Glass bead games: enumeration of possible polytypes based on two stacking vectors and applications to the iron-ore...

Polytypes can occur in many inorganic and organic compounds alike. In the most basic scenario, different polytypes of a compound are based on translationally equivalent layers and two equivalent arrangements of adjacent layers. This means there are only two distinct stacking vectors, t₁ and t₂. For this particular situation, we have enumerated the number of principally different polytypes for a given number m of layers in the stacking sequence, under the assumption of the validity of four constraints: (i) periodicity, (ii) exchangeability, (iii) reversibility and (iv) simplicity. Different results are obtained when the reversibility constraint is overturned, a factor that depends on the polar or non-polar character of the underlying layers. The results of this theoretical study have been applied to derive the existing polytypes up to m = 6 for two different polysomes of the family of so-called silico-ferrites of calcium and aluminium (SFCA and SFCA-I, respectively). These phases are of considerable interest to the steel industry, as they represent the primary constituents of the matrix in iron-ore sinters. Finally, the impact of polytypism on the powder diffraction patterns of the SFCAs was investigated and the influence of stacking disorder on the diffractograms was analysed. The resulting collection of simulated powder diffraction patterns may serve as a reference database for the identification of polytype effects in industrial sinters.