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.

Strength of thin-walled elliptical cylinders supported at the minor axis

In this investigation it was found that the instability failure of curved sheet is nearly independent of the type of loading and is primarily a function of the maximum stress, radius-thickness ration and modulus of elasticity. A method of correlating the critical stress of thin sheet under several different types of loading is given. An explanation for the experimental critical stress of thin walled cylinders under bending being greater than that for pure compression is given. The strength of unstiffened thin walled circular nose sections under pure bending was found to be controlled by local instability of the section, rather than a large scale instability. The equation of local instability of curved sheet gives values which are in fair agreement with those found experimentally.

The strength of elliptical cylinders supported at the minor axis under bending plus shear loads is governed primarily by the bending strength, and is little effected by the sheer force unless the amount of shear is quite large with respect to the moment. The effect of increasing the amount of elliptically greatly reduces the bending and shear strength of nose sections. Under torsional loads the stress at buckling falls off as the ration of the major to minor axis increases but the failure stress decreases at a slower rate than the buckling stress. The length effect of semi-circular sections under torsion is similar to that of a circular tube, and can be obtained by Donnell's theoretical equation.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

Improved Mechanical Properties of Compatibilized Polypropylene/Polyamide-12 Blends

Compatibilized blends of polypropylene (PP) and polyamide-12 (PA12) as a second component were obtained by direct injection molding having first added 20% maleic anhydride-modified copolymer (PP-g-MA) to the PP, which produced partially grafted PP (gPP). A nucleating effect of the PA12 took place on the cooling crystallization of the gPP, and a second crystallization peak of the gPP appeared in the PA12-rich blends, indicating changes in the crystalline morphology. There was a slight drop in the PA12 crystallinity of the compatible blends, whereas the crystallinity of the gPP increased significantly in the PA12-rich blends. The overall reduction in the dispersed phase particle size together with the clear increase in ductility when gPP was used instead of PP proved that compatibilization occurred. Young's modulus of the blends showed synergistic behavior. This is proposed to be both due to a change in the crystalline morphology of the blends on the one hand and, on the other, in the PA12-rich blends, to the clear increase in the crystallinity of the gPP phase, which may, in turn, have been responsible for the increase in its continuity and its contribution to the modulus.

A model for the erosive wear of rubber at oblique impact angles

A model has been developed to predict the erosive wear behaviour of elastomers under conditions of glancing impact by small hard particles. Previous work has shown the erosive wear mechanism of elastomers under these conditions to be similar in nature to that of abrasive wear by a sharp blade. The model presented here was developed from the model of Southern and Thomas for sliding abrasion, by combining their treatment of the growth of surface cracks with a model for particle impact in which the force - displacement relationship for an idealized flat-ended punch on a semi-infinite elastic solid was assumed. In this way an expression for the erosive wear rate was developed, and compared with experimental measurements of wear rate for natural rubber, styrene - butadiene rubber and a highly crosslinked polybutadiene rubber. Good qualitative agreement was found between the predictions of the model and the experimental measurements. The variation of erosion rate with impact velocity, impact angle, particle size, elastic modulus of the material, coefficient of friction and fatigue properties were all well accounted for. Quantitative agreement was less good, and the effects of erosive particle shape could not be accounted for. The reasons for these discrepancies are discussed. © 1992 IOP Publishing Ltd.

Measurement of the Mechanical Properties of Filtercakes

In order to improve drilling mud design to cater for specific well situations, a more comprehensive knowledge and understanding of filter cake failure is needed. This paper describes experimental techniques aimed at directly probing the mechanical properties of filter cakes, without having to take into account artefacts due to fluid flow in the substrate. The use of rheometers allows us to determine shear yield stress and dynamic shear modulii of cakes grown on filter paper. A new scraping technique measures the strength and moisture profiles of typical filter cakes with a 0.1 mm resolution. This technique also allows us to probe the adhesion between the filter cake and its rock substrate. In addition, œdometer drained consolidation and unloading of a filter cake give us compression parameters useful for Cam Clay modelling. These independent measurements give similar results as to the elastic modulus of different filter cakes, showing an order of magnitude difference between water based and oil based cakes. We find that these standard cakes behave predominantly as purely elastic materials, with a sharp transition into plastic flow, allowing for the determination of a well-defined yield stress. The effect ofsolids loading on a given type of mud is also studied.

Development of a universal stress sensor for graphene and carbon fibres

Carbon fibres are a significant volume fraction of modern structural airframes. Embedded into polymer matrices, they provide significant strength and stiffness gains by unit weight compared with competing structural materials. Here we use the Raman G peak to assess the response of carbon fibres to the application of strain, with reference to the response of graphene itself. Our data highlight the predominance of the in-plane graphene properties in all graphitic structures examined. A universal master plot relating the G peak strain sensitivity to tensile modulus of all types of carbon fibres, as well as graphene, is presented. We derive a universal value of - average - phonon shift rate with axial stress of around -5ω0 -1 (cm -1 Mpa-1), where ω0 is the G peak position at zero stress for both graphene and carbon fibre with annular morphology. The use of this for stress measurements in a variety of applications is discussed. © 2011 Macmillan Publishers Limited. All rights reserved.

Enhancement of magnetostriction in internally-biased Terfenol-D 2-2 composites

A key issue in the fabrication of Terfenol-D 2-2 composites with internal magnetic field biasing is the selection of appropriate constituent materials to obtain high magnetostriction while keeping optimum magnetomechanical properties. The fabrication process is costly and time consuming and, therefore, numerical methods to predict their properties are useful. In this paper, finite element analysis (FEA) of the magnetostriction of such composites has been carried out using the commercial package ABAQUS. It has been shown that composites fabricated using Nd2Fe14B for the permanent magnetic material layers possess the highest internal fields within the Terfenol-D layers, although the overall strain of these composites is limited to approximately 800 × 10-6 due to the high elastic modulus of Nd2Fe14B. Simulations showed that the strain can be enhanced by choosing a different material with a lower elastic modulus for the permanent magnetic layer even though the internal field is lower. The simulations showed that the strain can increase by 12% if the Nd 2Fe14B layer is substituted by SmCo5; by 23% if it is substituted by Sm2Co17; and by 35% if it is substituted by Alnico. © 2008 IEEE.

Elastic properties of crystalline-amorphous core-shell silicon nanowires

The pressure behavior of Raman frequencies and line widths of crystalline core-amorphous shell silicon nanowires (SiNWs) with two different core-to-shell ratio thicknesses was studied at pressures up to 8 GPa. The obtained isothermal compressibility (bulk modulus) of SiNWs with a core-to-shell ratio of about 1.8 is ∼20% higher (lower) than reported values for bulk Si. For SiNWs with smaller core-to-shell ratios, a plastic deformation of the shell was observed together with a strain relaxation. A significant increase in the full width at half-maximum of the Raman LTO-peak due to phonon decay was used to determine the critical pressure at which LTO-phonons decay into LO + TA phonons. Our results reveal that this critical pressure in strained core-shell SiNWs (∼4 GPa) is different from the reported value for bulk Si (∼7 GPa), whereas no change is observed for relaxed core-shell SiNWs. © 2013 American Chemical Society.

Physical properties of a hybrid and a nanohybrid dental light-cured resin composite.

This work was aimed at the study of some physical properties of two current light-cured dental resin composites, Rok (hybrid) and Ice (nanohydrid). As filler they both contain strontium aluminosilicate particles, however, with different size distribution, 40 nm-2.5 mum for Rok and 10 nm-1 mum for Ice. The resin matrix of Rok consists of UDMA, that of Ice of UDMA, Bis-EMA and TEGDMA. Degree of conversion was determined by FT-IR analysis. The flexural strength and modulus were measured using a three-point bending set-up according to the ISO-4049 specification. Sorption, solubility and volumetric change were measured after storage of composites in water or ethanol/water (75 vol%) for 1 day, 7 or 30 days. Thermogravimetric analysis was performed in air and nitrogen atmosphere from 30 to 700 degrees C. Surface roughness and morphology of the composites was studied by atomic force microscopy (AFM). The degree of conversion was found to be 56.9% for Rok and 61.0% for Ice. The flexural strength of Rok does not significantly differ from that of Ice, while the flexural modulus of Rok is higher than that of Ice. The flexural strengths of Rok and Ice did not show any significant change after immersion in water or ethanol solution for 30 days. The flexural modulus of Rok and Ice did not show any significant change either after immersion in water for 30 days, while it decreased significantly, even after 1 day immersion, in ethanol solution. Ice sorbed a higher amount of water and ethanol solution than Rok and showed a higher volume increase. Thermogravimetric analysis showed that Rok contains about 80 wt% inorganic filler and Ice about 75 wt%.

First-principles study of ground-state properties and high pressure behavior of ThO2

The mechanical properties, electronic structure and phonon dispersion of ground state ThO2 as well as the structure behavior up to 240 GPa are studied using first-principles density-functional theory. Our calculated elastic constants indicate that both the ground-state fluorite structure and high pressure cotunnite structure of ThO2 are mechanically stable. The bulk modulus, shear modulus, and Young's modulus of cotunnite ThO2 are all smaller by approximately 25% compared with those of fluorite ThO2. The Poisson's ratios of both structures are approximately equal to 0.3 and the hardness of fluorite ThO2 is 22.4 GPa. The electronic structure and bonding nature of fluorite ThO2 are fully analyzed, and show that the Th-O bond displays a mixed ionic/covalent character. The phase transition from the fluorite to cotunnite structure is calculated to occur at the pressure of 26.5 GPa, consistent with recent experimental measurement by ldiri et al. [1]. For the cotunnite phase it is further predicted that an isostructural transition takes place in the pressure region of 80-130 GPa.

Elasticity, band structure, and piezoelectricity of BexZn1-xO alloys

Lattice constants, elasticity, band structure and piezoelectricity of hexagonal wideband gap BexZn1-xO ternary alloys are calculatedusing firstprinciples methods. The alloys' lattice constants obey Vegard's law well. As Be concentration increases, the bulk modulus and Young's modulus of the alloys increase, whereas the piezoelectricity decreases. We predict that BexZn1-xO/GaN/substrate (x = 0.022) multilayer structure can be suitable for high-frequency surface acoustic wave device applications. Our calculated results are in good agreement with experimental data and other theoretical calculations. (c) 2008 Elsevier B.V. All rights reserved.

A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Pressure-induced phase transition of nanocrystalline zinc sulfide

In situ energy dispersive X-ray diffraction measurements on nanocrystalline zinc sulfide have been performed by using diamond anvil cell with synchrotron radiation. There is a phase transition which the ultimate structure is rocksalt when the pressure is up to 16.0GPa. Comparing the structure of body materials, the pressure of the phase transition of nano zinc sulfide is high. We fit the: Birch-Murnaghan equation of state and obtained its ambient pressure bulk modulus and its pressure derivative. The bulk modulus of nanocrystalline zinc sulfide is higher than that of body materials, it indicate that the rigidity of nanocrystalline zinc sulfide is high.

The main factor influencing the tensile properties of surface nano-crystallized graded materials

The improved mechanical properties of surface nano-crystallized graded materials produced by surface severe plastic deformation ((SPD)-P-2) are generally owing to the effects of the refined structure, work-hardened region and compressive residual stress. However, during the (SPD)-P-2 process, residual stress is produced simultaneously with work-hardened region, the individual contribution of these two factors to the improved mechanical properties remains unclear. Numerical simulations are carried out in order to answer this question. It is found that work hardening predominates in improving the yield strength and the ultimate tensile strength of the surface nano-crystallized graded materials, while the influence of the residual stress mainly emerges at the initial stage of deformation and decreases the apparent elastic modulus of the surface nano-crystallized graded materials, which agrees well with the experimental results. (C) 2010 Elsevier B.V. All rights reserved.