1. The most reasonable interpretation of these data is that alumina retains its semiconducting nature in the liquid state, and that the optical physics of the liquid differs only in degree from that already known and well characterized for the solid. Specifically, it appears that the emissivity of the liquid is controlled by impurities or native defects, just as in the solid, and is therefore variable. From studies on other materials it is known that the loss of long-range order in the liquid phase does not drastically change the optical properties if the short-range atomic order is retained.116.117 Such appears to be the case for liquid alumina. Strong Urbach tail absorption occurs inthe liquidbelow 400nm. strong multiphonon absorption above 4 pm, and weaker free-carrier emission dominates the 0.4 to 4 pm "valley" or "window" region. As expected, the Urbach tail and multiphonon absorption features are broader and the window region narrower in the liquid than in the solid. Despite large differences in individual measurements, all investigators observed free carrier visible and midinfrared emission which was much stronger than for crystalline sapphire at the melt point. The imaginary refractive index values for the liquid in the free carrier region were in the 104 to 10-3 range at the melt point temperature vs. roughly 10-7- 10-6 for pure sapphire. Based upon the red shift of the Urbach tail in the melt and also upon the observed activation energy of 50 - 60 kcallmole, the large increase in emission upon melting may possibly be attributed to a decrease in the band gap energy. (Strictly speaking, a liquid has a mobility gap instead of a band gap). Referringto Eq. (15), the approximate 10 - 20 kcal/mole reduction in activation energy upon melting corresponds to a factor of X 10- X 80 increase in the intrinsic free-carrier concentration. This presumes no change in the carrier effective mass. A reduction in the mobility gap energy would also decrease the activation energy and increase the ionization oi deeper Iying impurity and defect states.
2. The emissivities of liquid droplets in the rockel exhaust calculated from Mie theory and using the data of Figs. (4-7)range from roughly a few tenths oi a percent to several percent, depending upon droplet size, wavelength, and temperature and the data set or curve fit one chooses. Although individual droplet emissivities are not large, the combined effects of high number density and multiple scattering radiative transport combine to produce net plume emissivities which are high and comparable to observed heating rates. Although optical properties measurements of the melt have been helpful for understanding the general wavelength and temperature trends, there is currently no viable model for the mechanism or the intensity of the thermal infrared emission from the liquid.
3. Major uncertainties exist in rocket exhaust particle crystal phase, degree of undercooling, size distribution, completeness of combustion, and optical properties. In regard to optical properties, one must distinguish between extrinsic properties, which vary with impurity type and concentration, and intrinsic properties. The latter are due to the AI and 0 atoms and the associated underlying molecular structure of the material. Only intrinsic properties can be reliably modeled for rocket alumina. Examples include electronic interband transitions below approximately 200 nm, the near UV Urbach tail from 200 - 400 nm, the multiphonon transitions from roughly 4 - 12 pin, and the far infrared reststrahl bands from 12- 50 pm. The spectral interval of greatest importance to plume radiative heating, however, lies in the 0.5 to 4-pm band where the emissivity of alumina is due to free carriers. This emission is non-gray with an intensity roughly linearly proportional to wavelength. The observed wavelength dependence is consistent with the short carrier relaxation time determined from electrical conductivity measurements on the =2,000 K solid. Except for extremely pure samples at elevated temperatures, the free carriers in the solid are extrinsic, i.e., due to impurities and native defects. They are thus not amenable to modeling. Optical properties of pure sapphire can only be used to estimate a crude lower bound to the emission of solid-propellant rocket particles which is of little practical use. Measurements of actual solid-propellant rocket particles show emissivities from one to three orders of magnitude greater than for pure sapphire, depending upon contamination level. However, for energetic propellant formulations the plume heat transfer is dominated by liquid alumina droplets. The significant uncertainty in solid particle emissivities is therefore not a major contributor to uncertainty in the overall calculation of plume radiative heat transfer.
4. The emissivity of the iiquid is of greater importance to plume radiative heat transfer, as most of the thermal radiation from energetic propellants can be attributed to liquid alumina droplets in the near-field exhaust. The temperature and wavelength ranges of the various investigations of liquid alumina emissivity overlap only partially, making comparisons difficult. In addition, since no two measurements were performed in the same way or even with the same sample, it is not clear how much of the reported differences are real and how much are the result of systematic errors. Based upon the observed temperature dependence and the spectral location of the near-UV Urbach tail absorption, the qualitative optical properties and semiconducting nature of the hightemperature solid are evidently retained in the melt. All investigators agree that the visible and nearinfrared free-carrier emission of the liquid is very much greater than that of the crystalline solid or of pure powder heated to just below the melt point. This is consistent with the reduction in band gap of the liquid which may be inferred from the activation energy and the location of the Urbach tail. Shock tube measurements of pure vs. contaminated rocket particles above the melt point 78 provided initial evidence for the viewpoint that the free carriers in the liquid are intrinsic, as does the clustering of several experimentally determined activation energies near a common value of 50 - 60 kcal/mole. However, this is contraindicated by the considerable spread in absorption index values reported by different investigators and by the observaton of gas effects by Weber, et al.114 None of the available measurements simulated the exhaust gas composition of a typical solid-propellant rocket, but instead they were variously performed in argon, H2/02 flames, or hydrocarbon flames. In addition, the sample purities were generally not characterized well enough to answer questions regarding the possible effects of impurities. On the basis of the available data one must conclude that optical properties of the liquid in the important 0.5 to 4-pm region are controlled by extrinsic processes, just as in the solid, and will therefore vary with type and concentration of contaminants and the details of combustion. One must also distinguish between measurements of liquid alumina performed at fixed temperatures and those performed in cooling combustion or gas dynamic flows. In particular, three independent measurements of initially melted alumina cooled below the freezing point indicated no discontinuity in emissivity at the melt point temperature. The emissivity of the sub-cooled melt also differed widely between these investigators. Since rocket exhaust particles are formed in a rapid temperature quench, these data may actually be more relevant to plume radiative heating than data obtained with carefully controlled, steady temperatures.
5. In addition to uncertainty in the optical properties, there are other uncertainties associated with the proper application of such data to rocket exhaust alumina. For example, one does not know the precise nature or physical state of rocket exhaust alumina below the melt point. Numerous measurements have shown that alumina solidification kinetics are sluggish, suggesting that liquid alumina droplets in a nozzle expansion may possibly undercool 200 - 300 K or more. The relative importance of the metastable gamma alumina phases in solidification is poorly understood. Particle collections from non-afterburning plumes or possibly far-infrared reststrahl band measurements on small motors may help improve this situation. Exhaust plume calculations also indicate that substantial portions of the flow field will be occupied with mixed phase part solid - part liquid alumina with ill-definedoptical properties. The particle size distribution in the plume has proved very difficult to measure, and the available data are possibly subject to size biasing. Improved and preferably nonintrusivesizing techniques are very much needed. Contamination of rocket exhaust particles by unburned aluminum or carbon soot may possibly occur, leadingtoincreasedemissivity.Chemical characterization of particles collected from the plume far field may be misleading in this regard, as there is ample opportunity for physical and chemical processing between the nozzle exit and the far field. Finally, radiation measurements near the nozzle exit plane must account for scattered emission from the nozzle ( the so-called "searchlight effect"), as discussed by Laderman and Carlsonlla and by Reed, et a1.119