Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Vacancies in solids and the stability of surface morphology


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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

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.


  1. Ångström, A. J. New method of determining the thermal conductibility of bodies. Phil. Mag. 25, 130–143 (1863).

    Article  Google Scholar 

  2. Herring, C. in Structure and Properties of Solid Surfaces (eds Gomer, R. & Smith, C. S.) (Univ. Chicago Press, 1952).

    Google Scholar 

  3. Mullins, W. W. Flattening of a nearly plane solid surface due to capillarity. J. Appl. Phys. 30, 77–83 (1959).

    Article  Google Scholar 

  4. Bauer, E. Low-energy-electron microscopy. Rep. Prog. Phys. 57, 895–938 (1994).

    Article  CAS  Google Scholar 

  5. Jeong, H. C. & Williams, E. D. Steps on surfaces: experiment and theory. Surf. Sci. Rep. 34, 175–294 (1999).

    Article  Google Scholar 

  6. Giesen, M. & Ibach, H. Step edge barrier controlled decay of multilayer islands on Cu(111). Surf. Sci. 431, 109–115 (1999).

    Article  CAS  Google Scholar 

  7. Ibach, H., Giesen, M., Flores, T., Wuttig, M. & Treglia, G. Vacancy generation at steps and the kinetics of surface alloy formation. Surf. Sci. 364, 453-466 (1996).

    Article  Google Scholar 

  8. Bradley, A. J. & Taylor, A. An X-ray analysis of the nickel–aluminium system. Proc. R. Soc. Lond. A 159, 56–72 (1937).

    Article  CAS  Google Scholar 

  9. Wasilewski, R. J. Structure defects in CsCl intermetallic compounds—I theory. J. Phys. Chem. Solids 29, 39–49 (1968).

    Article  CAS  Google Scholar 

  10. Hagen, M. & Finnis, M. W. Point defects and chemical potentials in ordered alloys. Phil. Mag. A 77, 447–464 (1998).

    Article  CAS  Google Scholar 

  11. Korzhavyi, P. A. et al. Constitutional and thermal point defects in B2 NiAl. Phys. Rev. B 61, 6003–6018 (2000).

    Article  CAS  Google Scholar 

  12. Meyer, B. & Fahnle, M. Atomic defects in the ordered compound B2-NiAl: A combination of ab initio electron theory and statistical mechanics. Phys. Rev. B 59, 6072–6082 (1999).

    Article  CAS  Google Scholar 

  13. Meyer, B. & Fahnle, M. Atomic defects in the ordered compound B2-NiAl: A combination of ab initio electron theory and statistical mechanics [(Phys. Rev. B 59, 6072 (1999)]. Phys. Rev. B 60, 717–717 (1999).

    Article  CAS  Google Scholar 

  14. Mishin, Y. & Farkas, D. Atomistic simulation of point defects and diffusion in B2 NiAl. 1. Point defect energetics. Phil. Mag. A 75, 169–185 (1997).

    Article  Google Scholar 

  15. Davis, H. L. & Noonan, J. R. Rippled relaxation in the (110) surface of the ordered metallic alloy NiAl. Phys. Rev. Lett. 54, 566–569 (1985).

    Article  CAS  Google Scholar 

  16. Bai, B. & Collins, G. S. in High-Temperature Ordered Intermetallic Alloys VII, MRS Symposia Proceedings No. 552 (eds George, E. P., Yamaguchi, M. & Mills, M. J.) KK8.7.1 (Materials Research Society, Pittsburgh, 1999).

    Google Scholar 

  17. Smirnov, A. A. Anomaly in the temperature dependence of the vacancy concentration in NiAl type alloys. Sov. Phys. Dokl. 36, 479–480 (1991).

    Google Scholar 

  18. Zinke-Allmang, M., Feldman, L. C. & Grabow, M. H. Clustering on surfaces. Surf. Sci. Rep. 16, 377–463 (1992).

    Article  CAS  Google Scholar 

  19. Tanaka, S., Bartelt, N. C., Umbach, C. C., Tromp, R. M. & Blakely, J. M. Step permeability and the relaxation of biperiodic gratings on Si(001). Phys. Rev. Lett. 78, 3342–3345 (1997).

    Article  CAS  Google Scholar 

  20. Blakely, J. M. Effect of impurity on surfaces of heated gold. Trans. Faraday Soc. 57, 1164–1168 (1961).

    Article  CAS  Google Scholar 

  21. Maiya, P. S. & Blakely, J. M. Surface self-diffusion and surface energy of nickel. J. Appl. Phys. 38, 698–704 (1966).

    Article  Google Scholar 

  22. Hoehne, K. & Sizmann, R. Volume and surface self-diffusion measurements on copper by thermal surface smoothing. Phys. Status Solidi A 5, 577–589 (1971).

    Article  CAS  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

McCarty, K., Nobel, J. & Bartelt, N. Vacancies in solids and the stability of surface morphology. Nature 412, 622–625 (2001).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing