Exploring negative thermal expansion materials with bulk framework structures and their relevant scaling relationships through multi-step machine learning.

Discovering new negative thermal expansion (NTE) materials is a great challenge in experiment. Meanwhile, the machine learning (ML) method can be another approach to explore NTE materials using the existing material databases. Herein, we adopt the multi-step ML method with efficient data augmentation and cross-validation to identify around 1000 materials, including oxides, fluorides, and cyanides, with bulk framework structures as new potential NTE candidate materials from ICSD and other databases. Their corresponding coefficients of negative thermal expansion (CNTE) and temperature ranges are also well predicted. Among them, about 57 materials are predicted to have an NTE probability of 100%. Some predicted NTE materials were tested by the first-principles calculations with quasi-harmonic approximation (QHA), which indicates that the ML results are in good agreement with the first principles calculation results. Based on the comprehensive analysis of the existing and predicted NTE materials, we established three universal relationships of CNTE with an average electronegativity, porosity, and temperature range. From these, we also identified some important critical values characterizing the NTE property, which can serve as an important criterion for designing new NTE materials.

The formation energy, phase transition, and negative thermal expansion of Fe2-xScxW3O12.

Tungstates with a molecular formula A2W3O12 exhibits a wider negative thermal expansion (NTE) temperature range than molybdates but are challenging to synthesize, especially when A = Fe or Cr with metastable structures. To enhance the structural stability of Fe2W3O12, Sc with lower electronegativity is adopted to substitute Fe according to Fe2-xScxW3O12, considering the thermodynamic stability of Sc2W3O12. It is shown that the solid solutions can be easily synthesized and the phase transition temperature (PTT) can be tuned to well below room temperature (RT). Theoretical calculations and experimental results show that the formation energy decreases and the W-O bond in Fe-O-W gradually strengthens as the substitution of Sc in Fe2-xScxW3O12 increases, indicating an increase in structural stability. NTE is enhanced after phase transition with an increase in the Sc content. The reduction in PTT and the enhancement in NTE properties of Fe2W3O12 could result in a decrease in the effective electronegativity of the Fe-site elements, resulting in a low formation energy and strengthened W-O bond in Fe-O-W, which corresponds to a more stable structure.

A linear scaling law for predicting phase transition temperature via averaged effective electronegativity derived from A2M3O12-based compounds.

The chemical flexibility of A2M3O12-based compounds enables the design of materials with versatile functionalities such as ferroelastic switching, ion conduction and negative thermal expansion (NTE) above the ferroelastic transition temperature (Tt), which is promising for a variety of applications. Quantitative prediction of Tt is essential but lacking. Herein we propose a concept of averaged effective electronegativity (AEE) and establish a linear relationship between the Tt and AEE for A2M3O12-based compounds. The linear scaling law is validated using first principles calculations of the effective charge on oxygen and its effectiveness is verified experimentally by designing high entropy compounds Scx1Zrx2Hfx3Fex4Moy1Vy2O12 and a NTE compound Zr2MoVPO12 with expected Tt. Generalization of the linear scaling law to other NTE oxides with displacive phase transition is also demonstrated. The findings can be used as a simple and effective approach to guide the design of novel compounds with desired properties and Tt.

Understanding Negative Thermal Expansion of Zn2GeO4 through Local Structure and Vibrational Dynamics.

Zn2GeO4 is a multifunctional material whose intrinsic thermal expansion properties below ambient temperature have not been explored until now. Herein, the thermal expansion of Zn2GeO4 is investigated by synchrotron X-ray diffraction, with the finding that Zn2GeO4 exhibits very low negative (αv = -2.02 × 10-6 K-1, 100-300 K) and positive (αv = +2.54 × 10-6 K-1, 300-475 K) thermal expansion below and above room temperature, respectively. A combined study of neutron powder diffraction and extended X-ray absorption fine structure spectroscopy shows that the negative thermal expansion (NTE) of Zn2GeO4 originates from the transverse vibrations of O atoms in the four- and six-membered rings with ZnO4-GeO4 tetrahedra. In addition, the results of temperature- and pressure-dependent Raman spectra identify the low-frequency phonon modes (50-150 cm-1) with negative Grüneisen parameters softening upon pressuring and stiffening upon heating during the lattice contraction, thus contributing to the NTE. This study not only reports the interesting thermal expansion behavior of Zn2GeO4 but also provides further insights into the NTE mechanism of novel structures.

Hydrate formation and its effects on the thermal expansion properties of HfMgW3O12.

HfMgW3O12 is a representative material with negative thermal expansion in the ABM3O12 (A = Zr, Hf; B = Mg, Mn, Zn, M = W, Mo) family. Herein we report a novel feature of hydration in HfMgW3O12 and its effect on the thermal expansion and its structures which have not been determined previously. It is found that hydrate formation in HfMgW3O12 occurs under ambient or moisture conditions and restrain the low energy librational and translational and even high energy bending and stretching motions of the polyhedra. The coefficient of thermal expansion could be tailored from negative to zero and positive depending on the hydration levels. The unhydrated HfMgW3O12 adopts an orthorhombic structure with space group Pna21 (33) without phase transition at least from 80 K to 573 K, but pressure-induced structure transition and amorphization are found to occur at about 0.19 Gpa and above 3.93 GPa, respectively.

Structure and Negative Thermal Expansion in Zr0.3Sc1.7Mo2.7V0.3O12.

A2M3O12-based materials have received considerable attention owing to their wide range of negative thermal expansion (NTE) and chemical flexibility toward novel materials design. However, the structure and NTE mechanism remain challenging. Here, Zr4+ and V5+ are used as a unit to compensatorily replace Sc3+ and Mo6+ in Sc2Mo3O12 to tune its thermal expansion. Its crystal structure, phase transition, NTE property, and corresponding mechanisms are studied by high-resolution synchrotron X-ray diffraction, powder X-ray diffraction, ultralow-frequency Raman spectroscopy, and density functional theory calculations. The results show that Zr0.3Sc1.7Mo2.7V0.3O12 adopts an orthorhombic (Pbcn) structure at room temperature, with V atoms occupying the position of Mo1 atoms and Zr atoms occupying the position of Sc atoms, and transforms to monoclinic (P21/a) structure at ∼133 K (45 K lower than that of Sc2Mo3O12). It exhibits excellent NTE in a broader range. Most of the phonon modes below 350 cm-1 have negative Grüneisen parameters, of which the lowest and next-lowest frequency (38.5 and 45.8 cm-1) optical phonon modes arising from the translational vibrations of the Sc/Zr and Mo/V atoms in the plane of the nonlinear linkage Sc/Zr-O-Mo/V have the largest and next-largest negative Grüneisen parameters and positive total anharmonicity, and contribute most to the NTE.

Structural, vibrational and thermal expansion properties of Sc2W4O15.

A novel oxide material with the formula of Sc2W4O15 and orthorhombic symmetry is synthesized by solid state reactions and its structure, composition, vibrational properties and thermal expansion are investigated and identified by temperature-dependent X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectrometry (EDS), X-ray photoelectron spectrometry (XPS) and dilatometry. It is shown that the oxide material with an orthorhombic symmetry shows a similar structure to that of Sc2W3O12, but with W partially occupying the position of Sc, leading to not only the corner-sharing ScO6-WO4 connections but also the corner-sharing WO6-WO4 connections. Raman spectroscopic studies show that compared to Sc2W3O12, the FWHMs of most Raman modes in Sc2W4O15 increase due to the occupation of W6+ in the Sc3+ position. Besides, the W-O bonds in Sc2W4O15 are slightly harder than those in Sc2W3O12. An intrinsic thermal contraction in a wide range of temperatures (93-572 K) is demonstrated, which is attributed to the librational and translational vibrations of the corner-sharing polyhedra as well as the transverse vibrations of the bridging O atoms in the Sc-O-W and W-O-W linkages.

Near-Zero Thermal Expansion and Phase Transitions in HfMg1-x Zn x Mo3O12.

The effects of Zn2+ incorporation on the phase formation, thermal expansion, phase transition, and vibrational properties of HfMg1-x Zn x Mo3O12 are investigated by XRD, dilatometry, and Raman spectroscopy. The results show that (i) single phase formation is only possible for x ≤ 0.5, otherwise, additional phases of HfMo2O8 and ZnMoO4 appear; (ii) The phase transition temperature from monoclinic to orthorhombic structure of the single phase HfMg1-x Zn x Mo3O12 can be well-tailored, which increases with the content of Zn2+; (iii) The incorporation of Zn2+ leads to an pronounced reduction in the positive expansion of the b-axis and an enhanced negative thermal expansion (NTE) in the c-axes, leading to a near-zero thermal expansion (ZTE) property with lower anisotropy over a wide temperature range; (iv) Replacement of Mg2+ by Zn2+ weakens the Mo-O bonds as revealed by obvious red shifts of all the Mo-O stretching modes with increasing the content of Zn2+ and improves the sintering performance of the samples which is observed by SEM. The mechanisms of the negative and near-ZTE are discussed.