Unraveling microstrain-promoted structural evolution and thermally driven phase transition in $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals at high pressure

Here, we report an irreversible cubic-to-monoclinic structural transition in cubic $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals which occur at pressures above $\sim 8.9\mathrm{GPa}$ upon nonhydrostatic compression in association with a pronounced volume collapse. This phase-transition–induced anomaly is further confirmed by our experimental Raman spectroscopy measurements and theoretical predictions. After annealing, however, this high-pressure monoclinic $m\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ phase undergoes a reversible back-transformation to the cubic counterpart at $\sim 1123\mathrm{K}$ and 9.0 GPa. Our observed transition pressure of $\sim 8.9\mathrm{GPa}$ for the cubic-to-monoclinic structural evolution is significantly lower than that from the previously diamond-anvil-cell–based hydrostatic x-ray experiments because of the existence of internal microscopic stress and/or high-stress concentration in the specimen caused by grain-to-grain contacts upon nonhydrostatic compression, which promoted the cubic-to-monoclinic structural transition. Moreover, we have reported new thermoelastic properties of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals at simultaneous high-pressure and high-temperature conditions. These findings/results may have significant implications for the design of phase-switching devices and for the exploration of the structural relationship among sesquioxides for their uses in extreme environments.

Figure 1

Crystal structures of (a) cubic bixbyite-type structured ${\mathrm{Sc}}_2{\mathrm{O}}_3$ ($c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$; space group:$Ia\overline{3}$; $Z$ = 16) with six-coordinated scandium (Sc) cations and (b) high-pressure phase of monoclinic ${\mathrm{Sc}}_2{\mathrm{O}}_3$ structure ($m\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$; space group: $C2/m$; $Z$ = 6), where the six- and seven-coordinated sites are occupied by the Sc cations. Blue and red spheres represent Sc and oxygen (O) ions, respectively. (c) Refined energy-dispersive x-ray diffraction pattern of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals at ambient conditions, showing a cubic structure (space group:$Ia\overline{3}$).

Figure 2

(a) Representative x-ray diffraction patterns for ${\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals under nonhydrostactic compression in comparison with those at simultaneous high pressure and high temperature. (b) Enlarged x-ray diffraction patterns for ${\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals under nonhydrostatic high-pressure conditions (cold compression), showing the appearance of new peaks resulting from the pressure-induced cubic-to-monoclinic phase transition. The labeled blue asterisks are the new peaks (or trace) from monoclinic structured ${\mathrm{Sc}}_2{\mathrm{O}}_3$. The red tick marks correspond to the peak positions of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$.

Figure 3

(a) Synchrotron in situ x-ray diffraction pattern of monoclinic $m\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ at 12.3 GPa and 300 K upon compression. (b) In situ x-ray diffraction pattern of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ at 9.0 GPa and 1123 K, as back-transformed from the high-pressure monoclinic phase of $m\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ after annealing. Red crosses and green curves denote the observed and calculated profiles, respectively. The difference curve between the observed and the calculated profiles is shown in brown. The blue tick marks correspond to the peak positions.

Figure 4

(a) Lattice parameters and volumes per formula for ${\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals as a function of pressure (upon cold compression), showing a pronounced pressure-induced volume collapse at pressures above $\sim 8.9\mathrm{GPa}$ resulting from the cubic-to-monoclinic phase transition. The straight color lines are guides to the eyes. (b) Plot of $\mathrm{\Delta }{d}_{\mathrm{obs}}^2/d^2$ versus $d^2$ according to the modified Williamson-Hall equation for $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ nanocrystals at ambient conditions. It illustrates the determination of apparent strain and crystallite/grain size from the intercept and slope of the fitted linear lines. The raw data of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ are shown as the open red squares, and the solid red square denotes the extrapolated value. (c) Plot of $\mathrm{\Delta }{d}_{\mathrm{obs}}^2/d^2$ versus $d^2$ for $m\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ at 12.3 GPa (top) in comparison with the results at the highest $P-T$ conditions of 9.0 GPa and 1123 K for $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ (bottom). (d) Representative $d$-spacing ratio of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ as a function of pressure compared with those for metastable $m\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ at 12.3 GPa and the reconstructive $c\text{−}{\mathrm{Sb}}_2{\mathrm{O}}_3$ after annealing at 1123 K and 9.0 GPa, indicating an apparent microstrain-promoted reconstructive phase transition. The straight (dash) lines are guides to the eyes.

Figure 5

(a) $P-V-T$ relations of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ obtained from the current experiments (denoted in different color circles). The isothermal compression curves at various temperatures (in different color curves) are calculated by the third-order high-temperature Birch-Murnaghan equation of state (EOS) with the derived theromoelastic properties of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$. Comparison of room-temperature $P-V$ relations in $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ is shown as an inset. (b) The isothermal bulk modulus as a function of temperature (top); the bulk moduli at ambient pressure and various temperatures are derived by fitting the current $P-V$ data to the third-order Birch-Murnaghan EOS with a fixed $\partial B/\partial P=4.0$, yielding $\partial B/\partial T=-3.98\times {10}^{-2}\mathrm{GPa}/\mathrm{K}$. The unit-cell volume of $c\text{−}{\mathrm{Sc}}_2{\mathrm{O}}_3$ as a function of temperature (bottom), as described by $V=V_0\int \alpha \left(T\right)dT\left({\AA }^3\right)$, where the volumetric thermal expansivity at ambient pressure is $\alpha \left(T\right)=0.61\times {10}^{-5}+3.76\times {10}^{-8}T$ (K). The unit-cell volumes at atmospheric pressure and various temperatures are derived by fitting the present $P-V$ data to the third-order Birch-Murnaghan EOS with a fixed $\partial B/\partial P=4.0$.