Erratum: Anharmonicity and Universal Response of Linear Carbon Chain Mechanical Properties under Hydrostatic Pressure [Phys. Rev. Lett. 125, 105501 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.125.105501.

Erratum: Anharmonicity and Universal Response of Linear Carbon Chain Mechanical Properties under Hydrostatic Pressure [Phys. Rev. Lett. 125, 105501 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.125.105501.

Thermodynamics of Linear Carbon Chains.

Linear carbon chains (LCCs) are one-dimensional materials with unique properties, including high Debye temperatures and restricted selection rules for phonon interactions. Consequently, their Raman C-band frequency's temperature dependence is a probe to their thermal properties, which are well described within the Debye formalism even at room temperatures. Therefore, with the basis on a semiempirical approach we show how to use the C band to evaluate the LCCs' internal energy, heat capacity, coefficient of thermal expansion, thermal strain, and Grüneisen parameter, providing universal relations for these quantities in terms of the number of carbons atoms and the temperature.

Anharmonicity and Universal Response of Linear Carbon Chain Mechanical Properties under Hydrostatic Pressure.

Isolated linear carbon chains (LCCs) encapsulated by multiwalled carbon nanotubes are studied under hydrostatic pressure (P) via resonance Raman scattering. The LCCs' spectroscopic signature C band around 1850 cm^{-1} softens linearly with increasing P. A simple anharmonic force-constant model not only describes such softening but also shows that the LCCs' Young's modulus (E), Grüneisen parameter (γ), and strain (ϵ) follow universal P^{-1} and P^{2} laws, respectively. In particular, γ also presents a unified behavior for all LCCs. To the best of our knowledge, these are the first results reported on such isolated systems and the first work to explore universal P-dependent responses for LCCs' E, ϵ, and γ.