Determination of structure factors of germanium by the critical-voltage and convergent-beam diffraction methods

The structure factors for the 111 and the “forbidden” 222 reflections of germanium are consistently determined by combining two independent electron diffraction measurements: 1. the critical voltage Ec = (908.5 ± 6.4) kV for the 333 reflection and 2. the rocking curves in convergent-beam diffraction patterns taken at the 111 and 222 Bragg settings with incident electrons of 100 kV. The values obtained for these factors without thermal vibrations are F = −155.74 ± 0.07 and F = 1.24 ± 0.32. These correspond to the atomic scattering factor f111 = 27.53 ± 0.01 and the anti-centrosymmetric component of f222, f = −0.16 ± 0.04, respectively. The mean value of f111 is in good agreement with earlier X-ray measurements and its percentage error, 0.04%, is much smaller than other published values.