Ferroelastic phase transitions and anelastic dissipation in the ${\text{LaAlO}}_3{\text{-PrAlO}}_3$ solid solution series

Resonant ultrasound spectroscopy has been used on single-crystal samples to observe pseudoproper ferroelastic softening across the $\left(\text{La},\text{Pr}\right){\text{AlO}}_3$ solid solution. It is suggested that softening is due to the presence of an intrinsic zone-center instability in addition to the small Jahn-Teller stabilization expected for ${\text{Pr}}^{3+}$. Softening increases as smaller ${\text{Pr}}^{3+}$ ions are substituted for larger ${\text{La}}^{3+}$ which is attributed to a simple size effect as well as the possibility of bilinear coupling of the intrinsic instability with the weak Jahn-Teller effect. Superattenuation is observed above 600 K for all samples, which is consistent with twin wall related dissipation behavior seen in other perovskites with octahedral tilting. Superattenuation is also observed in the low-temperature monoclinic phase, implying a high mobility also for the monoclinic twin walls.

Figure 1

Hierarchy of possible phase transitions in ${\text{LaAlO}}_3{\text{-PrAlO}}_3$ due to octahedral tilting (three-component order parameter transforming as irrep ${\text{R}}_4^{+}$) and cooperative Jahn-Teller distortions (two-component order parameter transforming as irrep ${\Gamma }_3^{+}$), from Carpenter et al. (Ref. 8). Different nonzero ${\text{R}}_4^{+}$ components first give the tilted structures and then ${\Gamma }_3^{+}$ components are added. Solid lines represent transitions which are allowed by symmetry to be second order in character, broken lines are required to be first order and dotted lines represent isosymmetric transitions.

Figure 2

${\text{PrAlO}}_3{\text{-LaAlO}}_3$ phase diagram based on data from the literature (Refs. 3, 9, 10) with high-temperature phase transitions for compositions ${\text{Pr}}_0$, ${\text{Pr}}_1$, ${\text{Pr}}_3$, and ${\text{Pr}}_5$ from the present study shown as filled circles.

Figure 3

(Color online) Low-temperature RUS stacks for (a) ${\text{Pr}}_{100}$, (b) ${\text{Pr}}_{75}$, and (c) ${\text{Pr}}_{55}$. In (a) differences in the behavior of the elastic constants are illustrated by the first two peaks in the spectra. Weak peaks present at low frequency and low temperature are due to noise from the RUS instrumentation.

Figure 4

(Color online) Portions of (a) ${\text{Pr}}_1$ and (b) ${\text{Pr}}_{55}$ high-temperature stacks. Note that resonance peaks disappear above $\sim 600\text{K}$ as in ${\text{LaAlO}}_3$ (Ref. 12). Weak peaks that do not change frequency with increasing temperature are from the alumina rods and not from the sample.

Figure 5

(Color online) Changes in the square of the peak frequency (which is proportional to the elastic constants) with temperature for all compositions across the solid solution. Values of frequency squared have been scaled to the same value at 600 K for easier comparison between compositions. Peaks used are those that are at the lowest frequency, except in ${\text{Pr}}_0$ where a peak at a higher frequency was used as it could be followed to a lower temperature and so could better represent the elastic behavior. Small offsets at 300 K are due to the change between high- and low-temperature RUS instruments.

Figure 6

(Color online) Low-temperature part of the ${\text{LaAlO}}_3{\text{-PrAlO}}_3$ phase diagram with transition temperatures from the present study shown as open squares and triangles joined by lines. The values for the transition temperatures came from minima in the square of the peak frequencies for the $R\overline{3}c\text{−}Imma$ transition and the point where the $f^2$ values in Fig. 5 extrapolated to zero for the $Imma\text{−}C2/m$ transition. Values of $T_{\text{c}}^{\ast }$ are shown as crosses (x) joined by a line and $T_{\text{c}}$ by open circles joined by lines; these were obtained by fitting Eq. (2) to data in the $R\overline{3}c$ stability field. Crosses $(+)$ represent the temperature at which a softening trend with falling temperature became established in the $R\overline{3}c$ stability field. Red and blue crosses and open circles are data from the literature (Refs. 3, 9, 10).

Figure 7

(Color online) Changes in the inverse quality factor as a function of temperature. Increase in $Q^{-1}$ indicates increase in acoustic dissipation in the sample. Discrepancies at 300 K are due to a change in instrumentation between high- and low-temperature heads.