Derivation of equations of state for ideal crystals of simple structure

Кривцов, А. М.; Kuzkin, Vitaly A.

doi:10.3103/s002565441103006x

Cited by 41 publications

(41 citation statements)

References 6 publications

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“…Formulas (2) and (3) imply that the thermal pressure and thermal potential energy depend on vector A. Kinetic energy is represented in a similar form using Virial transformation (see, e.g., paper [20]):…”

Section: Micro-and Macro Parameters Of the Modelmentioning

confidence: 99%

“…3, 4, and 5). Three dimensional crystals with pair interactions demonstrate opposite behavior [20]. In three dimensions Mie-Grüneisen equation overestimates the pressure.…”

Section: Nonmonotonic Thermal Expansion Large Deformations Formulamentioning

confidence: 99%

“…However, the problem of accounting for anharmonicity is still far from being solved. An alternative approach is based on series expansion of pressure and thermal energy with respect to small parameter characterizing thermal motion [19,18,20]. The approach was successfully used in one, two, and three dimensions for derivation of equations of state describing thermal expansion in perfect crystals.…”

Section: Introductionmentioning

confidence: 99%

“…The approach was successfully used in one, two, and three dimensions for derivation of equations of state describing thermal expansion in perfect crystals. The expression for Grüneisen parameter of close-packed crystals with pair interactions was derived [18,20]. An approximate necessary and sufficient condition for a pair potential that give rise to NTE was formulated [21].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear positive/negative thermal expansion and equations of state of a chain with longitudinal and transverse vibrations

Kuzkin

Кривцов

2015

Physica Status Solidi (b)

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Thermal expansion of a classical chain with pair interactions performing longitudinal and transverse vibrations is investigated. Corresponding equations of state are derived analytically using series expansions of pressure and thermal energy with respect to deformations of the bonds caused by thermal motion. In the first approximation the equation of state has Mie–Grüneisen form. The dependence of Grüneisen parameter on deformation of the chain is obtained. For Lennard‐Jones‐like potential Grüneisen parameter varies with deformation from minus infinity (at zero stretching) to plus infinity (at the breakage point). Necessary and sufficient condition for negative thermal expansion at low thermal energies is formulated. Using this condition the potential giving rise to negative thermal expansion in the given range of deformations can be designed. It is shown that at small deformations and finite thermal energies Mie–Grüneisen equation of state strongly overestimates the absolute value of pressure. More accurate nonlinear equation of state is derived for this case. The equation implies that thermal pressure in the unstretched chain is proportional to square root of thermal energy. In the vicinity of the deformation, corresponding to zero Grüneisen parameter, the chain demonstrates negative thermal expansion at low temperatures and positive thermal expansion at higher temperatures. This phenomenon is qualitatively described by the nonlinear equation of state derived in the present paper. The theoretical findings are supported by the results of molecular dynamics simulations.

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Section: Micro-and Macro Parameters Of the Modelmentioning

confidence: 99%

“…3, 4, and 5). Three dimensional crystals with pair interactions demonstrate opposite behavior [20]. In three dimensions Mie-Grüneisen equation overestimates the pressure.…”

Section: Nonmonotonic Thermal Expansion Large Deformations Formulamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear positive/negative thermal expansion and equations of state of a chain with longitudinal and transverse vibrations

Kuzkin

Кривцов

2015

Physica Status Solidi (b)

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“…An approximate expression for Grüneisen parameter of undeformed simple close-packed lattice with pair force interactions in N -dimensional case is [11,12]: Unfortunately, to our knowledge, it is not present in literature.…”

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confidence: 98%

Comment on “Negative Thermal Expansion in Single-Component Systems with Isotropic Interactions”

Kuzkin

2014

J. Phys. Chem. A

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Vanishing‐Harmonicity and Phase‐Change Materials

Gaspard

2021

Physica Rapid Research Ltrs

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Phase‐change material (PCMs) store data using the contrast (electrical or optical) between two phases: a conductive crystalline phase and a weakly conductive amorphous phase. Most PCMs have a distorted octahedral structure. The contrast comes mainly from the electronic structure. In PCMs, a spontaneous symmetry breaking mechanism, the Peierls distortion, transforms the metallic crystalline structure into a lower‐density semiconducting structure. In a simple tight‐binding model of the covalent bond, the parameters that control this distortion, characterized by a parameter η, are analyzed. The effective interatomic potential E(η) is developed in a Landau‐type series in η: E(η) = E0 + E2η2 + E4η4. The PCMs with the largest contrast are those for which the effective potential E(η) of the crystalline phase has a disappearing harmonic contribution (E2=0) and a vanishing electronic gap. This is called as an “incipient Peierls distortion.” It coincides with the so‐called “incipient metal”. The hardness of the repulsive potential and the number of electrons per atom play an important role. The vibrational properties and the anomalous Grüneisen parameter, specific to PCMs, are also studied.

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Derivation of equations of state for ideal crystals of simple structure

Cited by 41 publications

References 6 publications

Nonlinear positive/negative thermal expansion and equations of state of a chain with longitudinal and transverse vibrations

Nonlinear positive/negative thermal expansion and equations of state of a chain with longitudinal and transverse vibrations

Comment on “Negative Thermal Expansion in Single-Component Systems with Isotropic Interactions”

Vanishing‐Harmonicity and Phase‐Change Materials

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