Recoil-free fraction anisotropy

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

The total cross-section in any direction is independent of polarisation, but the individual line cross-sections are not. A typical oriented crystal Mossbauer spectrum of FeCOa is shown in Fig. 6.15. One of the consequences of the modified theory is that the theoretical area ratio is comparatively insensitive to the recoil-free fraction and that it is unrealistic to determine it by an area ratio method. The presence of impurities and imperfections in the mineral specimens was held to explain some of the experimental deviations from prediction. No direct evidence for anisotropy of the recoil-free fraction was obtained, a conclusion since verified by Goldanskii [50], who made new polarisation measurements using single crystals of FeCOa as polariser and analyser. 

Major examples of lattice dynamical studies involving measurements of the recoil-free fraction and second-order Doppler shift over wide ranges of temperature, and followed by theoretical analysis of the vibrational properties of the impurity atoms, include the systems Co/V [89] Co/Au, Cu, Ir, Pd, Pt, Rh, and Ti [90] and Co/Pt, Pd, and Cu [91]. Anisotropy of the mean-squared displacement has been shown in, for example, Co/zinc [92]. 

An attempt has been made to study Co atoms on the surfaces of single crystals of tungsten and silver by measuring the anisotropy of the recoil-free fraction, but lack of detailed knowledge of the type of site occupied by the impurity nucleus at the surface precludes an unambiguous interpretation [102]. 

Tellurium metal shows a substantial quadrupole splitting [48]. The structure contains spiral chains of Te atoms, and a crude estimation of the electric field gradient at the tellurium nucleus leads to a value for the nuclear quadrupole moment of g = 0-20 bam [48]. This agrees well with an earlier value derived by similar means of 1 g = 0 17 bam [58]. Single-crystal measurements have also been made, showing that e qQ is negative [46]. An anisotropy of the recoil-free fraction was also claimed. 

The Mossbauer recoil-free fraction, the anisotropy in the recoil-free fraction and the thermal shift, when studied as a function of temperature, may all yield information on lattice dynamics which is as useful as that obtained from heat capacity or X-ray scattering measurements. One obvious advantage of the Mossbauer technique is the fact that it measures the vibrational modes of the Mossbauer probe, thereby yielding information on local modes which is unobtainable by other techniques. 

Studies with single-crystal absorbers can give the details of f 6). Mossbauer nuclei attached to a surface of a crystal, or embedded in other two-dimensional systems, e.g. Mossbauer nuclei intercalated into graphite, also exhibit large anisotropy in their recoil-free fraction. Several studies of single crystals and two-dimensional systems have been reported. In most cases the isotopes used for the studies were Sn and Fe (Herber Maeda, 1980 Howard Nussbaum, 1980). 

The possible contributions of the Mossbauer technique to the study of phase transitions has been outlined previously (Shenoy, 1973). Almost all phase transitions cause changes in the lattice dynamics of the crystal and these changes can be studied through measurements of the recoil-free fraction, its anisotropy and the second-order Doppler shift. The phase transition itself is in many cases also observed through changes in the hyperfme interaction parameters. 

The tilt angle and lattice contribution to the vibrational anisotropy in an H-phase of a mesogen was studied via the anisotropy of the recoil free fraction [23]. Other Mossbauer studies examined anisotropic diffusion at a glass transition involving an H phase to supercooled H phase transition temperature [24],... 

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