of solution treated alloys.

As Gd has a high absorption coefficient of X-ray generated by the Cu target, it is difficult to

confirm the phase using the laboratory X-ray apparatus [200, 201]; therefore, synchrotron

radiation diffraction is carried out in DESY to analyze the type of secondary phase in the

solution treated Mg-Gd alloy. The intermetallic phase in the solution treated Mg-Gd alloy is

identified to be GdH2, as illustrated in Fig. 5-14.

20 30 40 50 60 70 80 90

Inte

nsi

ty /

a.u

.

2

Mg-8Al

Mg-2.5Gd

Mg-2.5Sn

Mg-2.5Zn

Gd rich phase

Mg

5 Results

45

Fig. 5-14 Synchrotron diffraction pattern of the solution treated Mg-Gd alloy.

Composition of the intermetallic phase in the solution treated Mg-Zn alloy is analyzed by EDS

as in Fig. 5-15. The results show that its composition is very similar to that of the as-cast phase.

Therefore, the phase is supposed to be the undissolved Mg7Zn3 phase.

Fig. 5-15 Composition of the intermetallic phase in as-cast and solution treated Mg-Zn alloy.

5.1.3.2 Extruded alloy

Different solution treatment durations are performed on the extruded Mg-0.8Gd alloy to study

the influence of grain size on resistivity. As revealed in Fig. 5-11, the as-extruded alloy has

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

2

Inte

nsi

ty /

a.u

.

Mg PDF#35-0821

GdH2 PDF#51-1143

10μm

Elt. Line Conc. Units Error 2-sig

O Ka 3,977 wt.% 0,027

Mg Ka 48,072 wt.% 0,076

Zn Ka 47,951 wt.% 0,222

T4 treated Mg-2.5 Zn

10μm

As-Cast Mg-2.5 Zn

Elt. Line Conc. Units Error 2-sig

O Ka 1,717 wt.% 0,018

Mg Ka 52,341 wt.% 0,080

Zn Ka 45,942 wt.% 0,221

5 Results

46

equiaxial grains. Therefore, it is acceptable to consider that the grains in different directions

still have the same size after solution treatment. Fig. 5-16 shows the OM graphics of the

extruded Mg-0.8Gd alloy perpendicular to the extrusion direction after varying solution times.

The grain sizes are listed in Table 5-12; the results show that solution treatment can

significantly enlarge the grain size of the extruded alloy. The grains grow quickly at first, the

grain size increases from 42 μm to 116 μm at the first 2 hours. After that, the grain growth

slows down, the alloy solution treated for 48 hours has a grain size of 192 μm.

Fig. 5-16 OM of extruded Mg-0.8Gd alloy with different solution times.

(a) 2 hrs; (b) 8 hrs; (c) 24 hrs; (d) 48 hrs.

Table 5-12 Grain sizes of the extruded Mg-0.8Gd alloy after solution treatment.

Solution time 0 hrs

2 hrs 8 hrs 24 hrs 48 hrs Parallel Perpendicular

Grain size (μm) 42±16 38±14 116±68 128±84 162±75 192±102

5.1.4 Aged alloys

Precipitation is affected by both the temperature and solute content. A high solute content alloy

can accelerate the precipitation process compared to a low solute content one. Temperatures,

on the other hand, affect not only the precipitation kinetics but also the precipitation sequence.

2 mm

2 mm

2 mm

2 mm

a)

d)c)

b)

5 Results

47

Since the precipitation sequence plays a more important role in precipitation strengthening, the

influence of temperature on the precipitation sequence is of more interest in the current study.

Therefore, alloys with the highest solute content of each series are selected to represent the

precipitation behaviour under different ageing temperatures.

5.1.4.1 Mg-Al alloys

From Fig. 5-17 to Fig. 5-19, the microstructures of Mg-8Al alloys aged at 175 °C, 200 °C and

225 °C are shown. The precipitates in the peak-aged and over-aged condition (Fig. 5-32) are

determined using X-Ray diffraction (Fig. 5-20). The precipitates are confirmed to be Mg17Al12

phase in both conditions.

At the early stage of ageing at 175 °C, discontinuous precipitation first occurs at the grain

boundaries and no continuous precipitation is observed, as the sample was aged for 4 hours in

Fig. 5-17. The volume of discontinuous precipitation increases after the aged time extends to

32 hours and continuous precipitation occurs inside the grain. When the sample reaches peak-

aged for 96 hours, the precipitation occurs everywhere. Both discontinuous and continuous

precipitation exist in the alloy aged at 175 °C.

Fig. 5-17 Microstructures of Mg-8Al alloy aged at 175 °C.

Fig. 5-18 and Fig. 5-19 are microstructures of Mg-8Al alloys aged at 200 °C and 225 °C,

respectively. The main characteristics of the microstructure are similar to that aged at 175 °C,

50μm 50μm

20μm

4 hrs

96 hrs

32 hrs

5 Results

48

but the precipitation process is accelerated. In the sample aged at 175 °C for 32 hours,

discontinuous precipitation dominates and a small amount of continuous precipitation occurs

inside the grains. In the sample aged at 200 °C for 16 hours, except the discontinuous

precipitation, a large number of continuous precipitation occurs inside the grain. In the sample

aged at 225 °C for 8 hours, precipitation occurs through the entire sample.



50μm 50μm

20μm

4 hrs

96 hrs

16 hrs

4 hrs

32 hrs

8 hrs

50μm 50μm

20μm

5 Results

49

Fig. 5-20 X-Ray diffraction of Mg-8Al alloys aged at different conditions.

5.1.4.2 Mg-Gd alloys

Fig. 5-21 and Fig. 5-22 show the microstructures of Mg-2.5Gd alloys aged at different

conditions. Since God has a high absorption coefficient of X-ray generated by Cu target,

synchrotron radiation diffraction (Fig. 5-23) is used to analyse the peak-aged and over-aged

condition (Fig. 5-33). The results show that the phases in the peak-aged condition are the 𝛽′

phase, 𝛼-Mg and preformed GdH2 phase during solution treatment. In the over-aged condition,

the peaks of Mg5Gd are observed.

Fig. 5-21 Microstructures of Mg-2.5Gd alloys aged at 200 °C and 225 °C.

20 30 40 50 60 70 80 90

448 K_96 hrs

2 /

Inte

nsi

ty /

a.u

.

473 K_72 hrs

498 K_32 hrs

498 K_192 hrs

Mg17Al12

Mg

500 nm 1 μm

1 μm 1 μm

200 C-144 hrs

225 C-240 hrs

200 C-312 h

225 C-8 hrs

5 Results

50

As in Fig. 5-21, a high number density of precipitates are observed and uniformly distributed

in the magnesium matrix in the alloy aged at 200 °C for 144 hours. Although in the SEM

micrographs, no obvious phase is observed for alloy aged at 225 °C for 8 hours. The

synchrotron patterns show the existence of the 𝛽′ phase. The precipitates are not observed

because of the limited resolution of the SEM. In the alloy aged at 200 °C for 144 hours, a

solute-depleted area is observed near the grain boundary. This solute-depleted area is formed

due to the consumption of the solute atoms by the grain boundary precipitates. The

microstructures in the over-aged condition show only a slight difference to that in the peak-

aged condition. In the sample aged at 225 °C for 240 hours, a coarser and brighter phase is

observed. A solute-depleted area is also formed around the newly formed precipitates, suggest

that the newly formed phase has a high Gd content.

Fig. 5-22 shows the microstructure evolution of Mg-2.5Gd alloys aged at 250 °C. After aged

for 1 hour, the precipitation first occurs at the grain boundary. After aged for 2 hours, except

for the grain boundary precipitates, a large number of the 𝛽′ phases are observed inside the

grain. When the sample is over-aged to 16 hours, the dominant precipitates are still the 𝛽′ phase,

but the 𝛽′ phase becomes coarser. After extending the aged time to 240 hours, the 𝛽′ phase

becomes coarser and another type of phase, which is similar in the sample aged at 225 °C for

240 hours, is observed. According to the synchrotron diffraction pattern, this phase is the

equilibrium 𝛽 phase. The solute-depleted area around the 𝛽 phase is very clear.

Fig. 5-22 Microstructures of Mg-2.5Gd alloys aged at 250 °C.

1 μm

200 nm

1 μm

1 hrs

16 hrs

2 hrs

240 hrs

500 nm

5 Results

51

Fig. 5-23 Synchrotron diffraction of Mg-2.5Gd alloys aged at different conditions.

5.1.4.3 Mg-Sn alloys

From Fig. 5-24 to Fig. 5-26 are the microstructures of Mg-2.5Sn alloys aged at 175 °C, 200 °C

and 225 °C, respectively. The precipitates in the peak-aged and over-aged condition (Fig. 5-34)

are determined using X-Ray diffraction (Fig. 5-27). The precipitates are confirmed to be Mg2Sn

phase in both conditions.

Fig. 5-24 Microstructures of Mg-2.5Sn alloy aged at 200 °C.

1 2 3 4 5 6

523 K_2 hrs

Inte

nsi

ty /

a.u

.

2 /

Mg7Gd

Mg

Mg5Gd

GdH2

473 K_96 hrs

523 K_240 hrs

498 K_4 hrs

10μm 10μm

10μm

16 hrs

384 hrs

120 hrs

5 Results

52



Continuous precipitation is the primary type in Mg-Sn alloys. As in Fig. 5-24, grain boundary

precipitation and continuous precipitation occur in the sample aged at 200 °C for 16 hours.

When the ageing time is prolonged, the volume of continuous precipitation inside the grain

increases and discontinuous precipitation is not observed. The continuous precipitation has a

visible orientation relationship with the matrix grains. The precipitation processes at 225 °C

and 250 °C are similar to those at 200 °C, but with accelerated precipitation kinetics. After

being aged for 16 hours, the sample aged at 250 °C has a much higher density of precipitates

than those aged at 200 °C.

10μm 10μm

10μm

16 hrs

72 hrs

32 hrs

10μm 10μm

10μm

8 hrs

120 hrs

16 hrs

5 Results

53

Fig. 5-27 X-Ray diffraction of Mg-2.5Sn alloys aged at different conditions.

5.1.4.4 Mg-Zn alloys

From Fig. 5-28 to Fig. 5-30 are the microstructures of Mg-2.5Zn alloys aged at different

conditions. The precipitates in the peak-aged and over-aged condition (Fig. 5-35) are

determined using X-Ray diffraction (Fig. 5-31).

Fig. 5-28 Microstructures of Mg-2.5Zn alloy aged at 175 °C.

20 30 40 50 60 70 80 90

473 K_168 hrs

498 K_32 hrs

Mg2Sn

Mg

523 K_16 hrsIn

ten

sity

/ a

.u.

2 /

523 K_264 hrs

5 μm 1 μm

1 μm

1 hrs 24 hrs

240 hrs

5 Results

54



The precipitates are confirmed to be MgZn2 in the over-aged condition. In the peak-aged

condition, broad peaks appear around the same position as the MgZn2 phase. However, the

Mg4Zn7 phase also has peaks between 40 ° to 42 °, so the precipitates in the peak-aged

condition may be the Mg4Zn7 phase. Fig. 5-30 shows the typical microstructure evolution of

Mg-2.5Zn during ageing treatment. When peak-aged, large numbers of fine and elongated

precipitates are found inside the grain, some block-shaped precipitates also exist. If the ageing

time is prolonged to reach an over-aged condition, the elongated precipitates become coarse

2 μm 2 μm

2 μm

1 hrs 4 hrs

120 hrs

1 μm 2μm

2 μm

1 hrs 16 hrs

240 hrs

5 Results

55

and the number of the block-shaped precipitates increases. When the ageing time is further

prolonged to 240 hours, the coarsening of the elongated precipitates and increased number of

the block-shaped precipitates becomes more obvious. The microstructure characterization of

Mg-2.5Zn aged at 175 °C and 200 °C is similar to that aged at 225 °C with the fact that the

precipitation process takes a longer time due to the lower ageing temperatures.

Fig. 5-31 X-Ray diffraction of Mg-2.5Zn alloys aged at different conditions

5.2 Age hardening behaviour

5.2.1 Mg-Al alloys

The Mg-Al alloys are aged at 175 °C, 200 °C and 225 °C; the age hardening curves are shown

in Fig. 5-32. The Mg-8Al alloy shows a significant increase in hardness at all ageing

temperatures, while other Mg-Al alloys have little or no age hardening response during ageing

treatment. The hardness of Mg-8Al increases at first until it reaches the peak hardness; then it

decreases slightly. The details about the age hardening data of the Mg-8Al alloy are listed in

Table 5-13. As detailed in Table 5-13, the ageing temperature has a slight influence on the peak

hardness, but it can accelerate the age hardening process. As the ageing temperature increases

from 175 °C to 225 °C, reaching the peak hardness decreases from 96 hours to 32 hours.

20 30 40 50 60 70 80

448 K_24 hrs

Inte

nsi

ty /

a.u

.

2 /

473 K_4 hrs

498 K_2 hrs

498 K_72 hrs

MgZn2

Mg

5 Results

56

Table 5-13 Age hardening data of Mg-8Al alloy.

Ageing

temperatures

Hardness (kg mm-2) Time for reaching

peak hardness Initial Peak-aged

175 °C 52.4 83.3 96 hrs

200 °C 52.4 78.1 72 hrs

225 °C 52.4 80.4 32 hrs

Fig. 5-32 Age hardening curves of Mg-Al alloys.

(a) 175 °C; (b) 200 °C; (c) 225 °C.

5.2.2 Mg-Gd alloys

Fig. 5-33 shows the age hardening curves of Mg-Gd alloys at different conditions. The detailed

data is listed in Table 5-14. The results reveal that Mg-2.5Gd has a substantial age hardening

response and the values of peak hardness are close to each other under all ageing temperatures.

On the other hand, the increasing ageing temperature can enhance the age hardening kinetics

of the Mg-2.5Gd alloy. The time for reaching the peak hardness decreases from 96 hours to 2

hours, with the ageing temperature increasing from 200 °C to 250 °C. After peak-aged, the

5 Results

57

hardness of the Mg-2.5Gd alloy decreases significantly due to the over-aged that occurred at

all aged temperatures.

The peak hardness of Mg-1.5Gd alloy is influenced a lot by the ageing temperatures compared

to the Mg-2.5Gd alloy. The peak hardness decreases from 97 to 69 with the increasing ageing

temperature. On the other hand, the precipitation kinetics of Mg-1.5Gd alloy shows less

sensitivity to the temperature since the time to reach the peak hardness is 48 hours in Mg-1.5Gd

alloy when aged at 225 °C to 250 °C. However, in the Mg-2.5Gd alloy, it is only 4 hours and

2 hours when aged at 225 °C to 250 °C. The hardness decrease in Mg-1.5Gd alloy is

pronounced at 200 °C but not apparent at 250 °C.

Mg-0.8Gd alloy has a visible age hardening response only at 200 °C and the time for reaching

the peak hardness is 312 hours. When aged at 225 °C and 250 °C, Mg-0.8Gd alloy did not

show an obvious age hardening response.

Fig. 5-33 Age hardening curves of Mg-Gd alloys.

(a) 200 °C; (b) 225 °C; (c) 250 °C.

https://www.thesaurus.com/browse/pronounced

5 Results

58

Table 5-14 Age hardening data of Mg-Gd alloys.

Alloys Ageing

temperatures



Mg-0.8Gd 200 °C 42.5 54.8 312 hrs

225 °C 42.5 No obvious peak -


Mg-1.5Gd 200 °C 58.9 97.0 96 hrs

225 °C 58.9 81.1 48 hrs

250 °C 58.9 69.0 48 hrs

Mg-2.5Gd 200 °C 79.2 122.7 96 hrs

225 °C 79.2 120.9 4 hrs

250 °C 79.2 119.8 2 hrs

5.2.3 Mg-Sn alloys

The age hardening response of the Mg-Sn alloy is illustrated in Fig. 5-34. The detailed data is

listed in Table 5-15.

Table 5-15 Age hardening data of Mg-Sn alloys.

Alloys Ageing

temperatures



Mg-0.8Sn 200 °C 33.1 39.5 264 hrs

225 °C 33.1 40.1 192 hrs

250 °C 33.1 39.9 24 hrs

Mg-1.5Sn 200 °C 35.3 43.6 168 hrs

225 °C 35.3 45.9 96 hrs

250 °C 35.3 45.4 16 hrs

Mg-2.5Sn 200 °C 41.5 55.0 168 hrs

225 °C 41.5 52.8 32 hrs

250 °C 41.5 54.3 16 hrs

5 Results

59

The Mg-Sn alloys show an obvious age hardening response in all aged temperatures, as

illustrated in Fig. 5-34. The peak hardness is more sensitive to the solute content rather than

the ageing temperatures. The peak hardness of the Mg-Sn alloys has only a slight difference

when aged under different temperatures. On the other hand, a high ageing temperature can

significantly accelerate the age hardening process; for all alloys, reaching the peak hardness is

more than 160 hours when aged at 200 °C and decreases to less than 24 hours when aged at

250 °C. The decrease of hardness is not apparent in Mg-Sn alloys; the hardness value does not

drop at a high level for an extended time.

Fig. 5-34 Age hardening curves of Mg-Sn alloys.

(a) 200 °C; (b) 225 °C; (c) 250 °C.

5.2.4 Mg-Zn alloys

Fig. 5-35 shows the age hardening behaviour of Mg-Zn alloys. The detailed data is listed in

Table 5-16. Mg-Zn alloys have a noticeable age hardening response under all ageing

temperatures except the Mg-0.8Zn alloy. The peak hardness is influenced by both the solute

content and the ageing temperatures. It increases with the solute content and decreases with the

5 Results

60

ageing temperatures. Additionally, a higher ageing temperature and higher solute content can

accelerate the precipitation kinetics.

Fig. 5-35 Age hardening curves of Mg-Zn alloys. (a) 175 °C; (b) 200 °C; (c) 225 °C.

Table 5-16 Age hardening data of Mg-Zn alloys.

Alloys Ageing

temperatures



Mg-0.8Zn 175 °C 35.7 40.3 120 hrs



Mg-1.5Zn 175 °C 39.2 55.5 72 hrs

200 °C 39.2 51.5 8 hrs

225 °C 39.2 48.7 8 hrs

Mg-2.5Zn 175 °C 52.9 74.6 24 hrs

200 °C 52.9 69.9 2 hrs

225 °C 52.9 66.1 1 hrs

5 Results

61

5.3 Electrical resistivity

5.3.1 The resistivity of the as-cast alloys

5.3.1.1 Low and room temperatures

The resistivity of as-cast alloys at 77 K and 293 K is shown in Fig. 5-36. The resistivity

increases almost linearly with the solute content at 77 K for all alloys. At 293 K, the resistivity

also increases with the solute content except for the Mg-2.5Sn alloy. The resistivity of the Mg-

2.5Sn is slightly lower than that of the Mg-1.5Sn alloy. Gd has the strongest effects on the

resistivity in these four alloying elements, while Zn has the lowest one. At 77 K, Mg-2.5Gd

alloy has a resistivity of 198.3 nΩ∙m and Mg-2.5Zn has a resistivity of 20.0 nΩ∙m. The

resistivity measured at 293 K is higher than that measured at 77 K, which suggests that

temperature also influences the resistivity.

Fig. 5-36 The resistivity of as-cast alloys.

(a) 77 K; (b) 293 K.

5.3.1.2 Moderate temperatures

Fig. 5-37 illustrates the as-cast alloys’ resistivity at moderate temperature ranges from 323 K

to 473 K. As in Fig. 5-37, Mg-2.5Gd alloy has the highest resistivity and Mg-0.8Al alloy has

the lowest resistivity. The resistivity increases with temperature in all alloys and the increment

of resistivity is almost linear to the temperature. Except for the Mg-1.5Sn alloy, the slopes of

the temperature-dependent resistivity of different alloys show only a slight difference. The

results suggest that the influence of temperature on resistivity is insensitive to the alloying

elements and contents.

5 Results

62

Fig. 5-37 The resistivity of as-cast alloys.

5.3.2 The resistivity of the solution treated alloys

5.3.2.1 Cast alloys

Fig. 5-38 shows the resistivity of the solution treated alloys at 77 K and 293 K.

Fig. 5-38 The resistivity of solution treated alloys.

(a) 77 K; (b) 293 K.

The resistivity of the solution treated alloys also increases linearly with the solute content

which is the same for the as-cast alloys. Furthermore, in the as-cast alloys, the resistivity of

5 Results

63

Mg-2.5Sn alloys is slightly lower than that of Mg-1.5Sn alloy when measured at 293 K, which

disobeys the linear rule. When the alloys are solution treated, Mg-2.5Sn alloy has a higher

resistivity than that of Mg-1.5Sn alloy. The results imply that heat treatment influences the

resistivity of alloys. For the as-cast alloys, the resistivity measured at 293 K is higher than that

measured at 77 K. Fig. 5-39 shows the resistivity of the solution treated alloys at temperatures

ranging from 323 K to 473 K. As with the as-cast alloys, resistivity increases linearly with the

temperature in all alloys. The slopes of the temperature-dependent resistivity of different alloys

show only a slight difference except for the Mg-1.5Sn.

Fig. 5-39 The resistivity of solution treated alloys.

5.3.2.2 Extruded alloys

Fig. 5-40 shows the resistivity of the extruded Mg-0.8Gd alloy after various solution treatment

durations. With a different solution treatment duration, the extruded alloy has a different grain

size. Additionally, the resistivity of cast Mg-0.8Gd alloy without extrusion is also compared.

Thus, the influence of grain size on resistivity can be assessed. As shown in Fig. 5-40, the

alloys have almost the same resistivity at the same measuring temperatures despite the different

grain sizes. The resistivity of cast Mg-0.8Gd alloy is a little lower than that of the extruded

alloys. However, the difference is very small; it is less than 2.5%. The results imply that the

influence of grain size on resistivity is small.

5 Results

64

Fig. 5-40 Resistivity of Mg-0.8Gd alloy after solution treatment.

5.3.3 The resistivity of aged alloys

Fig. 5-41 shows the resistivity evolution of different alloys aged at 225 °C measured at 77 K.

The resistivity decreases with the ageing time in all alloys and the Mg-Zn alloy decreases to a

steady resistivity the fastest, as shown in Fig. 5-41. In order to have a more precise comparison

of the resistivity decreased kinetics, the length of time that the resistivity reaches a 50%

reduction (suggesting that the resistivity is stable after aged for 240 hours) is estimated and

listed in Table 5-17. The results indicate that the Mg-Zn has the highest kinetics, while the Mg-

Sn alloy has the lowest one.

Table 5-17 Resistivity of different alloys aged at 225 °C.

Alloys Initial resistivity

(nΩ m)

Final resistivity

(nΩ m)

Time for reaching a

50% reduction

Mg-8Al 123.9 60.9 ~8 hrs

Mg-2.5Gd 248.8 80.8 ~4 hrs

Mg-2.5Sn 107.7 16.7 ~9.5 hrs

Mg-2.5Zn 20.5 13.1 ~1 hrs

5 Results

65

Fig. 5-41 The resistivity of alloys aged at 225 °C.

5.3.4 In situ resistivity measurements during isothermal ageing

Fig. 5-42 illustrates the resistivity changes under different isothermal ageing temperatures of

binary Mg alloys. The resistivity increases at first because the sample is immersed in the oil

bath at room temperature. Within 3~5 minutes, the sample reaches the preset temperature

through heat conduction. Hence, the resistivity also increases to a maximum within 3~5

minutes due to the corresponding temperature. After that, the sample undergoes an isothermal

ageing process. As shown in Fig. 5-42, the curves decrease faster with a higher ageing

temperature in all alloys. After aged for a certain time, the resistivity of that under a higher

ageing temperature is higher than that for a lower ageing temperature, as illustrated by the Mg-

Zn alloy. In other alloys, although it cannot be seen directly from the resistivity curves, the

same conclusion can be conducted from the tending of the curves.

Another interesting finding is that the resistivity of Mg-Zn alloy after a long ageing time is

higher than that in the solution treated states, while in Mg-Al, Mg-Gd and Mg –Sn alloys, the

resistivity after a long ageing time is lower than the solution treated alloys. This result

demonstrates that the influence of temperature on resistivity is larger than that of the Zn

contents.

5 Results

66

Fig. 5-42 Resistivity changes during isothermal ageing.

(a) Mg-8Al; (b) Mg-2.5Gd; (c) Mg-2.5Sn; (d) Mg-2.5Zn.

6 Discussion

67

6 Discussion

The resistivity is very sensitive to the concentrations of impurities; therefore, the purity of the

alloys has a strong effect on the accuracy of the conclusion. In the current study, the

concentrations of the main impurities, Ni, Fe and Si, are less than 55 ppm (weight percent).

Therefore, the influence of the impurities is negligible and the results obtained based on these

alloys are reliable.

6.1 Microstructure

6.1.1 As-cast alloys

6.1.1.1 Intermetallic phases

Due to the fast cooling rate during casting, the solidification process is under a non-equilibrium

condition. Therefore, the as-cast intermetallic phases may deviate from the equilibrium phases.

According to the phase diagrams, the equilibrium phase in the current studying alloys should

be the Mg17Al12, Mg5Gd, Mg2Sn and MgZn. In Chapter 5, the as-cast intermetallic phases are

determined. The results show that in Mg-Al, Mg-Gd and Mg-Sn alloys, the intermetallic phases

are identical to the equilibrium phase. While in Mg-Zn alloy, the as-cast intermetallic phase is

different from the equilibrium phase.

In Mg-Al, Mg-Gd and Mg-Sn alloy systems, the as-cast intermetallic phases are the same as

the equilibrium phases; because no metastable phase or transition phase will form during

solidification. However, in the Mg-Zn alloy system, during solidification, eutectic reaction that

forms 𝛼-Mg and Mg7Zn3 phases will occur first. The Mg7Zn3 phase is thermodynamically

stable only at temperatures above 325 °C. If the solidification is in an equilibrium condition or

a low cooling rate, the Mg7Zn3 phase will decompose into the 𝛼 -Mg and MgZn phases.

However, due to the high cooling rate in the current study, the decomposition of the Mg7Zn3

phase is suppressed. Hence, the Mg7Zn3 phase is maintained in the as-cast alloy. Another

interesting fact is that, as listed in Table 6-1, the weight percent of the intermetallic phases in

Mg-Al and Mg-Zn alloy systems tend to be higher than the alloying element, especially with

the high alloying element contents. On the other hand, the weight percent of intermetallic

phases is always lower than that of the alloying elements in Mg-Gd and Mg-Sn alloy systems.

This phenomenon suggests that compared to Al and Zn, the Gd and Sn are easier to be dissolved

in the matrix. It can be supported by the BSE graphics in Fig. 6-2.

6 Discussion

68

Fig. 6-1 Phase diagrams of binary Mg alloys in the Mg-rich corner.

Table 6-1 Amount of alloying elements and intermetallic phases.

Alloys Alloying elements Intermetallic phases

wt. % at. % wt. % Volume fraction %

Mg-0.8Al 0.85 0.8 0 0

Mg-2.5Al 2.74 2.5 2.52 2.17

Mg-5Al 5.56 5.0 7.67 6.64

Mg-8Al 8.77 8.0 10.8 9.40

Mg-0.8Gd 4.93 0.8 0.35 0.22

Mg-1.5Gd 8.66 1.5 3.22 1.95

Mg-2.5Gd 13.3 2.5 7.84 4.85

Mg-0.8Sn 3.69 0.8 0.85 0.43

Mg-1.5Sn 6.55 1.5 1.77 0.93

Mg-2.5Sn 10.73 2.5 5.93 3.13

Mg-0.8Zn 2.06 0.8 1.5 0.92

Mg-1.5Zn 3.96 1.5 5.61 3.50

Mg-2.5Zn 6.91 2.5 9.51 5.98

a)

c)

b)

d)

6 Discussion

69

Fig. 6-2 BSE micrographs of as-cast alloys.


As in Fig. 6-2, segregation areas are obvious in as-cast Mg-Gd and Mg-Sn alloys, while they

are nearly invisible in the as-cast Mg-Al and Mg-Zn alloys. The segregation areas form during

casting because of the high solubility of Gd and Sn in Mg as well as the non-equilibrium

solidification. During solidification, the solute is rejected into the liquid at the advancing liquid-

solid interface. Therefore, along with the grains’ growth, the solute content in the remaining

liquid increases. Since the high solubility of Gd and Sn in Mg, a large amount of the solutes

can dissolve into the matrix and the solutes beyond the solubility will form intermetallic phases

with Mg. Hence, segregation areas are obvious in the Mg-Gd, Mg-Sn alloys. Because of the

dendritic growth of 𝛼-Mg, grain boundaries and the interdendritic regions are solidified at the

final stage. Therefore, segregation and the intermetallic phases are located in these areas.

6.1.1.2 Grain size

Normally, fine grain size is favourable for the mechanical properties; therefore, grain refiners

are usually added in commercial alloys. However, since the resistivity is very sensitive to the

composition, no grain refiner is used in the current study. Hence, the grain sizes of different

alloys are distinctive due to the particular influence of each alloying element.

As a rough conclusion, the influence of Gd and Sn on the grain size is negligible and Al and

Zn can refine the grain size. More specifically, in Mg-Al alloys the grain size decrease from

20 μm 20 μm

20 μm20 μm

Segregation

area

Segregation

area

a)

d)c)

b)

6 Discussion

70

841 μm to 187 μm as the Al increases from 0.8 at. % to 8 at. % and in Mg-Zn it decreases from

312 μm to 166 μm with the increasing Zn contents from 0.8 at. % to 2.5 at. %. On the other

hand, in Mg-Gd and Mg-Sn alloys grain sizes are approximately 1000 μm despite the changes

of the solute content.

The grain refinement of as-cast alloys can be classified into two types:

1) Increasing the number density of nuclei during solidification;

2) Restricting the growth of grains.

The number density of nuclei can be increased by enhancing undercooling, or heterogeneous

nucleation via introducing foreign particles and/or in situ synthesizing particles as effective

sites. Restricting the growth of grains, on the other hand, can be achieved by adding alloying

elements according to the concentration gradient mechanism [202]. The effect of solute

elements on grain size can be assessed by the growth restriction factor (GRF) [203]. The GRF

can be calculated using

𝐺𝑅𝐹 = 𝑚𝐶(𝑘 − 1) (6-1)

Where m is the slope of the liquid line (suggest it is a straight line), C is the concentration of

the alloying element and k is the equilibrium distribution coefficient. The parameters for

calculating GRFs of Al, Gd, Sn and Zn in Mg are calculated using the binary phase diagrams

and listed in Table 6-2.

Table 6-2 Parameters for calculating GRFs of different alloying elements

Elements m k m(k-1)

Al -6.04 0.38 3.74

Gd -2.80 0.64 1.01

Sn -2.74 0.35 1.78

Zn -5.95 0.11 5.30

Zr [203] 6.90 6.55 32.89

Y [203] -3.40 0.50 1.70

A higher value of the GRF means more effective in restricting the growth of the grains and

results in finer grain size. As in Table 6-2, when the concentration of each alloying elements is

at the same level, then the GRF values of them are Zn>Al>Sn>Gd. This implies that Mg-Zn

6 Discussion

71

alloys have the best effect in restricting the growth of the grains while Mg-Gd alloys have the

worst effect, which is coincident to the results in Chapter 5.

6.1.2 Solution treated alloys

6.1.2.1 Cast alloys

The solution treatment for the cast alloys used to dissolve all the as-cast intermetallic phase

into the matrix. Thus, the influence of different alloying elements and their contents on

resistivity can be measured.

As in Fig. 5-12, after solution treatment, the as-cast intermetallic phases in Mg-8Al and Mg-

2.5Sn alloys have been dissolved into the matrix. Therefore, it can be concluded that the

solution time is long enough for the Mg-Al and Mg-Sn series alloys to dissolve the as-cast

intermetallic phases. Because Mg-8Al and Mg-2.5Sn alloys have the highest contents of the

alloying elements and thus the highest amounts of intermetallic phases in Mg-Al and Mg-Sn

series alloys. Consequently, they need the longest time to dissolve the intermetallic phases into

the matrix compared to the alloys with lower contents. Despite the solute concentration being

different, the solution time is same for each alloy series as indicated in Table 4-2. With the fact

that the intermetallic phases in Mg-8Al and Mg-2.5Sn alloys are completely dissolved, it can

be speculated that the intermetallic phases in Mg-Al and Mg-Sn series alloys have been

dissolved.

In Fig. 5-12, some white rectangular phases are present in Mg-2.5Gd alloy and confirmed to

be GdH2 by synchrotron radiation diffraction analysis as in Fig. 5-14. The hydrides have been

found in many RE containing Mg alloys [204-208]. Vlček et al. [204] suggest that there are

four ways in which the RE hydrides are formed:

1) they are formed during casting by the reaction of the RE element with hydrogen

dissolved in raw materials;

2) they are developed as a result of hydrogen-induced decomposition of the as-cast

intermetallic phases during solution treatment;

3) they are brought out due to the water quenching after solution treatment;

4) they are introduced during the sample preparation in the presence of water.

In fact, except for the third mechanism, all other mechanisms have been verified in Mg-Gd

alloys by researchers [206, 208, 209]. In the current study, the as-cast alloys do not show

obvious GdH2 peaks in the X-ray patterns and the samples are prepared without water.

6 Discussion

72

Therefore, the GdH2 is formed mainly due to the hydrogen-induced decomposition of Mg5Gd

during solution treatment.

Nevertheless, the RE hydrides are quite stable; they will not decompose up to 1000 °C [209].

Therefore, their amounts will not change during the current isothermal ageing temperature

range (from 200 °C to 250 °C) and their influence on the resistivity is assumed as a constant.

Hence, it can be regarded as a systematic error and it will not affect the tendency of the

resistivity change.

In the Mg-2.5Zn alloy, intermetallic phases are still present after solution treatment and they

are considered as undissolved Mg7Zn3 phase. Usually, the existence of the as-cast intermetallic

phases means an insufficient solution treatment duration. A longer solution time is needed to

dissolve the intermetallic phases. However, things may be different in the current instance. As

in Table 5-1, the concentration of Zn in Mg-2.5Zn alloy is 2.68 at. %, which is higher than the

desired. According to the phase diagram in Fig. 6-1, the maximum solubility of Zn in Mg is

2.3 at. % at 340 °C. Therefore, the content of Zn is beyond its maximum solubility in Mg; in

this case, a longer solution time will not help dissolve the Mg7Zn3 phase. A BSE graphic of the

solution treated Mg-1.5Zn alloy with the same solution parameters is shown in Fig. 6-3. The

BSE graphic shows that the intermetallic phase is completely dissolved into the matrix.

Therefore, the results indicate that the solution time is long enough to dissolve the as-cast

Mg7Zn3 phase when the Zn content is less than the maximum solubility. The undissolved

Mg7Zn3 phase in Mg-2.5Zn alloys is due to the excess Zn, not the solution time.

Fig. 6-3 Microstructure of solution treated Mg-1.5Zn alloy.

T4 treated Mg-1.5 Zn

100μm

6 Discussion

73

The peaks shift in Fig. 5-13 is due to the different atomic radii of the solute elements. The

atomic radius of Mg is 145 pm and the radii of Al, Zn and Gd are 118 pm, 142 pm and 233 pm

respectively. The solute substitutes the Mg atoms in the matrix and thus changes the lattice

parameters. Since the radii of Al and Zn are smaller than Mg, they will decrease the lattice

parameters and, therefore, the interplanar distance of the matrix. On the other hand, Gd will

increase the interplanar distance of the matrix. According to Bragg’s law, the 2θ value will

change following the changes of the interplanar distance since the wavelength of the X-ray is

a fixed value.

6.1.2.2 Extruded alloy

As mentioned in chapter 2, grain boundaries will increase resistivity. Since the grain sizes of

the as-cast and solution treated alloys are quite different, it is necessary to clarify the influence

of grain sizes on resistivity. Therefore, the extruded Mg-0.8Gd alloy is also investigated in the

current study. The extruded Mg-0.8Gd alloy has an equiaxed and fine grain size, with different

solution times, various grain sizes are obtained as shown in Table 5-12. The equiaxed grain

size of the as-extruded alloy suggests that full recrystallization occurred during hot extrusion.

So the influence of the deformation-induced dislocations can be ignored. Hence, the only

difference between these solution treated alloys is the grain size. They will be used to assess

the influence of grain size on resistivity.

6.1.3 Aged alloys

As a general conclusion, the ageing temperature in the current study does not affect the

precipitation sequence but accelerates the precipitation kinetics. In the Mg-Al and Mg-Sn alloy,

the only observed precipitates are the Mg17Al12 and Mg2Sn phases, respectively. In the Mg-Gd

alloys, the precipitates under the peaking condition are the Mg7Gd phase and under the over-

aged condition, the Mg5Gd phase is observed. Although there is no direct observation of the

𝛽′′ and 𝛽1 phases due to the limited resolution of synchrotron diffraction. The observed results

are coincident with the former studies. Therefore, the precipitation sequence of Mg-Gd alloy

in the current study is thought to be SSSS → 𝛽′′ Mg3Gd → 𝛽′ Mg7Gd → 𝛽1 Mg3Gd → 𝛽

Mg5Gd. In the Mg-Zn alloy, the Mg4Zn7 and MgZn2 phases are observed under peak-aged and

over-aged conditions. According to Nie [5], the equilibrium precipitates in the over-aged

condition is the MgZn phase. However, in the current study, the precipitates under the over-

aged condition are still the MgZn2 phase; this may be attributed to the insufficient ageing time.

6 Discussion

74

Therefore, the precipitation sequence of Mg-Zn alloy is SSSS → 𝛽1′ Mg4Zn7 → 𝛽2

′ MgZn2 in

the current study.

Except for the precipitation kinetics, the ageing temperature also affects the growth of

discontinuous precipitation in Mg-Al alloys. A higher ageing temperature is favoured for

continuous precipitation, as shown in the microstructures that continuous precipitation occurs

early for higher ageing temperatures. The formation and growth of continuous precipitates

consume the supersaturated Al in the matrix, which will reduce the driving force for the growth

of discontinuous precipitation. Also, small continuous precipitates act as the obstacles to pin

the migration of grain boundaries hence inhibit the growth of discontinuous precipitation.

Therefore, a high ageing temperature can suppress the growth of discontinuous precipitation.

6.2 Age hardening mechanism

6.2.1 Initial state

Fig. 6-4 shows the hardness of each alloy at the as-solution treated states.

Fig. 6-4 Hardness of alloys in the as-solution treated states.

6 Discussion

75

The results show that Gd is the most significant alloying element in raising the hardness. In

contrast, Al has the weakest effect. The increase of the hardness per 1 at. % of Al, Gd, Sn and

Zn are 2.6, 21.5, 5.0 and 10.0, respectively.

The increase of hardness in the as-solution treated alloys is by so-called solid solution

strengthening. The most important contribution of the solute atoms to the strengthening is

usually due to the stress field produced in the surrounding crystal. The alloys in the current

study are substitution solutions due to the relatively large radii of the solute atoms according

to the Hume-Rothery rule. The substitutional atoms will cause a stress field in the surrounding

crystal due to the radii and modulus difference between the solute and solvent atoms, either a

compressive stress field or a tensile stress field. This stress field will interact with the stress

fields of the dislocations and anchor them; hence, the hardness is increased. The intensity of

the stress field is related to the alloying element and so is the hardness increase. Morinaga [210]

uses the DFT method to calculate the local strains of the nearest neighbouring Mg atoms as a

result of different alloying elements; the results are listed in Table 6-3. As in Table 6-3, Gd

causes the largest local strains and therefore it has the strongest effects in increasing the

hardness.

However, Sn behaves abnormally; although it caused the lowest local strain, its influence on

the hardness is more considerable than Al. The abnormal behaviour of Sn may be caused by

the electronegativity of the atoms. The electronegativity of Mg, Al, Gd, Sn and Zn are 1.31,

1.61, 1.20, 1.96 and 1.65, respectively . In general, the greater the difference in

electronegativity between two atoms, the stronger the bond between them [211]. Therefore,

higher stress is needed to break the Mg-Sn bond than the Mg-Al bond when the dislocation

moves past a solute atom, making Sn more effective than Al in increasing the hardness.

Table 6-3 Local strains of the nearest neighbouring Mg atoms from alloying elements [210].

Alloying element ∆a1/a1 (%) ∆a2/a2 (%) ∆c/c (%)

Al -0.76 -1.88 -1.11

Gd 1.41 2.41 1.37

Sn 0.33 0.14 0.16

Zn -1.18 -2.35 -1.21

6 Discussion

76

6.2.2 Peak-aged condition

Table 6-4 summarizes the data of different alloys aged at 225 °C and the results show that Gd

is the most effective alloying element in precipitation hardening, while Al and Sn are less

effective. The efficiency of the precipitation hardening is affected by the morphology and

distribution of the precipitates. Smaller and more numerous precipitates are more effective at

interfering with dislocation motion than larger and more widely spaced precipitates [212].

As discussed earlier, the precipitates at peak-aged conditions in Mg-Al and Mg-Sn alloys are

equilibrium phases Mg17Al12 and Mg2Sn, while in the Mg-Gd and Mg-Zn alloys are the

metastable phases Mg7Gd and Mg4Zn7. The size of the metastable phases are much smaller

than that of the equilibrium and the number density is much higher as in Chapter 5. Therefore,

Gd and Zn are more effective in precipitation strengthening. Except that, the shape and

orientation of precipitates also influence the precipitation strengthening. The plate-shaped

precipitates formed on prismatic planes of the matrix phase are most effective precipitation

strengthening and precipitate plates formed on the basal plane provide the least effective barrier

to gliding dislocations [50]. In the current study, the Mg7Gd phases are the prismatic

plates[119], while the Mg4Zn7 phases are basal plates and blocky particles or [0 0 0 1]α

rods/laths [96]. Hence, Gd has a stronger influence on precipitation hardening than Zn.

Table 6-4 Alloys aged at 225 °C.

Alloys

Solute content Hardness

Solubility

at 225 °C

(at. %)

Excess

solubility

(at. %)

Peak

hardness

Hardness

increase

Hardness

increase

per 1 at. %

Time for

reaching peak

hardness

Mg-8Al 3.24 4.56 80.4 53.44 % 11.72 % 32 hrs

Mg-2.5Gd 0.45 2.05 120.9 52.65 % 25.68% 4 hrs

Mg-2.5Sn 0.11 2.39 52.8 27.23 % 11.39 % 32 hrs

Mg-2.5Zn 1.28 1.22 66.1 24.95 % 20.45 % 1 hrs

Another interesting finding is that the time to reach the peak hardness in the Mg-Al alloy is

much longer than the Mg-Gd alloy. The longer time in Mg-Al alloy indicates that precipitation

in Mg-Al alloy is slower than that in Mg-Gd alloy. Since the precipitation is a diffusion-

controlled process [213], these results suggest that the diffusion rate of Gd in the Mg matrix is

higher than that of Al. Fig. 6-5 shows the calculated diffusion rate of Al, Gd, Sn and Zn

6 Discussion

77

elements in Mg matrix based on the works of Zhang et al. [214], Zhong et al. [215] and

Agarwal et al. [216]. The results show that Gd has a higher diffusion rate than Al at 225 °C,

which is coincident with current results. This result is quite interesting because the radii of Gd

and Al are 233 pm and 118 pm respectively. It is common to think that Gd has a lower diffusion

rate than Al based on common knowledge. However, the experimental data show the contrary

results.

Fig. 6-5 Calculated diffusion rate of alloying elements in Mg matrix at 225 °C.

6.2.3 Over-aged condition

If the ageing time of an alloy is allowed to exceed its peak-aged point, then it goes into the

over-aged stage. In the current study, the hardness of Mg-Gd and Mg-Zn alloys show a

significant decrease after the peak-aged; however, the decrease of hardness in Mg-Al and Mg-

Sn alloys is not so pronounced.

The decrease of the hardness is usually considered to be caused by coarsening of the distance

between precipitates. At the peak-aged condition, the precipitates are normally assumed to have

the maximum volume fraction; at the over-aged stage, precipitates are coarsened without

6 Discussion

78

changing their volume fraction [217]. The coarsening occurs where large precipitates grow at

the expense of small ones and it will increase the average spacing of precipitates [218].

According to the Orowan mechanism, the precipitation strengthening by dislocation looping is

given by [219]:

∆ =𝐺𝑏

𝐿 (6-2)

∆ is the increased strength, 𝐺 is the shear modulus, b is the Burger’s vector, L is the average

spacing of precipitates. The increased L caused the decrease in the hardness.

However, the coarsening of the average spacing of precipitates cannot explain the results in the

current study well. Since the hardness decreases a little in Mg-Al and Mg-Sn alloys at the over-

aged stage, while in Mg-Gd and Mg-Zn alloys it decrease significantly. Something else should

also contribute to the decrease of the hardness in Mg-Gd and Mg-Zn alloys. The main

difference in precipitation sequences among these alloys is that Mg-Gd and Mg-Zn alloys

experience the precipitation of metastable phases. In contrast, Mg-Al and Mg-Sn alloys

precipitate the equilibrium phases directly. Therefore, the pronounced decrease of hardness in

Mg-Gd and Mg-Zn alloys may relate to the transformation of the metastable phase.

At the peak-aged condition, the metastable phases Mg7Gd and Mg4Zn7 in Mg-Gd and Mg-Zn

alloys are fully coherent with the Mg matrix [138, 220, 221]. However, at the over-aged stage,

the metastable phases are transformed into semi-coherent or incoherent phases [116, 222]. The

fully coherent precipitates can provide coherency strengthening that arises from the elastic

coherency strain surrounding a particle that does not fit the matrix exactly [217]; when the

precipitates transform from fully coherent to semi-coherent or incoherent, the coherency

strengthening decrease. Therefore, the transformation of the fully coherent metastable phase to

a semi-coherent or incoherent phase also contributes to the decrement of hardness in the Mg-

Gd and Mg-Zn alloys.

6.3 Influencing factor of resistivity in binary magnesium alloys

6.3.1 Grain size

As mentioned before, the disordered arrangement of atoms in the grain boundary region

enhances the scattering of the electrons, so the resistivity is increased by the grain boundaries.

Therefore, the resistivity of an alloy having a fine grain size tends to be higher than that of an

6 Discussion

79

alloy having a large grain size. In the current study, the grain sizes of the as-cast and solution

treated alloys show a great difference. Hence, it is essential to quantify the influence of the

grain size on the resistivity.

The solution treated Mg-0.8Gd alloys with different grain sizes, are used to investigate the

influence of the grain size on the resistivity. As in Fig. 5-40, the grain size does not show

significant influence on the resistivity. The resistivity independent of the grain size in the Mg-

0.8Gd alloys may be due to the relatively large grain size. The grain boundary resistivity of Mg

has not been reported, but it is approximately 3.6×10-16 Ω∙m2 for Cu alloys [223], 4.45~6.2×10-

16 Ω∙m2 for Ni [224] and 2.56×10-16 Ω∙m2 for Al [225]. Theredore, it is reasonable to consider

the grain boundaries resistivity of Mg is also on the order of 10-16 Ω∙m2. Assuming an Mg alloy

has a grain size of 100 μm and the grains are spherical, then the grain boundary area per unit

volume is estimated to be 6×104 m-1. Then the contribution of the grain boundary to the total

resistivity is in the order of ~ 10-12 Ω∙m, which is far less than the bulk resistivity about ~ 10-8

Ω∙m. Therefore in the current study, the resistivity of the extruded Mg-0.8Gd after solution

treated is almost the same. However, the cast alloy after solution treatment has a slightly lower

resistivity than that of the extruded alloys; this is related to the different processing history.

In the current study, the Mg-2.5Zn alloy has the finest grain size in both the as-cast and solution

treated states, as the results in Chapter 5. Its grain sizes are 166 μm and 185 μm in the as-cast

and solution treated states, respectively. According to the previously calculated results, when

the grain size is larger than 100 μm the contribution of grain boundaries to the total resistivity

id negligible. So the contribution of the grain boundary to the total resistivity can be negligible

in the current study.

6.3.2 Temperature

According to Matthiessen’s Rule, the scattering of electrons could be roughly divided into two

types, the electron-phonon scattering and the electron-impurity scattering. The electron-

impurity scattering causes the residual resistivity and it relies on the impurity concentration but

independent of the temperature. The electron-phonon scattering results in the ideal resistivity

and it is temperature-dependent. The influence of temperature on the resistivity can be assessed

by the TCR as listed in Table 6-5.

As in Table 6-5, all alloys have a positive TCR, which illustrates that the resistivity increases

with the temperature. According to Matthiessen’s Rule, the temperature will only affect the

6 Discussion

80

electron-phonon scattering, so the TCR is exclusively related to the matrix and therefore it

should be the same value in all alloys even with different alloying elements and contents.

However, Table 6-5 shows a deviation from the Matthiessen’s Rule in these alloys since the

TCR values in different alloys are not the same, especially in the solution treated state. The

results indicate that the alloying elements do affect the electron-phonon scattering.

Except for the Mg-Gd alloys, the solution treated alloys has a lower TCR than the as-cast alloys.

These results suggest that the as-cast alloys are more sensitive to temperatures. In most cases,

both in the as-cast alloys and solution treated alloys, the alloy with a higher solute content tends

to have a lower TCR. The decrease of TCR with the increasing solute content has also been

observed in Mg-In, Mg-Ag, Mg-Cd, Mg-Tl and Mg-Pb alloys [20]. This is the results of the

changes in the phonon spectrum and the increased electron-per-atom ratio.

Table 6-5 TCR of different alloys.

Alloys TCR (nΩ∙m∙K-1)

As-Cast Solution treated

Mg-0.8Al 0.13 0.13

Mg-2.5Al 0.13 0.12

Mg-5Al 0.12 0.11

Mg-8Al 0.12 0.09

Mg-0.8Gd 0.13 0.14

Mg-1.5Gd 0.13 0.13

Mg-2.5Gd 0.10 0.11

Mg-0.8Sn 0.14 0.13

Mg-1.5Sn 0.17 0.14

Mg-2.5Sn 0.13 0.11

Mg-0.8Zn 0.17 0.14

Mg-1.5Zn 0.16 0.13

Mg-2.5Zn 0.16 0.15

Although the TCR varies with the alloying elements in the as-cast alloys, the TCR of Mg-Al

and Mg-Zn alloys seem to be solute content-independent, while in Mg-Sn and Mg-Gd alloys,

6 Discussion

81

the TCR is solute content-dependent. These results suggest that the electron-phonon scattering

in the as-cast Mg-Al and Mg-Zn alloys is more or less contents-independent. This is because,

during solidification, the solute that can be dissolved in the 𝛼-Mg matrix is limited. So the 𝛼-

Mg matrix is likely to be the same when the nominal contents are high. It can further explain

that the slightly higher TCR in the low content alloys, since the solute dissolved in the 𝛼-Mg

matrix does not reach the limit. The erratic changes of TCR in Mg-Gd and Mg-Sn alloys may

be due to the formation of segregation areas; with the segregation areas, the 𝛼-Mg matrix can

dissolve more solute, but it also makes the 𝛼-Mg matrix more inhomogeneous and makes the

TCR change randomly.

6.3.3 Alloying elements and their contents

The alloying elements always increase the total resistivity of pure metal. Fig. 6-6 shows the

resistivity increase due to different alloying elements and their content. The alloys are solution

treated and measured at 77 K to eliminate the influence of the intermetallic phases and

temperatures.

Fig. 6-6 Resistivity of solution treated alloys.

6 Discussion

82

As in Fig. 6-6, the resistivity increases almost linearly proportional to the solute content and

the slopes vary with different alloying elements. The Mg-8Al alloy deviates from the simulated

line because of the high solute concentration. The linear proportion law is a reasonable

approximate in a dilute alloy, in which the solute concentration is less than 2 % [149] or in

some papers, less than 5 % [21]. Nevertheless, Mg-8Al alloy is far beyond the functional area

of the linear proportion law. Therefore, it shows a bigger deviation from the linear proportional

law.

The resistivity increase per 1 at. % of alloying elements are listed in Table 6-6. The results

show that Gd has the most significant influence on resistivity, while Zn has the lowest effect.

The results are different from those of the specific hardness increase as in Table 6-4, suggest

that the influence mechanism of solute on resistivity is different from that on hardness.

According to Ying et al. [23], the increased resistivity is caused by the solute induced lattice

distortion. However, the distortion is caused not only by the difference in atomic radii of the

solute and magnesium, which may lead to local lattice expansion or contraction; but also by

the difference in the valence of a solute and magnesium, which affects the electronic structure

of magnesium and the shape of the Brillouin zone. As in Table 6-6, Zn has a similar atomic

radius and the same valence as Mg; therefore, the specific resistivity increase caused by Zn is

the smallest. The largest radii difference and the difference in valence between Gd and Mg

make Gd have the most significant influence on the specific resistivity increase.

Except for the radii and valence difference, Pan et al. [22] also claim that the configuration of

the extranuclear electron also affects the specific resistivity increase of alloying element. They

claim that an unfilled d subshell is likely to induce a higher specific resistivity since it is prone

to absorb the conduction electrons to obtain a stable state. This can explain the extremely high

specific resistivity of Gd since the d subshell of Gd is not fully filled.

Table 6-6 Specific resistivity increase and some physical properties of alloying elements.

Alloying element Mg Al Gd Sn Zn

Resistivity increment per 1

at. % (nΩ∙m) - 16.65 97.42 42.05 7.83

Atomic Radius (pm) 145 118 233 145 142

Valency +2 +3 +3 +4 +2

Extranuclear electrons 3s2 3s23p 4f75d6s2 4d105s25p2 3d104s2

6 Discussion

83

6.3.4 Heat treatment

Heat treatment plays an important role in material science, as it is an effective method to tailor

the properties. Therefore, it is of interest to investigate the resistivity changes during heat

treatment.

6.3.4.1 Solution treatment

Fig. 6-7 shows the resistivity of the cast alloys before and after solution treatment. The

measurement is conducted at 77 K to reduce the influence of temperature. As in Fig. 6-7, the

resistivity always increases after solution treatment. In addition, the higher the solute content,

the greater the increase of resistivity due to the solution treatment. The as-cast microstructure

is a mix of the 𝛼-Mg matrix and the as-cast intermetallic phases. According to the resistivity–

mixture rule [161], the effective resistivity of material with two distinct phases 𝛼 and 𝛽 can be

calculated by Eq.(6-3):

𝜌𝑒𝑓𝑓 = 𝑉𝛼𝜌𝛼 + 𝑉𝛽𝜌𝛽 (6-3)

𝜌𝑒𝑓𝑓 is the effective resistivity, 𝑉𝛼 and 𝑉𝛽 are the volume fractions of the 𝛼 and 𝛽 phases, 𝜌𝛼

and 𝜌𝛽 are the resistivity of 𝛼 and 𝛽 phases.

Fig. 6-7 Resistivity before and after solution treatment.

Solid lines are solution treated alloys; dash lines are as-cast alloys.

6 Discussion

84

However, the resistivity–mixture rule does not apply well when the phases are in a random

mixture. Instead, two semi-empirical rules, as in Eq.(6-4) are more useful in materials

engineering when phase 𝛽 is dispersed in a continuous phase 𝛼 [161].

𝜌𝑒𝑓𝑓 = 𝜌𝛼1+

1

2𝑉𝛽

1−𝑉𝛽 (𝜌𝛽 > 10𝜌𝛼)

𝜌𝑒𝑓𝑓 = 𝜌𝛼1−𝑉𝛽

1+1

2𝑉𝛽

(𝜌𝛽 < 0.1𝜌𝛼)

(6-4)

As in Eq.(6-4), the effective resistivity is a function of the 𝜌𝛼 and 𝑉𝛽 . During the solution

treatment, 𝜌𝛼 will increase due to the increase of dissolved solute. 𝑉𝛽 will decrease because of

dissolution of the intermetallic phases. In the current study, the resistivity always increases

after solution treatment, which suggests the alloying elements dissolved in Mg matrix influence

more the resistivity than that existing in the intermetallic phase.

Table 6-7 RRR values of the alloys.

Alloys RRR (ρ273/ρ77)

As-Cast Solution treated

Mg-0.8Al 2.85 2.75

Mg-2.5Al 1.82 1.68

Mg-5Al 1.50 1.35

Mg-8Al 1.33 1.22

Mg-0.8Gd 1.49 1.39

Mg-1.5Gd 1.26 1.19

Mg-2.5Gd 1.38 1.07

Mg-0.8Sn 1.98 1.83

Mg-1.5Sn 1.66 1.45

Mg-2.5Sn 1.48 1.27

Mg-0.8Zn 4.42 4.34

Mg-1.5Zn 3.63 3.28

Mg-2.5Zn 3.22 2.83

Generally, the dissolved solute can be treated as some type of “impurity” and they will increase

the resistivity. As mentioned before, the RRR value can be used to evaluate the purity of

6 Discussion

85

materials [185, 194]. The RRR values of these alloys before and after solution treatment are

calculated and listed in Table 6-7. The results show that the solution treatment decreases the

RRR values of all the alloys. The lower RRR value means the higher content of the “impurity”

and the higher resistivity, which is coincident with the results. It should be noted that the RRR

value is related to the influence on the resistivity rather than the real solute content since the

Mg-2.5Zn alloy has a larger RRR value than the Mg-0.8Al alloy.

6.3.4.2 Ageing treatment

The ageing treatment can somehow be treated as a reverse process of the solution treatment;

therefore, the resistivity should decrease during ageing, contrary to the increase of solute by

solution treatment. However, it is not always true that the ageing process will decrease

electrical resistivity. The formation of the G.P. zones at the early stage of ageing has been

confirmed to increase the resistivity [226].

In the current study, the resistivity of the alloys decreases monotonous with ageing time, as in

Fig. 5-41, which imply that the formation of G.P. zones did not occur. In Mg-Al and Mg-Sn

alloys, the precipitation processes do not involve the stage of G.P zone formation [5]. The

formation of G.P. zones in Mg-Zn alloys is restricted to the ageing temperature under 110 °C

[91-93]. Therefore, the decrease of resistivity in Mg-Al, Mg-Sn and Mg-Zn alloys is in line

with expectations. In contrast, the formation of G.P. zones has been reported [5, 129] at the

early stage of ageing in the Mg-Gd alloys when the ageing temperature ranges from 150 °C to

300 °C. The current results do not match that. Since the formation of G.P. zones is reported to

happen at the early stage of ageing and the first measurement of the Mg-Gd alloy in Fig. 5-41

is after 4 hours of ageing. It is possible that the formation of G.P. zones may stop within those

4 hours and the ex situ measurements in Fig. 5-41 could not illustrate the change of resistivity

due to the formation of G.P. zones. Therefore, in situ measurements are conducted as in Fig.

5-42. Except for the temperature-induced increase at the beginning, the resistivity decreases

monotonously through the entire ageing process. Therefore, it is concluded that no G.P. zones

are formed in all alloys under the current ageing conditions.

The effective resistivity can be predicted using Eq.(6-4). The volume fraction of the precipitates

is transformed from the weight fraction obtained by the Retiveled method. In the Mg-Gd and

Mg-Zn alloys, different precipitates are treated as one type to simplify the calculation. The

solute content in the 𝛼-Mg matrix are also obtained by the Retiveled method and using Fig. 6-6

the resistivity is calculated. Since the detailed data of the resistivity of the intermetallic phase

6 Discussion

86

has not been found, both formulas in Eq.(6-4) are used to calculate the effective resistivity. The

results are shown in Fig. 6-8, where ρα-Mg is the resistivity of the 𝛼-Mg matrix, ρp is the

resistivity of the precipitates.

Fig. 6-8 Resistivity of alloys aged at 225 °C.


In all alloys, the assumption that resistivity of the precipitates is ten times higher than that of

the 𝛼-Mg matrix improves the results. The calculated effective resistivity is smaller than that

of the measured data except for the Mg-Zn alloy. This is because Eq.(6-4) does not consider

the resistivity caused by phase boundaries. The phase boundaries that caused resistivity could

be omitted when the phase is large such as the as-cast intermetallic phase. However, the

precipitates formed during ageing are relatively small compared to the as-cast phase, so their

influence on resistivity should be considered.

In contrast, the calculated resistivity is a little higher than the measured resistivity in Mg-Zn

alloy. This is mainly due to the inappropriate use of Eq.(6-4). Eq.(6-4) provides a reasonable

prediction when the precipitates’ resistivity is either ten times higher or lower than the 𝛼-Mg

6 Discussion

87

matrix. However, the 𝛼-Mg matrix’s resistivity is approximately 10~20 nΩ∙m, as in Fig. 5-38.

At the same time, Andersson et al. [227] reported that the MgZn2 phase has a resistivity of

4~5×10-8 Ω∙m. Therefore, it is not satisfactory to use Eq.(6-4).

Another finding is that as in Table 5-17, the Mg-Gd alloy’s resistivity decreases more quickly

than that in the Mg-Al alloy, which further confirms that the diffusion rate of Gd in the Mg

matrix is higher than that of the Al.

6.4 Precipitation kinetics quantified by resistivity

Isothermal precipitation kinetics is of interest both from a theoretical point of view and for the

optimization of thermal treatments and alloy compositions in terms of mechanical or structural

properties [228]. Previous investigations indicated that hardness [229], differential scanning

calorimetry (DSC) and differential thermal analysis (DTA) [230], dilatometry [231] can be

used to quantify the precipitation kinetics. Electrical resistivity [145] offers another method to

investigate the precipitation kinetics.

The resistivity of an aged alloy can be described by Eq.(6-4) when the size of the precipitates

is sufficiently large and the deviation from Matthiessen’s rule is negligibly small [180]. The

results in Fig. 6-8 demonstrate that Eq.(6-4) is basically correct except for the deviation caused

by the phase boundaries. Therefore Eq.(6-4) is applied to calculate the volume fraction of

precipitates in the current study.

For a given binary alloy, the total solute content is settled and equals the amount dissolved in

the matrix plus that formed in the intermetallic phases. Suggesting that there is only one type

of precipitate, then the volume fraction of the precipitates can be expressed as a function of

alloying elements that formed precipitates. On the other hand, resistivity has a linear

relationship with the solute content dissolved in the matrix, as seen in Fig. 6-6. Therefore, in a

given binary alloy, resistivity is a unary function of the solute amount that formed precipitates;

there is a one to one correspondence between them. With the measured resistivity, the solute

amount that formed precipitates can be calculated and so is the volume fraction of the

precipitates.

In the current study, there is only Mg17Al12 and Mg2Sn precipitate in Mg-Al and Mg-Sn alloys,

respectively, so Eq.(6-4) is directly used. In Mg-Zn alloy, there are two types of precipitates,

the Mg4Zn7 and MgZn2 phases. It is assumed that MgZn2 is the only precipitate when using

6 Discussion

88

Eq.(6-4). Fig. 6-9 shows the volume fraction of the precipitates evolution during isothermal

aged at 498 K. The volume fraction is calculated using Eq.(6-4) with the measured resistivity,

also using the Retiveld methods with the X-Ray patterns and using the TC-PRISMA software

(Educational Package) based on the Kampmann-Wagner numerical (KWN) method coupled

with thermodynamic and mobility data from Zhang et al. [214]. As shown in Fig. 6-9, the

volume fraction of the precipitates calculated by different methods basically shows the same

tendency in all the alloys, except that the maximum volume fraction obtained using the Rietveld

method is a little higher.

Fig. 6-9 Volume fraction of the precipitates during isothermal aged at 225 °C.

(a) Mg-8Al; (b) Mg-2.5Sn; (c) Mg-2.5Zn.

The KWN method divides the precipitation process into three distinct stages, nucleation,

growth and coarsening. The volume fraction of the precipitates increase in the nucleation and

growth stages; in the coarsening stage, the larger precipitates grow at the expense of the smaller

ones, so the volume fraction remains unchanged. At the nucleation and growth stages, the

volume fraction calculated by the resistivity shows better consistency with the Rietveld results

than the TC-PRISMA results. However, the resistivity method does not show an obvious

a)

c)

b)

0 50 100 150 200 250

0.00

0.02

0.04

Volu

me

Fra

ctio

n o

f P

reci

pit

ate

s

Time / hrs

Retiveld

TC-PRISMA

Resistivity

0 50 100 150 200 250

0.00

0.02

0.04

0.06

0.08

0.10

Retiveld

TC-PRISMA

Resistivity

Volu

me

Fra

ctio

n o

f P

reci

pit

ate

s

Time / hrs

0 50 100 150 200 250

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Volu

me

Fra

ctio

n o

f P

reci

pit

ate

s

Time / hrs

Retiveld

TC-PRISMA

Resistivity

6 Discussion

89

transition from the growth stage into the coarsening stage; this is because, except for the volume

fraction of the precipitates, the phase boundaries also affect the resistivity, so the resistivity is

not a constant in the coarsening stage. Since Eq. (6-4) does not take the phase boundaries into

account, the changing resistivity is then regarded as the change of the precipitates’ volume

fraction. Nevertheless, the influence of the phase boundaries is negligible when the precipitates

are large enough; this can be verified by the steady volume fraction by resistivity method in

the Mg-Sn and Mg-Zn alloys as the ageing proceeding.

The results of all three methods show good agreements, which verifies the reliability of the

resistivity in predicting the precipitates’ volume fraction evolution during isothermal ageing.

Therefore a phenomenological model between resistivity and the volume fraction of

precipitates in binary alloys is built. The commonly used KWN approach for modelling

precipitation kinetics requires the Thermodynamics and Mobility database, which is not easily

obtained. In contrast, the resistivity measurement is easy to conduct; hence resistivity offers an

easy way to monitor the precipitation process.

7 Conclusion

90

7 Conclusion

Mg-Al, Mg-Gd, Mg-Sn and Mg-Zn binary alloys are studied in the current study. Their

resistivity in the as-cast, solution treated and aged states was measured to investigate the

influence of composition and microstructure on the resistivity. In situ resistivity measurements

were conducted to monitor the resistivity changes during isothermal ageing. Additionally, the

influence of temperature on resistivity was investigated. The conclusions are as follows:

1) The resistivity of Mg was increased due to the lattice distortion caused by the solute

elements. The distortion was caused by the difference in atomic radii and the difference

in the valence of solutes and magnesium. The configuration of the extranuclear electron

of the alloying element also affected the specific resistivity increase;

2) When the alloys are solution treated, the following equation can describe the

relationship between resistivity and solute contents:


ρ(T) is the resistivity of the alloy under a certain temperature, ρMg(T) is the resistivity

of pure Mg, δ(T) is the coefficient, and c is the concentration of the solute. δ(T) depends

on both the temperature and the type of solute.

3) All the alloys had a positive temperature coefficient of resistivity (TCR). The TCR

varies from different solute content, which demonstrated the deviation from

Matthiessen’s rule in Mg alloys;

4) The alloying elements dissolved in Mg matrix had a greater influence on resistivity

than that present in the intermetallic phase; when the grain size was large enough (>

100 μm), the influence of grain boundaries on the resistivity was negligible;

5) The resistivity decreased during isothermal ageing. The relationship between resistivity

and the fraction of precipitates can be roughly described in the following formula:


12𝑉𝛽

1 − 𝑉𝛽

𝜌𝑒𝑓𝑓 is the effective resistivity, 𝑉𝛽 is the volume fraction of the precipitates, 𝜌𝛼 is the

resistivity of the 𝛼-Mg matrix;

6) A phenomenological model between resistivity and the volume fraction of precipitates

in binary alloys was built. It can successfully predict the evolution of the volume

fraction of the precipitates during isothermal ageing in binary alloys.

Reference

91

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