Anharmonicity and scissoring modes in the negative thermal expansion materials <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ScF</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CaZrF</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>
Tobias A. Bird, J. Woodland-Scott, Lei Hu, Michael T. Wharmby, Jun Chen, Andrew L. Goodwin, Mark S. Senn
Abstract
We use a symmetry-motivated approach to analyzing x-ray pair distribution functions to study the mechanism of negative thermal expansion in two ${\mathrm{ReO}}_{3}$-like compounds: ${\mathrm{ScF}}_{3}$ and ${\mathrm{CaZrF}}_{6}$. Both average and local structures suggest that it is the flexibility of $M$-F-$M$ linkages $(M$ = Ca, Zr, Sc) due to dynamic rigid and semirigid ``scissoring'' modes that facilitates the observed negative thermal expansion (NTE) behavior. The amplitudes of these dynamic distortions are greater for ${\mathrm{CaZrF}}_{6}$ than for ${\mathrm{ScF}}_{3}$, which corresponds well with the larger magnitude of the thermal expansion reported in the literature for the former. We show that this flexibility is enhanced in ${\mathrm{CaZrF}}_{6}$ due to the rocksalt ordering mixing the characters of two of these scissoring modes. Additionally, we show that in ${\mathrm{ScF}}_{3}$ anharmonic coupling between the modes responsible for the structural flexibility and the rigid unit modes contributes to the unusually high NTE behavior in this material.