Some elastic constant data on minerals relevant to geophysics

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.

[1]  J. B. Walsh The effect of cracks in rocks on Poisson's ratio , 1965 .

[2]  Chi‐yuen Wang,et al.  Equation of State of Periclase and Birch's Relationship between Velocity and Density , 1968, Nature.

[3]  F. Birch Finite Elastic Strain of Cubic Crystals , 1947 .

[4]  P. Gielisse,et al.  Compressibility, Cohesive Energy, and Hardness of Non‐Metallic Solids , 1965 .

[5]  D. L. Anderson,et al.  Shock‐wave equations of state for rocks and minerals , 1968 .

[6]  Kenneth R. Janowski,et al.  Elastic Behavior of MgO Matrix Composites , 1967 .

[7]  G. Barsch Relation between Third‐Order Elastic Constants of Single Crystals and Polycrystals , 1968 .

[8]  G. K. White,et al.  Grüneisen Parameter of Magnesium Oxide , 1966 .

[9]  S. P. Marsh,et al.  Shock‐wave compression of iron‐nickel alloys and the Earth's core , 1966 .

[10]  R. A. Robie,et al.  Elastic Constants of Calcite , 1962 .

[11]  L. Knopoff,et al.  Approximate Compressibility of Elements and Compounds , 1965 .

[12]  Paul Mattaboni,et al.  Method of pulse transmission measurements for determining sound velocities , 1967 .

[13]  Eric L. Peterson,et al.  Polymorphism of Iron at High Pressure , 1956 .

[14]  J. Gilvarry Amplitudes of Thermal Vibration at Fusion , 1956 .

[15]  J. N. Plendl,et al.  Some New Interrelations in the Properties of Solids Based on Anharmonic Cohesive Forces , 1961 .

[16]  O. Anderson,et al.  Seismic parameter φ: Computation at very high pressure from laboratory data , 1966 .

[17]  William Klement,et al.  Representation for compressional velocity data near the lambda transition in limestones and marbles , 1969 .

[18]  D. Chung,et al.  The Voigt‐Reuss‐Hill Approximation and Elastic Moduli of Polycrystalline MgO, CaF2, β‐ZnS, ZnSe, and CdTe , 1967 .

[19]  F. Birch The velocity of compressional waves in rocks to 10 kilobars: 1. , 1960 .

[20]  E. Schreiber,et al.  Elastic Moduli of Single‐Crystal Spinel at 25°C and to 2 kbar , 1967 .

[21]  O. L. Anderson,et al.  Comments on the negative pressure dependence of the shear modulus found in some oxides , 1968 .

[22]  O. Anderson,et al.  Equation for thermal expansivity in planetary interiors , 1967 .

[23]  J. J. Gilvarry,et al.  Temperature‐Dependent Equations of State of Solids , 1957 .

[24]  J. B. Wachtman,et al.  Elastic Constants of Synthetic Single Crystal Corundum at Room Temperature , 1960, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[25]  N. Soga COMPARISON OF MEASURED AND PREDICTED BULK MODULI OF TANTALUM AND TUNGSTEN AT HIGH TEMPERATURES , 1966 .

[26]  C. J. Maiden,et al.  Measurement of the Very‐High‐Pressure Properties of Materials using a Light‐Gas Gun , 1966 .

[27]  F. Birch Elasticity and Constitution of the Earth's Interior , 1952 .

[28]  J. M. Ide,et al.  The Elastic Properties of Rocks: A Correlation of Theory and Experiment. , 1936, Proceedings of the National Academy of Sciences of the United States of America.

[29]  D. Chung,et al.  First Pressure Derivatives of Polycrystalline Elastic Moduli: Their Relation to Single‐Crystal Acoustic Data and Thermodynamic Relations , 1967 .

[30]  B. Bernstein Elastic Constants of Synthetic Sapphire at 27°C , 1963 .

[31]  R. K. Cook Variation of Elastic Constants and Static Strains with Hydrostatic Pressure: A Method for Calculation from Ultrasonic Measurements , 1957 .

[32]  G. R. Barsch,et al.  Pressure Derivatives of Second-Order Elastic Constants of MgO , 1968 .

[33]  Z. Chang,et al.  Pressure dependence of the elastic constants of single-crystalline magnesium oxide , 1969 .

[34]  W. Ludwig,et al.  Theory of Anharmonic Effects in Crystals , 1961 .

[35]  D. Schuele,et al.  Pressure derivatives of the elastic constants of NaCl and KCl at 295°K and 195°K , 1965 .

[36]  S. P. Marsh,et al.  Equation of State for Nineteen Metallic Elements from Shock‐Wave Measurements to Two Megabars , 1960 .

[37]  S. P. Marsh,et al.  Hugoniot equation of state of twelve rocks , 1967 .

[38]  W. L. Bond,et al.  Elastic Moduli of Diamond , 1957 .

[39]  O. Anderson,et al.  Revised data on polycrystalline magnesium oxide , 1968 .

[40]  Mineo Kumazawa,et al.  Elastic moduli, pressure derivatives, and temperature derivatives of single‐crystal olivine and single‐crystal forsterite , 1969 .

[41]  D. Bancroft,et al.  The Effect of Pressure on the Rigidity of Rocks. I , 1938, The Journal of Geology.

[42]  Charles S. Smith,et al.  Low temperature thermal expansion of RbI , 1964 .

[43]  J. Walsh,et al.  EQUATION OF STATE OF METALS FROM SHOCK WAVE MEASUREMENTS , 1955 .

[44]  F. Birch,et al.  Thermal expansion at high pressures , 1968 .

[45]  J. B. Walsh The effect of cracks on the compressibility of rock , 1965 .

[46]  Naohiro Soga,et al.  Simplified Method for Calculating Elastic Moduli of Ceramic Powder from Compressibility and Debye Temperature Data , 1966 .

[47]  F. Birch,et al.  Density and composition of mantle and core , 1964 .

[48]  O. Anderson,et al.  Pressure Derivatives of Elastic Constants of Single‐Crystal MgO at 23° and ‐195.8°C , 1966 .

[49]  O. Anderson,et al.  Correction to paper by E. Schreiber and O. L. Anderson, ‘Pressure derivatives of sound velocities of polycrystalline forsterite with 6% porosity’ , 1967 .

[50]  A. E. Ringwood,et al.  Phase transformations in the mantle , 1968 .

[51]  P. J. Reddy,et al.  Temperature dependence of elastic compliances of garnet , 1964 .

[52]  A. E. Ringwood,et al.  Density distribution and constitution of the mantle , 1964 .

[53]  Naohiro Soga,et al.  Temperature and pressure derivatives of isotropic sound velocities of α quartz , 1968 .

[54]  Murli H. Manghnani,et al.  Elastic constants of single‐crystal rutile under pressures to 7.5 kilobars , 1969 .

[55]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[56]  Brian J. Skinner,et al.  SECTION 6: THERMAL EXPANSION , 1966 .

[57]  Gordon E. Schacher,et al.  Determination of Elastic Constants from Sound‐Velocity Measurements in Crystals of General Symmetry , 1967 .

[58]  H. J. Mcskimin,et al.  4 – Ultrasonic Methods for Measuring the Mechanical Properties of Liquids and Solids , 1964 .

[59]  R. Meister,et al.  Variational Method of Determining Effective Moduli of Polycrystals with Tetragonal Symmetry , 1966 .

[60]  Harry G. Drickamer,et al.  Lattice Parameters of Nine Oxides and Sulfides as a Function of Pressure , 1966 .

[61]  S. Shtrikman,et al.  On some variational principles in anisotropic and nonhomogeneous elasticity , 1962 .

[62]  J. Henry,et al.  Equation of state and conduction bands of iron at high pressures , 1962 .

[63]  J. H. Gieske,et al.  Pressure Dependence of the Elastic Constants of Single Crystalline Aluminum Oxide , 1968 .

[64]  E. A. Kraut,et al.  New Melting Law at High Pressures , 1966 .

[65]  E. Hiedemann,et al.  Corrected Values of the Elastic Moduli of Sapphire , 1960 .

[66]  Gene Simmons,et al.  Elastic Constants of Pyrite , 1963 .

[67]  Dattatraya P. Dandekar,et al.  Elastic Constants of Calcite , 1968 .

[68]  T. B. Bateman,et al.  Elastic Moduli of Single‐Crystal Europium Iron Garnet and Yttrium Iron Garnet , 1966 .

[69]  R. W. Whitmore,et al.  Single and Double Pile‐Up of Dislocations in MgO Crystals , 1961 .

[70]  H. J. Mcskimin,et al.  Elastic Moduli of Silicon vs Hydrostatic Pressure at 25.0°C and − 195.8°C , 1964 .

[71]  D. Schuele,et al.  Pressure and temperature derivatives of the elastic constants of caF2 and BaF2 , 1968 .

[72]  K. M. Koliwad,et al.  Pressure Dependence of the Elastic Constants of NaCl at Low Temperatures , 1970 .

[73]  Dong M. Chay,et al.  Microstructure and Room‐Temperature Mechanical Properties of Hot‐Pressed Magnesium Aluminate as Described by Quadratic Multivariable Analysis , 1968 .

[74]  D. Bancroft The Velocity of Longitudinal Waves in Cylindrical Bars , 1941 .

[75]  Don L. Anderson,et al.  Brillouin scattering-a new geophysical tool , 1969 .

[76]  B. Chandler,et al.  Creep, Strength, Expansion, and Elastic Moduli of Sintered BeO As a Function of Grain Size, Porosity, and Grain Orientation , 1964 .

[77]  Naohiro Soga,et al.  Estimation of bulk modulus and sound velocities of oxides at very high temperatures , 1966 .

[78]  G. Alers Use of Sound Velocity Measurements in Determining the Debye Temperature of Solids , 1965 .

[79]  D. I. Bolef,et al.  Ultrasonic Propagation in RbMnF3. I. Elastic Properties , 1969 .

[80]  R. N. Thurston Ultrasonic data and the thermodynamics of solids , 1965 .

[81]  K. E. Bullen,et al.  Empirical Equations of State for the Earth's Lower Mantle and Core , 1968 .

[82]  N. Christensen,et al.  Compressional wave velocities in single crystals of alkali feldspar at pressures to 10 kilobars , 1966 .

[83]  R. Fürth On the equation of state for solids , 1944, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[84]  S. Clark,et al.  Remarks on thermal expansion , 1969 .

[85]  S. K. Joshi,et al.  Debye Characteristic Temperature of Solids , 1960 .

[86]  Taro Takahashi,et al.  Isothermal compression of the alloys of iron up to 300 kilobars at room temperature: Iron‐nickel alloys , 1968 .

[87]  R. Mcqueen,et al.  SHOCK-WAVE COMPRESSIONS OF TWENTY-SEVEN METALS. EQUATIONS OF STATE OF METALS , 1957 .

[88]  C. Swenson,et al.  Equation of state of cubic solids; some generalizations☆ , 1968 .

[89]  R. Meister,et al.  Variational Method of Determining Effective Moduli of Polycrystals: (A) Hexagonal Symmetry, (B) Trigonal Symmetry , 1965 .

[90]  Z. Chang,et al.  Nonlinear Pressure Dependence of Elastic Constants and Fourth-Order Elastic Constants of Cesium Halides , 1967 .

[91]  B. Skinner The Thermal Expansions of Thoria, Periclase and Diamond , 1957 .

[92]  A. E. Ringwood,et al.  Mineralogical constitution of the deep mantle , 1962 .

[93]  J. Ross Macdonald,et al.  Review of Some Experimental and Analytical Equations of State , 1969 .

[94]  O. Anderson,et al.  Derivation of Wachtman's Equation for the Temperature Dependence of the Elastic Moduli of Oxide Compounds , 1966 .

[95]  Charles S. Smith Macroscopic Symmetry and Properties of Crystals , 1958 .

[96]  D. L. Anderson A Seismic Equation of State , 1967 .

[97]  Naohiro Soga,et al.  Elastic constants of garnet under pressure and temperature , 1967 .

[98]  M. A. Durand The Temperature Variation of the Elastic Moduli of NaCl, KCl and MgO , 1936 .

[99]  Naohiro Soga,et al.  A restriction to the law of corresponding states , 1967 .

[100]  E. G. Spencer,et al.  Microwave Elastic Properties of Nonmagnetic Garnets , 1963 .

[101]  J. B. Walsh The effect of cracks on the uniaxial elastic compression of rocks , 1965 .

[102]  Leon Knopoff,et al.  Density-Velocity Relations for Rocks , 1967 .

[103]  R. Liebermann,et al.  Elastic constants of polycrystalline hematite as a function of pressure to 3 kilobars , 1968 .

[104]  O. Anderson,et al.  THE PRESSURE DERIVATIVES OF THE SOUND VELOCITIES OF POLYCRYSTALLINE MAGNESIA , 1965 .

[105]  O. Anderson,et al.  A simplified method for calculating the debye temperature from elastic constants , 1963 .

[106]  O. Anderson,et al.  Some remarks on the volume dependence of the Grüneisen parameter , 1968 .

[107]  T. Barron LXXXII. On the thermal expansion of solids at low temperatures , 1955 .

[108]  J. B. Wachtman,et al.  Linear Thermal Expansion of Aluminum Oxide and Thorium Oxide from 100° to 1100°K , 1962 .

[109]  Carl F. Cline,et al.  Elastic Constants of Hexagonal BeO, ZnS, and CdSe , 1967 .

[110]  E. Madelung,et al.  Kompressibilitätsmessungen an festen Körpern , 1921 .

[111]  R. N. Thurston,et al.  Elastic Moduli of Quartz versus Hydrostatic Pressure at 25 and-195.8C , 1965 .

[112]  J. J. Gilvarry,et al.  Temperature Correction of Birch's Equation of State , 1962 .

[113]  D. Chung Elastic moduli of single crystal and polycrystalline MgO , 1963 .

[114]  Gene Simmons,et al.  Velocity of compressional waves in various minerals at pressures to 10 kilobars , 1964 .

[115]  James E. Mackey,et al.  Some Combinations of Third‐Order Elastic Constants for Strontium Titanate Single Crystals , 1969 .

[116]  Gene Simmons,et al.  Velocity of shear waves in rocks to 10 kilobars, 1 , 1964 .

[117]  W. Klement,et al.  Effect of pressure on the melting of iron , 1965 .

[118]  V. K. Mathur,et al.  Anderson-Grüneisen parameter δ of NaCl-type alkali halides for Born-Mayer potential , 1968 .

[119]  Naohiro Soga,et al.  New measurements on the sound velocity of calcium oxide and its relation to Birch's law , 1967 .

[120]  E. D. Williamson,et al.  On the compressibility of minerals and rocks at high pressures , 1923 .

[121]  P. Debye Zur Theorie der spezifischen Wärmen , 1912 .

[122]  Naohiro Soga,et al.  Anomalous Behavior of the Shear‐Sound Velocity under Pressure for Polycrystalline ZnO , 1967 .

[123]  F. Birch,et al.  Composition of the Earth's Mantle , 1937 .

[124]  O. Anderson,et al.  Temperature dependence of the velocity derivatives of periclase , 1966 .

[125]  G. R. Barsch,et al.  Elastic constants of single‐crystal forsterite as a function of temperature and pressure , 1969 .

[126]  Gene Simmons,et al.  Pressure derivatives of the elastic properties of polycrystalline quartz and rutile. , 1969 .

[127]  W. P. Mason Effect of Impurities and Phonon Processes on the Ultrasonic Attenuation of Germanium, Crystal Quartz, and Silicon , 1965 .

[128]  O. Anderson,et al.  Pressure derivatives of the sound velocities of polycrystalline forsterite, with 6% porosity , 1967 .

[129]  G. R. Cowan,et al.  Shock compression of two iron‐silicon alloys to 2.7 megabars , 1966 .

[130]  R. Hill The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[131]  H. J. Mcskimin,et al.  Analysis of the Pulse Superposition Method for Measuring Ultrasonic Wave Velocities as a Function of Temperature and Pressure , 1962 .

[132]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[133]  Harry G. Drickamer,et al.  Effect of High Pressure on the Lattice Parameters of Diamond, Graphite, and Hexagonal Boron Nitride , 1966 .

[134]  Robert B. Gordon,et al.  Compression of Mercury at High Pressure , 1967 .

[135]  M. F. Lewis,et al.  Microwave Phonon Attenuation in Yttrium Iron Garnet , 1968 .

[136]  G. Simmons,et al.  Pressure and Temperature Dependences of the Isotropic Elastic Moduli of Polycrystalline Alumina , 1968 .

[137]  O. Anderson,et al.  Pressure Derivatives of the Sound Velocities of Polycrystalline Alumina , 1966 .

[138]  R. A. Robie,et al.  SECTION 5: X-RAY CRYSTALLOGRAPHIC DATA, DENSITIES, AND MOLAR VOLUMES OF MINERALS , 1966 .

[139]  W. Overton Relation between Ultrasonically Measured Properties and the Coefficients in the Solid Equation of State , 1962 .

[140]  Hiroo Kanamori,et al.  Equations of State of Matter from Shock Wave Experiments , 1966 .

[141]  R. J. Beals,et al.  Directional Dilatation of Crystal Lattices at Elevated Temperatures , 1957 .

[142]  H. G. Drickamer,et al.  The effect of pressure on the volume and lattice parameters of ruthenium and iron , 1964 .

[143]  K. E. Bullen,et al.  On Compressibility and Chemical Inhomogeneity in the Earth's Core , 1965 .

[144]  S. Bhagavantam Elastic properties of single crystals and polycrystalline aggregates , 1955 .

[145]  Don Berlincourt,et al.  Elastic and Piezoelectric Coefficients of Single-Crystal Barium Titanate , 1958 .

[146]  M. Guinan,et al.  Pressure derivatives of the elastic constants of α-iron to 10 kbs , 1967 .

[147]  O. Anderson,et al.  Measurement of compressibility in polycrystalline MgO using the reflectivity method , 1965 .

[148]  K. Bullen,et al.  Incompressibility at the earth's mantle-core boundary. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[149]  Naohiro Soga,et al.  Elastic properties of CaO under pressure and temperature. , 1968 .

[150]  Taro Takahashi,et al.  Effect of pressure and temperature on the molar volumes of Wüstite and of three (Fe, Mg)2SiO4 spinel solid solutions , 1969 .

[151]  Harry G. Drickamer,et al.  Effect of High Pressures on the Compressibilities of Seven Crystals Having the NaCl or CsCl Structure , 1965 .

[152]  Prashant K. Sharma,et al.  Grneisen Parameters of Cubic Metals , 1970 .

[153]  Taro Takahashi,et al.  The Composition of the Earth's Interior , 1965 .

[154]  M. Blackman On the Thermal Expansion of Solids , 1957 .

[155]  H. J. Mcskimin,et al.  Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in Solids , 1961 .

[156]  J. B. Wachtman,et al.  Elastic Constants of Rutile (TiO2) , 1962, Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry.

[157]  H. B. Huntington The Elastic Constants of Crystals , 1958 .

[158]  Leon Thomsen,et al.  On the distributions of density and temperature in the low‐velocity zone , 1967 .

[159]  K. E. Bullen,et al.  Models for the Density and Elasticity of the Earth's Lower Core , 1965 .

[160]  Thomas J. Ahrens,et al.  Calculated mineral reactions in the Earth's mantle , 1967 .

[161]  D. Chung,et al.  The elastic constants of a cubic crystal subjected to moderately high hydrostatic pressure , 1967 .

[162]  E. H. Bogardus Third‐Order Elastic Constants of Ge, MgO, and Fused SiO2 , 1965 .

[163]  Dattatraya P. Dandekar,et al.  Pressure Dependence of the Elastic Constants of Calcite , 1968 .

[164]  S. P. Marsh,et al.  On the composition of the Earth's interior , 1964 .

[165]  Y. A. Chang,et al.  On the temperature dependence of the bulk modulus and the Anderson-Grüneisen parameter δ of oxide compounds , 1966 .

[166]  E. Kröner,et al.  Elastic moduli of perfectly disordered composite materials , 1967 .

[167]  Don L. Anderson,et al.  Chemical inhomogeneity of the mantle , 1968 .

[168]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[169]  Gene Simmons,et al.  Elastic properties of polycrystalline periclase , 1969 .

[170]  H. Kaga,et al.  Third-Order Elastic Constants of Calcite , 1968 .

[171]  M. Blackman On negative volume expansion coefficients , 1958 .

[172]  F. Birch The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan's Theory of Finite Strain , 1938 .

[173]  F. Murnaghan The Compressibility of Media under Extreme Pressures. , 1944, Proceedings of the National Academy of Sciences of the United States of America.

[174]  L. Knopoff,et al.  Reduction of shock‐wave equations of state to isothermal equations of state , 1969 .

[175]  R. Hearmon,et al.  The Elastic Constants of Anisotropic Materials , 1946 .

[176]  W. M. Latimer,et al.  The Measurement of Coefficients of Expansion at Low Temperatures. Some Thermodynamic Applications of Expansion Data. , 1926 .

[177]  O. Anderson,et al.  A proposed law of corresponding states for oxide compounds , 1966 .

[178]  K. E. Bullen,et al.  An Index of Degree of Chemical Inhomogeneity in the Earth , 1963 .

[179]  Don L. Anderson,et al.  Phase Changes in the Upper Mantle , 1967, Science.

[180]  C. R. Cleavelin,et al.  Elastic constants of LiBr from 300° to 4.2°K , 1969 .

[181]  J. C. Jamieson,et al.  Shock-Wave Compression and X-Ray Studies of Titanium Dioxide , 1967, Science.

[182]  Don L. Anderson,et al.  Bulk modulus‐density systematics , 1969 .

[183]  R. E. Newnham,et al.  Elastic properties of fluorapatite , 1969 .

[184]  D. Hasselman,et al.  Effect of Small Fraction of Spherical Porosity on Elastic Moduli of Glass , 1963 .

[185]  E. Grüneisen,et al.  Theorie des festen Zustandes einatomiger Elemente , 1912 .

[186]  R.F.S. Hearmon,et al.  The elastic constants of anisotropic materials—II , 1956 .

[187]  A. C. Victor,et al.  Thermodynamic Properties of Magnesium Oxide and Beryllium Oxide from 298 to 1,200 °K1 , 1963, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[188]  Naohiro Soga,et al.  High‐Temperature Elasticity and Expansivity of Forsterite and Steatite , 1967 .

[189]  S. K. Joshi,et al.  Debye Θ and compressibility. III. Cubic metals , 1961 .

[190]  S. P. Marsh,et al.  On the equation of state of stishovite , 1963 .

[191]  O. Anderson,et al.  The bulk modulus-volume relationship for oxide compounds and related geophysical problems , 1965 .

[192]  R. Mcqueen,et al.  Compression of Solids by Strong Shock Waves , 1958 .

[193]  A. E. Ringwood,et al.  An experimental investigation of the Gabbro-Eclogite transformation and some geophysical implications , 1966 .

[194]  R. Liebermann,et al.  Critical thermal gradients in the mantle , 1969 .

[195]  T. Bateman Elastic Moduli of Single-Crystal Zinc Oxide , 1962 .

[196]  O. Anderson,et al.  SOUND VELOCITIES IN ROCKS AND MINERALS. , 1966 .

[197]  Harry G. Drickamer,et al.  Effect of High Pressure on the Lattice Parameters of Cr2O3 and α‐Fe2O3 , 1966 .

[198]  D. Chung,et al.  Relation of Single‐Crystal Elastic Constants to Polycrystalline Isotropic Elastic Moduli of MgO , 1963 .

[199]  T. Barron Grüneisen parameters for the equation of state of solids , 1957 .

[200]  O. Anderson Conditions for a density minimum in the upper mantle , 1965 .

[201]  Mineo Kumazawa,et al.  The elastic constants of single-crystal orthopyroxene , 1969 .

[202]  K. Brugger,et al.  Grüneisen Gamma from Elastic Data , 1967 .

[203]  L. Knopoff,et al.  The theory of finite strain and compressibility of solids , 1963 .

[204]  J. Mackenzie,et al.  The Elastic Constants of a Solid containing Spherical Holes , 1950 .

[205]  Jerry Wackerle,et al.  Shock‐Wave Compression of Quartz , 1962 .

[206]  R. J. Corruccini,et al.  Specific Heats and Enthalpies of Technical Solids at Low Temperatures: A Compilation from the Literature , 1960 .

[207]  Thomas J. Ahrens,et al.  Shock compression of feldspars , 1969 .

[208]  H. J. Mcskimin,et al.  Variations of the Ultrasonic Pulse‐Superposition Method for Increasing the Sensitivity of Delay‐Time Measurements , 1965 .

[209]  R. Verma,et al.  Elasticity of some high-density crystals , 1960 .

[210]  Anthony W. England,et al.  Universal equations of state for oxides and silicates , 1969 .

[211]  H. J. Mcskimin Ultrasonic Measurement Techniques Applicable to Small Solid Specimens , 1950 .

[212]  L. Knopoff,et al.  Comments on the interrelationships between Grüneisen's parameter and shock and isothermal equations of state , 1969 .

[213]  K. E. Bullen,et al.  Compressibility‐Pressure Gradient and the Constitution of the Earth's Outer Core , 1969 .

[214]  D. Schuele,et al.  The pressure derivatives of the elastic constants of CaF2 , 1967 .

[215]  P. Ho,et al.  Analysis of ultrasonic data and experimental equation of state for sodium , 1968 .

[216]  N. Soga Elastic Constants of Polycrystalline BeO as a Function of Pressure and Temperature , 1969 .

[217]  W. Voigt Bestimmung der Elastizitätskonstanten von Eisenglanz , 1907 .

[218]  D. Oliver,et al.  The Elastic Moduli of MnO , 1969 .

[219]  M. Lewis Elastic Constants of Magnesium Aluminate Spinel , 1966 .

[220]  A. E. Ringwood,et al.  A model for the upper mantle , 1962 .

[221]  Daniel L. Decker,et al.  Equation of State of NaCl and Its Use as a Pressure Gauge in High-Pressure Research , 1965 .

[222]  O. L. Anderson,et al.  2 - Determination and Some Uses of Isotropic Elastic Constants of Polycrystalline Aggregates Using Single-Crystal Data , 1965 .

[223]  Don L. Anderson,et al.  The Effect of Temperature and Partial Melting on Velocity and Attenuation in a Simple Binary System , 1968 .

[224]  E. Schrödinger Spezifische Wärme (theoretischer Teil) , 1926 .

[225]  Chi‐yuen Wang,et al.  Equation of state of periclase and some of its geophysical implications , 1969 .

[226]  K. E. Bullen,et al.  Compression in the Earth , 1968 .

[227]  Don L. Anderson,et al.  Equations of State and Crystal Structures of High-Pressure Phases of Shocked Silicates and Oxides , 1969 .

[228]  P. N. La Mori,et al.  Isothermal compressibility of kyanite, andalusite, and sillimanite from synthetic aggregates , 1969 .

[229]  F. Sheard Calculation of the thermal expansion of solids from the third-order elastic constants , 1958 .

[230]  F. Grønvold,et al.  ALPHA FERRIC OXIDE: LOW TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC FUNCTIONS , 1959 .

[231]  O. Anderson,et al.  The use of ultrasonic measurements under modest pressure to estimate compression at high pressure , 1966 .

[232]  A. Ruoff,et al.  Linear Shock‐Velocity‐Particle‐Velocity Relationship , 1967 .

[233]  J. Ross Macdonald,et al.  Some Simple Isothermal Equations of State , 1966 .

[234]  Leon Thomsen,et al.  On the high-temperature equation of state of solids. , 1969 .

[235]  E. Stern Theory of the Anharmonic Properties of Solids , 1958 .

[236]  O. Anderson,et al.  High‐Temperature Elastic Properties of Polycrystalline MgO and Al2O3 , 1966 .

[237]  G. Rupprecht,et al.  THE ELASTIC CONSTANTS OF STRONTIUM TITANATE , 1963 .