Showing papers on "Thermal expansion published in 1970"
TL;DR: Composite materials macroscopic thermoelastic properties relationships to constituents properties, discussing effective thermal expansion coefficients and specific heats are discussed in this paper, where the authors also discuss the effect of specific heats.
592 citations
TL;DR: The results of theoretical estimates for several thermal and thermoelastic constants of macroscopically isotropic composite materials are given in this paper, including elastic constants, thermal expansion coefficients, heat capacities (at constant volume and constant pressure), thermal conductivity, and related constants.
Abstract: The results of theoretical estimates are given for several thermal and thermoelastic constants of macroscopically isotropic composite materials. The composites considered consist of random mixtures of N isotropic constituents, at least ( N — 1) of which are presumed to be distributed in a particulate fashion, with the particles roughly spherical in shape. The results are based on "self-consistent" calcula tions, details of which are given in appendices.Equations (some of which are old, but are repeated for con venience) are given for the following quantities: elastic constants, thermal expansion coefficients, heat capacities (at constant volume and constant pressure), thermal conductivity, and, finally, Gruneisen and related constants.
253 citations
TL;DR: In this paper, the coefficients of thermal expansion of rutile and anatase were determined from 30° to 650°C and from 28° to 712°C, respectively, using a high-temperature powder camera.
Abstract: Lattice parameters of rutile and anatase were determined from 30° to 650°C and from 28° to 712°C, respectively, using a high-temperature powder camera These data were used to evaluate the coefficients of thermal expansion of rutile and anatase The temperature dependence of the coefficients, α11 and α1, parallel and perpendicular to the principal axis, respectively, are represented by the equations:
Rutile:
Anatase:
The relative magnitudes of the coefficients of thermal expansion of these polymorphs are explained in terms of the interionic distances
162 citations
TL;DR: The lattice parameter of AlAs has been very accurately measured as a function of temperature between 15° and 840°C, and the coefficient of thermal expansion has been determined as mentioned in this paper.
Abstract: The lattice parameter of AlAs has been very accurately measured as a function of temperature between 15° and 840°C, and the coefficient of thermal expansion has been determined. The lattice parameter at 0°C is 5.6605±0.0005 A and the coefficient of thermal expansion is (5.20±0.05) ×10−6/°C. A comparison is made to GaAs which indicates that there is a perfect lattice match at about 900°C and 0.14% lattice mismatch at room temperature.
127 citations
TL;DR: In this paper, the thermal expansion behavior of two duplex systems, lead-fused silica and aluminum-silicon, has been investigated experimentally above and below room temperature, and the role of microplastic yielding in high-inclusion-content composites is discussed.
Abstract: The thermal expansion behavior of the two duplex systems, lead‐fused silica and aluminum‐silicon, has been investigated experimentally above and below room temperature. The microstructure in the first case consisted of fused silica particles in a lead matrix, while silicon constituted the dispersed phase in the second. The expansion coefficients always fell below those predicted by the simple rule of mixtures. A model is proposed and a new formula for the calculation of the thermal expansion coefficient of duplex materials is derived. The new formula fits experimental results better than Turner's formula. The role of microplastic yielding in high‐inclusion‐content composites is discussed.
122 citations
TL;DR: In this article, the far infra-red absorption and Raman scattering were measured in vitreous silica, and the results were correlated with new measurements of ultrasonic absorption and thermal expansion in the same material.
Abstract: In vitreous silica, which has been compacted by irradiation with fast neutrons, the ultrasonic absorption, the excess heat capacity and the magnitude of the negative coefficient of thermal expansion decrease. In this work we report measurements of the far infra-red absorption and Raman scattering in such neutron compacted silica. These results are correlated with new measurements of ultrasonic absorption and thermal expansion in the same material. The results are consistent with an interpretation based on a decrease in the number of low-frequency modes.
94 citations
TL;DR: In this paper, the coefficients of thermal expansion of NaCl, KCl and CsBr were determined accurately at different temperatures using a diffractometer, Geiger counter, chart recorder and a specially designed furnace.
Abstract: The coefficients of thermal expansion of NaCl, KCl and CsBr are determined accurately at different temperatures using a diffractometer, Geiger counter, chart recorder and a specially designed furnace. Equations are given for the variation of the lattice constants with temperature. The temperature dependence of the thermal expansion at high temperatures is shown to be related to the concentration of thermally generated Schottky defects. The energies of formation of Schottky pairs in the three halides are estimated and are found to be consistent with those deduced from ionic conductivity studies. The reduced parameters α/(α)M/2 and T/TM give a common curve for all the halides, TM being the melting point and (α)M/2 the value of α at T = ½ TM. The curve is a straight line in the limits ~ 0.30 < T/TM < ~ 0.65 and is found to deviate considerably at higher temperatures. Assuming that the deviation is due to defects, the energies of formation of Schottky defects for the varies halides of Li, Na, K, Rb and Cs are estimated and found to agree excellently with the experimental and theoretical values.
89 citations
TL;DR: In this paper, an equation for predicting the thermal expansion coefficient of dilute binary composites is presented treating the dispersed particles as elastic spheres and taking into consideration the physical interactions between the dispersed phase and the matrix.
Abstract: An equation for predicting the thermal expansion coefficient of dilute binary composites is presented treating the dispersed particles as elastic spheres and taking into consideration the physical interactions between the dispersed phase and the matrix. Application of this particular equation to a variety of systems such as ceramic‐glass, glass‐metal, metal‐metal, and organic‐metal, is discussed, as well as the application of other equations to other material systems extant in the literature.
75 citations
TL;DR: In this paper, the isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed and the spin system is described by the Ising model with an exchange coupling depending on lattice spacing.
Abstract: The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearTc and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.
70 citations
01 Dec 1970
TL;DR: In this paper, the phase composition of pore water in three types of rock subjected to temperature below OC was explored by a variety of techniques, including differential thermal analysis, which yielded relationships between unfrozen water content and temperature.
Abstract: : The phase composition of pore water in three types of rock subjected to temperature below OC was explored by a variety of techniques. Freezing point depression was measured as a function of water content by differential thermal analysis, the results yielding relationships between unfrozen water content and temperature. In an effort to avoid the practical difficulties involved in differential thermal analysis, attempts were made to determine freezing characteristics indirectly by air penetration and mercury penetration techniques applied at ordinary room temperatures. Electrical conductivity measurements were made as a function of temperature down to -195C in an attempt to obtain information on characteristics of interfacial water films at low temperatures. Thermal strain was measured as a function of temperature in order to detect direct mechanical effects associated with phase changes, chiefly strain discontinuities brought about by volume changes in the pore water during rapid freezing and thawing. Finally, isothermal compressibility whether the rock underwent step changes in volumetric strain at pressures corresponding to those of the phase boundaries for ice polymorphs.
67 citations
TL;DR: In this article, a study of glasses containing 50 to 75 mol% SiO2 and up to 35 mol% ZnO was performed using thermal expansion, density, molar volume, refractive index, and molar refractivity.
Abstract: Glasses containing 50 to 75 mol% SiO2 and up to 35 mol% ZnO were studied using thermal expansion, density, molar volume, refractive index, molar refractivity, internal friction, and infrared absorption data. Increasing the zinc oxide content in the glasses decreased the thermal expansion and increased the density, refractive index, and the activation energy for the alkali-ion diffusion internal friction peak. Infrared absorption from 1500 to 70 cm-1 indicated the presence of both six and four oxygen coordination for the zinc cation.
TL;DR: The effect of pressure on the lattice parameters, hence the molar volume, of the hexagonal close-packed phase of rhenium (Re) was determined at room temperature up to 350 kbar by means of X-ray diffraction employing a diamond-anvil high-pressure cell as discussed by the authors.
TL;DR: In this article, the degree of long range order in the γ′-phase of the nickel-aluminum system was determined as a function of temperature by means of X-rays.
Abstract: The degree of long range order in the γ′-phase of the nickel–aluminum system was determined as a function of temperature by means of X-rays. The measurements were carried out on {h00} single crystals, using a high-temperature vacuum X-ray diffractometer. Two compositions were investigated: stoichiometric Ni3Al and an off-stoichiometric nickel-rich alloy. Complete long-range order was present to within 65°C of the melting point, the highest temperature measured. Line breadth measurements indicated a large, temperature independent anti-phase domain size. From the intensity variation of the 400 reflection with temperature, a Debye temperature of 360°K was deduced. The linear coefficient of thermal expansion between 25 and 800°C was found to be 15 x 10−6 per °C.
TL;DR: In this paper, the coefficients of linear thermal expansion and of isothermal compressibility have been measured for solid nitrogen in the temperature intervals from 4.2° to 40° K and 8°-40° K, respectively.
Abstract: The coefficients of linear thermal expansion and of isothermal compressibility have been measured for solid nitrogen in the temperature intervals from 4.2° to 40° K and 8° to 40° K, respectively. Length changes of the sample were detected with a resolution of 10 −9 cm using a dilatometer of the three-terminal capacitor variety contained inside a pressure vessel. Apparatus and experimental technique are described in detail. The thermal expansion and compressibility of α-N2 increase rapidly with increasing temperature above 20° K, and in the former case the length increase is exponential in 1/T above 24° K. A reproducible value for the volume discontinuity at the α-β crystallographic transformation at 35.6° K was obtained only if many hours were taken to effect the transformation. The data are discussed in relation to recent experimental and theoretical information obtained from studies of Raman and infrared spectra, nuclear quadrupole resonance, and specific heat. The anomalous thermal expansion is attributed to excited librational and translational states of large amplitude and appreciable anharmonic content. The adiabatic compressibility calculated from the experimental data agrees well with published values from sound velocity experiments. The Gruneisen parameter of α-N 2 is found to be strongly temperature dependent.
TL;DR: In this article, the temperature variation of the lattice parameters of KK2PO4 at various temperatures between 23.4 and 169.3 °C have been measured by using an accurate X-ray method recently developed by the authors.
Abstract: The lattice parameters of KH2PO4 at various temperatures between 23.4 and —169.3 °C have been measured by using an accurate X-ray method recently developed by the authors. Specifical emphasis was laid on their temperature dependence near the ferroelectric Curie point. Small but distinct thermal hysteresis was found to occur at the onset of the para-electric-ferroelectric phase transformation. The results of temperature variation of the lattice parameters are in fairly good agreement with those of other authors except in the vicinity of the Curie point. It is noticeable that a pure shear x in a plane perpendicular to the ferroelectric axis, which directly reflects the spontaneous polarization, begins to decrease more rapidly than Ps as temperature approaches the Curie point.
TL;DR: In this paper, a generalized Gruneisen theory was used in the quasiharmonic approximation to calculate the high and low-temperature limits for the two coefficients of linear thermal expansion.
Abstract: By use of the pulse‐echo technique, the hydrostatic pressure and uniaxial stress dependence of the ultrasonic wave velocities in single‐crystal Al2O3 have been measured, and the values of the 14 independent third‐order elastic stiffnesses were determined using a least‐squares fit to 31 different experimental measurements. A generalized Gruneisen theory was used in the quasiharmonic approximation to calculate the high‐ and low‐temperature limits for the two coefficients of linear thermal expansion. A numerical integration over 171 directions in the crystal was used for these calculations. The low‐temperature limit does not compare well with the available thermal data; however, measurements of thermal expansion below 100°K, which are needed for a realistic comparison, are not presently available.
TL;DR: The effect of substitution of one isotope for another in the LiH molecule has been investigated between − 196° and 240°C as mentioned in this paper, where the lighter element is the one undergoing substitution.
TL;DR: In this paper, a new theory of the principal thermal expansion coefficients of a graphite crystal was derived using the lattice dynamics obtained by Komatsu, and the theory was compared with new data on the low temperature thermal expansion coefficient of very highly oriented pyrolytic graphite and high temperature X-ray data.
TL;DR: The forced linear magnetostriction coefficient, h, of Invar has been measured parallel and perpendicular to the applied magnetic field using a capacitor dilatometer in the temperature range from 1 to 120 K and for fields from about 5 to 55 kOe as mentioned in this paper.
TL;DR: The strain dependence of the resistivity of thin epitaxial films of silver on mica has been measured for film thicknesses between 300 and 1400 A, in the temperature range 200°-350°K as mentioned in this paper.
Abstract: The strain dependence of the resistance of thin epitaxial films of silver on mica has been measured for film thicknesses between 300 and 1400 A, in the temperature range 200°–350°K. Analysis of the data includes geometrical and strain corrections, and considers the possible deviation from bulk of both the mechanical and electrical properties of the films. The films show a strain dependence of the resistivity equal to that of bulk silver, with deviations in individual films up to 30%. The effect is temperature independent, and shows no size effect. It is too small to account for the observed temperature variation of the film resistivities, which is smaller than in bulk, on the basis of strain due to the mismatch of thermal expansion of films and substrate.
TL;DR: In this paper, the thermal expansion behavior of unidirectional, balanced angle-ply, and complex laminated graphite-epoxy composites is studied, and the expansion coefficient is determined as a function of fiber orientation and is found to follow the simple equation αθ=αL cos2θ+αT sin 2θ.
Abstract: The thermal expansion behavior of unidirectional, balanced angle‐ply, and complex laminated graphite‐epoxy composites, is studied. The expansion coefficient of the unidirectional composites is determined as a function of fiber orientation and is found to follow the simple equation αθ=αL cos2θ+αT sin2θ. Results obtained on angle‐ply composites are in agreement with the predictions based on Halpin and Pagano's analysis. The applicability of the same approach to a panel of more complex construction is discussed. Hysteresis effects, observed in this panel, may be caused by interlayer stress relaxation.
TL;DR: The lattice parameters of NH4Br have been measured as a function of temperature from 5 to 150°K, a range which includes the region of the transition between cubic and tetragonal ordered phases as discussed by the authors.
Abstract: The lattice parameters of NH4Br have been measured as a function of temperature from 5 to 150°K, a range which includes the region of the transition between cubic and tetragonal ordered phases. The low-temperature CsCl-type phase exhibits normal thermal expansion up to ~ 108°K on warming, while the tetragonal diffraction pattern persists down to ~ 80°K on cooling. The present data are combined with previous measurements between 150 and 300°K to yield an overall picture of the variations associated with changes in ordering.
TL;DR: In this paper, temperature derivatives of specific volume were derived; it was estimated that they are accurate to better than 3 × 10−6 (cm3/g°C) and an interpolation formula was given.
Patent•
02 Mar 1970
TL;DR: In this article, a process for dispersing fibers in a refractory metal compound phase comprising coating fibers, e.g. graphite fibers, with a mixture of a refractive metal compound of extremely small particle size, i.e., NbC of 0.02 micron size, and sufficient binder, e.,g. polymerizable furfuryl alcohol and maleic anhydride, to form a slurry, forming the coated fibers to the desired shape and heating the formed coated fibers at high temperatures in the range of about 40% to about
Abstract: Process for dispersing fibers in a refractory metal compound phase comprising coating fibers, e.g. graphite fibers, with a mixture of a refractory metal compound of extremely small particle size, e.g. NbC of 0.02 micron size, and sufficient binder, e.g. polymerizable furfuryl alcohol and maleic anhydride, to form a slurry, forming the coated fibers to the desired shape and heating the formed coated fibers at high temperatures in the range of about 40% to about 98% of the melting point of the refractory compound, e.g. about 3,000 DEG C, to form a composite. The article produced by the above process is characterized by low thermal expansion values.
TL;DR: In this article, the lattice parameters of two garnet inclusions in diamonds have been measured by X rays as functions of temperature, with the inclusions first in situ and then freed from their hosts.
Abstract: The lattice parameters of two garnet inclusions in diamonds have been measured by X rays as functions of temperature, with the inclusions first in situ and then freed from their hosts. The included garnets have smaller lattice parameters than the free garnets and must therefore be under pressure. From an equation of state for garnet calculated from thermoelastic data, the pressures in situ are found to vary from 2 to 15 kbar for one garnet (D1) and from 2 to 7 kbar for the other (D2) as the temperature is increased. A model is proposed which assumes that, under uniform isotropic stress and temperature, diamond forms around garnets and behaves purely elastically thereafter. The model is used to calculate theoretical values for the difference in lattice parameters of free and included garnet; it gives the external pressure that removes shear stress in the host at each temperature, a curve that should pass through the temperature and the pressure of formation of the host. For diamond D1, whose behavior agreed with the model, this curve crosses the thermodynamic diamond-graphite equilibrium line at about 500°C; because some nonelastic processes may have occurred, the curve is proposed merely as a lower bound to pressures of formation of the diamond. The method cannot be applied to D2: below 400°C the thermal expansion of the included garnet was greater than that predicted by the model, and the curve obtained from the high-temperature data lies wholly in the region where graphite is stable. It is concluded that in D2 pressure has probably been released by a nonelastic mechanism during some stage of the diamond's history.
TL;DR: In this paper, the temperature dependence of the coefficient of thermal expansion of a number of ionic and partially ionic crystals is calculated using a modified rigid ion model and a shell model of lattice dynamics.
Abstract: The temperature dependence of the coefficient of thermal expansion of a number of ionic and partially ionic crystals is calculated using a modified rigid ion model and a shell model of lattice dynamics. The model parameters are obtained from long‐wavelength optic mode frequencies, elastic constants and the high‐and low‐frequency dielectric constants. Using the pressure derivatives of these quantities, mode‐Gruneisen parameters as functions of wave vectors are next obtained. Thermal expansion coefficient is calculated from the Gruneisen parameters in the quasiharmonic approximation. The calculated values compare well with experimental data.
TL;DR: In this article, the lattice parameters, thermal expansion coefficients, and Gruneisen parameters of tungsten were determined by an x-ray method in the temperature range of 180 −40 K without the use of liquid gases.
Abstract: Lattice parameters, thermal expansion coefficients, and Gruneisen parameters of tungsten are determined by an x‐ray method in the temperature range of 180–40 K without the use of liquid gases. Lattice parameters are expressed as a function of temperature. Thermal‐expansion coefficients decrease with temperature and show no anomaly in contrast to a hypothesis proposed by Featherston and Neighbours. Gruneisen parameters γ are decreasing with temperature in accordance with the theoretical predictions.
TL;DR: In this paper, the temperature dependence of the intensities of the Bragg peaks in the intensity plots gives values for the Debye temperature as a function of primary electron energy, in order to deduce the thermal expansion coefficient for the surface layers normal to the surface.
Abstract: Measurements of the temperature dependences of the intensities and energies of LEED peaks in the intensity plots for the specular beam from a (111) copper surface are reported. An analysis is made, for the peak shifts as a function of temperature, in order to attempt to deduce the thermal expansion coefficient for the surface layers normal to the surface. Several additional effects are accounted for but the shifts appear to be dominated by an unknown process and no deductions are drawn concerning the expansion coefficient. The temperature dependence of the intensities of the Bragg peaks in the intensity plots give values for the Debye temperature as a function of primary electron energy. The results indicate that this is not strongly dependent on diffraction condition. From the Debye temperature, the ratio of the mean square vibrational amplitude of the surface atoms perpendicular to the surface to that for the bulk is found to be 1.9 ± 0.1, in agreement with theoretical predictions.
TL;DR: In this paper, the thermodynamics of thermal expansion and the related Gruneisen function γ(T, V) are discussed first for cubic and isotropic solids, and the extension of the theory to noncubic and non-ionic solids is summarized, the strongly anisotropic example of zinc being used to illustrate the roles played by anisotropy in the elasticity and in the gruneisen tensor.
Abstract: The thermodynamics of thermal expansion and of the related Gruneisen function γ(T, V) is discussed first for cubic and isotropic solids. Vibrational effects are treated in the quasiharmonic approximation. For central force models two effects are distinguished‐that of the anharmonicity of the pair potential, normally contributing positively to the expansion, and that of the bond ``tensions,'' contributing negatively. The extension of the theory to noncubic solids is summarized, the strongly anisotropic example of zinc being used to illustrate the roles played by anisotropy in the elasticity and in the Gruneisen tensor. Recent work on central force lattice models, both ionic and nonionic, is reviewed. For ``internal expansion,'' in which the disposition of atoms within a unit cell varies with temperature, it is convenient to treat both internal and external strains on the same footing.
TL;DR: In this paper, a method for experimentally measuring rock response to induced thermal stresses from cyclic thermal expansion of the rock surface using strain-gauge technique is developed, which provides a new insight on the feasibility of fragmenting rock with thermal energy in vacuum environment.
Abstract: Rock is a complex composite solid generally consisting of heterogeneous granular aggregates of polycrystalline mineral constituents which are characteristically anisotropic. Thermal stresses induced during the heating or cooling of rocks cause fracture and fragmentation. Thermal expansion is a significant parameter for the creation of thermal stresses to fragment rocks by heat. A method for experimentally measuring rock response to induced thermal stresses from cyclic thermal expansion of the rock surface is developed using strain‐gauge technique. Rock fracture caused by internal thermal stresses during heating and cooling in atmosphere and vacuum environment is examined. The response of rock material to induced thermal stresses is shown to be independent of reduced environmental pressure down to 10−5 Torr. The results of reduced environmental pressure on thermal expansion behavior of some simulated lunar rocks are presented. These results provide a new insight on the feasibility of fragmenting rock with thermal energy in vacuum environment.