Competing dynamical and lattice instabilities in ${R\mathrm{VO}}_4$ rare-earth vanadium oxides under high pressure

Zircon-type ${R\mathrm{VO}}_4$ compounds (where R = rare-earth atom) constitute a family of ternary oxides which are abundant in both nature and the industrial field. Their structural systematics upon compression has been widely studied. According to the observed systematics, the high-pressure crystal structure is determined by the rare-earth cation size. Nonetheless, the mechanisms involved in the phase transitions remain relatively unexplored. Thus, we gathered the experimental data reported in the literature and compared it to our ab initio calculations, including not only enthalpy, but also the frequency of lattice modes and the value of elastic constants. Our study reveals systematic trends, where high-pressure phases appear only if they are thermodynamically stable and are always preceded by a mechanical or dynamical instability, which counteracts the effects of kinetic barriers in the zircon-to-monazite or -scheelite phase transition, respectively.

Figure 1

Selected planes of the zircon- (left) and scheelite-type (right) structures. The rotation of the ${\mathrm{VO}}_4$ units around the $c$-axis direction, corresponding to the softening of the $B_{1\mathrm{u}}$ mode, is represented in the upper part of the figure, between both structures.

Figure 2

(Left) Zircon-type ${R\mathrm{VO}}_4$ unit cell. Black arrows indicate the vibrational directions and amplitudes of the $B_{1\mathrm{u}}$ silent soft phonon. (Right) Zircon unit-cell distorted according to such phonon; ${R\mathrm{O}}_8$ and ${\mathrm{VO}}_4$ polyhedral units are depicted in purple and red, respectively.

Figure 3

Calculated pressure dependence of the frequency of the $B_{1\mathrm{u}}$ silent mode for ${\mathrm{HoVO}}_4$, ${\mathrm{DyVO}}_4$, ${\mathrm{ErVO}}_4$, and ${\mathrm{LuVO}}_4$. The frequency clearly shrinks to zero at pressures between 7 and 9 GPa.

Figure 4

Pressure evolution of the nonzero stiffness coefficients of zircon-type ${\mathrm{PrVO}}_4$. Inset: Pressure dependence of the smallest eigenvalue of the stiffness tensor, which shrinks to zero at 5.1 GPa.

Figure 5

Schematic representation of the steps required to transform the zircon into the monazite phase; the four images correspond to (a) projection of the zircon phase, (b) deformation of the zircon unit cell according to a pure shear distortion, (c) tilting of the ${\mathrm{VO}}_4$ tetrahedra in the distorted structure, and (d) projection of the monazite unit cell.

Figure 6

Experimental transition pressures (represented as vertical bars) of the ${R\mathrm{VO}}_4$ family from $R=\mathrm{Lu}$ to La, extracted from Refs. [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 41]. The results from our ab initio calculations are represented by symbols. The meaning of the different bar colors and symbols is indicated in the legend over the figure. The lanthanum symbol is labeled with an asterisk to note that we are dealing with metastable zircon-type ${\mathrm{LaVO}}_4$.