Polarization Effects in Mössbauer Absorption by Single Crystals
There are a number of reasons for analyzing Mössbauer intensity measurements in single crystal samples. By studying the total intensity as a function of direction in the crystal, one can hope to obtain the six parameters that describe the mean square displacement at a resonant site. By studying relative intensities in a nonmagnetic crystal, one can hope to obtain the three or four parameters describing the electric field gradient at a resonant site which are not determined by the line positions. In a magnetic crystal one can hope to find the internal field directions and hence to learn a great deal about the magnetic structure.
Since in practice it is rarely possible to work with single crystal absorbers thin enough that saturation effects can be neglected, it is necessary to have a method of analysis in which saturation is taken into account. In a single crystal the absorption cross section at any energy will, in general, be partially polarized. It is easy to see that this will affect the saturation of the absorption. For example, consider an unpolarized incident beam and a completely polarized absorber. No matter how thick the absorber is made, in this case only half the incident beam can be resonantly absorbed. Corresponding to each absorption resonance is a contribution to the real part of the index of refraction having the same polarization but a different energy dependence. These lead to birefringence effects, which, by altering the polarization of radiation propagating through the crystal, can in turn affect the absorption. Blume and Kistner have described an elegant method for treating both these effects by using a 2 × 2 complex matrix to represent the index of refraction of the absorber. If the internal field parameters and the mean square displacements in an absorber are known, the transmitted intensities can be calculated in a straightforward manner.
In the applications described above, it is necessary to go in the other direction and obtain the internal field parameters and mean square displacement values from the measured intensities. This is greatly simplified in several cases which will be described. The most important case is if measurements are made along certain high symmetry directions in otherwise arbitrarily complicated crystals. In these cases the incident gamma-ray beam may be decomposed into two components, each propagating through the crystal with its own complex index of refraction.
The deviation of the index of refraction from one may be regarded as due to the part of the incident radiation coherently scattered in the forward direction. Conditions for neglecting effects of coherent scattering in other directions are described.
Use of this analysis will be illustrated with several examples. These include determination of the mean square displacement tensor for Fe in siderite, determination of the mean square displacement and refinement of the electric field gradient for Fe in sodium nitroprusside, and explanation of some apparent anomalies which have appeared in the literature.
KeywordsDensity Matrix Polarization Effect Electric Field Gradient Internal Field Yttrium Iron Garnet
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