Thermal expansion and phase stability of BF3 ( B=Sc , Y, La, Al, Ga, In) from first principles

ScF₃ has attracted much attention because of its simple crystal structure and negative thermal expansion (NTE) over a wide temperature range. No other binary trifluoride has the same crystal structure and exhibits NTE in as wide a temperature range as ScF₃. There has hitherto been no sufficient explanation for this fact. Herein, to discuss the phase stability and the NTE behavior of ScF₃, the six binary trifluorides BF₃ (B = Sc, Y, La, Al, Ga, In) are thoroughly compared by using ab3. 33333pt{0ex}initio molecular-dynamics calculations with the on-the-fly machine-learning technique, first-principles lattice-dynamics calculations, and electronic-structure analyses based on group-representation theory and the band-unfolding method. The present study reveals that (i) the a^-a^-a^- octahedral rotational distortion (ORD) in ScF₃ increases the frequency of the crucial phonons for realizing NTE, leading to a weakening of the NTE behavior under hydrostatic pressure; (ii) the group-representation theory predicts the emergence of ORDs triggered by the second-order Jahn-Teller effect in cubic ScF₃, YF₃, AlF₃, GaF₃, and InF₃; (iii) cubic ScF₃ and YF₃ do not possess ORD without pressure due to their slight orbital overlap between the cations and anions; (iv) ScF₃ has a delicate balance between the repulsive force term and the energy stabilization term, induced by the octahedral rotational phonon modes; and (v) metastable cubic YF₃ and LaF₃ exhibit NTE behaviors. Our findings would provide an understanding of a material-design principle for realizing NTE.