Some comments on the mass effect in diffusion

Claire, A.D. Le

doi:10.1080/14786436608224292

Cited by 169 publications

(29 citation statements)

References 12 publications

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“…(A2) serves as a useful reference from which to compare the mass dependence on diffusion coefficients. For example, there is a substantial literature on isotopic diffusion in solids (Schoen, 1958;Rothman and Peterson, 1965;Le Claire, 1966;Mundy et al, 1966; many others), and deviations from the square-root-of-mass law are combined with theories of lattice or vacancy diffusion to infer diffusion mechanisms (cf. Section 1.3 in Watkins et al, 2009).…”

Section: Discussionmentioning

confidence: 99%

Influence of liquid structure on diffusive isotope separation in molten silicates and aqueous solutions

Watkins

DePaolo

Ryerson

et al. 2011

Geochimica et Cosmochimica Acta

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Molecular diffusion in natural volcanic liquids discriminates between isotopes of major ions (e.g., Fe, Mg, Ca, and Li). Although isotope separation by diffusion is expected on theoretical grounds, the dependence on mass is highly variable for different elements and in different media. Silicate liquid diffusion experiments using simple liquid compositions were carried out to further probe the compositional dependence of diffusive isotopic discrimination and its relationship to liquid structure. Two diffusion couples consisting of the mineral constituents anorthite (CaAl 2 Si 2 O 8 ; denoted AN), albite (NaAlSi 3 O 8 ; denoted AB), and diopside (CaMgSi 2 O 6 ; denoted DI) were held at 1450°C for 2 h and then quenched to ambient pressure and temperature. Major-element as well as Ca and Mg isotope profiles were measured on the recovered quenched glasses. In both experiments, Ca diffuses rapidly with respect to Si. In the AB-AN experiment, D Ca /D Si ~ 20 and the efficiency of isotope separation for Ca is much greater than in natural liquid experiments where D Ca /D Si ~ 1. In the AB-DI experiment, D Ca /D Si ~ 6 and the efficiency of isotope separation is between that of the natural liquid experiments and the AB-AN experiment. In the AB-DI experiment, D Mg /D Si ~ 1 and the efficiency of isotope separation for Mg is smaller than it is for Ca yet similar to that observed for Mg in natural liquids.The results from the experiments reported here, in combination with results from natural volcanic liquids, show clearly that the efficiency of diffusive separation of Ca isotopes is systematically related to the solvent-normalized diffusivity-the ratio of the diffusivity of the cation (D Ca ) to the diffusivity of silicon (D Si ). The results on Ca isotopes are consistent with available data on Fe, Li, and Mg isotopes in silicate liquids, when considered in terms of the parameter D cation /D Si . Cations diffusing in aqueous solutions display a similar relationship between isotopic separation efficiency and D cation =D H 2 O , although the efficiencies are smaller than in silicate liquids. Our empirical relationship provides a tool for predicting the magnitude of diffusive isotopic effects in many geologic environments and a basis for a more comprehensive theory of isotope separation in liquid solutions. We present a conceptual model for the relationship between diffusivity and liquid structure that is consistent with available data.

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Section: Discussionmentioning

confidence: 99%

Influence of liquid structure on diffusive isotope separation in molten silicates and aqueous solutions

Watkins

DePaolo

Ryerson

et al. 2011

Geochimica et Cosmochimica Acta

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“…Within the classical model of atomic jumps in a crystal presented by Vineyard (1957), the ratio of jump frequencies of the two isotopes has a simple relation to the isotope mass ratio when there is no coupling between the vibration of the jumping atom and the vibrations of the rest of the crystal: LeClaire, 1966). However, when the motion of the atom during a jump is not fully decoupled from the vibrations of the surrounding atoms, the mass dependence of the jump frequency may be reduced (Vineyard, 1957) and can be described by (Mullen, 1961):…”

Section: Theory Of the Isotope Effect In Crystalsmentioning

confidence: 99%

“…Schoen (1958) and Tharmalingam and Lidiard (1959) showed that the isotope effect for diffusion in crystalline solids diminishes in proportion to the degree to which the diffusion process deviates from that of a purely random walk. The basic equation that relates the diffusivities of two isotopes to their masses can be written as (LeClaire, 1966):…”

Section: Theory Of the Isotope Effect In Crystalsmentioning

confidence: 99%

Theoretical constraints on the isotope effect for diffusion in minerals

Orman

Krawczynski

2015

Geochimica et Cosmochimica Acta

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Please cite this article as: Van Orman, J.A., Krawczynski, M.J., Theoretical constraints on the isotope effect for diffusion in minerals, Geochimica et Cosmochimica Acta (2015), doi: http://dx. ABSTRACTIsotopes of the same element generally diffuse at slightly different rates within a mineral, due to the difference in their masses. The magnitude of the mass dependence of the diffusion coefficient depends on the product of the correlation coefficient f (representing the degree to which the diffusion process deviates from a random walk) and the coupling coefficient K (representing the degree to which the motion of an atom during a single jump is coupled to that of other nearby atoms). Whereas K has been found to vary over a relatively narrow range, f can vary over a wide range from ~0 to 1.Diffusive isotope effects are expected to be large for trace and minor cations that diffuse slowly relative to the major cations that occupy the same sites and diffuse by the same mechanism. Diffusive isotope effects are also expected to be large for elements that diffuse rapidly by a simple interstitial mechanism. In both of these cases, the correlation coefficient is similar to or equal to unity. Diffusive isotope effects are reduced when the diffusion process is correlated, as for (1) rapid diffusion of trace and minor cations by a vacancy mechanism, with a low migration barrier for the jump to a vacancy; (2) diffusion by an interstitialcy process, or a process involving interstitial-vacancy pairs; (3) diffusion in grain boundaries and dislocations, where both dimensional restrictions and non-uniformity of the structure enhance correlation. The correlation coefficient can be determined from independent experimental data on the jump frequencies involved in the diffusion process, and/or from theoretical calculations of the jump energies. Quantitative estimates of the isotope effect are made for several cations in periclase, olivine, magnetite and rutile.

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“…The vibrational frequency for a single atom varies as m -1/2 for a parabolic potential. The mass dependence of the change in vibrational frequency for two different isotopes is given by [Mullen, 1961;LeClaire, 1966]:…”

Section: Thermodynamic Diffusion Parametersmentioning

confidence: 99%

Diffusion in silicon isotope heterostructures

Silvestri¹

2004

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The simultaneous diffusion of Si and the dopants B, P, and As has been studied by the use of a multilayer structure of isotopically enriched Si. This structure, consisting of 5 pairs of 120 nm thick natural Si and 28 Si enriched layers, enables the observation of 30 Si self-diffusion from the natural layers into the 28 Si enriched layers, as well as dopant diffusion from an implanted source in an amorphous Si cap layer, via Secondary Ion Mass Spectrometry (SIMS). The dopant diffusion created regions of the multilayer structure that were extrinsic at the diffusion temperatures. In these regions, the Fermi level shift due to the extrinsic condition altered the concentration and charge state of the native defects involved in the diffusion process, which affected the dopant and selfdiffusion.The simultaneously recorded diffusion profiles enabled the modeling of the coupled dopant and self-diffusion. From the modeling of the simultaneous diffusion, the dopant diffusion mechanisms, the native defect charge states, and the self-and dopant diffusion coefficients can be determined. This information is necessary to enhance the physical modeling of dopant diffusion in Si. It is of particular interest to the modeling of pushing me to achieve. I am grateful to Ana for her unwavering love and support, for giving me the time during this busy year to write this thesis, but also for knowing when I need a break.

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Some comments on the mass effect in diffusion

Cited by 169 publications

References 12 publications

Influence of liquid structure on diffusive isotope separation in molten silicates and aqueous solutions

Influence of liquid structure on diffusive isotope separation in molten silicates and aqueous solutions

Theoretical constraints on the isotope effect for diffusion in minerals

Diffusion in silicon isotope heterostructures

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