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Vacancies in solids and the stability of surface morphology

Nature volume 412, pages 622–625 (2001)Cite this article

Abstract

Determining how thermal vacancies are created and destroyed in solids is crucial for understanding many of their physical properties, such as solid-state diffusion. Surfaces are known to be good sources and sinks for bulk vacancies, but directly determining where the exchange between the surface and the bulk occurs is difficult. Here we show that vacancy generation (and annihilation) on the (110) surface of an ordered nickel–aluminium intermetallic alloy does not occur over the entire surface, but only near atomic step edges. This has been determined by oscillating the sample's temperature and observing in real time the response of the surface structure as a function of frequency (a version of Ångström's method of measuring thermal conductivity1) using low-energy electron microscopy. Although the surface-exchange process is slow compared with bulk diffusion, the vacancy-generation rate nevertheless controls the dynamics of the alloy surface morphology. These observations, demonstrating that surface smoothing can occur through bulk vacancy transport rather than surface diffusion, should have important implications for the stability of fabricated nanoscale structures.

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Figure 1: Smoothing of the NiAl (110) surface.
Figure 2: Measurement of bulk-vacancy fluxes towards atomic step edges.
Figure 3: Interpretation of the frequency dependence of the vacancy fluxes to the surface.

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Acknowledgements

This work was supported by the Office of Basic Energy Sciences, Division of Materials Sciences of the US Department of Energy. We thank D. C. Dibble, N. Y. C. Yang and K. J. Gross for technical assistance and B. Poelsema, J. C. Hamilton, J. J. Hoyt, J. B. Hannon, P. J. Feibelman and G. E. Thayer for discussions.

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Authors and Affiliations

  1. Sandia National Laboratories, Livermore, 94551-0969, California, USA

    K. F. McCarty, J. A. Nobel & N. C. Bartelt

Authors
  1. K. F. McCarty
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  2. J. A. Nobel
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  3. N. C. Bartelt
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Corresponding author

Correspondence to K. F. McCarty.

Supplementary information

Two figures with legends

Movie 1

A video (Quicktime format) example of isothermal island decay on the NiAl (110) surface at 985°C. The imaged structure consists of a stack of islands, just like a tiered wedding cake. The dark lines in the low-energy electron microscopy (LEEM) images mark the surface steps, at which the height changes by one atomic layer between the atomically flat terraces. Thus the images are analogous to a topographic map with the steps corresponding to contours of constant elevation. Remarkable behavior is obvious in the movie -- all the islands are shrinking at once and at the same rate. Thus there is no evidence for mass being transported from the islands of highest curvature (the upper islands) to regions of lower curvature (the lower islands). While not shown, we also observe that adjacent islands of different size (radius of curvature) on the same terrace shrink at the same rate. That is, Ostwald ripening, where small (high chemical potential) islands shrink giving their mass to large (low chemical potential) islands, is also not occurring. The independence of the decay (smoothing) rate on the environment for both stacked and adjacent islands directly establishes that a surface diffusion process is not operative. The field of view is 5.8 x 5.8 μm2 and the elapsed time is 6.7 minutes.

Movie 2

A video (Quicktime format) example of what oscillating the sample temperature between 770 and 785°C does to surface morphology. The bar graphs show the sample temperature and area of the island topmost in the stack, respectively. As the temperature increases (decreases), the island area increases (decreases) by an amount strictly proportional to the step length of the island. These oscillations are superimposed upon a slow shrinkage of the island due to thermal smoothing. About half way through the movie, a dislocation (marked by the terminating surface step) moves into the field of view. While altering the local step configuration, the dislocation does not affect either the slow thermal smoothing or the size of the more rapid area changes. While the temperature oscillations of this example are quite small, larger temperature oscillations bring multiple layers to and from the surface (see Movies 3 and 4). The field of view is 3.9 x 3.6 μm2 and the elapsed time is 38 minutes.

Movie 3

A video (Quicktime format) example of what a large temperature increase does to the NiAl surface morphology. Over about 10 seconds, the NiAl crystal was heated from 924 to 1025°C. The field of view is 5.75 x 5.75 μm2. Individual images from this movie are shown in Fig. 1.

Movie 4

A video (Quicktime format) example of what a large temperature decrease does to the NiAl surface morphology. Over about 2 minutes, the NiAl crystal was cooled from 958 to 740°C. Since the thermal smoothing is slow on this time scale, nearly all the mass removed from the surface results from the temperature change. The field of view is 5 x 5 μm2. Individual images from this movie are shown in Fig. 2.

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McCarty, K., Nobel, J. & Bartelt, N. Vacancies in solids and the stability of surface morphology. Nature 412, 622–625 (2001). https://doi.org/10.1038/35088026

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