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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. Journal of the American Ceramic Society 06/2006; 50(5):239  242. · 2.43 Impact Factor

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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 , 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. Journal of the American Ceramic Society 06/2006; 49(7):355  359. · 2.43 Impact Factor

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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) : Journal of the American Ceramic Society 06/2006; 49(8):404  409. · 2.43 Impact Factor

Journal of Applied Mechanics. 01/1975; 42(3).

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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. Physics of The Earth and Planetary Interiors 01/1970; 3:6185. · 2.38 Impact Factor

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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. Reviews of Geophysics. 01/1968; 6(4).

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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. Journal of Applied Physics 07/1967; · 2.21 Impact Factor

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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. 03/1967;

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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 Journal of Geophysical Research 01/1967; 72(2). · 3.17 Impact Factor

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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. 01/1967;

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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) 10/1966;

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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. Journal of the American Ceramic Society 01/1966; 49(6):318322. · 2.43 Impact Factor

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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. 01/1966;

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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. 01/1966;

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. 01/1966;

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ABSTRACT: The sound velocities and the pressure derivatives of the sound velocities were measured on a small specimen of polycrystalline alumina by the method of “pulse superposition”. The pressure derivatives found from experiments up to 4 kbars at 25°C are: These values lead to the variation of Poisson's ratio with pressure of dσ/dP = 1.02 × 10−4/ kbar and to the variation of (isothermal) bulk modulus with pressure of dBT/dP= 3.99. Using the above values the compression is computed up to 400 kbars and compares well with shock wave measurements. Consequently, the measured pressure derivatives may hold up to several hundred kilobars. Journal of the American Ceramic Society 01/1966; · 2.43 Impact Factor

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ABSTRACT: It is known that the density of many minerals is related to the (average) index of refraction by a linear law called the GladstoneDale law. It is shown that this law is generally applicable only to minerals whose anton is oxygen and whose mean molecular weight is close to 21. Another relationship, called I)rude's law, which is deduced from classical dielec tric theory, fits the data just as well as the empirical linear law. The correlation between density and index includes the minerals arising from various combinations of SlOe, MgO, ALoO3, N.O, and K20. An implication is that densiW controls certain physical properties of oxides, independently of composition or crystal class. This is analogous to the rule found by Birch which relates sound velocity to density and holds for the same groups of minerals. Introduction. Birch (1961a) has shown that a large number of compounds of geophysical im portance have a mean atomic weight close to 21. Mean atomic weight is defined as molecular weight divided by the number of atoms in the chemical formula, M/p. Minerals likely to be associated with the earth's mantle are composed chiefly of the elements oxygen, silicon, mag nesium, aluminum, and iron. Following Birch (1961b), we shall be concerned with oxide com pounds with values of Mfp near 21 and shall thus exclude iron but include aluminum. In this paper, such materials will be said to obey Birch's law (i.e., M/p 21.0). Birch (1961b) has also shown that for the class of minerals where M/p 21.0 the sound velocity is roughly a linear function of density at an ambient pressure of i arm. Compounds having a large amount of lime, appear to be ex ceptions (Simmons, 1964). A similar relation between sound velocity and density was found by Nafe and Drake (1957) for marine sediments. If the sound velocity is indeed simply pro portional to the density in the mantle, as it ap pears to be (Birch, 1961a), relationships be tween physical properties of the earth's interior are simplified. It follows that it is important to verify the relationship between compressional wave velocity and density in a sample at an ambient pressure of I arm, as mentioned above. 01/1965;

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ABSTRACT: The sound velocities and the pressure derivatives of the sound velocities of a gemquality sample of polycrystalline MgO were measured by the 'phase comparison' tech nique. The pressure derivatives found from experiments at pressures up to 4 kb are dv,/dp  4.351 X 10 ' km/sec/kb and dvp/dp _ 7.711 X 10 8 km/sec/kb. Arguments are presented which indicate that these pressure derivatives hold up to at least 100 kb. These values yield a vanishingly small value of the pressure derivative of Poisson's ratio. The Grilneisen constants of the shear and longitudinal modes are calculated, from which the acoustic Grilneisen con stant is estimated to be 1.60. This agrees very well with the Griineisen constant obtained from thermal properties. Introduction. It is considered probable that MgO exists as a separate phase in the earth's mantle (Sclar et al., 1964; McQueen et al., 1964). The effect of pressure on the sound ve locities of MgO is therefore important to cur rent theories of the earth's interior. Our experiments were performed on a poly crystalline specimen obtained from the Mineral Technology Department of the University of California a.t Berkeley. This sample was a disk 5 cm wide and 0.95 cm thick, transparent in the visible spectrum. The grain size, as revealed by electron micrography is about 5/. The bulk density was measured at 3.5803 at 25øC which is to be compared to the Xray density of 3.5833 calculated by Skinner (1957). To measure the density to the desired accuracy, Archimedes' method was employed. Onemildiameter silver wire was used to suspend the specimen. Tem perature was controlled to 0.1øC. An analytical balance (ñ0.00003 g) was used for the mass de terminations. Corrections for air buoyancy, sur face tension, and temperature were applied. It is believed that the measurements are accurate to within 0.03%. On a single crystal purchased from SemiElements, Inc., the bulk density was measured as 3.5833 at 25øC. The infrared spec trum of the single crystal and the polycrystal were virtually identical. This specimen can be x Contribution 848 of Lamont Geological Ob servatory. 01/1965;

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ABSTRACT: The relationship between the sound velocity and density in various oxide compounds at atmospheric pressure is relevant to problems of the earth's interior. Here, data on elastic constants of various compounds are collected and analyzed. It is shown that the bulk modulusvolume per ion pair relationship for oxide compounds differs in a remarkable degree from that found for alkali halides, fluorides, selenides, sulfides, and covalent compounds. It is shown that a change of volume has the same effect on the bulk modulus of oxide compounds, whether the volume change is produced by pressure, compositional variation, phase changes, temperature, or porosity. It thus appears that volume is the primary variable affecting the elastic moduli of oxide compounds, and all other variables affect the moduli only insofar as they affect the volume itself. 01/1965;
