Atomic Ordering

Abstract

The sections in this article are Introduction Definition of Atomic Configurations Configurational Variables Point Variables Point Correlation Functions and Point Probabilities Pair Variables, Correlation Functions, and Probabilities Generalized Cluster Variables, Correlation Functions, and Probabilities Short‐Range Order ( sro ) Configurations–Long‐Range Order ( lro ) Configurations The Existence Domain and Configuration Polyhedron F . C . C . Structure, First‐Neighbor Interactions F . C . C . Structure, First and Second Neighbor Interactions B . C . C . Structure, First and Second Neighbor Interactions Ground States Pair Interactions Ground State Energies F . C . C . Structure, First‐Neighbor Interactions F . C . C . Structure, First and Second Neighbor Interactions B . C . C . Structure, First and Second Neighbor Interactions Energy Minimum at Constant Composition Canonical Energy of lro States Relevant Literature Effective Cluster Interactions ( ECIs ) Phase Equilibria at Finite Temperatures Cluster Variation Method Calculation of Phase Diagrams with the CVM Phase Diagram Calculation with the Monte Carlo Method Examples of Prototype Diagrams F . C . C . Structure, First Neighbor Interactions F . C . C . Structure, First and Second Neighbor Interactions B . C . C . Structure, First and Second Neighbor Interactions Hexagonal Lattice, Anisotropic Nearest‐Neighbor Interactions The Cluster Site Approximation ( CSA ) Application to Real Systems The Au  Ni System The Thermodynamic Factor of Ordered Phases The B . C . C . Fe  Al System The F . C . C . Ni – Al System Ternary Systems B . C . C . Fe – Ti – Al B . C . C . Ferromagnetic Fe – Co – Al H . C . P . Cd – Mg Concluding Remarks Appendix Acknowledgements

An improved CVM entropy functional for binary fcc alloys

“…Points of the types α and β. The K-B coefficients, γ, of the subclusters are calculated following the usual procedure [3] in terms of the modified multiplicity m 4 of the tetrahedron cluster as follows. The superscripts refer to the sublattices associated with the cluster sites for the ordered B2 structure.…”

“…These correlation functions were then utilized in the hybrid CE-CVM (using the modified CVM entropy functional) to obtain the configurational entropy. All the simulations were performed on a 16 3…”

“…A quantitatively reliable description of the thermodynamics of disordered and ordered phases present in alloys and their equilibria is essential for the development of newer alloys. The Monte Carlo (MC) method [1] and the cluster variation method (CVM) [2,3] are the methods most often applied to bulk alloy systems for this purpose.…”

Machine-learning the configurational energy of multicomponent crystalline solids

“…For example, the commonly used lattice-gas Hamiltonian emerges when ϕ σ i ð Þ ¼ 1 2 1 þ σ i ð Þ. 65 Sanchez 66 has shown how to construct a family of functions ϕ(σ i ) that are orthogonal under a particular definition of a scalar product in the discrete occupation variable space. For a ternary system, the occupation variables σ i assume one of three discrete values (e.g., −1, 0, and +1).…”

Termodinâmica de primeiros princípios aplicada a ligas de metais de transição

“…O método foi desenvolvido por Kikuchi em 1974 [62], para o caso puramente configuracional, e foi batizado de NIM (Natural Interation Method ). Outro método de minimização comumente utilizadoé o método de Newton-Raphson (NR) [63]. De maneira geral, podemos destacar as seguintes vantagens e desvantagens dos dois métodos:…”