Relationship between phonon thermal conductivity and crystal structure: a case study of carbon allotropes

The paper investigates the relationship between phonon thermal conductivity and the structural parameters of three-dimensional carbon allotropes – density and the average coordination number. It uses the SACADA database, which contains calculated values of elastic constants for $\sim 1500$ different carbon allotropes. The phonon components of thermal conductivity are calculated using the Clark, Cahill, and Slack models, and regression analysis is used to find relationships between the thermal conductivity and density and coordination numbers. The relationships found are highly accurate, with $\mathrm{R}^2$ values greater than $0.9$. These dependencies can be used to estimate the thermal conductivity of new three-dimensional carbon structures quickly.