Application of the Fourier transforms for analysis of the domain structure images of uniaxial ferroelectric
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ACE AND THIN FILMS
Application of the Fourier Transforms for Analysis of the Domain Structure Images of Uniaxial Ferroelectric A. L. Tolstikhina*, N. V. Belugina, and R. V. Gainutdinov Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, Moscow, 119333 Russia *e-mail: [email protected] Received December 14, 2016
Abstract—The formation of ferroelectric domains in triglycine sulfate crystal in the para–ferroelectric phase transition has been investigated in situ by piezoresponse force microscopy. The domain structure has been analyzed using the images of Fourier transforms of the scanned (010) surface of natural cleavage. The formation of a quasi-periodic one-dimensional structure of 180° domains with dominant components of one sign below TC near the transition point is revealed and crystallographic reference to the laboratory coordinate system is performed. DOI: 10.1134/S1063774517030221
INTRODUCTION Much attention has been paid for a long time to the second-order ferroelectric phase transition in triglycine sulfate (TGS) crystal due to the anomalous behavior of its properties near the transition point. The dynamics of domain formation has been studied using different microscopic methods. The development of new instrumentation made it possible to approach to the nanoscale level of measurements. Currently, atomic force microscopy (AFM) and its electric modifications (electrostatic force microscopy (EFM) and piezoresponse force microscopy (PFM)) are the most popular methods for these measurements. They provide high-resolution observation of ferroelectric domains in the stage of their formation and supply the quantitative information on the temperature dynamics of crystal domain structure, which is necessary for establishing the correlation relationship with the behavior of the main macroscopic parameters. The temperature and time dependences of the parameters of the domain structure of TGS crystals (nominally pure and with different degrees of structure imperfection) were analyzed in situ by AFM in the EFM [1, 2], contact dynamic EFM [3–5], and PFM [6–8] modes. According to the AFM data, a complex evolution of the domain structure is observed upon crystal cooling below TC; this evolution is accompanied by domain coarsening and a decrease in the total number of domain walls. The spatial correlation functions and characteristic length scales were calculated based on the images. The quantitative characteristics of the domain temperature evolution are significantly different and depend on the relaxation
conditions upon cooling and heating, as well as on the structure imperfection and sample history [1, 3–7]. The equilibrium domain density changes according to the power law (TC – Т)–γ, where γ exceeds the theoretical value obtained within the Landau phenomenological theory while moving away from TC [1, 4, 6]. However, in the close proximity to the phase-transition temperature in the range of TC – T ~ 0.3–0.5°C, one can observe good corr
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