Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 2.9, pp. 129-130

Section Self-diffusion

G. S. Smitha and C. F. Majkrzakb

a Manuel Lujan Jr Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Self-diffusion

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One of the simplest, yet powerful, examples of the use of neutron reflectivity is in the study of self-diffusion. Most techniques to measure diffusion coefficients rely on chemical and mechanical methods to measure density profiles after a sample has been annealed. Then a model for the diffusion is assumed, and the coefficients are calculated. Using standard techniques, researchers are unable to detect the movement of an atom through a sample of like atoms. However, using single bilayers of amorphous 10B and 11B, it was shown (Smith, Hamilton, Fitzsimmons, Baker, Hubbard, Nastasi, Hirvonen & Zocco, 1992[link]) through neutron-reflectivity measurements that the diffusion of boron in boron could be measured by studying the density profile (see Figs.[link] and[link] ) of one isotope in the other as a function of annealing time. Also, because of the sensitivity of the technique to the interfacial density profile, it was found that standard Fickian diffusion models could not explain the measured density profiles.


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Measured neutron reflectivities from boron bilayers [from Smith et al. (1992[link])].


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The fitted real part of the scattering density profiles for the measured reflectivities of Fig.[link]. Note the pinning of the concentration of 10B at the interface [after Smith et al. (1992[link])].


First citation Smith, G. S., Hamilton, W., Fitzsimmons, M., Baker, S. M., Hubbard, K. M., Nastasi, M., Hirvonen, J.-P. & Zocco, T. G. (1992). Neutron reflectivity study of thermally-induced boron diffusion in amorphous elemental boron. SPIE Proc. Ser. 1738, 246–253.Google Scholar

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