Electric dipolar systems: Examples of glassy state

ZrW₂O₈ has a negative coefficient of thermal expansion from 0.3 K to its decomposition temperature around 1050 K. The negative thermal expansion is isotropic and is not disrupted by the structural phase transition at 430 K. A complicated distribution in reciprocal space of Rigid Unit Mode (RUM) phonons has been found for ZrW₂O₈ using Lattice Dynamics. The RUMS are very low energy phonons which cause collective rotations of ZrO₆ octahedra and WO₄ tetrahedra within the crystal structure. These distortions enable ZrW₂O₈ to contract upon heating.     

Unusual thermal conductivity of the negative thermal expansion material, ZrW2O8

In order to investigate the relationship between negative thermal expansion and other thermal properties, the thermal conductivity of the α-phase of ZrW₂O₈ has been determined from 1.9 to 390 K. In addition, the heat capacity was measured from 1.9 to 300 K. The thermal conductivity of ZrW₂O₈ is low, glass-like and close to its theoretical minimum value. The phonon-phonon coupling of the highly anharmonic low-frequency modes which are responsible for negative thermal expansion in ZrW₂O₈ appears to be highly efficient, leading to short phonon mean free paths and exceptionally low thermal conductivity.     

Abnormal positive thermal expansion in Mo substituted ZrW2O8

ZrW₂O₈ displays the unusual property of an isotropic bulk contraction in volume as a function of temperature. We report here on the positive thermal expansion (PTE) property caused by substituting Mo for W sites in ZrW₂O₈ at room temperature. The room temperature crystal structure of ZrW_2−xMo_xO₈ compounds, which were synthesized using a low temperature route, could be divided into ordered phase with α-ZrW₂O₈ structure (0≤x≤0.5) and disordered phase with β-ZrW₂O₈ (0.5<x≤1.5) and c-ZrMo₂O₈ structure (1.5<x≤2). ZrW_2−xMo_xO₈ adopting β-ZrW₂O₈ structure shows abnormal PTE property at room temperature due to the existence of water molecules, while ZrW_2−xMo_xO₈ adopting the other two structures (α-ZrW₂O₈ and c-ZrMo₂O₈) shows negative thermal expansion (NTE) property from room temperature until decomposition for α-ZrW₂O₈ structure or trigonal phase transition for c-ZrMo₂O₈ structure. The reason lies in the fact that the oxygen migration caused by the Mo substitution leads to the re-arrangement of W(Mo)O₄ tetrahedra lying along the 3-fold axis, only particular W/Mo ratio (0.5<x≤1.5) produces a special crystal structure, which allows the entrance of water molecules.     

Synthesis hexagonal ZrW2O8 and its thermal properties

ZrW₂O₈ as the typical negative thermal expansion (NTE) material has attracted much attention for the potential applications in various fields such as tailored coefficient of thermal expansion (CTE) composites. The hexagonal ZrW₂O₈ (h-ZrW₂O₈), with the combination of ZrO₂ and WO₃ in a composite, was synthesized at a pressure of 2 GPa and the temperature between 600°C and 700°C. We found h-ZrW₂O₈ decomposes to ZrO₂+WO₃ oxides that start from 500°C and end at 800°C, and determined the CTE of h-ZrW₂O₈ is?16.3×10^?6°C^?1 in the temperature range from 150°C to 450°C. The results show that ZrW₂O₈ with a hexagonal structure is metastable and exhibits high NTE property like its cubic structure.     

Rapid synthesis and Raman spectroscopic study of the negative thermal expansion material of A (WO4)2 (A = Zr2+, Hf2+)

The crystal structure of ZrW₂O₈ and HfW₂O₈ displays unusual property of isotropic negative thermal expansion in a wide temperature range, which brings about a number of important potential applications. In this work, densely packed A (WO₄)₂ (A = Zr²⁺, Hf²⁺) are rapid synthesized by CO₂ laser. The result of XRD and Raman spectra show that the ZrW₂O₈ is γ phase with space group P2₁2₁2₁ and HfW₂O₈ is α phase with space group P2₁3. Due to the influence of compressive stress, laser rapid solidification technique is more suitable for industrial production of HfW₂O₈.     

Nuclear quadrupole interactions at 187W(β-) 187Re in ZrW2O8

In ZrW₂O₈, a material with negative thermal expansion, two nuclear quadrupole interactions at ¹⁸⁷W(β^-) ¹⁸⁷Re with equal populations were determined by time differential perturbed angular correlation to be (at 295 K): ν_{\mathrm{Q} 1} = 336(1) MHz, η₁ = 0 and ν_Q2 = 1391(2) MHz, η₂ = 0.053(4). The nuclear quadrupole interactions are assigned to two crystallographically distinct tungsten sites. These results are the bases for further TDPAC studies of the negative thermal expansion on a microscopic scale. This revised version was published online in August 2006 with corrections to the Cover Date.     

Terahertz time-domain spectroscopy and optical properties of AM2O8 (A=Zr,Hf and M=W,Mo)

Terahertz time domain spectroscopy and optical properties of cubic ZrW₂O₈ and HfW₂O₈, and trigonal ZrMo₂O₈ and HfMo₂O₈ have been studied for the first time. It is shown that α-ZrW₂O₈ and α-HfW₂O₈ exhibit absorption peaks around 1.23 THz (41 cm^?1) and 1.18 THz (39.5 cm^?1), respectively, whereas no corresponding absorptions are observed for trigonal ZrMo₂O₈ and HfMo₂O₈. These external modes are suggested to originate from the librational and/or translational motions of the linked ZrO₆/HfO₆ and WO₄ polyhedra and to contribute to the negative thermal expansion of α-ZrW₂O₈ and α-HfW₂O₈. The absorption coefficients and refractive indices of these materials are derived from the transmission amplitudes of the THz field passing through the samples. The results suggest that cubic ZrW₂O₈ and HfW₂O₈ have the potential for THz filters or attenuators.     

Synthesis and physical properties of negative thermal expansion materials Zr1−xMxW2O8−y (M=Sc, In, Y) substituted for Zr(IV) sites by M(III) ions

Zr_1−xM_xW₂O_8−y (M=Sc, In and Y) solid solutions substituted up to x=0.04 for Zr(IV) sites by M(III) ions were synthesized by a solid-state reaction. X-ray diffraction experiments from 90 to 560 K revealed that all solid solutions had a cubic crystal structure and showed negative thermal expansion coefficients. The lattice parameters of Zr_1−xM_xW₂O_8−y were smaller than that of ZrW₂O₈ probably due to oxygen defects, though the ionic radii of substituted M³⁺ ions were larger than that of Zr⁴⁺. Order-disorder phase transition temperatures of the substituted samples drastically decreased in the order of Y, In and Sc compared to the percolation theory, and decreased with increasing M content.     

Negative thermal expansion in framework compounds

We have studied negative thermal expansion (NTE) compounds with chemical compositions of NX₂O₈ and NX₂O₇ (N=Zr, Hf and X=W, Mo, V) and M₂O (M=Cu, Ag) using the techniques of inelastic neutron scattering and lattice dynamics. There is a large variation in the negative thermal expansion coefficients of these compounds. The inelastic neutron scattering experiments have been carried out using polycrystalline and single crystal samples at ambient pressure as well as at high pressures. Experimental data are useful to confirm the predictions made from our lattice dynamical calculations as well as to check the quality of the interatomic potentials developed by us. We have been able to successfully model the NTE behaviour of these compounds. Our studies show that unusual phonon softening of low energy modes is able to account for NTE in these compounds.      

Inelastic neutron scattering an ab-initio calculation of negative thermal expansion in Ag2O

The compound Ag₂O undergoes large and isotropic negative thermal expansion over 0–500 K. We report temperature dependent inelastic neutron scattering measurements and ab-initio calculations of the phonon spectrum. The temperature dependence of the experimental phonon spectrum shows strong anharmonic nature of phonon modes of energy around 2.4 meV. The ab-initio calculations reveal that the maximum negative Grüneisen parameter, which is a measure of the relevant anharmonicity, occurs for the transverse phonon modes that involve bending motions of the Ag₄O tetrahedra. The thermal expansion is evaluated from the ab-initio calculation of the pressure dependence of the phonon modes, and found in good agreement with available experimental data.     

Electrical conductivity and amorphization of Sc2(WO4)3 at high pressures and temperatures

Impedance spectroscopy measurements and synchrotron X-ray diffraction studies of Sc₂(WO₄)₃ at 400°C have been carried out as a function of pressure up to 4.4 GPa. Ionic conductivity shows normal decrease with increase in pressure up to 2.9 GPa, but then increases at higher pressures. The XRD results show that Sc₂(WO₄)₃ undergoes pressure-induced amorphization at pressures coincident with the reversal in conductivity behavior. The loss of crystal structure at high pressure is consistent with growing evidence of pressure-induced amorphization in negative thermal expansion materials, such as Sc₂(WO₄)₃. The increase in conductivity in the amorphized state is interpreted as the result of an increase in structural entropy and a concomitant reduction of energy barriers for ionic transport.     

Low-temperature anomalies in thermal expansion of HTSCs: System Bi2Sr2−x LaxCuO6

The data on thermal expansion at low temperatures have been obtained for HTSC single crystals of the system Bi₂Sr_2?x La_xCuO₆ with different doping levels. Anomalous (negative) thermal expansion is observed in the temperature range from 5 to 20 K. It is shown that the anomaly vanishes in an overdoped sample. An anomalously strong effect of magnetic fields of 2–4 T on the negative thermal expansion domain is observed. The effect of field screening, frozen field, doping level, defects and oxygen vacancies on the region of thermal expansion anomalies is investigated. The origin of the observed anomalies in the properties of the system Bi₂Sr_2?x La_xCuO₆, as well as other HTSC systems in which similar anomalies have been observed, is discussed.     

Low-temperature investigations of the open-framework material HfMgMo3O12

The A₂Mo₃O₁₂ family, where A³⁺ is a large trivalent cation, can show interesting thermal properties such as negative thermal expansion. One member of this family, HfMgMo₃O₁₂, where the two A³⁺ cations have been replaced by Hf⁴⁺ and Mg²⁺, has been shown to have a low positive coefficient of thermal expansion above room temperature. This property makes HfMgMo₃O₁₂ an attractive candidate as a component for solid solutions with near-zero thermal expansion. However, its properties below room temperature were unexplored. In this work we report the phase transition from orthorhombic Pnma to monoclinic P2₁/a at T～175 K with an enthalpy change of 0.27 kJ mol^?1. Relaxation calorimetry, from 5 K to 300 K, show only the small anomaly associated with this transition. The thermal conductivity, determined from 2 K to 300 K, was low, but not as low as some other materials exhibiting negative thermal expansion. Analysis of the low-temperature heat capacity indicates the presence of low-energy phonon modes in HfMgMo₃O₁₂, consistent with the low thermal conductivity. The upper bound of the Young's modulus, estimated from the effective Debye temperature derived from the low-temperature heat capacity, is 20 GPa, a relatively low value due to the flexibility of the framework structure.     

Ferroelastic phase transitions in (NH4)2TaF7

The heat capacity, unit cell parameters, permittivity, optical properties, and thermal expansion of the (NH₄)₂TaF₇ compound with a seven-coordinated anion polyhedron have been measured. It has been found that the compound undergoes two successive phase transitions with the symmetry change: tetragonal → (T ₁ = 174 K) orthorhombic → (T ₂ = 156 K) tetragonal. The ferroelastic nature of structural transformations has been established, and their entropy and susceptibility to hydrostatic pressure have been determined.     

Negative thermal expansion coefficient in the high-temperature superconductor Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>8 + <Emphasis Type="Italic">x</Emphasis></Subscript>

Powder and single-crystal samples of the high-temperature superconductor Bi₂Sr₂CaCu₂O_{8 + x} are studied by X-ray diffraction. Its thermal expansion coefficient is found to be negative over a wide temperature range (160–260 K). Possible causes of this effect are discussed.     

X-ray diffraction investigations of the crystallographic parameters and thermal expansion of β-BaB2O4 crystals

The lattice parameters a and c of β-BaB₂O₄ crystals have been measured in the temperature range 80–300 K by the x-ray diffraction method. The thermal expansion coefficients α are calculated from the measured values of the parameters. A substantial anisotropy of the thermal expansion is found. It is shown that the thermal expansion coefficient α _c along the c axis is an order of magnitude greater than the thermal expansion coefficient α _a in a plane perpendicular to this axis. It is established that α _a becomes negative in the temperature range 80–190 K. Fiz. Tverd. Tela (St. Petersburg) 39, 1038–1040 (June 1997)     

CDW-induced negative thermal expansion in two-dimensional conductor η-Mo4O11

Two-dimensional oxide η-Mo₄O₁₁ exhibits almost isotropic thermal expansion in the normal phase, while anisotropic negative thermal expansion (NTE) in the charge density wave (CDW) phase below T_c1=105 K, where a remarkable anomalous expansion occurs along the a-axis. The incommensurate nesting vector along the b-axis is independent of temperature, q₁=(0.000(1) 0.2335(1) 0.0000(5)). We propose that the CDW-induced NTE occurs as a result of the structural relaxation of the MoO₆ octahedra layers along the stacking direction with the aid of the open spaces around the MoO₄ tetrahedra.     

The study of thermal expansion properties in solid solutions Ln2−xCrxMo3O12 (Ln=Ho and Lu) by high temperature X-ray diffraction

A systematic study of the formation, crystal structures and thermal expansion properties of solid solutions Ln_2?xCr_xMo₃O₁₂ (Ln=Ho and Lu) has been performed. Rietveld refinement results indicate that compounds Ho_2?xCr_xMo₃O₁₂ with 0≤x≤0.2 and Lu_2?xCr_xMo₃O₁₂ with 0≤x≤0.5 have orthorhombic structures and show negative thermal expansion in the temperature range of 200–800 °C. Compounds Ln_2?xCr_xMo₃O₁₂ with 1.7≤x≤2.0 have monoclinic structures and show strong positive thermal expansion in the temperature range of 25–300 °C. While compounds Ln_2?xCr_xMo₃O₁₂ with 1.7≤x≤2.0 adopt orthorhombic structures and show very low positive thermal expansion from 500 to 800 °C. Though the crystal structure plays the key rule in determining the thermal expansion properties, chemical composition and temperature also show important effect on the thermal expansion properties of these compounds.     

Investigation of ion transport in Li<Subscript>8</Subscript>ZrO<Subscript>6</Subscript> and Li<Subscript>6</Subscript>Zr<Subscript>2</Subscript>O<Subscript>7</Subscript> solid electrolytes

Lithium ionic conductivity and spin-lattice relaxation rates were measured in Li₈ZrO₆ and Li₆Zr₂O₇ solid electrolytes. It was found that the Li₈ZrO₆ solid electrolyte undergoes a transition to the superionic state in the temperature range 673–703 K. It was shown that Li⁺ ions are mobile in particular lattice positions of the Li₆Zr₂O₇ phase, and that ionic conductivity is monotonic at an activation energy of 79.4 kJ/mol.     

Theoretical predictions of the structural,mechanical and lattice dynamical properties of XW2 (X = Zr,Hf) Laves phases

We have investigated the structural, mechanical and lattice dynamical properties of ZrW₂ and HfW₂ compounds in cubic C15 (space group Fd-3m), hexagonal C14 (space group P6₃/mmc) and C36 (space group P6₃/mmc) phases using generalized gradient approximation within the plane-wave pseudo-potential density functional theory. We have found that ZrW₂ and HfW₂ in cubic C15 phase are the most stable among the considered phases. From calculated elastic constants, it is shown that all phases are mechanically stable according to the elastic stability criteria. The related mechanical properties, such as bulk, shear and Young moduli, Poisson’s ratio, Debye temperature and hardness have been also calculated. The results show that ZrW₂ and HfW₂ compounds are ductile in nature with respect to the B/G and Cauchy pressure analysis. The phonon dispersion curves, phonon density of states and some thermodynamic properties are computed and discussed exhaustively for considered phases.