Quadrupole deformation of electron shells in the lattice dynamics of compressed rare-gas crystals

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

doi:10.1134/s1063783412060340

Cited by 12 publications

(6 citation statements)

References 27 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%

“…The quadrupole interaction parameters V q , T and the dimensionless polarizability b have the following form :

V_{q} = \frac{b {(2 W - U)}^{2}}{1 + 0.32673 \cdot b}; T = \frac{8 b W^{2}}{1 - 0.0661 \cdot b}; b = \frac{2 β_{44}}{a^{5}} .

Here, W , U are expressed in terms of the only non‐zero component of the tensor

D_{α β}^{l}

(9)

U = \frac{1}{e} [{\frac{a}{\sqrt{2}} \frac{d D_{x x} (r)}{d r}|}_{r_{0}} - D_{x x} (r_{0})]; W = \frac{1}{e} [\frac{a}{\sqrt{2}} {\frac{d D_{x x} (r)}{d r}|}_{r_{0}} + D_{x x} (r_{0})] .

…”

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%

“…The quadrupole interaction parameters V q , T and the dimensionless polarizability b have the following form :

V_{q} = \frac{b {(2 W - U)}^{2}}{1 + 0.32673 \cdot b}; T = \frac{8 b W^{2}}{1 - 0.0661 \cdot b}; b = \frac{2 β_{44}}{a^{5}} .

Here, W , U are expressed in terms of the only non‐zero component of the tensor

D_{α β}^{l}

(9)

U = \frac{1}{e} [{\frac{a}{\sqrt{2}} \frac{d D_{x x} (r)}{d r}|}_{r_{0}} - D_{x x} (r_{0})]; W = \frac{1}{e} [\frac{a}{\sqrt{2}} {\frac{d D_{x x} (r)}{d r}|}_{r_{0}} + D_{x x} (r_{0})] .

…”

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

confidence: 99%

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%

“…The general approach (see [30] and references therein) to the construction of the adiabatic potential U for the series Ne-Xe allows one to determine the most important interactions in these rare gases, i.e., the structure of interatomic potentials. The justified fairly exact form of the adiabatic potential obtained previously under the assumption of the pair inter atomic interaction [36,37,46] was generalized to the case of n atomic interactions [29].…”

Section: Calculation Of the Phonon Frequencies With The Inclusion Of mentioning

confidence: 99%

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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 many-body interaction and elastic properties of rare-gas crystals under pressure

Varyukhin

Troitskaya

Chabanenko

et al. 2013

Phys. Status Solidi B

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The short-range many-body forces induced by the overlap of electron shells of atoms have been investigated. The nonorthogonality of atomic orbitals of the nearest-neighbor atoms of a crystal leads to the appearance of terms in the potential energy, which depend on the coordinates of three, four, and more nearest-neighbor atoms. An expression has been obtained for the energy of the electron subsystem of the crystal in the Hartree-Fock approximation in the basis set of atomic orbitals exactly orthogonalized at different crystal sites. The behavior of the contributions from two-body and three-body interactions to the crystal energy under compression has been analyzed. The short-range three-body potential has been calculated from first principles and proposed in the simple form. The three-body forces, obtained change the behavior of the dispersion curves for all wave vectors, in particular, thus violating the Cauchy relation. The theoretical and experimental deviations from the Cauchy relation for Ne and Ar are in good agreement under pressure.ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Rare-gas crystals (RGC) are the simplest molecular crystals; therefore, they are often used as model objects to investigate the van der Waals forces. Particular interest expressed in RGC is associated with their unique properties exhibited at high pressures, which make it possible to use these materials as pressure-transmitting media in diamond anvil cells (DAC) [1].The adiabatic potential U, which is required to construct the dynamics of crystal lattices, can be calculated from first principles or approximated by the well-known function of the distance, i.e., by using the method of interatomic model (empirical) potentials. As new information concerning the phonon spectra and elastic properties of the crystals becomes available, the theory can be refined in the following ways: (i) by including the interaction of more distant neighbors [2,3], (ii) by introducing the long-range three-body interaction [4] and short-range three-body interaction [5][6][7][8][9][10], and also (iii) by taking into account the dipole deformation [11][12][13][14] and quadrupole deformation [15,16] of the atoms.Many physical properties of RGC at low pressures are adequately described using the ab initio or empirical

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Quadrupole deformation of electron shells in the lattice dynamics of compressed rare-gas crystals

Cited by 12 publications

References 27 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 many-body interaction and elastic properties of rare-gas crystals under pressure

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