Octahedral distortion induced magnetic anomalies in LaMn0.5Co0.5O3 single crystals

Single crystals of LaMn0.5Co0.5O3 belonging to the ferromagnetic-insulator and distorted perovskite class were grown using a four-mirror optical float zone furnace. The as-grown crystal crystallizes into an orthorhombic Pbnm structure. The spatially resolved 2D Raman scan reveals a strain-induced distribution of transition metal (TM)-oxygen (O) octahedral deformation in the as-grown crystal. A rigorous annealing process releases the strain, thereby generating homogeneous octahedral distortion. The octahedra tilt by reducing the bond angle TM-O-TM, resulting in a decline of the exchange energy in the annealed crystal. The critical behavior is investigated from the bulk magnetization. It is found that the ground state magnetic behavior assigned to the strain-free LaMn0.5Co0.5O3 crystal is of the 3D Heisenberg kind. Strain induces mean field-like interaction in some sites, and consequently, the critical exponents deviate from the 3D Heisenberg class in the as-grown crystal. The temperature-dependent Raman scattering study reveals strong spin-phonon coupling and the existence of two magnetic ground states in the same crystal. (C) 2014 AIP Publishing LLC.

Probing a spin-glass state in SrRuO3 thin films through higher-order statistics of resistance fluctuations

The complex perovskite oxide SrRuO3 shows intriguing transport properties at low temperatures due to the interplay of spin, charge, and orbital degrees of freedom. One of the open questions in this system is regarding the origin and nature of the low-temperature glassy state. In this paper we report on measurements of higher-order statistics of resistance fluctuations performed in epitaxial thin films of SrRuO3 to probe this issue. We observe large low-frequency non-Gaussian resistance fluctuations over a certain temperature range. Our observations are compatible with that of a spin-glass system with properties described by hierarchical dynamics rather than with that of a simple ferromagnet with a large coercivity.

Mixture of Fuels Approach for the Synthesis of SrFeO3-delta Nanocatalyst and Its Impact on the Catalytic Reduction of Nitrobenzene

A modified solution combustion approach was applied in the synthesis of nanosize SrFeO3-delta (SFO) using single as well as mixture of citric acid, oxalic acid, and glycine as fuels with corresponding metal nitrates as precursors. The synthesized and calcined powders were characterized by Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), thermogravimetric analysis and derivative thermogravimetric analysis (TG-DTG), scanning electron microscopy, transmission electron microscopy, N-2 physisorption methods, and acidic strength by n-butyl amine titration methods. The FT-IR spectra show the lower-frequency band at 599 cm(-1) corresponds to metal-oxygen bond (possible Fe-O stretching frequencies) vibrations for the perovskite-structure compound. TG-DTG confirms the formation temperature of SFO ranging between 850-900 degrees C. XRD results reveal that the use of mixture of fuels in the preparation has effect on the crystallite size of the resultant compound. The average particle size of the samples prepared from single fuels as determined from XRD was similar to 50-35 nm, whereas for samples obtained from mixture of fuels, particles with a size of 30-25 nm were obtained. Specifically, the combination of mixture of fuels for the synthesis of SFO catalysts prevents agglomeration of the particles, which in turn leads to decrease in crystallite size and increase in the surface area of the catalysts. It was also observed that the present approach also impacted the catalytic activity of the SFO in the catalytic reduction of nitrobenzene to azoxybenzene.

Noteworthy performance of La1-xCaxMnO3 perovskites in generating H-2 and CO by the thermochemical splitting of H2O and CO2

Perovskite oxides of the composition La1-xCaxMnO3 ( LCM) have been investigated for the thermochemical splitting of H2O and CO2 to produce H-2 and CO, respectively. The study was carried out in comparison with La1-xSrxMnO3, CeO2 and other oxides. The LCM system exhibits superior characteristics in high-temperature evolution of oxygen, and in reducing CO2 to CO and H2O to H-2. The best results were obtained with La0.5Ca0.5MnO3 whose performance is noteworthy compared to that of other oxides including ceria. The orthorhombic structure of LCM seems to be a crucial factor.

Electronic Structure of CH3NH3PbX3 Perovskites: Dependence on the Halide Moiety

A combination of measurements using photoelectron spectroscopy and calculations using density functional theory (DFT) was applied to compare the detailed electronic structure of the organolead halide perovskites CH3NH3PbI3 and CH3NH3PbBr3. These perovskite materials are used to absorb light in mesoscopic and planar heterojunction solar cells. The Pb 4f core level is investigated to get insight into the chemistry of the two materials. Valence level measurments are also included showing a shift of the valence band edges where there is a higher binding energy of the edge for the CH3NH3PbBr3 perovskite. These changes are supported by the theoretical calculations which indicate that the differences in electronic structure are mainly caused by the nature of the halide ion rather than structural differences. The combination of photoelectron spectroscopy measurements and electronic structure calculations is essential to disentangle how the valence band edge in organolead halide perovskites is governed by the intrinsic difference in energy levels of the halide ions from the influence of chemical bonding.

Magnetic frustration and dielectric relaxation in insulating Nd2NiMnO6 double perovskites

We have investigated structural, dielectric, and magnetic properties of polycrystalline double perovskite Nd2NiMnO6 compound. The compound crystallizes in monoclinic P2(1)/n symmetry and is partially B-site disordered depending on the synthesis conditions. It undergoes second-order ferromagnetic transition at 192K and shows glassy behaviour at low temperature. The glassy phase is due to anti-site disorder within the homogeneous sample. Temperature and frequency dependent dielectric measurements reveal colossal values of dielectric constant and is best interpreted using Maxwell-Wagner interfacial polarization model. Impedance spectroscopy has been used to analyse the intrinsic dielectric response. This enabled us to differentiate the conduction process at the grain and grain boundaries. Arrhenius behaviour is favoured at the grain boundary, while variable range hopping mechanism is considered most suitable within the grain region. dc conductivity measurements corroborate variable range hopping conduction. (C) 2015 AIP Publishing LLC.

Metastable monoclinic and orthorhombic phases and electric field induced irreversible phase transformation at room temperature in the lead-free classical ferroelectric BaTiO3

For decades it has been a well-known fact that among the few ferroelectric compounds in the perovskite family, namely, BaTiO3, KNbO3, PbTiO3, and Na1/2Bi1/2TiO3, the dielectric and piezoelectric properties of BaTiO3 are considerably higher than the others in polycrystalline form at room temperature. Further, similar to ferroelectric alloys exhibiting morphotropic phase boundary, single crystals of BaTiO3 exhibit anomalously large piezoelectric response when poled away from the direction of spontaneous polarization at room temperature. These anomalous features in BaTiO3 remained unexplained so far from the structural standpoint. In this work, we have used high-resolution synchrotron x-ray powder diffraction, atomic resolution aberration-corrected transmission electron microscopy, in conjunction with a powder poling technique, to reveal that at 300 K (i) the equilibrium state of BaTiO3 is characterized by coexistence of metastable monoclinic Pm and orthorhombic (Amm2) phases along with the tetragonal phase, and (ii) strong electric field switches the polarization direction from the 001] direction towards the 101] direction. These results suggest that BaTiO3 at room temperature is within an instability regime, and that this instability is the fundamental factor responsible for the anomalous dielectric and piezoelectric properties of BaTiO3 as compared to the other homologous ferroelectric perovskite compounds at room temperature. Pure BaTiO3 at room temperature is therefore more akin to lead-based ferroelectric alloys close to the morphotropic phase boundary where polarization rotation and field induced ferroelectric-ferroelectric phase transformations play a fundamental role in influencing the dielectric and piezoelectric behavior.

Investigation of dielectric relaxation, Jahn-Teller distortion, and magnetic ordering in Y substituted Pr1-xYxMnO3 (0.1 <= x <= 0.4)

We report structural, magnetic, and dielectric properties of the perovskite compound Pr1-xYxMnO3 (0.1 <= x <= 0.4) studied using dc magnetization, ac susceptibility, neutron powder diffraction, and dielectric techniques. These compounds crystallize in orthorhombic space group (Pnma) in the temperature range 5-300 K. The Mn-O-Mn bond angle decreases with the Y substitution along with an increase in the Jahn-Teller distortion. The Jahn-Teller distortion for Pr0.9Y0.1MnO3 shows an anomalous change near 50 K, below which it falls sharply. Neutron powder diffraction patterns of all reported compositions at low temperature constitute additional magnetic Bragg peaks that suggest magnetic ordering. Magnetic reflections were indexed in the nuclear lattice with the propagation vector k = (0, 0, 0). Rietveld refinement of powder patterns conform to A type antiferromagnetic ordering where moments are aligned ferromagnetically in a-c plane and coupled nearly antiferromagnetically along b-axis resulting in a net ferromagnetic component along the b-direction. The antiferromagnetic transition temperature was deduced from dc magnetization and ac susceptibility data. The transition temperature decreases by nearly 22 K (from 81 K to 59 K) as yttrium content (x) increases from 0.1 to 0.4. Measurements reveal strong frequency dispersion in dielectric constant and dielectric loss. Activation energy and relaxation time are estimated from the Arrhenius plot. It is further shown that relaxation behaviour is altered with yttrium doping concentration. (C) 2015 AIP Publishing LLC.

Interrelationship between Interphase Boundaries and Phase Contents near the Critical Compositions of Lead-Free Ferroelectric (Na0.5Bi0.5)TiO3-BaTiO3

Heterophase structures in lead-free perovskite-type ferroelectric solid solutions of (1 - z)(Na0.5Bi0.5)TiO3 - zBaTiO(3) are analysed for a few critical compositions near the morphotropic phase boundary (z = 0.05-0.07). Examples of the phase coexistence and elastic matching of the phases from different symmetry groups are considered to find optimum volume fractions of specific domain types and coexisting phases at the complete stress relief in two-phase samples. Some interrelations between these volume fractions are described using variants of the domain arrangement at changes in the composition and unit-cell parameters. The evaluated room-temperature volume fractions of the ferroelectric monoclinic (Cm symmetry) and tetragonal (P4mm symmetry) phases near the morphotropic phase boundary are in agreement with experimental data.

Role of (La, Gd) co-doping on the enhanced dielectric and magnetic properties of BiFeO3 ceramics

The effect of the La3+ and Gd3+ co-doping on the structure, electric and magnetic properties of BiFeO3 (BFO) ceramics are investigated. For the compositions (x=0 and 0 <= y <= 0.15) in the perovskite structured LaxGdyBi1-xFeO3 system, a tiny residual phase of Bi2Fe4O9 is noticed. Such a secondary phase is suppressed with the incorporation of `La' content (x). The magnitude of dielectric constant (epsilon(r) increases progressively by increasing the `La' content from x=0 to 0.15 with a remarkable decrease of dielectric loss. For x=0.15, the system LaxGdyBi1-x(x+y)FeO3 exhibits highest remanent magnetization (M-r) of 0.18 emu/g and coercive magnetic field (H-c) of similar to 1 Tin the presence of external magnetic field of 9 T at 300 K. The origin of enhanced dielectric and magnetic properties of LaxGdyBil (x+y)Fe03 and the role of doping elements, La3+, Gd3+ has been discussed. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Order-disorder phase transition and multiferroic behaviour in a metal organic framework compound (CH3)(2)NH2Co(HCOO)(3)

We have investigated the multiferroic and glassy behaviour of metal-organic framework (MOF) material (CH3)(2)NH2Co(CHOO)(3). The compound has perovskite-like architecture in which the metal-formate forms a framework. The organic cation (CH3)(2)NH2+ occupies the cavities in the formate framework in the framework via N-H center dot center dot center dot O hydrogen bonds. At room temperature, the organic cation is disordered and occupies three crystallographically equivalent positions. Upon cooling, the organic cation is ordered which leads to a structural phase transition at 155 K. The structural phase transition is associated with a para-ferroelectric phase transition and is revealed by dielectric and pyroelectric measurements. Further, a PE hysteresis loop below 155 K confirms the ferroelectric behaviour of the material. Analysis of dielectric data reveal large frequency dispersion in the values of dielectric constant and tan delta which signifies the presence of glassy dielectric behaviour. The material displays a antiferromagnetic ordering below 15 K which is attributed to the super-exchange interaction between Co2+ ions mediated via formate linkers. Interestingly, another magnetic transition is also found around 11 K. The peak of the transition shifts to lower temperature with increasing frequency, suggesting glassy magnetism in the sample. (C) 2016 AIP Publishing LLC.

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.

Metasomatism and magmatic assimilation at a gabbro-limestone contact, Christmas Mountains, Big Bend region, Texas

A composite stock of alkaline gabbro and syenite is intrusive into limestone of the Del Carmen, Sue Peake and Santa Elena Formations at the northwest end of the Christmas Mountains. There is abundant evidence of solution of wallrock by magma but nowhere are gabbro and limestone in direct contact. The sequence of lithologies developed across the intrusive contact and across xenoliths is gabbro, pyroxenite, calc-silicate skarn, marble. Pyroxenite is made up of euhedral crystals of titanaugite and sphene in a leucocratic matrix of nepheline, Wollastonite and alkali feldspar. The uneven modal distribution of phases in pyroxenite and the occurrence' of nepheline syenite dikes, intrusive into pyroxenite and skarn, suggest that pyroxenite represents an accumulation of clinopyroxene "cemented" together by late-solidifying residual magma of nepheline syenite composition. Assimilation of limestone by gabbroic magma involves reactions between calcite and magma and/or crystals in equilibrium with magma and crystallization of phases in which the magma is saturated, to supply energy for the solution reaction. Gabbroic magma was saturated with plagioclase and clinopyroxene at the time of emplacement. The textural and mineralogic features of pyroxenite can be produced by the reaction 2( 1-X) CALCITE + AN_XAB_l-X = (1-X) NEPHELINE+ 2(1-X) WOLLASTONITE+ X ANORTHITE+ 2(1-X) CO₂. Plagioclase in pyroxenite has corroded margins and is rimmed by nepheline, suggestive of resorption by magma. Anorthite and wollastonite enter solid solution in titanaugite. For each mole of calcite dissolved, approximately one mole of clinopyroxene was crystallized. Thus the amount of limestone that may be assimilated is limited by the concentration of potential clinopyroxene in the magma. Wollastonite appears as a phase when magma has been depleted in iron and magnesium by crystallization of titanaugite. The predominance of mafic and ultramafic compositions among contaminated rocks and their restriction to a narrow zone along the intrusive contact provides little evidence for the generation of a significant volume of desilicated magma as a result of limestone assimilation.

Within 60 m of the intrusive contact with the gabbro, nodular chert in the Santa Elena Limestone reacted with the enveloping marble to form spherical nodules of high-temperature calc-silicate minerals. The phases wollastonite, rankinite, spurrite, tilleyite and calcite, form a series of sharply-bounded, concentric monomineralic and two-phase shells which record a step-wise decrease in silica content from the core of a nodule to its rim. Mineral zones in the nodules vary 'with distance from the gabbro as follows:

0-5 m CALCITE + SPURRITE + RANKINITE + WOLLASTONITE
5-16 m CALCITE + TILLEYITE ± SPURRITE + RANKINITE + WOLLASTONITE
16-31 m CALCITE + TILLEYITE + WOLLASTONITE
31-60 m CALCITE + WOLLASTONITE
60-plus CALCITE + QUARTZ

The mineral of a one-phase zone is compatible with the phases bounding it on either side but these phases are incompatible in the same volume of P-T-X_CO2.

Growth of a monomineralio zone is initiated by reaction between minerals of adjacent one-phase zones which become unstable with rising temperature to form a thin layer of a new single phase that separates the reactants and is compatible with both of them. Because the mineral of the new zone is in equilibrium with the phases at both of its contacts, gradients in the chemical potentials of the exchangeable components are established across it. Although zone boundaries mark discontinuities in the gradients of bulk composition, two-phase equilibria at the contacts demonstrate that the chemical potentials are continuous. Hence, Ca, Si and CO₂ were redistributed in the growing nodule by diffusion. A monomineralic zone grows at the expense of an adjacent zone by reaction between diffusing components and the mineral of the adjacent zone. Equilibria between two phases at zone boundaries buffers the chemical potentials of the diffusing species. Thus, within a monomineralic zone, the chemical potentials of the diffusing components are controlled external to the local assemblage by the two-phase equilibria at the zone boundaries.

Mineralogically zoned calc-silicate skarn occurs as a narrow band that separates pyroxenite and marble along the intrusive contact and forms a rim on marble xenoliths in gabbro. Skarn consists of melilite or idocrase pseudomorphs of melili te, one or two . stoichiometric calcsilicate phases and accessory Ti-Zr garnet, perovskite and magnetite. The sequence of mineral zones from pyroxenite to marble, defined by a characteristic calc-silicate, is wollastonite, rankinite, spurrite, calcite. Mineral assemblages of adjacent skarn zones are compatible and the set of zones in a skarn band defines a facies type, indicating that the different mineral assemblages represent different bulk compositions recrystallized under identical conditions. The number of phases in each zone is less than the number that might be expected to result from metamorphism of a general bulk composition under conditions of equilibrium, trivariant in P, T and u_CO2. The "special" bulk composition of each zone is controlled by reaction between phases of the zones bounding it on either side. The continuity of the gradients of composition of melilite and garnet solid solutions across the skarn is consistent with the local equilibrium hypothesis and verifies that diffusion was the mechanism of mass transport. The formula proportions of Ti and Zr in garnet from skarn vary antithetically with that of Si Which systematically decreases from pyroxenite to marble. The chemical potential of Si in each skarn zone was controlled by the coexisting stoichiometric calc-silicate phases in the assemblage. Thus the formula proportion of Si in garnet is a direct measure of the chemical potential of Si from point to point in skarn. Reaction between gabbroic magma saturated with plagioclase and clinopyroxene produced nepheline pyroxenite and melilite-wollastonite skarn. The calcsilicate zones result from reaction between calcite and wollastonite to form spurrite and rankinite.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.