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ABSTRACT: The variation of elastic constants of MgO with pressure was determined by using McSkimin's pulse superposition technique. Measurements were made up to 2 kbars pressure at room temperature and liquid nitrogen temperature. The roompressure values of the adiabatic elastic constants, based on a density at 23°C of 3.5833 g/cm3, are (in kilobars) : No preview · Article · Jun 2006 · Journal of the American Ceramic Society

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ABSTRACT: Adiabatic bulk modulus, Bs, of polycrystalline MgO and Al2O3 was measured from 298° to 1473°K using the resonance technique. The Grüneisen constant, calculated from the measured bulk modulus, was constant over the whole temperature range (1.53 for MgO and 1.34 for Al2O3). Another important parameter, , is constant at high temperature and is 3.1 for MgO and 3.6 for Al2O3. The Poisson's ratio increases linearly with temperature for MgO and Al2O3. To describe the change of bulk modulus with temperature a theoretical equation was verified by using the foregoing constants. A practical form of this theoretical equation is
where Bs0 is the adiabatic bulk modulus at 0°K, δ is the quantity , γ is the Grüneisen constant, H is the enthalpy. The experimental data are described very well by this equation, which is equivalent to the empirical equation suggested by Wachtman et al., BsT= Bs0  CT exp (Tc/T), where C and Tc are empirical constants. No preview · Article · Jun 2006 · Journal of the American Ceramic Society

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ABSTRACT: The elastic constants and coefficients of thermal expansion of polycrystalline forsterite (Mg2SiO4) and steatite (MgSiO3) were determined from room temperature to 1000°K. Two elastic moduli, the adiabatic bulk modulus, Bs, and the shear modulus, G, decrease linearly with temperature above 500°K. The Grüneisen constant γ and a parameter δ, defined as — (dBs/dT)/αBs, calculated from the present data were virtually independent of temperature at the hightemperature range. Poisson's ratio, δ, rises linearly with temperature over the range of measurement; the slope is highest for materials with the lowest roomtemperature value of σ. No preview · Article · Jun 2006 · Journal of the American Ceramic Society

No preview · Article · Jan 1975 · Journal of Applied Mechanics

No preview · Article · Feb 1971 · Journal of Geophysical Research Atmospheres

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ABSTRACT: Lattice dynamical considerations and a Born repulsive potential between atoms lead to equations for the elastic constants of the cubic NaCl, CsCl and ZnS lattices as a function of compression. The NaCl lattice is unstable for n < 4.6 and the CsCl lattice is unstable for n < 7.2, where n is the exponent of the repulsive power law. The pressure derivatives of the shear constants (c′, c44) show a strong dependence upon crystallographic structure; for the ZnS lattice both dc′/dP and dc44/dP are negative for all reasonable values of n. The theoretical values of dcij/dP compare favorably with experimental results.For the isotropic shear modulus (μ), dμ/dP is determined by Poisson's ratio and the coordination of the ions in the lattice. Low (and possibly negative) values of dμ/dP are likely for several materials of importance to geophysics; such values would make lowvelocity zones possible and interpretation of shockwave data difficult. Vanishing of a shear constant predicts phase transitions at compression (V/V0) of 0.95 for the ZnS lattice, 0.75 for the NaCl lattice, and 0.60 for the CsCl lattice. The CsCl transition is predicted in spite of the fact that none of the elastic constants have a negative pressure derivative at zero pressure. The equation of state parameters, K0 and (dK/dP)0 (where K is the bulk modulus), are almost independent of crystallographic structure. K0 arises entirely from the Laplacian of the repulsive potential. so that the stability limits on n make it unlikely that (dK/dP)0 < 3.5 for the NaCl lattice or less than 5 for the CsCl lattice. No preview · Article · Dec 1970 · Physics of The Earth and Planetary Interiors

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ABSTRACT: Geophysical evidence has accumulated rapidly in the last few years for hypotheses of plate tectonics, which include the ideas of continental drift, seafloor spreading, transform faulting, underthrusting of the lithosphere at island arcs and the coherent movements of large blocks of the crust and uppermost mantle. The success of these concepts in explaining and synthesizing a great amount of geophysical data strongly suggests that these ideas should have broad application in geology. Plate tectonics, which is largely a kinematic description of relative movements of the earth's surface, also has stimulated interest in the processes driving plates and in the mechanical properties of the upper mantle below the lithosphere.To explore some of these new directions a Symposium on Mechanical Properties and Processes in the Mantle was held in Flagstaff, Arizona, June 29July 3, 1970, under the auspices of the International Upper Mantle Project and the U.S. National Academy of Sciences. This was the first major upper mantle symposium held in the United States. The scope of the conference included physical properties of materials likely to be present in the mantle, rocks of possible mantle origin and their mode of emplacement, convection currents, and other possible driving forces of global tectonics. The conference was not intended to be a review of geophysical evidence for plate movements, but rather to seek out new directions influenced by these ideas.h such special areas as satellite altimetry. No preview · Article · Jan 1970 · Eos Transactions American Geophysical Union

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ABSTRACT: Lynn R. Sykes was born in Pittsburgh, Pennsylvania, on April 16, 1937. He took his Bachelor's and Master's degrees at the Massachusetts Institute of Technology in 1960. He received his doctorate from Columbia University in 1965 working under Jack Oliver. His dissertation was entitled `The propagation of shortperiod seismic surface waves across oceanic areas.' He has since made numerous contributions in the fields of earthquake seismology and tectonics. He is presently Associate Professor of Geology at Columbia. No preview · Article · Jan 1970 · Eos Transactions American Geophysical Union

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ABSTRACT: In an earlier publication [Anderson and Schreiber, 1965], the pressure derivatives of the elastic toodull of a specimen of polycrystalline Mg0 were presented. Subsequent to this report, results obtained from a specimen of single crystal Mg0 were presented [Anderson and Andrearch, 1966], and a discrepancy between the results obtained from the polycrystalline and the singlecrystal specimens was noted. In particular, the adiabatic pressure derivatives of the bulk modulus were reported to. be 3.92 and 4.49 for the polycrystalline and singlecrystal specimens, respectively. The polycrystalline specimen employed in the experiment was of unusual quality, having essentially theoretical Xray density and being transparen.t. This quality was achieved in the fabrication process by the addition of several per cent of a fluoride compound to the raw material before hot pressing. Addition o.f a fluoride is recognized as enhancing the results of hot pressing by increasing the rate of vacancy diffusion and hence sintering without excessive grain growth. 0nly a few ppm of fluorine were found in a spectroscopic analysis of the finished specimen. Comparison of the P and S velocities measured on the polycrystalline specimen with averaged singlecrystal values from data available in the literature [Durand, 1936; Bhagavantam, 1955; $usse, 1961; Chou and Whirmore, 1961; Chung et al., 1963, 1966.; Anderson and Andrearch, 1966] suggested that the P velocity was higher than the VoigtReuss value obtained by averaging the singlecrystal constants. As a consequence, it was decided to procure a specimen of hotpressed Mg0 that had similar acoustic quality but that had been prepared with no additions of any kind. Such a specimen was obtained through the generosity of the Avco Corpo. ration, and the elastic properties and their pressure derivatives were determined for this specimen. The method and apparatus employed were the same as described earlier [Anderson and Schreiber, 1965]. The results obtained with this specimen are summarized in Table I and are compared with the results of the specimen previously reported. As can be seen from Table 1, the principal discrepancies appear in the values of v, and especially in the values of dv/dP (which differ by 10%), which give rise to the differences in the bulk modulus and its pressure derivative, the Potsson ratio, and the GrSneisen parameter. The agreement between the new data on polycrystalline Mg0 and the results derived from the measurements on a single crystal are quite good. The values of K and (r for the single crystal and the polycrystal are now reconciled. We recommend the value K8  1622 kb, as calculated from the singlecrystal data, as the best value to use for Mg0. The reason for the discrepancy noted between the two polycrystalline specimens is not under No preview · Article · Apr 1968 · Journal of Geophysical Research Atmospheres

Orson L. Anderson
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ABSTRACT: It is proposed that both the shockwave data and the acoustically determined parameters for equations of state be used together to construct an equation of state valid beyond the range of shockwave measurements. In the past few years, these two techniques have been used to crosscheck each other in the establishment of twoparameter equations of state. A threeparameter equation of state, such as proposed by Keane, is recommended. Two of these parameters are given by acoustic measurements at zero pressure, and the third is found by curve fitting the resulting Keane equation to shockwave data at high pressures. No preview · Article · Apr 1968 · Physics of The Earth and Planetary Interiors

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ABSTRACT: Measurements of the elastic constants and related pressure and temperature derivatives of ten compounds of interest to geophysical and geochemical theories are reported and analyzed. We discuss the corrections that are expected from effects of anisotropy and porosity and conclude that polycrystalline samples with porosities of 4% are not adequate for reliable acoustic measurements. We find that two anharmonic parameters, γth and δS, are independent of temperature at high temperature, and we use this result to estimate the temperature derivative of the bulk modulus at high temperatures. We present a number of correlations between the elastic constants and illustrate their use by attempting to predict the unmeasured elastic properties of fayalite. No preview · Article · Jan 1968

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ABSTRACT: A law was recently proposed [O. L. Anderson, 1966] in which pressure effects, temperature effects, and compositional effects were conjectured to be more or less equivalent for a class of materials called oxide compounds. This class included compounds for which ‘the dominant anion is oxygen, and the major cations are Mg, Si, Fe, Al, Ca, Na, and K.’ Oxygen compounds with other cations were specifically excluded from the law of corresponding states. The basis for proposing a law of corresponding states was given in Figures 1, 3, and 5 of the paper by Anderson and Nafe [1965]. Briefly, this consists of demonstrating that on a log K0  log V0 plot (where K0 is bulk modulus and V0 is molar volume of average atom pair) the points for oxide compounds, as defined above, did not fall on parallel lines with a slope of −1 as expected but, instead, fell on a line with a slope of −4. The data presented were based in part on measurements in our laboratory, but many points came from the older literature, and we relied heavily on Bridgman's data. We were suspicious about. some of the older data. which fell on the −4 slope line, in particular, BeO, CaO, Fe2O3, and garnet; therefore, we undertook an experimental program to remeasure the sound velocities of these materials. Using a hot press constructed while we were at Bell Laboratories, we were able to fabricate CaO into an isotropic aggregate suitable for ultrasonic measurements. The full results for CaO are presented by Soga [1967b]. A hotpressed pellet of BeO was obtained from Atomic International Inc., and the full results for this compound will be presented elsewhere [Soga, 1967c]. The results for garnet have been reported [Soga, 1967a], and the measurements upon magnetite are in progress. No preview · Article · Nov 1967

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ABSTRACT: The sound velocities, bulk modulus, and their pressure and temperature derivatives have been measured on a polycrystalline ZnO by means of a pulse‐superposition method. The pressure derivatives found from the experiments up to 3 kbar at 25°C are: (dv 1 /dP)=3.643×10<sup>3</sup> km/sec·kbar, (dv t /dP)=3.193×10<sup>3</sup> km/sec·kbar, and (dB s /dP)=4.78. The negative value of (dv t /dP) for ZnO is anomalous for crystalline solids. No anomalous behavior was observed in the temperature derivatives near 25°C. They are (dv 1 /dT)=1.871×10<sup>4</sup> km/sec·deg, (dv t /dT)=0.392×10<sup>4</sup> km/sec·deg, and (dB s /dT)=0.129 kbar/deg. The Grüneisen constant was calculated from the present pressure derivatives of elastic constants and was found to be negative, whereas the value calculated from the thermal‐expansion data at 25°C is positive. This result seems to indicate that the thermal expansivity of ZnO may be negative at very low temperatures. No preview · Article · Jul 1967 · Journal of Applied Physics

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ABSTRACT: A new technique for determining elasticity and anelasticity of small spheres, called the resonant sphere technique, is very useful in measuring the elastic constants of small specimens. We have used this technique to measure the elastic properties of two kinds of tektites. The shear and longitudinal sound velocities for a moldavite were found to be 3.627 and 5.918 km/sec, respectively, and those for an indochinite were 3.638 and 5.999 km/sec, respectively. The annealing points of these tektites were also obtained by determining the shear sound velocities of tektite specimens quenched from various temperatures. They are 750°C for a moldavite and 710°C for an indochinite. The temperature variations of shear sound velocity and Poisson's ratio were also determined from room temperature to 130°C. These results show that the resonant sphere technique is a valuable tool for tektite research. No preview · Article · Mar 1967

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ABSTRACT: The determination of the sound velocities of polycrystalline forsteritc under pressure has been an important objective of our laboratory at Lamont. We have obtained numerous polycrystalline samples prepared in several laboratories and, until recently, have not been able to pass ultrasound through them. We finally obtained a sample of forsteritc that yielded some weak echoes at 20 mhz, a barely marginal condition for measuring the elastic constants. We were able to determine the pressure derivatives of the sound velocities on this sample. The results should be of interest to the scientific community concerned with the physics of the earth's interior even though the results are on a porous sample, since they represent the only such data existing for forsteritc. Indeed, it may prove quite difficult to obtain a sample that is both ideal and measurable with precise techniques. Synthetic polycrystalline 'forsteritc' was obtained in the form of a rod about % inches in diameter and 8 inches long. The specimen was supplied by the Silk City Ceramic Company of Hawthorne, New Jersey. The density of this material was determined to be 3.021 or 94.0'% of theoretical density. The specimen consists essentially of forsteritc (95%) as determined by Xray diffraction. A second phase present is probably barium aluminum silicate, but positive identification was not possible. The average grain size of the specimen is about 12 microns. In a thin section, the grains appear to be equidimensional with no apparent preferred orientation. Examination of the polished surface as well as thin section indicated a porosity of 5 _4 1%, consistent with the measured deviation of the No preview · Article · Jan 1967 · Journal of Geophysical Research Atmospheres

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ABSTRACT: Bulk modulus and sound velocities of oxides and silicates up to very high temperatures are estimated from experimental data on sound velocity obtainable at relatively low temperatures. Data for MgO, Al2O3, and Mg2SiO4 are used to illustrate the method. The theoretical basis for this method is the establishment of a linear dependence of the bulk modulus on temperature at elevated temperatures by use of the MieGrüneisen equation of state. The parameters required are the roomtemperature values of the bulk modulus, density, thermal expansion, Grüneisen constant, and the measured enthalpy as a function of temperature. The variation of the shear and longitudinal velocities with temperature are determined from the calculated variation of the bulk modulus and shear modulus with temperature. The relations presented should apply to all materials likely to exist in the earth's mantle and, therefore, should provide a useful means of considering the effect of the geothermal gradient on the properties of rockforming compounds. No preview · Article · Nov 1966

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ABSTRACT: This stateoftheart report summarizes experiments and data on sound velocities in rocks and minerals and projects useful lines of research. The report discusses in detail the three common measuring techniques now employed: (1) resonance methods, (2) pulsetransmission methods (timeofflight), and (3) ultrasonicinterferometric methods. Promising techniques, both direct and indirect, are described, the most important of these is the resonance of small spheres. Methods of estimating elastic constants at high pressure and high temperature are indicated. The data extant on the sound velocities in rocks and minerals are considerable and are tabulated in several appendixes. The lack of systematic coverage and quality of these data is discussed. A method of estimating unmeasured properties in a class of rocks, using data already reported for that class, is reviewed. Techniques of estimating isotropic sound velocities from singlecrystal elasticconstant data are reviewed. (Author) No preview · Article · Oct 1966

Orson L. Anderson
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ABSTRACT: Recent measurements on two oxides show that there exists a pressure P* for Al2O3 (and for MgO) for which the density and the bulk modulus at that pressure have the same values as those for stishovite at room temperature. For Al2O3, P* is 271 kb; and for MgO, P* is 438 kb. It can be shown that the properties of MgO at 205 kb are equivalent, in this sense, to the properties of Al2O3 at 1 atm. Data on similar properties of other oxide compounds (oxides, silicates, and minerals with oxygen anions), though not as definitive, reveal the same trend. The following law of corresponding states is therefore proposed as a working hypothesis for mechanical properties of the earth's mantle: The value of specific volume and bulk modulus of one oxide compound can be converted to the corresponding quantities appropriate to another oxide compound by a change in scale of either pressure or temperature. No preview · Article · Oct 1966

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ABSTRACT: The temperature dependence of the sound velocity in polycrystalline MgO has been determined from ]80 to 80øC at atmospheric pressure and to 2 kb at 78.5øC. These results are compared with previous measurements to 4 kb at 34.6øC. From these measurements the critical temperature gradient (OT/OP),, for MgO was determined. Because (T/OP),, was found to be greater for P waves than for $ waves in MgO, and both are small compared with previously reported values of (OT/OP),, for the earth, it is possible to explain the marked presence of a lowvelocity zone for $ waves and the absence of a lowvelocity zone for P waves in a homogeneous earth. No preview · Article · Jun 1966

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ABSTRACT: A method is presented for calculating the isotropic elastic moduli of ceramic powder from the compressibility and the Debye temperature. Young's and shear moduli of polycrystalline MgO, Al2O3, BeO, and TiO2 were computed from compressibility and Debye temperature data by the present method and compared with values determined by the standard resonance method; values agreed within a few percent. An advantage of the present method is its applicability to specimens too small for the resonance method, because both compressibility and Debye temperature can be determined on powder or thinfilm forms. No preview · Article · Jun 1966 · Journal of the American Ceramic Society