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On crystal‐field parametrization in a uniformly strained crystal lattice
Author(s) -
Mulak J.
Publication year - 2003
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200301849
Subject(s) - triclinic crystal system , crystal (programming language) , monoclinic crystal system , dimensionless quantity , moduli , symmetry group , physics , condensed matter physics , degenerate energy levels , orthorhombic crystal system , superposition principle , symmetry operation , bravais lattice , crystal system , symmetry (geometry) , crystal structure , quantum mechanics , mathematics , geometry , crystallography , diffraction , chemistry , computer science , programming language
Abstract The general consequences of uniform strain of a crystal lattice or coordination complex in phenomenological parametrization of the crystal‐field potential are considered. The analysis is based on the three‐dimensional derivatives of intrinsic crystal‐field parameters within the superposition model of the crystal‐field potential. The problem of the lowest possible symmetry of a uniformly strained crystal is discussed. Some limitations of the admissible deformations arise from the invariance of symmetry planes and inversion centre with respect to uniform strains. For any uniform strain, the crystal‐field potentials that are expressible by q ‐even terms only can never be reduced to potentials requiring q ‐odd terms. Therefore, their maximal symmetry lowering must terminate at a monoclinic point symmetry group. However, for a general uniform strain, some real derivatives of parameters of orthorhombic character II k 2 for 2 ≤ k ≤ 6, apart from the axial ones B k 0 for 1 ≤ k ≤ 6, can always occur. As a consequence, the decrease in symmetry for point groups that are characterized by an odd‐fold axis ( q ‐odd) and lack of any symmetry plane is unrestricted down to the triclinic systems. However, some incomplete sets of crystal‐field parameters compared with those predicted by group theory are needed. Uniform strains in crystals occur generally as a response to external stress used in pressure studies. The calculation method of the relative dimensionless changes of d B kq / B kq as a function of pressure using the stress–strain data (elastic stiffness moduli) is given. Such successful calculations for the Pr 3+ : LiYF 4 system based only on the crystallographic data and the t k exponents (in the distance dependence of B kq ) are presented as an example. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)