Optical and structural study of the pressure-induced phase transition of ${\mathrm{CdWO}}_4$

The optical absorption of ${\mathrm{CdWO}}_4$ is reported at high pressures up to 23 GPa. The onset of a phase transition was detected at 19.5 GPa, in good agreement with a previous Raman spectroscopy study. The crystal structure of the high-pressure phase of ${\mathrm{CdWO}}_4$ was solved at 22 GPa, employing single-crystal synchrotron x-ray diffraction. The symmetry changes from space group $P2/c$ in the low-pressure wolframite phase to $P{2}_1/c$ in the high-pressure postwolframite phase accompanied by a doubling of the unit-cell volume. The octahedral oxygen coordination of the tungsten and cadmium ions is increased to [7]-fold and [6+1]-fold, respectively, at the phase transition. The compressibility of the low-pressure phase of ${\mathrm{CdWO}}_4$ has been reevaluated with powder x-ray diffraction up to 15 GPa, finding a bulk modulus of $B_0=123$ GPa. The direct band gap of the low-pressure phase increases with compression up to 16.9 GPa at 12 meV/GPa. At this point an indirect band gap crosses the direct band gap and decreases at $-2$ meV/GPa up to 19.5 GPa where the phase transition starts. At the phase transition the band gap collapses by 0.7 eV and another direct band gap decreases at –50 meV/GPa up to the maximum measured pressure. The structural stability of the postwolframite structure is confirmed by ab initio calculations, finding the postwolframite-type phase to be more stable than the wolframite at 18 GPa. Lattice dynamic calculations based on space group $P{2}_1/c$ explain well the Raman-active modes previously measured in the high-pressure postwolframite phase. The pressure-induced band gap crossing in the wolframite phase as well as the pressure dependence of the direct band gap in the high-pressure phase are further discussed with respect to the calculations.

Figure 1

Projections along (a) the [010] direction of the wolframite and (b) the [011] direction of the postwolframite-type structures of ${\mathrm{CdWO}}_4$. The large white and black spheres represent the Cd and W atoms, respectively. The small spheres are the O atoms.

Figure 2

Optical absorption spectra of ${\mathrm{CdWO}}_4$ at different pressures up to 23 GPa. The inset shows the change of the shape of the absorption edge at 16.9 GPa compared to the spectrum at 15.0 GPa.

Figure 3

(a) Fits to the Urbach's rule (red line) to two spectra at 5.8 and 21.7 GPa (black points) that correspond to the low-pressure and high-pressure phases of ${\mathrm{CdWO}}_4$, respectively. (b) Linear dependence of ${\alpha }^{1/2}$ of the spectrum at 16.9 GPa showing the indirect nature of the band gap at this pressure.

Figure 4

Pressure dependence of the band-gap energy of ${\mathrm{CdWO}}_4$. Open circles represent data from Ref. [10], while filled circles are from data collected in this study. The continuous red lines show the fits.

Figure 5

Pressure dependencies of (a) unit-cell volume, (b) unit-cell axes, and (c) monoclinic $\beta$ angle of ${\mathrm{CdWO}}_4$. Data shown by solid symbols are from Macavei and Schulz [13] (black), and data shown by black (red) open symbols are from the powder XRD (SXRD) experiment. Fits of the data by Macavei and Schulz [13] and of the data including our powder diffraction data up to 15 GPa to Birch-Murnaghan equations of state (EOS) of second order are drawn by black solid and dashed lines, respectively. At the highest pressure of 22 GPa, only half of the unit-cell volume of the postwolframite phase is shown to compare with that of the wolframite phase. Lattice parameters at 22 GPa were transformed to those of the respective wolframite cell parameters for comparison. Blue lines represent the calculations.

Figure 6

Calculated enthalpy difference of ${\mathrm{CuWO}}_4$-, scheelite-, and postwolframite-type phases of ${\mathrm{CdWO}}_4$ with respect to the enthalpy of the low-pressure wolframite-type phase. The enthalpy of wolframite is taken as reference.

Figure 7

Calculated Raman mode frequencies $\left({\omega }_{\mathrm{calc}}\right)$ represented as a function of the experimentally measured values [12] $\left({\omega }_{\exp }\right)$ (black points) to show their linear relation with slope 1 (red line).

Figure 8

Calculated pressure dependence of the direct $\left(Z\to Z\right)$ and indirect $\left(\mathrm{\Gamma }B\to Z\right)$ band gaps of the low-pressure phase of ${\mathrm{CdWO}}_4$.

Figure 9

Electronic band structure of the postwolframite phase of ${\mathrm{CdWO}}_4$ at 18 (black) and 22.8 GPa (red). The Fermi level is shown as a dotted line. The right panel shows the corresponding partial and total electron density of states at 18 GPa.