Calculation of elastic and thermal properties of alkali metals by the pseudopotential method

The elastic and thermal properties of alkali metals are analyzed from the viewpoint of effective ion-ion interaction in rectilinear space. Consideration is given to the approximation of pair interaction between ions. The atomic-interaction potential is calculated on the basis of the pseudopotential method. Numerical calculations are made of the elastic constants, the second and fourth moments of the frequency spectrum, the temperature dependence of the Debye temperature, the specific heat, and the vibrational free energy of Na, K, Rb, and Cs. The calculations are in good agreement with the experimental values. The influence of exchange-correlation effects on the given properties is discussed. The results obtained indicate that the pseudopotential method may be successfully used for the calculation of the thermodynamic properties of metals by a traditional scheme, restricting consideration to the first two coordination spheres.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 25–33, February, 1979.     

用赝势方法计算简单金属的弹性常数

本文利用单参数Heine-Abarenkov模型势及Hubbard-Sham介电函数计算了七种简单金属(Li,Na,K,Rb,Cs,Al和Pb)的二阶与三阶弹性常数,两个可调参数用零温零压下晶体的弹性常数C₄₄与晶格常数的实验值来确定,计算结果与实验值或其他作者的理论计算值符合得比较好,尤其是Al的三阶弹性常数,本文的计算结果比其他作者的计算结果更接近于实验值。 关键词：     

Analysis of the pressure derivatives of the shear modulii in ionic solids

Suitably modified theory based on Lundqvist potential of ionic cohesion, to explain the pressure derivatives of the solids, has been applied to evaluate the pressure derivatives of second order elastic (SOE) constants and the values of third order elastic (TOE) constants of ionic solids. The calculated values of the pressure derivatives of SOE constants are in good agreement with the experimental values.     

Optical properties from time-dependent current-density-functional theory: the case of the alkali metals Na,K, Rb,and Cs

We present the optical conductivity as well as the electron-energy loss spectra of the alkali metals Na, K, Rb, and Cs calculated within time-dependent current-density functional theory. Our ab initio formulation describes from first principles both the Drude-tail and the interband absorption of these metals as well as the most dominant relativistic effects. We show that by using a recently derived current functional [Berger, Phys. Rev. Lett. 115, 137402 (2015)] we obtain an overall good agreement with experiment at a computational cost that is equivalent to the random-phase approximation. We also highlight the importance of the choice of the exchange-correlation potential of the ground state.     

Elastic and thermodynamic properties of alkali hydrides XH (X = K,Rb and Cs)

The calculation of the structural, mechanical and thermodynamic properties of the alkali hydrides XH (X?=?K, Rb and Cs) in rock-salt (RS), cesium chloride (CsCl), zinc-blende (ZB) and wurtzite (WZ) phases are done by using the full-potential linearized augmented plane wave (FP-LAPW) method within the frame work of the density functional theory (DFT) as implemented in the WIEN2K code. The Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) was used for the exchange-correlation potential.The elastic constants and their related properties, as well as the thermodynamic properties, were obtained by using the IRelast package. The calculated elastic constants for the alkali hydrides, with the four structures RS, CsCl, ZB and WZ, at ambient pressure are mechanically stable. The elastic constants and their related properties in the RS structure are changeable with increasing pressure. Elastic constants, bulk modulus, shear modulus (stiffness) and Debye temperatures of these compounds are decreased as going from K to Cs in the periodic table. These compounds in the RS structure are mechanically stronger at ambient conditions.     

Lattice dynamics,third order elastic constants and low temperature lattice thermal expansion of zirconium

The lattice dynamics and the anharmonic properties of the hexagonal Zirconium are worked out using Keating's approach. The dispersion curves are fitted using twelve second order parameters and the six second order elastic constants are evaluated. The ten third order elastic constants are calculated using five third order parameters. The experimental measurements on the pressure derivatives of the second order elastic constants in Zirconium are in good agreement with the calculated values. The low-temperature limit of the lattice thermal expansion is calculated which agrees well with the value obtained from thermal expansion data. The variation of the generalised GPs of the elastic modes with the direction of propagation is illustrated by polar diagram.     

Calculation of Grüneisen parameter and temperature dependence of elastic constants in alkali metals

The pseudopotential method is used to determine the Grüneisen constant and the temperature dependence of the elastic constants for T > in alkali metals. An analysis is made of the influence of exchange-correlational effects in the electronic gas on the quantities mentioned above. The calculated values are in good agreement with experimental data in Na, K, Rb, and Cs. The results of the paper indicate that the considered anharmonic characteristics of alkali metals are determined primarily by the interaction in the first two coordination spheres.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 36–39, April, 1979.     

用赝势方法计算某些简单金属的状态方程

本文提出了一种确定简化的Heine-Abarenkov模型赝势参数的新方法,使用零温、零压下晶体的体积模量和晶格常数的实验值来确定赝势参数γ_c以及电子-离子平均相互作用能的修正系数H。用这种模型势和二阶微扰理论计算了十一种简单金属的状态方程。在293K计算出的压力-体积关系与实验数据进行了比较。除了Zn在不同实验数据之间本身就偏离较大外,理论与实验的符合都比较好。 关键词：     

Dispersion relations and lattice thermal expansion of dysprosium

The lattice dynamics, second and third order elastic constants and the lattice thermal expansion of dysprosium have been calculated using Keating's approach. The ten third order elastic constants are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of dysprosium well. The low and high temperature limits γ?_I and γ?_H of the lattice thermal expansion are evaluated and the agreement between the calculated γ?_H and that obtained from the thermal expansion and specific heat data is satisfactory.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

Lattice dynamics,third order elastic constants and thermal expansion of gadolinium

A systematic investigation of the lattice dynamics, second and third order elastic constants and the temperature variation of the effective Grüneisen functions has been carried out in gadolinium using Keating's approach. The ten third order elastic constants are calculated using five anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of gadolinium well. The low and high temperature limits gg_L and gg_H of the lattice thermal expansion are evaluated. The agreement between the calculated gg_H and that obtained from the thermal expansion and specific heat data of gadolinium is good.     

Lattice dynamics,third order elastic constants and thermal expansion of rhenium

A systematic investigation of the lattice dynamics, second and third order elastic constants and thermal expansion has been carried out in rhenium using Keating's approach. The ten third-order elastic constants of rhenium are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants well. The low and high temperature limits γ̄L and γ̄H of the lattice thermal expansion are calculated. The agreement between the calculated γ̄H and that obtained by Gschneidner from the thermal expansion and specific heat data of rhenium is satisfactory.     

Lattice dynamics,third order elastic constants and thermal expansion of Cadmium

The lattice dynamics, second and third order elastic constants, pressure derivatives of the second order elastic constants and the temperature variation of the lattice thermal expansion of Cadmium have been worked out utilising Keating's approach. The ten TOE constants are calculated using four anharmonic parameters. The model used here reproduces the measured pressure derivatives of the SOE constants of Cadmium extremely well. The low temperature limit of the volume Gruneisen function γ_L is found to be nearer to the value of Andres. The high temperature limit γ_v(T) is in good agreement with the value calculated by Gschneidner Jr. from the Cv data for Cadmium. The lattice dynamics of Cadmium is found to be essentially similar to that of Zinc.     

An equation of state and non-linear parameter from sound velocity measurements for liquid alkali metals

In the present paper, an equation of state has been obtained in case of liquid alkali metals like Na, K, Rb and Cs from sound velocity measurements. The theory developed gives very good agreement for both the sound velocity and the volume as a function of pressure at different temperatures in these liquid alkali metals. Further, the variation of non-linear parameter,B / A, as a function of pressure and temperature is also studied.     

High pressure behavior of alkaline earth tellurides

We have predicted high pressure structural behavior and elastic properties of alkaline earth tellurides (AETe; AE = Ca, Sr, Ba) by using two body interionic potential approach with modified ionic charge (Z _m e). This method has been found quite satisfactory in case of the rare earth compounds. The equation of state curve, structural phase transition pressure from NaCl (B1) to CsCl (B2) phase and associated volume collapse at transition pressure of alkaline earth tellurides (AETe) obtained from this approach, so have been compared with experimentally measured data reveal good agreement. We have also investigated bulk modulus, second and third order elastic constants and pressure derivatives of second order elastic constants at ambient pressure which shows predominantly ionic nature of these compounds. First time, we have calculated the Poisson ratio, Young and Shear modulus of these compounds.      

Third order elastic constants and thermal expansion of terbium

The third-order elastic constants and the temperature variation of the effective Grüneisen functions of terbium have been calculated on the basis of Keating's method. The pressure derivatives of the second order elastic constants of terbium have been obtained by interpolation of the experimental pressure derivatives of gadolinium and dysprosium. The ten third order elastic constants of terbium are calculated using four third order anharmonic parameters obtained from its interpolated pressure derivatives. The low and high temperature limits $\text{λ}{}_{\mathrm{L}}$ and $\text{λ}{}_{\mathrm{H}}$ of the lattice thermal expansion are evaluated. The agreement between the calculated $\text{λ}{}_{\mathrm{H}}$ and that obtained from thermal expansion and specific heat data of terbium is good.     

Third order elastic constants of V3Si and V3Ge

General expressions have been derived for the second order elastic constants and third order elastic constants of the A-15 structure compounds with the nearest neighbour central interaction. The second order elastic constants, the third order elastic constants and the pressure derivatives of the second order elastic constants of V₃Si and V₃Ge are reported and compared with the available experimental measurements.     

Analysis of anharmonic and thermoelastic properties of non-centrosymmetric crystals

In the present paper an analytical potential form is used for overlap repulsive energy, derived by Harrison from quantum mechanical considerations, along with the composite effect of three-body forces and intersublattice displacement. The short-range overlap parameters in Harrison's potential form have direct correlation with the valence state energies for outermost electrons. The potential model is applied to calculate the third and fourth order elastic constants, first and second pressure derivatives of second order elastic constants, Grüneisen parameter and its volume dependence, Anderson parameter, and thermal expansion coefficient for three non-centrosymmetric crystals, viz. CaF₂, SrF₂ and BaF₂. The calculated values of various physical quantities are found to be in good agreement with experimental data.The authors are grateful to Dr. Mansour Khalef, the Head of Physics Department, TNRC, Tajura (Tripoli) for the facilities and encouragements.     

密度泛函理论研究碱金属原子在完美氧化镁(001)表面的吸附

基于平面波赝势法的密度泛函理论系统地研究了孤立碱金属原子(锂、钠、钾、铷、铯)在完美氧化镁(001)表面的吸附. 锂在氧位表面上的吸附能是0.72 eV,大约是其它碱金属的3倍. 锂和表面氧之间较强的相互作用主要是来源于共价键的作用,这可由态密度和差分电荷密度的分析所证实. 讨论碱金属在MgO(001)表面吸附的成键机理.     

Computation of collective excitations and elastic constants of expanded trigonal tellurium

The potential function derived from experimental structure factor data gives a repulsive minimum and also an attractive minimum. These two minima correspond to the first and second nearest-neighbour distances. Similar results have been obtained through the use of Percus-Yevick (PY) and hyper-netted chain (HNC) equations. The Hafner molecular dynamics results also show a similar trend. The first, second and third derivatives of the potential function have been obtained from the expression of the potential function. The first and second derivatives have been used to compute the phonon frequencies using Bhatia and Singh's (BS) method. The phonon frequencies obtained from Hubbard and Beeby's (HB) method show similar results. The elastic constants have also been calculated and the values obtained for C₁₁ by different methods are in good agreement. The Grüneisen constant has been calculated by two different methods which are in very good agreement with each other. From the Grüneisen constant the pressure derivative of the diffusion coefficient has been obtained and has been compared with that of Swalin's equation. The results are in excellent agreement with each other.