dependence of electrical resistivity on temperature and ...€¦ · dependence of electrical...

Dependence of electrical resistivity ontemperature and composition of Al–Cu alloys

H. Kaya*

Different compositions of Al–Cu alloys were directionally solidified upward with constant growth

rate (V>18?6 mm s21) and constant temperature gradient (G>4?7 K mm21) using a Bridgman

type growth apparatus. The variations in electrical resistivity r with temperature for directionally

solidified Al–Cu alloys were measured in the range of 3732773 K using a standard four-point

probe technique. According to the present experimental results, the resistivity of directionally

solidified Al–Cu alloys linearly increases with increasing temperature and composition of Cu in the

Al–Cu alloys. The variations in Lorenz number with the temperature and composition of Cu in the

Al–Cu alloys were also determined from the Wiedemann–Franz law using the measured values of

thermal and electrical conductivities for the same alloys.

Keywords: Al alloys, Crystal growth, Electrical resistivity, Thermal conductivity, Lorenz number

IntroductionThe development of new workable Al based light alloysis a key issue in current materials science. The distinctivecharacteristics of these alloys are low density, highmelting temperature, good thermal conductivity andexcellent oxidation resistance. Aluminium casting alloyscontaining copper are ubiquitous in technical applica-tions: they are the main components of screw machineproducts, truck frames, aircraft structures, jet engineimpellers and aircraft engine cylinder heads.1 Moreover,Al–Cu alloys are the focus of numerous academicstudies that are especially concerned with solidificationprocesses and consider, for instance, the columnar–equiaxed transition,2 the formation of macrosegregationzones3 and the visualisation of dendritic growth.4

Among all the physical properties, the electricalresistivity r and conductivity s characteristics of thesolid phase play a prominent role in controlling theperformance and stability of materials, and they arethe main fundamental properties of materials, such asdensity, melting point, entropy and crystal structureparameters. While the electrical properties (resistivityand conductivity) of pure materials change with thetemperature, the electrical properties of alloys changewith the composition of alloy as well as temperature.

The aim of the present work is to experimentallyinvestigate the dependence of the electrical resistivity rand electrical conductivity s on copper composition (3,6, 15, 24 and 33 wt-%Cu) and temperature in Al–Cualloys and also find out the influence of temperature onthe temperature coefficient of resistivity and Lorenznumber for the same alloys.

ExperimentalUsing vacuum melting and hot filling furnaces, Al–(3, 6,15, 24 and 33) wt-%Cu alloys have been prepared undervacuum atmosphere using 99?999% pure aluminium and99?99% pure copper. After allowing time for melthomogenisation, the molten alloy was poured into fivegraphite crucibles (250 mm in length, 4 mm i.d. and6?35 mm o.d.) held in a specially constructed hot fillingfurnace at ,50 K above the melting point of alloys. Themolten metal was then directionally solidified frombottom to top to ensure that the crucible was completelyfull. Then, each specimen was positioned in a computercontrolled Bridgman type furnace (Fig. 1). The details ofthe apparatus and experimental procedures are given inthe previous work.5 Unidirectional solidification of thesamples with a constant thermal gradient (4?7 K mm21)was performed with a maximum furnace temperature of1050 K. After stabilising the thermal conditions in thefurnace under argon atmosphere, the samples were grownby pulling it downwards by means of two different speedsynchronous motors. After 10–12 cm of steady stategrowth, the samples were quenched by rapidly pulling itdown into the water reservoir. The temperature of waterin the reservoir was kept at 283 K to an accuracyof ¡0?1 K using a PolyScience digital 9102 heating/refrigerating circulating bath to get a well quenched solid/liquid interface in this work. The temperature of thesample was also controlled to an accuracy of ¡0?1 Kusing a Eurotherm 2604 controller. Solidification of thesamples was carried out with constant growth rate(V>18?6 mm s21) and different temperature gradient(G>1?5–5?8 K mm21).

The temperature of the specimen was measured withK type 0?25 mm in diameter insulated three thermo-couples, which were fixed within the sample with spacingof 10–20 mm. All the thermocouple’s ends wereconnected to the measurement unit consisting of data

Department of Science Education, Faculty of Education, ErciyesUniversity, Kayseri 38039, Turkey

*Corresponding author, email [email protected]

� W. S. Maney & Son Ltd. 2012Received 31 August 2011; accepted 27 October 2011DOI 10.1179/1433075X11Y.0000000041 Materials Research Innovations 2012 VOL 16 NO 3 224

logger and computer. The cooling rates were recordedwith a data logger via computer during the growth.When the solid/liquid interface was at the secondthermocouple, the temperature difference between thefirst and second thermocouples DT was read from thedata logger record. The time taken for the solid_liquidinterface to pass the thermocouples separated by knowndistances was read from the data-logger record. Thus,the value of the growth rate (V5DX/Dt) for each samplewas determined using the measured value of Dt andknown value of DX. The temperature gradient (G5DT/DX) in the liquid phase for each sample was alsodetermined using the measured values of DT and DX.

The quenched samples were removed from thegraphite crucible and they were cropped off anddiscarded 3 cm in length from the top and bottom.The longitudinal and transverse sections of the groundsamples were then cold mounted with epoxy resin.The longitudinal and transverse sections were wetground down to grit 2500 and mechanically polishedusing 6, 3, 1 and 1/4 mm diamond paste. Finally, thespecimens were etched with a Keller’s etch (1?5%HCl–0?5%HF–2?5%HNO3–95?5%H2O) for ,15 s to revealthe microstructure. After metallographic preparation,the microstructures of the samples were revealed. Themicrostructures were characterised from both transverseand longitudinal sections of samples using an OlympusBX-51 optical microscope. The transverse and long-itudinal sections of the specimen were examined forporosity, crack and casting defects to make sure thatthese would not introduce any errors to the measure-ments. Some typical images of growth morphologies ofdirectionally solidified Al–Cu alloys are shown in Fig. 2.As can be seen from Fig. 2, the characteristics of themicrostructures changed with increasing Cu composi-tion in the Al–Cu alloys. As seen in Fig. 2, the

microstructures of Al–6 wt-%Cu and Al–24 wt-%Cuare dendritic, whereas that of Al–33 wt-%Cu is eutectic.

The temperature dependence of the electrical resistiv-ity for Al–Cu alloys was measured by the four-pointprobe method.6 Today, the four-point probe method isthe most widely used technique for electrical profilemeasurement of materials. In this method, the material’sresistivity r can be expressed as

r~RCFVmeasured

Imeasured

(1)

where RCF is the resistivity correction factor. RCF takesthe size of the test structure, the thickness of thematerial, the size of the electrodes and the position ofthe electrodes with respect to the boundary of the teststructure into account.7

The measurements of electrical resistivity were madein the range of 373–773 K on circular shape sampleswith typical 4 mm diameter using a standard four-pointprobe dc method. The measuring unit was interfacedwith a PC for online data acquisition and processing. AKeithley 2400 sourcemeter was used to provide constantcurrent of 1 A, and the potential drop was detected by aKeithley 2700 multimeter (Fig. 3). As seen from Fig. 3,platinum wires with a diameter of 0?5 mm wereemployed as current and potential electrodes. Thetemperature of the sample was changed by a control-lable Nabertherm type P320 furnace.

The electrical resistivity strongly depends on tempera-ture. In metals, the electrical resistivity increases alongwith increasing temperature. The temperature coefficientof resistivity a is often expressed as a slope in the electricalresistivity versus temperature graph and can be given as

a~r{ro

ro(T{To)~

1

ro

Dr

DT(2)

1 a block diagram of experimental set-up and b details of Bridgman type directional solidification furnace

Kaya Dependence of electrical resistivity on temperature and composition of Al–Cu alloys

Materials Research Innovations 2012 VOL 16 NO 3 225

where r is the electrical resistivity at temperature T, ro isthe electrical resistivity at room temperature, To5300 Kand a is the temperature coefficient of resistivity.

Results and discussionHeat in solid is conducted by various carriers: electrons,lattice waves or phonons, magnetic excitations and, insome cases, electromagnetic radiation. The total thermalconductivity is additively composed of contributionsfrom each type of carrier. The principal carriers of heatin metals are electron and lattice waves.

The temperature dependence of electrical resistivitywas measured in the range of from 373 to 773 K (Fig. 4)in this work. Electrical resistivity measurements werecarried out for five different Al–Cu alloys [Al–(3, 6, 15,24 and 33) wt-%Cu]. The experimental values of r are(4?4, 5?2, 5?7, 6?2 and 6?7)61028 V m for Al–(3, 6, 15,24 and 33) wt-%Cu alloys respectively at 373 K Themeasuredr values in this work are a little higher than thevalues of 3?5761028 and 2?2261028 V m for the pureAl and Cu metals respectively at 373 K.8–10 The

variations in electrical resistivity with Cu compositionwere also investigated at different temperatures (seeFig. 5). Figure 5 shows that resistivity increases (from14?461028 to 22?761028 V m) with increasing Cu com-position at 773 K. The measured r values in this work aresmaller than the values (8?3561028, 7?6961028,11?1461028, 13?0561028, 15?6861028 V m) obtainedby Touloukian et al.11 for Al–14 wt-% Cu, Brandesand Brook12 for Al26 wt-%Cu and Ashram-Shalaby13

for Sn–0?7 wt–%Cu, Sn–0?7Cu–0?5wta –%Zn and Sn–0?7 wt-%Cu–0?5 wt-%Bi alloy systems respectively.Furthermore, the values of r in this work are smallerthan the values (15?861028 and 21?0161028 V m)obtained by Saatci et al.14 for Zn–1.3 at-%Cd andCadırlı et al.15 for Sn–3 wt-%Cu alloys respectively atthe same temperature.

Variations in the temperature coefficients of resisti-vity a with Cu composition were also investigated.The values of a change from 8?9161023 to10?8661023 K21.

As shown in Table 1 and Fig. 4, the temperaturecoefficients of resistivity a for Al–Cu alloys can be

a1, a2 Al–6 wt-%Cu; b1, b2 Al–24 wt-%Cu; c1, c2 Al–33 wt-%Cu eutectic alloy2 Typical optical images of growth morphologies of directionally solidified at constant G (4?7 K mm21) and constant V

(18?6 mm s21) of Al–Cu alloys



determined in the range of 8?9161023–10?8661023

K21. The values of a increase with increasing Cu contentat a constant temperature. The obtained values of a(8?9161023–10?8661023 K21) in this work are veryclose to the values of 7?2461023 K21 obtained by Cadırlıet al.15 for Cu alloys but higher than the range of values a(1?261023–1?461023 K21) theoretically calculated byAksoz et al.16 for Al–Cu alloys.

The variations in electrical resistivity with thecompositions of Cu were also plotted and given inFig. 5. As shown in Fig. 5, the dependence of electricalresistivity on the composition of Cu is not linear, but thevalue of r exponentially decreases with increasingcomposition of Cu. As can be seen in Fig. 5, a linear

relation of r–Co was observed at 373 and 473 Ktemperatures. However, this linear relation of r–Co

deteriorated for 573 K and higher temperatures. Suchtendency is a quite natural result. Because the changes inresistivity of pure metals and alloys depending ontemperature may be different, this difference can beinterpreted as indicating that some other mechanisms,such as electron–electron interaction, grain boundary/impurity scattering, etc., are involved in the electricalconduction process.17 Recently, several studies18,19 havebeen carried out on impurity, phonon and electroncontributions to the electrical resistivity of metals andalloys. The similar trend is supported by Boekelheideet al.18

3 Schematic diagram showing four-probe used electrical resistivity measurements

Table 1 Electrical conductivity, thermal conductivity and Lorenz number of Al–Cu alloys at different temperatures

Al–3 wt-%Cu Al–6 wt-%Cu Al–15 wt-%Cu Al–24 wt-%Cu Al–33 wt-%Cu

Temperature/K Electrical conductivity s/6106 V21 m21

373 22.68 19.42 17.48 16.18 14.35473 14.62 13.16 11.96 10.50 8.95573 11.42 9.87 8.62 7.24 6.69673 8.75 7.86 6.59 5.82 5.33773 7.07 6.45 5.62 4.77 4.39

Thermal conductivity16 K/W K21 m21

373 175.42 162.49 138.44 131.14 125.00473 167.43 158.16 133.35 125.13 122.00573 162.22 149.23 129.54 122.75 120.00673 157.94 141.19 123.55 117.54 116.00773 144.96 134.40 118.77 113.14 113.00

Lorenz number L/61028 W V K22

373 2.07 2.24 2.12 2.17 2.34473 2.42 2.54 2.36 2.52 2.88573 2.48 2.64 2.62 2.96 3.13673 2.68 2.67 2.79 3.00 3.23773 2.65 2.69 2.73 3.06 3.33



Electrical conductivity is a measure of a material’sability to conduct an electric current and is one of theprimary physical properties of materials. The relation-ship between thermal and electrical conductivities hasbeen established by the Wiedemann2Franz law, whichis based upon the fact that heat and electrical transportboth involve free electrons in the metal as

K

s~LT (3)

where K (50?909LsTz10?5) is the thermal conductiv-ity, s is the electrical conductivity, T is the tem-perature and L is the constant of proportionality(2?4561028 W V K22), which is called the Lorenznumber.20

The thermal conductivities of Al–(3, 6, 15, 24 and33) wt-%Cu alloys were measured using a radial heatflow apparatus in the previous work by the author andco-workers.16 The radial heat flow method is an idealtechnique to measure the thermal conductivity of solidphase. In the radial heat flow method, a cylindricalsample was heated radially using a single heating wire,keeping the sample in a very stable temperature gradientfor a period to achieve a steady state condition.

The variation in electrical conductivity with tempera-ture was also determined for Al–Cu alloys. The ratios ofthermal conductivity/electrical conductivity as a func-tion of temperature for Al–Cu alloys were determinedusing the values of K and s. The thermal and electricalconductivities of pure materials change with tempera-ture, but the thermal and electrical conductivities ofalloys change with composition of alloy as well astemperature. The variations in Lorenz number with thecomposition of Cu in Al–Cu alloys were calculated inthe temperature interval between 373 and 773 K fromequation (3). The variation in Lorenz number versustemperature was plotted in Fig. 6. The Lorenz numbersfor aluminium and copper are 2?2461028 W V K22

(Ref. 21) and 2?2361028 W V K22 (Ref. 8) respec-tively. The Lorenz number L for Al–Cu alloys in thiswork has been calculated in the range of 2?0161028–3?3361028 W V K22 using electrical conductivity, ther-mal conductivity and equation (3). It can be seen fromTable 1 that the Lorenz number slightly increases withincreasing temperature and composition of Cu. Theexperimental results show that the Lorenz numberslightly deviates from the Wiedemann–Franz law.Deviations from the Wiedemann–Franz law in form ofthe presence and strength of particular (inelastic)scattering process might influence the carrier dynamics.The Wiedemann–Franz law strictly compares thethermal conductivity with the electrical conductivity.In metals that have a substantial phonon contribution tothe overall thermal conductivity (in pure metals andalloys), the ratio with the measured values of thermaland electrical conductivities will naturally lead to alarger magnitude of the constant L because the overallthermal conductivity will contain a significant contribu-tion from phonons.

ConclusionsThe main conclusions of this investigation can besummarised as follows.

The electrical resistivity of Al–Cu alloys increasedfrom 4?4061028 to 22?7461028 V m by increasing thetemperature and Cu composition in the Al–Cu alloy.

The temperature coefficients of resistivity for Al–Cualloys were determined to be in the range of 8?9161023–10?8661023 K21.

6 Lorenz number versus temperature for Al–Cu

4 Electrical resistivity of pure Al, Cu and Al–Cu alloys

versus temperature

5 Electrical resistivity versus composition of Cu in Al–Cu

system



Variations in the Lorenz numbers with temperatureand Cu composition in the Al–Cu alloys were obtainedfrom the Wiedemann–Franz law using the experimentalvalues of K and s. The determined values of Lorenznumbers slightly deviate from the Wiedemann–Franzlaw.

Acknowledgement

This project was supported by the Erciyes UniversityScientific Research Project Unit under contractno. FBA-10-3376.

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