Thermodynamic self-consistency issues related to the Cluster Variation Method: The case of the BCC Cr–Fe (Chromium–Iron) system

Inden, Gerhard; Schön, Cláudio Geraldo

doi:10.1016/j.calphad.2008.09.012

Cited by 7 publications

(5 citation statements)

References 55 publications

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“…36 Mixed models, including chemical and magnetic interactions, have been proposed. 30,[37][38][39] The Ising model by Ackland, with magnetic moments of constant amplitude, reproduces some key features of the Fe-Cr alloys. The magnetic cluster expansion of Lavrentiev et al 38,39 is able to reproduce the ab initio mixing energies with much fewer interactions than a purely chemical CE and it can take into account the variation of the magnetic moments with the concentration, but its phase diagram has never been calculated in the α-α region.…”

Section: Introductionmentioning

confidence: 92%

“…[30][31][32] However, to be able to reproduce the ab initio mixing energies of Fe-Cr, a purely chemical CE (i.e., that does not take explicitly into account the magnetic moments) requires a large set of many-body interactions. 31,32 The difficulty of obtaining a small set of effective interactions was also reported by authors using a screened generalized perturbation method.…”

Section: Introductionmentioning

confidence: 99%

“…Cluster expansion (CE) techniques, based on a rigid lattice approximation with N -body concentrationindependent interactions, have been proposed to model the thermodynamics of Fe-Cr alloys [30][31][32] . However, to be able to reproduce the ab initio mixing energies of Fe-Cr, a purely chemical CE (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The screen generalized perturbation model has been used to show how the effective cluster interactions depend on the magnetic state of the alloy and therefore on the temperature 33 and the composition 36 . Mixed models including chemical and magnetic interactions have been proposed 30,[37][38][39] . The Ising model by Ackland, with magnetic moments of constant amplitude, reproduces some key features of the Fe-Cr alloys.…”

Section: Introductionmentioning

confidence: 99%

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Simple concentration-dependent pair interaction model for large-scale simulations of Fe-Cr alloys

Levesque

Martínez²,

Fu³

et al. 2011

Phys. Rev. B

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International audienceThis work is motivated by the need for large-scale simulations to extract physical information on the iron-chromium system that is a binary model alloy for ferritic steels used or proposed in many nuclear applications. From first-principles calculations and the experimental critical temperature we build a new energetic rigid lattice model based on pair interactions with concentration and temperature dependence. Density functional theory calculations in both norm-conserving and projector augmented-wave approaches have been performed. A thorough comparison of these two different ab initio techniques leads to a robust parametrization of the Fe-Cr Hamiltonian. Mean-field approximations and Monte Carlo calculations are then used to account for temperature effects. The predictions of the model are in agreement with the most recent phase diagram at all temperatures and compositions. The solubility of Cr in Fe below 700 K remains in the range of about 6 to 12%. It reproduces the transition between the ordering and demixing tendency and the spinodal decomposition limits are also in agreement with the values given in the literature

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simple concentration-dependent pair interaction model for large-scale simulations of Fe-Cr alloys

Levesque

Martínez²,

Fu³

et al. 2011

Phys. Rev. B

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show abstract

“…[28]) and, as a consequence, the transition temperatures and phase boundary compositions may differ significantly from the experimental data. The disagreement can be attributed either to the fact that we ignore relevant thermodynamic degrees of freedom [29] and the different approximations involved in our calculations (for example, contributions to the free energy originated from magnetic and vibrational entropy were not taken into account), or to a lack of convergence of the cluster expansion [30]. These approximations are necessary due to the complexity of the system under study.…”

Section: Cluster Variation Methods (Cvm) Calculationsmentioning

confidence: 99%