Ga + ,  In+, and Tl+ impurities in alkali halide crystals: Distortion trends

Abstract

A computational study of the doping of alkali halide crystals (AX: A = Na, K; X = Cl, Br) by ns 2 cations (Ga + , In + and Tl + ) is presented. Active clusters of increasing size (from 33 to 177 ions) are considered in order to deal with the large scale distortions induced by the substitutional impurities. Those clusters are embedded in accurate quantum environments representing the surrounding crystalline lattice. The convergence of the distortion results with the size of the active cluster is analyced for some selected impurity systems. The most important conclusion from this study is that distortions along the (100) and (110) crystallographic directions are not independent. Once a reliable cluster model is found, distortion trends as a function of impurity, alkali cation and halide anion are identified and discussed. These trends may be useful when analycing other cation impurities in similar host lattices.

Quantum Mechanical Study of the Lattice Distortions Induced by Aliovalent Pb2+ Impurities in Alkali Halides

“…[34][35][36][37]. The theoretical details specific to the case at hand are the same as those described in our previous publications [8,25], so in order to save journal space we refer the reader to those works for a full account of the method.…”

“…The different active clusters employed in this work have been constructed following the same physical rules: a) they are embedded in accurate quantum environments including Coulombic, exchange, and orthogonality effects [8]. When the cation vacancy is well separated from the impurity position, it is not explicitly represented as this would be prohibitly expensive.…”

“…Taking into account small self-embedding corrections [6][7][8], the distortions have been calculated using the following formula:…”

“…In the case of isovalent impurities in their ground ns 2 electronic configuration, it is mainly the size mismatch between impurity and host ions that determines the lattice distortion: a radial breathing displacement of several coordination shells of ions about the impurity [6][7][8]. Even this ''simple" distortion is computationally challenging as it involves up to eight coordination shells around the impurity [6][7][8].…”

“…Even this ''simple" distortion is computationally challenging as it involves up to eight coordination shells around the impurity [6][7][8]. Moreover, the dis- placements of the different coordination shells are coupled to each other [8]. Thus, a large number of ions has to be explicitly included in the calculations, making the whole procedure very time consuming.…”