Analysis of Theoretical Models for Nonlinear Fitting of Experimental Data: Dielectric Permittivity of Pb_4.95Ge₃O₁₁ Crystals

Abstract

We implement nonlinear fitting and select the best theoretical model for description of experimental data, basing on the programming language Java. This is achieved using the Levenberg-Marquardt algorithm and the bootstrapping for determining confidence intervals for the fitting parameters. The main technical procedures are illustrated on the temperature dependence of dielectric permittivity of non-stoichiometric LG crystals in their paraelectric phase. Our results confirm that the model incorporating a temperature-independent dielectric background and a normal spatial distribution of Curie points assumed for the case of diffused phase transitions can be used as a statistically significant hypothesis.

Nonlinear background corrections to dielectric permittivity of ferroics and multiferroics

“…As a result, the dielectric data can be successfully explained in terms of the Curie-Weiss behavior with a non-negligible temperature-dependent background, rather than by assuming a diffuse PT. Note that the above result somewhat differs from the conclusion drawn in our earlier work [38] for the 𝜀(𝑇) function obtained at a different electric-field frequency. However, only the particular cases of formula (3.1) with 𝜀 𝐵 = 0 and formula (3.2) with 𝜀 𝐵 = const were compared in the study [38] as theoretical models.…”

“…Note that the above result somewhat differs from the conclusion drawn in our earlier work [38] for the 𝜀(𝑇) function obtained at a different electric-field frequency. However, only the particular cases of formula (3.1) with 𝜀 𝐵 = 0 and formula (3.2) with 𝜀 𝐵 = const were compared in the study [38] as theoretical models.…”

“…Our data confirm that a constant dielectric-background approximation can turn out to be insufficient. In particular, this is proved by a comparison with our earlier data for PGO [38]. It is important that consideration of the temperaturedependent 𝜀 𝐵 (𝑇) term for the magnetoelectric Sr 2 IrO 4 single crystals notably improves the accuracy obtained for the PT parameters.…”