A two-dimensional spin model of Al/Si order in feldspars: visualization of short-range and long-range order

Ordering schemes analogous to the Al,Si ordering in albite and anorthite are simulated using a two-dimensional spin model. Equilibrium calculations are performed using the square approximation of the cluster variation method. A stochastic algorithm is developed to visualize ordering patterns and domain textures of typical Al,Si configurations with short- and long-range order. At the rather low Al/Si ratio of albite a high degree of short-range order (SRO) is expected as a consequence of strong interaction within first-neighbour Al,Si pairs. At a higher Al/Si ratio of anorthite long-range order (LRO) of anorthite-type appears to be a better alternative to the SRO. The SRO/LRO transition occurs due to the destabilization of anti-phase boundaries between short-range ordered domains. LRO of albite-type is stabilized mainly by the interaction within second-neighbour Al,Si pairs, which is less strong in comparison to the first-neighbor interaction.