EXTENSION OF THE RAMAN BEHAVIOR-TYPE METHOD TO THE ANALYSIS OF POLARIZED-SCATTERING INTENSITIES OF DEFECTS IN TETRAGONAL CRYSTALS
|ALKALI-HALIDES; CUBIC-CRYSTALS; KCL; Materials Science; Materials Science, Multidisciplinary; Physics; Physics, Applied; Physics, Condensed Matter; SPECTRA
|AMERICAN PHYSICAL SOC
|PHYSICAL REVIEW B
In polarized Raman scattering of point defects in crystals the spectrum is a spatial average of discrete energetically equivalent orientations. Recently, Zhou et al. have introduced the behavior-type (BT) method. The primary aim of the BT method is the determination of the defect symmetry O1 and its vibrational modes, which is reflected in the group-theoretical form of the Raman tensor of the single defect. In cubic systems partial or complete preferential orientation of the defects is often necessary to compete for the loss of information in an ensemble average, in order to yield sufficient discriminating power. In the BT theory an orientating operator F acting on the population numbers of the defects in their discrete orientations is introduced. Instead of solving the set of equations for the polarized Raman intensities for the tensor components, the method focuses on the appearance of symmetry-induced, simple algebraic relations among the so-called Raman intensity parameters (IP's), which are characteristic for the possible symmetries of a defect mode. It introduces the concept of the behavior type of a mode, which denotes the complete set of IP's, together with the algebraic relations among them. The extension of the BT method to tetragonal crystals necessitates the compilation of the appropriate tables needed for a practical application. The main features of the method introduced by the symmetry of the tetragonal axis can be summarized as follows: (i) The total of 80 possible modes within 25 different symmetry groups O1 can be classified into 20 sets of representative modes, of which 16 can possibly be distinguished by the method. For comparison in cubic systems there are 124 possible modes in 33 symmetry groups O1, classified into 24 sets of representative modes, of which 15 can be distinguished. (ii) The optical anisotropy induced by the tetragonal axis reduces the number of possible scattering configurations for polarized light. (iii) The lowered crystal symmetry weakens the averaging effect such that the discriminating power of the method is increased. This holds especially for cases when the defects cannot be orientated, leaving still 13 distinguishable sets of modes compared to only 7 sets in cubic systems. A series of tables essentially contains all the results: In the theoretical part they provide the summary of all possible modes and their classification into sets of representative modes, the influence of preferential orientation, the listing of all possible characteristic BT's, and the relation to the symmetries O1 of the mode and of the orientating operator F to which the BT's belong. Tables compiled for a practical application provide the relations of the polarized scattering intensities to the IP's, and a guide to select the suitable symmetry of F as well as the discriminating Raman polarization geometries.
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checked on Mar 1, 2024