Deformation Of Electron Shells Research Articles

Удельная теплоемкость и температура Дебая сжатого кристаллического неона в модели деформируемых атомов

The thermodynamic properties of compressed neon crystal has been theoretically investigated within the ab initio approach taking into account the many-body interaction in the model of deformable atoms. In the short-range repulsive potential, along with the three-body interaction associated with the overlap of the electron shells of atoms, deformation of electron shells of dipole-type atoms is taken into account in the pair and three-particle approximations. The specific heat capacities and the Debye temperature in a wide pressure and temperature range have been calculated using the dynamic matrix constructed with the ab initio short-range repulsive potential and integration over the mean value points of the Chadi–Kohen method. It is shown that the contributions of three-body forces associated with both the overlap of the electron shells of atoms and the deformation of the electron shells increase the value of specific heat of compressed neon face-centered cubic crystals even at zero pressure. The temperature dependences are obtained in good agreement with the available experiment data and calculation results obtained by other researchers.

Energy of Phonons and Zero-Point Vibrations in Compressed Rare-Gas Crystals

A dynamic matrix of rare-gas crystals is constructed within the model of deformable and polarizable atoms based on the nonempirical short-range repulsion potential taking into account the three-body interaction and deformation of electron shells of dipole-type atoms within the pair and three-body approximations. Ab initio calculations of the phonon energy for compressed rare-gas crystals are performed at two and ten mean-value points of the Chadi–Kohen method in a wide pressure range. It is shown that the contribution of three-body forces to the phonon frequencies due to overlap of electron shells of neighboring atoms is small as compared to the pair interaction even at a high pressure and most pronounced for Xe. The contributions of the deformation of electron shells within the pair and three-body approximations differ for different mean-value points and increase with an increase in pressure. The zero-point energies calculated by the Chadi–Kohen method for crystals of the Ne–Xe series are compared with the known experimental data at p = 0 and calculation results obtained by other researchers.

Абсолютная неустойчивость ГЦК-решетки кристаллов инертных газов под давлением

AbstractOn the basis of ab initio calculations of the phonon frequencies of compressed rare-gas crystals in the model of deformable and polarizable atoms, dynamic instability of the fcc lattice of these crystals is studied. In addition to the earlier-considered three-body interaction, which is associated with the overlapping of the electron shells of atoms, the short-range potential includes three-body forces caused by the mutual deformation of the electron shells of neighboring atoms. It is shown that the allowance for the deformation of the dipole-type electron shells of atoms in the pair and three-body approximations leads to softening of the critical vibrations and absolute instability of the fcc lattice at pressures higher than the critical values, p > p _ c . For light crystals of Ne and Ar under compressions of 0.76 ( p _ c = 422 GPa) and 0.71 ( p _ c = 405 GPa), respectively, the softening of the longitudinal mode is observed at the boundary of the Brillouin zone at the point L ; for heavy crystals of Kr and Xe under compressions of 0.686 ( p _ c = 240 GPa) and 0.605 ( p _ c = 88 GPa), the transverse mode T _1 is softened in the direction Σ. The behavior of second-order Fuchs elastic moduli of compressed rare-gas crystals is discussed.

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

On the basis of ab initio calculations of the phonon frequencies of compressed rare-gas crystals in the model of deformable and polarizable atoms, dynamic instability of the fcc lattice of these crystals is studied. In addition to the earlier-considered three-body interaction, which is associated with the overlapping of the electron shells of atoms, the short-range potential includes three-body forces caused by the mutual deformation of the electron shells of neighboring atoms. It is shown that the allowance for the deformation of the dipole-type electron shells of atoms in the pair and three-body approximations leads to softening of the critical vibrations and absolute instability of the fcc lattice at pressures higher than the critical values, p > pc. For light crystals of Ne and Ar under compressions of 0.76 (pc = 422 GPa) and 0.71 (pc = 405 GPa), respectively, the softening of the longitudinal mode is observed at the boundary of the Brillouin zone at the point L; for heavy crystals of Kr and Xe under compressions of 0.686 (pc = 240 GPa) and 0.605 (pc = 88 GPa), the transverse mode T1 is softened in the direction Σ. The behavior of second-order Fuchs elastic moduli of compressed rare-gas crystals is discussed.

Many-body interaction and deformation of the atomic electron shells in the lattice dynamics of compressed atomic cryocrystals

The lattice dynamics of compressed atomic cryocrystals are based on ab initio quantum-mechanical theories of deformable and polarizable atoms (Tolpygo model), while taking into account the many-body interaction. The parameters of the three-particle interaction and deformation of the atomic electron shells, which are calculated in terms of the overlap integrals of atomic orbitals and their derivatives, have the same order of magnitude thus demonstrating that they must be considered in tandem. Accounting for the deformation effects of the electron shells in the dipole approximation when calculating phonon frequencies leads to a “softening” of the longitudinal modes at points L and X, for an entire series of Ne-Xe crystals, and of the transverse modes in the directions Σ and Λ for Xe, under high compression. It is shown that it impossible to adequately reproduce the observed deviation from the Cauchi relation δ(p) for compressed atomic cryocrystals, without accounting for the deformation of electron shells of atoms in a quadrupole approximation. The inputs from a three-particle and quadrupole interaction for Ne, Kr, and Xe crystals are mutually compensated, which provides a weak dependence on pressure for δ(p). We found a good agreement between the calculated phonon frequencies, Birch and Fuchs elastic moduli, the deviation from the Cauchi relation for the total number of Ne-Xe crystals in a wide range of pressures, and existing experiments.

Elastic properties of compressed cryocrystals in a deformed atom model

A model with deformed atom shells was built to investigate the elastic properties of rare-gas Ne and Kr crystals under high pressure. It is shown that the observed deviation from the Cauchy relation δ cannot be adequately reproduced when taking into account only the many-body interaction. The individual pressure dependence of δ is the result of competition of the many-body interaction and the quadrupole interaction associated with the quadrupole-type deformation of electron shells of the atoms during the displacement of the nuclei. Each kind of interaction makes a strongly pressure dependent contribution to δ. In the case of Ne and Kr, contributions of these interactions are compensated to a good precision, providing δ being almost constant against pressure.

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

The lattice dynamics of rare-gas crystals has been constructed taking into account the deformation of electron shells of the atoms of the dipole and quadrupole types, depending on the displacement of the nuclei. The obtained equations of lattice vibrations have been investigated in the long-wavelength approximation. The role played by the three-body interaction and the deformation of the electron shells in the violation of the Cauchy relation has been discussed. The calculated Birch elastic moduli for Xe and deviations from the Cauchy relation are in good agreement with the available experimental data over a wide range of pressures.

PRESSURE INDUCED PHASE TRANSITION (B3–B1) AND ELASTIC PROPERTIES OF II–VI ZnSe SEMICONDUCTORS

We evolve an effective interionic interaction potential (EIoIP) to investigate the pressure induced phase transitions from Zinc blende (B3) to Rocksalt (B1) structure in ZnSe semiconductor. The developed potential consists of the long-range Coulomb and three-body interactions (TBI) and the Hafemeister and Flygare type short-range (SR) overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The three-body interactions arise from the electron-shell deformation when the nearest-neighbor ions overlap and has been employed for detailed studies of pressure-induced phase-transition behavior of ZnSe semiconductors. Our calculated value of the phase transition pressure (Pt) is higher and the magnitude of the discontinuity in volume at the transition pressure is consistent with reported data. The variation of second-order elastic constants with pressure resembles that observed in some binary semiconductors. It is inferred that the vdW interaction is effective in obtaining the Debye temperature, Gruneisen parameter, thermal expansion coefficient and compressibility. It is argued that the model with TBI (model II) has yielded somewhat more realistic predictions of the phase-transition and high-pressure behavior as compared to usual two-body potentials (model I) based on phenomenological approach.

Theoretical analysis of phonon dynamical behaviour of Cesium Chloride at various temperatures

We have developed a new model to investigate the complete lattice dynamics of cesium chloride at 78 K and at room temperature (298 K). The new model, van der Waals three body force shell model (VTSM) incorporates the effect of van der Waals interactions and three-body interactions in the frame work of rigid shell model where short range interactions are effective up to the second neighbour. A good agreement has been obtained between theory and experiment for dependant properties also. Cesium halides have been given a keen interest to most of the workers in the field of lattice dynamics due to the paramount importance of such binary solids, as the nature and physical properties of such crystal reveals to an understanding of their vibrational, thermo-dynamical, elastic, optical, thermal and numerous physical properties. The availability of a lot of measured data on elastic constants (1-4), dielectric constants (5,7), phonon dispersion curves (6,7,8), Debye temperature variations (9-11), two phonon IR and Raman spectra (12-15), third and fourth order elastic constants and their pressure derivatives (16,17), for all of them (CsCl, CsBr, CsI) and their interpretations by means of theoretical models (18-25) with moderate success, has motivated the present author to the basic need for a lattice dynamical model for the satisfactory description of their interesting properties. Various experimental and theoretical workers have given evolution for the study of phonon behaviour of CsCl structure. The first and most important model considered the ions of the crystal to be rigid, undeformable and unpolarizable spherical particle is rigid ion model (RIM) of Kellermann (25) which could not interpret well the dynamical, optical and elastic properties. Further efforts have been put as deformation dipole model (DDM) of Karo and Hardy (19) and rigid shell model (RSM) of Dick and Overhauser (26) and Woods et al. (23) by two different groups of workers. The DDM allows only the redistribution of charges in deformed electron cloud while the shell model considers the relative displacement. Therefore both effects (deformation and displacement) are present in ionic crystals. A general way to remove this deficiency is to include the deformation of electron shells in the framework of RSM. The most prominent amongst them are breathing shell model (BSM) of Schroder (20), the deformable shell model (DSM) of Basu and Sengupta (21), three-body force shell model (TSM) of Verma and Singh (27) and further Singh et al. (1) used extended three-body-force shell model (ETSM) which is an amalgamation of RSM and DDM. It is emergent from the descriptions that the most realistic model for the lattice dynamics and statics of these crystals can be developed by introducing the effect of van der Waals interactions (VWI), and three body interactions (TBI) in the framework of RSM, where the short-range interactions have been considered up to the second neighbours. The development of such a lattice dynamical model is the chief aim of the present work. This model is known as van der Waals three body force shell model (VTSM). A formal description of VWI and three-body interactions in the framework of RSM has been described in section 2. The present model VTSM in a way as outline above has been applied to investigate the complete lattice dynamics of cesium halides (CsCl, CsBr, CsI). The motivation behind the choice of the present system of solids lies in the fact that they are characterized by high energy gap, some discrepancies in PDCs and Cauchy violations. The effect of TBI and VWI are quite significant and play a vital role in the description of lattice dynamics of cesium halides. The proposed investigations have been carried out by adopting a simple method to determine a consistent set of 14-parameters )

Polarization Effects in Superfluid 4He

A theory of thermoelectric phenomena in superfluid $^4He$ is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid $^4He$ generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.

Pressure-induced phase transition phenomena in NpSe and NpTe

A three-body interaction potential (TBIP) has been formulated by incorporating the effects of long-range coulomb interaction, three-body interaction and short-range repulsive interactions effective up to second neighbor ions. The three-body interactions arise from the electron-shell deformation when the nearest-neighbor overlaps. This TBIP has been employed for detailed studies of pressure-induced phase transition and high-pressure behavior of NpSe and NpTe. The model has yielded fairly good description of the cohesive energy, compressibility, molecular force constant, reststralhlen frequency and Debye temperature in case of these actinide monochalcogenides.

Lattice dynamics in light rare-gas crystals under pressure

The lattice dynamics of compressed neon and argon crystals has been theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly includes the deformation of electron shells. The energy of zero-point vibrations, mean-square displacements, and specific heat capacities of compressed neon and argon face-centered cubic crystals have been calculated in the harmonic approximation using the dynamic matrix constructed with the ab initio short-range repulsive potential and integration over the mean-value points in the Brillouin zone. The calculated temperature dependences of the specific heat capacity and the Debye temperature are in good agreement with the data available in the literature on the experiment at zero pressure. The role of zero-point vibrations in the thermodynamics of the entire series of rare-gas crystals and, in particular, in the validity of the Lindemann melting criterion has been analyzed.

Theoretical study of vibration spectra of sensitizing dyes for photoelectrical converters based on ruthenium(II) and iridium(III) complexes

Quantum-chemical method of the density functional theory was employed to calculate, with the use of a B3LYP hybrid exchange-correlation functional, the IR absorption and Raman spectra of [Ru(bpy)2(CN)2] and [Ir(bpy)2(CN)2]+ complexes. All the normal vibrational frequencies were analyzed and new assignments of a number of bands in the IR absorption and Raman spectra were made. The role of vibrational motions of metal atoms and ligands in the vibronic deformation of electron shells in the course of electron transfer was discussed. This was done using data on surface-enhanced Raman spectra of [Fe(bpy)2(CN)2] and [Ru(bpy)3]2+ complexes adsorbed on the surface of colloid silver.

Structural stability of TiO and TiN under high pressure

Abstract The high pressure phase transition and elastic behavior of Transition Metal Compounds (TiO and TiN) which crystallize in NaCl-structure have been investigated using the three body potential model (TBPM) approach. These interactions arise due to the electron-shell deformation of the overlapping ions in crystals. The TBP model consists of a long range Coulomb, three body interactions, and the short-range overlap repulsive forces operative up to the second neighboring ions. The authors of this paper estimated the values of the phase transition pressures, associated volume collapses, and elastic constants, all of which were found to be closer to available experimental data than other calculations. Thus, the TBPM approach promises to predict the phase transition pressure and pressure variations of elastic constants of Transition Metal compounds.

Structural study of Novel (superhard) material: NiO

We have investigated the pressure-induced phase transition of NiO and other structural properties using three-body potential approach. NiO undergoes phase transition from B1 (rocksalt) to B2 (CsCl) structure associated with a sudden collapse in volume showing first-order phase transition. A theoretical study of high pressure phase transition and elastic behaviour in transition metal compounds using a three-body potential caused by the electron shell deformation of the overlapping ion was carried out. The phase transition pressure and other properties predicted by our model is closer to the phase transition pressure predicted by Eto et al.

Phonons and electron-phonon interactions in rare-gas crystals at high pressures

The lattice dynamics of compressed rare-gas crystals is theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly allows for the deformation of electron shells. The deformation of the electron shells is associated with the retardation of the electron response and treated as a nonadiabaticity (the electron-phonon interaction). This approach and the ab initio short-range repulsive potentials are used to construct the dynamic matrix, which makes it possible to calculate the phonon frequencies and the electron-phonon interaction of crystals in the series Ne-Xe at any point of the Brillouin zone. The contributions of the long-range Coulomb and van der Waals forces to the dynamic matrix are the structure sums that depend only on the lattice type. The structure sums for the face-centered cubic lattice are calculated using the Ewald and Emersleben methods, as well as the direct summation over the vectors of the face-centered cubic lattice. The use of 20 spheres in the last case provides an accuracy of no less than four significant figures. An analysis of the role played by the phonon-electron interaction at five points of high symmetry in the Brillouin zone (X, L, U, K, W) at high pressures demonstrates that not only the longitudinal phonon modes (at the points X and L) but also the transverse phonon modes (at the points U, K, and W) are softened. The inclusion of the electron-phonon interaction at the point X improves agreement between the theoretical and experimental phonon frequencies for the argon crystal.

Phase transition in CeSe, EuSe and LaSe under high pressure

AbstractThe high pressure phase transition and elastic behavior of rare earth monoselenides (CeSe, EuSe and LaSe) which crystallize in a NaCl-structure have been investigated using the three body interaction potential (TBIP) approach. These interactions arise due to the electronshell deformation of the overlapping ions in crystals. The TBP model consists of a long range Coulomb, three body interactions and the short range overlap repulsive forces operative up to the second neighboring ions. The authors of this paper estimated the values of the phase transition pressure and the associated volume collapse to be closer than other calculations. Thus, the TBIP approach also promises to predict the phase transition pressure and pressure variations of elastic constants of lanthanide compounds.

Pressure dependence of elastic properties of ZnX (X = Se,S and Te): Role of charge transfer

An effective interaction potential (EIOP) is developed to invoke the pressure induced phase transition from zinc blende (B3) to rocksalt (B1) structure and anharmonic properties in ZnX (X = Se, S, Te) semiconductors. The effective interaction potential incorporates the long range Coulomb interaction, van der Waals interaction and short-range repulsive interaction up to second neighbour ions within the Hafemeister and Flygare approach as well as the charge transfer effects caused by the electron-shell deformation of the overlapping ions. The van der Waals coefficients are computed by the Slater Kirkwood variation method as a first step. Later on, we evaluate volume collapse, second order and third order elastic constants with pressure pointing to the systematic trends in all compounds of zinc blende structure and their thermal properties such as force constant, Gruneisen parameter, compressibility, Debye temperature etc. The vast volume discontinuity in pressure-volume (PV) phase diagram identifies the structural phase transition from zinc blende (B3) to rock salt (B1) structure and is consistent with those revealed from earlier reports.

Study of Elastic Properties and Their Pressure Dependence of Semi Magnetic Semiconductors

A theoretical study of the elastic behavior in diluted magnetic semiconductors Zn 1- x Mn x Se ( x =0.016, 0.026 and 0.053) using a three-body interaction (TBI) caused by the electron-shell deformation of the overlapping ions is carried out. The estimated values of phase transition pressure and the vast volume discontinuity in pressure–volume (PV) phase diagram indicate the structural phase transition from zinc blende ( B 3) to rock salt ( B 1). The variation of second-order elastic constants with pressure resembles that observed in other compounds of zinc blende structure family. However, the inconsistency in the value of pressure derivative of theoretical and the experimental value of bulk modulus is attributed to the fact that we have derived our expressions neglecting thermal effects and assuming the overlap repulsion significant only up to nearest neighbors. The present approach has also succeeded in predicting the Born and relative stability criteria. It is revealed that interionic potential approac...

High pressure phase transition and variation of elastic constants of diluted magnetic semiconductors

AbstractA theoretical study of the high‐pressure phase transition and elastic behavior in diluted magnetic semiconductors Zn0.83Mn0.17Se, using a three‐body interaction (TBI) potential caused by the electron‐shell deformation of the overlapping ions is carried out. The estimated values of phase transition pressure and the vast volume discontinuity in pressure‐volume (PV) phase diagram indicate the structural phase transition from zincblende (B3) to rock salt (B1). The variation of second‐order elastic constants with pressure resembles that observed in some binary semiconductors. The inconsistency in the deduced value of pressure derivative of second order elastic constant with the available data is attributed to the fact that we derive expressions neglecting thermal effects and assuming the overlap repulsion significant only up to nearest neighbors. The vdW interaction is effective in obtaining the thermodynamical parameters such as Debye temperature, Gruneisen parameter, thermal expansion coefficient, compressibility as well phase stability in diluted magnetic semiconductors. It is revealed that TBI model has a promise to predict the phase transition pressure and the pressure variation of elastic constants of other semiconductors as well. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)