Ordering Conditions. I. For Alloys Represented by Generalized Ising Models

Philhours, Joel; Hall, George L.

doi:10.1103/physrev.163.460

Cited by 11 publications

(2 citation statements)

References 6 publications

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“…Philhours and Hall [17] have suggested, and Clapp and Moss [7] have formally shown that a sufficient (but not necessary) condition for a stable ground state is that the wave vector of concentration waves corresponding to an ordered phase lie in the positions of the minima of the Fourier transform of the pair energy function…”

Section: The Krivoglatz-clapp-moss Analysismentioning

confidence: 99%

Study of phase stability of MnCr using the augmented space recursion based orbital peeling technique

Banerjee

Mookerjee

2009

Physica B: Condensed Matter

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In an earlier communication we have developed a recursion based approach to the study of phase stability and transition of binary alloys [1]. We had combined the recursion method introduced by Haydock, Heine and Kelly[2] and the our augmented space approach[3] with the orbital peeling technique proposed by Burke [4] to determine the small energy differences involved in the discussion of phase stability. We extend that methodology for the study of MnCr alloys.

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Section: The Krivoglatz-clapp-moss Analysismentioning

confidence: 99%

Study of phase stability of MnCr using the augmented space recursion based orbital peeling technique

Banerjee

Mookerjee

2009

Physica B: Condensed Matter

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“…which is the necessary condition of stability (or metastability) of the disordered state of the alloy [28]. Notice that the boundary of the interval of the values of µ that satisfy the condition (4.1) is characterized by a singular behaviour of the quantity α R= = N −1 q α q as a function of µ, due to the vanishing (under the change of sign) of the quantity α −1 k for the definite wave vectors at a value of µ corresponding to the boundary.…”

Section: Solution Of the Equation (17)mentioning

confidence: 99%

Anaytical methods for calculation of the short-range order in alloys: II. Numerical accuracy study

Chepulskii

Bugaev

1998

J. Phys.: Condens. Matter

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The numerical accuracy of the analytical approximations elaborated in part I and of a variety of other approximations advanced to date is examined, accepting the data on the short-range order parameters obtained by the Monte Carlo method as a standard. The approximations exhibiting the most promise for description of actual alloys and other lattice systems (for instance, interstitial alloys, semiconductors and magnetics) including those with a long-range character of atomic interactions are revealed. It is stated that, in the framework of the lattice gas model within a modified thermodynamic perturbation theory, the choice of the inverse effective number of atoms interacting with one fixed atom as a small parameter of the cumulant expansion along with taking account of the contributions from only linked irreducible diagrams ensures the fastest convergence of expansion. It is demonstrated that the use of the grand canonical ensemble yields the highest numerical accuracy in the statistical-thermodynamic description within the framework of all approximations elaborated in part I.

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Order-disorder transition and stability of ordered state

Козлов¹

1976

Soviet Physics Journal

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Ordering Conditions. I. For Alloys Represented by Generalized Ising Models

Cited by 11 publications

References 6 publications

Study of phase stability of MnCr using the augmented space recursion based orbital peeling technique

Study of phase stability of MnCr using the augmented space recursion based orbital peeling technique

Anaytical methods for calculation of the short-range order in alloys: II. Numerical accuracy study

Order-disorder transition and stability of ordered state

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