Showing papers on "Thermal expansion published in 1968"
TL;DR: In this article, the authors derived bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropy phases by employing extremum principles of thermoelasticity.
Abstract: Bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropic phases are derived by employing extremum principles of thermoelasticity
1,049 citations
TL;DR: In this paper, lattice parameter data for MgO, CaO, and several isotropic compositions of LiH were measured from 12°K up to 300°K. Thermal expansion coefficients were derived by fitting the data to a second-degree polynomial.
Abstract: Lattice parameter data for MgO, CaO, and several isotropic compositions of LiH were measured from ~ 12 °K up to ~ 300 °K. Thermal expansion coefficients were derived by fitting the data to a second-degree polynomial.
133 citations
TL;DR: In this article, measurements of the elastic constants and thermal expansion of PbTe have been made from 4.2° to 303.2 degrees K. The linear coefficient of thermal expansion was found to be 20.4±0.6/°C at room temperature, and the 0°K Debye temperature was calculated to be 176.7°± 0.5°K.
Abstract: Measurements of the elastic constants and thermal expansion of PbTe have been made from 4.2° to 303.2°K. The extrapolated 0°K values for C44, (C11−C12)/2, and (C11+2C12)/3, respectively, are 1.514±0.009, 6.184±0.066, and 4.560±0.042×1011 dyn/cm2. At 303.2°K these values are 1.344±0.008, 5.016±0.057, and 4.107±0.037×1011 dyn/cm2. Intermediate values are presented graphically, as are the thermal‐expansion data. The linear coefficient of thermal expansion is found to be 20.4±0.4×10−6/°C at room temperature. The 0°K Debye temperature is calculated to be 176.7°±0.5°K.
127 citations
122 citations
110 citations
TL;DR: In this paper, the problem of deducing theoretically the shrinkage of a two-phase composite material in terms of the properties of its components has been considered, and it has been shown that the problem has a wider application and is also identical with the problem for deducing the coefficient of thermal expansion for a similar material.
Abstract: THE problem of deducing theoretically the shrinkage of a two phase composite material in terms of the properties of its components has been considered by Pickett1 and by Hansen and Nielsen2. They were specifically interested in concrete, but the problem has a wider application and is also identical with the problem of deducing the coefficient of thermal expansion for a similar material.
91 citations
TL;DR: In this paper, the thermal expansion behavior of synthetic β-spodumenes and several β-Spodumene-silica solid solutions was studied using high-temperature X-ray diffraction techniques.
Abstract: Synthetic β-Spodumene and several β-Spodumene-silica solid solutions were prepared, and their thermal expansion behavior was studied using high-temperature X-ray diffraction techniques. Data indicate that all β-Spodumenes are characterized by a pronounced anisotropy of thermal expansion much the same as that of the silica polymorph keatite. Anisotropy increases slightly and the volume expansion decreases as the compositions become richer in SiO2. Specimens with more than 80.8 wt% SiO2 at 130O°C and 1 atm contain P-cristobalite along with β-Spodumene. The lattice parameters of β-Spodumene compositions throughout the solid solution range were determined. The structural aspects of the anisotropy of thermal expansion are discussed.
89 citations
TL;DR: In this article, the anisotropic thermal expansion of α-titanium has been determined by the X-ray method, and it has been shown that αc (5.6 × 10−6.
Abstract: In order to resolve the discrepancy found in earlier work, the anisotropic thermal expansion of α-titanium has been determined by the X-ray method. If a small range of temperature is used the coefficient of expansion observed along the hexagonal axis (αc) is smaller than that in the basal plane (αa). The nature of the deviation of the α-titanium structure from ideal hexagonal close-packing and the room temperature elastic behaviour of the metal have been shown to be in agreement with the result that αc (5.6 × 10−6. °C−1) is smaller than αa (9.5 × 10−6. °C−1).
78 citations
TL;DR: The crystal structure of CS2 was determined at two temperatures from intensity data measured with a proportional counter and a modified Weissenberg apparatus as discussed by the authors, where the coefficients of thermal expansion were αa,αb,αc, αc,αa, αb, α c,α c, αα,ααα, αβ,αγ, αγ,αβα, βα,γα,βαβ, ββ,γβ,βγ,γγ, β,γ β, β β,β β,α α,α
Abstract: The crystal structure of CS2 was determined at two temperatures from intensity data measured with a proportional counter and a modified Weissenberg apparatus. The orthorhombic cell [(a) 6.3437(8), (b) 5.5244(4), (c) 8.9971(7), 143°K, Cmca, Z = 4] exhibited marked anisotropic thermal expansion, the coefficients of thermal expansion being αa = 630 × 10−6 °C−1, αb = 570 × 10−6 °C−1, αc = −630 × 10−6 °C−1. Positional and anisotropic thermal parameters were refined using upper‐angle data (sinθ / λ ≥ 0.35) and the x‐ray results were compared with data from spectroscopic sources on the molecular motion of CS2 in the solid. The unweighted reliability indices for the two refinements were 0.039 (148°K) and 0.056 (133°K). The carbon–sulfur bond length corrected for foreshortening due to libration was 1.560(3) A (133°K) and 1.559 A (148°K), in agreement with calculations of the length in the gas from spectral data (1.558 ± 0.0005) and electron diffraction (1.559 ± 0.002).
77 citations
74 citations
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TL;DR: Saturation magnetization was measured for alloy systems (FexNi1−x)92M8, where M=Cu, Co, Mn, Cr, and V, and also for Fe70(RexPt1 −x)30 at 4.2°K as discussed by the authors.
Abstract: Anomalous thermal expansion and its relation to magnetic properties are surveyed for various Invar alloys. Saturation magnetization was measured for alloy systems (FexNi1−x)92M8, where M=Cu, Co, Mn, Cr, and V, and also for Fe70(RexPt1−x)30 at 4.2°K. Sharp drop of the saturation moment occurs at the average electron concentration, N=8.13 to 8.52, for all the Invar alloys including the above‐mentioned alloy systems and N=8.21 to 8.52 for all the Fe–Ni base alloys. When, however, it was plotted against the electron concentration of the matrix surrounding less electropositive impurity atoms such as Mn, Cr, or V, all the alloy systems were found to exhibit a sharp drop of the moment in narrower concentration range of 8.48 to 8.60 for all the Fe–Ni base alloys. Saturation moment and a reversible susceptibility in the saturation range were also measured at room temperature for (110) [001] and (001) [110] rolled single crystals of the composition 29 at.% Ni–Fe. It was found that saturation moment was reduced from...
TL;DR: In this paper, the adiabatic elastic constants of molybdenum and rhenium alloyed in solid solution with 7.0, 16.6, and 26.9 at.
Abstract: The adiabatic elastic constants of molybdenum and molybdenum alloyed in solid solution with 7.0, 16.6, and 26.9 at.% rhenium were measured in the temperature range −190°C to +100°C. Rhenium additions decrease (c11−c12)/2 and the twinning shear (c11−c12+c44)/3, and increase the bulk modulus and c44. The 26.9 at.% alloy is elastically isotropic. Alloy additions strengthen nearest‐neighbor interactions and weaken second‐nearest‐neighbor interactions. Debye temperatures calculated from the measured elastic constants agree well with those determined by calorimetry. Thermal expansion of the alloys was found to be essentially the same as for molybdenum in this temperature range.
TL;DR: In this article, the density, thermal expansion coefficient, and thermal pressure coefficient for polyisobutylene of mol wt 40,000 have been accurately determined from 0 to 150°.
Abstract: The density, thermal expansion coefficient, and thermal pressure coefficient for polyisobutylene of mol wt 40,000 have been accurately determined from 0 to 150°. Results are compared with the reduced equation of state employed in the theory of solutions. The characteristic parameters v*, T*, and p* required for the treatment of polyisobutylene solutions are obtained from the experimental results.
TL;DR: In this paper, the temperature coefficient of resistance of a thin-film resistor depends on the mismatch in the thermal expansion coefficient between the film and its substrate, and the effect can be quite significant for typical thin films.
Abstract: The temperature coefficient of resistance of a thin‐film resistor depends on the mismatch in the thermal expansion coefficient between the film and its substrate This Letter presents a calculation of this effect and shows that the effect can be quite significant for typical thin films
TL;DR: In this paper, the low temperature thermal expansion of several aluminium, nickel, copper, and iron base alloys was measured from liquid hydrogen temperature to room temperature, and the thermal expansion coefficient, (1/L293)/(dL/dT) was tabulated as a function of temperature.
TL;DR: A high-temperature x-ray study of pure iron has shown that a small but easily detectable, lattice parameter anomaly, representing a decrease in the mean linear thermal expansion coefficient, occurs over a narrow range of temperature (similar 35 degc) about the Curie point.
Abstract: A high-temperature x-ray study of pure iron has shown that a small, but easily detectable, lattice parameter anomaly, representing a decrease in the mean linear thermal expansion coefficient, occurs over a narrow range of temperature (similar 35 degc) about the Curie point. The total volume change associated with the ferromagnetic-paramagnetic transition in pure iron obtained from the experimental measurements gave values in good agreement with those calculated directly from volume magnetostriction data, although for an alternative method of calculation the agreement was poor.
01 Feb 1968
TL;DR: In this article, an investigation on the basis of the ASPHALTS of THERMAL EXPANSION and CONTRACTION of ASPHALTIC CONCRETE was conducted.
Abstract: AN INVESTIGATION ON THE BASIC ASPHALTS OF THERMAL EXPANSION AND CONTRACTION OF ASPHALTIC CONCRETE WAS CONDUCTED. ASPHALTIC CONCRETE EXHIBITS TWO DIFFERENT THERMAL COEFFICIENTS OF EXPANSION AND CONTRACTION SIMILAR TO ASPHALT CEMENT IN THE TEMPERATURE RANGE MINUS 10 TO 140 F. THESE HAVE BEEN CALLED THE SOLID AND FLUID THERMAL COEFFICIENTS. A TRANSITION TEMPERATURE WAS FOUND FOR ASPHALTIC CONCRETE. ABOVE THIS TEMPERATURE ASPHALTIC CONCRETE EXHIBITS ITS FLUID COEFFICIENT, AND BELOW, ITS SOLID COEFFICIENT. ASPHALT CONTENT WAS FOUND TO BE A MAJOR CONTRIBUTOR TO THERMAL- EXPANSION-CONTRACTION OF ASPHALTIC CONCRETE. A RELATIONSHIP WAS DERIVED WHICH PREDICTS THE THERMAL COEFFICIENT OF EXPANSION-CONTRACTION OF ASPHALTIC CONCRETE IN THE SOLID STATE. THE THERMAL EXPANSION OF THE ASPHALT AND QUARTZITE AGGREGATE USED WERE DETERMINED BY MEANS OF A DILATOMETER. ASPHALTIC CONCRETE WAS FOUND TO EXHIBIT A DIFFERENT THERMAL COEFFICIENT IN EXPANSION THAN IN CONTRACTION. PERMANENT LENGTH CHANGES WERE OBSERVED WHEN ASPHALTIC CONCRETE SPECIMENS WERE HEATED AND COOLED IN A FLUID STATE. THE THERMAL EXPANSION IN THE FLUID STATE IS LESS THAN THERMAL CONTRACTION RESULTING IN PERMANENT SHRINKAGE. THIS PHENOMENEN HAS BEEN ATTRIBUTED TO ABSORPTION OF ASPHALT INTO THE AGGREGATES AND BY DENSIFICATION OF THE ASPHALTIC CONCRETE CAUSED BY AN IRREVERSIBLE PROCESS OF EXPANSION AND CONTRACTION OF ASPHALT INTO THE AIR VOIDS. THE EXPANSION AND CONTRACTION IN THE SOLID STATE WERE IDENTICAL FOR FREE AND FRICTION CONDITIONS. THE TEST METHOD UTILIZING DIAL DEFLECTION GAGES PROVIDES AN EXCELLENT METHOD TO MEASURE THE THERMAL EXPANSION AND CONTRACTION OF ASPHALTIC CONCRETE IN THE SOLID AND FLUID STATE.
TL;DR: In this article, a detailed study of the thermal expansion of the sodalite group of minerals is presented, where the authors use powder X-ray diffraction methods to obtain thermal expansion data up to 920 − C for four noseans, five haiiynes, and one sodalites.
Abstract: Summary. Thermal expansion data up to 920 ~ C by powder X-ray diffraction methods are presented for four noseans, five haiiynes, and one sodalite. The rate of thermal expansion is at first high and increases with temperature ; this is interpreted as due to the untwisting of the partially collapsed framework. Above a certain temperature (which depends on the mineral and its composition) the rate of thermal expansion is much lower and is linear with temperature; this corresponds to the rate of thermal expansion of the more fully expanded framework. Sodalite does not show this second stage below 920 ~ C. The thermal expansion behaviour of other framework silicates is interpreted in analogy to that of the sodalite group. T HE thermal expansion behaviour of the framework silicates poses interesting problems. Consisting essentially of a partially covalently bonded three-dimensional framework, they might be expected to have low thermal expansion rates. Unfortunately, there has been little detailed work on the thermal expansion of framework silicates, apart from the silica minerals and the feldspars. The simple picture of a three-dimensional framework is complicated by the fact that their frameworks show varying degrees of collapse at room temperature, which depend on the interframework ions (except for silica), A detailed study of the thermal expansion of the sodalite group of minerals might be expected to give a general understanding of the thermal expansion of framework silicates. The members of the sodalite group of minerals have essentially the same aluminosilicate framework (A16Si6024). Dependent on whether chlorine or sulphate is the predominant interframework anion, the common rock-forming sodalite minerals can be divided into sodalite proper (NasA16Si60~4Cl~) the nosean-hafiyne solid solution series (Nas_sK0_lCa0_2[~o_l)s(AlsSi~024)(S04)l_ 2 . nH~O. According to Taylor (1967) haiiyne possesses the space group P43n and is richer in calcium and sulphate than nosean, which possesses the space group P43m. The specimens used in this study are taken from the series of sodalite i Present address: Doulton Research Limited, Hanworth Lane, Chertsey, Surrey.
TL;DR: In this paper, the lattice parameters of zinc oxide have been determined accurately at different temperatures between 27°C and 619°C, and these data have been processed to evaluate the temperature variation of the coefficients of thermal expansion αa and αc.
Abstract: Lattice parameters of zinc oxide have been determined accurately at different temperatures between 27°C and 619°C. These data have been processed to evaluate the temperature variation of the coefficients of thermal expansion αa and αc and the results could be represented as follows: αa = 6.05 × 10−6 + 2.20 × 10−9t + 2.29 × 10−12t2°C−1 // αc = 3.53 × 10−6 + 2.38 × 10−9t + 9.24 × 10−14t2°C−1 where t is the temperature in °C.
TL;DR: Calibration procedures and results for several low expansion materials are discussed and a rod type vitreous silica dilatometer is used for specimen temperature control and a high output, linear variable differential transformer serves as the extensometer.
Abstract: Recent critical applications for ultralow expansion materials have required thermal expansion measurements with very high precision and accuracy. A Fizeau interferometer employing a helium-neon laser has given a precision of +/-0.1 x 10(-6) cm/cm. A second, more rapid method consists of a rod type vitreous silica dilatometer. A stirred water bath is used for specimen temperature control and a high output, linear variable differential transformer serves as the extensometer. Precision of this method is +/-0.5 x 10(-6) cm/cm. Calibration procedures and results for several low expansion materials are discussed.
TL;DR: In this article, the linear thermal expansion coefficients of silver and palladium have been measured in the temperature range 20°K to 273°K by an interferometric method, and the results of the investigation have been used in conjunction with earlier heat capacity and elasticity data to calculate the Gruneisen parameters.
Patent•
05 Nov 1968TL;DR: In this article, a low thermal expansion insulating cement is formulated from a high temperature resinous varnish and a finely divided inert inorganic filler having a negative coefficient of thermal expansion.
Abstract: A low thermal expansion insulating cement is formulated from a high temperature resinous varnish and a finely divided inert inorganic filler having a negative coefficient of thermal expansion. The composition is employed as an insulator and binder in microminiature circuit devices employing microminiature circuit elements.
Patent•
03 Oct 1968TL;DR: In this article, a method of coating with polythyltric carbon dioxide (PYTOLYTIC CARBON) to provide a COATED article with high strength and robustness is described.
Abstract: A METHOD OF COATING WITH PYROLYTIC CARBON TO PROVIDE A COATED ARTICLE HAVING HIGH STRENGTH CHARACTERISTICS. DEPOSITION OF PYROLYTIC CARBON IS EFFECTED ON AN ARTICLE FROM A CARBONACEOUS ATMOSPHERE AT A PRESELECTED TEMPERATURE UNDER CONDITIONS THAT RESULT IN FORMATION OF CARBON HAVING A PRESELECTED COEFFICIENT OF THERMAL EXPANSION WHICH IS LESS THAN THAT OF THE ARTICLE. DURING COOLING OF THE COATED ARTICLE TO AMBIENT TEMPERATURE, THE DIFFERENCE BETWEEN THE COEFFICIENTS OF THERMAL EXPANSION OF THE ARTICLE AND THE PYROLYTIC CARBON CAUSES THE PYTOLYTIC CARBON COATING TO BE PLACED UNDER, SUBSTANTIAL COMPRESSIVE TANGENTIAL STRESS. DEPOSITION IS USUALLY CARRIED OUT AT A TEMPERATURE OF ABOUT 1500*C. OR BELOW TO DEPOSIT FAIRLY DENSE ISOTROPIC OR LAMINAR CARBON. THE COEFFICIENT OF THERMAL EXPANSION OF THE ARTICLE BEING COATED IS USUALLY BETWEEN ABOUT 6 TO 9X10**-4/0C., WITH THE PREFERRED MATERIAL BEING GRAPHITE.
TL;DR: In this article, the ion motion is taken as a harmonic oscillation and it is shown that the difference in oscillation frequencies for surface and inner ions is mainly responsible for the temperature dependence of the surface tension.
Abstract: The surface‐tension temperature dependence is calculated for liquid metals. In this calculation the ion motion is taken as a harmonic oscillation and it is shown that the difference in oscillation frequencies for surface and inner ions is mainly responsible for the temperature dependence of the surface tension. There is, however, a second influence caused by the change of particle density due to thermal expansion. An expression for the surface tension is derived and comparison is made with experimental values. The change of oscillator frequency, the surface tension at zero temperature, and a characteristic temperature corresponding to the critical temperature are calculated.
TL;DR: In this article, accurate lattice parameters (at 25 and 48°C), density, thermal expansion coefficients, the indexed powder pattern, and optical data are given for Ba(4+x)Na(2−2x)Nb10O30, where x = 0.13±0.013, grown by pulling from a nominally stoichiometric melt.
Abstract: Accurate lattice parameters (at 25 and 48°C), density, thermal expansion coefficients, the indexed powder pattern, and optical data are given for Ba(4+x)Na(2−2x)Nb10O30, where x = 0.13±0.013, grown by pulling from a nominally stoichiometric melt.
01 Jan 1968
TL;DR: The bond lengths between segments of a polymer chain are virtually independent of temperature and impose restraints on the expansion which occurs as the temperature is raised as mentioned in this paper, and polymer systems therefore have lower expansivities than related liquids which are not polymeric.
Abstract: The bond lengths between segments of a polymer chain are virtually independent of temperature and impose restraints on the expansion which occurs as the temperature is raised. Polymer systems therefore have lower expansivities than related liquids which are not polymeric. Below the glass temperature the expansivity is reduced still further because of the absence of structural changes which contribute to expansion in liquids.