Absolute Instability of FCC Lattice of Rare-Gas Crystals under Pressure

Troitskaya, E. P.; Pilipenko, E. A.; Gorbenko, Ie. Ie.

doi:10.1134/s1063783419010281

Cited by 6 publications

(2 citation statements)

References 38 publications

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“…140 We showed recently that the fcc phase is stabilized by phonon dispersion at 0 K. 34 As phonon contributions play a lesser role at increased pressures, one can speculate that three-body and higher body contributions must be responsible for the phase change to hcp at higher pressures. 141 From a theoretical point of view, to simulate a phase transition with such small enthalpy differences remains a major challenge. If experimental data were fitted to many-body potentials, based for example on the embedded atom model, one can obtain more accurate results.…”

Section: ■ Methodsmentioning

confidence: 99%

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

2021

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Analytical formulas are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc, and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard-Jones and Ingham in 1924, Corner in 1939, and Wallace in 1965. The formulas are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulas give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.

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Section: ■ Methodsmentioning

confidence: 99%

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

2021

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“…136 We showed recently that the fcc phase is stabilized by phonon dispersion at 0 K. 32 As phonon contributions play a lesser role at increased pressures, one can speculate that threeand higher body contributions must be responsible for the phase change to hcp at higher pressures. 137 From a theoretical point of view, to simulate a phase transition with such small enthalpy differences remains a major challenge. If experimental data fitted to many-body potentials, based for example on the embedded atom model, one can obtain more accurate results.…”

Section: The Equation Of State For Solid Heliummentioning

confidence: 99%

The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

Schwerdtfeger,

Burrows,

Smits

2020

Preprint

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Analytical formulae are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc and fcc) and for the hexagonal closepacked structure. This extends the work done by Lennard Jones and Ingham in 1924, Corner in 1939 and Wallace in 1965. The formulae are based on the description of twobody energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques.We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulae give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.

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Zero-Point Energy of Compressed Rare-Gas Crystals in the Model of Deformable Atoms

Gorbenko

Pilipenko

Вербенко

et al. 2023

Springer Proceedings in Materials

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Absolute Instability of FCC Lattice of Rare-Gas Crystals under Pressure

Cited by 6 publications

References 38 publications

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

Zero-Point Energy of Compressed Rare-Gas Crystals in the Model of Deformable Atoms

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