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29-11-2018 | Computation

Atomic interactions in C15 Laves phases

Authors: J.-C. Crivello, J.-M. Joubert, T. Mohri

Published in: Journal of Materials Science | Issue 6/2019

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Abstract

The C15 phase (\(Fd\bar{3}m\)) has been extensively studied by several methodologies to evaluate its atomic interactions. Ideally ordered at the \(AB_2\) composition, this Laves phase is known to present a non-stoichiometry domain accommodated by substitutional atomic disorder at high temperature. With the Cu–Mg system as an example, a cluster expansion method study revealed that first neighbors pair interaction is positive yielding a favorable mixing of Cu and Mg atoms in 16d site and a homogeneity extended in the Mg-richer side. To guide the thermodynamic modeling of the C15 phase, special quasi-random structure cells have been generated at several compositions to simulate atom mixing with and without the merging of 8a and 16d sites. Combined with electronic density functional theory, calculation on several systems (Ta–V, Cr–Nb, Mo–Zr and Cr–Ti) was done to estimate the mixing energies on the two different sublattices. The results are compared to published assessments and open a discussion on the acceptability of the traditional thermodynamic model.

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Appendix
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Footnotes
1
According to Eq. (15), the interaction parameters are comparable to mixing energy at half of the occupation (\(y^\alpha _A=y^\alpha _B=\frac{1}{2}\)) with: \(\varDelta H_\mathrm{mix}=\frac{1}{4} L^0(A,B:*)\)
 
Literature
1.
go back to reference Andersson JO, Guillermet A, Hillert M, Jansson B, Sundman B (1986) A compound-energy model of ordering in a phase with sites of different coordination numbers. Acta Metall 34(3):437–445CrossRef Andersson JO, Guillermet A, Hillert M, Jansson B, Sundman B (1986) A compound-energy model of ordering in a phase with sites of different coordination numbers. Acta Metall 34(3):437–445CrossRef
2.
go back to reference Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50(24):17953–17979CrossRef Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50(24):17953–17979CrossRef
3.
go back to reference Connolly JWD, Williams AR (1983) Density-functional theory applied to phase transformations in transition-metal alloys. Phys Rev B 27(8):5169–5172CrossRef Connolly JWD, Williams AR (1983) Density-functional theory applied to phase transformations in transition-metal alloys. Phys Rev B 27(8):5169–5172CrossRef
4.
go back to reference Danon C, Servant C (2004) A thermodynamic evaluation of the Ta–V system. J Alloys Compd 366(1):191–200CrossRef Danon C, Servant C (2004) A thermodynamic evaluation of the Ta–V system. J Alloys Compd 366(1):191–200CrossRef
5.
go back to reference Frank FC, Kasper JS (1958) Complex alloy structures regarded as sphere packings. i. Definitions and basic principles. Acta Crystallogr 11(3):184–190CrossRef Frank FC, Kasper JS (1958) Complex alloy structures regarded as sphere packings. i. Definitions and basic principles. Acta Crystallogr 11(3):184–190CrossRef
6.
go back to reference Frank FC, Kasper JS (1959) Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures. Acta Crystallogr 12(7):483–499CrossRef Frank FC, Kasper JS (1959) Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures. Acta Crystallogr 12(7):483–499CrossRef
7.
go back to reference Ghosh G (2002) Thermodynamic and kinetic modeling of the Cr–Ti–V system. J Phase Equilibria 23(4):310–328CrossRef Ghosh G (2002) Thermodynamic and kinetic modeling of the Cr–Ti–V system. J Phase Equilibria 23(4):310–328CrossRef
8.
go back to reference Jacob A, Schmetterer C, Khvan A, Kondratiev A, Ivanov D, Hallstedt B (2016) Liquidus projection and thermodynamic modeling of the Cr–Fe–Nb ternary system. Calphad 54:1–15CrossRef Jacob A, Schmetterer C, Khvan A, Kondratiev A, Ivanov D, Hallstedt B (2016) Liquidus projection and thermodynamic modeling of the Cr–Fe–Nb ternary system. Calphad 54:1–15CrossRef
9.
go back to reference Joubert JM (2008) Crystal chemistry and calphad modeling of the \(\sigma \) phase. Prog Mater Sci 53:528–583CrossRef Joubert JM (2008) Crystal chemistry and calphad modeling of the \(\sigma \) phase. Prog Mater Sci 53:528–583CrossRef
10.
go back to reference Joubert JM, Crivello JC (2012) Non-stoichiometry and Calphad modeling of Frank–Kasper phases. Appl Sci 2(3):669–681CrossRef Joubert JM, Crivello JC (2012) Non-stoichiometry and Calphad modeling of Frank–Kasper phases. Appl Sci 2(3):669–681CrossRef
11.
go back to reference Joubert JM, Phejar M (2009) Crystal chemistry and calphad modeling of the \(\chi \) phase. Prog Mater Sci 54:945–980CrossRef Joubert JM, Phejar M (2009) Crystal chemistry and calphad modeling of the \(\chi \) phase. Prog Mater Sci 54:945–980CrossRef
12.
go back to reference King R, Kleppa O (1964) A thermochemical study of some selected laves phases. Acta Metall 12:87–97CrossRef King R, Kleppa O (1964) A thermochemical study of some selected laves phases. Acta Metall 12:87–97CrossRef
13.
go back to reference Kohn W, Sham L (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):A1133–1140CrossRef Kohn W, Sham L (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):A1133–1140CrossRef
14.
go back to reference Kresse G, Furthmüller J (1996) Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6(1):15–50CrossRef Kresse G, Furthmüller J (1996) Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6(1):15–50CrossRef
15.
go back to reference Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758–1775CrossRef Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758–1775CrossRef
16.
go back to reference Lu HJ, Wang WB, Zou N, Shen JY, Lu XG, He YL (2015) Thermodynamic modeling of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr system. Calphad 50:134–143CrossRef Lu HJ, Wang WB, Zou N, Shen JY, Lu XG, He YL (2015) Thermodynamic modeling of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr system. Calphad 50:134–143CrossRef
17.
go back to reference Parlinski K, Li ZQ, Kawazoe Y (1997) First-principles determination of the soft mode in cubic \(\text{ ZrO }_{2}\). Phys Rev Lett 78(21):4063–4066CrossRef Parlinski K, Li ZQ, Kawazoe Y (1997) First-principles determination of the soft mode in cubic \(\text{ ZrO }_{2}\). Phys Rev Lett 78(21):4063–4066CrossRef
18.
go back to reference Pavlů J, Vřeštál J, Chen X, Rogl P (2011) Thermodynamic modeling of laves phases in the Ta–V system: reassessment using first-principles results. Calphad 35(1):103–108CrossRef Pavlů J, Vřeštál J, Chen X, Rogl P (2011) Thermodynamic modeling of laves phases in the Ta–V system: reassessment using first-principles results. Calphad 35(1):103–108CrossRef
19.
go back to reference Pavlů J, Vřeštál J, Šob M (2010) Thermodynamic modeling of laves phases in the Cr–Hf and Cr–Ti systems: reassessment using first-principles results. Calphad 34(2):215–221CrossRef Pavlů J, Vřeštál J, Šob M (2010) Thermodynamic modeling of laves phases in the Cr–Hf and Cr–Ti systems: reassessment using first-principles results. Calphad 34(2):215–221CrossRef
20.
go back to reference Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868CrossRef Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868CrossRef
21.
go back to reference Pérez RJ, Sundman B (2003) Thermodynamic assessment of the Mo–Zr binary phase diagram. Calphad 27(3):253–262CrossRef Pérez RJ, Sundman B (2003) Thermodynamic assessment of the Mo–Zr binary phase diagram. Calphad 27(3):253–262CrossRef
22.
go back to reference Sanchez J (2010) Cluster expansion and the configurational theory of alloys. Phys Rev B 81(22):224202-1–224202-13CrossRef Sanchez J (2010) Cluster expansion and the configurational theory of alloys. Phys Rev B 81(22):224202-1–224202-13CrossRef
23.
go back to reference Sanchez J, Ducastelle F, Gratias D (1984) Generalized cluster description of multicomponent systems. Phys A 128:334–350CrossRef Sanchez J, Ducastelle F, Gratias D (1984) Generalized cluster description of multicomponent systems. Phys A 128:334–350CrossRef
24.
go back to reference School for Advanced Thermodynamic Assessments (SATA) (2007) Training of thermodynamic assessment on Mg–Cu system. In: Presqu’île de Giens, CEA organisation, France School for Advanced Thermodynamic Assessments (SATA) (2007) Training of thermodynamic assessment on Mg–Cu system. In: Presqu’île de Giens, CEA organisation, France
25.
go back to reference Sundman B, Ågren J (1981) A regular solution model for phases with several components and sublattices, suitable for computer applications. J Phys Chem Solids 42:297–301CrossRef Sundman B, Ågren J (1981) A regular solution model for phases with several components and sublattices, suitable for computer applications. J Phys Chem Solids 42:297–301CrossRef
26.
go back to reference Sundman B, Chen Q, Du Y (2018) A review of Calphad modeling of ordered phases. J Phase Equilibria Diffus 39(5):678–693CrossRef Sundman B, Chen Q, Du Y (2018) A review of Calphad modeling of ordered phases. J Phase Equilibria Diffus 39(5):678–693CrossRef
28.
go back to reference Sundman B, Lukas HL, Fries SG (2007) Computational thermodynamics: the Calphad method. Cambridge University Press, Cambridge Sundman B, Lukas HL, Fries SG (2007) Computational thermodynamics: the Calphad method. Cambridge University Press, Cambridge
30.
go back to reference van de Walle A, Asta M, Ceder G (2002) The alloy theoretic automated toolkit: a user guide. Calphad 26(4):539–553CrossRef van de Walle A, Asta M, Ceder G (2002) The alloy theoretic automated toolkit: a user guide. Calphad 26(4):539–553CrossRef
31.
go back to reference van de Walle A, Sun R, Hong QJ, Kadkhodaei S (2017) Software tools for high-throughput calphad from first-principles data. Calphad 58:70–81CrossRef van de Walle A, Sun R, Hong QJ, Kadkhodaei S (2017) Software tools for high-throughput calphad from first-principles data. Calphad 58:70–81CrossRef
32.
go back to reference van de Walle A, Tiwary P, de Jong M, Olmsted D, Asta M, Dick A, Shin D, Wang Y, Chen LQ, Liu ZK (2013) Efficient stochastic generation of special quasirandom structures. Calphad 42:13–18CrossRef van de Walle A, Tiwary P, de Jong M, Olmsted D, Asta M, Dick A, Shin D, Wang Y, Chen LQ, Liu ZK (2013) Efficient stochastic generation of special quasirandom structures. Calphad 42:13–18CrossRef
33.
go back to reference Zinkevich M, Mattern N (2002) Thermodynamic assessment of the Mo–Zr system. J Phase Equilibria 23(2):156–162CrossRef Zinkevich M, Mattern N (2002) Thermodynamic assessment of the Mo–Zr system. J Phase Equilibria 23(2):156–162CrossRef
34.
go back to reference Zunger A, Wei SH, Ferreira LG, Bernard JE (1990) Special quasirandom structures. Phys Rev Lett 65(3):353–356CrossRef Zunger A, Wei SH, Ferreira LG, Bernard JE (1990) Special quasirandom structures. Phys Rev Lett 65(3):353–356CrossRef
Metadata
Title
Atomic interactions in C15 Laves phases
Authors
J.-C. Crivello
J.-M. Joubert
T. Mohri
Publication date
29-11-2018
Publisher
Springer US
Published in
Journal of Materials Science / Issue 6/2019
Print ISSN: 0022-2461
Electronic ISSN: 1573-4803
DOI
https://doi.org/10.1007/s10853-018-3169-4

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