Precise lattice parameter determinations of diamond silicon and germanium by the asymmetric method

The construction of the apparatus for production of powder patterns at a definite temperature and the technique for evaluation of x-ray powder patterns by the asymmetric method are described in detail, and the mode of error elimination is discussed. A new scanning device is designed for use in x-ray diffraction work. A modified method is described for the determination of densities of solids, which eliminates some of the difficulties interfering with other similar methods thus far proposed. Formulae are derived for the calculation of density as well as for reduction of density at a desired temperature. The following conclusion are drawn from the results of the present investigation: The minor impurities found in the diamond samples are not dissolved but are included mechanically in the diamond crystals. The coefficient of expansion of diamond and silicon lattices, as determined by the present experiments, are in agreement with the respective data in the literature. Although there are no data available in the literature concerning the coefficient of expansion of germanium, the value reported here (5.93 x 10-6) is reliable. The density values of the purest elements, silicon and germanium, deviate considerably from those recorded in the literature. The crystal lattices of diamond, silicon, and germanium are sound or contain imperfections of the order of magnitude not exceeding the respecting limits of error of the present experiments. The diamond is more reliable than quartz for use as a standard substance in the x-ray diffraction work. The asymmetric method is precise and convenient in its application to accurate determinations of the unit cell dimensions of crystalline materials. The method requires no standard substances and no mathematical corrections for calculation of lattice constants except that for refraction of x-rays. The densities of purest silicon and germanium should be investigated more thoroughly, preferably using the modified procedure described. It is further recommended that a study be made of the effects of impurities on the lattice coefficients of expansion of silicon and germanium --Abstract