Order?Disorder Transformations in Alloys. The Inclusion of Non-nearest Neighbour Interactions in Cluster Variation Methods. I. Critical Temperature and High Temperature Specific Heats for Body Centred Cubic Lattices

1981 ◽  
Vol 34 (1) ◽  
pp. 61 ◽  
Author(s):  
Joan M Hanley ◽  
Thomas E Peacock
Keyword(s):  
High Temperature ◽  
Critical Temperature ◽  
Marked Effect ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Nearest Neighbour ◽  
Configurational Energy ◽  
Specific Heats ◽  
Cubic Lattices ◽  
Cluster Variation

The Sanchez and de Fontaine formulation of the cluster variation method is used in a study of order-disorder phase transformations in a body centred cubic (b.c.c.) lattice. The method is modified to include second neighbour interactions in the configurational energy term. The dependence of the critical temperature on the ratio a of second neighbour to nearest neighbour interaction energy is studied. The method is also used to study. the dependence of the high temperature specific heat on a. It is found that the sign and magnitude of a have a marked effect on both of these properties.

Order?Disorder Transformations in Alloys. The Inclusion of Non-nearest Neighbour Interactions in Cluster Variation Methods. II. Low Temperature Specific Heats for Body Centred Cubic Lattices

1981 ◽  
Vol 34 (1) ◽  
pp. 75 ◽  
Author(s):  
Joan M Hanley ◽  
Thomas E Peacock
Keyword(s):  
Critical Temperature ◽  
Low Temperature ◽  
Specific Heat ◽  
Interaction Energy ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Nearest Neighbour ◽  
Specific Heats ◽  
Low Temperature Specific Heat ◽  
Cluster Variation

In Part I, the Sanchez and de Fontaine formulation of the cluster variation method was used to study the dependence of the critical temperature and the high temperature specific heat on the ratio of second neighbour to nearest neighbour interaction energy. This method can be extended to find solutions for the ordered state. The dependence of the low temperature specific heat on the interaction energy ratio is studied. As with the critical temperature and high T specific heat studies, it is found that both the sign and magnitude of ex affect the low temperature specific heat.

Thermodynamics of (Zn,Fe)S sphalerite. A CVM approach with large basis clusters

2000 ◽  
Vol 64 (5) ◽  
pp. 923-943 ◽  
Author(s):  
A. I. Balabin ◽  
R. O. Sack
Keyword(s):  
Long Range ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Nearest Neighbour ◽  
Many Body ◽  
Mean Values ◽  
Equilateral Triangles ◽  
Cluster Variation ◽  
Long Range Ordering ◽  
Many Body Interactions

AbstractWe have developed a cluster variation method (CVM) model based on cuboctahedral and octahedral basis clusters containing 13 and 6 atoms, respectively, and applied it to the analysis of the thermodynamic mixing properties of (Zn,Fe)S solid solutions. The model, in which the internal energy of the lattice is approximated by next to nearest neighbour (nnn) pair interactions and many-body interactions associated with nearest neighbour (nn) equilateral triangles, describes the FeS contents of sphalerites equilibrated with pyrrhotite and pyrite, and with pyrrhotite and iron metal within experimental uncertainties. The model predicts moderate deviations from ideality; the mean values of the Lewis and Randall activity coefficient of FeS and ZnS are, 1.48 and 1.03, respectively. Predictions of the model are in qualitative agreement with cell-edge data. The model also predicts that sphalerites undergo long-range ordering to lower-symmetry structures at temperatures only slightly below those investigated experimentally, a result in agreement with inferences from an existing Mössbauer investigation of synthetic sphalerites.More realistic models in which interactions are ascribed to larger species (nn triangular and centred square species) predict that such long-range ordering occurs at even higher temperatures and underscore the need for better characterization of the structures of (Zn,Fe)S minerals.

General Algorithm for the Cluster-Variation Method

1983 ◽  
Vol 28 (5) ◽  
pp. 565-568 ◽  
Author(s):  
J S Desjardins ◽  
O Steinsvoll
Keyword(s):  
Cluster Variation Method ◽  
General Algorithm ◽  
Variation Method ◽  
Cluster Variation
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