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Carbyne nanocrystal (CN), as a kind of one-dimensional (1D) sp-hybridized carbon allotrope, has attracted much attention due to its excellent optical and transport properties. However, the lattice properties of 1D CNs under high temperature remain unclear. In our work, we investigate the stability and lattice properties of 1DCNs based on the atomic-bond-relaxation (ABR) approach and first-principles calculations. We find the change of transverse vibration frequencies and bond kinks induced by the thermal effect plays a significant role in the mechanical properties of 1D CNs. We establish a relationship between kink angle and phonon vibration modes, giving a deep inside into high frequency and low-frequency vibration behavior of 1D CNs. Our results indicate the phonon vibration modes modulated by kinks under applied temperatures can lead to a negative thermal expansion behavior in the axial direction of 1D CNs, suggesting an effective way to control the thermal properties of 1D CNs for practical applications.

Carbyne nanostructures, including carbyne chain and carbyne ring, have been triggered substantial research due to their exotic mechanical and outstanding electronic properties. In order to clarify the bond nature of carbyne nanostructures under thermal environment, the thermal properties of single and triple bonds modulated by length and curvature effects are investigated based on the density functional theory (DFT) and atomic-bond-relaxation (ABR) correlation mechanism. We find that the discrepancies of elastic and thermal properties between single and triple bonds are determined by the difference of thermal expansion coefficients (TECs). Moreover, the length and curvature effects play a significant role on the TECs of carbyne nanostructures. Our results are consistent with the numerical simulations, illustrating the underlying mechanism on the thermal properties of carbyne nanostructures at the atomic-level.