THE COVALENT BOND OF SILICON AND DIAMOND AS SEEN BY LATTICE DYNAMICS
J. Kulda1, R. Bauer2, H. Sterner2, D. Strauch2
1Institut Laue-Langevin, BP 156, 38042
Grenoble Cedex, France
2 Institut für theoretische Physik,
Universität Regensburg, Regensburg, Germany
Keywords: diamond,
silicon, covalent bond, charge densities, lattice dynamics
The exceptional hardness of diamond has no counterpart similarly to the rare negative thermal expansion of silicon and germanium at low temperatures. Obviously these features are related to differences in the topology of charge densities in their covalent bonds, addressed by theory and X-ray diffraction experiments since long ago. The ab initio calculations reached unprecedented accuracy in the last decade and provide quite clear pictures of bond charge distributions in both elements, differing in a subtle but qualitative manner. While the diamond bond is characterised by a cloud joining in a continuous manner the pairs of neighbouring ions, the bond charge of silicon can be characterised as a pseudo-atom [1] separated from either ion by a narrow valley of a negative deformation density. As a consequence the tangential strength of the silicon bonds is much weaker than the radial one as opposed to the diamond case.
A direct verification of these predictions is straightforward in principle - a Fourier synthesis of the charge densities from observed X-ray structure factors - but difficult in reality. While normal experimental data deduced from Bragg reflection intensities usually do not reach sufficient accuracy because of a variety of experimental uncertainties (absorption, extinction, thermal motion,...) the sets of structure factors determined from Pendellosung oscillations existing for diamond and silicon are quite limited in the momentum transfer range and need thus - despite their unmatched accuracy - a special treatment of the truncation effects to provide a confirmation for the calculated topologies [2,3].
As a logical continuation of the ab initio charge density calculations the lattice dynamics of a crystal can be predicted within the density-functional perturbation theory [4]. Such calculation is carried out selfconsistently using as input only quantities referring to the unperturbed crystal with atoms in their undisplaced positions. A comparison of calculated and observed phonon frequencies and polarisation vectors can then provide another, less direct, but under circumstances more significant experimental test of the theory.
We have carried out such calculations for diamond [4] and silicon [5] and confronted their results with new, high accuracy experimental data obtained by neutron inelastic scattering [5-7]. Contrary to usual experimental investigations of lattice dynamics limited to determination of the phonon frequencies, we have refined also the eigenvectors from the observed inelastic structure factors to complete the determination of the dynamical matrix. The excellent agreement we have obtained between observed and calculated parameter values, describing the dramatic qualitative differences in lattice dynamics of the two materials, fully confirms the adequacy of the bond charge density picture provided by the ab initio calculations.