Extended Voigt-based analytic lineshape method for determining N-dimensional correlated hyperfine parameter distributions in Mossbauer spectroscopy

We present a model of the total Probability Density Distribution (PDD) of static hyperfine parameters for Fe-57 Mossbauer spectroscopy that permits the analysis of independent, partially or fully correlated arbitrary-shape partial distributions of center shift (delta) and quadrupole splitting (Delta) or center shift, quadrupole shift (epsilon) acid hyperfine magnetic Zeeman splitting (z). This PDD is shown to yield an analytical lineshape for the Mossbauer signal, in the form of a sum of Voigt lines, making it suitable for fast numerical analysis of spectra. The two specific cases relevant to (1) paramagnetic materials with 2D correlated delta-Delta distributions and (2) magnetically ordered materials with 3D correlated delta-epsilon-z distributions, in the usual perturbation limit (epsilon << z), are treated in detail. The effects of varying degrees of correlations among the various hyperfine parameters are compared to those arising from either zero correlations or perfect correlations corresponding to the usual models that impose a linear coupling between a primary distributed parameter and various slave parameters. Spectral characteristics are identified that arise from correlated N-dimensional PDDs and that cannot be modelled by the usual linear coupling models without requiring many more fitting parameters and leading to significantly different distributions. Finally, we apply our method to the room temperature spectrum of a real magnetically ordered material, a splat quenched Fe50Ni50 alloy, and show its advantages relative to the usual approach.