Optical radiation from shock-compressed materials and interfaces

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. Comparing this model to experiments on Fe‐Fe‐Al_2O_3 and Fe-Fe‐LiF targets, we note that: 1) Fe at Fe‐Al_2O_3 interfaces releases from shock‐compressed states between 245 and 300 GPa to interface states between 190 and 230 GPa, respectively, with temperatures ≈200–2000 K above model calculations for Fe experiencing no reshock at smooth Fe‐Al_2O_3 interfaces. This is so for both Fe foils and films. Below 190 GPa, reshock heating does not apparently affect the temperature of Fe‐Al_2O_3 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 Al_2O_3); the data and model imply that Fe experiences little or no reshock at Fe‐LiF interfaces up to 140 GPa (where the data end). Both the Fe‐Al_2O_3 data and the model suggest that the degree of reshock is strongly pressure dependent above the solid Fe‐liquid Fe phase boundary. LiF appears to be a more ideal window than Al_2O_3 also because it is a poorer thermal‐inertia match to Fe than is Al_2O_3. 2) In the absence of energy sources and significant energy flux from other parts of the target, the rate of change of the film/foil‐window interface temperature, (dT_(INT)/dt), is proportional to‐μexp(−μ2), where $$\mu \equiv \delta _{{\rm FW}} /2\sqrt {\kappa _{\rm F} t} ,\,\delta _{{\rm FW}}$$ is the thickness of the 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). On this basis, the temperature of a thin $$(\delta _{{\rm FW}} \ll 2\sqrt {\kappa _{\rm F} t_{\exp } } )$$ reshockled layer relaxems much faster than that of a thick $$(\delta _{{\rm FW}} \gg 2\sqrt {\kappa _{\rm F} t_{\exp } } )$$ layer. We estimate $$\sqrt {\kappa _{\rm F} t_{\exp } } \sim 10\,\mu {\rm m}$$ 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 almost instantaneously (i.e., on a time scale much less than t_(exp)) to a temperature just above T_(INT)(∞). 3) Greybody fits to an Fe‐Fe film‐Al_2O_3 experiment produce a gradually increasing effective greybody emissivity, $$\hat \varepsilon _{{\rm gb}} (t)$$, and a gradually decreasing greybody temperature, T_(gb)(t). This behavior is characteristic of most Fe‐Fe‐Al_2O_3 experiments. The decrease of T_(gb)(t) can be explained in terms of the 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, $$\sqrt {\kappa _{\rm F} t_{\exp } } ( \sim 10\,\mu {\rm m for}\,{\rm Fe})$$. Further, assuming T gb(t)=T INT(t), the greybody fit constrains the amount of reshock, ΔT_(FW), to ≲2000 K with σ_(WF), the film/foil‐window thermal mismatch, ∼0.1, and $$\delta _{{\rm FW}} \le 2\sqrt {\kappa _{\rm F} t_{\exp } }$$. A slight decrease of the Al2O3 absorption coefficient upon shock compression can explain the slight increase of $$\hat \varepsilon _{{\rm gb}} (t)$$ with time; this may be consistent with the observation that the refractive index of Al_2O_3 seems to decrease with pressure. 4) In contrast to the Fe‐Fe‐Al_2O_3 results, greybody fits to data from an Fe‐Fe foil‐LiF target 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 $$\hat \varepsilon _{{\rm gb}} (t)$$ 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.

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