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The maximal axial parameters in equivalent parametrizations of high symmetry crystal‐field Hamiltonians
Author(s) -
Mulak Jacek,
Mulak Maciej,
Gonczarek Ryszard
Publication year - 2007
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.200642384
Subject(s) - tetragonal crystal system , parametrization (atmospheric modeling) , crystal (programming language) , hexagonal crystal system , field (mathematics) , coupling (piping) , symmetry (geometry) , physics , crystallography , crystal structure , mathematics , geometry , chemistry , materials science , quantum mechanics , pure mathematics , metallurgy , computer science , programming language , radiative transfer
The variation ranges of the axial B k 0 crystal‐field parameters (in Wybourne parametrization), for k = 2, 4, 6, of tetragonal (including cubic) and hexagonal crystal‐field Hamiltonians ℋ CF for all possible orientations of the relevant reference frame are studied. The distinguished z ‐axis directions fixed by the maximal absolute values of B k 0 are analyzed. The diagrams for any tetragonal and hexagonal ℋ CF parametrization depicting the maximal values of | B k 0 |/ M k , where M k is the 2 k ‐pole modulus, as a function of the x = B k 4 / B k 0 or B 66 / B 60 ratios, together with the distinguished directions are presented. The| B k 0 |/ M k magnitudes and the relevant distinguished directions are the discriminants of all the equivalent parametrizations. They vary within the intervals (0.7395,1], (0.6074,1] and (0.6717,1] for tetragonal k = 4, tetragonal k = 6 and hexagonal k = 6ℋ CF components, respectively. Such specified directions determine the mutual spatial orientation of the component 2 k ‐poles of the ℋ CF , and due to their rigid coupling in the ℋ CF , they also refer to the global ℋ CF parametrization. This approach demonstrates the difference in fitting capability between the real and complex isomodular ℋ CF parametrizations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)