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The interatomic force constants and the phonon dispersion curves of AlP, AlAs, and AlSb are obtained from the electronic theory of solids by using our presented binding force, which includes mainly covalent interactions in the pseudopotential formalism and partially ionic interactions. The potential-parameter, effective ionic charge and ionic fraction of AlP and AlAs are estimated from those of AlSb and other III–V tetrahedrally- bonded compounds in spite of no experimental information on the band- calculation and the neutron scattering data of AlP and AlAs. Numerical data for the crystal energy of AlP and AlAs are in good agreement with the observed data, and the obtained results for the phonon dispersion curves and bulk modulus are useful to study the lattice dynamics and anharmonic properties of these compounds.

Using our presented treatment with the volume effect on the force constants of the pure constituent, we study the thermal properties of Si-Ge solid solution from first principle in the electronic theory of solids. The specific heat at constant volume of Si 1− x Ge x solid solution is monotonous function of the concentration x and is approximately given by the linear interpolation of atomic fraction. The Gruneisen constant and the thermal expansion coefficient of Si 1− x Ge x system have the characteristic concentration dependence. The almost constant value at high temperatures and the negative minimum at low temperature of the Gruneisen constant are not monotonous as function of x , and show a maximum near x = 0.7 and a minimum near x = 0.2, respectively. Then, the linear thermal expansion coefficient at low and high temperatures deviate largely from the linear interpolation of the atomic fraction.

The lattice dynamics of the tetrahedrally-bonded compounds is formulated from first principle by using a model of binding force proposed by us, which mainly includes covalent interactions in the perturbational treatment based on the pseudopotential formalism and also partly on ionic interactions. Numerical calculations are performed for GaP and ZnS. In spite of our introducing no adjustable parameter except the optical phonon-frequency splitting in the long-wavelength limit, the resulting phonon dispersion curves are qualitatively in good agreement with the observed data. We show that ionic contributions are important for the optical phonon frequencies of these compounds.

The elastic stiffness constants under pressure of Si and Ge are studied theoretically using the higher-order perturbational formalism and the local Heine-Abarenkov model pseudopotential, and the mode Gruneisen parameters for long-wave phonons are estimated as a function of the compressed volume. The results obtained for atmospheric pressure are in good agreement with the experimental data. The long-wave LA mode Gruneisen parameters decrease slightly as the volume is reduced by compression. The TA mode Gruneisen parameters show a large decrease as function of the volume strain, and become negative near the covalent-metallic phase transition. The volume-dependences of the long-wave mode Gruneisen parameters are useful in the study of the anharmonic properties of Si and Ge.

Using the total crystal energy expression with the overlap potential energy by Moriarty and with the model pseudopotential by Kulshrestha et al., the pressure-volume relations of noble metals are studied and the obtained results are in good agreement with the observed data. Then, the elastic stiffness constants B, C44 and C′ under pressure are obtained by the homogeneous deformation method, and our calculated data will be useful to describe the typical pressure effect on the elastic constants of noble metals.

The lattice vibrational contributions to the Helmholtz free energy and the thermal pressure of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe are investigated from the electronic theory of solids in the dynamical treatment based on our presented binding force. The temperature dependence of Helmholtz free energy and thermal pressure from lattice vibrational term are quantitatively obtained, and vibrational contributions to free energy are small compared with the static crystal energy. The influence of the thermal pressure is important to the equation of state in high temperatures, and the reformulation of the volume scale for the pressure-volume relation is given by considering the thermal pressure.

The temperature dependence of the thermal expansion for GaAs and InP is investigated theoretically using the experimental pressure derivatives of elastic stiffness constants and phonon frequencies. The linear correlation between the transverse acoustical mode Gruneisen parameter γXTA and the metallic transion pressure Pt obtained by Weinstein is not satisfied for GaAs and InP, but the observed thermal expansion of GaAs is well reproduced. In addition, the linear expansion coefficient of InP is predicted theoretically as a function of temperature. Then, the phonon dispersion curves of GaAs and InP at their covalent-metallic transition pressures are quantitatively shown.

We present the simplified treatment where the lattice vibrations of Si or Ge atoms in the Si-Ge solid solution are replaced with that of pure Si or Ge crystal at lattice constants of the alloy. Considering the volume effect on the force constants of the pure constituent, we obtain the phonon dispersion curves of the local and band modes for Si 0.91 Ge 0.09 and Si 0.11 Ge 0.89 systems and the concentration x -dependence of the local and band modes frequencies in the Si 1− x Ge x solid solutions. Then, from the calculation of the effective mode Gruneisen parameter γ i for the average phonon modes in the Si 1− x Ge x systems, we obtain the predominant correlation between TA mode Gruneisen parameter γ X TA at the point X and the phase transition pressure P t , and the softening of TA modes is related to the pressure-induced phase transition of the Si-Ge solid solution.

The lattice dynamics of II–VI tetrahedral compounds is studied by using our previously presented treatment from first principle in the electronic theory of solids. Our binding force for these compounds involves mainly covalent interactions in the perturbational method based on the pseudopotential formalism and partially ionic interaction. Representative numerical calculations are performed for ZnSe and CdTe. The phonon dispersion curves obtained are qualitatively in good agreement with the observed data in spite of introducing no adjustable parameter except for the frequency-splitting of the optical modes in the long wavelength limit.

The mode Gruneisen parameters γi(q) and those γi(q→0) for long-wave phonons of GaP and InP are studied from the electronic theory of solids by using the lattice dynamical method and the homogeneous deformation method. The agreement of the obtained results for γi(q) and γi(q→0) with the experimental data available for GaP and InP is excellent. The temperature dependence of the average Gruneisen constant γ(T) and the thermal expansion coefficient α(T) for GaP and InP obtained for the calculated Gruneisen parameters is also presented. The obtained α(T) for GaP becomes negative at low temperatures by summing the phonon mode over the irreducible 1 48-th part of the Brillouin zone, contrary to the previous prediction of the positive thermal expansion. The simplified treatment by the weighted averaging in the symmetry directions such as [100], [110] and [111] does not give the correct results for γ(T) and α(T).

Lindeman's criterion for melting of covalent crystals is formulated using Debye's model. The contribution of the acoustical, especially transverse-like acoustical phonon modes to the total mean-square displacement is predominant at higher temperatures and essential to the melting scheme. Using the volume-dependence of the transverse-like Gruneisen constant at higher temperatures, the volume effect on the melting temperature of Si and Ge is studied by Lindeman's melting law. The obtained melting curve decreases as function of the compressed volume, and is qualitatively in agreement with the observed tendency for Si and Ge.

The volume-dependence of phonon frequencies for Si and Ge is studied using higher-order perturbation and local Heine-Abarenkov model pseudopotential. The obtained mode Gruneisen parameters at atmospheric pressure are in good agreement with the experimental data. The mode Gruneisen parameters obtained for the Raman, TO, LO and LA modes increase slightly with decreasing volume. The other TA mode Gruneisen parameters decrease strongly as function of the volume strain, and give important contribution to the anharmonic properties of Si and Ge. The pressure dependence of phonon frequencies for Raman and some modes at the zone boundaries are estimated over the whole region of the compressed volume before the pressure induced covalent-metallic phase transition.

The mean-square displacement of alkali metals is studied theoretically using our local Heine-Abarenkov-type model potential in the perturbational scheme. The temperature-dependent mean-square displacement of alkali metals decreases as function of the compressed volume. Lindemann's criterion for melting xm, which is defined as the ratio of two times the root-mean-square displacement to the nearest-neighbour distance, is found to be nearly constant for five alkali metals. The volume effect on the melting temperature of alkali metals is studied by keeping xm constant. The obtained melting curve increases as function of the compressed volume and are qualitatively in good agreement with the observed tendency for alkali metals.

The pressure-volume relation and the compression effect on the bulk modulus of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe are investigated from the electronic theory of solids by using our recently presented binding force, which includes mainly covalent interactions in the pseudopotential formalism and partially ionic interactions. The calculated results of the pressure-volume relations involving the pressure-induced phase transition are useful when comparing with the experimental data under high pressure. The calculated bulk modulus of these compounds increases as the crystal volume decreases. Further, the pressure derivative of bulk modulus is not constant and decreases with the reduction of the crystal volume.

The phase transition of AlP, AlAs and AlSb under pressure is studied from the electronic theory of solids by using our presented binding force, which includes mainly covalent interactions in the pseudo-potential formalism and partially ionic interactions. The partially ionic forces bring the essential contributions to the high-pressure phase of AlP, AlAs and AlSb, and stabilize the NaCl-type structure for the high-pressure phase of these compounds, although not reported experimentally. Then, numerical results for the transition pressure, the volume discontinuity, the transition heat and the lattice parameter in NaCl-type lattice of AlP, AlAs and AlSb are predicted theoretically.

The phase transition of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe under pressure is investigated from the electronic theory of solids by using our recently presented binding force, which includes mainly covalent interactions in the pseudopotential formalism and partially ionic interactions. The partially ionic forces give the important contributions to the high-pressure phase and stabilize the NaCl-type structure for the high-pressure phase of these compounds, although not reported for GaP experimentally. Then, the numerical results such as the transition pressure, the volume-discontinuity, the transition heat with respect to the pressure-induced phase transition from the zinc-blende-to the NaCl-type lattice are obtained theoretically.

The temperature dependence of specific heat CV and thermal expansion coefficient α for AlP, AlAs and AlSb are studied theoretically from first principle by using the lattice dynamical method. No such experimental data are available for AlP and AlAs. The compression effect on phonon frequencies vi(q), i.e. the mode Gruneisen parameters γi(q) are also computed. The theoretical values of α for AlP and AlAs become slightly negative at low temperatures (below 30 K), a fact which differs other tetrahedral crystals. Our data of γi(q), Cv and α for AlP, AlAs and AlSb should be useful for discussing experimental information and for studying the anharmonic properties of these compounds.

The equation of state and the pressure effect on the bulk modulus of AlP, AlAs and AlSb are studied from the electronic theory of solids by using our presented binding force, although not reported experimentally. The obtained results of the pressure-volume relations involving the pressure- induced phase transition are useful to estimate the experimental data of these compounds. The obtained bulk modulus increases with the crystal volume compressed, and the pressure derivative of the bulk modulus for AlP, AlAs and AlSb is estimated theoretically.