Structure and order parameters in the pressure-induced continuous transition in TeO2

Abstract

Lattice parameters of Te${\mathrm{O}}_2$ have been measured from 0 to 32.5 kbar by time-of-flight neutron diffraction. Atomic-position parameters have also been measured to 20 kbar for both the low-pressure tetragonal paratellurite phase and the high-pressure orthorhombic phase, which we determined to have a structure belonging to the $D_2^4\left(P{2}_1{2}_1{2}_1\right)$ space group. We found no hysteresis in the lattice parameters or position parameters in cycling through the transition. We also found that $\frac{{\mathrm{}(b-a)\mathrm{}}^2}{a_0^2}$ in the high-pressure phase varied linearly with pressure with a slope of 2.53(1) × ${10}^{-4\mathrm{}}$/kbar, going to zero at 9.1 kbar. We detected no discontinuity in volume or the $c$ parameter, but observed anomalies in the slopes $\frac{\mathrm{dV}}{\mathrm{dP}}$, $\frac{d(a+b)\mathrm{}}{\mathrm{dP}}$, and $\frac{\mathrm{dc}}{\mathrm{dP}}$. All of these observations are additional experimental evidence for the continuous nature of the transition. The observed $D_2^4$ structure of the high-pressure phase is a subgroup of order 2 of the $D_4^4$ paratellurite phase which means that the free energy is an even function of the order parameter, but third-order terms coupling the primary order parameter with secondary or induced order parameters can still be formed. These can be nonzero without affecting the second-order nature of the transition. The primary order parameter ${\eta }_1=e_1-e_2$ and the two induced order parameters which we observed, ${\eta }_2=e_1+e_2$ and ${\eta }_3=e_3$, have been used to derive a Landau-like free-energy expansion describing the thermodynamics of the transition. Very little displacement of the Te atoms was observed in going through the transition, but the oxygen atoms underwent large displacements as a function of pressure. There is no change of size of the unit cell at the transition so it is a pure strain transition of the type first discussed by Anderson and Blount.