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Three problems involving heat transfer from a protein crystal to a cooling agent are analyzed: flash-cooling in a cold nitrogen- or helium-gas stream, plunge-cooling into liquid nitrogen, propane or ethane and crystal heating in a cold gas stream owing to X-ray absorption. Heat transfer occurs by conduction inside the crystal and by convection from the crystal's outer surface to the cooling fluid. For flash-cooling in cold gas streams, heat transfer is limited by the rate of external convection; internal temperature gradients and crystal strains during cooling are very small. Helium gas provides only a threefold improvement in cooling rates relative to nitrogen because its much larger thermal conductivity is offset by its larger kinematic viscosity. Characteristic cooling times vary with crystal size L as L3/2 and theoretical estimates of these times are consistent with experiments. Plunge-cooling into liquid cryogens, which can give much smaller convective thermal resistances provided that surface boiling is eliminated, can increase cooling rates by more than an order of magnitude. However, the internal conduction resistance is no longer negligible, producing much larger internal temperature gradients and strains that may damage larger crystals. Based on this analysis, factors affecting the success of flash-cooling experiments can be ordered from most to least important as follows: (1) crystal solvent content and solvent composition, (2) crystal size and shape, (3) amount of residual liquid around the crystal, (4) cooling method (liquid plunge versus gas stream), (5) choice of gas/liquid and (6) relative speed between cooling fluid and crystal. Crystal heating by X-­ray absorption on present high-flux beamlines should be small. For a fixed flux and illuminated area, heating can be reduced by using crystals with areas normal to the beam that are much larger than the beam area.

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