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. 2015 Apr 13;373(2039):20140230.
doi: 10.1098/rsta.2014.0230.

How does your crystal grow? A commentary on Burton, Cabrera and Frank (1951) 'The growth of crystals and the equilibrium structure of their surfaces'

D P Woodruff  1
Affiliations

Affiliation

  • 1 Department of Physics, University of Warwick, Coventry CV4 7AL, UK d.p.woodruff@warwick.ac.uk.

How does your crystal grow? A commentary on Burton, Cabrera and Frank (1951) 'The growth of crystals and the equilibrium structure of their surfaces'

D P Woodruff. Philos Trans A Math Phys Eng Sci. .
. 2015 Apr 13;373(2039):20140230.
doi: 10.1098/rsta.2014.0230.

Author

D P Woodruff  1

Affiliation

  • 1 Department of Physics, University of Warwick, Coventry CV4 7AL, UK d.p.woodruff@warwick.ac.uk.

Abstract

The key ideas presented in the classic paper 'The growth of crystals and the equilibrium structure of their surfaces' by W. K. Burton, N. Cabrera and F. C. Frank, published in Philosophical Transactions A in 1951, are summarized and put in the context of both the state of knowledge at the time of publication and the considerable amount of work since that time that has built on and developed these ideas. Many of these developments exploit the huge increase in the capabilities of computer modelling that complement the original analytic approach of the paper. The dearth of relevant experimental data at the time of the original publication has been transformed by the application of increasingly sophisticated modern methods of surface science. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Keywords: crystal growth; equilibrium crystal shape; screw dislocations; surface roughening; surface steps; two-dimensional nucleation.

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Figures

Figure 1.

Figure 1.

Schematic showing the presence of…

Figure 1.

Schematic showing the presence of a kink on a single atomic layer step,…

Figure 1.
Schematic showing the presence of a kink on a single atomic layer step, effectively treating individual atoms as cubes.
Figure 2.

Figure 2.

Schematic (‘cubic atom’) diagram showing…

Figure 2.

Schematic (‘cubic atom’) diagram showing the intersection of a screw dislocation with a…

Figure 2.
Schematic (‘cubic atom’) diagram showing the intersection of a screw dislocation with a crystal surface.
Figure 3.

Figure 3.

Schematic of growth spirals in…

Figure 3.

Schematic of growth spirals in plan and side views resulting from growth at…

Figure 3.
Schematic of growth spirals in plan and side views resulting from growth at the intersection of a single screw dislocation and a crystal surface (a) and a pair of such dislocations and a surface (b). From BCF [1] (Copyright The Royal Society).
Figure 4.

Figure 4.

( a ) The solid…

Figure 4.

( a ) The solid line shows an example of a polar plot…

Figure 4.
(a) The solid line shows an example of a polar plot of the surface free energy per unit area, γ, of a crystal as a function of orientation. The dashed lines show the resultant equilibrium shape obtained from the Wulff construction. (b) Schematic diagram of the terrace–ledge–kink model of a surface of some arbitrary (high-index) or vicinal orientation.
See this image and copyright information in PMC

References

    1. Burton WK, Cabrera N, Frank FC. 1951. The growth of crystals and the equilibrium structure of their surfaces. Proc. R. Soc. Lond. A 243, 299–358. ( 10.1098/rsta.1951.0006) - DOI
    1. Gibbs JW. 1878. Collected works. London, UK: Longmans Green & Co.
    1. Stranski IN. 1928. Zur Theorie der Kristallwachstums. Z. Phys. Chem. 136, 259–278.
    1. Becker R, Döring W. 1935. Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Ann. Phys. 416, 719–752. ( 10.1002/andp.19354160806) - DOI
    1. Kaischew R. 1981. On the history of the creation of the molecular-kinetic theory of crystal growth: honouring the memory of I.N. Stranski. J. Cryst. Growth 51, 643–650. ( 10.1016/0022-0248(81)90452-8) - DOI

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