Showing papers on "Thermal expansion published in 1969"

Thermal expansion and structure in water and aqueous solutions

Abstract: The thermodynamic equation (∂CP/∂P)T = −T(∂2V/∂T2)P is used as a basis for relating thermal expansion to structure (at several temperatures and pressures) of water and "normal" liquids. Similar con...

Lattice parameters, densities, expansion coefficients and perfection of structure of Cu and of Cu–In α phase

Abstract: Spectroscopically pure Cu has a lattice parameter a25 = 3.61491 A (corrected for refraction), and a thermal expansion coefficient α = 14.87 × 10−6°C−1 between 15 and 55°C. The measured density d25 is 8.9314 ± 0.0002 g.cm−3 in agreement with the calculated value dx = 8.9316. In the α solid solution region additions of In increase the lattice parameter of Cu according to ax = 3.6149 + 0.0091x up to x = 10.4 (x = atomic % In, balance Cu). The thermal expansion coefficients between 15 and 65°C of the homogeneous alloys increase from 14.87 (pure Cu) to 17.2 × 10−6°C−1 at the solid solubility limit (10.4 atomic % In, quenched from 650°C). With the increase of In content the experimental densities become increasingly lower than the calculated ones because of void formation. Upon cold rolling the voids close and the differences disappear. The α phase represents a substitutional solid solution without structural defects. Alloys quenched from the liquid state do not show any microporosity; the voids appear after homogenization at 800°C. Micropore formation is explained by differential shrinkage of the various crystalline fractions formed during solidification, giving rise to internal stresses in the solid alloy. Relief of stresses results in vacancies or micropores, which coalesce into voids upon heat treatment.

Thermal Expansion of Silicon and Zinc Oxide (I)

Abstract: Coefficients of thermal expansion α‖c and α ⊥ c between 4 and 800°K have been measured for zinc oxide using an interferometric and a capacitance method. Thermal properties of wurtzite lattices (two coefficients of thermal expansion and a pyroelectric constant) can be described in terms of three thermal equations of state. Two mechanical and one electrical Gruneisen parameters are defined and their temperature dependence is calculated from experimental results. The high- and low-temperature limits of the Gruneisen parameters are compared with results obtained in other experiments. The values predicted from a rigid ion model are discussed.

Axial thermal expansion of ZrO2 and HfO2 in the range room temperature to 1400°C

Abstract: The axial thermal expansion of monoclinic and tetragonal ZrO2 and of monoclinic HfO2 was studied over the temperature range from room temperature to 1400 °C. The linear thermal expansion coefficients were calculated. Thermal expansion along (x 106 per °C) a = 10.31 monoclinic ZrO2, 11.60 tetragonal ZrO2, 9.34 monoclinic HfO2; b = 1.35 monoclinic ZrO2, – tetragonal ZrO2, 2.98 monoclinic HfO2; c = 14.68 monoclinic ZrO2, 16.08 tetragonal ZrO2, 13.10 monoclinic HfO2. Some aspects of the present study, such as anisotropy of thermal expansion and a pretransformation vibrational anomaly, are discussed briefly.

Thermal Expansion of Lithium Tantalate and Lithium Niobate Single Crystals

Abstract: The principal thermal expansion coefficients of single crystals of LiTaO3, LiNbO3 and α quartz (for reference purposes) have been determined by an x‐ray diffraction technique in the temperature range 25°–500°C. All three materials crystallize in the trigonal system, the first two in class 3m and the last one in class 32, and are characterized by only two principal expansion coefficients, parallel and normal to the c or Z axis. The Bragg x‐ray angle data were fitted to suitable polynomials in the temperature deviations from an arbitrary reference of 25°C, and the expansion coefficients up to second order calculated from the coefficients of these polynomials. The Z‐axis expansion of LiTaO3 showed a definite maximum at about 250°C. Similar behavior was indicated in the Z‐axis expansion of LiNbO3, but at a much higher temperature (at the high extreme of the measurement range). The expansion of all three crystals normal to the Z axis was quite regular.

Concentration Fluctuations and Anomalous Properties of the Invar Alloy

Abstract: It is pointed out that concentration fluctuations affect the magnetic properties of Fe-Ni Invar alloys, which behaves as collection of cells containing equally 60 atoms whose mean concentrations are different from cell to cell. The fluctuation can be expressed by a Gaussian distribution law when the proportion of the number of the cells having the same concentration is plotted against the mean concentration. The saturation magnetization vs. nickel concentration relation, the deviation of the magnetic saturation moment σ vs temperature T curves form the standard Brillouin function, the small thermal expansion coefficient around room temperature and other anomalous physical properties of the alloy were accounted for on the basis of the present model of the concentration fluctuations.

Moment-Induced Magnetic Scattering and Magnetovolume Effect in Fe65(Ni1-xMnx)35 Alloys

Abstract: The temperature dependences of electrical resistivity and thermal expansion were measured for face-centered cubic Fe 65 (Ni 1- x Mn x ) 35 ternary alloys. The electrical resistivity of ferromagnetic alloys ( x 0.3) increases below the Neel temperature and shows a resistance minimum. These behaviors are explained in terms of the magnetic scattering by induced moments below the magnetic ordering temperature. The expansion of volume due to the magnetic ordering was observed in both ferro- and antiferromagnetic alloys. To explain the volume expansion by the magnetic ordering, a new mechanism of magnetovolume effect based on the change of cohesive energy due to the spin polarization in 3 d band is proposed.

Experimental Study of the Equation of State of Liquid Argon

Abstract: The density of liquid argon has been measured at 10 temperatures from 100.9° to 143.1°K and at pressures up to 680 atm. The results have been expressed as an equation of state in the form of a double Chebyshev expansion. This equation has been used to estimate, at regular intervals of temperature and pressure, the following properties: molar volume, isothermal compressibility, coefficient of thermal expansion, thermal pressure coefficient, and configurational internal energy. Comparison is made between the present results and previous work on liquid argon, both at the saturation vapor pressure and at higher pressures.

Theory of Melting Based on Lattice Instability

Abstract: A lattice instability which may be related to melting is proposed as follows: The energy of thermal vibration cannot exceed a critical value, because of anharmonicity, and the lattice may be unstable above the temperature corresponding to this critical energy. The effect of anharmonicity arises from the effective increase in interatomic distances due to the lattice vibrations. This increase is called "vibrational elongation." The critical temperature of instability is written in terms of atomic volume, elastic constants, and the Gr\"uneisen parameter under the assumption of a linear dispersion relation, and is shown to be in fairly good agreement with the observed melting point. The Lindemann formula and the empirical law that the product of thermal expansivity and melting point is approximately constant are examined on the basis of the present theory. The thermal expansion and the elastic properties predicted by the theory up to the melting point are qualitatively consistent with the observed values.

Thermal Expansion of Fused Quartz

Abstract: Results of a series of observations on the linear thermal expansion coefficient of transparent fused quartz are given in the temperature range of 300 °C to 1065°C, with particular attention being given to the region of 1000 °C. The experiments are carried out by the comparator method. The ten specimens, which could conveniently be classified into three types, were supplied by the Thermal Syndicate Ltd., England and by three manufacturers, the Toshiba Ceramics Ltd., the Nippon Sekiei Garasu Ltd. and the Kimmon Manufacturing Ltd., in Japan. Different value is obtained in thermal expansion of the specimens each type for which an empirical formula is given.

Effect of induced thermal stresses on the coefficients of thermal expansion and densities of filled polymers

Abstract: It is demonstrated that in a filled polymer the thermal stresses resulting from the difference in the thermal expansion coefficients of the filler and the polymer have significant effect on the apparent coefficient of thermal expansion of the composite. A model is constructed to aid the thermal stress analysis, and the results are found to agree well with the experimental data obtained from other sources. An expression for the apparent densities of filled polymers is also obtained but the agreement between the present prediction with an existing test result is found to be only qualitative.

Low temperature thermal expansion measurements on optical materials.

Abstract: A three-terminal capacitance type dilatometer has been developed for investigating the thermal expansion of optical materials at low temperatures. The method is applicable when only small sample lengths (13 mm or less) are available. The thermal expansion coefficients of six polycrystalline materials (the Irtrans) and of one nonoxide glass have been determined in the range from room temperature down to about 60 K. Minute changes of the length of a sample produce a change of the spacing of a parallel plate capacitor with guard ring; the resulting change of capacitance is measured on a highly sensitive bridge. The expansion coefficients are then determined by relating the change of capacitance to the change of dimensions of the sample.

Magnetovoloume Effects of Itinerant Electron Ferromagnets. I. Thermal Expansion Anomaly of the Invar Alloy

Abstract: The spontaneous volume magnetostriction of metallic ferromagnets is discussed based on the band theory. Dependences on lattice parameter of the band width and of the molecular field coefficient are taken into account. The difference between the lattice parameters in the ferromagnetic and paramagnetic states at 0°K is expressed in terms of the difference between the energies in the ferromagnetic and paramagnetic states. It is understood qualitatively why the absolute value of negative spontaneous volume magnetostriction ( e.g. in Ni) is generally small while that of positive one ( e.g. in Invar) is sometimes large. By assuming a simple but reasonable density of states curve for fcc Fe–Ni alloys the spontaneous volume magnetostriction of the alloys is calculated. The calculated value for Invar alloy is seven times larger than that for Ni metal in absolute value; the agreement with experimental results is satisfying.

Thermal Expansion of the Polyethylene Unit Cell

Abstract: The 719–730‐cm−1 doublet in the infrared spectrum of polyethylene (PE) is known to shift to higher frequencies with decreasing temperature. In this work we have measured these peak positions as a function of temperature down to 10°K for three bulk polyethylene samples of three different degrees of crystallinity, as well as solution‐grown single polyethylene crystals both treated and untreated by fuming nitric acid. All these samples were found to behave similarly. X‐ray diffraction measurements were performed for PE single crystals at four temperatures: 10°, 80°, 20°, and 300°K. The unit cell dimensions of polyethylene at these temperatures were found to correlate linearly with the infrared peak positions. On the basis of this correlation, a specific volume–temperature plot was made for the PE unit cell, from which thermal expansion coefficients were obtained as a function of temperature. The latter data can be fitted by the Debye–Gruneisen equation. Values of Gruneisen parameters were estimated and were found to increase monotonically with decreasing temperature.

The Thermal Expansion of Axial Metals

Abstract: The thermal expansion of axial metals is surveyed with particular reference to recent very low temperature data for zinc, cadmium, magnesium, β-tin, indium, bismuth and antimony. For a given solid, the independent thermal expansion coefficients α⊥ and α‖ are conveniently compared at low temperatures by plotting α⊥/T 3 and α‖/T 3 against T. The plots show clearly how contraction in one principal symmetry direction ensues from rapid expansion in the other direction. The Gruneisen functions γ⊥ and γ‖ are discussed for each solid using data from lattice-dynamical models and neutron-diffraction measurements. They show how features of the individual thermal expansions arise from a combination of vibrational, elastic and electronic effects. For these solids and for zirconium, titanium, yttrium and thallium the larger of γ⊥ and γ‖ at high temperatures is that referring to strains in the direction of the stronger forces (judged from the axial ratio). At lower temperatures the inequality reverses, except f...

Determination of the Firing Temperature of Ancient Ceramics by Measurement of Thermal Expansion

Abstract: THE thermal expansion method for determining firing temperatures1–3 is based on the assumption that, when clays are fired, shrinkage occurs as a result of various sintering processes such as vitrification. Consequently when a clay ceramic is heated up from room temperature (see Fig. 1) it typically exhibits a reversible expansion, characteristic of its mineralogical composition, until temperatures comparable with the original firing temperature are reached. With continued increase in temperature the ceramic begins to contract because superimposed on the reversible expansion there is an irreversible shrinkage associated with resumption of sintering (that is, the firing of the ceramic is being continued beyond the point reached during the original firing). The temperature (Ta) at which a net shrinkage is first observed should therefore provide an indication of the original firing temperature (Te) of the ceramic.

Thermal Expansion Coefficients and the Primary and Secondary Pyroelectric Coefficients of Animal Bone

Abstract: SINCE the first reports of the electromechanical behaviour of bone1, the properties of bone as a physical material have attracted increasing attention. I now report some thermal expansion coefficients for animal bone and some calculations for the piezoelectric contribution to the pyroelectric effect at constant stress.

Thermal stresses in fibre reinforced composites

Abstract: A theoretical analysis is made of the dimensional changes, stresses and plastic flow accompanying an allotropic transformation in one component of a fibre composite, taking into account the simultaneous stress relaxation which occurs. The theory predicts the transformation dimensional changes observed experimentally under various temperature cycling conditions and provides an estimate of the stresses. Extending the theory to include the effect of a variation in temperature, several categories of coefficients of thermal expansion are obtained, none of which correspond to the rule of mixtures. The predicted transition from one coefficient of expansion to another during continuous cooling is confirmed experimentally and the resulting dimensional changes verified.

Thermally Induced Strains in Diamond Cubic, Tetragonal, Orthorhombic, and Hexagonal Films

Abstract: When thin films adhere to a substrate which has a different thermal expansion coefficient, changing the temperature of the composite will induce strains in both film and substrate. Calculations of strain and strain energy have been made for various polycrystalline diamond cubic, tetragonal, orthorhombic, and hexagonal films on substrates which are assumed to be undeformable and to have isotropic thermal expansion and elastic properties in directions parallel to the surface of the substrate. Computer programs were developed to calculate the above quantities for the diamond cubic semiconductors Ge and Si, the tetragonal metals Sn and In, the orthorhombic metal Ga, and the hexagonal metals Be, Cd, Co, Mg, Ti, Zn, and Zr. Each film was assumed to have been deposited on glass or on sodium chloride at room temperature and cooled to approximately liquid air temperature. The induced thermal strains and strain energies for many different crystallographically oriented grains were calculated. The particular (hkl) or...

X-ray studies on the thermal expansion of ruthenium dioxide

Abstract: A precise X-ray determination of the lattice constants of ruthenium dioxide, RuO2, has been made in the temperature range 30° to 702°C using a Unicam 19 cm high-temperature powder camera. It has been observed that the c parameter decreases with increasing temperature as in the case of FeF2 and CrO2 which also have a ruffle-type structure.

Thermal Coefficient of Refractive Index of Optical Glasses

Abstract: The thermal coefficients of refractive index have been determined for 23 commercial glasses. The interferometric procedure consisted of determining both the change of optical path of each glass with a change of temperature at a given wavelength and set coefficient of linear thermal expansion of the glass for the same temperature range. A relationship for the dispersion of the thermal coefficient of the refractive index has been found. It has also been possible to relate the chemical composition of glass with the thermal coefficient of the refractive index.

Elastic properties and thermal expansion of niobium mono-carbide to high temperatures

Abstract: The temperature dependence of Young's modulus of polycrystalline NbC0.969, with a density of 95.8% of theoretical, follows Wachtman's equation and may be expressed as E = 4.6039 × 1012 −5.7289 × 108Texp(−200.5/T) dynes/cm2 from 285 ° to 2173 °K. The temperature dependence of the shear modulus is linear and may be expressed as G = 1.9286 × 1012 −2.4848 × 108T dynes/cm2 from 284 ° to 2173 °K. Above 2173 °K the moduli decrease rapidly, possibly due to viscous grain boundary slip. This temperature corresponds to 0.56 of the absolute melting point maximum for niobium monocarbide. The dilatometric linear thermal expansion was found to be 2.04% from 17 ° to 2447 °C.

Low-expansion, low-melting zinc phosphovanadate glass compositions

Abstract: Low-melting, low-expansion, lead-free glass compositions are provided for sealing ceramics parts and encapsulating ceramic substrates. In addition to having a thermal expansion matching that of alumina, the glass compositions provide for the formation of a glass-to-alumina seal in the 380 DEG to 450 DEG C. temperature range.

The thermal expansion of palladium-silver alloys at low temperatures

Abstract: Interferometric measurements of the thermal expansion of palladium, silver and five alloys of these metals are reported in the temperature range 30 to 270 °K. The experimental uncertainties rise from approximately 1% at 270 °K to 15% at 30 °K. The variation of thermal expansion with concentration is non-linear and the form of the variation is not substantially affected by temperature in the range covered. A degree of correlation has been found with related thermodynamic properties of the alloys, and the need has been established for a rigorous theory of the thermal expansion of binary alloys on an atomic scale.