Statistical Thermodynamics and Model Calculations

2010

Mater. Trans.

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Detailed analyses of the free energy behavior near the order-disorder transition temperature on a simple cubic lattice are attempted by cluster variation method (CVM). The entropy is formulated within a cubic approximation of the CVM and two kinds of nearest neighbor pair interaction energies are assumed in the internal energy; one is independent of an atomic distance, r, and the other depends on r through LennardJones type pair potential. In both cases, it is found that the order of the transition is of second order.

Section: Free Energymentioning

confidence: 69%

Order of Phase Transition on a Simple Cubic Lattice Determined by Cluster Variation Method

Kiyokane

2010

Mater. Trans.

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“…[3,4] Recently, the author and his coworkers have performed first-principles calculations of L1 0 -disorder phase boundary in a series of Fe-based alloys including Fe-Ni, Fe-Pd and Fe-Pt systems. [5][6][7][8] And it has been demonstrated that the L1 0 -disorder transition temperatures were obtained with very high accuracy for Fe-Pd and Fe-Pt systems. For Fe-Ni system, the first-principles calculations revealed [9] the existence of an L1 0 ordered phase although this phase has been missing in the conventional phase diagram.…”

Section: Introductionmentioning

confidence: 99%

“…The lattice-vibration effects are evaluated based on the Debye-Grüneisen theory within the quasi-harmonic approximation. [10] The procedure of calculating the vibrational contributions has been amply demonstrated in previous articles [5][6][7][8][9]11,12] and the reader interested in the procedure should consult them. The binding energy curve which is equivalent to the heat of formation curve for each phase n provides with the bulk modulus, Debye temperature and Grüneisen constant, and based on this information, vibrational energy and entropy are derived in a straightforward manner.…”

Section: Phase Equilibria Calculationsmentioning

confidence: 99%

First-Principles Calculations of Spinodal Ordering Temperature and Diffuse Intensity Scattering Spectrum for Fe-Pt System

J. Phase Equilib. Diffus.

2011

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First-principles calculations are performed to derive a L1 0 -disorder phase diagram, spinodal ordering temperature and short-range-order diffuse-intensity spectrum for the Fe-Pt system. L1 0 -disorder transition is confirmed to be of the first order by both the temperature dependence of the long-range-order parameter and the large separation between the transition temperature and spinodal ordering temperature. Short-range-order diffuse-intensity maximum appears at AE100ae which is intensified as the spinodal-ordering temperature is approached. The consistency among all these results supports the reliability of the description of the cluster variation free energy used for this study.

“…In fact, it has been amply demonstrated 15) that the cluster probabilities x p i and y pq,k ij are related to point and pair correlation functions f² p 1 g and f² pq;k 2 g through…”

Section: Free Energy Modelmentioning

confidence: 99%

Analysis of Dislocation Core Structure in B2 Ordered Phase by Cluster Variation Method

Yamada

2012

Mater. Trans.

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Theoretical framework of the Cluster Variation Method (CVM) is extended in two directions. One is the construction of a supercell in which the basic clusters are aligned in two dimensional directions. The other one is the introduction of the atomic displacement in the flexible lattice. These extensions of the conventional CVM enable us to calculate a core structure of two parallel superpartial dislocations in B2 ordered phase at finite temperatures. It is shown that a large stacking fault is formed inside the two superpartial dislocations at lower temperatures, while the stacking fault appears outside the superpartial dislocations at higher temperatures.