Department of Applied Physics, Higher Institute for Applied Sciences and Technology,
Faculty of Sciences, Department of Physics, Baath University,
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In a crystal, interaction potentials are dominant in calculating the quadratic correlation moment (QCM) and the mean square relative displacements (MSRD) which express the effective amplitudes of atomic vibrations. These quantities hold close relationship to the density fluctuations. The importance of the dynamic correlations is seen in that some melting criteria are defined in terms of the MSRD. The QCM and MSRD have been calculated by the dynamical theory of crystal lattices but these results are valid only at sufficiently low temperature because this theory relies upon the harmonic approximation and the account of anharmonicity on its basis by using perturbation theory is rather complicated. Since then, several other approaches have been developed to take into account the anharmonic effects, among which the most prominent is the self-consistent phonon theory. In this theory, the harmonic force constants are averaged self-consistently over a trial set of harmonic oscillator functions. For low temperatures, it has faced problems with hard-core potentials that were handled by a more adequate treatment of the short-range correlations instead of using a simple cutoff procedure. It should be mentioned as well the simulation techniques widely used in recent years, especially a Monte Carlo formalism in which the quantum mechanical effects are included by making a modification of the potential energy. This formalism has its origin in a previous illustration by Feynman of the use of the path-integral form of the partition function in statistical mechanics, and is known as the method of the effective potential and effective Hamiltonian. The ansymmetrized self-consistent field method ASCFM, is free from the hard-core potential problem and it is based on the assumption that the classical phase probability density or the quantum density matrix is not symmetric with respect to the interchange of coordinates of identical atoms. So, the determination of different potential parameters could not lose its importance with time.