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

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.

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A First Principles Examination of Phase Stability in Fcc-Based Ni-V Substitutional Alloys

MRS Proceedings ◽

10.1557/proc-186-83 ◽

1990 ◽

Vol 186 ◽

Author(s):

J. Mikalopas ◽

P.E.A. Turchi ◽

M. Sluiter ◽

P.A. Sterne

Keyword(s):

Phase Stability ◽

Ground State ◽

First Principles ◽

Cluster Variation Method ◽

Variation Method ◽

Many Body ◽

Cluster Variation ◽

Many Body Interactions ◽

Ground State Energies ◽

Substitutional Alloys

AbstractThe phase stability of fcc-based Ni-V substitutional alloys is investigated using linear muffin-tin orbitals total energy (LMTO) calculations. The method of Connolly and Williams (CWM) is used to extract many body interactions from the ground state energies of selected ordered configurations. These interactions are used in conjunction with the cluster variation method (CVM) to calculate the alloy phase diagram. The dependence of the interactions on the choice of configurations used to calculate them is examined.

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First Principles Calculation of Phase Stability of High Temperature Intermetallic Alloys

MRS Proceedings ◽

10.1557/proc-213-119 ◽

1990 ◽

Vol 213 ◽

Author(s):

J. Mikalopas ◽

P.A. Sterne ◽

M. Sluiter ◽

P.E.A. Turchi

Keyword(s):

First Principles ◽

Strong Dependence ◽

Cluster Variation Method ◽

First Principles Calculation ◽

Variation Method ◽

Many Body ◽

Coherent Phase Diagram ◽

Cluster Variation ◽

The Many ◽

Many Body Interactions

ABSTRACTOne way to calculate the coherent phase diagram of an alloy based on first principles methods is to compute the ground state total energy for various ordered configurations, from which many-body interactions can be calculated and employed in a thermodynamic model. If the Connolly and Williams method (CWM) is used to extract the many-body interactions from the calculated total energies, the resulting many-body interactions can exhibit a strong dependence on the choice of ordered configurations and multi-site clusters, and the accuracy and convergence of the CWM energy expansion is not assured. To overcome this difficulty, a successful systematic method for implementing the CWM is proposed. This approach is applied to a study of the fcc-based Ni-V and Pd-V substitutional alloys and these interaction parameters together with the cluster variation method (CVM) are used to calculate phase diagrams.

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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

Australian Journal of Physics ◽

10.1071/ph810061 ◽

1981 ◽

Vol 34 (1) ◽

pp. 61 ◽

Cited By ~ 2

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.

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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

Australian Journal of Physics ◽

10.1071/ph810075 ◽

1981 ◽

Vol 34 (1) ◽

pp. 75 ◽

Cited By ~ 1

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.

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