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

Abstract

An embedded cluster analysis of the lattice distortions induced by a Pb 2þ substitutional impurity in NaI, RbI and CsF crystals is presented. Active clusters containing more than 100 atoms and embedded in a quantum representation of the crystalline environment are used. Charge compensation is achieved by introducing a cation vacancy in the host lattice. Both nearest-neighbor (NN) and next-nearest-neighbor (NNN) vacancy positions are explicitly considered, as well as the case where vacancy and impurity are well separated from each other. Only in the first two cases, the impurity adopts an off-center equilibrium position. Distortion trends as a function of the host lattice are identified and discussed. These trends are then employed to advance the expected distortions in similar crystals. The examples of Pb 2þ -doped RbF and KBr are found to behave according to the expectations. Finally, the relative stability of the NN and NNN configurations is discussed.

Lattice Distortions Induced by As3+, Sb3+, and Bi3+ Substitutional Impurities in KCl: An Embedded Cluster Study

“…13,54 We have calculated the formation-energy difference between NN and NNN defect configurations and have found that the NN configuration is more stable in all three cases by an amount (0.51 eV) that is quite independent of the specific impurity. We already found in the case of doubly charged aliovalent impurities 28 that purely electrostatic effects are more important in determining distortions and relative stabilities than are overlap repulsive terms (associated with the size mismatch effect). From the discussion of the distortions shown above, it is clear that this is even more the case when the substituted cation is triply charged.…”

“…This situation is different from the case of doubly charged substitutional impurities, which try to approach the electrostatic field of the only neighboring vacancy. 28 The presence of two vacancies, allocated symmetrically with respect to the impurity, prevents this approach from happening, which might well be the reason that the optical properties seem to be less affected by the vacancy effect in the case of triply charged impurities than in the case of doubly charged impurities. 34 Another technical comment may be in order here.…”

“…26 Theoretical consideration of the lattice distortions induced by doubly charged aliovalent impurities in alkali halides and of the off-center equilibrium position adopted by these cations has also been undertaken by us in previous work. 28 It was found that the electrostatic effects associated with the aliovalent character of the impurity are more important than the size mismatch effect in determining the distortions.…”