Zero Thermal Expansion and Ferromagnetism in Cubic Sc1–xMxF3 (M = Ga, Fe) over a Wide Temperature Range

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.

Atomic Layer Deposition of ScF3 and ScxAlyFz Thin Films

In this paper, we present an ALD process for ScF3 using Sc(thd)3 and NH4F as precursors. This is the first material made by ALD that has a negative thermal expansion over a wide-temperature range. Crystalline films were obtained at the deposition temperatures of 250-375 °C, with a growth per cycle (GPC) increasing along the deposition temperature from 0.16 to 0.23 Å. Saturation of the GPC with respect to precursor pulses and purges was studied at 300 °C. Saturation was achieved with Sc(thd)3, whereas soft saturation was achieved with NH4F. The thickness of the films grows linearly with the number of applied ALD cycles. The F/Sc ratio is 2.9:3.1 as measured by ToF-ERDA. The main impurity is hydrogen with a maximum content of 3.0 at %. Also carbon and oxygen impurities were found in the films with maximum contents of 0.5 and 1.6 at %. The ScF3 process was also combined with an ALD AlF3 process to deposit ScxAlyFz films. In the AlF3 process, AlCl3 and NH4F were used as precursors. It was possible to modify the thermal expansion properties of ScF3 by Al3+ addition. The ScF3 films shrink upon annealing, whereas the ScxAlyFz films show thermal expansion, as measured with HTXRD. The thermal expansion becomes more pronounced as the Al content in the film is increased.

Mixed anion control of negative thermal expansion in a niobium oxyfluoride

A significant change in thermal expansion with anion composition has been identified in the niobium oxyfluoride, NbO2-xF1+x from 0 < x < 0.6. Fluorine doping leads to a transition from positive thermal expansion to unusual zero and negative thermal expansion caused by transverse anionic vibrations. This work has consequences for the development of advanced technological materials with tuneable low thermal expansion and is the first example of the use of multiple anions to control thermal expansion.

Antiferroelectricity-Induced Negative Thermal Expansion in Double Perovskite Pb2 CoMoO6

Materials with negative thermal expansion (NTE) attract significant research attention owing to their unique physical properties and promising applications. Although ferroelectric phase transitions leading to NTE are widely investigated, information on antiferroelectricity-induced NTE remains limited. In this study, single-crystal and polycrystalline Pb2 CoMoO6 samples are prepared at high pressure and temperature conditions. The compound crystallizes into an antiferroelectric Pnma orthorhombic double perovskite structure at room temperature owing to the opposite displacements dominated by Pb2+ ions. With increasing temperature to 400 K, a structural phase transition to cubic Fm-3m paraelectric phase occurs, accompanied by a sharp volume contraction of 0.41%. This is the first report of an antiferroelectric-to-paraelectric transition-induced NTE in Pb2 CoMoO6 . Moreover, the compound also exhibits remarkable NTE with an average volumetric coefficient of thermal expansion αV = -1.33 × 10-5 K-1 in a wide temperature range of 30-420 K. The as-prepared Pb2 CoMoO6 thus serves as a prototype material system for studying antiferroelectricity-induced NTE.

Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Reversible electric-field-induced phase transition in Ca-modified NaNbO3 perovskites for energy storage applications

Sodium niobate (NaNbO₃) is a potential material for lead-free dielectric ceramic capacitors for energy storage applications because of its antipolar ordering. In principle, a reversible phase transition between antiferroelectric (AFE) and ferroelectric (FE) phases can be induced by an application of electric field (E) and provides a large recoverable energy density. However, an irreversible phase transition from the AFE to the FE phase usually takes place and an AFE-derived polarization feature, a double polarization (P)-E hysteresis loop, does not appear. In this study, we investigate the impact of chemically induced hydrostatic pressure (p_chem) on the phase stability and polarization characteristics of NaNbO₃-based ceramics. We reveal that the cell volume of Ca-modified NaNbO₃ [(Ca_xNa_1-2xV_x)NbO₃], where V is A-site vacancy, decreases with increasing x by a positive p_chem. Structural analysis using micro-X-ray diffraction measurements shows that a reversible AFE-FE phase transition leads to a double P-E hysteresis loop for the sample with x = 0.10. DFT calculations support that a positive p_chem stabilizes the AFE phase even after the electrical poling and provides the reversible phase transition. Our study demonstrates that an application of positive p_chem is effective in delivering the double P-E loop in the NaNbO₃ system for energy storage applications.

Switch of Thermal Expansions Triggered by Itinerant Electrons in Isostructural Metal Trifluorides

Manageable thermal expansion (MTE) of metal trifluorides can be achieved by introducing local structure distortion (LSD) in the negative thermal expansion ScF₃. However, an open issue is why isostructural TiF₃, free of LSD, exhibits positive thermal expansion. Herein, a combined analysis of synchrotron X-ray diffraction, X-ray pair distribution function, and rigorous first-principles calculations was performed to reveal the important role of itinerant electrons in mediating soft phonons and lattice dynamics. Metallic TiF₃ demonstrates itinerant electrons and a suppressed Grüneisen parameter γ ≈ -20, while insulating ScF₃ absence of itinerant electrons has a considerable γ ≈ -120. With increasing electron doping concentrations in ScF₃, soft phonons become hardened and the γ is repressed significantly, identical to TiF₃. The presented results update the thermal expansion transition mechanism in framework structure analogues and provide a practical approach to obtaining MTE without inducing sizable structure distortion.

Chemical pressure in functional materials

Chemical pressure, a strange but familiar concept, is a lattice internal force caused by lattice strain with chemical modifications and arouses great interest due to its diversity and efficiency to synthesize new compounds and tune functional materials. Different from physical pressure loaded by an external force that is positive, chemical pressure can be either positive or negative (contract a lattice or expand it), often through flexible and mild chemical synthesis strategies, which are particularly important as a degree of freedom to manipulate material behaviors. In this tutorial review, we summarize the features of chemical pressure as a methodology and demonstrate its role in synthesizing and discovering some typical magnetically, electrically, and thermally responsive functional materials. The measure of chemical pressure using experimental lattice strain and elastic modulus was proposed, which can be used for quantitative descriptions of the correlation between lattice distortion and properties. From a lattice strain point of view, we classify chemical pressure into different categories: (i) chemical substitution, (ii) chemical intercalation/de-intercalation, (iii) size effect, and (iv) interface constraint, etc. Chemical pressure affects chemical bonding and rationalizes the crystal structure by modifying the electronic structure of solids, regulating the lattice symmetry, local structure, phonon structure effects etc., emerging as a general and effective method for synthesizing new compounds and tuning functional materials.

Chemical Diversity for Tailoring Negative Thermal Expansion

Negative thermal expansion (NTE), referring to the lattice contraction upon heating, has been an attractive topic of solid-state chemistry and functional materials. The response of a lattice to the temperature field is deeply rooted in its structural features and is inseparable from the physical properties. For the past 30 years, great efforts have been made to search for NTE compounds and control NTE performance. The demands of different applications give rise to the prominent development of new NTE systems covering multifarious chemical substances and many preparation routes. Even so, the intelligent design of NTE structures and efficient tailoring for lattice thermal expansion are still challenging. However, the diverse chemical routes to synthesize target compounds with featured structures provide a large number of strategies to achieve the desirable NTE behaviors with related properties. The chemical diversity is reflected in the wide regulating scale, flexible ways of introduction, and abundant structure-function insights. It inspires the rapid growth of new functional NTE compounds and understanding of the physical origins. In this review, we provide a systematic overview of the recent progress of chemical diversity in the tailoring of NTE. The efficient control of lattice and deep structural deciphering are carefully discussed. This comprehensive summary and perspective for chemical diversity are helpful to promote the creation of functional zero-thermal-expansion (ZTE) compounds and the practical utilization of NTE.

Efficient and thermally stable broadband near-infrared emission from near zero thermal expansion AlP3O9:Cr3+ phosphors

A near zero thermal expansion NIR phosphor, AlP3O9:Cr3+, with high emission efficiency and excellent thermal stability is synthesized. A compact NIR pc-LED is fabricated and has a promising application in advanced nondestructive analysis technology.

Investigation of the Anisotropic Thermal Expansion Mechanism of AgxGaxGe1-xSe2 Crystals

Quaternary nonlinear optical single crystals Ag_xGa_xGe_1-xSe₂ (x = 0.250, 0.167) were grown by the Bridgman method in a four-zone furnace. The thermal expansion behavior of Ag_xGa_xGe_1-xSe₂ (x = 0.25, 0.167) was studied by the method of single-crystal X-ray diffraction from 150 to 295 K and powder X-ray diffraction in the range of 298-773 K. Both results show the crystals have positive linear thermal expansion coefficients in different directions and a positive volume thermal expansion coefficient, and it is observed that they satisfy the relationship of α_a > α_c > α_b and α_V ≈ α_a + α_b + α_c for the orthorhombic structure. It is found that the Ag_xGa_xGe_1-xSe₂ (x = 0.25, 0.167) unit cells varying with temperature were mainly dominated by variations in framework geometry (AgSe₄ tetrahedron), and the thermal motion of Ag atoms in the AgSe₄ tetrahedron. As it was revealed, according to the powder X-ray diffraction, it is found that the isotropic thermal atomic displacement parameter of the Ag atoms is much larger than those of the Se and Ga(Ge) atoms in the AgSe₄ tetrahedron. Furthermore, anisotropic atomic displacement parameters (ADPs) of Ag atoms are extracted from the single-crystal diffraction; the ADPs along the a axis, b axis, and c axis have a significant difference, which means the thermal vibration of Ag atoms is anisotropic. It is of great significance for improving crystal growth technology and understanding the thermal properties of this kind of crystals.

Chemical-Pressure-Modulated BaTiO3 Thin Films with Large Spontaneous Polarization and High Curie Temperature

Although BaTiO₃ is one of the most famous lead-free piezomaterials, it suffers from small spontaneous and low Curie temperature. Chemical pressure, as a mild way to modulate the structures and properties of materials by element doping, has been utilized to enhance the ferroelectricity of BaTiO₃ but is not efficient enough. Here, we report a promoted chemical pressure route to prepare high-performance BaTiO₃ films, achieving the highest remanent polarization, P_r (100 μC/cm²), to date and high Curie temperature, T_c (above 1000 °C). The negative chemical pressure (∼-5.7 GPa) was imposed by the coherent lattice strain from large cubic BaO to small tetragonal BaTiO₃, generating high tetragonality (c/a = 1.12) and facilitating large displacements of Ti. Such negative pressure is especially significant to the bonding states, i.e., hybridization of Ba 5p-O 2p, whereas ionic bonding in bulk and strong bonding of Ti e_g and O 2p, which contribute to the tremendously enhanced polarization. The promoted chemical pressure method shows general potential in improving ferroelectric and other functional materials.

Bridging Structural Inhomogeneity to Functionality: Pair Distribution Function Methods for Functional Materials Development

The correlation between structure and function lies at the heart of materials science and engineering. Especially, modern functional materials usually contain inhomogeneities at an atomic level, endowing them with interesting properties regarding electrons, phonons, and magnetic moments. Over the past few decades, many of the key developments in functional materials have been driven by the rapid advances in short-range crystallographic techniques. Among them, pair distribution function (PDF) technique, capable of utilizing the entire Bragg and diffuse scattering signals, stands out as a powerful tool for detecting local structure away from average. With the advent of synchrotron X-rays, spallation neutrons, and advanced computing power, the PDF can quantitatively encode a local structure and in turn guide atomic-scale engineering in the functional materials. Here, the PDF investigations in a range of functional materials are reviewed, including ferroelectrics/thermoelectrics, colossal magnetoresistance (CMR) magnets, high-temperature superconductors (HTSC), quantum dots (QDs), nano-catalysts, and energy storage materials, where the links between functions and structural inhomogeneities are prominent. For each application, a brief description of the structure-function coupling will be given, followed by selected cases of PDF investigations. Before that, an overview of the theory, methodology, and unique power of the PDF method will be also presented.

Achieving High Performances of Ultra-Low Thermal Expansion and High Thermal Conductivity in 0.5PbTiO3-0.5(Bi0.9La0.1)FeO3@Cu Core-Shell Composite

Achieving high performances of ultra-low thermal expansion (ULTE) and high thermal conductivity remains challenging, due to the strong phonon/electron-lattice coupling in ULTE materials. In this study, the challenge has been solved via the construction of the core-shell structure in 0.5PbTiO₃-0.5(Bi_0.9La_0.1)FeO₃@Cu composites by the electroless plating, which can simultaneously combine the advantages of the negative thermal expansion material of 0.5PbTiO₃-0.5(Bi_0.9La_0.1)FeO₃ in controlling thermal expansion, and copper metal in high thermal conductivity. By changing the volume fraction of copper, the coefficient of thermal expansion of composites can be adjusted continuously from positive to negative. In particular, a ULTE (ΔT = 400 K) has been achieved in the composite of 35 vol % Cu. Intriguingly, a 3D thermal conductive network copper structure is formed for thermal conducting, which can double the thermal conductivity of the 35 vol % Cu composite from the methods by the traditional mixing (32 W·m^-1·K^-1) up to the core-shell structure (60 W·m^-1·K^-1). The present work not only provides a composite material with excellent comprehensive properties but also proposes a general chemical method to resolve the problem of low thermal conductivity in most ULTE materials.

Zero Thermal Expansion in Ta2Mo2O11 by Compensation Effects

Although zero thermal expansion (ZTE) materials have broad application prospects for high precision engineering, they are rare. Here, a new ZTE material, Ta₂Mo₂O₁₁ (α_l = 0.37 × 10^-6 K^-1, 200-600 K), is reported. A joint study of high-resolution synchrotron X-ray diffraction, temperature- and pressure-dependent Raman spectroscopy, and first-principles calculations was performed to investigate the structure and dynamics of Ta₂Mo₂O₁₁ with the aim of understanding its ZTE mechanism. Ta₂Mo₂O₁₁ displays a layered structure, stacking along the [001] direction. Analysis of the phonon modes indicates that positive and negative contributions to thermal expansion are balanced, and a shrinkage occurs along the layers, while the interlayer distance expands with increasing temperature, thus giving rise to the ZTE behavior of Ta₂Mo₂O₁₁. The present study provides a promising ZTE material and new insights into the mechanisms of thermal expansion.

Effect of H2O Molecules on Thermal Expansion of TiCo(CN)6

Understanding the role of guest molecules in the lattice void of open-framework structures is vital for tailoring thermal expansion. Here, we take a new negative thermal expansion (NTE) compound, TiCo(CN)₆, as a case study from the local structure perspective to investigate the effect of H₂O molecules on thermal expansion. The in situ synchrotron X-ray diffraction results showed that the as-prepared TiCo(CN)₆·2H₂O has near-zero thermal expansion behavior (100-300 K), while TiCo(CN)₆ without water in the lattice void exhibits a linear NTE (α_l = -4.05 × 10^-6 K^-1, 100-475 K). Combined with the results of extended X-ray absorption fine structure, it was found that the intercalation of H₂O molecules has the clear effect of inhibiting transverse thermal vibrations of Ti-N bonds, while the effect on the Co-C bonds is negligible. The present work displays the inhibition mechanism of H₂O molecules on thermal expansion of TiCo(CN)₆, which also provides insight into the thermal expansion control of other NTE compounds with open-framework 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.

Uniaxial thermal expansion behaviors and ionic conduction in a layered (NH4)2V3O8

The zero/negative thermal expansion (ZTE/NTE), which is an intriguing physical property of solids, has been observed in a few families of materials. ZTE materials possess practical applications in specific circumstances such as space-related applications, engineering structures and precision instrument. Generally, NTE materials are used as additives to form a composite of the ZTE material with positive thermal expansion material. It is still a tremendous challenge to design new families of ZTE/NTE materials. Herein, we presented a temperature-dependent single crystal structure analysis in 110-300 K for a layered (NH4)2V3O8, which crystallizes in a tetragonal space group P4bm and comprises mixed valence [V3O82-]∞ monolayers and NH4+ residual in the interlayer spaces. Along the c-axis, (NH4)2V3O8 demonstrated uniaxial expansion behaviors, i.e., ZTE with αc = -1.10 × 10-6 K-1 in 110-170 K and NTE with αc = -16.25 × 10-6 K-1 in 170-220 K. Along the a-axis, (NH4)2V3O8 exhibited ZTE with αa = + 2.06 × 10-6 K-1 in 240-300 K. The mechanisms of ZTE and NTE were explored using structural analysis. The conduction of NH4+ ions in the interlayer space was studied, indicating that the conductivity rapidly rises with the expansion of interlayer space at temperatures of >293 K. This study discloses that layered vanadates are promising ZTE/NTE materials.

Substitutions of Zr4+/V5+ for Y3+/Mo6+ in Y2Mo3O12 for Less Hygroscopicity and Low Thermal Expansion Properties

In this investigation, Zr_xY_2-xV_xMo_3-xO₁₂ (0 ≤ x ≤ 1.4) is developed and the effects of the substitutions of Zr⁴⁺/V⁵⁺ for Y³⁺/Mo⁶⁺ in Y₂Mo₃O₁₂ on the hygroscopicity and thermal expansion property are investigated. For the smaller substitution content (x ≤ 0.5), their crystal structures remain orthorhombic, while there is crystal water still in the lattice. The linear coefficients of thermal expansions (CTEs), for x = 0.1, 0.3, 0.5, and 0.7, are about -4.30 × 10^-6, -0.97 × 10^-6, 0.85 × 10^-6, and 0.77 × 10^-6 K^-1, respectively, from 476 to 773 K, which means that the linear CTE could be changed linearly with the substitution content of Zr⁴⁺/V⁵⁺ for Y³⁺/Mo⁶⁺ in Y₂Mo₃O₁₂. As long as the substitution content reaches x = 1.3/1.4, almost no hygroscopicity and low thermal expansion from room temperature are obtained and are discussed in relation to the crystal structure and microstructure.

Accordion and layer-sliding motion to produce anomalous thermal expansion behaviour in 2D-coordination polymers

Solvent-free (1) and solvated (2) 2D-coordination polymers have been synthesised by varying the amount of solvent during crystallisation. 1 undergoes a unique accordion motion of 2D zig-zag interwoven layers whereas 2 experiences layer-sliding within 2D layers to produce anomalous thermal expansion behaviour.

Growth from the Melt and Properties Investigation of ScF3 Single Crystals

ScF3 optical quality bulk crystals of the ReO3 structure type (space group P m 3 ¯ m , a = 4.01401(3) Å) have been grown from the melt by Bridgman technique, in fluorinating atmosphere for the first time. Aiming to substantially reduce vaporization losses during the growth process graphite crucibles were designed. The crystal quality, optical, mechanical, thermal and electrophysical properties were studied. Novel ScF3 crystals refer to the low-refractive-index (nD = 1.400(1)) optical materials with high transparency in the visible and IR spectral region up to 8.7 µm. The Vickers hardness of ScF3 (HV ~ 2.6 GPa) is substantially higher than that of CaF2 and LaF3 crystals. ScF3 crystals possess unique high thermal conductivity (k = 9.6 Wm−1К−1 at 300 K) and low ionic conductivity (σ = 4 × 10−8 Scm−1 at 673 К) cause to the structural defects in the fluorine sublattice.

Negative Thermal Expansion in (Hf,Ti)Fe2 Induced by the Ferromagnetic and Antiferromagnetic Phase Coexistence

Negative thermal expansion (NTE) is an intriguing physical phenomenon that can be used in the applications of thermal expansion adjustment of materials. In this study, we report a NTE compound of (Hf,Ti)Fe₂, while both end members of HfFe₂ and TiFe₂ show positive thermal expansion. The results reveal that phase coexistence is detected in the whole NTE zone, in which one phase is ferromagnetic (FM), while the other is antiferromagnetic (AFM). With increasing temperature, the FM phase is gradually transformed to the AFM one. The NTE phenomenon occurs in the present (Hf,Ti)Fe₂ because of the fact that the unit cell volume of the AFM phase is smaller than that of the FM phase, and the mass fraction of the AFM phase increases with increasing temperature. The construction of phase coexistence can be a method to achieve NTE materials in future studies.

Adjustable Magnetic Phase Transition Inducing Unusual Zero Thermal Expansion in Cubic RCo2-Based Intermetallic Compounds (R = Rare Earth)

Metallic materials that exhibit negligible thermal expansion or zero thermal expansion (ZTE) have great merit for practical applications, but these materials are rare and their thermal expansions are difficult to control. Here, we successfully tailored the thermal expansion behaviors from strongly but abruptly negative to zero over wide temperature ranges in a series of (Gd,R)(Co,Fe)₂ (R = Dy, Ho, Er) intermetallic compounds by tuning the composition to bring the first-order magnetic phase transition to second-order. Interestingly, an unusual isotropic ZTE property with a coefficient of thermal expansion of α _l = 0.16(0) × 10^-6 K^-1 was achieved in cubic Gd_0.25Dy_0.75Co_1.93Fe_0.07 (GDCF) in the temperature range of 10-275 K. The short-wavelength neutron powder diffraction, synchrotron X-ray diffraction, and magnetic measurement studies evidence that this ZTE behavior was ascribed to the rare-earth-moment-dominated spontaneous volume magnetostriction, which can be controlled by an adjustable magnetic phase transition. The present work extends the scope of the ZTE family and provides an effective approach to exploring ZTE materials, such as by adjusting the magnetism or ferroelectricity-related phase transition in the family of functional materials.

Effect of Si substitution in ferromagnetic Pr2Fe17: a magnetocaloric material with zero thermal expansion operative at high temperature

This article deals with the magnetic and thermal expansion properties of Pr2Fe16Si. This compound has been well characterized from the structural point of view by analysing X-ray diffraction (XRD) patterns. The temperature dependent behaviour of magnetization (M) and the structural parameters (lattice parameters, unit cell volume) suggest that the compound undergoes a second order phase transition from a paramagnetic to a ferromagnetic state at TC = 390 K, driven by an increase in bond length between iron atoms at 6c sites. The field-dependent behaviour of M below TC, and comparatively lower value of coercivity (Hc) have been explained by the role of Si atoms as pinning centres. In the ferromagnetic phase, the system is found to behave like an inhomogenous mean field system. The study of thermal expansion properties establishes that the compound is a zero thermal expansion material (αv = 5.3 × 10-6 K-1) operative in the temperature range T = 200-340 K. As a magnetocaloric material, Pr2Fe16Si possesses high RCP (87 J kg-1 at μ0H = 1.5 T), high operating temperature (390 K) and moderate |ΔSM|max.

Inorganic–organic hybridization induced uniaxial zero thermal expansion in MC4O4 (M = Ba, Pb)

We report two inorganic–organic hybrid materials with pillar-layered architectures, BaC₄O₄ and PbC₄O₄, which show uniaxial zero thermal expansion (ZTE) along the hybrid direction over a wide temperature range.

Large Negative Thermal Expansion Induced by Synergistic Effects of Ferroelectrostriction and Spin Crossover in PbTiO3-Based Perovskites

The discovery of unusual negative thermal expansion (NTE) provides the opportunity to control the common but much desired property of thermal expansion, which is valuable not only in scientific interests but also in practical applications. However, most of the available NTE materials are limited to a narrow temperature range, and the NTE effect is generally weakened by various modifications. Here, we report an enhanced NTE effect that occurs over a wide temperature range α ‾ V = - 5.24 × 10 - 5 ∘ C - 1 , 25 - 575 ∘ C , and this NTE effect is accompanied by an abnormal enhanced tetragonality, a large spontaneous polarization, and a G-type antiferromagnetic ordering in the present perovskite-type ferroelectric of (1-x)PbTiO3-xBiCoO3. Specifically, for the composition of 0.5PbTiO3-0.5BiCoO3, an extensive volumetric contraction of ~4.8 % has been observed near the Curie temperature of 700 °C, which represents the highest level in PbTiO3-based ferroelectrics. According to our experimental and theoretical results, the large NTE originates from a synergistic effect of the ferroelectrostriction and spin crossover of cobalt on the crystal lattice. The actual NTE mechanism is contrasted with previous functional NTE materials, in which the NTE is simply coupled with one ordering such as electronic, magnetic, or ferroelectric ordering. The present study sheds light on the understanding of NTE mechanisms, and it attests that NTE could be simultaneously coupled with different orderings, which will pave a new way toward the design of large NTE materials.

Negative thermal expansion in cubic FeFe(CN)6 Prussian blue analogues

A new isotropic negative thermal expansion compound of FeFe(CN)₆ has been found, in which the transverse vibrations of N atoms dominate in its NTE behavior.

Tunable thermal expansion and high hardness of (0.9−x)PbTiO3–xCaTiO3–0.1Bi(Zn2/3Ta1/3)O3 ceramics

Ceramic materials with controllable thermal expansion (positive, zero, and negative) and high hardness have been achieved in perovskites through chemical modifications.

Guest-dependent negative thermal expansion in a lanthanide-based metal–organic framework

A lanthanide-based metal–organic framework (MOF) named SION-2, displays strong and tuneable uniaxial negative thermal expansion (NTE).

Continuous negative-to-positive tuning of thermal expansion achieved by controlled gas sorption in porous coordination frameworks

Control of the thermomechanical properties of functional materials is of great fundamental and technological significance, with the achievement of zero or negative thermal expansion behavior being a key goal for various applications. A dynamic, reversible mode of control is demonstrated for the first time in two Prussian blue derivative frameworks whose coefficients of thermal expansion are tuned continuously from negative to positive values by varying the concentration of adsorbed CO₂. A simple empirical model that captures site-specific guest contributions to the framework expansion is derived, and displays excellent agreement with the observed lattice behaviour.

Achieving control over the thermomechanical properties of functional materials is desirable, yet remains highly challenging. Here, the authors demonstrate continuous negative-to-positive tuning of thermal expansion in two Prussian blue analogues, by varying the concentration of adsorbed CO₂.

Isotropic Low Thermal Expansion over a Wide Temperature Range in Ti1- xZr xF3+ x (0.1 ≤ x ≤ 0.5) Solid Solutions

TiF₃ exhibits a rhombohedral to ReO₃-type cubic phase transformation at ∼340 K. Here we report that, by introducing ZrF₄ into TiF₃, the cubic phase is stabilized at least down to 123 K in the Ti_{1- x}Zr _xF_{3+ x} compounds. All compounds exhibit low thermal expansion (LTE) between 123 and 623 K, and a nearly zero thermal expansion (ZTE) was obtained in Ti_0.7Zr_0.3F_3.3 (α_L = 0.91 ppm/K). The analysis of pair distribution function reveals that the cation-centered octahedra are partially changed to pentagonal bipyramids in Ti_{1- x}Zr _xF_{3+ x} due to the excess fluorines relative to the case of TiF₃. Therefore, the cooperative rotation of the polyhedra tends to be restricted, and the cubic phase is thus stabilized. The restrained polyhedral rotations compete against the lattice softening caused by the introduction of Zr⁴⁺, giving rise to the LTE. Our present strategy is applicable to other rhombohedral metal trifluorides for the design of new isotropic ZTE materials.

Positive and Negative Two-Dimensional Thermal Expansion via Relaxation of Node Distortions

The ability to tune physical properties is attractive for the development of new materials for myriad applications. Understanding and controlling the structural dynamics in complicated network structures like coordination polymers (CPs) is particularly challenging. We report a series of two-dimensional CPs [Mn(salen)]₂[M(CN)₄]· xH₂O (M = Pt (1), PtI₂ (2), and MnN (3)) incorporating zigzag cyano-network layers that display composition-dependent anisotropic thermal expansion properties. Variable-temperature single-crystal X-ray structural analyses demonstrated that the thermal expansion behavior is caused by double structural distortions involving [Mn(salen)]⁺ units incorporated into the zigzag layers. Thermal relaxations produce structural transformations resulting in positive thermal expansion for 2·H₂O and negative thermal expansion for 3. In the case of 1·H₂O, the relaxation does not occur and zero thermal expansion results in the plane between 200 to 380 K. The present study proposes a new strategy based on structural distortions in coordination networks to control thermal responsivities of frameworks.

Negative Thermal Expansion, Response to Pressure and Phase Transitions in CaTiF6

Strong volume negative thermal expansion over a wide temperature range typically only occurs in ReO₃-type fluorides that retain an ideal cubic structure to very low temperatures, such as ScF₃, CaZrF₆, CaHfF₆, and CaNbF₆. CaTiF₆ was examined in an effort to expand this small family of materials. However, it undergoes a cubic ( Fm3̅ m) to rhombohedral ( R3̅) transition on cooling to ∼120 K, with a minimum volume coefficient of thermal expansion (CTE) close to -42 ppm K^-1 at 180 K and a CTE of about -32 ppm K^-1 at room temperature. On compression at ambient temperature, the material remains cubic to ∼0.25 GPa with K₀ = 29(1) GPa and K'₀ = -50(5). Cubic CaTiF₆ is elastically softer and shows more pronounced pressure induced softening, than both CaZrF₆ and CaNbF₆. In sharp contrast to both CaZrF₆ and CaNbF₆, CaTiF₆ undergoes a first-order pressure induced octahedral tilting transition to a rhombohedral phase ( R3̅) on compression above 0.25 GPa, which is closely related to that seen in ScF₃. Just above the transition pressure, this phase is elastically very soft with a bulk modulus of only ∼4 GPa as octahedral tilting associated with a reduction in the Ca-F-Ti angles provides a low energy pathway for volume reduction. This volume reduction mechanism leads to highly anisotropic elastic properties, with the rhombohedral phase displaying both a low bulk modulus and negative linear compressibility parallel to the crystallographic c-axis for pressures below ∼2.5 GPa. At ∼3 GPa, a further phase transition to a poorly ordered phase occurs.

Synthesis, structure, and polymorphic transitions of praseodymium(iii) and neodymium(iii) borohydride, Pr(BH4)3 and Nd(BH4)3

In this work, praseodymium(iii) borohydride, Pr(BH4)3, and an isotopically enriched analogue, Pr(11BD4)3, are prepared by a new route via a solvate complex, Pr(11BD4)3S(CH3)2. Nd(BH4)3 was synthesized using the same method and the structures, polymorphic transformations, and thermal stabilities of these compounds are investigated in detail. α-Pr(BH4)3 and α-Nd(BH4)3 are isostructural with cubic unit cells (Pa3[combining macron]) stable at room temperature (RT) and a unit cell volume per formula unit (V/Z) of 180.1 and 175.8 Å3, respectively. Heating α-Pr(BH4)3 to T ∼ 190 °C, p(Ar) = 1 bar, introduces a transition to a rhombohedral polymorph, r-Pr(BH4)3 (R3[combining macron]c) with a smaller unit cell volume and a denser structure, V/Z = 156.06 Å3. A similar transition was not observed for Nd(BH4)3. However, heat treatment of α-Pr(BH4)3, at T ∼ 190 °C, p(H2) = 40 bar and α-Nd(BH4)3, at T ∼ 270 °C, p(H2) = 98 bar facilitates reversible formation of another three cubic polymorph, denoted as β, β' and β''-RE(BH4)3 (Fm3[combining macron]c). Moreover, the transition β- to β'- to β''- is considered a rare example of stepwise negative thermal expansion. For Pr(BH4)3, ∼2/3 of the sample takes this route of transformation whereas in argon only ∼5 wt%, and the remaining transforms directly from α- to r-Pr(BH4)3. The β-polymorphs are porous with V/Z = 172.4 and 172.7 Å3 for β''-RE(BH4)3, RE = Pr or Nd, respectively, and are stabilized by the elevated hydrogen pressures. The polymorphic transitions occur due to rotation of RE(BH4)6 octahedra without breaking or forming chemical bonds. Structural DFT optimization reveals the decreasing stability of α-Pr(BH4)3 > β-Pr(BH4)3 > r-Pr(BH4)3.

Twin Crystal Induced near Zero Thermal Expansion in SnO2 Nanowires

Knowledge of controllable thermal expansion is a fundamental issue in the field of materials science and engineering. Direct blocking of the thermal expansions in positive thermal expansion materials is a challenging but fascinating task. Here we report a near zero thermal expansion (ZTE) of SnO₂ achieved from twin crystal nanowires, which is highly correlated to the twin boundaries. Local structural evolutions followed by pair distribution function revealed a remarkable thermal local distortion along the twin boundary. Lattice dynamics investigated by Raman scattering evidenced the hardening of phonon frequency induced by the twin crystal compressing, giving rise to the ZTE of SnO₂ nanowires. Further DFT calculation of Grüneisen parameters confirms the key role of compressive stress on ZTE. Our results provide an insight into the thermal expansion behavior regarding to twin crystal boundaries, which could be beneficial to the applications.

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 HfMg_1-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 HfMg_1-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.

Mesopores induced zero thermal expansion in single-crystal ferroelectrics

For many decades, zero thermal expansion materials have been the focus of numerous investigations because of their intriguing physical properties and potential applications in high-precision instruments. Different strategies, such as composites, solid solution and doping, have been developed as promising approaches to obtain zero thermal expansion materials. However, microstructure controlled zero thermal expansion behavior via interface or surface has not been realized. Here we report the observation of an impressive zero thermal expansion (volumetric thermal expansion coefficient, −1.41 × 10⁻⁶ K⁻¹, 293–623 K) in single-crystal ferroelectric PbTiO₃ fibers with large-scale faceted and enclosed mesopores. The zero thermal expansion behavior is attributed to a synergetic effect of positive thermal expansion near the mesopores due to the oxygen-based polarization screening and negative thermal expansion from an intrinsic ferroelectricity. Our results show that a fascinating surface construction in negative thermal expansion ferroelectric materials could be a promising strategy to realize zero thermal expansion.

Zero thermal expansion materials—often composites of negative and positive coefficient materials—are needed for applications that see large temperature changes. Here, the authors demonstrate that polarization around pores in single-phase mesoporous lead titanate can be used to tune thermal expansion to near zero.

Zero Thermal Expansion in Magnetic and Metallic Tb(Co,Fe)2 Intermetallic Compounds

Due to the advantage of invariable length with temperatures, zero thermal expansion (ZTE) materials are intriguing but very rare especially for the metals based compounds. Here, we report a ZTE in the magnetic intermetallic compounds of Tb(Co,Fe)₂ over a wide temperature range (123-307 K). A negligible coefficient of thermal expansion (α_l = 0.48 × 10^-6 K^-1) has been found in Tb(Co_1.9Fe_0.1). Tb(Co,Fe)₂ exhibits ferrimagnetic structure, in which the moments of Tb and Co/Fe are antiparallel alignment along the c axis. The intriguing ZTE property of Tb(Co,Fe)₂ is formed due to the balance between the negative contribution from the Tb magnetic moment induced spontaneous magnetostriction and the positive role from the normal lattice expansion. The present ZTE intermetallic compounds are also featured by the advantages of wide temperature range, high electrical conductivity, and relatively high thermal conductivity.

Synthesis of Zr2WP2O12/ZrO2 Composites with Adjustable Thermal Expansion

Zr₂WP₂O₁₂/ZrO₂ composites were fabricated by solid state reaction with the goal of tailoring the thermal expansion coefficient. XRD, SEM and TMA were used to investigate the composition, microstructure, and thermal expansion behavior of Zr₂WP₂O₁₂/ZrO₂ composites with different mass ratio. Relative densities of all the resulting Zr₂WP₂O₁₂/ZrO₂ samples were also tested by Archimedes' methods. The obtained Zr₂WP₂O₁₂/ZrO₂ composites were comprised of orthorhombic Zr₂WP₂O₁₂ and monoclinic ZrO₂. As the increase of the Zr₂WP₂O₁₂, the relative densities of Zr₂WP₂O₁₂/ZrO₂ ceramic composites increased gradually. The coefficient of thermal expansion of the Zr₂WP₂O₁₂/ZrO₂ composites can be tailored from 4.1 × 10^-6 K^-1 to -3.3 × 10^-6 K^-1 by changing the content of Zr₂WP₂O₁₂. The 2:1 Zr₂WP₂O₁₂/ZrO₂ specimen shows close to zero thermal expansion from 25 to 700°C with an average linear thermal expansion coefficient of -0.09 × 10^-6 K^-1. These adjustable and near zero expansion ceramic composites will have great potential application in many fields.

Colossal Volume Contraction in Strong Polar Perovskites of Pb(Ti,V)O3

The unique physical property of negative thermal expansion (NTE) is not only interesting for scientific research but also important for practical applications. Chemical modification generally tends to weaken NTE. It remains a challenge to obtain enhanced NTE from currently available materials. Herein, we successfully achieve enhanced NTE in Pb(Ti_1-xV_x)O₃ by improving its ferroelectricity. With the chemical substitution of vanadium, lattice tetragonality (c/a) is highly promoted, which is attributed to strong spontaneous polarization, evidenced by the enhanced covalent interaction in the V/Ti-O and Pb-O2 bonds from first-principles calculations. As a consequence, Pb(Ti_0.9V_0.1)O₃ exhibits a nonlinear and much stronger NTE over a wide temperature range with a volumetric coefficient of thermal expansion α_V = -3.76 × 10^-5/°C (25-550 °C). Interestingly, an intrinsic giant volume contraction (∼3.7%) was obtained at the composition of Pb(Ti_0.7V_0.3)O₃ during the ferroelectric-to-paraelectric phase transition, which represents the highest value ever reported. Such volume contraction is well correlated to the effect of spontaneous volume ferroelectrostriction. The present study extends the scope of the NTE family and provides an effective approach to explore new materials with large NTE, such as through adjusting the NTE-related ferroelectric property in the family of ferroelectrics.

Isotropic Zero Thermal Expansion and Local Vibrational Dynamics in (Sc,Fe)F3

Scandium fluoride (ScF₃) exhibits a pronounced negative thermal expansion (NTE), which can be suppressed and ultimately transformed into an isotropic zero thermal expansion (ZTE) by partially substituting Sc with Fe in (Sc_0.8Fe_0.2)F₃ (Fe20). The latter displays a rather small coefficient of thermal expansion of -0.17 × 10^-6/K from 300 to 700 K. Synchrotron X-ray and neutron pair distribution functions confirm that the Sc/Fe-F bond has positive thermal expansion (PTE). Local vibrational dynamics based on extended X-ray absorption fine structure indicates a decreased anisotropy of relative vibration in the Sc/Fe-F bond. Combined analysis proposes a delicate balance between the counteracting effects of the chemical bond PTE and NTE from transverse vibration. The present study extends the scope of isotropic ZTE compounds and, more significantly, provides a complete local vibrational dynamics to shed light on the ZTE mechanism in chemically tailored NTE compounds.