High-pressure study of the $\beta$-to-$\alpha$ transition in ${\mathrm{Ga}}_2{\mathrm{O}}_3$

The high-pressure behavior of ${\mathrm{Ga}}_2{\mathrm{O}}_3$ is studied up to $40\mathrm{GPa}$ using synchrotron x-ray diffraction and Raman spectroscopy in diamond anvil cells. A phase transformation from the monoclinic $\beta$-phase $(C2∕m)$ is observed at a pressure above 20–$22\mathrm{GPa}$. The high-pressure polymorph is identified as the $\alpha$-phase that is isostructural with corundum ($R\overline{3}c$ symmetry) from the x-ray diffraction data. However, considerable anion disorder is indicated by the appearance of broad bands in the Raman spectra. The experimental results are complemented by ab initio theoretical calculations of the energetics of the two structures and the lattice dynamics.

Figure 1

(a) projection of the monoclinic structure of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ on to the $a$-$c$ plane. Note the ${\mathrm{Ga}}^{3+}$ cations that occupy both tetrahedral and octahedral interstices within the ccp lattice of ${\mathrm{O}}^{2-}$ ions. (b) $a$-$c$ projection of corundum-structured $\alpha \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, containing only octahedrally coordinated ${\mathrm{Ga}}^{3+}$ ions, within an hcp ${\mathrm{O}}^{2-}$ sublattice.

Figure 2

X-ray diffraction patterns obtained during compression of the $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ phase at ambient temperature.

Figure 3

Evolution of the cell parameters of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ with pressure. The solid lines are drawn as a guide to the eye.

Figure 4

(a) Plot of measured $V∕V_0$ for $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ as a function of pressure (points) along with a third-order Birch-Murnaghan equation of state fitted to the data with $K_0=202\left(7\right)\mathrm{GPa}$ and $K_0^{\prime }=2.4\left(6\right)$. The $K_0$ and $K_0^{\prime }$ values were obtained from a reduced variable $\left(F\text{−}f\right)$ plot. (b) Plot of the normalized pressure $\left(F\right)$ as a function of the Eulerian strain variable $\left(f\right)$ for $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$.

Figure 5

An example of a profile-refined x-ray diffraction data set collected at $38.6\mathrm{GPa}$. The open symbols represent experimental data; the solid curve running through the data corresponds to the calculated pattern. The tick marks indicate the positions of calculated Bragg reflections of $\alpha \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ (indexed on the pattern), and also for Re used as the gasket material. Asterisks show additional peaks that can be assigned to a trace amount of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, remaining in the sample even at this high pressure.

Figure 6

Unpolarized Raman spectrum of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ obtained after annealing a commercial sample. A weak peak at $222{\mathrm{cm}}^{-1}$ is due to a trace of $\alpha \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ remaining after the heat treatment.

Figure 7

Unpolarized Raman spectrum of $\alpha \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ obtained from the synthesis described in Ref. 11. The sample was obtained from Prof. A.V. Chadwick, University of Kent at Canterbury.

Figure 8

Raman spectra of ${\mathrm{Ga}}_2{\mathrm{O}}_3$ obtained during “slow” compression.

Figure 9

Calculated VDOS for $\alpha \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, using ab initio (LDA) theoretical methods.

Figure 10

Raman spectra of ${\mathrm{Ga}}_2{\mathrm{O}}_3$ obtained during “rapid” compression.

Figure 11

Raman spectra of ${\mathrm{Ga}}_2{\mathrm{O}}_3$ during “slow” decompression.

Figure 12

Raman spectra of ${\mathrm{Ga}}_2{\mathrm{O}}_3$ during “rapid” decompression.