He, C. Y., L. Z. Sun, et al. (2012). "Four superhard carbon allotropes: a first-principles study." Physical Chemistry Chemical Physics 14(23): 8410-8414.

Using a generalized genetic algorithm, we propose four new sp(3) carbon allotropes with 5-6-7 (5-6-7-type Z-ACA and Z-CACB) or 4-6-8 (4-6-8-type Z4-A(3)B(1) and A4-A(2)B(2)) carbon rings. Their stability, mechanical and electronic properties are systematically studied using a first-principles method. We find that the four new carbon allotropes show amazing stability in comparison with the carbon phases proposed recently. Both 5-6-7-type Z-ACA and Z-CACB are direct band-gap semiconductors with band gaps of 2.261 eV and 4.196 eV, respectively. However, the 4-6-8-type Z4-A(3)B(1) and A4-A(2)B(2) are indirect band-gap semiconductors with band gaps of 3.105 eV and 3.271 eV, respectively. Their mechanical properties reveal that all the four carbon allotropes proposed in present work are superhard materials, which are comparable to diamond.