Microstructure dynamics in orthorhombic perovskites

Anelastic loss mechanisms associated with phase transitions in ${\text{BaCeO}}_3$ have been investigated at relatively high frequency $\sim 1\text{MHz}$ and low stress by resonant ultrasound spectroscopy (RUS), and at relatively low frequency $\sim 1\text{Hz}$ and high stress by dynamic mechanical analysis (DMA). Changes in the elastic moduli and dissipation behavior clearly indicate phase transitions due to octahedral tilting: $Pnma\leftrightarrow Imma\leftrightarrow R\overline{3}c\leftrightarrow Pm\overline{3}m$ structures at 551 K, 670 K, and 1168 K, and strain analysis shows that they are tricritical, first-order, and second-order phase transitions, respectively. Structures with intermediate tilt states ($R\overline{3}c$ and $Imma$ structures) show substantial anelastic softening and dissipation associated with the mobility of twin walls under applied stress. The $Pnma$ structure shows elastic stiffening which may be due to the simultaneous operation of two discrete order parameters with different symmetries. In contrast with studies of other perovskites, ${\text{BaCeO}}_3$ shows strong dissipation at both DMA and RUS frequencies in the stability field of the $Pnma$ structure. This is evidence that ferroelastic twin walls might become mobile in $Pnma$ perovskites and suggests that shearing of the octahedra may be a significant factor.

Figure 1

[(a) and (b)] Lattice parameter data (Ref. 19) given in terms of the pseudocubic unit cell. The straight line in (a) represents the reference lattice parameter, $a_{\text{o}}$, obtained by fitting to data in the temperature interval 1198–1273 K. (c) Symmetry-adapted strains, with respect to the parent $Pm\overline{3}m$ structure, derived from the lattice parameters in (a) and (b). A straight line fit to data for $e_4$ of the $R\overline{3}c$ structure in the temperature interval 693–1083 K extrapolates to zero at $T_{\text{c}}=1170\pm 2\text{K}$. Broken lines are fits to $e_4$ and $e_{\text{tx}}$ of the $Imma$ structure constrained to have $T_{\text{c}}=1170\text{K}$. (d) Variations in linear strains of the $Pnma$ structure defined with respect to the $Imma$ structure as reference state. In this case $e_2^2$ and $e_3^2$ vary approximately linearly with temperature, implying close to tricritical character for the $Imma\leftrightarrow Pnma$ transition, with $T_{\text{c}}\approx 530\text{K}$.

Figure 2

(a) Intensities of R-point and M-point superlattice reflections, reproduced from Ref. 24. (b) Relationships between symmetry-adapted strains and R-point superlattice reflection intensities. For $e_{\text{a}}$, data relating to all three superstructure types fall on the same trend, implying that the coupling coefficient between the volume strain and the order parameter is constant. For $e_4$ there is a small break between data for the $R\overline{3}c$ and $Imma$ structures, implying that coupling between $e_4$ and the order parameter is slightly weaker in the $Imma$ structure than in the $R\overline{3}c$ structure. Data for $e_4$ of the $Pnma$ structure fall off the trend due to the influence of an additional order-parameter component.

Figure 3

Stacks of RUS scans. (a) Low temperatures: the weak background peaks at very low temperatures are noise from somewhere in the sample holder. (b) High temperatures: the regularly spaced background peaks are due to alumina rods.

Figure 4

Temperature dependencies of elastic moduli and inverse quality factor $Q^{-1}$ determined by RUS.

Figure 5

(Color online) Temperature dependencies of storage modulus $E^{\prime }$ and dissipation $\text{tan}\delta$ measured at different frequencies by DMA during cooling. Static $\text{force}=60\text{mN}$, dynamic $\text{force}=50\text{mN}$, $\text{gain}=1$, $\text{amplitude}=5\mu \text{m}$, maximum $\text{deformation}=100\mu \text{m}$, and cooling $\text{rate}=3°\text{C}/\text{min}$. s1 and s2 represent different samples.

Figure 6

$\text{ln}\left(f\right)$ vs $1/T$ with frequency and temperature determined for maxima in dissipation of peak ${\text{P}}_4$. The fitting gives activation energy $E_{\text{a}}=29.8\pm 0.4\text{kJ}/\text{mol}$ and $f_0=44.4\text{MHz}$.

Figure 7

(Color online) Temperature dependence of dissipation $\text{tan}\delta$ measured at different frequencies by DMA. (a) During heating. (b) During cooling. Static $\text{force}=60\text{mN}$, dynamic $\text{force}=50\text{mN}$, $\text{gain}=1$, $\text{amplitude}=5\mu \text{m}$, maximum $\text{deformation}=100\mu \text{m}$, heating $\text{rate}=3°\text{C}/\text{min}$, and cooling $\text{rate}=3°\text{C}/\text{min}$. s1, s2, s3, and s4 represent different samples. The data appear to include multiple overlapping peaks through the temperature interval $\sim 350–600\text{K}$, and it has not been possible to extract an activation energy from them.

Figure 8

Double logarithmic plot $\text{ln}\left(\text{tan}\delta \right)$ vs $\text{ln}\left(f\right)$ for maxima in dissipation of peak ${\text{P}}_1$. Two fitting processes were used to determine values of $\text{tan}\delta$. The first was for no baseline correction (zero baseline). The second used a baseline tangential to data points at $\sim 600$ and $\sim 750\text{K}$. The decay is consistent with power law $\text{tan}\delta =A{f}^n$, where $-0.301<n<-0.122$.