Cecylia Malinowska-Adamska

Physical properties of Ni fcc lattice in terms of the self-consistent phonon theory

The results of studies of physical properties of Ni fcc lattice obtained with the help of the reduced all-neighbour approximation of the self-consistent phonon theory are presented. The interatomic interactions are described by the modified form of the generalized Morse potential, proposed lately by Akgun and Ugur, with parameters derived from the experimental data for the lattice constant, cohesive energy, bulk modulus and elastic constants. As a test of the validity of both the model of interatomic interactions and the model of lattice dynamics the temperature variations of selected physical properties of Ni are given and compared with experimental and other theoretical data.

High-temperature properties of the fcc metallic crystals in anharmonic approximation

The reduced second-order approximation of the self- consistent phonon theory was applied some years ago for cubic metallic crystals those interatomic were approximated by the Morse and Lennard-Jones pair potentials were generally obtained with the help of semi-classical method basin on the classical static relationships between ground- state properties of a crystal and its interatomic potential, and the zero-point vibrations were taken into account only by certain corrections to the experimental data. Moreover, the further self-consistent calculations were being carried out semi-analytically which required some simplifications. In this paper we can reject them because all essential calculations are being carried out numerically. In the studies at high-temperature properties of selected fcc metallic crystal we take as a model of interatomic interactions the Buckingham, Lennard-Jones and Morse pair potentials with the parameters determined self-consistently with the help of the experimental data for the zero-point lattice constant, cohesive energy and isothermal compressibility. Our new theoretical result for pressure variations of the limiting temperatures of dynamical and thermodynamical stability and for the stability criteria are collected and compared with available experimental data.

Dynamics and thermodynamics of quantum crystals near the instability point in the self-consistent phonon theory

Formally one can distinguish between the thermodynamic stability conditions and the dynamical ones. These last consists are easily formulated in the self-consistent phonon theory (SCPT) base don the thermodynamic double-time Greens function method. According to it the dynamic instability temperature Ts for a simple Bravais lattice defines the temperature at which the bound crystalline state of atoms vanishes that really means that the phonon frequencies become complex at sufficiently high temperatures T<EQTs. Using the reduced second order approximation of the SCPT the dynamics of crystal lattice and the thermodynamical properties of the quantum crystal in the vicinity of the instability point are investigated. The results of calculations of the pressure dependence of the instability temperature, melting criterion, internal and free energy, free Gibbs energy gas well as selected dynamic properties obtained with the help of the generalized form of the Buckingham, the Lennard-Jones and the Morse self-consistent potentials are given and compared with experimental data of solid hcp 4He and fcc 20Ne. Comparison of the theoretical and experimental results allows us to state that the limiting temperature of the dynamical stability obtained for the above-mentioned models pair potentials always appear to be the upper estimations of the real melting temperature.

Self-consistent description of the lattice destabilization phenomenon for the heavier rare gas solids

In this paper we study the problem of lattice stability of the heavier rare gas solids (i.e. Ar, Kr, Xe) in terms of the reduced second-order self-consistent approximation, developed by Plakida and Siklos on the basis of the double- time Greens functions method. As a model of interatomic interactions we take the (n,m) Lennard-Jones, (exp,m) Buckingham and (exp,exp) Morse pair potentials with the parameters determined self-consistently with the help of the experimental data for the zero-point lattice constant, energy of sublimation and isothermal compressibility. Apart from the pressure variations of the limiting temperature of stability we also investigate the behavior of selected thermodynamical properties of crystal near the limit of stability. The mentioned theoretical results are compared with available experimental data.

Interatomic interaction and physical properties of quantum crystals in the self-consistent phonon theory

Every complete lattice theory of solid state consists of two basic elements, namely the description of the interatomic forces and the theory connecting them with the dynamical and thermodynamical properties of the crystal. In the present paper we have discussed the application of the self- consistent phonon theory formulated independently by various authors with the help of the modern techniques of many-body method to the quantum crystals. The results of theoretical investigations of the high-temperature and pressure properties of solid b.c.c. 3He, h.c.p. 4He and f.c.c. 20Ne in terms of the interatomic potential energy curves proposed by Beck, Murrel-Shaw, Morse, Buckingham and Lennard-Jones are given and compared with available experimental data. Extensive comparison of theoretical and experimental results allows us to discuss the suitability the above self-consistent potential energy functions as real interatomic potential modes in solid helium and neon.

Dynamics and thermodynamics of quantum crystals in the self-consistent phonon theory

The results of the self-consistent phonon theory developed by Plakida and Siklos with the generalized form of the Lennard- Jones (n,m) model of interatomic interactions in the lattice of bcc 3He and ideally hcp 4He are given. Theoretical values for the pressure and temperature variations of the dynamic and thermodynamic function of strongly anharmonic crystals of helium are compared with experimental data.

Dynamic and thermodynamic properties of strongly anharmonic cubic crystals in the self-consistent phonon theory

On the basis of the reduced second-order self-consistent phonon approximation, based on the Greens functions method, the temperature and pressure variations of the dynamic and thermodynamic functions of strongly anharmonic crystals are computed and compared with experimental and other theoretical data. The system of self-consistent equations is solved for the generalized form of the Lennard-Jones (n,m) interatomic potential.

Application of the Lennard-Jones (n,m) potential functions to rare gas solids in the self-consistent phonon approximation

The reduced second-order self-consistent phonon approximation is applied to the calculations of the effect of pressure on the instability temperature and relative displacement of atoms. As the model of nearest-neighbors central force interaction is used the Lennard-Jones (n,m) self- consistent potential. The results of calculations are compared with experimental and other theoretical data for the anharmonic rare gas solids.

Study of crystal properties of rare gas solids in terms of the Singh and Neb potential model

On the basis of the reduced second-order self-consistent phonon theory the dynamic functions of rare gas solids are computed and compared with experimental and other theoretical data in the low temperature limit. The system of self-consistent equations is solved for the Singh and Neb model of interatomic interaction.