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This repository contains Python scripts specifically developed for structural refinement of Zirconium Vanadate (ZrV₂O₇), a material known for its negative thermal expansion (NTE). The scripts implement Pair Distribution Function (PDF) analysis to refine crystal structures directly from experimental X-ray diffraction (XRD) data. The refinement workflow is built around the DiffPy-CMI library, enhanced with custom functionalities tailored for ZrV₂O₇ and similar oxide materials.
How experimental and computational methods allow us to design negative thermal expansion materials
(2026)
Combined experimental and computational methods allow a comprehensive understanding, design, and tailoring of material properties. We focus on a well-known negative thermal expansion (NTE) material, zirconium vanadate (ZrV2O7), and address its synthesis, characterisation, and computational validation of results. Experimental and computational X-ray diffraction and Raman spectroscopy data highlighted differences between phase-pure and multiphase ceramics. The total-scattering method enabled us to distinguish subtle differences in the material's structure. Based on ab initio simulated phonon data, we could interpret the Raman spectra, visualise Raman-active atomic vibrations, and gain deeper insight into the local structure. Computational models provided deeper insight and enabled further experimental improvements, while high-quality experimental data validated and improved the computational simulation strategy.
Zirconium vanadate (ZrV2O7) is a well-known negative thermal expansion (NTE) material which stands out for its remarkable isotropic unit cell contraction over a broad temperature range (130°C < T < 800°C). This enables the fabrication of composites where the overall expansion coefficient can be tailored to a specific negative, positive, or neutral value. Consequently, such composite materials are attractive for many device applications because they can compensate for damage caused by thermal expansion. They are relevant to optical systems, electronic and biomedical applications.
In this study, we implement ab-initio-based vibrational computations with partially treated anharmonicity (quasi-harmonic approximation (QHA), temperature-dependent effective harmonic potentials (TDEP)[5]) in combination with experimental methods to follow and rationalize the negative thermal expansion in this material, including the influence of the local structure disorder, microstructure, and defects. In analytical techniques that can provide structural information such as pair distribution function analysis (PDF), X-ray diffraction (XRD), and Extended X-ray Absorption Fine Structure (EXAFS), molecules and atoms are fit geometrically without consideration of atom interactions. Therefore, in combination with these methods, we also consider potential energy surfaces and conclude what structures are likely to form energetically in the full NTE temperature range, in addition to fitting experimental data geometrically. We also optimise experimentally fitted structures to their lowest energy configurations and re-generate comparative data to observe what differences would be visible experimentally.
Zirconium vanadate (ZrV2O7) is a well-known negative thermal expansion (NTE) material that exhibits significant isotropic contraction over a broad temperature range (~150°C < T < 800°C). Therefore, it can be used to create composites with controllable expansion coefficients and prevent thermal stress, fatigue, cracking, and deformation at interfaces. We implement interdisciplinary research to analyze such material. We study the influence of the synthesis methods and their parameters on the sample's purity, crystallinity, and homogeneity. Moreover, we implement ab initio-based vibrational computations with partially treated anharmonicity in combination with experimental methods to follow temperature-induced structural changes and rationalize the negative thermal expansion in this material, including the influence of the local structure disorder.
Zirconium vanadate (ZrV2O7) is a well-known negative thermal expansion (NTE) material which exhibits significant isotropic contraction over a broad temperature range (~150°C < T < 800°C). The linear thermal expansion coefficient of ZrV2O7 is −7.1×10-6 K-. Therefore, it can be used to create composites with controllable expansion coefficients and prevent destruction by thermal shock.
Material characterization, leading to application, requires pure, homogenous samples of high crystallinity via a reliable synthesis route. While there is a selection of described syntheses in the literature, it still needs to be addressed which synthesis route leads to truly pure and homogenous samples. Here, we study the influence of the synthesis methods (solid-state, sol-gel, solvothermal) and their parameters on the sample's purity, crystallinity, and homogeneity. The reproducibility of results and data obtained with scanning electron microscopy (SEM), X-ray diffraction (XRD), differential scanning calorimetry, and thermogravimetric analysis (DSC/TGA) were analyzed extensively. The sol-gel method proves superior to the solid-state method and produces higher-quality samples over varying parameters. Sample purity also plays an important role in NTE micro and macro-scale characterizations that explain the impact of porosity versus structural changes.
Moreover, we implement ab-initio-based vibrational computations with partially treated anharmonicity (quasi-harmonic approximation, temperature-dependent effective harmonic potentials) in combination with experimental methods to follow and rationalize the negative thermal expansion in this material, including the influence of the local structure disorder, microstructure, and defects. Khosrovani et al. and Korthuis et al., in a series of diffraction experiments, attributed the thermal contraction of ZrV2O7 to the transverse thermal motion of oxygen atoms in V-O-V linkages. In addition to previous explanations, we hypothesize that local disorder develops in ZrV2O7 crystals during heating.
We are working on the experimental ZrV2O7 development and discuss difficulties one might face in the process as well as high-quality sample significance in further investigation. The obtained samples are currently used in the ongoing research of structure analysis and the negative thermal expansion mechanism.
Zirconium vanadate (ZrV2O7) is a well-known negative thermal expansion (NTE) material which exhibits significant isotropic contraction over a broad temperature range (~150°C < T < 800°C). The linear thermal expansion coefficient of ZrV2O7 is −7.1×10-6 K-. Therefore, it can be used to create composites with controllable expansion coefficients and prevent destruction by thermal shock.
Material characterization, leading to application, requires pure, homogenous samples of high crystallinity via a reliable synthesis route. While there is a selection of described syntheses in the literature, it still needs to be addressed which synthesis route leads to truly pure and homogenous samples. Here, we study the influence of the synthesis methods (solid-state, sol-gel, solvothermal) and their parameters on the sample's purity, crystallinity, and homogeneity. The reproducibility of results and data obtained with scanning electron microscopy (SEM), X-ray diffraction (XRD), differential scanning calorimetry, and thermogravimetric analysis (DSC/TGA) were analyzed extensively. The sol-gel method proves superior to the solid-state method and produces higher-quality samples over varying parameters. Sample purity also plays an important role in NTE micro and macro-scale characterizations that explain the impact of porosity versus structural changes.
Moreover, we implement ab-initio-based vibrational computations with partially treated anharmonicity (quasi-harmonic approximation, temperature-dependent effective harmonic potentials) in combination with experimental methods to follow and rationalize the negative thermal expansion in this material, including the influence of the local structure disorder, microstructure, and defects. Khosrovani et al. and Korthuis et al., in a series of diffraction experiments, attributed the thermal contraction of ZrV2O7 to the transverse thermal motion of oxygen atoms in V-O-V linkages. In addition to previous explanations, we hypothesize that local disorder develops in ZrV2O7 crystals during heating.
We are working on the experimental ZrV2O7 development and discuss difficulties one might face in the process as well as high-quality sample significance in further investigation. The obtained samples are currently used in the ongoing research of structure analysis and the negative thermal expansion mechanism.
Structural evolution of ZrV2O7: supercell persistence revealing local and global structure duality
(2025)
In the AM2O7 family of negative thermal expansion materials (NTE), evidence of supercell at room temperature was reported following the Völlenke et al. discovery of missed superlattice due to the apparent linearity of the M-O-M bond in GeP2O7. Korthuis et al. and Khosrovani et al. demonstrated it to be true for cubic ZrV2O7 as well. It was concluded that at room temperature, the structure consists of 27 'subcells' with bent M2O7 groups that appear to form a linear configuration due to refinement of averaged position. However, around 100 °C, the transition to the “parent” cell was reported, where the cell volume increases, and the M-O-M angles are constrained by the Pa-3 space group symmetry to be 180°.
We followed structural changes in the ZrV2O7 at high temperatures to demonstrate partial disorder within the crystal, local and global structural duality and supercell persistence at high temperatures. Total scattering measurements and Pair Distribution Function (PDF) analysis revealed that the experimental pattern cannot be fitted with the “parent structure” model, and only the 3×3×3 supercell model can correspond to local and global structures throughout the full 25-700 °C temperature range.
We also show how short and long-range order within the crystal changes when approaching the phase transition, which might indicate the existence of coherent structural domains that evolve between order and disorder with increasing temperature. We further hypothesize how this can be related to the negative thermal expansion mechanism and the interpretation of structure solutions presenting data from high-temperature X-ray absorption fine structure (XAFS) and Transmission Electron Microscopy (TEM) measurements.
Zirconium vanadate (ZrV2O7) is a well-known negative thermal expansion (NTE) material which exhibits significant isotropic contraction over a broad temperature range (~150°C < T < 800°C). The linear thermal expansion coefficient of ZrV2O7 is −7.1×10-6 K-1. Therefore, it can be used to create composites with controllable expansion coefficients and prevent destruction by thermal shock.
Material characterization, leading to application, requires pure, homogenous samples of high crystallinity via a reliable synthesis route. While there is a selection of described syntheses in the literature, it still needs to be addressed which synthesis route leads to truly pure and homogenous samples. Here, we study the influence of the synthesis methods (solid-state, sol-gel, solvothermal) and their parameters on the sample's purity, crystallinity, and homogeneity. The reproducibility of results and data obtained with scanning electron microscopy (SEM), X-ray diffraction (XRD), differential scanning calorimetry, and thermogravimetric analysis (DSC/TGA) were analyzed extensively. The sol-gel method proves superior to the solid-state method and produces higher-quality samples over varying parameters. Sample purity also plays an important role in NTE micro and macro-scale characterizations that explain the impact of porosity versus structural changes.
Moreover, we implement ab-initio-based vibrational computations with partially treated anharmonicity (quasi-harmonic approximation, temperature-dependent effective harmonic potentials) in combination with experimental methods to follow and rationalize the negative thermal expansion in this material, including the influence of the local structure disorder, microstructure, and defects. Khosrovani et al. and Korthuis et al., in a series of diffraction experiments, attributed the thermal contraction of ZrV2O7 to the transverse thermal motion of oxygen atoms in V-O-V linkages. In addition to previous explanations, we hypothesize that local disorder develops in ZrV2O7 crystals during heating.
We are working on the experimental ZrV2O7 development and discuss difficulties one might face in the process as well as high-quality sample significance in further investigation. The obtained samples are currently used in the ongoing research of structure analysis and the negative thermal expansion mechanism.
Extended hydrogen initiatives promote the urgency of research on water splitting technologies and, therein, oxygen evolution reaction catalysts being developed. A route to access a ZrF4 supported high-entropy fluoride catalyst using a facile sol–gel route is presented. The high-entropy character of the catalyst was confirmed by scanning transmission electron microscopy and energy dispersive X-ray spectroscopy (STEM-EDX) as well as inductively coupled plasma-mass spectrometry (ICP-MS). Additional investigations on the local structure were performed using extended X-ray absorption fine structure spectroscopy (EXAFS) and pair distribution function (PDF) analysis. The catalyst shows significant potential for oxygen evolution reaction (OER) in alkaline media with a current density of 100 mA cm−2 at approximately 1.60 V, thus outperforming benchmark materials such as IrO2, despite a significant reduction in electrochemical mass loading. A potential mechanism is suggested based on free energy calculation using DFT calculations.
How experimental and computational methods allow us to design negative thermal expansion materials
(2024)
Combined experimental and computational methods allow comprehensive understanding, design, and tailoring of material properties. We focus on a wellknown negative thermal expansion (NTE) material, zirconium vanadate (ZrV2O7), and address synthesis, characterisation and validation of results with computational simulations. Experimental and computational X-ray diffraction and Raman spectroscopy data highlighted differences between phase-pure and multiphase ceramics. These techniques allowed us to distinguish subtle differences in the structure of the material. Based on ab initio simulated phonon data, unaffected by impurities or instrumental errors, we could interpret the Raman spectra and visualise Raman active atom vibrations. These computational models allowed better insight and further experimental improvement while high-quality experimental data granted the validation and improvement of computational simulation strategy.
