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 ${D}_{2}^{4}(P{2}_{1}{2}_{1}{2}_{1})$ space group. We found no hysteresis in the lattice parameters or position parameters in cycling through the transition. We also found that $\frac{{(b\ensuremath{-}a)}^{2}}{{a}_{0}^{2}}$ in the high-pressure phase varied linearly with pressure with a slope of 2.53(1) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$/kbar, going to zero at 9.1 kbar. We detected no discontinuity in volume or the $c$ parameter, but observed anomalies in the slopes $\frac{\mathrm{dV}}{\mathrm{dP}}$, $\frac{d(a+b)}{\mathrm{dP}}$, 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 ${\ensuremath{\eta}}_{1}={e}_{1}\ensuremath{-}{e}_{2}$ and the two induced order parameters which we observed, ${\ensuremath{\eta}}_{2}={e}_{1}+{e}_{2}$ and ${\ensuremath{\eta}}_{3}={e}_{3}$, 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.