Domain structures (mixed VPFM images at two scan sizes) in as a function of composition for (a, d) 10%PT, (b, e) 32%PT, and (c, f) 35%PT.
VPFM and LPFM in as a function of composition. (a)–(c) Mixed VPFM and (d)–(f) mixed LPFM for (a, d) 10%PT, (b, e) 32%PT, and (c, f) 35%PT. VPFM and LPFM data were measured sequentially and have not been corrected for possible tip-drift.
(a) Relaxation curves for PMN-10%PT, , and mica. The observed dynamics suggest that the contribution of possible instrumental and atmospheric artifacts (e.g., electrocapillary effect) to relaxation is minimal. (b) Relaxation curves for PMN-10%PT in bias-on (during the application of 10 V pulse) and bias-off (after bias pulse) states. Several superimposed curves illustrate typical repeatability of experiments. Reproduced with permission from Ref. 40.
Relaxation behavior in PMN-10%PT after switching off the 30 ms pulses of different magnitude in (a) linear and (b) logarithmic coordinates. Bias dependence of (c) intercept and (d) slope of the relaxation curve in logarithmic coordinates. Vertical dashed line corresponds to the onset of the state with induced polarization.
Bias length dependence (for 10 V pulse) of relaxation behavior in PMN-10%PT in (a) linear and (b) logarithmic coordinates. Bias dependence of (c) intercept and (d) slope of the relaxation curve in logarithmic coordinates.
Normalized polarization response vs time for different values of parameters, , 0.1, 1, 10 (values near the curves), and [log-log scale (a) and log-linear scale (b)], [linear-log scale (c) and log-linear scale (d)] at fixed bias pulse durability. Dashed lines in (b, d) indicate the linear (log) regions.
(a) Polarization relaxation at different initial values (curves 1), (curves 2), and (curves 3) for nonergodic (solid), ergodic (dashed), and exponential (dotted) cases. (b) Polarization relaxation calculated from Eq. (17) at different initial voltages (values near the curves) and with parameter .
(a) Pulse sequence during the acquisition of a PFM hysteresis loop and (b) sequence of measurements at a single pulse. Schematics of a hysteresis loop for (c) ferroelectric and (d) ergodic relaxor state. In a classical ferroelectric material, the hysteresis loop shape is dominated by the spatial dispersion of the signal. The nucleation biases define the conditions for the nucleation of a stable domain of opposite polarity, and the slope of the loop after nucleation is determined by the bias and time dependence of the domain size. In comparison, in a relaxor ferroelectric, the hysteresis loop is dominated by the time dispersion of the signal, and the nucleation bias corresponds to a bias at which the lifetime of the bias-induced state becomes larger than the measurement time. The slope after nucleation is determined by the bias-dependence of the lifetime. Finally, for , the bias-induced state is stable, whereas for , relaxation is unstable.
Hysteresis loops in as a function of composition. Shown are (a, b, c) work of switching maps [in the (−10, 10 V) bias window] and (d, e, f) selected hysteresis loops for (c, d) 10%PT, (b, e) 32%PT, and (e, f) 35%PT.
Switching spectroscopy mapping of PMN-10%PT. (a) Mixed PFM signal, (b) switchable polarization, (c) stability map [PNB-NNB], and (d) built-in field map. Histograms of (e) PNB and NNB and (f) PNB-NNB.
Switching spectroscopy mapping of PMN-32%PT. (a) Mixed PFM signal, (b) switchable polarization, (c) stability map [PNB-NNB], and (d) built-in field map. Histograms of (e) PNB and NNB and (f) PNB-NNB. Panel b was measured from the center of (a). Panels (c) and (d) have the same scale as (b).
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