Densities and Imperfections of Single Crystals

The densities of Si, Al, Ca${\mathrm{F}}_2$, CsI, Ge, TlCl, TlBr, and Si${\mathrm{O}}_2$ (quartz) have been computed from lattice constants and molecular weights obtained from International Atomic Weights, and compared with the densities as determined by hydrostatic weighing of large single crystals. The hydrostatic density of Ge proves too large by 0.00193. This discrepancy disappears when the mass-spectroscopic atomic weight is used for the density calculation. Also for Si, Al, and Ca${\mathrm{F}}_2$ a better agreement results with mass-spectroscopic atomic weights. Therefore, we conclude that the mass-spectroscopic atomic weights are more reliable than the officially accepted ones. From measured densities and lattice constants of Si, Al, Ca${\mathrm{F}}_2$, and Ge, Avogadro's number is obtained as 6.02368×${10}^{23}$ ${\mathrm{mole}}^{-1\mathrm{}}$ (chemical scale). The relative density defects for our samples of Si, Al, Ca${\mathrm{F}}_2$, and Ge proves to be negligible within the limit of our measurements (${10}^{-6\mathrm{}}$). We consider these crystals the most perfect that we have obtained up to the present time. A somewhat higher relative density defect in quartz (11×${10}^{-6\mathrm{}}$) may be caused by uncertainty of the data used for the computation of the density and that for CsI (13×${10}^{-6\mathrm{}}$) by Rb contamination. TlCl and TlBr show the greatest relative density defects, 43×${10}^{-6\mathrm{}}$ and 40×${10}^{-6\mathrm{}}$, respectively. These crystals may contain vacancies or dislocations in the order of ∼5×${10}^{18}$ per cc, as is known also for the silver halides.