Analytical expressions for the Morse potential parameters of diamond crystals have been derived. They contain the energy of sublimation, the compressibility and the lattice constant. Numerical calculations have been carried out for Si and Sn, and the results reflect fundamental properties of this potential. The obtained Morse potential parameters have been used for calculation of the anharmonic correlated effective potentials of these crystals in XAFS theory showing clearly anharmonic effects .
A new procedure for calculation and analysis of dispersion relation and real atomic vibration of fcc crystals containing dopant atom has been developed using anharmonic effective potential. Analytical expressions for dispersion relation separated by acoustic and optical branches; forbidden zone; effective force constant; Debye frequency and temperature; amplitude and phase of real vibration of atomic chain containing dopant atom have been derived. They contain Morse potential parameters characterizing vibration of each pair of atoms. ...
A new procedure for calculation and analysis of XAFS (X-ray Absorption Fine Structure) cumulants of hcp crystals containing dopant atom has been derived based on quantum statistical theory with generalized anharmonic correlated Einstein model. Analytical expressions for effective local force constants, correlated Einstein frequency and temperature, first cumulant or net thermal expansion, second cumulant or Debye Waller factor and third cumulant of hcp crystals containing dopant atom have been derived.
Analytical expression for the Displacement-displacement Correlation Function (DCF) C R has been derived based on the derived Mean Square Relative Displacement (MSRD) σ and the Mean Square Displacement (MSD) u for fcc
crystals. The effective interaction potential of the system has been considered by taking into account the influences of nearest atomic neighbors, and it contains the Morse potential characterizing the interaction of each pair of atoms.