Colossal Pressure-Induced Softening in Scandium Fluoride

The counterintuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behavior that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealized model and neutron diffraction at variable temperature and pressure, we show the existence of extraordinary and unprecedented pressure-induced softening in the negative thermal expansion material scandium fluoride ${\mathrm{ScF}}_3$. The pressure derivative of the bulk modulus $B$, $B^{\prime }=(\partial B/\partial P{)}_{P=0}$, reaches values as low as $-220\pm 30$ at 50 K, and is constant at $-50$ between 150 and 250 K.

Figure 1

(a) Representation of the potential energy of a bond between two atoms as a function of separation $r$: the mean separation increases with temperature. (b) Illustration of the tension effect: transverse motions of an atom connected to two other atoms will pull the neighboring atoms together if the motions do not stretch the bonds. (c) Crystal structure of ${\mathrm{ScF}}_3$ showing transverse motions of the F atoms by representing the atoms as ellipsoids whose major axes reflect the thermal motion. (d) Top: A perfect alignment of atomic octahedra as in ${\mathrm{ScF}}_3$. In this arrangement compression (stretching) along the horizontal axis involves compression (stretching) of the bonds. Bottom: An elevated-temperature configuration where the thermal motion has rotated the octahedra. Compression or stretching now involves rotations of the bonds.

Figure 2

$P(V)$ curves showing data from molecular dynamics simulation (a) and diffraction experiment (b) shown as filled circles, with the fitted third-order Birch-Murnaghan equation of state [Eq. (1)] shown as curves.

Figure 3

Temperature dependence of $B_0$ (a) and $B^{\prime }$ (b) obtained from fitting the third-order Birch-Murnaghan equation of state to crystal volume obtained from molecular dynamics simulation of our idealized model for ${\mathrm{ScF}}_3$. The actual fitting is shown in Fig. 2.

Figure 4

Temperature dependence of $B_0$ (a) and $B^{\prime }$ (b) obtained from fitting the third-order Birch-Murnaghan equation of state to experimental data for the crystal volume as obtained from Rietveld analysis of diffraction data. The fitting is shown in Fig. 2.

Figure 5

Mean-squared transverse displacement of the F atoms obtained from refinement of the crystal structure.