Towards an ab initio theory for the temperature dependence of electric field gradients in solids: Application to hexagonal lattices of Zn and Cd
Abstract
Based on ab initio bandstructure calculations we formulate a general theoretical method for description of the temperature dependence of an electricfield gradient in solids. The method employs a procedure of averaging multipole electrondensity component (l ≠0 ) inside a sphere vibrating with the nucleus at its center. As a result of averaging, each Fourier component (K ≠0 ) on the sphere is effectively reduced by the square root of the DebyeWaller factor [exp(W )] . The electricfield gradient related to a sum of K components most frequently decreases with temperature (T ), but under certain conditions because of the interplay between terms of opposite signs, it can also increase with T . The method is applied to calculations of the temperature evolution of the electricfield gradients of pristine zinc and cadmium crystallized in the hexagonal lattice. For calculations within our model, of crucial importance is the temperature dependence of meansquare displacements which can be taken from experiment or obtained from the phonon modes in the harmonic approximation. For the case of Zn, we have used data obtained from singlecrystal xray diffraction. In addition, for Zn and Cd, we have calculated meansquare displacements with the densityfunctional perturbation treatment of the uc(quantum espresso) package. With the experimental data for displacements in Zn, our calculations reproduce the temperature dependence of the electricfield gradient very accurately. Within the harmonic approximation of the uc(quantum espresso) package, the decrease in electricfield gradients in Zn and Cd with temperature is overestimated. Our calculations indicate that the anharmonic effects are of considerable importance in the temperature dependence of electricfield gradients.
 Publication:

Physical Review B
 Pub Date:
 February 2020
 DOI:
 10.1103/PhysRevB.101.064310
 arXiv:
 arXiv:1912.05579
 Bibcode:
 2020PhRvB.101f4310N
 Keywords:

 Condensed Matter  Materials Science;
 Condensed Matter  Other Condensed Matter;
 Nuclear Experiment
 EPrint:
 13 pages, 11 figures