Size and crystal symmetry breaking effects on negative thermal expansion in ScF3 nanostructures

Nowadays, one of the most typical and important potential applications of negative thermal expansion (NTE) materials is to prepare zero thermal expansion or controllable coefficient thermal expansion materials by compounding them with positive thermal expansion materials. The research on NTE properties at the nanoscales is the basis and premise for the realization of high-quality composites. Here, using first-principles calculations, we take a typical open framework material ScF3 as an example to study a new NTE mechanism at the nanoscale, which involves edge and size effects, as well as crystal symmetry breaking. By analyzing the vibrational modes in ultrathin ScF3 films, three effects contributing to the NTE properties are identified, namely, the acoustic mode (ZA mode) induced by surface truncation, the enhanced rotations of ScF6 octahedra in the surface layer and the suppressed rotations of ScF6 octahedra in the inner layer due to crystal symmetry breaking. With increasing thickness, the effect of the ZA mode vibration gradually weakens, while the rotations of the ScF6 octahedra in the surface and inner layers are enhanced. Ultimately, the approximately mutual compensation of these three effects makes the NTE coefficients of different thicknesses almost unchanged. Finally, we simply generalize our conclusions to zero dimensional nanoparticles. This work reveals a new NTE mechanism in low-dimensional open framework materials, which serves as a guide in designing NTE materials at the nanoscale.