Anisotropic negative thermal expansion in high-pressure phases of ScF₃

Negative thermal expansion (NTE) is a counterintuitive phenomenon, in which materials undergo contraction as they are heated. ScF₃, a well-known NTE material, has been reported to show NTE coefficients up to 1000 K. Under ambient conditions, ScF₃ crystallizes in a cubic symmetry (Pm3̄m space group), the same as that in the ReO₃-type structures. Crystal structure predictions (CSPs) show that at P = 1 GPa, a phase transition occurs in cubic ScF₃ to form the rhombohedral phase (R3̄C space group). Quasi-harmonic approximation (QHA) calculations under high pressure conditions show that this new phase can show anisotropic NTE coefficients. The stability of this phase persists until 4 GPa. Beyond 4 GPa, the rhombohedral phase further undergoes a phase transition into an orthorhombic phase (Immm space group) with a non-corner-shared polyhedron network. This phase exhibits NTE along only one crystallographic axis, while the other two axes show no NTE response. On further increasing the pressure to 6 GPa, a trigonal-prismatic arrangement of ScF₃ is obtained (R32 space group), which shows a reasonably better NTE than the previous phase due to the corner shared framework and remains stable until 9 GPa. All the phases show mechanical stability. Ab initio molecular dynamics (AIMD) simulations show that both the cubic and the rhombohedral phases show bond-length elongation as well as deviation in dihedral angle confirming their NTE.