Physical Metallurgy ofHigh‐Entropy Alloys (HEAs)

that I know

Sheng Guo

Docent Lecture

Materials and Manufacturing Technology Chalmers University of Technology

March 18th, 2016, Chalmers

Outline High‐Entropy Alloys: what are they and why people are interested?

Physical Metallurgy of High‐Entropy Alloys Phase Selection RulesMeta‐Stability of SSMechanical Behavior Solidification Behavior

Alloy & Solid Solution‐ an alloy is a mixture of metals, or a mixture of metals and

other elements (C, Si, etc.).

‐ an alloy may be a solid solution of alloying elements (a single phase), ora mixture of multiple phases.

‐ a solid solution is a solid‐state solution of one or more solutes ina solvent. Such a mixture is considered a solution, rather thana compound, when the crystal structure of the solvent remainsunchanged by addition of the solutes, and when the mixture remains ina single homogeneous phase.

‐ (substitutional) solid solutions, in accordance with the Hume‐Rothery rules, may form if the solute and solvent have:o similar atomic radii (< 15%)o same crystal structureo similar electronegativities (< 0.4)o similar valancy

William Hume‐Rothery

breaking of H‐R limit?

XRD patterns of Ce3Al at high pressure Atomic structure models of Ce‐Al alloy

(MGto SS)

(From ‐Ce3Al)

(‐Ce3Alto SS)

(random fcc Ce‐Al solid solution)

(Zeng et al., PNAS, 2009)

Intermetallic compounds  solid solution

“opposite” side of H‐R rules

Pd42.5Cu30Ni7.5P20 BMG

80*85 mm

(Nishiyama, Intermetallics, 2012)

volu

me

melt spinning

A Inoue (1990) Inoue’s three empirical rules to prepare BMGs (>1 mm):• at least 3 alloying elements; • large mismatching atomic sizes ofconstituent elements• large negative heat of mixingamong major alloying elements

3.4 Kg!

(Duwez, William Hume‐Rothery Award, 1982)

(Inoue, Acta Gold Medal, 2010 & Johnson, William Hume‐Rothery Award, 1996)

(Miedema, William Hume‐Rothery Award, 1981)

Conventional alloys Conventional alloys normally have only 1 principal element (e.g., Fe in steels) 

Typical compositions of stainless steels

High entropy alloys (multi‐principal‐element alloys/compositionally  complex alloys)

High‐entropy alloys have at least 5 (4?) principal metallic elements, and have equal or close‐to‐equal compositions

Example, 6‐element Al‐Co‐Cr‐Cu‐Fe‐Ni systemEquimole: AlCoCrCuFeNiNon‐equimole: AlCo0.5CrCuFe1.5Ni1.2Minor element addition: AlCo0.5CrCuFe1.5Ni1.2B0.1C0.15

So why “high‐entropy”? And what’s the big deal?

Entropy & Entropy of mixing o Entropy: In thermodynamics, entropy (S) is a measure of the number of

microstates that may realize a thermodynamic system in a defined statespecified by macroscopic variables; a measure of molecular disorder within amacroscopic system.

o Boltzmannʹs equation: , where is the number of microstates.

o Entropy of mixing (∆Smix): increase in thetotal entropy when several initially separatesystems of different composition are mixed.

The mixing entropy reaches the maximum, when elements are mixed equiatomically. 

50/50

It is more convenient to define HEAs by the magnitude ofconfiguration entropy in the high temperature (ideal or regularsolution) state: ∆Smix > 1.5R

(Miracle et al., Entropy, 2014)

Do high‐entropy alloys really possess high entropy? How high is high anyway?

High‐entropy stabilizes the formation of solid solution phases

△Gmix =△Hmix ‐T△Smix

single phase solid solutionco‐existence of two solid solution phases

(Murty, Yeh and Ranganathon, High Entropy 

Alloys, Elsevier, 2014)

in the middle

High‐entropy stabilizes the formation of solid solution phases

Era of High‐Entropy Alloys?

(Adv.Eng.Mater, 2004)

(Yeh, et al., Mater Chem Phys, 2007)

N=1

N=2

N=3

N=4

N=5

N=6

N=7

Highly concentrated solid solutions

Mechanical Properties of HEAs

Very high hardness can be achieved

(after 1000 oc/12h)

(Yeh, et al., Adv Eng Mater, 2004)

AlCoCrFeNiTi0.5

y=2.26GPa

f=3.14GPa

p=23.3%

(Zhou et al., APL, 2007)

Disordered bcc solid solution was reserved after annealing at 1400 oc for 19h

(Senkov, et al., Intermetallics, 2011)

460 MPa@1600 oCbetter than superalloys

Refractory high entropy alloys

(Gludovatz et al., Science, 2014)

CoCrFeMnNi

(Ritchie, Acta Gold Medal, 2014)

(Nature, 1993)1

lnN

mix i ii

S R c c

lnmixS R N

Based on the confusion principle and high entropy points of view, we can easily understand that  random solid solutions tend to be stable in HEAs.

but, why not form a glassy (amorphous) phase then?

when N elements are mixing in equiatomic ratio (c1=c2=…=cN), the mixing entropy reaches the maximum:

Q1:Solid solution or amorphous phase? 

(Gao et al., J Non-Crys. Solids, 2011)

High‐entropy bulk metallic glasses (Ma et al., Mater Trans, 2002)

(Takeuchi et al., Intermetallics, 2011)

(1.5mm)

Intermetallic compounds can certainly form in equiatomic multi‐component alloys

For example:

XRD patterns of the CoCrCuFeNiTixsamples (x = 0, 0.5, 0.8, and 1)

(Wang et al., Intermetallics, 2007) (Yang et al., Mater Chem Phys, 2007)So, can we predict the phase selection (solid solution, amorphous phase and intermetallic compound) in equiatomic multi‐component alloys?

Reminder of Darken‐Gurry map

Forming Ta‐X solid solution

(Cahn and Haasen, Physical Metallurgy, 1996)

Cahn: Acta Gold Medal, 2002

Haasen, Acta Gold Medal, 1994

Massalski, Acta Gold Medal, 1995 &

William Hume-Rothery Award, 1980

Darken, William Hume-Rothery Award, 1979

19

fccprototype

bcc prototype

(Guo et al., Prog Nat Sci: Mater Int, 2011;Guo et al., Intermetallics, 2013)

A1: 2‐parameter map for phase selection in HEAs

Solid solution phases form when  is small, and △Hmix is either slightly positive or insignificantly negative; Amorphous phases form when  is large, and △Hmix is noticeably negative; In the intermediate conditions (in terms of  and △Hmix ) , intermetallic compounds compete with both amorphous phases & solid solution phases. 

2

1

(1 / )n

i ii

c r r

，1

n

i ii

r c r

1 ,

n

i ji j

ii

x im jc cH

4 A B

i j m i xH

atomic size difference

mixing enthalpy

(Guo et al., Intermetallics, 2013)

(Sheikh et al., J Appl Phys, 2015)

Improvement of ‐ ∆Hmix mapusing the concept of Md, d‐orbital energy level

solid solution strengthening

precipitationstrengthening

this overlappingis a concern

(Tong et al., Metall Mater A, 2005)

fccfccfcc

bccbcc

AlxCoCrCuFeNi

fcc+bccfcc+bccfcc+bccfcc+bccfcc+bccfcc+bccfcc+bccfcc+bcc

(Yeh, et al., Mater Chem Phys, 2007)

N=1

N=2

N=3

N=4

N=5

N=6

N=7

x=0

x=3

Q2: fcc or bcc solid solution?

Why is that?!

Q2: fcc or bcc solid solution?

Reminder of Hume‐Rothery electron concentration rule

(Mizutani, William Hume‐Rothery Award, 2005)(Mizutani, Hume‐Rothery Rules for Structurally ComplexAlloy Phases, 2011)

5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5

8.0

bcc+fcc fcc

AlCo0.5CrCuFeNi; AlCoCr0.5CuFeNi AlCoCrCu0.5FeNi; AlCoCrCuFe0.5Ni AlCoCrCuFeNi0.5; AlCoxCrCu0.5FeNi AlCoxCrCu0.5FeNi; AlCoxCrCu0.5FeNi AlCoCrxCu0.5FeNi; AlCoCrCu0.5FexNi AlCoCrCu0.5FeNix; AlCoCrCu0.5FeNix

CrCuFeMnNi; CoCrFeMnNi AlxCrCuFeMnNi; AlxCrCuFeMnNi Al0.8CrCu1.5FeMnNi; Al0.8CrCuFe1.5MnNi Al0.8CrCuFeMn1.5Ni; MoNbTaW MoNbTaVW; AlBxMnNiTi AlxC0.2CuFeMnNi

Valence electron concentration

bcc

6.87

(Guo et al., JAP, 2011)

A2: Valence electron concentration is the key

A higher VEC favors the formation of fcc solid solutions, while a smaller VEC tends to stabilize the bcc solid solutions A mixture of fcc and bcc solid solutions forms at intermediate VEC

Mechanical behaviorCase I: Ductile Refractory High Entropy Alloys: single bcc solid solution

interested block

Mechanical behaviorCase II: Eutectic High‐Entropy Alloys: dual‐phase (soft/hard) solid solutions

(Wani et al., Mater Res Lett, 2016)

Summary High‐entropy alloys are highly concentrated, multi‐component alloys (the name is a bit controversial, but a name is just a name) Empirical science, like Hume‐Rothery rules, are very useful even for this type of new and compositionally complicated materials (old wisdom is classical) Electron theory helps a lot (phase selection/mechanical behavior) New materials  new properties(high‐temperature/cryogenic temperature, etc.) & new applications (???) Structural or functional properties?(always a dilemma) 

Every material