Rietveld refinement has become an essential tool for the quantitative analysis of crystal structures in polycrystalline systems using X-ray diffraction data. This tutorial paper focuses on the background, case studies, and practical implementation of Rietveld refinement using the open-source software PROFEX. Key structural parameters, such as lattice constants and phase fractions, can be quantitatively extracted through full-pattern fitting. Case studies involving compositional variation, electric fields, temperature changes, and battery cycling demonstrate the broad applicability of Rietveld refinement in materials science, energy storage, and catalysis. A step-by-step procedure for performing Rietveld refinement is presented using Bi_1/2Na_1/2TiO₃ perovskite ceramic as an example, providing guidance on software installation, preparing crystal structure information files, performing Rietveld refinement, evaluating results using R-factor and χ² values, and summarizing the results. This tutorial aims to improve understanding and accessibility of Rietveld refinement for researchers seeking to investigate structure-property relationships in complex material systems.

In functional materials, in situ experimental techniques as a function of external stimulus (e.g., electric field, magnetic field, light, etc.) or changes in ambient environments (e.g., temperature, humidity, pressure, etc.) are highly essential for analyzing how the physical properties of target materials are activated/evolved by the given stimulation. In particular, in situ electric-field-dependent X-ray diffraction (XRD) measurements have been extensively utilized for understanding the underlying mechanisms of the emerging electromechanical responses to external electric field in various ferroelectric, piezoelectric, and electrostrictive materials. This tutorial article briefly introduces basic principles/key concepts of in situ electric-field-dependent XRD analysis using a lab-scale XRD machine. We anticipate that the in situ XRD method provides a practical tool to systematically identify/monitor a structural modification of various electromechanical materials driven by applying an external electric field.

Lead zirconate titanate/poly-vinylidene fluoride (PZT/PVDF) piezoelectric devices were fabricated by incorporating carbon nanotubes (CNTs), for use as flexible energy harvesting devices. CNTs were added to maximize the formation of the β phase of PVDF to enhance the piezoelectricity of the devices. The phase transition of PVDF induced by the addition of CNTs was confirmed by analyzing the X-ray diffraction patterns, scanning electron microscopy images, and atomic force microscopy images. The enhanced output efficiency of the PZT/PVDF piezoelectric devices was confirmed by measuring the output current and voltage of the fabricated devices. The maximum output current and voltage of the PZT/PVDF piezoelectric devices was 200 nA and 350 mV, respectively, upon incorporation of 0.06 wt% CNTs.

We investigated the dielectric relaxation properties 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 ceramics with CuO addition. With increasing CuO addition, the lattice parameter was increased by substitution of small amount Cu2+ ion in B-site of 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 ceramics. Also the grain size and the maximum dielectric constant of 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 ceramics was decreased with increasing amounts of CuO addition. Moreover, the diffused phase transition properties (γ) of 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 ceramics was increased by compositional fluctuation with increasing of CuO amount, changed from 1.45 at 1 wt% CuO addition to 1.94 at 7 wt% CuO addition.

Phase transition properties of the copolymer films of polyvinylidene fluoride (PVDF) and trifluoroethylene(TrFE), P(VDF-TrFE), were studied with X-ray diffraction (XRD) and polarization modulated ellipsometry (PME). XRD studies on both Langmuir-Blodgett (LB) films and spin coated films exhibit conversions from ferroelectric phase to paraelectric phase at 108±2℃ on heating and paraelectric phase to ferroelectric phase at 78±2℃ on cooling. The presence of the ferroelectric-paraelectric phase transition is also confirmed by the PME technique for the first time in this study. PME was proved to be a very sensitive tool in the measurement of the structural changes at the nano-thickness films.