Ming-Hung Tsai and Jien-Wei Yeh, Mater. Res. Lett., Vol. 2, No. 3 (2014) 107-123. 3. M. C. Gao, Jien-Wei Yeh, P. K. Liaw, Yong Zhang, High-Entropy Alloys, ...
Ab initio calculations of structure and elastic properties of light weight HEAs Natalia E. Koval, I. Nechaev, J. I. Juaristi, R. D´ıez Muin˜o, M. Alducin Materials Physics Center (MPC/CFM) and Donostia International Physics Center (DIPC), San Sebastia´n, Spain – EUROMAT 2017 (17-22 September, Thessaloniki, Greece) –
Introduction
Four HEA core effects
High Entropy Alloys (HEAs) are a new class of metallic alloys with 5 or more principal elements, with the concentration of 5% to 35% each one. Despite the complex composition, HEAs mostly form simple crystal structures, depending on the valence electron concentration VEC (BCC if VEC8, mixed phases in between)1,2,3. Due to their unusual design, these alloys often exhibit special properties. The combination of such properties as low density, high strength, and corrosion resistance makes possible many potential applications of HEAs in aviation, engineering, orthopedics (bone implants), etc. The aim of our work is to study ab initio the microstructure, electronic, and elastic properties of HEAs.
1. The high entropy effect. High configurational entropy favors the formation of solid solution (SS) phases over intermetallic ones. 2. The ”cocktail” effect. Macroscopic properties of HEA cannot be predicted only by the properties of individual components. 3. The lattice distortion effect, due to the difference in atomic sizes, strengthens the SS phase formation, reduces electrical and thermal conductivity, increases hardness. 4. The sluggish diffusion effect. Slow diffusion due to 3. leads to structural stability.
Methods
Co4Cr4Fe4Ni4 high entropy alloy obtained with USPEX
For structure prediction, we use USPEX4 - an evolutionary algorithm which predicts ab initio the stable crystal structure for a particular chemical composition. The stability parameter is the total ground state energy (calculated with VASP). For calculations of elastic properties, we use VASP5 code. The total elastic tensor is determined by performing six finite distortions of the lattice and deriving the elastic constants (Cij , i, j = 1, .., 6) from the strain-stress relationship.
CoCrFeNi vs Co4Cr4Fe4Ni4 CoCrFeNi (cell×4)
DOS
Definitions
Co4Cr4Fe4Ni4 (unit cell)
1. Composition: five or more components, 5% to 35% - the concentration of each.
Electronic Density of States CoCrFeNi 8 7
Co spin up Co spin down Cr spin up Cr spin down Fe spin up Fe spin down Ni spin up Ni spin down
6 5 4
Enthalpy (eV/atom): -7.5750 Enthalpy (eV/atom): -7.5647 Density (g/cm3): 8.366 Density (g/cm3): 8.399 Elastic properties: Bulk modulus (GPa): B = 203.8 B = 202 Shear modulus (GPa): G = 118.6 G = 120.8 Poisson ratio: ν = 0.256 ν = 0.251 < 0.33 → brittle Young’s modulus (Gpa): E = 298 E = 302 B/G : 1.71 1.67 < 1.75 → brittle G Anisotropy AG (%) = 4.978 A vr vr (%) = 3.85 0 0 Zener ratio (C44/C ) Az = 1.91 Az = 1.77 [C = (C11−C12)/2] The difference in elastic moduli is less than 2% for different structures → no need to use large unit cells. Anisotropy reduces for larger cell.
Al20Be20Fe10Si15Ti35 – LWHEA
Density (states/eV)
3 2 1
2. Entropy: the configurational entropy n X Sconf = −R ci ln ci > 1.61R. i
0
Some HEAs, so-called in the literature, are in fact MediumEA (0.69R < Sconf < 1.61R).
-1 -2 -3 -4 -5 -6 -7 -10
-8
-6
-4
-2
0 Energy (eV)
2
4
6
8
10
Only d electrons contribute to the DOS. Pseudo-gap at the Fermi level.
6
3. Single phase is required or not? Many alloys in the literature have mixed, intermetallic phases, or even metallic glass structures. Still are called HEA. → there is no agreement yet on the definition.
Mg20Al20Cu20Mn20Zn20 – LWHEA
Experimental micro-hardness (Hv) : 911 In USPEX we model it as Al4Be4Fe2Si3Ti7. HEA Sconf = 1.53R < 1.61R => MEA (but the authors use another definition, Sconf > 1.5R) VEC = 7.6 (BCC + FCC); USPEX structure: ?
6
Experimental micro-hardness (Hv) : 429 In USPEX we model it as Mg2Al2Cu2Mn2Zn2. Sconf = 1.61R => HEA VEC = 7 (BCC + FCC); USPEX structure: FCC
Elastic properties: B (GPa) = 135.45 G (GPa) = 75.24 ν = 0.266 < 0.33 → brittle E (GPa) = 190.45 AVR (%) = 1.93 Az = 1.495 B/G = 1.8 > 1.75 → ductile Density (g/cm3) : 4.121
There are 4-element HEAs in the literature.
Elastic properties: B (GPa) = 88.07 G (GPa) = 49.82 ν = 0.26 < 0.33 → brittle E (GPa) = 125.75 AVR (%) = 4.62 Az = 1.87 B/G = 1.77 > 1.75 → ductile Density (g/cm3) : 5.415
1. D.B. Miracle, O.N. Senkov, Acta Materialia 122 (2017) 448-511. 2. Ming-Hung Tsai and Jien-Wei Yeh, Mater. Res. Lett., Vol. 2, No. 3 (2014) 107-123. 3. M. C. Gao, Jien-Wei Yeh, P. K. Liaw, Yong Zhang, High-Entropy Alloys, Fundamentals and Applications, Springer, 2016. 4. A.R. Oganov and C.W. Glass, The Journal of Chemical Physics, 124 (2006) 244704; C.W. Glass, A.R. Oganov, and N. Hansen, Comp. Phys. Comm., 175 (2006) 713-720 5. G. Kresse and J. Hafner, Phys. Rev. B 47 , 558 (1993); ibid. 49 , 14 251 (1994); G. Kresse and J. Furthmu¨ller, Comput. Mat. Sci. 6 , 15 (1996); G. Kresse and J. Furthmu¨ller, Phys. Rev. B 54 , 11 169 (1996); G. Kresse and D. Joubert, Phys. Rev. 59 , 1758 (1999). 6. Amit Kumar and Manoj Gupta, Metals 2016, 6, 199; doi:10.3390/met6090199
Acknowledements: ELKARTEK Project KK-2017/00007 financed by Gobierno Vasco and Spanish Ministerio de Econom´ıa, Industria y Competitividad Grant No. FIS2016-76471-P.
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