Abstract
We show the ability to map the phase diagram of a relaxor-ferroelectric system as a function of temperature and composition through local hysteresis curve acquisition, with the voltage spectroscopy data being used as a proxy for the (unknown) microscopic state or thermodynamic parameters of materials. Given the discrete nature of the measurement points, we use Gaussian processes to reconstruct hysteresis loops in temperature and voltage space, and compare the results with the raw data and bulk dielectric spectroscopy measurements. The results indicate that the surface transition temperature is similar for all but one composition with respect to the bulk. Through clustering algorithms, we recreate the main features of the bulk diagram, and provide statistical confidence estimates for the reconstructed phase transition temperatures. We validate the method by using Gaussian processes to predict hysteresis loops for a given temperature for a composition unseen by the algorithm, and compare with measurements. These techniques can be used to map phase diagrams from functional materials in an automated fashion, and provide a method for uncertainty quantification and model selection.
Highlights
Phase diagrams serve as descriptors of material behavior and material properties, and their forms are intrinsically linked to the underpinning physics driving the system
We show the use of these methods in exploring the 379 and 385 K having high dielectric constant, low loss tangent, phase diagram of a relaxor-ferroelectric system, (1−x) Pb (Fe0.5Nb0.5)O3−xNi0.65Zn0.35Fe2O4 (x = 0, 0.10, 0.20, and 0.30)
The phase transition temperatures as measured by piezoresponse force microscopy (PFM) are slightly different from the bulk, especially for the PN2 sample
Summary
Phase diagrams serve as descriptors of material behavior and material properties, and their forms are intrinsically linked to the underpinning physics driving the system. The predictions of hysteresis loops using GP regression (and the RBF kernel) along the temperature axis for the PN2 case is seen, for different individual voltages, along with a confidence interval (2 s.d.) filled in blue This uncertainty quantification is an advantageous feature of GP regression, and can be useful for applying or developing models to describe the nature of the phase transition. In a sense, this is the price to be paid for unknown functional forms; while other methods (such as polynomial or spline interpolation) could work, the uncertainty estimates would not be accurate (given that this uncertainty depends on the model choice, which is largely arbitrary, especially for ferroelectric hysteresis loops[45]). The actual measured values are within 1 s.d. of the prediction bound, suggesting good agreement and validation of the GP model
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