New Insights into the Negative Thermal Expansion: Direct Experimental Evidence for the “Guitar-String” Effect in Cubic ScF3

Sensitive Thermochromic Behavior of InSeI, a Highly Anisotropic and Tubular 1D van der Waals Crystal

Thermochromism, the change in color of a material with temperature, is the fundamental basis of optical thermometry. A longstanding challenge in realizing sensitive optical thermometers for widespread use is identifying materials with pronounced thermometric optical performance in the visible range. Herein, it is demonstrated that single crystals of indium selenium iodide (InSeI), a 1D van der Waals (vdW) solid consisting of weakly bound helical chains, exhibit considerable visible range thermochromism. A strong temperature-dependent optical band edge absorption shift ranging from 450 to 530 nm (2.8 to 2.3 eV) over a 380 K temperature range with an experimental (dEg/dT)max value extracted to be 1.26 × 10-3 eV K-1 is shown. This value lies appreciably above most dense conventional semiconductors in the visible range and is comparable to soft lattice solids. The authors further seek to understand the origin of this unusually sensitive thermochromic behavior and find that it arises from strong electron-phonon interactions and anharmonic phonons that significantly broaden band edges and lower the Eg with increasing temperature. The identification of structural signatures resulting in sensitive thermochromism in 1D vdW crystals opens avenues in discovering low-dimensional solids with strong temperature-dependent optical responses across broad spectral windows, dimensionalities, and size regimes.

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.

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.

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.

Negative Thermal Expansion in the Polymorphic Modification of Double Sulfate β-AEu(SO4)2 (A-Rb+, Cs+)

New polymorphic modifications of double sulfates β-AEu(SO₄)₂ (A-Rb⁺, Cs⁺) were obtained by the hydrothermal method, the structure of which differs significantly from the monoclinic modifications obtained earlier by solid-state methods. According to single-crystal diffraction data, it was found that the compounds crystallize in the orthorhombic system, space group Pnna, with parameters β-RbEu(SO₄)₂: a = 9.4667(4) Å, b = 13.0786(5) Å, c = 5.3760(2) Å, V = 665.61(5) ų; β-CsEu(SO4)2: a = 9.5278(5) Å, b = 13.8385(7) Å, c = 5.3783(3) Å, V = 709.13(7) ų. The asymmetric part of the unit cell contains one-half Rb⁺/Cs⁺ ion, one-half Eu³⁺ ion, both in special sites, and one SO₄^2- ion. Both compounds exhibit nonlinear negative thermal expansion. According to the X-ray structural analysis and theoretical calculations, the polarizing effect of the alkali metal ion has a decisive influence on the demonstration of this phenomenon. Experimental indirect band gaps of β-Rb and β-Cs are 4.05 and 4.11 eV, respectively, while the direct band gaps are 4.48 and 4.54 eV, respectively. The best agreement with theoretical calculations is obtained using the ABINIT package employing PAW pseudopotentials with hybrid PBE0 functional, while norm-conserving pseudopotentials used in the frame of CASTEP code and LCAO approach in the Crystal package gave worse agreement. The properties of alkali ions also significantly affect the luminescent properties of the compounds, which leads to a strong temperature dependence of the intensity of the ⁵D₀ → ⁷F₄ transition in β-CsEu(SO₄)₂ in contrast to much weaker dependence of this kind in β-RbEu(SO₄)₂.

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.

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.

Two-Dimensional Negative Thermal Expansion in a Facile and Low-Cost Oxalate-Based Metal-Organic Framework

Two-dimensional negative thermal expansion (NTE) is achieved in a tetragonal oxalate-based metal-organic framework (MOF), CdZrSr(C₂O₄)₄, within a temperature range from 123 to 398 K [space group I4̅m2, α_a = -2.4(7) M K^-1, α_c = 11.3(3) M K^-1, and α_V = 6.4(1) M K^-1]. By combining variable-temperature X-ray diffraction, a high-resolution synchrotron X-ray pair distribution function, and thermogravimetry-differential scanning calorimetry, we shows that NTE within the ab plane derives from the oriented rotation of an oxalate ligand in zigzag chains (-CdO₈-ox-ZrO₈-ox-)_∞. That is simplified to the Zr atom rotating with an unchanged Zr···Cd distance as the radius, which also gives rise to the deformation of a hingelike connection along the c axis and results in its positive thermal expansion. By virtue of the facile and low-cost oxalate ligand, the present NTE MOF may show application prospects in the future.

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.

Molecular tiltation and supramolecular interactions induced uniaxial NTE and biaxial PTE in bis-imidazole-based co-crystals

Uniaxial NTE and biaxial PTE has been observed in bis-imidazole-based co-crystals induced by molecular tiltation and supramolecular interactions.

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.

Local Structure Engineering in Lanthanide-Doped Nanocrystals for Tunable Upconversion Emissions

Upconversion emissions from lanthanide-doped nanocrystals have sparked extensive research interests in nanophotonics, biomedicine, photovoltaics, photocatalysis, etc. Rational modulation of upconversion emissions is highly desirable to meet the requirements of specific applications. Among the diverse developed methods, local structure engineering is fundamentally feasible, through which the upconversion emission intensity, selectivity, wavelength shift, and lifetime can be tuned effectively. The underlying mechanism of the local-structure-dependent upconversion emissions lies in the degree of parity hybridization and energy level splitting of lanthanide ions as well as the interionic energy transfer efficiency. Over the past few years, there has been significant progress in local-structure-engineered upconversion emissions. In this Perspective, we first introduce the principles of upconversion emissions and typical characterization methods for local structure. Subsequently, we summarize recent achievements in tuning of upconversion emissions through local structure engineering, including host composition adjustment, external field regulation, and interfacial strain management. Finally, we propose a few perspectives that should tackle the current bottlenecks. This Perspective is expected to deepen the understanding of local-structure-dependent upconversion emissions and arouse adequate attention to the engineering of local structure for desired properties of inorganic nanocrystals.

Anomalous Thermal Expansion in Ta2WO8 Oxide Semiconductor over a Wide Temperature Range

Expansion of material is one of the major impediments in the high precision instrument and engineering field. Low/zero thermal expansion compounds have drawn great attention because of their important scientific significance and enormous application value. However, the realization of low thermal expansion over a wide temperature range is still scarce. In this study, a low thermal expansion over a wide temperature range has been observed in the Ta₂WO₈ oxide semiconductor. It is a balance effect of the negative thermal expansion of the a axis and the positive thermal expansion of the b axis and the c axis to achieve low thermal expansion behavior. The results of the means of variable temperature X-ray diffraction and variable pressure Raman spectroscopy analysis indicated that the transverse vibration of bridging oxygen atoms is the driving force, which is corresponding to the low-frequency lattice modes with a negative Grüneisen parameter. The present study provides one wide band gap semiconductor Ta₂WO₈ with anomalous thermal expansion behavior.

Intrinsic volumetric negative thermal expansion in the "rigid" calcium squarate

The calcium squarate with a rigid framework is found to exhibit volumetric negative thermal expansion (NTE) with the coefficient -9.51(5) × 10^-6 K^-1 and uniaxial zero thermal expansion (ZTE, -0.14(4) × 10^-6 K^-1) over a wide temperature. Detailed comparison of the long-range and local structure sheds light on the fact that the anomalous thermal expansion originates from the transverse vibration of the bridging squarate ligand, although it has been tightly bonded by five calcium ions. We believe that this study can provide a deep insight into the origin of NTE and the structural flexibility of metal organic frameworks (MOFs).

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.

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.

Negative and zero thermal expansion in α-(Cu2-xZnx)V2O7 solid solutions

Negative or zero thermal expansion (NTE or ZTE) of materials is intriguing for controllable thermal expansion. We report a series of orthorhombic α-Cu2-xZnxV2O7 (x = 0, 0.1, 0.2), in which the volumetric coefficients of thermal expansion are successfully tuned from -10.19 × 10-6 K-1 to -1.58 × 10-6 K-1 in the temperature range of 100-475 K by increasing the content of Zn2+. It has been revealed that the transverse vibrations of oxygen bonded with vanadium are dominant in the contraction of the bc plane, leading to the overall volume NTE in α-Cu2V2O7. The introduction of Zn2+ densifies the crystal structure, which is presumed to suppress the space of transverse vibrations and results in the ZTE in α-Cu1.8Zn0.2V2O7. This work presents an effective method to realize ZTE in anisotropic framework systems.

Colossal Pressure-Induced Softening in Scandium Fluoride

The counterintuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behavior that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealized model and neutron diffraction at variable temperature and pressure, we show the existence of extraordinary and unprecedented pressure-induced softening in the negative thermal expansion material scandium fluoride ScF_{3}. The pressure derivative of the bulk modulus B, B^{'}=(∂B/∂P)_{P=0}, reaches values as low as -220±30 at 50 K, and is constant at -50 between 150 and 250 K.

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.

Discovering Large Isotropic Negative Thermal Expansion in Framework Compound AgB(CN)4 via the Concept of Average Atomic Volume

Exploring isotropic negative thermal expansion (NTE) compounds is interesting, but remains challenging. Here, a new concept of "average atomic volume" is proposed to find new NTE open-framework materials. According to this guidance, two NTE compounds, AgB(CN)₄ and CuB(CN)₄, have been discovered, of which AgB(CN)₄ exhibits a large NTE over a wide temperature range (α_v = -40 × 10^-6 K^-1, 100-600 K). The analysis by extended X-ray absorption fine structure spectroscopy and first-principles calculation indicate that (i) the NTE driving force comes from the transverse vibrations of bridge chain atoms of C and N, corresponding to the low-frequency phonon modes; and (ii) the same transverse vibration direction of C and N atoms is a key factor for the occurrence of strong NTE in AgB(CN)₄. The present concept of "average atomic volume" can be a simple parameter to explore new NTE compounds especially in those open-framework materials.

Infrared lattice dynamics in negative thermal expansion material in single-crystal ScF3

Simple cubic 'open' perovskite ScF₃ stands out among trifluoride materials in its large, isotropic negative thermal expansion (NTE), but also its proximity of its zero-temperature state to a structural phase transition. Here we report a temperature- and frequency-dependent lattice dynamical study of Brillouin zone center lattice excitations of single crystals of ScF₃ using infrared reflectivity measurements. In addition to quantifying the mode strengths and energies in single crystals of this interesting material, we also find strong evidence for multiphonon absorption processes which excite the zone-edge incipient soft modes associated with NTE and the structural quantum phase transition. In this way, we identify an optically-allowed pathway to excite soft modes provides a means to athermally populate modes associated with NTE in ScF₃.

Evidence of the enhanced negative thermal expansion in (1 − x)PbTiO3-xBi(Zn2/3Ta1/3)O3

Enhanced polarization displacement in (1 − x)PbTiO₃-xBi(Zn_2/3Ta_1/3)O₃ solutions has been reported.

Perovskite-related ReO3-type structures

Materials with the perovskite ABX3 structure play a major role across materials chemistry and physics as a consequence of their ubiquity and wide range of useful properties. ReO3-type structures can be described as ABX3 perovskites in which the A-cation site is unoccupied, giving rise to the general composition BX3, where B is typically a cation and X is a bridging anion. The chemical diversity of such structures is extensive, ranging from simple oxides and fluorides, such as WO3 and AlF3, to complex structures in which the bridging anion is polyatomic, such as in the Prussian blue-related cyanides Fe(CN)3 and CoPt(CN)6. The same ReO3-type structure is found in metal-organic frameworks, for example, ln (im)3(im = imidazolate) and the well-known MOF-5 structure, where the B-site cation is polyatomic. The extended 3D connectivity and openness of this structure type leads to compounds with interesting and often unusual properties. Notable among these properties are negative thermal expansion (for example, ScF3), photocatalysis (for example, CoSn(OH)6), thermoelectricity (for example, CoAs3) and superconductivity in a phase that is controversially described as SH3 with a doubly interpenetrating ReO3 structure. We present an account of this exciting family of materials and discuss future opportunities in the area.

Entropic elasticity and negative thermal expansion in a simple cubic crystal

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF₃, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter.

Negative Thermal Expansion in Nanosolids

Nanosolids usually exhibit a variety of peculiar physical features due to the size effect. The unique surface electronic states and coordination structures of nanosolids make them particularly important as promising functional materials. After several decades of research effort on the preparation processes and formation mechanisms of nanomaterials, the attention of nanoscience has been shifted to their functionalization and utilization. In the development of nanodevices, the thermal expansion matching between nanosized components is becoming increasingly important for the selection of units and design of nanodevices. In nanosolids, particularities of bonding features and coordination environments lead to size-dependent thermal expansion behavior that is significantly different from the behavior of their bulk counterparts. Thus, size tuning becomes one of the most efficient techniques in tailoring lattice thermal expansion. Unlike the traditional tailoring methods like chemical doping, the modification of chemical bonds and lattice vibration modes mainly contributing to the abnormal thermal expansion of nanosolids can be realized by adjustment of local coordination on the surface and surface/interface lattice strain. With the introduction of the nanosizing effect, the functional properties of nanosolids can be thoroughly remolded, which provides a huge space for functional applications of negative thermal expansion (NTE) nanosolids. However, understanding the origin of novel thermal expansion in nanosolids remains a challenging issue because of the lack of knowledge of precise atomic arrangements at both long-range and local structure levels. In this Account, by virtue of various advanced characterization techniques, we provide a comprehensive understanding at the atomic level of the abnormal thermal expansion behaviors in nanosized PbTiO₃-based compounds, oxides, fluorides, and bimetallic alloys. Our results demonstrate that nanoscale structural features can be used to alter the spontaneous polarization, surficial/interfacial coordination, local lattice symmetry, and elemental distribution, resulting in the crossover of thermal expansion from the bulk and the generation of zero thermal expansion (ZTE). Furthermore, structural peculiarities in nanosolids, e.g., the lack of long-range coherence, abnormal surficial/interfacial bonding, lattice imperfection, and distribution of local phases, open the door for local-scale manipulations of the physical properties of electronic structure and lattice vibration during adjustment of thermal expansion. For the development of nanodevices with high thermostability, atomic-level information on the nanostructure thermal evolution provides a guideline for intelligent designs of the functional components and matrix. Understanding of the structural transformation in nanosolids will help future exploration of functional nanomaterials based on short-range atomistic design and optimization.

Negative Thermal Expansion of Ni-Doped MnCoGe at Room-Temperature Magnetic Tuning

Compounds that exhibit the unique behavior of negative thermal expansion (NTE)-the physical property of contraction of the lattice parameters on warming-can be applied widely in modern technologies. Consequently, the search for and design of an NTE material with operational and controllable qualities at room temperature are important topics in both physics and materials science. In this work, we demonstrate a new route to achieve magnetic manipulation of a giant NTE in (Mn_0.95Ni_0.05)CoGe via strong magnetostructural (MS) coupling around room temperature (∼275 to ∼345 K). The MS coupling is realized through the weak bonding between the nonmagnetic CoGe-network and the magnetic Mn-sublattice. Application of a magnetic field changes the NTE in (Mn_0.95Ni_0.05)CoGe significantly: in particular, a change of Δ L/ L along the a axis of absolute value 15290(60) × 10^-6-equivalent to a -31% reduction in NTE-is obtained at 295 K in response to a magnetic field of 8 T.

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.

Mechanistic Insights into the Superexchange-Interaction-Driven Negative Thermal Expansion in CuO

The negative thermal expansion (NTE) in CuO is explained via electron-transfer-driven superexchange interaction. The elusive connection between the spin-lattice coupling and NTE of CuO is investigated by neutron scattering and principal strain axes analysis. The density functional theory calculations show as the temperature decreases, the continuously increasing electron transfer accounts for enhancing the superexchange interaction along [101̅], the principal NTE direction. It is further rationalized that only when the interaction along [101̅] is preferably enhanced to a certain level compared to the other competing antiferromagnetic exchange pathways can the corresponding NTE occur. Outcomes from this work have implications for controlling the thermal expansion through superexchange interaction, via, for example, optical manipulation, electron or hole doping, etc.

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.

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.

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.

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.

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.

Low-Frequency Phonon Driven Negative Thermal Expansion in Cubic GaFe(CN)6 Prussian Blue Analogues

The understanding of the negative thermal expansion (NTE) mechanism is vital not only for the development of new NTE compounds but also for effectively controlling thermal expansion. Here, we report an interesting isotropic NTE property in cubic GaFe(CN)₆ Prussian blue analogues (α _l = -3.95 × 10^-6 K^-1, 100-475 K), which is a new example to understand the complex NTE mechanism. A combined study of synchrotron X-ray diffraction, X-ray total scattering, X-ray absorption fine structure, neutron powder diffraction, and density functional theory calculations shows that the NTE of GaFe(CN)₆ originates from the low-frequency phonons (< ∼100 cm^-1), which are directly related to the transverse vibrations of the atomic -Ga-N≡C-Fe- chains. Both the Ga-N and Fe-C chemical bonds are much softer to bend than to stretch. The direct evidence that transverse vibrational contribution to the NTE of GaFe(CN)₆ is dominated by N, instead of C atoms, is illustrated. It is interesting to find that the polyhedra of GaFe(CN)₆ are not rigid, which is a starting assumption in some models describing the NTE properties of other systems. The NTE mechanism can be vividly described by the "guitar-string" effect, which would be the common feature for the NTE property of many open-framework functional materials, such as Prussian blue analogues, oxides, cyanides, metal-organic frameworks, and zeolites.

Structural, vibrational and thermal expansion properties of Sc2W4O15

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

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.

Transverse vibration driven large uniaxial negative and zero thermal expansion in boron bridged REPt3B framework materials

In this work anomalous uniaxial thermal expansion behaviour at low temperatures along the c-direction of the tetragonal phase of different members of the antiperovskite REPt3B (RE = Sm, Gd-Tm) compounds is reported. Negative or zero thermal expansion (NTE/ZTE) behaviour in these compounds arises due to the transverse vibration of boron atoms in the linear Pt-B-Pt linkage. The coefficient of thermal expansion along the c-axis tends to become more negative in annealed compounds in comparison to those estimated for as-cast samples. While the as-cast TmPt3B and HoPt3B exhibit essentially ZTE behaviour, the NTE coefficient of annealed GdPt3B (∼-28 ppm K-1) is found to be even larger than that of the well known framework material ZrW2O8 (∼-9 ppm K-1) reported in the literature.

Group 3 metal trihalide complexes with neutral N-donor ligands - exploring their affinity towards fluoride

Fluorination of [ScCl3(Me3-tacn)] (Me3-tacn = 1,4,7-trimethyl-1,4,7-triazacyclononane) and [ScCl3(BnMe2-tacn)] (BnMe2-tacn = 1,4-dimethyl-7-benzyl-1,4,7-triazacyclononane) by Cl/F exchange with 3 mol. equiv. of anhydrous [NMe4]F in CH3CN solution yields the corresponding [ScF3(R3-tacn)] (R3 = Me3 or BnMe2). These are the first examples of scandium fluoride complexes containing neutral co-ligands. The fluorination occurs stepwise, and using a deficit of [NMe4]F produced [ScF2Cl(Me3-tacn)]. Attempts to fluorinate [YCl3(Me3-tacn)], [YI3(Me3-tacn)], [LaCl3(Me3-tacn)(OH2)] or [MCl3(terpy)] (M = Sc, Y or La; terpy = 2,2':6'2''-terpyridyl) using a similar method were unsuccessful, due to the Cl/F exchange being accompanied by loss of the neutral ligand from the metal centre. Fluorination of [ScCl3(Me3-tacn)] or [ScCl3(terpy)] with Me3SnF was also successful. The products were identified as the very unusual heterobimetallic [Sc(Me3-tacn)F2(μ-F)SnMe3Cl] and [Sc(terpy)F(μ-F)2(SnMe3Cl)2], in which the Me3SnCl formed in the reaction behaves as a weak Lewis acid towards the scandium fluoride complex, linked by Sc-F-Sn bridges. [Sc(terpy)F(μ-F)2(SnMe3Cl)2] decomposes irreversibly in solution but, whilst multinuclear NMR data show that [Sc(Me3-tacn)F2(μ-F)SnMe3Cl] is dissociated into the [ScF3(Me3-tacn)] and Me3SnCl in CH3CN solution, the bimetallic complex reforms upon evaporation of the solvent. The new scandium fluoride complexes and the chloride precursors have been characterised by microanalysis, IR and multinuclear NMR (1H, 19F, 45Sc) spectroscopy as appropriate. X-ray crystal structures provide unambiguous evidence for the identities of [Sc(Me3-tacn)F2(μ-F)SnMe3Cl], [ScF2Cl(Me3-tacn)], [YI3(Me3-tacn)], [{YI2(Me3-tacn)}2(μ-O)], [ScCl3(terpy)], [YCl3(terpy)(OH2)], and [{La(terpy)(OH2)Cl2}2(μ-Cl)2]. Once formed, the [ScF3(R3-tacn)] complexes are stable in water and unaffected by a ten-fold excess of Cl- or MeCO2-, although they are immediately decomposed by excess F-. The potential use of [ScF3(R3-tacn)] type complexes as platforms for 18F PET (positron emission tomography) radiopharmaceuticals is briefly discussed. Attempts to use the Group 3 fluoride "hydrates", MF3·xH2O, as precursors were unsuccessful; no reaction with R3-tacn or terpy occurred either on reflux in CH3CN or under hydrothermal conditions (H2O, 180° C, 15 h). PXRD data showed that these "hydrates" actually contain the anhydrous metal trifluorides with small amounts of surface or interstitial water.

Negative thermal expansion in molecular materials

Some mechanisms resulting in negative thermal expansion in molecular materials are summarized.

Strong negative thermal expansion in the hexagonal polymorph of ScF3

A new hexagonal polymorph of scandium fluoride (ScF₃) displays strong negative thermal expansion in a wide temperature range at normal pressure.

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.

Large Positive Thermal Expansion and Small Band Gap in Double-ReO3-Type Compound NaSbF6

Double-ReO₃-type structure compound NaSbF₆ undergoes a low-temperature rhombohedral to high-temperature cubic phase between 303 and 323 K, as revealed by temperature-dependent X-ray diffractions. Although many double-ReO₃-type fluorides exhibit either low thermal expansion or negative thermal expansion (NTE), NaSbF₆ exhibits positive thermal expansion (PTE) with a large volumetric coefficient of thermal expansion, α_v = 62 ppm/K, in its cubic phase. Raman spectroscopy reveals that the low-frequency transverse vibration of fluorine atoms is stiffened in NaSbF₆, compared with the typical NTE compound CaZrF₆ with the same structure. The related weak contraction associated with the polyhedral rocking would be overcome by the notable elongation of the Na-F bond length on heating, thus leading to the large volumetric PTE. Unlike ScF₃ and CaZrF₆ which are insulators with a wide band gap, a relative small band gap of 3.76 eV was observed in NaSbF₆. The small band gap can be attributed to the hybridization between the Sb 5s and F 2p orbitals.

Tunable thermal expansion in framework materials through redox intercalation

Thermal expansion properties of solids are of fundamental interest and control of thermal expansion is important for practical applications but can be difficult to achieve. Many framework-type materials show negative thermal expansion when internal cages are empty but positive thermal expansion when additional atoms or molecules fill internal voids present. Here we show that redox intercalation offers an effective method to control thermal expansion from positive to zero to negative by insertion of Li ions into the simple negative thermal expansion framework material ScF₃, doped with 10% Fe to enable reduction. The small concentration of intercalated Li ions has a strong influence through steric hindrance of transverse fluoride ion vibrations, which directly controls the thermal expansion. Redox intercalation of guest ions is thus likely to be a general and effective method for controlling thermal expansion in the many known framework materials with phonon-driven negative thermal expansion.

The positive thermal expansion exhibited by most materials at increased temperatures is a severe issue for many high precision applications. Here, Xing and co-workers show that redox intercalation of Li ions into a ScF₃ framework offers effective control of the thermal expansion for this simple material.

Spring-like motion caused large anisotropic thermal expansion in nonporous M(eim)2(M = Zn, Cd)

Spring-like thermal motion caused large anisotropic thermal expansion in nonporous coordination polymers.

Local structure and controllable thermal expansion in the solid solution (Mn1−xNix)ZrF6

Controllable thermal expansion in the cubic solid solutions of (Mn_1−xNi_x)ZrF₆through atomic linkage flexibility.