Allotropes of Carbon

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For more information, view Chapter 17:
Nature of Solid Molecular Bond of the Three Allotropes of Carbon

Allotropes of Carbon

Go to: Diamond | C₆₀ Fullerene | Graphite

Diamond

The tetrahedral crystal structure of diamond shown with 51 carbon atoms. Click to enlarge.

The 3D model is included in the Millsian software beta.

Below are calculated and experimental values for select parameters. Calculations are exact, closed-form solutions containing physical constants only.

	Calculated	Experimental
C-C Bond length (a₀)	1.53635	1.54428 [1]
Total Energy (eV)	3.74829	3.704 [2]
C_bC_aC_c Bond Angle (°)	109.5	109.5 [2,3]

C₆₀ Fullerene

The C₆₀ fullerene has been solved in closed-form using CQM. The 3D model is included in the Millsian software beta.

Hover to view semi-transparent image. Click to enlarge.

C₆₀ has 60 carbon atoms and 90 bonds, 60 of which are single bonds, and 30 of which are aromatic double bonds. It has 20 hexagonal structures and 12 pentagonal structures. The pentagonal structures contain the single bonds, and and the bridging bonds between pentagonal structures contain the double bonds.

Below are calculated and experimental values for select parameters. Calculations are exact, closed-form solutions containing physical constants only.

	Calculated	Experimental
C-C Bond length (a₀)	1.45345	1.455 [4]
C=C Bond length (a₀)	1.39140	1.391 [4]
C₆₀ Total Bond Energy (eV)	419.75539	419.73367 [5]
C=C-C Bond Angle (°)	120.00	120.00 [6]
C-C-C Bond Angle (°)	108.00	108.00 [6]

Graphite

The structure of graphite, shown with layers of planes. Click to enlarge.

The 3D model of a layer of graphite is included in the Millsian software beta.

Below are calculated and experimental values for select parameters. Calculations are exact, closed-form solutions containing physical constants only.

	Calculated	Experimental
C=C Bond length (a₀)	1.39140	1.42 [7]
Total Energy (eV)	4.91359	4.89866 [8, 9]
CCC Bond Angle (°)	119.33	120 [10]

References:

1. D. R. Lide, CRC Handbook of Chemistry and Physics, 86th Edition, CRC Press, Taylor & Francis, Boca Raton, (2005-6), p. 4-150.

2. D. R. Lide, CRC Handbook of Chemistry and Physics, 86th Edition, CRC Press, Taylor & Francis, Boca Raton, (2005-6), p. 5-18; 5-45.

3. See http://newton.ex.ac.uk/research/qsystems/people/sque/diamond/

4. W. I. F. David, R. M. Ibberson, J. C. Matthewman, K. Prassides, T. J. S. Dennis, J. P. Hare, H. W. Kroto, R. Taylor, D. R. M. Walton, “Crystal structure and bonding of C₆₀”, Nature, Vol. 353, (1991), pp. 147-149.

5. D. R. Lide, CRC Handbook of Chemistry and Physics, 86th Edition, CRC Press, Taylor & Francis, Boca Raton, (2005-6), p. 5-42.

6. J. M. Hawkins, “Osmylation of C₆₀: proof and characterization of the soccer-ball framework”, Acc. Chem. Res., (1992), Vol. 25, pp. 150-156.

7. J. -C. Charlier, J. -P. Michenaud, "Energetics of multilayered carbon tubles," Phys. Rev. Letts., Vol 70. No. 12, (19930, pp. 1858-1861))

8. M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J Frurip, R. A. McDonald, A. N. Syverud, JANAF Thermochemical Tables, Third Edition, Part II, Cr-Zr, J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, (1985), p. 536.

9. M. C. Schabel, J. L. Martins, "Energetics of interplanar binding in graphite," Phys. Rev. B. Vol 46, No. 11, (1992), pp. 7185-7188.

10. D. R. McKenzie, D. Muller, B. A. Pailthorpe, "Compressive-stress-induced formation of thin-film tetrahedral amorphous carbon," Phys. Rev. Lett., (1991), Vol. 67, No. 6, pp. 773-776.

Go to: Diamond | C₆₀ Fullerene | Graphite

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