Phonon density of states and negative thermal expansion in ZrW2O8

Antithermal Quenching Upconversion Luminescence via Suppressed Multiphonon Relaxation in Positive/Negative Thermal Expansion Core/Shell NaYF4:Yb/Ho@ScF3 Nanoparticles

Thermal quenching (TQ) has been naturally entangling with luminescence since its discovery, and lattice vibration, which is characterized as multiphonon relaxation (MPR), plays a critical role. Considering that MPR may be suppressed under exterior pressure, we have designed a core/shell upconversion luminescence (UCL) system of α-NaYF4:Yb/Ln@ScF3 (Ln = Ho, Er, and Tm) with positive/negative thermal expansion behavior so that positive thermal expansion of the core will be restrained by negative thermal expansion of the shell when heated. This imposed pressure on the crystal lattice of the core suppresses MPR, reduces the amount of energy depleted by TQ, and eventually saves more energy for luminescing, so that anti-TQ or even thermally enhanced UCL is obtained.

Tunable assembly of host-guest colloidal crystals

Entropy compartmentalization provides new self-assembly routes to colloidal host-guest (HG) structures. Leveraging host particle shape to drive the assembly of HG structures has only recently been proposed and demonstrated. However, the extent to which the guest particles can dictate the structure of the porous network of host particles has not been explored. In this work, by modifying only the guest shape, we show athermal, binary mixtures of star-shaped host particles and convex polygon-shaped guest particles assemble as many as five distinct crystal structures, including rotator and discrete rotator guest crystals, two homoporous host crystals, and one heteroporous host crystal. Edge-to-edge alignment of neighboring stars results in the formation of three distinct pore motifs, whose preferential formation is controlled by the size and shape of the guest particles. Finally, we confirm, via free volume calculations, that assembly is driven by entropy compartmentalization, where the hosts and guests contribute differently to the free energy of the system; free volume calculations also explain differences in assembly based on guest shape. These results provide guest design rules for assembling colloidal HG structures, especially on surfaces and interfaces.

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.

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.

Shape-driven entropic self-assembly of an open, reconfigurable, binary host-guest colloidal crystal

Entropically driven self-assembly of hard anisotropic particles, where particle shape gives rise to emergent valencies, provides a useful perspective for the design of nanoparticle and colloidal systems. Hard particles self-assemble into a rich variety of crystal structures, ranging in complexity from simple close-packed structures to structures with 432 particles in the unit cell. Entropic crystallization of open structures, however, is missing from this landscape. Here, we report the self-assembly of a two-dimensional binary mixture of hard particles into an open host-guest structure, where nonconvex, triangular host particles form a honeycomb lattice that encapsulates smaller guest particles. Notably, this open structure forms in the absence of enthalpic interactions by effectively splitting the structure into low- and high-entropy sublattices. This is the first such structure to be reported in a two-dimensional athermal system. We discuss the observed compartmentalization of entropy in this system, and show that the effect of the size of the guest particle on the stability of the structure gives rise to a reentrant phase behavior. This reentrance suggests the possibility for a reconfigurable colloidal material, and we provide a proof-of-concept by showing the assembly behavior while changing the size of the guest particles in situ. Our findings provide a strategy for designing open colloidal crystals, as well as binary systems that exhibit co-crystallization, which have been elusive thus far.

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.

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.

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.

Structure and Negative Thermal Expansion in Zr0.3Sc1.7Mo2.7V0.3O12

A₂M₃O₁₂-based materials have received considerable attention owing to their wide range of negative thermal expansion (NTE) and chemical flexibility toward novel materials design. However, the structure and NTE mechanism remain challenging. Here, Zr⁴⁺ and V⁵⁺ are used as a unit to compensatorily replace Sc³⁺ and Mo⁶⁺ in Sc₂Mo₃O₁₂ to tune its thermal expansion. Its crystal structure, phase transition, NTE property, and corresponding mechanisms are studied by high-resolution synchrotron X-ray diffraction, powder X-ray diffraction, ultralow-frequency Raman spectroscopy, and density functional theory calculations. The results show that Zr_0.3Sc_1.7Mo_2.7V_0.3O₁₂ adopts an orthorhombic (Pbcn) structure at room temperature, with V atoms occupying the position of Mo1 atoms and Zr atoms occupying the position of Sc atoms, and transforms to monoclinic (P2₁/a) structure at ∼133 K (45 K lower than that of Sc₂Mo₃O₁₂). It exhibits excellent NTE in a broader range. Most of the phonon modes below 350 cm^-1 have negative Grüneisen parameters, of which the lowest and next-lowest frequency (38.5 and 45.8 cm^-1) optical phonon modes arising from the translational vibrations of the Sc/Zr and Mo/V atoms in the plane of the nonlinear linkage Sc/Zr-O-Mo/V have the largest and next-largest negative Grüneisen parameters and positive total anharmonicity, and contribute most to the NTE.

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.

Core–shell structures with metallic silver as nucleation agent of low expansion phases in BaO/SrO/ZnO/SiO2 glasses

The role of silver as a nucleating agent in BaO/SrO/ZnO/SiO₂ glasses is studied with a range of microstructure-characterization techniques, such as scanning transmission electron microscopy, ultraviolet-visible spectroscopy, and X-ray diffraction.

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.

Negative Thermal Expansion Near the Precipice of Structural Stability in Open Perovskites

Negative thermal expansion (NTE) describes the anomalous propensity of materials to shrink when heated. Since its discovery, the NTE effect has been found in a wide variety of materials with an array of magnetic, electronic and structural properties. In some cases, the NTE originates from phase competition arising from the electronic or magnetic degrees of freedom but we here focus on a particular class of NTE which originates from intrinsic dynamical origins related to the lattice degrees of freedom, a property we term structural negative thermal expansion (SNTE). Here we review some select cases of NTE which strictly arise from anharmonic phonon dynamics, with a focus on open perovskite lattices. We find that NTE is often present close in proximity to competing structural phases, with structural phase transition lines terminating near T=0 K yielding the most prominent displays of the SNTE effect. We further provide a theoretical model to make precise the proposed relationship among the signature behavior of SNTE, the proximity of these systems to structural quantum phase transitions and the effects of phase fluctuations near these unique regions of the structural phase diagram. The effects of compositional disorder on NTE and structural phase stability in perovskites are discussed.

First-Principles Structural, Mechanical, and Thermodynamic Calculations of the Negative Thermal Expansion Compound Zr2(WO4)(PO4)2

The negative thermal expansion (NTE) material Zr₂(WO₄)(PO₄)₂ has been investigated for the first time within the framework of the density functional perturbation theory (DFPT). The structural, mechanical, and thermodynamic properties of this material have been predicted using the Perdew, Burke and Ernzerhof for solid (PBEsol) exchange-correlation functional, which showed superior accuracy over standard functionals in previous computational studies of the NTE material α-ZrW₂O₈. The bulk modulus calculated for Zr₂(WO₄)(PO₄)₂ using the Vinet equation of state at room temperature is K ₀ = 63.6 GPa, which is in close agreement with the experimental estimate of 61.3(8) at T = 296 K. The computed mean linear coefficient of thermal expansion is -3.1 × 10^-6 K^-1 in the temperature range ∼0-70 K, in line with the X-ray diffraction measurements. The mean Grüneisen parameter controlling the thermal expansion of Zr₂(WO₄)(PO₄)₂ is negative below 205 K, with a minimum of -2.1 at 10 K. The calculated standard molar heat capacity and entropy are C _P ⁰ = 287.6 and S ⁰ = 321.9 J·mol^-1·K^-1, respectively. The results reported in this study demonstrate the accuracy of DFPT/PBEsol for assessing or predicting the relationship between structural and thermomechanical properties of NTE materials.

Efficient Calculation of the Negative Thermal Expansion in ZrW2O8

We present a study of the origin of the negative thermal expansion (NTE) on ZrW₂O₈ by combining an efficient approach for computing the dynamical matrix with the Lanczos algorithm for generating the phonon density of states in the quasi-harmonic approximation. The simulations show that the NTE arises primarily from the motion of the O-sublattice, and in particular, from the transverse motion of the O atoms in the W–O and W–O–Zr bonds. In the low frequency range these combine to keep the WO₄ tetrahedra rigid and induce internal distortions in the ZrO₆ octahedra. The force constants associated with these distortions become stronger with expansion, resulting in negative Grüneisen parameters and NTE from the low frequency modes that dominate the positive contributions from the high frequency modes. This leads us to propose an anharmonic, two-frequency Einstein model that quantitatively captures the NTE behavior.

Negative Thermal Expansion of Ultrathin Metal Nanowires: A Computational Study

Most materials expand upon heating because the coefficient of thermal expansion (CTE), the fundamental property of materials characterizing the mechanical response of the materials to heating, is positive. There have been some reports of materials that exhibit negative thermal expansion (NTE), but most of these have been in complex alloys, where NTE originates from the transverse vibrations of the materials. Here, we show using molecular dynamics simulations that some single crystal monatomic FCC metal nanowires can exhibit NTE along the length direction due to a novel thermomechanical coupling. We develop an analytic model for the CTE in nanowires that is a function of the surface stress, elastic modulus, and nanowire size. The model suggests that the CTE of nanowires can be reduced due to elastic softening of the materials and also due to surface stress. For the nanowires, the model predicts that the CTE reduction can lead to NTE if the nanowire Young's modulus is sufficiently reduced while the nanowire surface stress remains sufficiently large, which is in excellent agreement with the molecular dynamics simulation results. Overall, we find a "smaller is smaller" trend for the CTE of nanowires, leading to this unexpected, surface-stress-driven mechanism for NTE in nanoscale materials.

Large Magnetovolume Effect Induced by Embedding Ferromagnetic Clusters into Antiferromagnetic Matrix of Cobaltite Perovskite

Materials that show negative thermal expansion (NTE) have significant industrial merit because they can be used to fabricate composites whose dimensions remain invariant upon heating. In some materials, NTE is concomitant with the spontaneous magnetization due to the magnetovolume effect (MVE). Here the authors report a new class of MVE material; namely, a layered perovskite PrBaCo₂ O_5.5+x (0 ≤ x ≤ 0.41), in which strong NTE [β ≈ -3.6 × 10^-5 K^-1 (90-110 K) at x = 0.24] is triggered by embedding ferromagnetic (F) clusters into the antiferromagnetic (AF) matrix. The strongest MVE is found near the boundary between F and AF phases in the phase diagram, indicating the essential role of competition between the F-clusters and the AF-matrix. Furthermore, the MVE is not limited to the PrBaCo₂ O_5.5+x but is also observed in the NdBaCo₂ O_5.5+x . The present study provides a new approach to obtaining MVE and offers a path to the design of NTE materials.

A novel negative thermal expansion material of Zr0.70V1.33Mo0.67O6.73

A novel negative thermal expansion (NTE) material of Zr_0.70V_1.33Mo_0.67O_6.73 was synthesized.

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.

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.

Ba(1-x)Sr(x)Zn2Si2O7--A new family of materials with negative and very high thermal expansion

The compound BaZn2Si2O7 shows a high coefficient of thermal expansion up to a temperature of 280 °C, then a transition to a high temperature phase is observed. This high temperature phase exhibits negative thermal expansion. If Ba(2+) is successively replaced by Sr(2+), a new phase with a structure, similar to that of the high temperature phase of BaZn2Si2O7, forms. At the composition Ba0.8Sr0.2Zn2Si2O7, this new phase is completely stabilized. The crystal structure was determined with single crystal X-ray diffraction using the composition Ba0.6Sr0.4Zn2Si2O7, which crystallizes in the orthorhombic space group Cmcm. The negative thermal expansion is a result of motions and distortions inside the crystal lattice, especially inside the chains of ZnO4 tetrahedra. Dilatometry and high temperature X-ray powder diffraction were used to verify the negative thermal expansion. Coefficients of thermal expansion partially smaller than -10·10(-6) K(-1) were measured.

Synthesis, Structure, and Rigid Unit Mode-like Anisotropic Thermal Expansion of BaIr2In9

This Article reports the synthesis of large single crystals of BaIr2In9 using In flux and their characterization by variable-temperature single-crystal and synchrotron powder X-ray diffraction, resistivity, and magnetization measurements. The title compound adopts the BaFe2Al9-type structure in the space group P6/mmm with room temperature unit cell parameters a = 8.8548(6) Å and c = 4.2696(4) Å. BaIr2In9 exhibits anisotropic thermal expansion behavior with linear expansion along the c axis more than 3 times larger than expansion in the ab plane between 90 and 400 K. This anisotropic expansion originates from a rigid unit mode-like mechanism similar to the mechanism of zero and negative thermal expansion observed in many anomalous thermal expansion materials such as ZrW2O8 and ScF3.

Low Temperature Synthesis and Characterization of AlScMo₃O12

Recent interest in low and negative thermal expansion materials has led to significant research on compounds that exhibit this property, much of which has targeted the A₂M₃O₁₂ family (A = trivalent cation, M = Mo, W). The expansion and phase transition behavior in this family can be tuned through the choice of the metals incorporated into the structure. An undesired phase transition to a monoclinic structure with large positive expansion can be suppressed in some solid solutions by substituting the A-site by a mixture of two cations. One such material, AlScMo₃O₁₂, was successfully synthesized using non-hydrolytic sol-gel chemistry. Depending on the reaction conditions, phase separation into Al₂Mo₃O₁₂ and Sc₂Mo₃O₁₂ or single-phase AlScMo₃O₁₂ could be obtained. Optimized conditions for the reproducible synthesis of stoichiometric, homogeneous AlScMo₃O₁₂ were established. High resolution synchrotron diffraction experiments were carried out to confirm whether samples were homogeneous and to estimate the Al:Sc ratio through Rietveld refinement and Vegard’s law. Single-phase samples were found to adopt the orthorhombic Sc₂W₃O₁₂ structure at 100 to 460 K. In contrast to all previously-reported A₂M₃O₁₂ compositions, AlScMo₃O₁₂ exhibited positive thermal expansion along all unit cell axes instead of contraction along one or two axes, with expansion coefficients (200–460 K) of α_a = 1.7 × 10⁻⁶ K⁻¹, α_b = 6.2 × 10⁻⁶ K⁻¹, α_c = 2.9 × 10⁻⁶ K⁻¹ and α_V = 10.8 × 10⁻⁶ K⁻¹, respectively.

Unidirectional thermal expansion in KZnB3O6: role of alkali metals

The size and mass of alkali metals have profound effects on the area zero thermal expansion behavior of edge-sharing KZnB₃O₆.

Thermal expansion anomaly regulated by entropy

Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe₃Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.

Self-assembly of three-dimensional open structures using patchy colloidal particles

Open structures can display a number of unusual properties, including a negative Poisson's ratio, negative thermal expansion, and holographic elasticity, and have many interesting applications in engineering. However, it is a grand challenge to self-assemble open structures at the colloidal scale, where short-range interactions and low coordination number can leave them mechanically unstable. In this paper we discuss the self-assembly of three-dimensional open structures using triblock Janus particles, which have two large attractive patches that can form multiple bonds, separated by a band with purely hard-sphere repulsion. Such surface patterning leads to open structures that are stabilized by orientational entropy (in an order-by-disorder effect) and selected over close-packed structures by vibrational entropy. For different patch sizes the particles can form into either tetrahedral or octahedral structural motifs which then compose open lattices, including the pyrochlore, the hexagonal tetrastack and the perovskite lattices. Using an analytic theory, we examine the phase diagrams of these possible open and close-packed structures for triblock Janus particles and characterize the mechanical properties of these structures. Our theory leads to rational designs of particles for the self-assembly of three-dimensional colloidal structures that are possible using current experimental techniques.

Local vibrations and negative thermal expansion in ZrW2O8

We present an x-ray pair distribution function (XPDF) analysis and extended x-ray absorption fine structure (EXAFS) data for ZrW2O8 (10-500 K) with a focus on the stiffness of the Zr-O-W linkage. The XPDF is highly sensitive to W-Zr and W-W correlations, but much less so to O-O or W-O correlations. The Zr-W peak in the XPDF data has a weak temperature dependence and, hence, this linkage is relatively stiff and does not permit bending of the Zr-O-W link. We propose that the low energy vibrational modes that lead to negative thermal expansion involve correlated rotations of ZrO6 octahedra that produce large <111> translations of the WO4 tetrahedra, rather than a transverse motion of O atoms that imply a flexible Zr-O-W linkage.

Structure and thermal expansion of the tungsten bronze Pb2KNb5O15

Negative thermal expansion and abnormal spontaneous polarization direction along b axis in tetragonal tungsten bronze Pb₂KNb₅O₁₅ are presented. A Pb–O covalency, octahedrons cooperative rotation mechanism is proposed.

Phase transitions, prominent dielectric anomalies, and negative thermal expansion in three high thermally stable ammonium magnesium-formate frameworks

We present three Mg-formate frameworks, incorporating three different ammoniums: [NH4][Mg(HCOO)3] (1), [CH3CH2NH3][Mg(HCOO)3] (2) and [NH3(CH2)4NH3][Mg2(HCOO)6] (3). They display structural phase transitions accompanied by prominent dielectric anomalies and anisotropic and negative thermal expansion. The temperature-dependent structures, covering the whole temperature region in which the phase transitions occur, reveal detailed structural changes, and structure-property relationships are established. Compound 1 is a chiral Mg-formate framework with the NH4(+) cations located in the channels. Above 255 K, the NH4(+) cation vibrates quickly between two positions of shallow energy minima. Below 255 K, the cations undergo two steps of freezing of their vibrations, caused by the different inner profiles of the channels, producing non-compensated antipolarization. These lead to significant negative thermal expansion and a relaxor-like dielectric response. In perovskite 2, the orthorhombic phase below 374 K possesses ordered CH3CH2NH3(+) cations in the cubic cavities of the Mg-formate framework. Above 374 K, the structure becomes trigonal, with trigonally disordered cations, and above 426 K, another phase transition occurs and the cation changes to a two-fold disordered state. The two transitions are accompanied by prominent dielectric anomalies and negative and positive thermal expansion, contributing to the large regulation of the framework coupled the order-disorder transition of CH3CH2NH3(+). For niccolite 3, the gradually enhanced flipping movement of the middle ethylene of [NH3(CH2)4NH3](2+) in the elongated framework cavity finally leads to the phase transition with a critical temperature of 412 K, and the trigonally disordered cations and relevant framework change, providing the basis for the very strong dielectric dispersion, high dielectric constant (comparable to inorganic oxides), and large negative thermal expansion. The spontaneous polarizations for the low-temperature polar phases are 1.15, 3.43 and 1.51 μC cm(-2) for 1, 2 and 3, respectively, as estimated by the shifts of the cations related to the anionic frameworks. Thermal and variable-temperature powder X-ray diffraction studies confirm the phase transitions, and the materials are all found to be thermally stable up to 470 K.

Entropic effects in the self-assembly of open lattices from patchy particles

Open lattices are characterized by low-volume-fraction arrangements of building blocks, low coordination number, and open spaces between building blocks. The self-assembly of these lattices faces the challenge of mechanical instability due to their open structures. We theoretically investigate the stabilizing effects of entropy in the self-assembly of open lattices from patchy particles. A preliminary account of these findings and their comparison to experiment was presented recently [Mao, Chen, and Granick, Nat. Mater. 12, 217 (2013)]. We found that rotational entropy of patchy particles can provide mechanical stability to open lattices, whereas vibrational entropy of patchy particles can lower the free energy of open lattices and, thus, enables the selection of open lattices verses close-packed lattices which have the same potential energy. These effects open the door to significant simplifications of possible future designs of patchy particles for open-lattice self-assembly.

Phonons and colossal thermal expansion behavior of Ag3Co(CN)6 and Ag3Fe(CN)6

Recently colossal volume thermal expansion has been observed in the framework compounds Ag(3)Co(CN)(6) and Ag(3)Fe(CN)(6). We have measured phonon spectra using neutron time-of-flight spectroscopy as a function of temperature and pressure. Ab initio calculations were carried out for the sake of analysis and interpretation. Bonding is found to be very similar in the two compounds. At ambient pressure, modes in the intermediate frequency part of the vibrational spectra in the Co compound are shifted slightly to higher energies as compared to the Fe compound. The temperature dependence of the phonon spectra gives evidence for a large explicit anharmonic contribution to the total anharmonicity for low-energy modes below 5 meV. We have found that modes are mainly affected by the change in size of the unit cell, which in turn changes the bond lengths and vibrational frequencies. Thermal expansion has been calculated via the volume dependence of phonon spectra. Our analysis indicates that Ag phonon modes within the energy range 2-5 meV are strongly anharmonic and major contributors to thermal expansion in both systems. The application of pressure hardens the low-energy part of the phonon spectra involving Ag vibrations and confirms the highly anharmonic nature of these modes.

First-principles mode Gruneisen parameters and negative thermal expansion in α-ZrW2O8

Mode Grüneisen parameters were estimated for α-ZrW(2)O(8) zone-center modes by means of density functional theory calculations and the temperature dependence of the coefficient of thermal expansion was obtained according to the Debye-Einstein model of the quasiharmonic approximation. The lowest energy optic modes were identified at 45 and 46 cm(-1), and were shown to be the main modes responsible for negative thermal expansion at low temperature. Experimental evidence of the lowest energy, triply degenerated infrared active optic mode, was also found in the far infrared spectrum of α-ZrW(2)O(8). Upon increasing temperature, other optic modes with E<25 meV (particularly at 96, 100, 133, 161, and 164 cm(-1)) also contribute significantly to the coefficient of thermal expansion near room temperature. An analysis was made of selected zone-center modes in light of previously proposed models for explaining negative thermal expansion in open framework materials.