ANALYSIS OF TEXTURE AND VIBRATIONAL ANISOTROPY BY MÖSSBAUER SPECTROSCOPY

Abstract

The study of the line intensities in a hyperfine pattern makes possible an analysis of the texture or VA. The basic principles of the method are : The (unknown) texture distribution is expanded in a series of spherical harmonics and also the angular dependencies of the resonant absorbed y-radiation which appear in the intensity integrals. These integrals thus are simplified to a k i t e sum of spherical harmonics with the unknown expansion coefficients of the texture function as factors. Respecting the relations for rotation of spherical harmonics a set of intensity ratio measurements for different angle positions of source (polarized) and absorber can be solved for the texture expansion coefficients by a least square fit procedure. Application of this method to the vibrational anisotropy problem makes possible the determination of the anisotropy parameter and allows to distinguish between texture and Goldanskii-Karyagin effect. 1. Basic concept of texture investigation by Mossbauer effect. The spatial orientational distribution of many physical parameters such as grain distribution inia polycrystalline metal or distribution of the spins in a magnetic material, are important as well for technical and metallurgical applications as especially in respect to spin structure problems in physical research. For the orientation of an assembly we will adopt the expression texture, where the degree of orientation may range from ideal, complete orientation (e. g. monocrystal) over preferred orientation (texture in its proper sense) until random orientation. The physical parameters whose texture we will deal with here are the principal axis of the electric field gradient (Vz',,, q = 0) or the internal magnetic field on the nucleus site. There are several possibilities of representing a texture. We characterize it here by a function D (8, cp) where D represents the probability to find spins or VZzfs directed with the polar and azimuthal angles (8, cp) towards a surface element dQ (cf. [I]) of an unit sphere. For instance a random texture will be where we respected the normalization condition