Dimensional analysis of interstitial phases with the AlCr2C structure

Abstract

A dimensional analysis is reported of interstitial phases with the hexagonal AlCr2C, NM2C, structure, which is based on examining the variation of the unit-cell parameters a and c as functions of DM and DN, the diameters of the M and N components for CN 12. The observed behaviour is uniquely different to that of phases with all other structures so examined, there being a drastic change of the DN dependences of a and c in the region where a ≃ DN. Nevertheless, equations are derived which reproduce the a and c dependences on DM, DN and the valency of the M component to better than 0.5% and which indicate the atomic arrays that control the cell dimensions. It is found that the M-M distances that do not lie in (0001) planes and which form half of the sides of the M octahedra surrounding the metalloid atoms, are an invariant feature of the structure for phases with the same M component. This invariant distance couples a, c and z, the atomic parameters of the M atoms, and it causes e dependences on 6.5DN (a > DN) and -1.65DN (a < DN), which could not possibly arise through the intrinsic contacts of the N atoms. The electronic distribution from the M atoms to M-M and M-N contacts and also to bands derived from the metalloid 2p states and transition-metal d states, is further analysed to account for the apparent dependence of a and c on the M-atom valency. The cell dimensions of SnM2C phases with the AlCr2C structure do not follow the systematic variations discussed above; reasons are advanced for this.