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Anisotropic diffusion in a finite cylinder, with geochemical applications

Watson, E. Bruce and Wanser, Keith H. and Farley, Kenneth A. (2010) Anisotropic diffusion in a finite cylinder, with geochemical applications. Geochimica et Cosmochimica Acta, 74 (2). pp. 614-633. ISSN 0016-7037.

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Atomic diffusion in minerals may not be well represented by solutions to the diffusion equation for a sphere with a singlevalued diffusivity, either because they have platy or elongated habits or because the energetics of diffusion is sensitive to crystallographic direction. In many cases, a cylinder having characteristic radial and axial diffusivities is arguably a better model, but rigorous solutions to the anisotropic diffusion equation for a finite cylinder have not been available. Here we develop general analytical solutions that capture both the internal distribution of diffusant as a function of time, C(r, z, t), and the fraction, F, of diffusant lost during a specified thermal history. These solutions are shown to conform with existing analytical expressions for limiting cases of diffusion in a slab or infinite cylinder. We present, in addition, a simple numerical (finite difference) approach that not only reproduces the results of our analytical expressions but also enables us to move beyond some of the limitations of the equations to simulate complex natural scenarios involving non-zero and time-dependent boundary conditions, arbitrary initial distribution of diffusant within the cylinder and simultaneous diffusion and radiogenic ingrowth. The complementary nature of the two approaches is emphasized and several illustrative applications to ‘real-world’ problems are described, including noble-gas thermochronometry and halogen–hydroxyl interdiffusion in apatite.

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Farley, Kenneth A.0000-0002-7846-7546
Additional Information:© 2009 Elsevier. Received 3 June 2009; accepted 1 October 2009. Associate editor: Peter W. Reiners. Available online 14 October 2009. This work was supported by National Science Foundation Grants Nos. EAR-0440228 and EAR-0738843 to EBW and EAR-0738627 to KAF. We thank Daniele Cherniak for helpful discussion and advice. Sumit Chakraborty, Todd Ehlers, Peter Zeitler and an anonymous reviewer provided valuable official reviews.
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Issue or Number:2
Record Number:CaltechAUTHORS:20100128-135201520
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17341
Deposited By: Jason Perez
Deposited On:29 Jan 2010 21:23
Last Modified:03 Mar 2020 13:01

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