Tetrahedral structures in amorphous carbons

Abstract

SHORT COMMUNICATIONS have the 4d 1° configuration in the ground state and have a preference for the tetrahedral sites. The dsp ~ hybridiza-tion for In 3+, suggested by Goodenough & Loeb (1955), does not appear feasible on energy considerations, l~e-cently Miller (1959) has calculated site preference energy in spinels for different cations, and accordingly it can be concluded that the 'inverse' structure is more stable than the 'normal' by about 11 kcal./g.mol, and hence the structure should be almost completely 'inverse' at room temperature. Further discussion of the structure along with the infrared absorption analysis results will be published elsewhere. Our thanks are due to Dr A. P. B. Sinha for valuable discussions. The two well-known crystalline forms of carbon are graphite and diamond (face-centered cubic). X-ray diagrams of amorphous carbon contain three or more diffuse bands. Heretofore emphasis has been placed on the fact that the angular positions of these bands correspond approximately to the positions of the (002), (100), (110), etc., reflections of graphite. Strong peaks at the angular positions of the (00l) reflections of graphite lattice tend to support the presence of graphite-like layers (turbostratic) in carbons (Warren, 1941; Biscoe & Warren, 1942). However, some non-graphitizing (Franklin, 1951) carbons have weak peaks at these angular positions and qualitative and quantitative deductions regarding their structure are based on profile analyses of the scattering intensities in terms of the (h/c) reflections of graphite-like layers and Fourier transforms of the scattering intensities (Franklin, 1950). The hardness, density and non-graphitizability of some carbons do not appear to be entirely compatible with a graphite-like structure. Therefore, theoretical work on the scattering intensities of tetrahedrally-bonded structures of carbon appeared desirable. Preliminary results are presented here, and full details will be published later. A graphite-like layer containing 26 carbon atoms (Fig. 1, Model No. 20) was first considered. The intensity J(s) in atomic units, scattered at any angle 20, was computed by the Debye formula (Debye, 1915): J(s) =.~, (n(r)/N) sin 2~rs/(2rtrs) r where s=2 sin 0/A, n(r) is the number of interatomic distances of length r within the molecule, irrespective of direction, and N is the total number of atoms in the molecules. All carbon bonds were taken to be of equal length, 1-4174 A (cf. Diamond, 1957) and all interbond angles to be 120 °. After determining the interatomie distances and their number, intensity data were computed numerically on the Univac 120. The results are shown in Fig. 2 (solid line). A molecule containing 26 carbon atoms arranged in a diamond type lattice shown in Fig. 1 (Model No. 12) * Special Coal Research Section, Bureau of Mines, Region V, U.S. Department of the Interior, Pittsburgh, Pa., U.S.A. was next considered. The molecule formed a tetrahedron. All carbon bonds were taken to be 1-5420 /~ in length and all interbond angles 109 ° 28.4', the tetrahedral bond angle. The computed curve is shown in Fig. 2 (dashed line). In a diamond lattice carbon atoms form cross-linked buckled layers composed of six-membered rings (chair type). Cross-linking is in such a manner that it yields a face centered cubic lattice, i.e., the projections on the (111) planes of the adjacent buckled layers do not superimpose. If the projections do superimpose a hexagonal Model No. 20. Graphite-like layer /A\\ / \ / / \ / \ // \ /// \\\\ Model No. 12. Projection of tetrahedron on {lid plane of diamond lattice. Shaded circles show superimposed atoms. Model No. 19. Projection of hexagonal lattice on (1001 plane. Fig. 1. Diagrams of models considered.