The charge density in beryllium metal

Two of the four electrons of the beryllium atom are valence electrons. The bonding in the metallic solid must be accomplished by a combination of 2s and 2p orbitals if not, the s band would be completely filled and Be would be an insulator, or perhaps not a room-temperature solid at all. In the orbital description, the two valence electrons of each Be atom participate in two 2s2p hybrid electron pair bonds, spread over the 12 nearest neighbors of the hep structure. 

In a metal like Be, extinction can be a cumbersome effect, especially if unrecognized, as appears to have been the case of the early 1972 data. It was very small in the LH data collected on a small sample, but significant in the 0.12 A 

The reliable experimental information on the absolute scale and thermal vibrations of beryllium metal made it possible to analyze the effect of the model on the least-squares scale factor, and test for a possible expansion of the 1 s core electron shell. The 0.03 A y-ray structure factors were found to be 0.7% lower than the LH data, when the scale factor from a high-order refinement (sin 6/X) 0.65 A l) is applied. Larsen and Hansen (1984) conclude that because of the delocalization of the valence electrons, it is doubtful that diffraction data from a metallic substance can be determined reliably by high-order refinement, even with very high sin 0/X cut-off values. This conclusion, while valid for the lighter main-group metals, may not fully apply to metals of the transition elements, which have much heavier cores and show more directional bonding. 

A K-refinement of the 0.12 A y-ray data reproduces the absolute scale poorly when the neutron UtJ thermal parameter values are used (Hansen et al. 1987). The discrepancy can be removed by introduction of a core-tc-parameter, which refines t0 Kcore = 0.988 (2), corresponding to a 1.2% linear expansion. This is supported by a similar result obtained with the LH X-ray data, and related to the scale factor discrepancy noted above. Hansen, Schneider, Yellon, and Pearson (1987), conclude that without independent knowledge of either the scale or the thermal parameters, good agreement with experiment can be achieved, but the resulting scale factor may be in error by as much as 2.5%. 

Though the core expansion leads to the appropriate fit, it may not be the proper explanation for the scale factor discrepancy. Hansen et al. (1987) note that the expansion of the core would lead to a decrease of 7.5 eV in the kinetic energy of the core electrons, at variance with the HF band structure calculations of Dovesi et al. (1982), which show the decrease to be only about 1.5 eV. An alternative interpretation by von Barth and Pedroza (1985) is based on the condition of orthogonality of the core and valence wave functions. The orthogonality requirement introduces a core-like cusp in the s-like valence states, but not in the p-states. Because of the promotion of electrons from s - p in Be metal, the high-order form factor for the crystal must be lower than that for the free atom. It is this effect that can be mimicked by the apparent core expansion. 

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