Elastic properties of compressed crystalline Ne in the model of deformable atoms

Troitskaya, E. P.; Chabanenko, V. V.; Zhikharev, I. V.; Gorbenko, Ie. Ie.; Pilipenko, E. A.

doi:10.1134/s1063783413020340

Cited by 11 publications

(7 citation statements)

References 25 publications

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“…This analysis is valid for all the rare‐gas crystals at any pressure. However, the contributions of the elastic moduli

B_{i j}^{t}

and

B_{i j}^{q}

increase in the series Ne, Ar, Kr, and Xe . The total contributions of the three‐body and quadrupole interactions to the elastic moduli B ij for Kr and Xe are most clearly shown in Figs.…”

Section: Calculation Of the Elastic Properties Of Rare‐gas Crystals Umentioning

confidence: 93%

“…In accordance with Ref. , we set

V_{sr} \approx A_{i} \frac{S^{2} (r^{l l^{'}})}{|r^{l l^{'}}|},

where | r ll ′ | is the distance between atoms l and l ′ (for the nearest neighbors,

|r^{l l^{'}}| = a \sqrt{2}

), A i is the weakly pressure‐dependent coefficient .…”

Section: Birch Elastic Moduli and Cauchy Relation In The Model Of Defmentioning

confidence: 99%

“…We found the functional relationship for the quadrupole parameter V q but we have so far failed to determine its absolute value. Consequently, as in the case of Ne in further calculations we propose to use the initial value of the parameter

V_{q}^{0} (p \approx 0)

, which was obtained taking into account the experimental value

δ_{\exp}^{0}

V_{q}^{\exp} = \frac{3}{13} \frac{2 a^{4}}{e^{2}} (δ_{\exp}^{0} - δ_{t}), V_{q}^{0} = V_{q}^{\exp} .

…”

Section: Birch Elastic Moduli and Cauchy Relation In The Model Of Defmentioning

confidence: 99%

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Adiabatic potential and elastic properties of compressed rare‐gas crystals in the model of deformable atoms

Varyukhin

Troitskaya

Gorbenko

et al. 2014

Physica Status Solidi (b)

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The quantum-mechanical model of deformable and polarizable atoms has been developed for the purpose of investigating the elastic properties of crystals of rare gases Ne, Kr, and Xe over a wide range of pressures. The inclusion of the deformable electron shells in the analysis is particularly important for the shear moduli of heavy rare-gas crystals. It has been shown that the observed deviation from the Cauchy relation d(p) for Kr and Xe cannot be adequately reproduced when considering only the many-body interaction. The individual dependence d(p) for each of the rare-gas crystals is the result of two competitive interactions, namely, the many-body and electron-phonon interactions, which manifests itself in a quadrupole deformation of the electron shells of the atoms due to displacements of the nuclei. The contributions of these interactions in Ne, Kr, and Xe are compensated with good accuracy, which provides a weakly pressure-dependent value for the parameter d. The ab initio calculated dependences d(p) for the entire series Ne-Xe are in good agreement with the experiment.

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“…This analysis is valid for all the rare‐gas crystals at any pressure. However, the contributions of the elastic moduli

B_{i j}^{t}

and

B_{i j}^{q}

increase in the series Ne, Ar, Kr, and Xe . The total contributions of the three‐body and quadrupole interactions to the elastic moduli B ij for Kr and Xe are most clearly shown in Figs.…”

Section: Calculation Of the Elastic Properties Of Rare‐gas Crystals Umentioning

confidence: 93%

“…In accordance with Ref. , we set

V_{sr} \approx A_{i} \frac{S^{2} (r^{l l^{'}})}{|r^{l l^{'}}|},

where | r ll ′ | is the distance between atoms l and l ′ (for the nearest neighbors,

|r^{l l^{'}}| = a \sqrt{2}

), A i is the weakly pressure‐dependent coefficient .…”

Section: Birch Elastic Moduli and Cauchy Relation In The Model Of Defmentioning

confidence: 99%

V_{q}^{0} (p \approx 0)

, which was obtained taking into account the experimental value

δ_{\exp}^{0}

V_{q}^{\exp} = \frac{3}{13} \frac{2 a^{4}}{e^{2}} (δ_{\exp}^{0} - δ_{t}), V_{q}^{0} = V_{q}^{\exp} .

…”

Section: Birch Elastic Moduli and Cauchy Relation In The Model Of Defmentioning

confidence: 99%

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Adiabatic potential and elastic properties of compressed rare‐gas crystals in the model of deformable atoms

Varyukhin

Troitskaya

Gorbenko

et al. 2014

Physica Status Solidi (b)

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“…For example, for the wave vector k directed along the [001] direction, their contributions to the frequen cies and , according to formula (29) [34], are equal respectively to (29) The signs of t 1 and t 3 can be estimated using the Schwarz inequality. By introducing the vectors X, Y, and Z with the components (30) we find (31) For the quantity (32) the sign remains unknown. However, using the geo metrical representation, we obtain (33) and, since the geometric mean does not exceed the arithmetic mean, we have Thus, in the considered example of the frequencies Ω L and Ω T for the [001] direction, the three body forces act in the same direction as the electronphonon forces, thus decreasing the frequencies of short wavelength phonons.…”

Section: Three Body Forces Generated By the Mutual Deformation Of Thementioning

confidence: 99%

“…In [29][30][31][32], it was shown that the inclusion of the many body interaction and the deformation of the electron shells of atoms in the analysis is important for the adequate description of the elastic properties of rare gas crystals under pressure.…”

Section: Introductionmentioning

confidence: 99%

Ab initio theory of many-body interaction and phonon frequencies of rare-gas crystals under pressure in the model of deformable atoms

et al. 2015

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Ab initio calculations of phonon frequencies of compressed rare gas crystals have been performed taking into account the many body interaction in the model of deformable atoms. In the short range repul sive potential, along with the previously considered three body interaction associated with the overlap of the electron shells of atoms, the three body forces generated by the mutual deformation of the electron shells of the nearest neighbor atoms have been investigated in the dipole approximation. The relevant forces make no contribution to the elastic moduli but affect the equation for lattice vibrations. At high compressions, the soft ening of the longitudinal mode at the points L and X is observed for all the rare gas crystals, whereas the trans verse mode T 1 is softened in the direction Σ and at the point L for solid xenon. This effect is enhanced by the three body forces. There is a good agreement between the theoretical phonon frequencies and the experi mental values at zero pressure.

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Ab Initio Theory of the Equations of State for Light Rare-Gas Crystals

Gorbenko

Troitskaya

Pilipenko

et al. 2019

Springer Proceedings in Physics

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Elastic properties of compressed crystalline Ne in the model of deformable atoms

Cited by 11 publications

References 25 publications

Adiabatic potential and elastic properties of compressed rare‐gas crystals in the model of deformable atoms

Adiabatic potential and elastic properties of compressed rare‐gas crystals in the model of deformable atoms

Ab initio theory of many-body interaction and phonon frequencies of rare-gas crystals under pressure in the model of deformable atoms

Ab Initio Theory of the Equations of State for Light Rare-Gas Crystals

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