Elemental site substitutions in R-Fe compounds

A model is proposed for calculating the probabilities of atomic substitutions (atom X for atom A) in different A-sites in an A-containing compound. The model consists of three terms. The first term describes the chemical affinity between the X or A atom and its nearest neighbours. The second term accounts for the elastic energy due to the volume mismatch between the X atom and the x A-site. The third term is a structural energy term and is present only for d-electron atoms and accounts for the preference of these metals to crystallize in the bcc, fcc or hcp structures depending on the number of valence electrons per atom. The probability of the substitution is calculated using the Boltzmann distribution assuming that each formula unit of the compound has a maximum of one X atom, and that the X atoms are uniformly distributed throughout the compound.The model was tested successfully for Fe-substitutions in various compounds. The experimental fractional site occupations of the X atoms in the Fe-sites were determined from neutron diffraction measurements. The results show that the model precisely determines the sites preferentially occupied by the X atoms; calculated values are within 40% of the experimental values for all X elements. Moreover, the model correctly predicts sites that are avoided by the X elements.The model calculations for site occupations show that all three terms have to be taken into account to give a quantitative explanation to the experimentally observed substitutions. The agreement between the experimental and calculated values obtained for Fe-substitutions in the 2-17, 3-29, 1-12 and 2-14-1 structures can be improved if the structural term for Fe is assumed to be zero as the Fe structural transition (from bcc to fcc) occurs near the annealing temperatures of the compounds and thus the difference in the structural energy between bcc-Fe and fcc-Fe could be neglected at that temperature. A further improvement can be made if one assumes that the sites which have an irregular shape, such as 9d (2-17), 8j1 (2-14-1), 2c, 4e, 8j4 (3-29) and 8f (1-12) have smaller "effective" volumes, i.e. the "effective" radii of the spherical holes are estimated from the average distances of the closest nearest neighbours. An understanding of the site substitution mechanisms in intermetallic compounds allows us to explain structure-sensitive physical phenomena even in cases where experimental structural data are unavailable. We have studied the anomalous thermal expansion along the c-axis in 2-17 compounds and the reduced rate of the nitrogen bulk diffusion in Nd2Fe 17-deltaXdelta for some X elements.The proposed model for calculating site occupancies is general in scope and can be applied to any intermetallic compound where the site occupations of elemental substitutions need to be determined. The model can be improved if one can determine the contribution of the structural term in the formation of compounds containing two or more transition metals. In order to improve the precision of the elastic term experimental data on the temperature dependence of the bulk and shear moduli of the elements and the compounds will be needed