Systematic and Controllable Negative, Zero, and Positive Thermal Expansion in Cubic Zr1–xSnxMo2O8

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.

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.

Antiferroelectricity-Induced Negative Thermal Expansion in Double Perovskite Pb2 CoMoO6

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

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.

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.

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.

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.

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.

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

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

Zero Thermal Expansion in Ta2Mo2O11 by Compensation Effects

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

Intrinsic Isotropic Near-Zero Thermal Expansion in Zn4B6O12X (X = O, S, Se)

Zero thermal expansion (ZTE) materials, keeping size constant as temperature varies, are valuable for resisting the deterioration of the performance from environmental temperature fluctuation, but they are rarely discovered due to the counterintuitive temperature-size effect. Herein, we demonstrate that a family of borates with sodalite cage structure, Zn₄B₆O₁₂X (X = O, S, Se), exhibits intrinsic isotropic near-ZTE behaviors from 5 to 300 K. The very low thermal expansion is mainly owing to the coupling rotation of [BO₄] rigid groups constrained by the bonds between Zn and cage-edged O atoms, while the central atoms in the cage have a negligible contribution. Our study has significant implications on the understanding of the ZTE mechanism and exploration of new ZTE materials.

Room Temperature Zero Thermal Expansion in a Cubic Cobaltite

Zero thermal expansion (ZTE) materials are highly desired in modern industries where high-precision processing is necessary. However, ZTE materials in pure form are extremely rare. The most widely used are Invar alloys, where the ZTE is intimately associated with spontaneous magnetic ordering, known as the magnetovolume effect (MVE). Despite tremendous studies, there is still no consensus on the microscopic origin of MVE in Invar alloys. Here, we report the discovery of room-temperature isotropic ZTE in a pure-form cobaltite perovskite, A-site disordered La_0.5Ba_0.5CoO_3-x. The temperature window of the anomalous thermal expansion shows large tunability by simply altering the oxygen content, making this material a promising candidate for practical applications. Furthermore, we unveil with compelling experimental evidence that the ZTE originates from an isostructural transition between antiferromagnetic large-volume phase and ferromagnetic small-volume phase, which might shed light on the MVE in Invar alloys.

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.

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

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

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

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

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.

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

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

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

Anisotropic Near-Zero Thermal Expansion in REAg xGa4- x ( RE = La-Nd, Sm, Eu, and Yb) Induced by Structural Reorganization

In this work, we have discovered the anisotropic near-zero thermal expansion (NZTE) behavior in a family of compounds REAg _xGa_{4- x} ( RE = La-Nd, Sm, Eu, and Yb). The compounds adopt the CeAl₂Ga₂ structure type and were obtained as single crystals in high yield by metal flux growth technique using gallium as active flux. Temperature-dependent single crystal X-ray diffraction suggests that all the compounds exhibit near zero thermal expansion along c direction in the temperature range of 100-450 K. Temperature-dependent X-ray absorption near-edge spectroscopic study confirmed ZTE behavior is due to the geometrical features associated within the crystal structure. The anisotropic NZTE behavior was further established by anisotropic magnetic measurements on selected single crystals. The atomic displacement parameters, apparent bond lengths, bond angles, and structural distortion with respect to the temperature reveal that geometric features associated with the structural distortion cause the anisotropic NZTE along c-direction. The preliminary magnetic studies suggest all the compounds are paramagnetic at room temperature except LaAgGa₃. Electrical resistivity study reveals that compounds from this series are metallic in nature.

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

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

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.

Twin Crystal Induced near Zero Thermal Expansion in SnO2 Nanowires

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

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.

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

The effects of Zn²⁺ incorporation on the phase formation, thermal expansion, phase transition, and vibrational properties of HfMg_1-x Zn _x Mo₃O₁₂ are investigated by XRD, dilatometry, and Raman spectroscopy. The results show that (i) single phase formation is only possible for x ≤ 0.5, otherwise, additional phases of HfMo₂O₈ and ZnMoO₄ appear; (ii) The phase transition temperature from monoclinic to orthorhombic structure of the single phase HfMg_1-x Zn _x Mo₃O₁₂ can be well-tailored, which increases with the content of Zn²⁺; (iii) The incorporation of Zn²⁺ leads to an pronounced reduction in the positive expansion of the b-axis and an enhanced negative thermal expansion (NTE) in the c-axes, leading to a near-zero thermal expansion (ZTE) property with lower anisotropy over a wide temperature range; (iv) Replacement of Mg²⁺ by Zn²⁺ weakens the Mo-O bonds as revealed by obvious red shifts of all the Mo-O stretching modes with increasing the content of Zn²⁺ and improves the sintering performance of the samples which is observed by SEM. The mechanisms of the negative and near-ZTE are discussed.

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

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

Negative thermal expansion in molecular materials

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

A rough guide to molecular solid solutions: design, synthesis and characterization of mixed crystals

Recent literature on molecular solid solutions is reviewed and general empirical rules to help synthesize mixed crystals are summarised.

Crystal structures, phase transitions and thermal expansion properties of NaZr2(PO4)3–SrZr4(PO4)6 solid solutions

Structures and phase transitions depending on compositions and temperature between R3̄c and R3̄ in Na_(2−2x)Sr_x[ ]_xZr₄(PO₄)₆ have been investigated.

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

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

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

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

Investigating anomalous thermal expansion of copper halides by inelastic neutron scattering and ab initio phonon calculations

We investigate the detailed lattice dynamics of copper halides, CuX (X = Cl, Br, and I), using neutron inelastic scattering measurements and ab initio calculations aimed at a comparative study of their thermal expansion behavior. We identify the low energy phonons which soften with pressure and are responsible for negative thermal expansion. The eigenvector analysis of these modes suggests that softening of the transverse-acoustic modes would lead to NTE in these compounds. The calculations are in very good agreement with our measurements of phonon spectra and thermal expansion behavior as reported in the literature. Our calculations at high pressure further reveal that a large difference in negative thermal expansion behavior in these compounds is associated with the difference in the unit cell volume.

Zero Thermal Expansion and Semiconducting Properties in PbTiO3-Bi(Co, Ti)O3 Ferroelectric Solid Solutions

Zero thermal expansion (ZTE) behavior is rare but important for both fundamental studies and practical applications of functional materials. Until now, most available ZTE materials are either electrical insulating oxides or conductive metallic compounds. Very few ZTE materials exhibit the semiconductor feature. Here we report a ZTE in a semiconducting ferroelectric of 0.6PbTiO₃-0.4Bi(Co_0.55Ti_0.45)O_3-δ. Its unit cell volume exhibits a negligible change over a broad temperature range from room temperature to 500 °C. The ZTE is supposed to be correlated with the spontaneous volume ferroelectronstriction. Intriguingly, the present ZTE material also exhibits the semiconducting characteristic accompanied by negative temperature coefficient of resistance. The mechanism of electric conduction is attributed to the electronic hopping from one ion (Ti³⁺) to another (Ti⁴⁺). The semiconductor nature has also been confirmed by the noticeable visible-light absorption with the relatively lower band gap (E_g) value of 1.5 eV, while the ferroelectric property can be well-maintained with large polarization. The first-principles calculations reveal that the drastically narrowed E_g is related to the Co-Ti substitution. The present multifunctional material containing ZTE, semiconducting, and ferroelectric properties is suggested to enable new applications such as the substrate for solar conversion devices.

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.

Controlling Thermal Expansion: A Metal-Organic Frameworks Route

Controlling thermal expansion is an important, not yet resolved, and challenging problem in materials research. A conceptual design is introduced here, for the first time, for the use of metal-organic frameworks (MOFs) as platforms for controlling thermal expansion devices that can operate in the negative, zero, and positive expansion regimes. A detailed computer simulation study, based on molecular dynamics, is presented to support the targeted application. MOF-5 has been selected as model material, along with three molecules of similar size and known differences in terms of the nature of host-guest interactions. It has been shown that adsorbate molecules can control, in a colligative way, the thermal expansion of the solid, so that changing the adsorbate molecules induces the solid to display positive, zero, or negative thermal expansion. We analyze in depth the distortion mechanisms, beyond the ligand metal junction, to cover the ligand distortions, and the energetic and entropic effect on the thermo-structural behavior. We provide an unprecedented atomistic insight on the effect of adsorbates on the thermal expansion of MOFs as a basic tool toward controlling the thermal expansion.

Negative Poisson's Ratio in Modern Functional Materials

Materials with negative Poisson's ratio attract considerable attention due to their underlying intriguing physical properties and numerous promising applications, particularly in stringent environments such as aerospace and defense areas, because of their unconventional mechanical enhancements. Recent progress in materials with a negative Poisson's ratio are reviewed here, with the current state of research regarding both theory and experiment. The inter-relationship between the underlying structure and a negative Poisson's ratio is discussed in functional materials, including macroscopic bulk, low-dimensional nanoscale particles, films, sheets, or tubes. The coexistence and correlations with other negative indexes (such as negative compressibility and negative thermal expansion) are also addressed. Finally, open questions and future research opportunities are proposed for functional materials with negative Poisson's ratios.

Near-Zero Thermal Expansion and High Ultraviolet Transparency in a Borate Crystal of Zn4 B6 O13

Intrinsic isotropic near-zero thermal expansion is discovered in borate crystal Zn₄ B₆ O₁₃ with high transparency in the ultraviolet region. First-principles calculations demonstrate that the very low thermal expansion originates mainly from the invariability of the solid [B₂₄ O₄₈ ] truncated octahedra that are fixed by the [Zn₄ O₁₃ ] clusters in the ZBO structure.

Hydration and Thermal Expansion in Anatase Nanoparticles

A tunable thermal expansion is reported in nanosized anatase by taking advantage of surface hydration. The coefficient of thermal expansion of 4 nm TiO2 along a-axis is negative with a hydrated surface and is positive without a hydrated surface. High-energy synchrotron X-ray pair distribution function analysis combined with ab initio calculations on the specific hydrated surface are carried out to reveal the local structure distortion that is responsible for the unusual negative thermal expansion.

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

Negative thermal expansion (NTE) is the phenomenon in which materials shrink rather than expand on heating. Although NTE had been previously observed in a few simple materials at low temperature, it was the realisation in 1996 that some materials have NTE over very wide ranges of temperature that kick-started current interest in this phenomenon. Now, nearly two decades later, a number of families of ceramic NTE materials have been identified. Increasingly quantitative studies focus on the mechanism of NTE, through techniques such as high-pressure diffraction, local structure probes, inelastic neutron scattering and atomistic simulation. In this paper we review our understanding of vibrational mechanisms of NTE for a range of materials. We identify a number of different cases, some of which involve a small number of phonons that can be described as involving rotations of rigid polyhedral groups of atoms, others where there are large bands of phonons involved, and some where the transverse acoustic modes provide the main contribution to NTE. In a few cases the elasticity of NTE materials has been studied under pressure, identifying an elastic softening under pressure. We propose that this property, called pressure-induced softening, is closely linked to NTE, which we can demonstrate using a simple model to describe NTE materials. There has also been recent interest in the role of intrinsic anharmonic interactions on NTE, particularly guided by calculations of the potential energy wells for relevant phonons. We review these effects, and show how anhamonicity affects the response of the properties of NTE materials to pressure.