Showing papers on "Thermal expansion published in 1991"

Effect of pressure, temperature, and composition on lattice parameters and density of (Fe,Mg)SiO3-perovskites to 30 GPa

Abstract: High-pressure, high-temperature properties of MgSiO3, (Fe01Mg09)SiO3, and (Fe02Mg08)SiO3 perovskites have been investigated using a newly developed X ray diffraction technique involving monochromatic synchrotron radiation The first direct measurements of unit cell distortions and equation-of-state parameters of the orthorhombic perovskite as functions of composition and simultaneous high pressure and high temperature were obtained The experiments were conducted under hydrostatic pressure up to 30 GPa, into the stability field of the perovskite The results demonstrate that the perovskite is elastically anisotropic, with the lattice parameter b being 25% less compressible than a and c Under increasing pressures the orthorhombic perovskite is distorted further away from the ideal cubic structure in agreement with theoretical predictions The 298-K isothermal equations of state of the three perovskites are indistinguishable within the uncertainty limits of the experiment The zero-pressure bulk modulus KT0 = 261 (±4) GPa with its pressure derivative KT0′ = 4 is close to that determined in previous static high pressure measurements The thermal expansion obtained from the high P - T experiments are consistent with previous measurements carried out at zero pressure but shows a strong volume dependence The temperature derivative of the isothermal bulk modulus at constant pressure (∂KT/∂T)p is −63(±05)×10−2 GPa/K Analyses of the high-temperature data give a value for the Anderson-Gruneisen parameter δT of 65–75, which is significantly higher than that used in recent lower mantle models

Analytic embedded-atom potentials for fcc metals : application to liquid and solid copper

Abstract: A simple analytic embedded-atom model that includes more than nearest neighbors is presented. Parameters for Cu, Ag, Au, Ni, Pd, and Pt have been obtained. The model has been applied to study the thermodynamic properties of copper with molecular dynamics. The calculated fractional density change on melting, heat of fusion, linear coefficients of thermal expansion, and heat capacities above room temperature are in good agreement with experimental results.

High Thermal Expansion Phosphate Glasses. Part 2

Abstract: The purpose of the research was to find effective ways of improving the chemical durability of phosphate glasses while maintening a thermal expansion coefficient superior to 175.10 -7 °C -1 and retaining other desirable properties which are needed for sealing to low melting, high expansion metals and alloys.The general composition investigated were M 2 O-MO-M 2 O 3 -P 2 O 5 , where M 2 O=Ag 2 O, Na 2 O, or K 2 O, MO=BaO or PbO, and M 2 O 3 =Al 2 O 3 or Fe 2 O 3

Theory of the thermal expansion of Si and diamond

Abstract: Phonon-dispersion curves, lattice mode Gr\"uneisen parameters, and the coefficients of thermal expansion are calculated for Si and C within a tight-binding model. The results are in good agreement with experimental data. The origin of the negative thermal expansion in Si is examined, and we find that the different thermal-expansion behaviors between Si and C can be explained by the different relative strengths of bond-bending and bond-stretching forces.

Development of an N-body interatomic potential for hcp and bcc zirconium.

Abstract: An interatomic potential based on the second-moment approximation of the tight-binding scheme is developed for zirconium, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of the hcp phase. In this work we attempt to model realistically two different crystallographic phases of a solid with the same potential. The reliability of our potential is tested in both the hcp and the bcc phases with regard to defect properties, thermal expansion, phonon properties, and mean-square displacements. For this purpose, we perform quenched molecular-dynamics relaxations, quasiharmonic lattice-dynamics calculations, and molecular-dynamics simulations. The low vacancy-formation and migration energies found in the bcc phase are consistent with the fast diffusivity experimentally observed. Unlike some other N-body potentials recently proposed to model bcc transition metals, our potential is not affected by the flaw of unphysical or even negative thermal expansion. We obtain thermal expansions that agree well with experiments in both phases, although they turned out to be slightly too large. The phonon-dispersion curves and, in particular, the anomalies in the bcc phase are well reproduced. We emphasize the stabilization with temperature of the T1 N-point phonon of the bcc phase, which is related to the bcc- to hcp-phase transition. We obtain a temperature dependence of this mode much weaker than in the experimental case. This influences the temperature behavior of the vibrational properties: In particular the mean-square displacement is markedly higher than the one extracted from experiments in the bcc phase at high temperatures. On the other hand, mean-square displacements in the hcp phase are in excellent agreement with experiment. The results are quite satisfactory in view of the small number of fitting parameters and the difficulties commonly encountered in matching the properties of bcc metals.

The Anomalous Negative Thermal Expansion and the Compressibility Maximum of Molten Ge-Te Alloys

Abstract: The high energy γ-ray attenuation and sound velocity have been measured to investigate the bonding nature and structural changes in liquid Ge-Te system. The results have been used to deduce the molar volume and adiabatic compressibility. The volume for Te rich alloys around the eutectic composition shows anomalous increase as the liquidus temperature is approached. Correspondingly the thermal expansion coefficient and adiabatic compressibility show very sharp extrema at around 400°C, which indicates that rapid structural changes occur in the liquid. At high temperatures, the composition dependences of the volume and compressibility show small positive deviation from the linear interpolations where anomalies in the magnetic susceptibility and electrical properties have been found.

Thermomechanical and thermo-optical properties of the LiCaAlF 6 :Cr 3+ laser material

Abstract: Measurements of the intrinsic thermomechanical and thermo-optical properties of the new laser material LiCaAlF6:Cr3+ (known as Cr:LiCAF) are performed. Thermal diffusivity, heat capacity, thermal expansion, elastic constants, fracture toughness, and dispersion and temperature variation of the refractive index are all characterized for this material. In addition, the magnitude of the thermal lensing induced in a flash-lamp-pumped laser rod of Cr:LiCAF is measured and compared with the results obtained for an alexandrite laser rod in the same laser head. We find that the thermal lensing of Cr:LiCAF is favorably small and that the thermomechanical properties are expected to be adequate for applications at low and medium average power.

Thermodynamic evidence for a structural transition of liquid Te in the supercooled region

Abstract: The specific heat, thermal expansion coefficient and compressibility of liquid Te have been measured to investigate the structural transition expected in the supercooled state. All these thermodynamic functions have extrema at 353+or-3 degrees C, a fact which provides clear evidence for the structural change of Te to the twofold liquid in the supercooled region. It is shown that Ehrenfest's relations are satisfied among the excess specific heat, isothermal compressibility and thermal expansion coefficient associated with the structural change.

Phase Transition and Thermal Expansion of MgSiO3 Perovskite

Abstract: Results from in situ x-ray diffraction experiments with a DIA-type cubic anvil apparatus (SAM 85) reveal that MgSiO3 perovskite transforms from the orthorhombic Pbnm symmetry to another perovskite-type structure above 600 kelvin (K) at pressures of 7.3 gigapascals; the apparent volume increase across the transition is 0.7%. Unit-cell volume increased linearly with temperature, both below (1.44 x 10-5 K–1) and above (1.55 x 10–5 K–1) the transition. These results indicate that the physical properties measured on the Pbnm phase should be used with great caution because they may not be applicable to the earth9s lower mantle. A density analysis based on the new data yields an iron content of 10.4 weight percent for a pyrolite composition under conditions corresponding to the lower mantle. All current equation-of-state data are compatible with constant chemical composition in the upper and lower mantle; thus, these data imply that a chemically layered mantle is unnecessary, and whole-mantle convection is possible.

Controlling the Crystal Orientations of Lead Titanate Thin Films

Abstract: Various substrates were investigated for use in crystal-oriented PbTiO3 thin films deposited by rf magnetron sputtering. In fabricating ferroelectric thin films with controlled crystal orientations, a close relationship was found between the thermal expansion coefficients of the films and substrates. Where the thermal expansion coefficient of the substrate was larger than that of the film, as in the case of a single-crystal MgO substrate, horizontal compressive mechanical stress along the plane of the film led to a c-axis-oriented film. Conversely, where the thermal expansion coefficient of the substrate was smaller than that of the film, as in the case of a quartz glass substrate, tensile stress in the film gave rise to an a-axis-oriented film. The Curie point of the film material determined the amount of mechanical stress present during cooling. Based on the above, new substrates of glass ceramics for use in c-axis-oriented films were developed.

Thermal stabilization of aluminium titanate and properties of aluminium titanate solid solutions

Abstract: Aluminium titanate has a near zero thermal expansion coefficient (α=0.8×10−6 °C−1) in the range 20 to 1000 °C, nevertheless it decomposes below 1200 °C.

Thermal expansion of SrZrO3 and BaZrO3 perovskites

Abstract: High-temperature X-ray diffraction studies of SrZrO3 and BaZrO3 perovskites have been carried out to 1200° C. The diffraction patterns are analyzed with Rietveld method so as to refine the unit cell dimensions. The volumetric thermal expansion coefficient are observed to be 2.98*10-5K-1 for orthorhombic Pbnm phase, 3.24*10-5K-1 for orthorhombic Cmcm phase, 3.75*10-5K-1 for tetragonal I4/mcm phase of SrZrO3 perovskite, and 2.06*10-5K-1 for cubic Pm3m phase of BaZrO3 perovskite, respectively. The linear thermal expansion coefficients of SrZrO3 perovskite show considerable anisotropy of α a >α c >α b for orthorhombic Pbnm phase, which reflect the decrease of distortion of the perovskite. It is demonstrated that thermal expansion of the centrosymmetrically distorted ABX3 perovskite can be empirically expressed as a combination of the changes of [B-X] bond length and tilting angle of BX6 octahedral framework. The octahedral tilting is considered to be the primary order parameter for the ferroelastic type of structural phase transitions in perovskite. Thermodynamically, the tilting induced volume change denotes the “excess volume” and the corresponding thermal expansion represents the “excess thermal expansion” for the lower symmetry phase with respect to its prototype of the cubic perovskite.

Anisotropic thermal expansion of densely cross-linked oriented polymer networks

Abstract: Densely cross-linked oriented polymer networks are made by in-situ photopolymerization of oriented liquid-crystalline diacrylates. Freestanding films that exhibited highly, anisotropic thermal expansion were prepared. The influence of the molecular structure and type and degree of orientation on the anisotrpic thermal expansion is described. The expansion coefficient of uniaxially oriented networks in the direction of the molecular orientation is slightly positive at temperatures below the glass transition of the networks and becomes negative as soon as this transition sets in the result is an effectively zero expansion over a wide temperature range. By introducing a molecular helix in, the network perpendicular to the film surface, a low thermal expansion is established in two directions in the plane of the film or coating.

Platinum—A thermal expansion reference material

Abstract: Platinum has a face-centered cubic crystal structure and does not have any phase changes between absolute zero and its melting point at 2045 K High-purity platinum can be readily obtained in rod and sheet form and thus provides an excellent thermal expansion standard Five investigations that used accurate and precise experimental techniques were used to establish analytical expressions for the coefficients of thermal expansion from 0 to 1800 K

Synthesis, sintering and thermal expansion of Ca1-xSrxZr4P6O24 : an ultra-low thermal expansion ceramic system

Abstract: Ca1-x Sr x Zr4P6O24 (O ⩽ × ⩽ 1.0) system which belongs to a new large family of low thermal expansion materials known as NZP or CTP, was synthesized by the solid state and the sol-gel methods. The conventional sol-gel method was modified by introducing a seeding step which resulted in significant improvement in the sintering characteristics and the microstructure of the sintered material. Sintering data were compared with those obtained by the powder mixing technique. Thermal expansion of the sintered samples was measured by classical dilatometry and by high-temperature X-ray diffractometry. It was found that CaZr4P6O24 (x= 0) and SrZr4P6O24 (x= 1) phases had opposite anisotropies in their respective axial thermal expansions. This behaviour led to the development of a crystalline solution composition of nearly zero expansion characteristic. Microstructures of the sintered specimens were examined by scanning electron microscopy.

Zn-al Matrix Composites - Investigation of the Thermal-expansion, Creep Resistance and Fracture-toughness

Abstract: Composites of Zn-A1 alloys (ZA8 and ZA27) reinforced by fibres of alumina, carbon or steel have been prepared by squeeze casting. Microstructural observations reveal the segregation of the zinc-rich phase around the fibres. The composites exhibit a greatly reduced creep rate in comparison with the matrix alloys. The thermal expansion coefficient is also significantly decreased. The impact toughness has been studied by Charpy tests.

Thermal mismatch dislocations produced by large particles in a strain-hardening matrix

Abstract: Silver chloride containing particles of irregular form of the order of 1-mu-m in diameter is used as a model material for particle-reinforced metal matrix composites (MMCs). Matrix dislocations due to the mismatch of the coefficients of thermal expansion of the two phases are made visible to transmission optical microscopy through bulk decoration performed at room temperature. The plastic zone around the particles takes two forms, similar to what is observed around the glass microspheres: (a) rows of coaxial prismatic dislocation loops punched into the matrix and (b) a plastic zone of irregular form containing partially resolved tangled dislocations. A relationship between the inclusion volume and the volume of the plastic zone around the inclusion-developed for the geometrically tractable problem of a sphere embedded in a strain-hardening matrix deforming by slip-is found to be valid for particles of irregular form as well, which are more representative of the reinforcement used in MMCs than spheres are.

Thermooptic Coefficients of Some Standard Reference Material Glasses

Abstract: The thermooptic coefficients, i.e., the change in refractive index with temperature (dn/dT), of four National Institute of Standards and Technology standard reference material (SRM) glasses have been measured over the range of 25° to 125°C. The thermooptic coefficients of all four glasses, NBS-710 (a soda-lime silicate), SRM-711 (a lead silicate), SRM-717 (a borosilicate), and SRM-739 (silica) are positive and range in value from 2 × 10−6/K to 9.8 × 10−6/K. The differences in the dn/dT of these glasses arise from differences in the coefficient of thermal expansion and the temperature coefficient of the electronic polarizability.

Thermal Expansion Anisotropy and Acoustic Emission of NaZr2P3O12 Family Ceramics

Abstract: Most members of the NaZr{sub 2}P{sub 3}O{sub 12} (NZP) family possess low, near zero, overall thermal expansion coefficients. However, they also exhibit anisotropy of axial thermal expansion. Some compounds have opposite anisotropy; for example, the a parameter of CaZr{sub 4}P{sub 6}O{sub 24} contracts on heating and that of SrZr{sub 4}P{sub 6}O{sub 24} expands, while the c parameter expands for the Ca compound and contracts for the Sr compound. The anisotropy of the axial thermal expansion of these materials is believed to induce microcracking. The acoustic emission method was employed here to detect microcracking in ceramics due to the axial thermal expansion anisotropy. Acoustic signals were observed during cooling of the Ca and Sr compounds from 500 {degrees} C, and Na and K compounds from 600 {degrees} C. On the other hand, no acoustic emission signal is detected in Ca{sub 0.5}Sr{sub 0.5}Zr{sub 4}P{sub 6}O{sub 24} ceramics, in which the lattice parameters a and c remain nearly unchanged in the temperature range of room temperature to 500 {degrees}C. Thus, a direct correlation between microcracking of ceramics and their anisotropic axial thermal expansion coefficients was established by employing acoustic emission monitoring techniques.

Chemistry and structure of glass-ceramic materials for high precision optical applications

Abstract: Li 2 O–Al 2 O 3 –SiO 2 -based glass-ceramics are materials that are used in large volumes in applications in which low thermal expansion is the property of prime importance. Although these glass-ceramics are low-expansion materials in a broad sense, the very low-expansion characteristic for which they are famous is achieved only in certain temperature ranges. The deviation of the coefficient of thermal expansion from the ideal zero-value and the temperature ranges in which close to zero-values are achieved are dependent on the chemical composition of the glass-ceramic base glass and the ceramization conditions. Some principal rules by which the desired expansion characteristics can be adjusted are illustrated. For materials that are used in precision optical applications representative data of commercially available products are given. These data include the expansion characteristics as well as homogeneity. Recently the development of the microstructure in glass-ceramics with Zerodur-type composition has been further elucidated. It has been shown that phase separation precedes nucleation. In addition, some specially developed microstructures suggest the existence of an epitaxial relationship between the nuclei and the crystalline phase of the glass-ceramic. Examples of applications of Zerodur-type glass-ceramics together with some of the requirements for these applications are discussed.

Model for stress and volume changes of a thin film on a substrate upon annealing: Application to amorphous Mo/Si multilayers

Abstract: A model is given for the stress change in a thin film on a thick substrate during annealing. It takes into account temperature changes, volume changes, viscous flow, and anelastic relaxation occurring in the film. The stress change in amorphous Mo/Si multilayer films deposited on Si single-crystal substrates was obtained from in situ wafer-curvature measurements during annealing at temperatures below the glass temperature. The thickness change and the interdiffusion coefficient were obtained from the position and the intensity of the first-order multilayer x-ray reflection. The unconstrained volume change was derived from the measured stress and thickness changes. The free-volume model for amorphous solids has been used to interpret the interdiffusion in and the volume change of the amorphous Mo/Si multilayers. The stress change as it occurred during isothermal annealing was explained by free-volume annihilation, viscous flow, and anelastic relaxation. If anisotropy of the volume change is accepted, the stress change could also be described with free-volume annihilation and viscous flow alone. The product of the experimentally observed viscosity and diffusion coefficient for amorphous Mo/Si multilayers was compared to the value expected from the free-volume-model-based equivalent of the Stokes-Einstein relation.

Thermal expansion behavior of particulate-filled composites I: Single reinforcing phase

Abstract: The effect of reinforcement geometry on the thermal expansion behavior of particulate-filled bis-maleimide matrix composites has been examined both experimentally and theoretically. To clarify the geometrical effect, a wide range of reinforcement shapes, from short fiber to flake, was used. The comparison was made between experimentally obtained thermal expansion coefficients and those theoretically predicted by the use of Eshelby's equivalent inclusion method. The predicted values were shown to agree reasonably well with the experimental values. An attempt was then made to obtain the relation between the reinforcement geometry and processability condition. It was found that spherical-particle-filled composites exhibited superior thermal expansion behavior compared with short-fiber- or flake-reinforced composites from the viewpoint of processability, including void-free formation. In part II of this paper the effect of multi-reinforcing phases on the thermal expansion behavior of a composite is studied and the results of the following paper are compared with those of the present paper.

Isothermal Compressibility and Thermodynamics of Structural Transitions in the Liquid Se-Te System

Abstract: Sound velocity, υ s , has been measured to examine the thermodynamics of structural transitions in the liquid Se-Te system. The isothermal compressibility, κ T , deduced from υ s together with the thermal expansion coefficient, α P , the constant pressure specific heat, C P , and the density shows a broad maximum when plotted as a function of temperature or concentration. It has been shown that κ T is significantly enhanced by the structural change. Evidence has been presented that the Ehrenfest's relations are satisfied among the excess parts of κ T , α P and C P associated with the structural change.