Atomistic calculations of lattice constants of mullite with its compositions

We calculate lattice constants a and b of mullite with its compositions (Al2[Al2+2xSi2−2x]O10−x) using the constant stress molecular dynamics (MD) method. The Matsuiʹs and Winklerʹs interatomic models for aluminosilicate are adapted. Two sets of mullite models are considered, one with a random distribution of oxygen vacancies and Al/Si substitutions and the other with a partially ordered Al occupancy at the T* sites. All the simulation results predict the trend observed in experiments in which the lattice constant a increases while b decreases when the x-value increases. The expansion mechanism induced by Al/Si substitutions is supported by bond length analysis. The reduction of lattice constant b is supported by the locally anisotropic atom displacement in the a and b directions sensed by the oxygen vacancies. We conclude that the causes of lattice expansion and reduction are tightly interwoven with the coexistence of vacancies and Al/Si substitutions and their inherent influence on atom displacements.