Order-disorder transformations in a generalized Ising alloy

Baal, C. M. van

doi:10.1016/0031-8914(73)90010-4

Cited by 230 publications

(34 citation statements)

References 17 publications

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“…They are selected to serve as illustration only. The interactions give the classical fcc phase diagram [74][75][76][77] for the solid state A-B alloy with a critical order-disorder temperature of about 1100 K at equiatomic composition. Concerning the vacancy formation energies in pure A and B, we consider two cases: (a) the strong asymmetric case with vacancy formation energies in pure A (B) of 2 (1) [Eq.…”

Section: B Alloy With Ordering Tendencymentioning

confidence: 99%

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

Zhang

Sluiter

2015

Phys. Rev. B

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Vacancy properties in concentrated alloys continue to be of great interest because nowadays ab initio supercell simulations reach a scale where even defect properties in disordered alloys appear to be within reach. We show that vacancy properties cannot generally be extracted from supercell total energies in a consistent manner without a statistical model. Essential features of such a model are knowledge of the chemical potential and imposition of invariants. In the present work, we derive the simplest model that satisfies these requirements and we compare it with models in the literature. As illustration we compute ab initio vacancy properties of fcc Cu-Ni alloys as a function of composition and temperature. Ab initio density functional calculations were performed for SQS supercells at various compositions with and without vacancies. Various methods of extracting alloy vacancy properties were examined. A ternary cluster expansion yielded effective cluster interactions (ECIs) for the Cu-Ni-Vac system. Composition and temperature dependent alloy vacancy concentrations were obtained using statistical thermodynamic models with the ab initio ECIs. An Arrhenius analysis showed that the heat of vacancy formation was well represented by a linear function of temperature. The positive slope of the temperature dependence implies a negative configurational entropy contribution to the vacancy formation free energy in the alloy. These findings can be understood by considering local coordination effects.

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Section: B Alloy With Ordering Tendencymentioning

confidence: 99%

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

Zhang

Sluiter

2015

Phys. Rev. B

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“…[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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confidence: 99%

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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“…It was van Baal 10) who first applied the CVM to the calculation of a phase diagram. Then, Kikuchi and de Fontaine 11,12) demonstrated that the Cu-Au type phase diagram was reproduced much more accurately as compared with the one 13) obtained based on the traditional Bragg-Williams (BW) approximation.…”

Section: Cluster Variation Methods and Path Probability Methodsmentioning

confidence: 99%

Glass Transition within Cluster Variation and Path Probability Methods

Mohri

2005

Mater. Trans.

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Thermodynamic framework of Crystal-Glass transition is described within the Cluster Variation Method (CVM). Free energy is calculated as a function of order parameter at various temperatures and T 0 diagram is obtained. It is demonstrated that the glass transition temperature can be interpreted as the spinodal ordering temperature in the order-disorder transition. The advantage of the present description is that the kinetic behavior can be investigated within the same framework by employing Path Probability Method (PPM). Therefore, the combination of the CVM and PPM provides a unique theoretical tool to study Crystal-Glass transition in a consistent manner covering thermodynamics and kinetics.

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Order-disorder transformations in a generalized Ising alloy

Cited by 230 publications

References 17 publications

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

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

Glass Transition within Cluster Variation and Path Probability Methods

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