Thermal expansion of continuous random networks of carbon

Homogeneous and isotropic continuous random networks (CRNs) of carbon were created spanning a large portion of hybridization space, from sp3-rich configurations up to 70% sp2 carbon. For each of these CRNs, the volumetric coefficient of thermal expansion (CTE) was calculated according to the quasi-harmonic approximation using the Brenner potential. The CTE of H-free, sp3-rich CRNs is similar to that of diamond and almost constant up to about 50% sp2-C. The CTE at 300 K varies from about 3.5 ×10−6K−1 to 5.5×10−6K−1, linearly increasing with the sp2-C content for CRNs above ca. 40% sp2-C, in good agreement with previous experimental studies. A small fraction of 10% to 15% of the CRNs, irrespective of composition, exhibit volumetric negative thermal expansion (NTE) over a limited temperature range around 100 K to 200 K.