Generalized cluster description of multicomponent systems

Sanchez, Juan M; Ducastelle, F.; Gratias, D.

doi:10.1016/0378-4371(84)90096-7

Cited by 1,688 publications

(1,309 citation statements)

References 21 publications

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“…Only Ga or Zn atoms occupy the cation sublattice, and N or O atoms occupy the anion sublattice. A cluster expansion (CE) [18][19] [20] model was constructed. Ising parameters σ i describe the i th site occupancy, with σ = 1 denoting Ga and N and σ = −1 denoting Zn and O.…”

Section: Methodsmentioning

confidence: 99%

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)_1−x(ZnO)_x

Liu¹,

Pedroza²,

Misch³

et al. 2014

J. Phys.: Condens. Matter

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Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN) 1−x (ZnO) Abstract. We present total energy and force calculations on the (GaN) 1−x (ZnO) x alloy. Site-occupancy configurations are generated by Monte Carlo (MC) simulations, based on a cluster expansion (CE) model proposed in a previous study. Surprisingly large local atomic coordinate relaxations are found by density-functional calculations using a 432-atom periodic supercell, for three representative configurations at x = 0.5. These are used to generate bond length distributions. The configurationally averaged composition-and temperature-dependent short-range order (SRO) parameters of the alloys are discussed. Entropy is approximated in terms of pair distribution statistics and thus related to SRO parameters. This approximate entropy is compared with accurate numerical values from MC. An empirical model for the dependence of bond length on local chemical environments is proposed.

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Section: Methodsmentioning

confidence: 99%

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)_1−x(ZnO)_x

Liu¹,

Pedroza²,

Misch³

et al. 2014

J. Phys.: Condens. Matter

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“…19 Here, for a system with two coupled lattices of nonexchangeable configurations, we expand the formation energy as …”

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confidence: 99%

Configurational Thermodynamics of Alloyed Nanoparticles with Adsorbates

2014

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Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core-shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having Ocoverage up to a monolayer, we fully detail the core-shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design. ABSTRACT: Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core−shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having O-coverage up to a monolayer, we fully detail the core−shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design.

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“…At somewhat higher temperatures where entropic contributions to the free energy become important, methods have been available for some time for calculating the configurational entropy of alloys. [12][13][14][15][16] For pure elements, the entropy S may be written as a sum of contributions from electrons and phonons, S el and S ph , provided the electrons and phonons do not interact. The entropy of electronic excitations is often calculated from the density of states near the Fermi level, obtained from electronic structure calculations.…”

Section: Introductionmentioning

confidence: 99%

Neutron scattering measurements of phonons in nickel at elevated temperatures

et al. 2007

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Measurements of elastic and inelastic neutron scatterings from elemental nickel were made at 10, 300, 575, 875, and 1275 K. The phonon densities of states ͑DOSs͒ were calculated from the inelastic scattering and were fit with Born-von Kármán models of the lattice dynamics. With ancillary data on thermal expansion and elastic moduli, we found a small, negative anharmonic contribution to the phonon entropy at high temperature. We used this to place bounds on the magnetic entropy of nickel. A significant broadening of the phonon DOS at elevated temperatures, another indication of anharmonicity, was also measured and quantified.

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Generalized cluster description of multicomponent systems

Cited by 1,688 publications

References 21 publications

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)_1−x(ZnO)_x

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)_1−x(ZnO)_x

Configurational Thermodynamics of Alloyed Nanoparticles with Adsorbates

Neutron scattering measurements of phonons in nickel at elevated temperatures

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Generalized cluster description of multicomponent systems

Cited by 1,688 publications

References 21 publications

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)1−x(ZnO)x

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)1−x(ZnO)x

Configurational Thermodynamics of Alloyed Nanoparticles with Adsorbates

Neutron scattering measurements of phonons in nickel at elevated temperatures

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Product

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Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)_1−x(ZnO)_x

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)_1−x(ZnO)_x