Orientation dependence of shock-induced heating in anharmonic molecular crystals

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Abstract
A significant development in the field of detonics is the observation of direction dependence of shock wave initiation to detonation of single crystals of energetic materials. Various mechanisms have been proposed to account for this direction dependence, but the seemingly simplest possibility not previously considered, that the direction dependence is due mainly to the anisotropy in the temperature increase generated by the shock, is investigated in this work. The temperature increase depends on the anharmonic potential. In the model system studied here, naphthalene, the anharmonic intermolecular potential is available from the literature. Using this potential, we calculate the directional compressibility, the mode Grüneisen parameters, and the bulk Grüneisen parameters along different crystallographic directions. These results show the temperature increase is quite a bit greater for a shock of given pressure along the a or b axes than along the c axis, mainly because the compressibility along the c axis is smaller. Using thermochemical data for energetic materials, it is shown the temperature increase anisotropy is large enough to lead to reaction rates which differ by several orders of magnitude, when typical initiating shocks are incident along different crystallographic directions.