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Structural modelling of octahedral tilts in perovskites is typically doneusing the symmetry constraints of the resulting space group. In most cases,this introduces more degrees of freedom than those strictly necessary todescribe only the octahedral tilts. It can therefore be a challenge todisentangle the octahedral tilts from other structural distortions such ascation displacements and octahedral distortions. This paper reports on thedevelopment of constraints for modelling pure octahedral tilts and implementedthe constraints in diffpy-CMI, a powerful package to analyse pair distributionfunction (PDF) data. The program allows features in the PDF that come fromrigid tilts to be separated from non-rigid relaxations, provides an intuitivepicture of the tilting, and as it has many fewer refinable variables than theunconstrained space-group fits, provides robust and stable refinements of thetilt components. It further demonstrates the use of the model on the canonicaltilted perovskite CaTiO$_3$ which has a known Glazer tilt system $\alpha^+\beta^- \beta^-$. The Glazer model fits comparably to the corresponding spacegroup model $Pnma$ below $r$ = 14 A and becomes progressively worse than thespace group model at higher $r$ due to non-rigid distortions in the realmaterial.

Refining perovskite structures to pair distribution function data using collective Glazer modes as a basis