Citation
Miller, Gregory Hale (1990) The Equation of State and Petrogenesis of Komatiite. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/r0pt2227. https://resolver.caltech.edu/CaltechTHESIS:03272015161328191
Abstract
(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 (FO_{94}) 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 garnetmajorite may be less dense than this komatiitic liquid in the 2024 GPa interval, however pyropicgarnet 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 shockcompressed 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 (≈500670 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 coremantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with ironenriched 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 secondorder NavierStokes equations. These numerical experiments indicate that shock instabilities may occur even when the KontorovichD'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_{OS}θT_{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 MieGrüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Geology 
Degree Grantor:  California Institute of Technology 
Division:  Geological and Planetary Sciences 
Major Option:  Geology 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  27 April 1990 
Record Number:  CaltechTHESIS:03272015161328191 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:03272015161328191 
DOI:  10.7907/r0pt2227 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  8806 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  30 Mar 2015 18:35 
Last Modified:  19 Apr 2021 22:35 
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