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The Second and Third Crystal Field Splitting Moments in Verification of the Trigonal and Hexagonal Crystal Field Parametrizations
Author(s) -
Mulak Maciej,
Mulak Jacek
Publication year - 2018
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.201800115
Subject(s) - crystal (programming language) , field (mathematics) , scalar field , trigonal crystal system , hamiltonian (control theory) , mathematics , crystallography , condensed matter physics , crystal structure , physics , geometry , chemistry , quantum mechanics , pure mathematics , computer science , mathematical optimization , programming language
The paper, as the third in a series, presents the complete formulas for the crystal field splitting third moment of free ion states as functions of the relevant crystal field parameters in the case of the trigonal and hexagonal crystal fields. The additive structure of the expressions consists of 21 independent components for the trigonal symmetry, 12 for the hexagonal one and only 4 components for the ideal hexagonal coordination. The two scalar characteristics of the crystal field Hamiltonian H CF – the crystal field splitting second and third moments – enable us to verify the H CF parametrizations solely in an algebraic way. Such verification concerns the multipolar structure of the parametrizations as well as the signs of the crystal field parameters. Both the crystal field splitting moments can ensure us in what degree the comprehensive H CF parametrizations are adequate with respect to the individual ionic states of the electron configuration. As an example two chosen H CF parametrizations, one for the hexagonal system Nd 3+ :LaCl 3 of the C 3h symmetry, and the second for the trigonal system Tb 3+ :Y 2 O 2 S of the C 3v symmetry are subjected to in depth analysis. The presented approach provides a critical insight into the crystal field parametrizations from a different point of view, i.e., omitting the conventional fitting procedure. After the extended verification the studied classical H CF parametrizations withstand, in principle, the test of time.