Cluster variation method in the computational materials science
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Cited by (23)
Evaluation of the genetic algorithm performance for the optimization of the grand potential in the cluster variation method
2018, Calphad: Computer Coupling of Phase Diagrams and ThermochemistryCitation Excerpt :The cluster variation method is a very efficient tool used not only in the computation procedure of alloy phase diagrams but also in many applications of materials science in connection to phase transitions. In fact, such method can be used with a satisfactory accuracy to calculate phase equilibrium configurations in solid solutions characterized by the nature of the involved phases, which varies only in the permutation of atoms and clusters at the level of the lattices sites [4–7]. The cluster variation method has been proposed initially by Kikuchi in a series of pioneering works as an approximate approach to model order-disorder phenomena by providing analytical formulations for the configuration entropy, internal and free energies of the system as a function of the cluster probability variables [8–11].
Quantitative modeling and experimental verification of carbide precipitation in a martensitic Fe-0.16 wt%C-4.0 wt%Cr alloy
2016, Calphad: Computer Coupling of Phase Diagrams and ThermochemistryCitation Excerpt :Unfortunately, it is impossible to measure the interfacial energy directly and thus there are large uncertainties to the reported values. The available data is mainly derived from indirect methods such as inverse modeling of experimental data [35], first-principles calculations [36], the cluster variation method (CVM) [37], the cluster/site approximation (CSA) [38] and the embedded atom method (EAM) [39]. However, all of the above calculation methods are not easy to apply to multicomponent commercial alloys.
Ab initio calculation of the BCC Fe-Al-Mo (Iron-Aluminum-Molybdenum) phase diagram: Implications for the nature of the τ<inf>2</inf> phase
2009, Calphad: Computer Coupling of Phase Diagrams and ThermochemistryCitation Excerpt :As already mentioned, the present model uses a rigid lattice approximation and, therefore, important contributions to the free energy are neglected. The most important is, probably, the entropic effect of the vibrational degrees of freedom, which has been found to cause a homogeneous depression of the temperature scale of the calculated phase diagram of the order of 40% to 60% compared to the corresponding rigid lattice case [24,54]. The temperature scale reported in the present work, therefore, must be analyzed with consideration to this effect of the missing vibrational entropy.
Thermodynamic self-consistency issues related to the Cluster Variation Method: The case of the BCC Cr-Fe (Chromium-Iron) system
2008, Calphad: Computer Coupling of Phase Diagrams and ThermochemistryCitation Excerpt :In fact, two indirect evidences point to this relevant aspect of the vibrational degrees of freedom in the alloy thermodynamics. The first evidence is based on the results reported by Kikuchi and Masuda-Jindo, using the CD-CVM in the pair approximation [20,21]. These authors showed that the relaxation of the rigid lattice constraint results in the reduction of about 40%–50% in the temperature scale of prototype phase diagrams (both phase separating and alloying systems).
A generalized defect correlation model for B2 compounds
2008, Solid State SciencesCitation Excerpt :Moreover, these approaches assume random distribution of point defects and are therefore not able to describe phenomena which are related to point defect cluster formation in highly ordered crystals. Within the framework of the Cluster-Variation Method (CVM) [17,18], where entropy and free energy of a binary alloy system are written in terms of cluster probability variables, cooperative phenomena leading to SRO can be described properly. However, to our knowledge, CVM has not been applied to point defect cluster formation in highly ordered B2 structure alloy phases up to now.