Electronic charge distribution in crystalline germanium

We use a recently published set of high-accuracy structure factors, based on γ-ray measurements [Dewey et al., Phys. Rev. B 50, 2800 (1994)] to derive the charge density distribution in crystalline germanium with a millielectron-level resolution. We use a multipole expansion model of the charge densities represented as a superposition of orbital-dependent, nonspherical atomic charge densities. We include in the model anharmonic and nonrigid atomic thermal motions. This model is then fit to the measured structure factors. We find (i) a considerable improvement in the fit residuals (especially for the low-order structure factors) relative to our previous analysis, based on earlier measurements; (ii) a factor-of-2 improvement in the agreement between experiment and our earlier ab initio density-functional calculated structure factors; (iii) the evidence for the existence of nonrigid atomic thermal motion is marginal; (iv) a clear ∼15% expansion of the valence orbital density relative to the free Ge atom; and (v) a twofold reduced upper limit on the anharmonic force constant. These bring the structure of germanium into better agreement with those of silicon and diamond.