Atomic displacement parameters, vibrational spectra and thermodynamic functions for crystals: a strong connection

摘要

In crystallography, atomic motion is usually accounted for by considering the Fourier transform of the probability density function (pdf) of an atom around its mean position, which is often called a "temperature factor". For "anisotropic" displacement, such "temperature factors" T_i(hkl) can be written as. T_i(h) chemical bounds exp(-2 #pi# ~2H~TUH) where the U's (chemical bounds u_iu_j>) are second-rank tensors and are called anisotropic atomic displacement parameters or ADP's and H is the reciprocal-lattice vector referred to a set of Cartesian axes, or (more frequently) to a set of reference axes of unit length cinciding in direction with the reciprocal axes. There are also more complex forulations, involving higher temrs in the cumulant expansion, leading to higher-rank tensors (see, for instance, Johnson [22-24]).