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How Hot Is Hot?
Conservation of momentum, mass, and energy are implicit in Hugoniot curves, but the curves provide no direct way to derive temperature at high pressures. Even after 20 years of study, scientists still do not agree on the melting temperature of iron at pressures above 100 gigapascals (1 gigapascal equals 10,000 times atmospheric pressure at Earth's surface). Recall that temperature is a critical variable in a material's equation of state.
Temperatures in a gas-gun experiment can reach as high as 7,000 kelvin, which contrasts with the relatively cool 5,800 kelvin at the surface of the Sun. The only way now to measure such high temperatures during an experiment is with optical pyrometry. A pyrometer measures the radiance—a combination of brightness and color—of the shocked sample. A simple calculation then translates radiance to temperature. That sounds good in theory, but the reality is not so easy.
All measurements of shocked metals and other opaque materials must be taken through a window. A window made of a strong material preserves the surface of the sample at high pressure while allowing light from the sample to pass through to a fiber-optic detector. "But," notes Holmes, "at very high temperatures, the window can absorb light and emit its own light, and the window's presence changes the final state of the sample." Researchers are just beginning to be able to account for the effects of the window on overall radiance and hence on measured temperature.
Physicist Dave Hare is studying the properties of window materials. Lithium fluoride has been used as a window material for gas-gun experiments for many years. For many experiments, it is fine. But for planetary studies and some other types of experiments, the window material needs to be stiffer (harder to compress) to be an effective window in gas-gun experiments. Most of Hare's research centers around sapphire, another window material used for many years by Livermore researchers. "Sapphire should be a great window," he says. "It is dense and stiff, and its optical transparency at room temperature and pressure is excellent. But at shock pressures above 200 gigapascals, its transparency degrades too much for it to be useful. I've been trying to figure out why."
In one series of experiments, Hare has found that the orientation of the sapphire crystal relative to the direction of the shock wave makes a big difference in determining its light emissions when shocked. Besides providing an understanding of how sapphire stands up to strong shock waves, these data also help to show how strong materials are deformed by shock waves.
Measuring thermal conductivities under high-pressure conditions is not easy. But thermal conductivity measurements of window and sample materials are crucial to deriving accurate temperatures of the sample's interior. While the pyrometer measures the sample's surface temperature, the interior temperature is the real subject of concern. Because the sample and the window are usually at different temperatures when shocked, heat can flow from the hot sample to the colder window, altering the temperature that the pyrometer measures. Once the thermal conductivity of the window and the sample are known, experimenters can correct their data to derive a more accurate temperature of the sample's interior.
Physicist Jeff Nguyen is tackling another area that is critical to converting radiance data to temperature. In these calculations, emissivity—which measures how effectively a hot body radiates energy—is assumed to be constant at all pressures and wavelengths. Physicists have known that this is not in fact the case but have had no way to determine the precise changes with pressure. According to Nguyen, "To say that emissivity at high pressures is not well understood is an understatement. Right now, there are virtually no data on emissivity at high pressures."
Emissivity measurements at ambient pressures and high temperatures have been done routinely. But no definitive theoretical or experimental work has been done at high pressure, especially at the pressures produced by shock compression.
Nguyen's emissivity experiments of sample materials under shock conditions were performed on metals such as aluminum, copper, and iron. In the experiments, a laser was reflected off a metal target that was shocked, and Nguyen measured the change in the light's polarization as the metal underwent shock compression. These experiments were the first of their kind. The results are expected to have a major effect on the study of phase diagrams.
"Our goal," says Holmes, "is to do a shock experiment and know accurately what the temperature inside a sample is. Temperature is a fundamental property. It is, after all, the `thermo' in thermodynamic. But first, we need to know enough about window properties, the emissivity of metals, and the conductivity of windows and metals to separate the sample's radiance from the window's." |