(1) Equation of State of Komatiite
The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity,US, and particle velocity, UP, in km/s follow the linear relationship US = 3.13(±0.03) + 1.47(±0.03)UP. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this US-UP relationshipgives the isentropic bulk modulus KS = 27.0 ± 0.6 GPa, and its first and second isentropic pressurederivatives, 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 compressionresults of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO94) will be neutrallybuoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would alsobe neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiiticliquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser thanthis komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskitemay be neutrally buoyant near 70 GPa.
At 40 GPa, the density of shock-compressed molten komatiite would be approximately equalto the calculated density of an equivalent mixture of dense solid oxide components. This observationsupports 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 spectrumof melts from basaltic through peridotitic that are related to the experimentally studied komatiiticliquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the densityof basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquidsare 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 fromascending 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 generatedby adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or thelower mantle (>670 km). The great depth of incipient melting implied by this model, and the meltdensity 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 bediapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotterthan the sources of MORBs and derived from great depth.
We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our modelconsiders the thermal structure of the magma ocean, density constraints on crystal segregation, andapproximate phase relationships for a nominally chondritic mantle. Crystallization will begin at thecore-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratifiedlower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantlemay be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation ofa dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but thisseptum must be permeable.
(2) Viscosity Measurement with Shock Waves
We have examined in detail the analytical method for measuring shear viscosity from thedecay of perturbations on a corrugated shock front The relevance of initial conditions, finite shockamplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditionsare discussed. The validity of the viscous perturbation approach is examined by numerically solvingthe second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilitiesmay occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimentalresults for water at 15 GPa are discussed, and it is suggested that the large effective viscositydetermined by this method may reflect the existence of ice VII on the Rayleigh path of theHugoniot This interpretation reconciles the experimental results with estimates and measurementsobtained by other means, and is consistent with the relationship of the Hugoniot with the phasediagram 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 effectiveviscosity estimates.
(3) Equation of State of Molybdenum at 1400°C
Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, arepresented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'S. of 244±2 GPa andits pressure derivative, K'OS of 4. A fit of shock velocity to particle velocity gives the coefficients ofUS = CO+S UP to be CO = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, CO, 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, θKOSθT|P, isapproximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamicGrüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisenequation of state adequately describes the high temperature behavior of molybdenumunder the present range of shock loading conditions.
