The document provides an overview of high entropy alloys (HEAs), detailing their composition, thermodynamics, phase formation rules, and unique properties such as high mixing entropy and sluggish diffusion. It emphasizes the beneficial effects of HEAs, including improved mechanical properties and resistance to intermetallic compound formation, while also noting potential challenges such as reduced thermal and electrical conductivity. The document includes various sources, figures, and experimental results to support the information presented.

1. High Entropy Alloys
(HEA)
By: Andreas Sugiarto
Image Source: [1] Pham, M. (2020)

2. GENERAL OVERVIEW
Image Source: [2] Gludovatz, B. (2014)

3. Brief History of
HEA
Multicomponent alloying  Considered
useless  Require high temperature &
unattractive properties
Cantor (1981)  Co20Cr20Fe20Mn20Ni20 
Single FCC phase (Solid Solution)
Yeh (1995)  Entropy improve mixing &
Reduce phase. 20 equiatomic alloys 
Promising properties
Ranganathan (2003)  First HEA’s
publication  Propagated HEA’s research
2
Source: [3] Cantor, B., et al. (2004)
Source: [4] Yeh, J.W., et al. (2004)
Source: [5] Ranganathan, S. (2003)

4. Definition of
HEA
Based on Composition: [6]
nmajor ≥ 5, 5% ≤ Xi ≤ 35%
nminor ≥ 0, Xj ≤ 5%
Based on Configurational Entropy: [6]
ΔSconf ≥ 1.5R
3
Source: [6] Yeh, J.W. (2013)
Thermodynamics
of HEA

5. Thermodynamics of HEA
◦ When liquid and solid solutions formed [4]
ΔGmix = ΔHfmix -TΔSmix
Enthalpy  Intermetallic formed
vs
Entropy  Solid solution formed
◦ Mixing Entropy: Configurational is dominant
over vibrational, magnetic dipole, electronic
randomness [4]
◦ Consider an equi-atomic alloy in its liquid or
regular solid solution state
ΔSconf = R ln n (from Boltzmann equation)
[4]
4
Table 1 Ideal configurational entropies in terms of R for
equiatomic alloys with constituent elements up to 10 [6]
Configurational entropy increases as the
number of element increases [6]
Source: [4] Yeh, J.W., et al. (2004)
[6] Yeh, J.W. (2013)
Example Cr-Cu: [6]
Formation enthalpy of intermetallic = 12 kJ/mol
Entropy for solid solution = 1.06R
Entropy ≥ 1.5R (12.471), will have
probability to win against enthalpy
From table 1.1  at least five elements[6]

6. Definition of
HEA
Based on Composition: [6]
nmajor ≥ 5, 5% ≤ Xi ≤ 35%
nminor ≥ 0, Xj ≤ 5%
Based on Configurational Entropy: [6]
ΔSconf ≥ 1.5R
5
Source:
[6] Yeh, J.W. (2013)
[7] Gao, M.C., et al. (2015)
Principle: Has High Mixing Entropy [7]
- Enhance the formation of solid solution
- Inhibit the formation of intermetallic compounds
These definitions are just guidelines,
not laws [7]
- Fitting only one of the two definitions
- Close to the lower limits of both definitions
Considered
HEA [7]

7. Phase
Formation Rules
Thermodynamics:
ΔHfmix vs TΔSmix
Geometry:
Atomic Size Difference
Ω Parameter:
Electron
Concentration:
VEC and e/a
Source: [8] Guo, S., et al. (2011)
6
Solid solution will form when:
δ = small
ΔHfmix = not negative enough
to form compound
Fig. 1 Phase selection diagram of HEAs and BMGs based on the enthalpy of mixing, ΔHmix, and the atomic size difference, Delta ( )
δ [8]
Atoms easily substitute
for each other &
Have similar probability
to occupy lattice sites [8]

8. Phase
Formation Rules
Thermodynamics:
ΔHfmix vs TΔSmix
Geometry:
Atomic Size Difference
Ω Parameter: [9]
Electron
Concentration:
VEC and e/a
Source: [9] Yang, X. et al. (2012)
[10] Zhang, Y. et al. (2014) 7
Fig. 2 Phase selection diagram of HEAs and BMGs based on Ω and δ [10]
New criteria for forming solid
solution phases in HEA [10]
Solid solution formed:
Ω ≥ 1.1
δ ≤ 6.6 %

9. Phase
Formation Rules
Thermodynamics:
ΔHfmix vs TΔSmix
Geometry:
Atomic Size Difference
Ω Parameter:
Electron
Concentration:
VEC and e/a
Source: [10] Zhang, Y. et al. (2014)
8
Fig. 3 Dependence of crystal structures on the enthalpy of mixing, ΔHmix, and the atomic size mismatch, ,
δ in various HEAs [10]
Atomic size difference has limited use 
Controlling the formation of crystal structure
FCC : Small δ
BCC : Larger δ
Ways to control the formation of crystal structure (common: BCC, FCC, HCC)
FCC and BCC
overlapping each
other (middle region)
However,

10. Phase
Formation Rules
Thermodynamics:
ΔHfmix vs TΔSmix
Geometry:
Atomic Size Difference
Ω Parameter:
Electron
Concentration:
VEC and e/a
9
VEC  Transition Metal Alloys
e/a  Noble Metal Alloys [11]
e/a: average number of itinerant electrons per atom ratio (e.g. Cu = 1)
VEC: number of total electron, including d in valence band (e.g. Cu = 11)
Home-Rothery
Rules [11]
Fig. 4 Relationship betweenVEC and the phase stability for fcc and bcc solid solutions in various HEAs [12]
Source: [11] Mizutani, U. (2011)
[12] Guo, S., et al. (2011)

11. Phase
Formation Rules
Thermodynamics:
ΔHfmix vs TΔSmix
Geometry:
Atomic Size Difference
Ω Parameter:
Electron
Concentration:
VEC and e/a
9
Fig. 4 Relationship betweenVEC and the phase stability for fcc and bcc solid solutions in various HEAs [12]
• Based on experimental results from cast alloys
• No intermetallic compounds formed
• Maybe disordered and ordered solid solutions
• BCC / FCC maybe multiphase
• Quantitative measurement may vary in different
alloy systems
BCC : Lower (6.87 ≤VEC < 8)
FCC : Higher (VEC ≥ 8)
notes
Source: [12] Guo, S., et al. (2011)

12. PHYSICAL METALLURGY
Image Source: [2] Gludovatz, B. (2014)

13. Four Core
Effects of
HEA [13]
1. High Entropy Effect (Thermodynamics)
2. Sluggish Diffusion Effect (Kinetics)
3. Severe-Latice-Distortion Effect (Structure)
4. Cocktail Effect (Properties)
10
Fig. 5 The scheme of physical metallurgy in which those areas influenced by four core effects of HEAs are indicated [13]
Source: [13] Yeh, J.W. (2006)

14. 4 Core Effects
High Entropy
Effect
Sluggish
Diffusion Effect
Severe Lattice
Distortion Effect
Cocktail Effect
11
Source: [14] Senkov, O.N., et al. (2011)
High entropy tends to stabilize high-entropy phases
(solid solution) rather than intermetallic compounds
(0 entropy) [14]
Beneficial  Avoid complex and brittle
microstructure [14]
ΔGmix = ΔHfmix -TΔSmix
Intermetallic
Compound
Solid Solution
Phase

15. 4 Core Effects
High Entropy
Effect
Sluggish
Diffusion Effect
Severe Lattice
Distortion Effect
Cocktail Effect
12
Source: [15] Swalin, R.A. (1972)
[16] Tsai, K.Y. (2013)
Slower diffusion rate compared to conventional alloys  A
vacancy surrounded and competed by different element atoms
 Slower phase transformation [15]
Fig. 6 Temperature dependence of the diffusion coefficients for Cr, Mn, Fe, Co, and Ni in different matrices [16]

16. 4 Core Effects
High Entropy
Effect
Sluggish
Diffusion Effect
Severe Lattice
Distortion Effect
Cocktail Effect
13
Slower diffusion rate compared to conventional alloys
 A vacancy surrounded and competed by different
element atoms  Slower phase transformation [15]
- Easiness to get supersaturated state
- Fine precipitates
- Slower grain growth
- Increase creep resistance
Benefit on its Mechanical Properties [17]
Source: [15] Swalin, R.A. (1972)
[17] Tongi, C.J., et al. (2005)

17. 4 Core Effects
High Entropy
Effect
Sluggish
Diffusion Effect
Severe Lattice
Distortion Effect
Cocktail Effect
14
Source: [18] Yeh, J.W., et al. (2004) [20] Kao, Y.F., et al. (2011)
[19] Senkov, O.N., et al. (2010)
In HEA, every atom is surrounded by different kinds of atom 
Suffers lattice strain and stress [18]
Fig. 7 Schematic diagram showing the severely distorted lattice and the various interactions with dislocations, electrons,
phonons, and x-ray beam [17]
Advantages:
Increase Strength &
Hardness [19]
Disadvantages:
Reduce Thermal &
Electrical Conductivity [20]

18. 4 Core Effects
High Entropy
Effect
Sluggish
Diffusion Effect
Severe Lattice
Distortion Effect
Cocktail Effect
15
Source: [5] Ranganathan, S. (2003)
Unexpected properties can be obtained after mixing
many elements [5]
HEAs have many potential applications

19. Dislocations in HEAs
16
Lower dislocation energy than conventional alloys: [7]
- Easy Relaxation Effect
- Severe Lattice Distortion Effect
Dislocations are harder to
move in HEAs [7]
Source: [7] Gao, M.C., et al. (2016)

20. Stacking Faults
HEAs have low SFE: [7]
- Suzuki Interaction (Suitable T)
 Relaxation
 Segregation
- Severe Lattice Distortion Effect
17
SFE decrease as number of
elements increase
Fig. 8 SFE as a function of the number of composing elements from Ni to
NiCoFeCrMn alloy [21]
Source: [7] Gao, M.C., et al. (2016)
[21] Lee, C., et al. (2013)

21. Stacking Faults
Important  dislocation movement [22]
- Low SFE gives larger separation
between partial dislocations (cross-slip
or double cross-slip will be harder)
- Easier to twin (twin boundary is half
thickness of a stacking fault)
- Dislocation structure will be more
uniform in planar (strain hardening)
18
Low SFE in FCC HEAs is
beneficial for good toughness
at cryogenic temperature
Fig. 9 Typical stress-strain curves CoCrFeMnNi HEA obtained
by tensile testing at 77, 200, and 293 K. [1]
Source: [22] Zaddach, A.J., et al. (2013)
[1] Gludovatz, B., et al. (2014)

22. Grain Boundaries
19
Lower grain boundary energy than conventional alloys: [7]
- Segregation layer of solute atoms along grain boundary
- High level of distorted matrix
Atoms has low mobility  Stable grain
structure at higher temperature 
Good creep resistance [7]
Source: [7] Gao, M.C., et al. (2016)

23. MECHANICAL PROPERTIES
IMPROVEMENT
Image Source: [2] Gludovatz, B. (2014)

24. Mechanical Properties
Improvements
1. Design crystal structure to obtain
the desired properties
- Control δ, VEC
- Add: Al / Cr as BCC stabilizer
Ni / Co as FCC stabilitizer
20

25. Mechanical Properties
Improvements
2. Choose appropriate fabrication
techniques
- Arc melting : most common, but hard
to control
- BST : good for microstructure control
- Lasser cladding : can minimize defects,
resulting superior properties
20

26. Mechanical Properties
Improvements
3. Use Surface Modification
Technique
InduceTWIP to improve its properties
on RT
20
Listyawan,T.A., et al. (2020) [23]
Used UNSM technique
Source: [23] Listyawan, T.A., et al. (2020)
Fig. 10 Vickers microhardness of UNSM treated specimens measured from
the top surface down to the middle of the specimens. [23]
Hardness increased with
increasing static load 
Deformation twinning increase

27. References
1. Pham, M., Dovgyy, B., Hooper, P.A., Gourlay, C.M., and Piglione, A. (2020). The role of side-branching in microstructure development in laser powder-
bed fusion. Nature Communications, 11(749), p. 6.
2. Gludovatz, B., Hohenwarter, A., Catoor, D., Chang, E.H., George, E.P., and Ritchie, R.O. (2014). A fracture-resistant high-entropy alloy for cryogenic
applications. Science, 345, p. 1156.
3. Cantor, B., Chang, I.T.H., Knight, P., and Vincent, A.J.B. (2004). Microstructural Development in Equiatomic Multicomponent Alloys. Mater Sci Eng A,
375–377, pp. 213–218.
4. Yeh, J.W., Chen, S.K., Lin, S.J., Gan, J.Y., Chin, T.S., Shun, T.T., Tsau, C.H., and Chang, S.Y. (2004). Nanostructured high-entropy alloys with multiple
principal elements: novel alloy design concepts and outcomes. Adv Eng Mater, 6, pp. 299–303.
5. Ranganathan, S. (2003). Alloyed pleasures: multimetallic cocktails. Curr Sci, 85, pp. 1404–1406.
6. Yeh, J.W. (2013) Alloy design strategies and future trends in high-entropy alloys. JOM, 65, pp. 1759–1771.
7. Gao, M.C., Yeh, J.W., Liaw, P.K., and Zhang, Y. (2016). High-entropy alloys. Cham: Springer International Publishing.
8. Guo, S. and Liu, C.T. (2011). Phase stability in high entropy alloys: formation of solid-solution phase or amorphous phase. Prog Nat Sci:Mater Int, 21(6),
pp. 433–446.
9. Yang, X. and Zhang, Y. (2012). Prediction of high-entropy stabilized solid-solution in multi-component alloys. Mater Chem Phys, 132(2–3), pp. 233-238.
10. Zhang, Y., Lu, Z.P., Ma, S.G., Liaw, P.K., Tang, Z., Cheng, Y.Q., and Gao, M.C. (2014). Guidelines in predicting phase formation of high-entropy alloys.
MRS Commun, 4(2), pp. 57–62.
21

28. References
11. Mizutani, U. (2011). Hume-Rothery rules for structurally complex alloy phases. CRC Press: Boca Raton.
12. Guo, S., Ng, C., Lu, J., and Liu, C.T. (2011). Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys. J Appl Phys,
109(10), p. 103505
13. Yeh JW (2013) Alloy design strategies and future trends in high-entropy alloys. JOM 65:1759–1771
14. Senkov ON, Scott JM, Senkova SV, Miracle DB, Woodward CF (2011) Microstructure and room temperature properties of a high-entropy TaNbHfZrTi
alloy. J Alloys Compd 509:6043–6048
15. Swalin RA (1972) Thermodynamics of solid, 2nd edn. Wiley, New York, pp 263–266
16. Tsai KY, Tsai MH, Yeh JW (2013) Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys. Acta Mater 61:4887–4898
17. Tong CJ, Chen YL, Chen SK, Yeh JW, Shun TT, Tsau CH, Lin SJ, Chang SY (2005) Microstructure characterization of AlxCoCrCuFeNi high-entropy
alloy system with multi- principal elements. Metall Mater Trans A 36A:881–893
18. Yeh JW, Chen SK, Gan JY, Lin SJ, Chin TS, Shun TT, Tsau CH, Chang SY (2004) Formation of simple crystal structures in solid-solution alloys with
multi-principal metallic elements. Metall Mater Trans A 35A:2533–2536
19. Senkov ON, Wilks GB, Miracle DB, Chuang CP, Liaw PK (2010) Refractory high-entropy alloys. Intermetallics 18:1758–1765
20. Kao YF, Chen SK, Chen TJ, Chu PC, Yeh JW, Lin SJ (2011) Electrical, magnetic, and hall properties of AlxCoCrFeNi high-entropy alloys. J Alloys
Compd 509:1607–1614
21. Lee C, Yeh JW (2013) Study on deformation behaviors of equimolar alloys from Ini to CoCrFeMnNi. Master’s thesis, National Tsing Hua University
22

29. References
22. Zaddach AJ, Niu C, Kock CC, Irving DL (2013) Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. J Appl Meteorol
65:1780–1789
23. Listyawan, T.A., Lee, H., Park, N., and Lee, U. (2020). Microstructure and mechanical properties of CoCrFeMnNi high entropy alloy with ultrasonic
nanocrystal surface modification process. Materials Science & Technology, 57, pp. 121-130.
23