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Two problems that arise frequently in Mössbauer measurements of ⁵⁷Fe in mineral powders are: (1) relating measured areas to quantitative Fe²⁺/Fe³⁺ ratios, and (2) assigning relative contributions of texture, relaxation phenomena and anisotropy in sample recoilless fractions (Goldanskii-Karyagan Effect) to explain asymmetries in quadrupole doublets. Implicit in both is a knowledge of sample recoilless fractions. This quantity is fundamental to Mössbauer spectroscopy, but paradoxically, it is difficult to measure unambiguously. Historically, three approaches have been used: (1) temperature-dependent measurement of second-order Doppler shifts in powders, (2) use of X-ray determined mean-squared-displacements (MSD's) and, (3) direct Mössbauer measurement of the <MSD> tensor in single crystals. The first two methods have several disadvantages, so we have focused on the third method. The need for high signal quality and corrections for thickness and polarisation have previously limited the application of the third method to large, thin crystals; however use of the milliprobe technique (see Sect. 3.2g) enables single crystals in the size range 200 - 500 µm to be studied successfully.

We have measured Mössbauer spectra of cubic garnet crystals, maximum dimension approximately 200 µm, of predominantly pyrope-almandine composition obtained as diamond inclusions from George Creek (see Sect. 3.2g). The electric-field gradient tensor and principal directions of the <MSD> tensor are completely known from previous magnetic-field dependent measurements and from crystal symmetry. The remaining <MSD> principal values can then be determined unambiguously from area-ratio measurements in relatively few crystal orientations. From the single crystal results the expected powder spectra can be computed and compared to experiment and to that calculated from X-ray determined MSD's.

We are also studying single-crystals of pyroxene. We have obtained good small crystals of selected endmember pyroxenes and plan to determine completely both the electric-field gradient (EFG) and <MSD> tensors. Previous work has shown that 'microscopic' EFG's (i.e. for individual lattice sites) can be determined uniquely when simultaneously refined with <MSD> data, even for low symmetry sites where conventionally only a 'macroscopic' (average) EFG has been measured.