Biaxial negative thermal expansion in carbon nets - graphyne and derivatives.

Materials that shrink during heating are important for advanced applications. Graphene has shown negative thermal expansion (NTE) up to 1000 K, which drives further research towards new two-dimensional allotropes of carbon to achieve higher performance. In this article, we have shown high NTE for Graphynes having sp-sp connectivity and that are stable at high temperature. The effect of heteroatom substitution in NTE for some graphynes and their periodic trends are also studied. Quasi-harmonic approximation (QHA) calculations show that thermal expansion remains negative at least until 1000 K for some graphynes. The results are in good agreement with ab-initio molecular dynamics (AIMD) simulations. The high NTE in the graphynes is understood based on their rigid unit modes (RUMs).