Mechanisms and Materials for NTE

Classifying and Predicting the Thermal Expansion Properties of Metal-Organic Frameworks: A Data-Driven Approach

Metal-organic frameworks (MOFs) are versatile materials for a wide variety of potential applications. Tunable thermal expansion properties promote the application of MOFs in thermally sensitive composite materials; however, they are currently available only in a handful of structures. Herein, we report the first data set for thermal expansion properties of 33,131 diverse MOFs generated from molecular simulations and subsequently develop machine learning (ML) models to (1) classify different thermal expansion behaviors and (2) predict volumetric thermal expansion coefficients (αV). The random forest model trained on hybrid descriptors combining geometric, chemical, and topological features exhibits the best performance among different ML models. Based on feature importance analysis, linker chemistry and topological arrangement are revealed to have a dominant impact on thermal expansion. Furthermore, we identify common building blocks in MOFs with exceptional thermal expansion properties. This data-driven study is the first of its kind, not only constructing a useful data set to facilitate future studies on this important topic but also providing design guidelines for advancing new MOFs with desired thermal expansion properties.

Evolution of structure and spectroscopic properties of a new 1,3-diacetylpyrene polymorph with temperature and pressure

A new polymorph of 1,3-diacetylpyrene has been obtained from its melt and thoroughly characterized using single-crystal X-ray diffraction, steady-state UV-Vis spectroscopy and periodic density functional theory calculations. Experimental studies covered the temperature range from 90 to 390 K and the pressure range from atmospheric to 4.08 GPa. Optimal sample placement in a diamond anvil cell according to our previously presented methodology ensured over 80% data coverage up to 0.8 Å for a monoclinic sample. Unrestrained Hirshfeld atom refinement of the high-pressure crystal structures was successful and anharmonic behavior of carbonyl oxygen atoms was observed. Unlike the previously characterized polymorph, the structure of 2°AP-β is based on infinite π-stacks of antiparallel 2°AP molecules. 2°AP-β displays piezochromism and piezofluorochromism which are directly related to the variation in interplanar distances within the π-stacking. The importance of weak intermolecular interactions is reflected in the substantial negative thermal expansion coefficient of -55.8 (57) MK-1 in the direction of C-H...O interactions.

Growth of Size-Tunable Ag2O Polyhedra and Revelation of Their Bulk and Surface Lattices

By primarily adjusting the reagent amounts, particularly the volume of AgNO3 solution introduced, Ag2O cubes with decreasing sizes from 440 to 79 nm, octahedra from 714 to 106 nm, and rhombic dodecahedra from 644 to 168 nm are synthesized. 733 nm cuboctahedra are also prepared for structural analysis. With in-house X-ray diffraction (XRD) peak calibration, shape-related peak shifts are recognizable. Synchrotron XRD measurements at 100 K reveal the presence of bulk and surface layer lattices. Bulk cell constants also deviate slightly. They show a negative thermal expansion behavior with shrinking cell constants at higher temperatures. The Ag2O crystals exhibit size- and facet-dependent optical properties. Bandgaps red-shift continuously with increasing particle sizes. Optical facet effect is also observable. Moreover, synchrotron XRD peaks of a mixture of Cu2O rhombicuboctahedra and edge- and corner-truncated cubes exposing all three crystal faces can be deconvoluted into three components with the bulk and the [111] microstrain phase as the major component. Interestingly, while the unheated Cu2O sample shows clear diffraction peak asymmetry, annealing the sample to 450 K yields nearly symmetric peaks even when returning the sample to room temperature, meaning even moderately high temperatures can permanently change the crystal lattice.

Giant Negative Thermal Expansion in Ultralight NaB(CN)4

Negative thermal expansion (NTE) is crucial for controlling the thermomechanical properties of functional materials, albeit being relatively rare. This study reports a giant NTE (αV ∼-9.2 ⋅ 10-5  K-1 , 100-200 K; αV ∼-3.7 ⋅ 10-5  K-1 , 200-650 K) observed in NaB(CN)4 , showcasing interesting ultralight properties. A comprehensive investigation involving synchrotron X-ray diffraction, Raman spectroscopy, and first-principles calculations has been conducted to explore the thermal expansion mechanism. The findings indicate that the low-frequency phonon modes play a primary role in NTE, and non-rigid vibration modes with most negative Grüneisen parameters are the key contributing factor to the giant NTE observed in NaB(CN)4 . This work presents a new material with giant NTE and ultralight mass density, providing insights for the understanding and design of novel NTE materials.

Electronic origin of negative thermal expansion in samarium hexaboride revealed by X-ray diffraction and total scattering

Samarium hexaboride, SmB6, is a negative thermal expansion (NTE) material whose structure is similar to other known NTE materials such as the family of Prussian blues. In the Prussian blues, NTE is due to a phonon mechanism, but we recently showed from DFT calculations that this is unlikely in SmB6 (Li et al., Phys. Chem. Chem. Phys. 2023, 25, 10749). We now report experimental X-ray diffraction and pair distribution function analysis of this material in the temperature range 20-300 K. The interatomic distances shown by both methods are consistent with the NTE instead arising from an electronic effect, by which the samarium atoms lose electrons and thus have a smaller ionic radius as the temperature increases.

Sintering Temperature Effect of Near-Zero Thermal Expansion Mn3Zn0.8Sn0.2N/Ti Composites

Metal matrix composites with near-zero thermal expansion (NZTE) have gained significant popularity in high-precision industries due to their excellent thermal stability and mechanical properties. The incorporation of Mn3Zn0.8Sn0.2N, which possesses outstanding negative thermal expansion properties, effectively suppressed the thermal expansion of titanium. Highly dense Mn3Zn0.8Sn0.2N/Ti composites were obtained by adjusting the fabrication temperature. Both composites fabricated at 650 °C and 700 °C exhibited NZTE. Furthermore, finite element analysis was employed to investigate the effects of thermal stress within the composites on their thermal expansion performance.

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.

Electronic Structure and Core Spectroscopy of Scandium Fluoride Polymorphs

Microscopic knowledge of the structural, energetic, and electronic properties of scandium fluoride is still incomplete despite the relevance of this material as an intermediate for the manufacturing of Al-Sc alloys. In a work based on first-principles calculations and X-ray spectroscopy, we assess the stability and electronic structure of six computationally predicted ScF₃ polymorphs, two of which correspond to experimentally resolved single-crystal phases. In the theoretical analysis based on density functional theory (DFT), we identify similarities among the polymorphs based on their formation energies, charge-density distribution, and electronic properties (band gaps and density of states). We find striking analogies between the results obtained for the low- and high-temperature phases of the material, indirectly confirming that the transition occurring between them mainly consists of a rigid rotation of the lattice. With this knowledge, we examine the X-ray absorption spectra from the Sc and F K-edge contrasting first-principles results obtained from the solution of the Bethe-Salpeter equation on top of all-electron DFT with high-energy-resolution fluorescence detection measurements. Analysis of the computational results sheds light on the electronic origin of the absorption maxima and provides information on the prominent excitonic effects that characterize all spectra. A comparison with measurements confirms that the sample is mainly composed of the high- and low-temperature polymorphs of ScF₃. However, some fine details in the experimental results suggest that the probed powder sample may contain defects and/or residual traces of metastable polymorphs.

Metamaterial with Tunable Positive and Negative Hygrothermal Expansion Inspired by a Four-Fold Symmetrical Islamic Motif

A metamaterial with controllable positive and negative thermal and hygroscopic expansions is investigated herein by inspiration from a range of Islamic geometric patterns. Constructing from eight pairs of pin-jointed Y-elements, each unit cell manifests eight rhombi that are arranged circumferentially, thereby manifesting four axes of symmetry. By attachment of bimaterial spiral springs of contrasting expansion coefficients to the far arms of the paired Y-elements, a change in the environment’s thermal or hygroscopic condition alters the offset angle of the paired Y-elements such that the unit cell of the metamaterial ranges from the eight-pointed star to the regular octagon. The effective coefficient of thermal expansion (CTE) and the coefficient of moisture expansion (CME) of this metamaterial were developed for small and large changes in environmental fluctuations using infinitesimal and finite models, respectively. Generated data indicates that the sign and magnitude of the effective thermal and hygroscopic expansion coefficients can be controlled by geometrical descriptors of the bimaterial spiral spring—such as its coil number and the ratio of its mean radius to its thickness—as well as the properties of the bimaterial’s layers such as their expansion coefficients, Young’s moduli and, in the case of effective hygroscopic expansion, their relative absorptivity. The obtained results suggest that the proposed metamaterial can be designed to perform as highly sensitive thermal and/or moisture sensors, as well as other functional materials or devices that take advantage of environmental changes as stimuli.

Sign change in c-axis thermal expansion constant and lattice collapse by Ni substitution in transition-metal zirconide superconductor Co1-xNixZr2

Recently, c-axis negative thermal expansion (NTE) was observed in a CoZr₂ superconductor and related transition-metal zirconides. Here, we investigated the structural, electronic, and superconducting properties of Co_1-xNi_xZr₂ to achieve systematic control of c-axis NTE and switching from NTE to positive thermal expansion (PTE) by Ni substitution. At x ≤ 0.3, c-axis NTE was observed, and the thermal expansion constant α_c approached zero with increasing x. At x = 0.4-0.6, c-axis thermal expansion close to zero thermal expansion (ZTE) was observed, and PTE appeared for x ≥ 0.7. On the superconducting properties, we observed bulk superconductivity for x ≤ 0.6, and bulk nature of superconductivity is suppressed by Ni heavy doping (x ≥ 0.7). For x ≤ 0.6, the evolution of the electronic density of states well explains the change in the superconducting transition temperature (T_c), which suggests conventional phonon-mediated superconductivity in the system. By analyzing the c/a ratio, we observed a possible collapsed transition in the tetragonal lattice at around x = 0.6-0.8. The lattice collapse would be the cause of the suppression of superconductivity in Ni-rich Co_1-xNi_xZr₂ and the switching from NTE to PTE.

Tuning Negative Thermal Expansion in AlPO4-17 by Insertion of Guest Molecules

The very strong negative thermal expansion in the porous aluminophosphate AlPO₄-17 with a hexagonal erionite structure was tuned by the insertion of oxygen molecules at high pressure. The structure of the oxygen-filled material was determined in situ at high pressure by synchrotron, single-crystal X-ray diffraction. The thermal expansion of this material was measured precisely at 0.38 GPa by synchrotron X-ray powder diffraction. Whereas the overall volume thermal expansion only exhibits a small change with respect to empty AlPO₄-17 at ambient pressure, the expansion along the a direction decreases almost to zero and the expansion along c increases by a factor of 7. Such highly anisotropic thermal expansion properties are of great interest for mechanical and optical applications as in two directions the dimensions of the material are extremely stable, whereas a very strong linear negative thermal expansion of -2.2 × 10^-5 K^-1 is observed in the perpendicular direction. Guest insertion is thus a very powerful tool for tuning the thermal expansion properties of porous materials.

Tailoring Negative Thermal Expansion via Tunable Induced Strain in La-Fe-Si-Based Multifunctional Material

Zero thermal expansion (ZTE) composites are typically designed by combining positive thermal expansion (PTE) with negative thermal expansion (NTE) materials acting as compensators and have many diverse applications, including in high-precision instrumentation and biomedical devices. La(Fe_1-x,Si_x)13-based compounds display several remarkable properties, such as giant magnetocaloric effect and very large NTE at room temperature. Both are linked via strong magnetovolume coupling, which leads to sharp magnetic and volume changes occurring simultaneously across first-order phase transitions; the abrupt nature of these changes makes them unsuitable as thermal expansion compensators. To make these materials more useful practically, the mechanisms controlling the temperature over which this transition occurs and the magnitude of contraction need to be controlled. In this work, ball-milling was used to decrease particles and crystallite sizes and increase the strain in LaFe_11.9Mn_0.27Si_1.29H_x alloys. Such size and strain tuning effectively broadened the temperature over which this transition occurs. The material's NTE operational temperature window was expanded, and its peak was suppressed by up to 85%. This work demonstrates that induced strain is the key mechanism controlling these materials' phase transitions. This allows the optimization of their thermal expansion toward room-temperature ZTE applications.

Extrinsic Point Defects in Low-Positive Thermal Expansion Al2W3O12 and Their Effects on Thermal and Optical Properties

A₂M₃O₁₂-type ceramics are potentially useful in a variety of applications due to their peculiar thermal and mechanical properties. In addition, their intrinsic coefficients of thermal expansion can be finely tuned through different mechanisms. Despite the great influence of extrinsic point defects on physical properties, only a few reports have dealt with their relationship to thermal expansion and thermal conductivity. Extrinsic oxygen vacancies in orthorhombic Al₂W₃O₁₂, in different concentrations, were formed through heat treatments in argon or hydrogen atmospheres. X-ray powder diffraction, diffuse reflectance spectroscopy, and Raman and electron paramagnetic resonance spectroscopies were used to study the as-formed vacancies, and X-ray photoelectron spectroscopy was employed to propose a charge compensation mechanism. It was found that the intrinsic coefficient of thermal expansion of orthorhombic Al₂W₃O₁₂ was severely affected by extrinsic oxygen vacancies. Thermal expansion was decreased up to 40% (from 25 to 400 °C) with respect to the extrinsic-point-defect-free counterpart. Unit-cell volumes of defective orthorhombic Al₂W₃O₁₂ were larger, while their W-O bonds were weaker, likely leading to higher lattice flexibility and enhanced low-energy transverse acoustic modes. Extrinsic oxygen vacancies could be an additional mechanism for fine-tuning the intrinsic coefficients of thermal expansion in A₂M₃O₁₂-type ceramics and in other framework structures built through two or threefold linkages.

Negative Thermal Expansion in Fluoroapatite Pb5(VO4)3F Enhanced by the Steric Effect of Pb2

Negative thermal expansion (NTE) is an unusual thermophysical phenomenon and has gained attention as a way of controlling thermal expansion. Here, we report a substantial NTE in fluoroapatite Pb₅(VO₄)₃F in a limited temperature range. The dilatometric study revealed volume shrinkage below 150 K, giving a linear thermal expansion coefficient of α_L = -44 ppm/K in the temperature range from 140 to 120 K upon heating. The NTE behavior is associated with a structural transition from the hexagonal (P6₃/m) phase to the monoclinic (P2₁/b) phase. Such a structural transition has been found in other apatite-type compounds, but the magnitude of the volume change in Pb₅(VO₄)₃F is remarkable. Our structural analysis revealed that the structural transition is classified as an antiferroelectric-to-paraelectric transition and the volume change during the transition is enhanced by the steric effect of 6s² lone-pair electrons of Pb²⁺.

Understanding Large Negative Thermal Expansion of NdFe(CN)6 through the Electronic Structure and Lattice Dynamics

A large negative thermal expansion (NTE) (α_v = -4.1 × 10^-5 K^-1, 100-525 K) has been discovered in NdFe(CN)₆. Here, the synchrotron X-ray diffraction and lattice dynamics calculations using the density functional theory were conducted to understand the NTE in NdFe(CN)₆. The information obtained on the bond nature of the Nd-N≡C-Fe linkage and on the atomic thermal vibrations suggests that the transverse vibrations of the -N≡C- group, in particular from N atoms, produced the NTE in NdFe(CN)₆. This is corroborated by the calculated Grüneisen parameters, which confirm the relationship between NTE and CN atomic vibrations. The results provide a helpful contribution toward the realization of new materials with negative or controllable thermal expansion.

Realization of Negative Thermal Expansion in Lead-Free Bi0.5K0.5VO3 by the Suppression of Tetragonality

Bi_1/2K_1/2VO₃ is a lead-free PbTiO₃-type compound with a tetragonality (c/a = 1.054) comparable to that of typical ferroelectric PbTiO₃ (c/a = 1.064) with negative thermal expansion (NTE) during the tetragonal-to-cubic phase transition; therefore, Bi_1/2K_1/2VO₃ is a potential lead-free NTE material if its metastable perovskite structure can be maintained at high temperatures. In the present experiment, electron doping in Bi_1/2K_1/2VO₃ was conducted through substituting K⁺ with La³⁺ to suppress the tetragonality and achieve NTE. La substitution successfully suppressed the tetragonality of Bi_1/2K_1/2VO₃ and also improved its thermal stability. Moreover, both composition- and temperature-induced tetragonal-to-cubic phase transitions occurred. In particular, a large volume shrinkage with a large negative thermal coefficient of expansion (CTE) was obtained for Bi_0.5K_0.46La_0.04VO₃ during the tetragonal-to-cubic phase transition (ΔV = -0.66%). Hence, this study extends the NTE family and also sheds light on the exploration of lead-free piezoelectric materials with controllable thermal expansion.

A Proposal for a Composite with Temperature-Independent Thermophysical Properties: HfV2-HfV2O7

The HfV2-HfV2O7 composite is proposed as a material with potentially temperature-independent thermophysical properties due to the combination of anomalously increasing thermoelastic constants of HfV2 with the negative thermal expansion of HfV2O7. Based on literature data, the coexistence of both a near-zero temperature coefficient of elasticity and a coefficient of thermal expansion is suggested for a composite with a phase fraction of approximately 30 vol.% HfV2 and 70 vol.% HfV2O7. To produce HfV2-HfV2O7 composites, two synthesis pathways were investigated: (1) annealing of sputtered HfV2 films in air to form HfV2O7 oxide on the surface and (2) sputtering of HfV2O7/HfV2 bilayers. The high oxygen mobility in HfV2 is suggested to inhibit the formation of crystalline HfV2-HfV2O7 composites by annealing HfV2 in air due to oxygen-incorporation-induced amorphization of HfV2. Reducing the formation temperature of crystalline HfV2O7 from 550 °C, as obtained upon annealing, to 300 °C using reactive sputtering enables the synthesis of crystalline bilayered HfV2-HfV2O7.

Suppression of wear in dry sliding friction induced by negative thermal expansion

Surface temperature is among crucial factors which control wear during sliding dry contact. Using computer modeling, we study the possibility to achieve close to zero rate of surface wear during sliding friction of the special type of materials which possess negative thermal expansion. The numerical simulations reveal two wear regimes for materials with negative thermal expansion coefficient as dependent on the applied normal stress level. When the applied stress is lower than that of a critical level, a steady almost zero wear rate and nanorough surface are achieved during friction. Otherwise, wear rate is of the same order of magnitude as for "traditional" materials with positive thermal expansion coefficient. The critical stress value is analyzed depending on the material's mechanical, thermophysical, and surface roughness characteristics.

Electronic origin of negative thermal expansion in V2OPO4

Unusual negative thermal expansion in V₂OPO₄ is discovered to arise from phase coexistence around the charge ordering transition at 605 K.

Enhanced tetragonality and large negative thermal expansion in a new Pb/Bi-based perovskite ferroelectric of (1 − x)PbTiO3–xBi(Zn1/2V1/2)O3

With the introduction of Bi(Zn_1/2V_1/2)O₃, both tetragonality and negative thermal expansion of PbTiO₃ have been enhanced.