Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation

Significant Enhancement of Negative Thermal Expansion Under Low Pressure in Cu2P2O7

Much effort is made to achieve the negative thermal expansion (NTE) control, but rare methods reached the improvement of intrinsic NTE. In the present work, a significantly enhanced NTE is realized in Cu2P2O7 by applying low pressure. Especially, the volumetric coefficient of thermal expansion (CTE) of Cu2P2O7 reached to -50.0 × 10-6 K-1 (150-325K) under 0.25 GPa, which is increased by 47.5% compared to its NTE in a similar temperature range under atmosphere pressure. This character enables a more effective manifestation of the thermal compensation role of Cu2P2O7 in composites. The enhanced NTE mechanisms are analyzed by high pressure synchrotron X-ray diffraction, neutron diffraction at variable temperature and pressure, as well as density functional theory (DFT) calculations. The results show that applied pressure accelerates the contraction of the distance between adjacent CuO layers and CuO columns. Meanwhile, the low-frequency phonon contribution to NTE in α-Cu2P2O7 is improved. This work is meaningful for the exploration of methods to enhance NTE and the practical application of NTE materials.

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.

Local Structure and Dynamics in MPt(CN)6 Prussian Blue Analogues

We use a combination of X-ray pair distribution function (PDF) measurements, lattice dynamical calculations, and ab initio density functional theory (DFT) calculations to study the local structure and dynamics in various MPt(CN)6 Prussian blue analogues. In order to link directly the local distortions captured by the PDF with the lattice dynamics of this family, we develop and apply a new "interaction-space" PDF refinement approach. This approach yields effective harmonic force constants, from which the (experiment-derived) low-energy phonon dispersion relations can be approximated. Calculation of the corresponding Grüneisen parameters allows us to identify the key modes responsible for negative thermal expansion (NTE) as arising from correlated tilts of coordination octahedra. We compare our results against the phonon dispersion relations determined using DFT calculations, which identify the same NTE mechanism.

Scaling laws for lattice distortions: Application to high entropy alloys

Lattice distortions are intrinsic features of all solid solution alloys associated with varying atomic radii; this phenomenon facilitates the formation of single-phase solid solutions. Using high-entropy alloys (HEAs), as an example, we investigate the influence of variations in inter-atomic separations for stabilizing and controlling their structural, mechanical, and thermodynamic properties. This is done through a combination of statistical mechanics analysis and molecular dynamics simulations on simplified 2D systems, as well as a 3D crystals with harmonic and anharmonic inter-atomic bonds with varying natural inter-atomic separations. We demonstrate that the impact of this inter-atomic length disorder (representing static lattice distortion) and temperature fluctuations (representing dynamic lattice distortion) on fundamental and universal thermodynamic, structural, and elastic characteristics are similar and can be unified through effective temperature; i.e. a scaling law for HEAs that establishes a relationship between these factors. This scaling law reveals that different HEAs (i.e. varying degrees of local lattice distortions) collapse onto a single curve when plotted against the effective temperature. We demonstrate that lattice distortion significantly enhances the stability of solid solution alloys (relative to phase separation or ordering by effectively increasing the temperature of the system; this stabilization effect is particularly pronounced in HEAs).

Anisotropic Thermal Expansion of Structurally Related Lanthanide-Mercury(II) Cyanide Coordination Polymers

Three sets of related lanthanide-mercury(II) cyanide coordination polymers were synthesized by the reaction of LnCl3·xH2O (Ln = Ce, Nd, Eu, Gd, Tb, Dy, Ho, Tm, Yb, and Lu) with Hg(CN)2 and structurally characterized. [Ce(OH2)5][Hg(CN)2Cl]3·2H2O is a 3-D material with sheet-based architecture; its thermal expansion behavior shows uniaxial negative thermal expansion (-18.3(8), 39(2), and 68.3(16) ppm K-1 along the a, b, and c axes, respectively). This anisotropic thermal behavior is postulated to be driven elastically by weak Hg···Cl interactions: large area expansion of the sheets causes negative thermal expansion in the perpendicular direction. Using lanthanides heavier than Ce yielded 2-D sheet-based compounds with the formula [Ln(OH2)x]2[Hg(CN)2]5Cl6·2H2O (Ln = Nd and Eu, x = 7; Ln = Gd, Tb, Dy, Ho, Tm, Yb, and Lu, x = 6). Although there was also evidence for elastic behavior within these materials, both showed uniaxial zero thermal expansion (Ln = Nd: 27.9(17), 22.4(10), and 0.6(12) ppm K-1 along the I, II, and III principal axes, respectively; Ln = Tb: 39.6(12), 1.1(17), and 36.1(7) ppm K-1 along the a, b, and c axes, respectively). Despite their similar structural architecture, this zero thermal expansion was found to occur in different directions─within the plane of the 2-D sheets for [Nd(OH2)7]2[Hg(CN)2]5Cl6·2H2O but in the direction perpendicular to the 2-D sheets for [Tb(OH2)6]2[Hg(CN)2]5Cl6·2H2O. Overall, this system of compounds reveals the delicate relationship between coordination polymer structure and thermal expansion.

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.

Anti-thermal quenching of luminescence in Y2W3O12:Yb3+/RE3+ (RE = Er/Ho/Tm) and its temperature sensing application

Herein, a series of Y2W3O12:10%Yb3+/x%RE3+ (RE = Er/Ho/Tm) phosphors is prepared via a solid-state reaction. The upconversion and downshift luminescence properties of the phosphors were investigated under an excitation of 980 nm. The bright blue light emission from Tm3+ ion and the green and red light emissions from Ho3+(Er3+) ions were observed. The near-infrared light intensity of NIR-I (Tm3+, ∼850 nm), NIR-II (Er3+: ∼1550 nm; Tm3+: ∼1783 nm) and NIR-III (Ho3+: ∼2050 nm) were analyzed. In particular, the dramatic thermal enhancement phenomenon in visible and NIR regions was exhibited by the Y2W3O12:10%Yb3+/x%RE3+ (RE = Er/Ho/Tm) phosphors. Among them, the green light intensity of Er3+ ions increased 26.77 times, from 303 to 573 K. The NIR-II emission band (∼1783 nm) intensity of Tm3+ ions at 533 K increased 168.7 times compared to that at 313 K. The possible thermal enhancement mechanism is illustrated by the negative thermal expansion (NTE) and Frenkel defect of the Y2W3O12 host. Finally, the optical temperature sensing performances of Y2W3O12:10%Yb3+/x%RE3+ (RE = Er/Ho/Tm) samples are investigated according to the luminescence intensity dependence relationship on temperature. The maximum value of SR reached 4.24% K-1 at 353 K for Y2W3O12:10%Yb3+/0.6%Ho3+ phosphor. The results indicate that the Y2W3O12:10%Yb3+/x%RE3+ (RE = Er/Ho/Tm) phosphors possess anti-thermal quenching properties and are suitable for developing optical temperature sensors.

Mechanism of Negative Thermal Expansion in Monoclinic Cu2P2O7 from First Principles

Negative thermal expansion (NTE) materials generally have high-symmetry space groups, large average atomic volumes, and corner-sharing octahedral and tetrahedral coordination structures. By contrast, monoclinic α-Cu2P2O7, which has a small average atomic volume and edge-sharing structure, has been reported to exhibit NTE, the detailed mechanism of which is unclear. In this study, we investigate the A2B2O7 polymorphs and analyze the NTE behavior of α-Cu2P2O7 using first-principles lattice-dynamics calculations. From the polymorphism investigation in 20 A2B2O7 compounds using 6 representative crystal structures, small A and B cationic radii are found to stabilize the α-Cu2P2O7-type structure. We then analyze the NTE behavior of α-Cu2P2O7 using quasi-harmonic approximation. Our calculated thermal expansion coefficients and anisotropic atomic displacement parameters were in good agreement with those of the experimental reports at low temperatures. From the mode-Grüneisen parameter distribution plotted over the entire first-Brillouin zone, we found that the phonon contributing most significantly to NTE emerges not into the special points but between them. In this phonon mode, the O connecting two PO4 tetrahedra rotates, and the Cu and O vibrate perpendicular to the bottom of the CuO5 pyramidal unit, which folds the ac lattice plane. This vibration behavior can explain the experimentally reported anisotropic NTE behavior of α-Cu2P2O7. Our results demonstrate that the most negative mode-Grüneisen parameter contributing to NTE behavior is not always located on high-symmetry special points, indicating the importance of lattice vibration analyses for the entire first-Brillouin zone.

Storage and Diffusion of Carbon Dioxide in the Metal Organic Framework MOF-5─A Semi-empirical Molecular Dynamics Study

Metal-organic frameworks (MOFs) have attracted increasing attention due to their high porosity for exceptional gas storage applications. MOF-5 belongs to the family of isoreticular MOFs (IRMOFs) and consists of Zn4O6+ clusters linked by 1,4-benzenedicarboxylate. Due to the large number of atoms in the unit cell, molecular dynamics simulation based on density functional theory has proved to be too demanding, while force field models are often inadequate to model complex host-guest interactions. To overcome this limitation, an alternative semi-empirical approach using a set of approximations and extensive parametrization of interactions called density functional tight binding (DFTB) was applied in this work to study CO2 in the MOF-5 host. Calculations of pristine MOF-5 yield very good agreement with experimental data in terms of X-ray diffraction patterns as well as mechanical properties, such as the negative thermal expansion coefficient and the bulk modulus. In addition, different loadings of CO2 were introduced, and the associated self-diffusion coefficients and activation energies were investigated. The results show very good agreement with those of other experimental and theoretical investigations. This study provides detailed insights into the capability of semi-empirical DFTB-based molecular dynamics simulations of these challenging guest@host systems. Based on the comparison of the guest-guest pair distributions observed inside the MOF host and the corresponding gas-phase reference, a liquid-like structure of CO2 can be deduced upon storage in the host material.

Influence of A/B Element Substitution on Negative Thermal Expansion in AB(CN)6 (A = Al, Ga, In; B = Co, Fe, Mn, Cr, V, Ti): A Density Functional Theory Study

Negative thermal expansion as an abnormal physical behavior of materials has promising applications in a high sophisticated equipment field, but the materials are rare. Here, we use the first-principles calculations based on density functional theory combined with the recently developed average atomic volume (AAV = V/N, where V is unit cell volume and N is the number of atoms in the unit) rule to predict the large isotropic negative thermal expansion materials of Prussian blue analogues AB(CN)6 (A = Al, Ga, In; B = Co, Fe, Mn, Cr, V, Ti) in a wide temperature range. Our results clearly show that the coefficient of negative thermal expansion has a near-linear relationship with the average atomic volume of the systems and is also influenced by the element substitution at the A or B site. Lattice dynamic simulations indicate that the main contribution to the negative thermal expansion comes from the low-frequency transverse vibration of the (B)-C≡N-(A) groups, especially the transverse vibration of the N atoms. Thus, the element substitution at the A site (binding to N) can tune the negative thermal expansion behavior of the systems more effectively than that at the B site (binding to C), indicating the different roles of bonds on the negative thermal expansion. Our present work not only expands the kinds of isotropic materials but also gives some insights into the relationship between the average atomic volume and negative thermal expansion.

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.

Giant uniaxial negative thermal expansion in FeZr2 alloy over a wide temperature range

Negative thermal expansion (NTE) alloys possess great practical merit as thermal offsets for positive thermal expansion due to its metallic properties. However, achieving a large NTE with a wide temperature range remains a great challenge. Herein, a metallic framework-like material FeZr₂ is found to exhibit a giant uniaxial (1D) NTE with a wide temperature range (93-1078 K, [Formula: see text]). Such uniaxial NTE is the strongest in all metal-based NTE materials. The direct experimental evidence and DFT calculations reveal that the origin of giant NTE is the couple with phonons, flexible framework-like structure, and soft bonds. Interestingly, the present metallic FeZr₂ excites giant 1D NTE mainly driven by high-frequency optical branches. It is unlike the NTE in traditional framework materials, which are generally dominated by low energy acoustic branches. In the present study, a giant uniaxial NTE alloy is reported, and the complex mechanism has been revealed. It is of great significance for understanding the nature of thermal expansion and guiding the regulation of thermal expansion.

Phase behaviour of coarse-grained fluids

Soft condensed matter structures often challenge us with complex many-body phenomena governed by collective modes spanning wide spatial and temporal domains. In order to successfully tackle such problems, mesoscopic coarse-grained (CG) statistical models are being developed, providing a dramatic reduction in computational complexity. CG models provide an intermediate step in the complex statistical framework of linking the thermodynamics of condensed phases with the properties of their constituent atoms and molecules. These allow us to offload part of the problem to the CG model itself and reformulate the remainder in terms of reduced CG phase space. However, such exchange of pawns to chess pieces, or 'Hamiltonian renormalization', is a radical step and the thermodynamics of the primary atomic and CG models could be quite distinct. Here, we present a comprehensive study of the phase diagram including binodal and interfacial properties of a dissipative particle dynamics (DPD) model, extended to include finite-range attraction to support the liquid-gas equilibrium. Despite the similarities with the atomic model potentials, its phase envelope is markedly different featuring several anomalies such as an unusually broad liquid range, change in concavity of the liquid coexistence branch with variation of the model parameters, volume contraction on fusion, temperature of maximum density in the liquid phase and negative thermal expansion in the solid phase. These results provide new insight into the connection between simple potential models and complex emergent condensed matter phenomena.

Effect of Octahedral Connectivity on the Negative Thermal Expansion of SrZrS3

Sulfide perovskites (ABX₃) are under increasing investigation for use in photovoltaic, optoelectronic, dielectric, and thermoelectric devices due to their favorable band gaps, dynamical properties, environmental stability, and structural diversity. A key material parameter to optimize in such devices is the constituent materials' coefficient of thermal expansion (CTE) in order to minimize thermomechanical stress during fabrication and operation. This can be done by avoiding materials that have large CTE mismatch or by compensating positive thermal expansion by including materials with negative thermal expansion (NTE). Here, we evaluate the CTE of (edge-connected) α- and (corner-connected) β-SrZrS₃ with density functional theory and the self-consistent quasiharmonic approximation. We find that both materials exhibit positive thermal expansion at 0 GPa and host pressure-induced negative thermal expansion. The β phase has a smaller CTE (37 × 10^-6 K^-1) at room temperature and ambient pressure and also has a larger NTE response under pressure due to its more flexible corner-connected framework structure. We use our findings to suggest that corner-shared motifs should be prioritized over edge- or face-shared octahedral networks to maximize NTE arising from vibrational (phononic) mechanisms.

Phonon mechanism for the negative thermal expansion of zirconium tungstate, ZrW2O8

Negative thermal expansion (NTE) in ZrW₂O₈ was investigated using a flexibility analysis of ab initio phonons. It was shown that no previously proposed mechanism adequately describes the atomic-scale origin of NTE in this material. Instead it was found that the NTE in ZrW₂O₈ is driven, not by a single mechanism, but by wide bands of phonons that resemble vibrations of near-rigid WO₄ units and Zr-O bonds at low frequency, with deformation of O-W-O and O-Zr-O bond angles steadily increasing with increasing NTE-phonon frequency. It is asserted that this phenomenon is likely to provide a more accurate explanation for NTE in many complex systems not yet studied.

Concepts and use cases for picosecond ultrasonics with x-rays

This review discusses picosecond ultrasonics experiments using ultrashort hard x-ray probe pulses to extract the transient strain response of laser-excited nanoscopic structures from Bragg-peak shifts. This method provides direct, layer-specific, and quantitative information on the picosecond strain response for structures down to few-nm thickness. We model the transient strain using the elastic wave equation and express the driving stress using Grüneisen parameters stating that the laser-induced stress is proportional to energy density changes in the microscopic subsystems of the solid, i.e., electrons, phonons and spins. The laser-driven strain response can thus serve as an ultrafast proxy for local energy-density and temperature changes, but we emphasize the importance of the nanoscale morphology for an accurate interpretation due to the Poisson effect. The presented experimental use cases encompass ultrathin and opaque metal-heterostructures, continuous and granular nanolayers as well as negative thermal expansion materials, that each pose a challenge to established all-optical techniques.

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.

Anharmonic Interaction in Negative Thermal Expansion Material CaTiF6

Although the quasi-harmonic approximation (QHA) method applies to many materials, it is necessary to study the anharmonic interaction for extremely anharmonic materials. In this work, the unusual negative thermal expansion (NTE) property of CaTiF₆ is studied by combing QHA and anharmonic interaction. The improved self-consistent phonon approximation (ISCPA), which treats anharmonic effects in solids nonperturbatively, is employed. The agreement of NTE behavior between the calculation and the experiment can be further promoted from qualitative consistency by QHA to quantitative consistency by the ISCPA. From mode Grüneisen parameters, it is found that the low-frequency phonons, especially acoustic phonons, contribute greatly to the NTE behavior of CaTiF₆. The rigid unit modes (RUMs) of low-frequency optical phonons can be identified. The phonon lifetime of CaTiF₆ is calculated from three-phonon interactions; thereby, the NTE mechanism can be further explored by phonon lifetimes of phonons with different frequencies on heating. The anomalous lattice thermal conductivity (LTC) is predicted using the Boltzmann transport equation within the relaxation time approximation. The glasslike LTC can occur in crystal CaTiF₆.

Insight into the Relationship between Negative Thermal Expansion and Structure Flexibility: The Case of Zn(CN)2-Type Compounds

High structure flexibility can lead to large negative thermal expansion (NTE), but the reason is not clear. In this work, first-principles calculations have been carried out to investigate the relationship between NTE and structure flexibility in Zn(CN)₂-type compounds. Smaller bulk modulus corresponds to larger compressibility, thus making the crystal structure more flexible and more suitable for NTE. It indicated that the ionic nature of the bond and the bond length jointly affect the structural flexibility and then act on the transverse vibration of C and N atoms. The results of lattice dynamic suggested that higher structural flexibility promotes a greater number of low-frequency optical modes with negative Grüneisen parameters, resulting in a larger NTE. This work also gives us new insight into the design of NTE materials.

Dynamic magnetic crossover at the origin of the hidden-order in van der Waals antiferromagnet CrSBr

The van-der-Waals material CrSBr stands out as a promising two-dimensional magnet. Here, we report on its detailed magnetic and structural characteristics. We evidence that it undergoes a transition to an A-type antiferromagnetic state below T_N ≈ 140 K with a pronounced two-dimensional character, preceded by ferromagnetic correlations within the monolayers. Furthermore, we unravel the low-temperature hidden-order within the long-range magnetically-ordered state. We find that it is associated to a slowing down of the magnetic fluctuations, accompanied by a continuous reorientation of the internal field. These take place upon cooling below T_s ≈ 100 K, until a spin freezing process occurs at T* ≈ 40 K. We argue this complex behavior to reflect a crossover driven by the in-plane uniaxial anisotropy, which is ultimately caused by its mixed-anion character. Our findings reinforce CrSBr as an important candidate for devices in the emergent field of two-dimensional magnetic materials.

Tunable uniaxial, area, and volume negative thermal expansion in quartz-like and diamond-like metal-organic frameworks

This paper proposes that it will be an effective way to discover and explore organic negative thermal expansion (NTE) materials based on the specific topologies in inorganic NTE materials. Various NTE behaviors from the uniaxial, area, and volume-NTE can be achieved by adjusting the topology, for instance, quartz-like and diamond-like. Zn(ISN)₂ and InH(BDC) metal-organic frameworks (MOFs) with quartz-like topology have been studied by first principles calculations. The calculated area-NTE of Zn(ISN)₂ and uniaxial-NTE of InH(BDC) within quasi-harmonic approximation (QHA) agree well with the experimental data. Through the calculation of Grüneisen parameters, it is shown that low-frequency optical phonons appear dominant resulting in their NTE, but the coupling to high-frequency phonons is of greater ultimate importance. The lattice vibrational modes of great contribution to area-NTE of Zn(ISN)₂ and uniaxial-NTE of InH(BDC) are analyzed in detail. Also, four MOFs with diamond-like topology are predicted to exhibit volume-NTE behavior. Moreover, it is found that there is a bulk modulus anomaly in some studied MOFs with the quartz-like and diamond-like framework, where the temperature dependence of bulk modulus does not follow the inverse dependence on that of volume. These specific topologies provide key geometric frameworks for various NTE behaviors of MOFs, and meanwhile, the local structure and bond environment in MOFs can lead to abnormal interatomic force, i.e., bulk modulus anomaly. This abnormal elastic property also deserves more attention.

Suppression of phase-transition temperature in aluminium indium tungstate and aluminium indium molybdate

Aluminium indium tungstate (AlInW3O12) and aluminium indium molybdate (Al0.84In1.16Mo3O12) were synthesized by non-hydrolytic sol–gel chemistry, and their crystal structures, phase transition and thermal expansion behavior were studied using variable-temperature synchrotron powder diffraction. AlInW3O12 adopts an orthorhombic phase above 260 K and gradually transitions to a monoclinic polymorph below this temperature. Al0.84In1.16Mo3O12 also shows a gradual transition between the monoclinic and orthorhombic structures between 330 and 445 K. Both materials display much lower phase-transition temperatures than predicted on the basis of the parent compounds and Vegard's law. This suppression is attributed to the large size difference between Al3+ and In3+. Interestingly, both samples display positive thermal expansion along all unit-cell axes instead of the typically observed negative expansion of orthorhombic A 2 M 3O12 compositions.

Pressure enhanced negative thermal expansion in 2H CuScO2 from first-principles calculations

Finding materials with negative thermal expansion (NTE) property is challenging. Tuning NTE is of fundamental and technological importance. Pressure enhanced negative thermal expansion behavior in 2H CuScO₂ is found and expounded using density functional theory (DFT) and quasi-harmonious approximation (QHA). The frequencies of low energy modes and Grüneisen parameters decrease under pressure, but the bulk modulus increases with pressure. The transverse vibration of Cu atoms becomes stronger under pressure and the materials undergo thermal softening. These factors including thermal softening, pressure induced decrease of Grüneisen parameters and pressure induced strengthening of transverse vibration of Cu atoms all contribute to the enhanced negative thermal expansion property in 2H CuScO₂ in view of the thermodynamic relationship , Grüneisen's theory of thermal expansion and the mechanism of NTE, respectively.

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.

Direct determination of thermal expansion coefficients from the profile fitting of a diffractogram

This paper presents a set of files for working with TOPAS software in order to calculate the thermal expansion coefficients of a crystal phase as a function of the temperature from a set of powder diffractograms. All the calculations and profile fittings are performed in the same run, in cascade and without interruption. Free graphics software GNUPLOT reads the output files in order to display both the characteristic three-dimensional thermal expansion surface and any section of this surface. The results are also generated as text files. The files also calculate the thermal expansion coefficients in any [u, v, w] direction and at any temperature, and the angles between the principal axes and the crystallographic axes. The user can modify the input text files to their requirements. The calculations have been checked with calculated diffractograms at different temperatures for a triclinic, monoclinic and tetragonal phase. The calculated coefficients have been compared with previous works and show good agreement. The extent to which the peak/noise ratio of the diffractogram affects the calculated thermal expansion coefficients is also discussed.

Thermally boosted upconversion and downshifting luminescence in Sc2(MoO4)3:Yb/Er with two-dimensional negative thermal expansion

Rare earth (RE³⁺)-doped phosphors generally suffer from thermal quenching, in which their photoluminescence (PL) intensities decrease at high temperatures. Herein, we report a class of unique two-dimensional negative-thermal-expansion phosphor of Sc₂(MoO₄)₃:Yb/Er. By virtue of the reduced distances between sensitizers and emitters as well as confined energy migration with increasing the temperature, a 45-fold enhancement of green upconversion (UC) luminescence and a 450-fold enhancement of near-infrared downshifting (DS) luminescence of Er³⁺ are achieved upon raising the temperature from 298 to 773 K. The thermally boosted UC and DS luminescence mechanism is systematically investigated through in situ temperature-dependent Raman spectroscopy, synchrotron X-ray diffraction and PL dynamics. Moreover, the luminescence lifetime of ⁴I_13/2 of Er³⁺ in Sc₂(MoO₄)₃:Yb/Er displays a strong temperature dependence, enabling luminescence thermometry with the highest relative sensitivity of 12.3%/K at 298 K and low temperature uncertainty of 0.11 K at 623 K. These findings may gain a vital insight into the design of negative-thermal-expansion RE³⁺-doped phosphors for versatile applications.

Rare-earth doped phosphors with negative thermal expansion (NTE) may display thermally-enhanced emission, but their performance is generally limited. Here the authors report thermally-boosted green upconversion luminescence and near-infrared downshifting luminescence in Sc₂(MoO₄)₃:Yb/Er phosphors with two-dimensional NTE, and their application in temperature sensing.

Anisotropic thermal expansion and electronic transitions in the Co3BO5 ludwigite

The investigations of the crystal structure, magnetic and electronic properties of Co₃BO₅ at high temperatures were carried out using powder X-ray diffraction, magnetic susceptibility, electrical resistivity, and thermopower measurements. The orthorhombic symmetry (Sp.gr. Pbam) was observed at 300 K and no evidence of structural phase transitions was found up to 1000 K. The compound shows a strong anisotropy of the thermal expansion. A large negative thermal expansion along the a-axis is observed over a wide temperature range (T = 300-600 K) with α_a = -35 M K^-1 at T = 500 K with simultaneous expansion along the b- and c-axes with α_b = 70 M K^-1 and α_c = 110 M K^-1, respectively. The mechanisms of thermal expansion are explored by structural analysis. The activation energy of the conductivity decreases significantly above 700 K. Electronic transport was found to be a dominant conduction mechanism in the entire temperature range. The correlations between the thermal expansion, electrical resistivity, and effective magnetic moment were revealed and attributed to the evolution of the spin state of Co³⁺ ions towards the spin crossover and gradual charge-ordering transition.

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.

Biaxial negative thermal expansion in Zn[N(CN)2]2

A 2D-layered network Zn[N(CN)2]2, is reported in which the transverse vibrations of C atoms and the rotation of ZnN4 tetrahedra dominate its biaxial NTE behavior.

The ferroelastic phase transition in hydrogen cyanide studied by density functional theory

We report calculations of the crystal structures and lattice dynamics of the tetragonal and orthorhombic phases of the molecular crystal hydrogen cyanide, HCN, using density functional theory methods. By treating negative pressure as a proxy for raising temperature we show that the ferroelastic phase transition involves softening of a transverse acoustic mode, and confirm that the phase transition is discontinuous. Analysis of the complete phonon spectrum shows that the acoustic modes are responsible both for the very large thermal expansion seen in HCN and also for the thermodynamic driving force for the phase transition.

Size and crystal symmetry breaking effects on negative thermal expansion in ScF3 nanostructures

Nowadays, one of the most typical and important potential applications of negative thermal expansion (NTE) materials is to prepare zero thermal expansion or controllable coefficient thermal expansion materials by compounding them with positive thermal expansion materials. The research on NTE properties at the nanoscales is the basis and premise for the realization of high-quality composites. Here, using first-principles calculations, we take a typical open framework material ScF₃ as an example to study a new NTE mechanism at the nanoscale, which involves edge and size effects, as well as crystal symmetry breaking. By analyzing the vibrational modes in ultrathin ScF₃ films, three effects contributing to the NTE properties are identified, namely, the acoustic mode (ZA mode) induced by surface truncation, the enhanced rotations of ScF₆ octahedra in the surface layer and the suppressed rotations of ScF₆ octahedra in the inner layer due to crystal symmetry breaking. With increasing thickness, the effect of the ZA mode vibration gradually weakens, while the rotations of the ScF₆ octahedra in the surface and inner layers are enhanced. Ultimately, the approximately mutual compensation of these three effects makes the NTE coefficients of different thicknesses almost unchanged. Finally, we simply generalize our conclusions to zero dimensional nanoparticles. This work reveals a new NTE mechanism in low-dimensional open framework materials, which serves as a guide in designing NTE materials at the nanoscale.

Current Status of Research on the Modification of Thermal Properties of Epoxy Resin-Based Syntactic Foam Insulation Materials

As a lightweight and highly insulating composite material, epoxy resin syntactic foam is increasingly widely used for insulation filling in electrical equipment. To avoid core burning and cracking, which are prone to occur during the casting process, the epoxy resin-based syntactic foam insulation materials with high thermal conductivity and low coefficient of thermal expansion are required for composite insulation equipment. The review is divided into three sections concentrating on the two main aspects of modifying the thermal properties of syntactic foam. The mechanism and models, from the aspects of thermal conductivity and coefficient of thermal expansion, are presented in the first part. The second part aims to better understand the methods for modifying the thermal properties of syntactic foam by adding functional fillers, including the addition of thermally conductive particles, hollow glass microspheres, negative thermal expansion filler and fibers, etc. The third part concludes by describing the existing challenges in this research field and expanding the applicable areas of epoxy resin-based syntactic foam insulation materials, especially cross-arm composite insulation.

Thermal expansion properties of organic crystals: a CSD study

The thermal expansion properties of crystalline organic compounds are investigated by data mining of the Cambridge Structural Database (CSD). The mean volumetric thermal expansion coefficient is 168.8 × 10-6 K-1 and the mean uniaxial thermal expansion coefficient is 71.4 × 10-6 K-1, based on 745 and 1129 different observations, respectively. Normal and anomalous coefficients can be identified using these values and the associated standard deviations. The anisotropy of the thermal expansion is also evaluated and found to have a very broad distribution. 4719 different structures, comprising 4093 different molecular compounds and 626 additional polymorphs have been analyzed on their thermal expansion properties. Approximately 34% of these structures may have at least one orthogonal axis with negative thermal expansion, much more than generally believed. Moreover 127 structures have been identified which could have negative volumetric thermal expansion. Experimental validation using a robust protocol with data collected at more than 2 different temperatures is required to validate these cases.

Negative X-ray expansion in cadmium cyanide

Cadmium cyanide, Cd(CN)₂, is a flexible coordination polymer best studied for its strong and isotropic negative thermal expansion (NTE) effect. Here we show that this NTE is actually X-ray-exposure dependent: Cd(CN)₂ contracts not only on heating but also on irradiation by X-rays. This behaviour contrasts that observed in other beam-sensitive materials, for which X-ray exposure drives lattice expansion. We call this effect 'negative X-ray expansion' (NXE) and suggest its origin involves an interaction between X-rays and cyanide 'flips'; in particular, we rule out local heating as a possible mechanism. Irradiation also affects the nature of a low-temperature phase transition. Our analysis resolves discrepancies in NTE coefficients reported previously on the basis of X-ray diffraction measurements, and we establish the 'true' NTE behaviour of Cd(CN)₂ across the temperature range 150-750 K. The interplay between irradiation and mechanical response in Cd(CN)₂ highlights the potential for exploiting X-ray exposure in the design of functional materials.

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 (α_v = -2.02 × 10^-6 K^-1, 100-300 K) and positive (α_v = +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.

Diverse physical functionalities of rare-earth hexacyanidometallate frameworks and their molecular analogues

The combination of rare-earth metal complexes and hexacyanidometallates of transition metals is a fruitful pathway for achieving functional materials exhibiting a wide scope of mechanical, magnetic, optical, and electrochemical properties.

Linear negative thermal expansion in Pd(acac)2

We propose that chemical interactions in the coordination compound Pd(acac)2 can be mapped on a wine-rack network, explaining linear negative thermal expansion in a classic coordination compound based on concepts known from network materials.

Structural flexibility in crystalline coordination polymers: a journey along the underlying free energy landscape

In this perspective, we discuss structural flexibility in crystalline coordination polymers. We identify that the underlying free energy landscape unites scientific disciplines, and discuss key areas to advanced the field.

Magnetic structure and uniaxial negative thermal expansion in antiferromagnetic CrSb

Negative thermal expansion (NTE) has been found in a growing number of ferromagnetic and ferrimagnetic materials; however, it remains a challenge to discover antiferromagnetic (AFM) NTE materials. Here, we report the uniaxial NTE properties of AFM intermetallic CrSb systematically, and reveal its uniaxial NTE mechanism for the first time. The present AFM intermetallic CrSb shows uniaxial NTE at high temperature and over a broad temperature window (αa = -6.55 × 10-6 K-1, 360-600 K). The direct experimental evidence of neutron powder diffraction reveals that NTE is induced by the AFM ordering of the Cr atom. The present study demonstrates that due to the transition from an AFM ordered structure to a paramagnetic disordered configuration, the negative contribution to the thermal expansion from the magnetovolume effect overwhelms the positive contribution from anharmonic phonon vibration. This study is of interest to find antiferromagnetic NTE 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.

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.

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.

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.

Large and tunable negative thermal expansion induced by a synergistic effect in M2II[MIV(CN)8] Prussian blue analogues

Designing negative thermal expansion (NTE) materials with a larger NTE coefficient and a wider temperature window is a great challenge nowadays, leading to the limitation of existing NTE materials such that only about 150 kinds of NTE materials have been discovered since 1996. Here, using first-principles calculations combined with the quasi-harmonic approximation (QHA), we find that the synergistic effect of different vibrational modes can significantly enhance the NTE in open framework compounds. We systematically investigate the NTE properties of the M₂^IIM^IV(CN)₈ (M^II = Ni, Co, Fe, and Mn; M^IV = Mo and W) family, which is the first kind of Prussian blue analogues (PBAs) with a 2D and 3D topology structure, to explore the synergistic enhancement effect in NTE. We reveal that both the optical modes of the rotational motion of [W(CN)₈] and [Ni(NC)₄] rigid units and the low frequency acoustic modes of the transverse vibration contribute significantly to the NTE. Furthermore, the coefficients of NTE increase monotonously with increasing ionic radius upon substituting Ni in M₂^IIW(CN)₈ with Co, Fe, or Mn, respectively. Analyzing the vibrational modes of the substituted systems indicates that the dramatic changes in NTE originate from a highly synergistic effect, in which all the frequencies of these NTE modes have the same trend, i.e. the lower the frequencies, the larger the coefficient of NTE. This work clearly presents a synergistic mechanism of enhancing NTE in PBA materials, and sheds light on designing new materials with better properties.

Graphene Origami with Highly Tunable Coefficient of Thermal Expansion

The coefficient of thermal expansion, which measures the change in length, area, or volume of a material upon heating, is a fundamental parameter with great relevance for many applications. Although there are various routes to design materials with targeted coefficient of thermal expansion at the macroscale, no approaches exist to achieve a wide range of values in graphene-based structures. Here, we use molecular dynamics simulations to show that graphene origami structures obtained through pattern-based surface functionalization provide tunable coefficients of thermal expansion from large negative to large positive. We show that the mechanisms giving rise to this property are exclusive to graphene origami structures, emerging from a combination of surface functionalization, large out-of-plane thermal fluctuations, and the three-dimensional geometry of origami structures.