Pressure induced solid-solid reconstructive phase transition in $\mathrm{LiGa}{\mathrm{O}}_2$ dominated by elastic strain

Pressure induced solid-solid reconstructive phase transitions for graphite-diamond, and wurtzite-rocksalt in GaN and AlN occur at significantly higher pressure than expected from equilibrium coexistence and their transition paths are always inconsistent with each other. These indicate that the underlying nucleation and growth mechanism in the solid-solid reconstructive phase transitions are poorly understood. Here, we propose an elastic-strain dominated mechanism in a reconstructive phase transition, $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ to $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$, based on in situ high-pressure angle dispersive x-ray diffraction and single-crystal Raman scattering. This mechanism suggests that the pressure induced solid-solid reconstructive phase transition is neither purely diffusionless nor purely diffusive, as conventionally assumed, but a combination. The large elastic strains are accumulated, with the coherent nucleation, in the early stage of the transition. The elastic strains along the $\langle 100\rangle$ and $\langle 001\rangle$ directions are too large to be relaxed by the shear stress, so an intermediate structure emerges reducing the elastic strains and making the transition energetically favorable. At higher pressures, when the elastic strains become small enough to be relaxed, the phase transition to $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$ begins and the coherent nucleation is substituted with a semicoherent one with Li and Ga atoms disordered.

Figure 1

(a) ADXRD patterns for $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ at different pressures at room temperature. The red asterisks mark the new peaks of $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$; (b) detailed ADXRD patterns of the (110) and (011) peaks; (c) pressure dependence of the (110) and (011) peaks’ positions.

Figure 2

(a) Rietveld refinements for $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ at 2.4 and 11.1 GPa, respectively; (b) Rietveld refinement for the quenched $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$; insets represent the atomic structures.

Figure 3

(a) Pressure-dependent lattice parameters of $\beta -\mathrm{LiGa}{\mathrm{O}}_2$; (b) volume changes under high pressure for $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ and $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$ are fitted to a third-order Birch-Murnaghan equation; the blue dots represent experiments done with an ethanol-methanol mixture (1:4) as the pressure transmitting medium and the red asterisks represent experiments with NaCl; (c) Pressure dependence of $d$ spacing of ${\left(201\right)}_{\beta }$ and ${\left(101\right)}_{\gamma }$; (d) pressure-dependent lattice parameters of $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$.

Figure 4

(a,b) Lattice strains for $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ and $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$ with increasing pressure; (c,d) pressure dependence of the microscopic elastic strains for $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ and $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$.

Figure 5

(a) Typical Raman spectra of $\beta -\mathrm{LiGa}{\mathrm{O}}_2$ at different pressures. The red asterisks denote the occurrence of the intermediate structure; (b) pressure dependence of the Raman modes in both structures.

Figure 6

Evolution of the ${\mathrm{A}}_{1\mathrm{TO}}$ and ${\mathrm{A}}_{1\mathrm{LO}}$ modes at varying pressures; (a) Lorentzian fits for the ${\mathrm{A}}_{1\mathrm{TO}}$ and ${\mathrm{A}}_{1\mathrm{LO}}$ modes at different pressures; the red asterisk represents the new peak of the intermediate structure; (b) Raman shift of the ${\mathrm{A}}_{1\mathrm{TO}}$ and ${\mathrm{A}}_{1\mathrm{LO}}$ modes as a function of pressure; the red asterisks represent the new peak values, associated with the intermediate structure; the inset is the atomic displacement for the two modes in the $\langle 100\rangle$ and $\langle 100\rangle$ directions.

Figure 7

Mechanism of the structural transformation from β- to $\gamma -\mathrm{LiGa}{\mathrm{O}}_2$; the small arrows in the intermediate structure show the directions to which the internal atomic coordinates are shifted. The coherent ${\left(201\right)}_{\beta }$ and ${\left(101\right)}_{\gamma }$ planes are presented before and after the transition.