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On crystal‐field parametrization in a uniformly strained crystal lattice

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 IIk2 for 2 ≤ k ≤ 6, apart from the axial ones Bk0 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 dBkq/Bkq as a function of pressure using the stress–strain data (elastic stiffness moduli) is given. Such successful calculations for the Pr3+ : LiYF4 system based only on the crystallographic data and the tk exponents (in the distance dependence of Bkq) are presented as an example. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)