Electronic theory of the alloy phase stability of Cu-Ag, Cu-Au, and Ag-Au systems

Terakura, Kiyoyuki; Oguchi, Tamio; Mohri, Tetsuo; Watanabe, Katsuya

doi:10.1103/physrevb.35.2169

Cited by 155 publications

(46 citation statements)

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“…Several methods 81,82 yield concentration-dependent effective interactions, providing in principle equally valid schemes for representing ∆H direct (σ) in terms of a cluster expansion. In the present work, we select compositionindependent interactions, since these can be directly compared to previous Ising model treatments [25][26][27][28][29][30][31][32][33][34][48][49][50][51][52][53][54][55] of the noble metal alloy phase diagrams.…”

Section: Basic Ideology and Methodologymentioning

confidence: 99%

“…[48][49][50][51][52][53][54][55] The essential difference in philosophy between the classical application of Ising models to CuAu [25][26][27][28][29][30]33 and more modern approaches based on the density functional formalism 64 is that in the former approach the range and magnitudes of the interactions are postulated at the outset (e.g., first or second neighbor pair interactions), while the latter approaches make an effort to determine the interactions from an electronic structure theory. However, despite recent attempts, [48][49][50][51][52][53][54] it is still not clear whether the noble metal alloys can be essentially characterized as systems with short-range pair interactions, or not. Now that first-principles cluster expansion approaches 65,66 have advanced to the stage where both T = 0 ground state structures and finite-temperature thermodynamic quantities can be predicted without any empirical information, it is interesting to take a global look at the noble metal alloy family.…”

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confidence: 99%

“…[25][26][27][28][29][30][31][32] More recently, noble metal binary alloys have been treated theoretically via empirical fitting of the constants in Ising hamiltonians, [25][26][27][28][29][30][31][32][33][34] semiempirical interatomic potentials, [35][36][37][38][39][40][41][42][43][44][45][46][47] and via first-principles cluster expansions. [48][49][50][51][52][53][54][55] The essential difference in philosophy between the classical application of Ising models to CuAu [25][26][27][28][29][30]33 and more modern approaches based on the density functional formalism 64 is that in the former approach the range and magnitudes of the interactions are postulated at the outset (e.g., first or second neighbor pair inter...…”

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Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures

1998

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The classic metallurgical systems -noble metal alloys -that have formed the benchmark for various alloy theories, are revisited. First-principles fully relaxed general potential LAPW total energies of a few ordered structures are used as input to a mixed-space cluster expansion calculation to study the phase stability, thermodynamic properties and bond lengths in Cu-Au, Ag-Au, CuAg and Ni-Au alloys. (i) Our theoretical calculations correctly reproduce the tendencies of Ag-Au and Cu-Au to form compounds and Ni-Au and Cu-Ag to phase separate at T = 0 K. (ii) Of all possible structures, Cu3Au (L12) and CuAu (L10) are found to be the most stable low-temperature phases of Cu1−xAux with transition temperatures of 530 K and 660 K, respectively, compared to the experimental values 663 K and ≈ 670 K. The significant improvement over previous first-principles studies is attributed to the more accurate treatment of atomic relaxations in the present work. (iii) LAPW formation enthalpies demonstrate that L12, the commonly assumed stable phase of CuAu3, is not the ground state for Au-rich alloys, but rather that ordered 100 superlattices are stabilized. (iv) We extract the non-configurational (e.g., vibrational) entropies of formation and obtain large values for the size mismatched systems: 0.48 kB/atom in Ni0.5Au0.5 (T = 1100 K), 0.37 kB/atom in Cu0.141Ag0.859 (T = 1052 K), and 0.16 kB/atom in Cu0.5Au0.5 (T = 800 K). (v) Using 8 atom/cell special quasirandom structures we study the bond lengths in disordered Cu-Au and Ni-Au alloys and obtain good qualitative agreement with recent EXAFS measurements.

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Section: Basic Ideology and Methodologymentioning

confidence: 99%

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Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures

1998

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“…This procedure is originated in eq. (ll) and has been amply demonstrated in the previous literatures (Terakura et al,1987;Mohri et al,1988;Mohri et al,1991). For the entropy part, TetrahedronOctahedron approximation of the CVM was employed, for which 32 independent configurationa!…”

Section: Generalized Susceptibilitymentioning

confidence: 99%

Properties of Complex Inorganic Solids

1997

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“…NA!N8! (41) so that the energy of the completely random state of concentration cO=N B/(N A +N B) is, by Eq. (38) (43) where the disordered state energy Edis is the energy of the completely disordered medium, in a given.…”

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The Cluster Variation Method and the Calculation of Alloy Phase Diagrams

Fontaine

1989

Alloy Phase Stability

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INTRODUCTIONI was asked by the Workshop organizers to write a tutorial on the Cluster Variation Method (CVM) in phase diagram calculations. Hence I shall present an elementary treatment of the essential features of the method rather than a comprehensive review.As is well known. the CVM was originally proposed by Kikuchi 1 in 1951 as a hierarchy of approximation for the Ising model. in principle. in an arbitrary number of dimensions. The basic idea consists of handling local order as accurately as possible, then of expressing the configurational entropy in terms of small cluster probabilities. The corresponding free energy is then minimized with respect to independent configuration (cluster) variables. Higher cluster correlations are essentially treated by a superposition approximation. Hence. in the limit, the CVM is a classical theor\ Much of the early work in the field was devoted by Kikuchi and collaborators to a S), !tematic comparison of different levels of cluster approximations with known exact solutions such as that of Onsager's solution of the two-dimensional Ising model in zero field. In favorable cases, the CVM transition temperature turned out to be very close to the exact one. Unfortunately. the CVM being a classical theory. predicts critical exponents with classical values. That fact tended to discredit the CVM in the eyes of critical phenomena specialists.Kikuchi's original approach to deriving CVM entropy formulas for various lattices and cluster approximations was an essentially geometrical one. Soon. however. other, more analytical (and simpler) methods appeared. those of Barker 2 and of Hijmans and de Boer3. Later. a very general and systematic method was developed by Sanchez4-6 . This method. based on the idea of expressing the CVM free energy in terms of linearly independent corre!ation functions. is the most widely used today; it will be reviewed in this article.A convenient method of minimizing the CVM free energy is the Natural Iteration Method. also developed by Kikuchi 7 . It was proposed just after Van BaalS had demonstrated the use of the CVM in the calculation of temperature/composition phase diagrams for binary alloys. Subsequently it was shown that Van Baal's ideas could be used to produce a rather faithful approximation to the crystalline equilibria in the Cu-Au phase diagram9.10.Because of its importance for alloy thermodynamics. development of the CVM is being pursued very actively in both theoretical and practical aspects. The most general and sophisticated formulation of the method is that developed initially independently by Sanchez and by Ducastelle and presented in a joint publication 11. The present description is a simplified version of this approach. Recently. significant frogress has been made in the derivation of suitable criteria for the selection of clusters 2.11. Finel presented the essence of his method at the Workshop; a complete description thereof can be found in

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Electronic theory of the alloy phase stability of Cu-Ag, Cu-Au, and Ag-Au systems

Cited by 155 publications

References 14 publications

Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures

Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures

Properties of Complex Inorganic Solids

The Cluster Variation Method and the Calculation of Alloy Phase Diagrams

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