Intermetallic compounds AB5 type (A = rare-earth atoms, B = transition metal) are known to store reversibly large amounts of hydrogen and as that are discussed in this work. It was shown that the alloy cycling stability can be significantly improved by employing the so-called non-stoichiometric compounds AB5+x and that is why analysis of change of structure turned out to be interesting. A tendency for ordering of hydrogen atoms is one of the most intriguing problems for the unsaturated hydrides. The symmetry analysis method in the frame of the theory of space group and their representation gives opportunity to find all possible transformations of the parent structure. In this work symmetry analysis method was applied for AB5+x structure type (P 6/mmm parent symmetry space group). There were investigated all possible ordering types and accompanying atom displacements in positions 1a, 2c, 3g (fully occupied in stoichiometric compounds AB 5 ), in positions 2e, 6l (where atom B could appear in non-stoichiometric compounds) and also 4h, 6m, 6k, 12n, 12o, which could be partly occupied by hydrogen as a result of hydrides. An analysis was carried out of all possible structures of lower symmetry, following from P 6/mmm for k = (0, 0, 0). Also the way of getting the structure described by the P 6 3 mc space group with double cell along the z-axis k = (0, 0, 0.5), as it is suggested in the work of Latroche et al. is discussed by the symmetry analysis. The analysis was obtained by computer program MODY. The program calculates the so-called basis vectors of irreducible representations of a given symmetry group, which can be used for calculation of possible ordering modes.
Symmetry analysis was applied in this work to discuss the behavior of the family R6M23 compounds upon hydrogenation (deuteration), where different structural transformations and magnetic properties, depending on the type of R and M atoms and hydrogen (deuterium) concentrations, have been found. The crystallographic structure of these compounds is described by the Fm3m space group and contain 116 atoms per unit cell occupying the positions 24e(R), 4b, 24d, 32f1 and 32f2(M). Additionally in the elementary cell, there could be up to 100 atoms of hydrogen (or deuterium) occupying the interstitial positions 4a, 32f3, 96j1 and 96k1. The symmetry analysis in the frame of the theory of space groups and their representation gives the opportunity to find all possible transformations from high symmetry parent structure to the structures with symmetry belonging to one of its subgroups. For a given transformation it indicates possible displacements of atoms from initial positions in the parent structure, ordering of hydrogen over interstitial sites and also ordering of magnetic moments, described by the smallest possible number of free parameters. The analysis was carried out by means of the MODY computer program for vectors k = (0; 0; 0) and k = (0; 0; 1) describing the changes of translational symmetry and all positions occupied by the R, M and D atoms.
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