Karyagin effect

In anisotropic crystals, the amplitudes of the atomic vibrations are essentially a function of the vibrational direction. As has been shown theoretically by Karyagin [72] and proved experimentally by Goldanskii et al. [48], this is accompanied by an anisotropic Lamb-Mossbauer factor/which in turn causes an asymmetry in quadra-pole split Mossbauer spectra, for example, in the case of 4 = 3/2, f = 1/2 nuclear transitions in polycrystalline absorbers. A detailed description of this phenomenon, called the Goldanskii-Karyagin effect, is given in [73]. The Lamb-Mossbauer factor is given by... 

NFS spectra recorded at 300 K for -cut and c-cut crystals are shown in Fig. 9.17 [48]. The/factors for the two orientations were derived from the speed-up of the nuclear decay (i.e., from the slope of the time-dependent intensity in Fig. 9.17a and from the slope of the envelope in Fig. 9.17b). The factors obtained f ( P = 0.122 (10) and f = 0.206(10) exhibit significant anisotropic vibrational behavior of iron in GNP. This anisotropy in f is the reason for the observed asymmetry in the line intensity of the quadrupole doublet (in a conventional Mossbauer spectrum in the energy domain) of a powder sample of GNP caused by the Goldanskii-Karyagin effect [49]. 

Fig. 28. Asymmetry of quadrupole split peaks due to the Gol danskii-Karyagin effect. 7t = +j - transition a — i - i transition c = (27t/7)2( - <.x2 . z and x are parallel and perpendicular, respectively to the surface normal. Figure according to Suzdalev and Makarov (208).

Arnold and Hobert (231) studied the chemisorption of ferrocene, (C5H5)2Fe, on a silica surface from an alcohol solution. Ferrocene itself shows a symmetric quadrupole splitting. After chemisorption this doublet is no longer symmetric, and the authors explain this in terms of a Gol danskii-Karyagin effect, where the iron atoms in the adsorbed state have a larger mean square displacement perpendicular to the silica surface than parallel to it. 

Rather less information is available for the oxide derivatives of tin(Il). The crystal structure of black, tetragonal SnO is known [63], and was referred to in Chapter 14.1 in the discussion of the nuclear quadrupole moment. The Mossbauer parameters are given in Table 14.4 together with those for SnS, which has a considerably distorted NaCl lattice [64], SnSe (isostructural with SnS) [65], and SnTe, which has a cubic NaCl lattice [66]. Application of high pressure to SnO causes the formation of some Sn02 and tin metal [67]. A detailed lattice dynamical study of SnS between 60 and 320 K has shown evidence for a Karyagin effect [68]. 

The adsorption of Sn " atoms on zeolite and silica-gel surfaces has been studied [122]. The bonding appears to become stronger as the pore size of the material decreases towards molecular dimensions. The asymmetry of the tin(II) quadrupole splitting was held to indicate a Karyagin effect because of the anisotropy of surface atoms. 

The other possible reason for the intensity asymmetry (A2M1 1) of the quadrupole split doublet can be the so-called Goldanskii-Karyagin effect (Goldanskii et al. 1963), which is caused by the angular dependence of the Mossbauer-Lamb factor due to the anisotropy of lattice vibrations (jf(0) depends on 0). 

For a comparison of the Goldanskii-Karyagin effect with the effect of texture see, e.g., Pfannes and Gonser (1973). 

The purpose of this chapter is to review the application of Mossbauer spectroscopy to the study of dynamics. The main emphasis will be on the new areas in which significant advances have been made in recent years, such as the study of diffusive processes, the influence of motion on lineshape, time-dependent studies and dynamics at phase transitions. Rather less attention will be devoted to areas such as /-factors in solids, the Goldanskii-Karyagin effect and temperature shift, which have been studied more extensively in the past. The trends towards future areas for this research will also be considered, together with an evaluation and comparison between Mossbauer spectroscopy and other methods for investigating these phenomena. 

Information about the bond strength of the If/ If anions in the (CH) matrix can be obtained by measuring the absorption strength (/-factor) in oriented samples as well as the temperature dependence of the /-factor and of the Goldanskii-Karyagin effect (GKE) in non-oriented samples. We performed such studies on non-oriented S-(CH1 ) ,. samples, applying both I and I resonance. Typical spectra are shown in Figure 3.11. 

Fig. 11. Quadrupole hyperfine spectrum of Np in Np metal. The bar diagram shows the decomposition into two quadrupole patterns meaning that Np occupies two lattice sites with different local symmetries. In both cases the electric field gradient is not rotationally symmetric (rj 0). The fit (solid line) includes the Goldanskii-Karyagin effect (see text). The dashed line shows the spectrum expected in case of full isotropy. [Taken from Dunlap et al. (1970).]...

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