Theoretical analysis of occupational ordering in hexagonal interstitial compounds: carbides, nitrides and oxides with “ε-type” superstructures

Abstract

Different types of N-ordering assigned to the ε-phase in the system Fe/N, ε-Fe 3N 1+ x , serve as prototypes for the very common so-called “ε-type” occupational ordering of interstitials: in hexagonal interstitial compounds MX y with y≤0.5 and M in an hcp arrangement with X in octahedral interstices, ordering of X leads to a 3 1/2×3 1/2×1 superstructure. The relevant space group symmetries of these “ε-type” structures are P6 322 , P 3 1m and P312. The variety of theoretically possible structures of “ε-type” ordered interstitial compounds is analysed for the general case of partial order and varying composition. It appears advantageous to describe the distribution of the interstitial atoms, i.e. the occupancies of the six octahedral sites within the unit cell, using so-called static concentration waves (SCWs). Their parameters are closely related to the (powder) diffraction patterns of the phases. This relation makes it easy to show which information about the interstitial atom distribution may be extracted from diffraction patterns and which information is lost. In certain cases this may lead to homometric structures of different space group symmetries. Landau theory can eliminate some of the structural ambiguities resulting from the analysis of diffraction patterns. Within its framework the SCW parameters are closely related to order parameters. This allows us to analyse and classify phases and compounds (many transition metal carbides, nitrides or oxides) with “ε-type” ordering and possible order–disorder phase transitions.