Diffusion Coefficients of Noble Gases in Natural Minerals: An Apparent Experimental Time Dependence Caused by Domain Size Spectra

Noble gas diffusion coefficients in natural minerals are of use for evaluating geochronometric dates and other geochemical data. Usually, they are determined by degassing at elevated temperatures grain powders of natural samples containing radiogenic or cosmogenic noble gases. For conventional evaluations of diffusion parameters from degassing experiments, the grains should be uniform with respect to structure, composition, shape, and size. The shape and size prerequisites can hardly be fulfilled, because even two very narrowly meshed sieves produce spectra of domain sizes, partly because of the inhomogeneity of the minerals. Accurate determination of the actual spectrum is difficult and hardly practicable. Calculations of the fractional gas loss of a sample with a spectrum of domain sizes, presented in this study, show that almost any domain size spectrum leads to apparent diffusion coefficients that depend on the extent of degassing. The exception of this rule is given. The deviation from the physical diffusion coefficient can be several orders of magnitude as shown by examples. This effect, resulting from shape and width of the domain size spectra, possibly is responsible both for the large spread of Arrhenius parameters for the same mineral in the literature and for the deviation from linearity of some published Arrhenius lines. For limited domain size spectra and short degassing times, the formula for fractional gas loss is very similar to the formula of the fractional gas loss of a single domain size. An effective domain radius, which ensures that at least the measured diffusion coefficient for very short degassing times equals the physical diffusion coefficient, is given. In addition, the dimensionless treatment of the problem is presented that leads to a method to determine Arrhenius parameters without knowing the domain size spectrum. Accurate diffusion measurements of samples with a spectrum of domain sizes may also be possible if the domain size spectrum is taken into consideration. To this end the domain size spectra should be approximated by Taylor-expandable functions or by series of discrete domain sizes. For both cases, the formulae are given.