Dynamic nanoscale spatial heterogeneity in a perovskite to brownmillerite topotactic phase transformation

Abstract

Phase transitions are omnipresent in modern condensed matter physics and its applications. In solids, phase transformations typically occur by nucleation and growth under non-equilibrium conditions. Under constant external conditions, $\textit{e.g.}$, constant heating temperature and pressure, the nucleation and growth dynamics are often thought of as spatially and temporally independent. Here, $\textit{in-situ}$ Bragg X-ray photon correlation spectroscopy (XPCS) reveals nanoscale spatial and dynamical heterogeneity in the perovskite to brownmillerite topotactic phase transformation in La$_{0.7}$Sr$_{0.3}$CoO$_3$ (LSCO) thin films under constant reducing conditions over a time-span of multiple hours. Specifically, a timescale associated with domain growth remains stable, with a corresponding domain wall speed of $v_d = 6 \pm 0.5 \times10^{-4}$ nm/s ($2 \pm 0.2$ nm/h), while a slower timescale, associated with temperature driven de-pinning of domains, leads to accelerating dynamics with timescales following an aging power law with exponent $-2.2 \pm 0.5$. The experiment demonstrates that Bragg XPCS is a powerful tool to study nanoscale dynamics in phase transformations. The results are relevant for phase engineering of phase-change devices, as they show that nanoscale dynamics, linked to domain and domain-wall motion, can continuously evolve and speed up with time, even hours after the initiation of the phase transformation, with potential repercussions on electrical performance.

Figures (3)

• Figure 1: Coherent x-ray diffraction setup. Brownmillerite BM(006) half-order diffraction Bragg peak (right) observed at 240 $^\circ$C (a) and 550 $^\circ$C (b). Illustrations (left) of a dilute (a) and dense (b) BM phase distribution that can lead to such diffraction patterns. The distance $\Delta Q_{FWHM}$ in Q-space is inversely proportional to the mean domain size $d_{avg}$, similarly $Q_{min}$ is inversely proportional to the largest distance between domains within the X-ray beam $d_{max}$. (c) XRD measurements throughout the experiment, starting at 25 $^\circ$C (light blue), heating incrementally to 550 $^\circ$C (dark red), and cooling to 25 $^\circ$C (black). The crystal structure of the two observed phases is illustrated on the bottom. (d) Perovskite P(002) peak measured at 25 $^\circ$C and 550 $^\circ$C. (e) Illustration of the XPCS experiment. (f) Correlation decay of the speckle images measured at all temperatures on the BM(006) peak (left) and the P(002) peak (right), showing a clear increase in dynamics associated with the BM(006) at 550 $^\circ$C.
• Figure 2: Dynamic heterogeneity of the phase transformation. (a) Two-time correlation $G($t$_1$,t$_2)$ measured on the brownmillerite (BM) peak at 550 $^\circ$C. The black arrows indicates the direction of increasing t$_{age}$ and follows $G($t$_1$,t$_2$=t$_1)$. Perpendicular colored arrows indicate the data used to calculate the one-time correlation functions $g_2^{t_{age}}$(t) shown in (b). (b) t$_{age}$ dependent correlation decay $|F_{t_{age}}$(t)$|^2$ obtained from the $g_2^{t_{age}}$(t) arrows in (a). Dashed lines are fit to the data with the double exponential decay given in Eq. \ref{['exp_fit_eq']}.
• Figure 3: Timescales associated with the brownmillerite phase at 550 $^\circ$C. (a) Slow and fast timescales, $\tau_s$ and $\tau_f$, respectively. $\tau_s$ decreases at t$>$5000 s and is fit with a power law (dashed line) with exponent -2.2$\pm$0.5. (b) Contrast as a function of t$_{age}$, obtained from the second derivative of the fits to Fig. \ref{['fig_g2_fits']}. Increase in contrast indicates that a larger percentage of the diffracting phase is dynamical.