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 evaluat ing geochronometric dates and other geochemical data. Usually, they are det ermined by degassing at elevated temperatures grain powders of natural samp les containing radiogenic or cosmogenic noble gases. For conventional evalu ations of diffusion parameters from degassing experiments, the grains shoul d be uniform with respect to structure, composition, shape, and size. The s hape and size prerequisites can hardly be fulfilled, because even two very narrowly meshed sieves produce spectra of domain sizes, partly because of t he inhomogeneity of the minerals. Accurate determination of the actual spec trum is difficult and hardly practicable. Calculations of the fractional ga s 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 coe fficients that depend on the extent of degassing. The exception of this rul e is given. The deviation from the physical diffusion coefficient can be se veral orders of magnitude as shown by examples. This effect, resulting from shape and width of the domain size spectra, possibly is responsible both f or the large spread of Arrhenius parameters for the same mineral in the lit erature and for the deviation from linearity of some published Arrhenius li nes. For limited domain size spectra and short degassing times, the formula for fractional gas loss is very similar to the formula of the fractional g as loss of a single domain size. An effective domain radius, which ensures that at least the measured diffusion coefficient for very short degassing t imes 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 considerati on. To this end the domain size spectra should be approximated by Taylor-ex pandable functions or by series of discrete domain sizes. For both cases, t he formulae are given.