Optical Radiation from Shock-Compressed Materials

Citation

Svendsen, Robert Frederik, Jr. (1988) Optical Radiation from Shock-Compressed Materials. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/m809-aq12. https://resolver.caltech.edu/CaltechTHESIS:04192010-095015524

Abstract

Recent observations of shock-induced radiation from oxides, silicates and metals of geophysical interest constrain the shock-compressed temperature of these materials. In these experiments, a projectile impacts a target consisting of a metal driver plate, metal film or foil layer, and transparent window. We investigate the relationships between the temperature inferred from the observed radiation and the temperature of the shock-compressed film or foil and/or window. Changes of the temperature field in each target component away from that of their respective shock-compressed states occur because of: 1) shock-impedance mismatch between target components, 2) thermal mismatch between target components, 3) surface roughness at target interfaces, and 4) conduction within and between target components. In particular, conduction may affect the temperature of the film/foil-window interface on the time scale of the experiments, and so control the intensity and history of the dominant thermal radiation sources in the target. We use this type of model to interpret the radiation emitted by a variety of shock-compressed materials and interfaces.

In a series of experiments on films (~ 1 μm thick) and foils (~ 10-100 μm thick) of Fe in contact with Al₂O₃ and LiF windows, Fe at Fe-Al₂O₃ interfaces releases from experimental shock-compressed states between 245 and 300 GPa to interface states at pressures between 190 and 230 GPa, respectively, and temperatures between 4000 and 8000 K, respectively. These temperatures are ≈ 200-1500 K above model calculations for Fe experiencing no reshock at ideal (smooth) Fe-Al₂O₃ interfaces. We attribute this discrepancy to localized dissipation at the Fe-Al₂O₃ interface, producing higher interface temperatures than uniform compression and energy transfer. This behavior is observed for both Fe foils and films. Both 190 GPa, localized heating due to gaps or interface-surface roughness does not apparently affect the temperature of Fe-Al₂O₃ interfaces. In contrast, from the same range of shock states, Fe at Fe-LiF interfaces releases to states between 130 and 160 GPa (because it has a lower shock impedance than Al₂O₃); both the data and model imply that Fe-LiF interfaces respond ideally to shock-compression up to 140 GPa (where the data end). Both the Fe-Al₂O₃ data and the model suggest that the degree of reshock and localized heating is strongly pressure-dependent above the solid Fe-liquid Fe phase boundary. LiF appears to be a more ideal window than Al₂O₃ also because it is a poorer thermal inertia (i. e., kρc_P, where k is the thermal conductivities, ρ is the mass density, and c_P is the specific heat at constant pressure) match to Fe than is Al₂O₃.

In the absence of energy sources and significant energy flux from other parts of the target, the rate of change of the film/window or foil/window, interface temperature, dT_INT(t)/dt, is proportional to -μexp(-μ²), where μ ≡ δ_FW/2√(κ_Ft), δ_FW is the thickness of the high-temperature (reshocked) zone in the film/foil layer at the film/foil-window interface, κ_F, is the thermal diffusivity of the film/foil material, and 0 ≤ t ≤ t_exp (t_exp is the time scale of the experiment, 200- 400 ns). On this basis, the temperature of a thin (δ_FW << 2√(κ_Ft_exp) reshocked layer relaxes much faster than that of a thick (δ_FW >> 2√(κ_Ft_exp)) layer. We estimate √(κ_Ft_exp) ~ 10 μm for Fe under the conditions of Fe-Al₂O₃ and Fe-LiF interfaces at high pressure. In this case, a 100-μm-thick reshocked Fe layer would relax very little, remaining near T_INT(0) on the time scale of the experiment, while a 1-μm-thick reshocked Fe layer would relax on a time scale of ≾ 10 nsec, which is much less than t_exp, to a temperature just above T_INT(∞), i.e., the temperature of the ideal (smooth) interface.

Greybody model fits to radiation from an Fe film-Al₂O₃ interface resolve a gradually increasing effective greybody emissivity, ε̂_gb(t), and a gradually decreasing greybody temperature, T_gb(t). This behavior is characteristic of most Fe-Al₂O₃ interface experiments. The decrease of T_gb(t) can be explained in terms of the reshock model for the film/foil-window interface temperature, T_INT(t). For this experiment, the model implies that the thickness of the reshocked film layer, δ_FW, is approximately equal to the conduction length scale in the film, √(κ_Ft_exp) (~10 μm for Fe). Further, assuming 1) T_gb(t) = T_INT(t), 2) the thermal inertia of the film is an order of magnitude less than the window, and δ_FW ≾ 2√(κ_Ft_exp), the greybody constrains the temperature rise due to localized heating through reshock ΔT_FW to ≾ 2000K. A slight decrease of the Al₂O₃ absorption coefficient upon shock compression can explain the slight increase of ε̂_gb(t) with time; this may be consistent with the low-pressure observation that the refractive index of Al₂O₃ seems to decrease with pressure.

In contrast to the Fe-Al₂O₃ results, greybody fits to radiation from an Fe foil-LiF interface show a relatively constant greybody temperature, and a decreasing greybody emissivity. The constant greybody temperature implies a constant interface temperature, as expected for an interface experiencing minimal reshock, while the decaying ε̂_gb(t) is consistent with a shock-induced increase in the absorption coefficient of LiF. Setting T_INT(0) = T_gb(0), we fit a simplified version of the full radiation model to these data and obtain an estimate of the absorption coefficient (~100 m⁻¹) of LIF shock-compressed to 122 GPa.

Shock-compressed MgO radiates thermally at temperatures between 2900 and 3700 K in the 170-200 GPa pressure range. A simple energy-transport model of the shocked-MgO-targets allows us to distinguish between different shock-induced radiation sources in these targets and to estimate spectral absorption-coefficients, a_λMgO, for shocked MgO (e.g., at 203 GPa, a_λMgO ~ 6300, 7500, 4200 and 3800 m⁻¹, at 450, 600, 750 and 900 nm, respectively). The experimentally inferred temperatures of the shock-compressed states of MgO are consistent with temperatures calculated for MgO, assuming that 1) it deforms as an elastic fluid, 2) it has a Dulong-Petit value for specific heat at constant volume in its shocked-state, 3) it undergoes no phase transformation below 200 GPa, and 4) the product of the equilibrium thermodynamic Gruneisen's parameter, γ, and the mass density, ρ, is a constant and equal to 4729.6 kg/m³.

Optical radiation from shock-compressed crystal CaMgSi₂O₆ (diopside) constrains crystal CaMgSi₂O₆ Hugoniot temperatures of 3500-4800 K in the 150-170 GPa pressure range, while glass CaMgSi₂O₆, with a density 87% of that of crystal CaMgSi₂O₆, achieves Hugoniot temperatures of 3600-3800 K in the 105-107 GPa pressure range. The radiation history of each of these materials implies that the shock-compressed states of each are highly absorptive, with effective absorption coefficients of ≳ 500-1000 m⁻¹. Calculated Hugoniot states for these materials, when compared to the experimental results, imply that crystal CaMgSi₂O₆ Hugoniot states in the 150-170 GPa range represent a high-pressure phase (HPP) solid (or possibly liquid) phase with an STP density of ≈ 4100 ± 200 kg/m³, STP Grüneisen's parameter of ≈ 1.5 ± 0.5 and STP HPP-LPP specific internal energy difference, Δe_i^β-α, of 0.9 ± 0.5 MJ/kg. These results are consistent with a CaSiO₃-MgSiO₃ perovskite high-pressure phase assemblage. For glass CaMgSi₂O₆, we have the same range of HPP properties, except that Δe_i^β-α, is 2.3 ± 0.5 MJ/kg, a strong indication that the glass CaMgSi₂O₆ Hugoniot states occupy the liquid phase in the system CaMgSi₂O₃. Comparison of the pressure-temperature Hugoniot of crystal CaMgSi₂O₆ with the Hugoniots of its constituent oxides (i.e., SiO₂, CaO and MgO) demonstrates the primary influence of the HPP STP density of these materials on the magnitude of the temperature in their shock-compressed states. The crystal Di pressure-temperature Hugoniot constrained by the experimental results lies at 2500-3000 K between 110 and 135 GPa, within the plausible range of temperature profiles in the mantle near the core-mantle boundary.

In the context of the above model considerations, we constrain the Hugoniot temperature of Fe shock-compressed to 300 GPa via thermal radiation from the Fe film/foil-window interfaces discussed above. The temperature of the film/foil-window interface is obtained from measurements of the spectral radiance of the interface, for the duration of the shock transit through the window, using a 4-wavelength optical radiometer. The model indicates that the experimental observations constrain the interface temperature, rather than the the temperature of the Al₂O₃ or LiF windows. Our results further imply that Al₂O₃ remains at least partially transparent to at least 230 GPa and ~ 9,000 K. Without correcting the Hugoniot temperatures inferred from the interface temperatures for the effects of reshock, we infer a melting temperature of Fe along its Hugoniot of 6700 ± 400 K at 243 GPa. Combining these estimates with the lower-pressure (≤ 100 GPa) static Fe melting data of Williams and Jeanloz (1986), we infer a melting temperature for Fe of approximately 7800 ± 500 K at the pressure of the Earth's outer-inner boundary. Assuming that Fe or an Fe-light element alloy is forming the inner core from an Fe-light element mixture in the liquid outer core, this temperature also represents an upper bound to the temperature at the outer-inner core boundary.

Liquid-state and solid-state model fits to melting data for Fe, FeS and FeO provide constraints for calculating ideal phase relations in Fe-FeS and Fe-FeO systems in the pressure range corresponding to the earth's outer core. The liquid-state model fit to the Fe melting data of Williams and Jeanloz (1986) places constraints on the temperature and other properties along the liquidus above the range of their data. The temperature along the best-fit Fe liquidus is 5000 K at 136 GPa and 7250 K at 330 GPa, which is somewhat lower than that implied by the Hugoniot results (~ 7800 K). This discrepancy may be due to the reshock effect discussed above, or some inaccuracy in the extrapolation, presuming the Hugoniot results represent the equilibrium melting behavior of Fe. Constraints on the solidi of FeS and FeO from the comparison of data and solid-state model calculations imply that FeS and FeO melt at approximately 4610 K and 5900 K, respectively, at 136 GPa, and approximately 6150 K and 8950 K, respectively, at 330 GPa. Calculations for the equilibrium thermodynamic properties of solid and liquid Fe along the coincident solidus and liquidus imply that the entropy of melting for Fe is approximately independent of pressure at a value of approximately R (where R is Ryberg's constant), while the change in the molar heat capacity across the transition increases with pressure from approximately 0.5 R to 4R between standard pressure and 330 GPa. We use these constraints to construct ideal-mixing phase diagrams for Fe-FeS and Fe-FeO systems at outer core pressures, assuming that Fe and FeS, or Fe and FeO, respectively, are the solid phases in equilibrium with the liquid Fe-FeS or Fe-FeO mixtures, respectively.

The composition of the Fe-X (X = 0 or S) liquid mixture relative to the eutectic composition of the Fe-FeX system determines whether Fe or FeX will solidfy at the liquidus. For these ideal mixing calculations, the eutectic composition is controlled by the ratio of the end-member (i.e., Fe and FeX) melting temperatures at a given pressure. If Fe and FeX have the same melting temperature, for example, the eutectic composition is 25 mole % X; if the melting temperature of FeX is greater or less than Fe, the eutectic composition will be displaced to more Fe or FeX rich compositions, respectively. Since, as quoted above, the melting temperature of FeO is about 1500 K greater than that of Fe at 330 GPa, which is in turn about 1000 K greater than that of FeS at this pressure, we note that calculated Fe-FeO eutectic compositions at 330 GPa (15-20 mole % O) are less than 25 mole % O, while calculated Fe-FeS eutectic compositions at 330 GPa (23-30 mole % S) are generally greater than 25 mole % S. The mass density of the Earth's outer core just above the inner core boundary is approximately 12160 kg/m³, and we note that this is also the density of an ideal mixture of 93 mole % Fe and 7 mole % S (i.e., 14 mole % FeS), and a similar mixture of approximately 72 mole % Fe and 28 mole % 0 (56 mole % FeO). Consequently, these calculations and considerations imply that an O-rich outer core is more likely to lie on the FeO-rich side of the Fe-FeX eutectic, while an S-rich outer core is more likely to lie on the Fe-rich side of the Fe-FeX eutectic.

The temperature of the Fe-FeS eutectic is lower than the Fe-FeO eutectic, being approximately 5000 K at 330 GPa. Note that the eutectic temperature represents a lower bound to temperatures at the outer-inner core boundary under the hypothesis that this boundary represents the liquidus in an Fe-X mixture. Eutectic and end-member melting temperatures in both the Fe-FeS and Fe-FeO systems imply, in the context of the outer-inner core boundary-phase boundary hypothesis, that previous widely-accepted temperature profiles for the outer core, ranging from ≾ 3000 K at the 136 GPa, the core-mantle boundary, to ≾ 4200 K at 330 GPa, the outer-inner core boundary, are about 1000-1500 K too low. This possibility implies that at least one boundary layer of 1000-1500 K exists in the mantle, possibly at its base in the D" region.

Thesis Files