It is conjectured and found in this work that the grain densities (suitably normalized) of vapour-deposited solid materials depend principally on competition between the successful arrival rate of their reagent molecules and the surface diffusion rate of admolecules on their growing surfaces. The ratio of these two rates defines an important dimensionless Damkohler number, called here the "burial" parameter, beta. Available grain density data for seven vapour deposited materials [silicon (Si), gallium arsenide (GaAs), silicon carbide (SiC), silicon nitride (Si3N4), titanium oxide (TiO2), boron nitride (BN) and graphite (C)] are used to establish and test the "universality" of the proposed normalized grain density versus burial parameter correlation. As anticipated, these data show that the normalized grain densities of these materials increase with their corresponding burial parameters. Moreover, for estimated burial parameters much less than unity, the deposits formed are indeed reported to be amorphous, while the deposits are observed to be crystalline under conditions for which beta much greater than 1 is estimated. As the burial parameter decreases, the reported grain densities of turbostratic, "layered", materials are found to decrease more gradually than for materials with no turbostratic structure. While the present implementation of this basic hypothesis cannot be regarded as "complete", it is argued that a rationally-based, reasonably "universal" vapour deposit density correlation of this general form can be quite useful in making rational predictions of deposit quality. Moreover, it appears that this path to such mechanistically plausible correlations, which, using available experimental data, can be implemented/tested even in the absence of a "complete" theory, can be broadened to include other important deposit characteristics via the introduced of additional characteristic time ratios.