Density-Driven to Phonon-Dominated: Crossover in Heat Capacity of Amorphous Carbons

The heat capacity of amorphous carbon, a fundamental yet elusive property, is pivotal for its thermal applications, but it lacks a predictive model across its vast density spectrum. Here, large-scale neuroevolution potential molecular dynamics simulations show a pronounced nonmonotonic dependence. Across 1.1-4.0 g cm^-3, the volumetric heat capacity (C_V) first increases in the low- and medium-density regimes but surprisingly decreases upon further densification in the high-density regime. This reversal is associated with a fundamental crossover in governing physics: C_V is initially controlled by atomic densification (void collapse), then modulated by phonon softening during the sp²-to-sp³ transition, and ultimately dominated by phonon stiffening (blueshift in the phonon density of states (PDOS)) under high pressure, which overrides the density effect. Phonon dispersion analysis directly visualizes this mechanistic shift, correlating it with the structural evolution from graphitic networks to diamond-like structures. This work provides a quantitative, regime-specific framework that decouples the competing roles of density and PDOS, providing a fundamental basis for the rational design of amorphous carbon in advanced thermal management.