We present a study on the interpretation of conversion electron Mossbauer spectra reflecting an infinite number of sites, in casu Mossbauer spectroscopy on Fe1-xSi layers on Si, synthesized by pulsed laser annealing. These spectra display a broad double-peaked resonance, reflecting the numerous different environments of the Fe-57 probe due to a distribution of vacancies on the Fe sublattice. The spectra can be fitted in many different ways; hence finding a reliable physical interpretation is not straightforward. Therefore ab initio calculations have been performed in order to obtain a priori information about the hyperfine interaction parameter distributions. For this material, the electric-field gradient on the Fe-57 atoms turns out to depend on details in the configuration of neighbors as far as the sixth neighbor shell. The isomer shift appears to be determined by the number of Fe atoms in the first and second Fe neighbor shells only. This leads to the construction of an ab initio based model predicting the mean isomer shift and its distribution for a given Fe1-xSi layer with a known Fe concentration profile. By applying this model new information from the experimental data can be extracted: we show that after applying one or two laser pulses, the Fe atoms are not completely randomized at an atomic scale. The relation of this model to other approaches of analyzing Mossbauer spectra with a distribution of sites is discussed, as well as the difference between the present results on [CsCl]Fe1-xSi and earlier interpretations in the literature. This work reveals how a combination of Mossbauer experiments and ab initio calculations leads to a more reliable interpretation of Mossbauer spectra reflecting an infinite number of sites.