An empirical model describing the diffusion kinetics of oxygen in silicate minerals under hydrothermal conditions has been established for temperatures between 773 and 1073 Kelvin at 100 megapascals of water pressure. The equation, log D = alpha + (beta/T) + [(gamma + (delta/T))Z], where D is the diffusion coefficient, alpha, beta, gamma, and delta are constants, T is the Kelvin temperature, and Z is the total ionic porosity, may be used to predict diffusion coefficients, in most cases to within the reported experimental reproducibility of a factor of 2. For oxygen diffusion, alpha = -2, beta = -3.4 x 10(4)K, gamma = -0.13, and delta = 6.4 x 10(2)K, for D in square centimeters per second. Limited data for the diffusion of argon in silicates suggest that the model describes this system as well.

Trade tensions, resource nationalism, and various other factors are increasing concerns regarding the supply reliability of nonfuel mineral commodities. This is especially the case for commodities required for new and emerging technologies ranging from electric vehicles to wind turbines. In this analysis, we use a conventional risk-modeling framework to develop and apply a new methodology for assessing the supply risk to the U.S. manufacturing sector. Specifically, supply risk is defined as the confluence of three factors: the likelihood of a foreign supply disruption, the dependency of U.S. manufacturers on foreign supplies, and the ability of U.S. manufacturers to withstand a supply disruption. The methodology is applied to 52 commodities for the decade spanning 2007-2016. The results indicate that a subset of 23 commodities, including cobalt, niobium, rare earth elements, and tungsten, pose the greatest supply risk. This supply risk is dynamic, shifting with changes in global market conditions.