Crystallised ideas

Fractal Concepts in Surface Growth
February 9, 1996

This is a curious book. The authors have applied fractal concepts and statistical mathematical models to explain a wide variety of crystal growth situations. They extend their discussions to other problems, such as the growth of bacterial colonies, the propagation of flame fronts, the wetting of paper and so on.

The book is divided into seven parts and needs to be studied in the order it is presented. The first chapters provide an excellent introduction to concepts of scaling, correlation and fractal analysis. The second part (five chapters) deals with nonequilibrium roughening and introduces the main statistical mechanical framework around which the authors' whole approach is based. Parts three and four cover some experimental and applied aspects. For example, interfaces in random media are illustrated by the behaviour of bacterial colonies, the wetting of paper and movement of a fire-front. The large section devoted to molecular beam epitaxy is likely to disappoint many. This technique has been widely adopted to grow highly ordered semiconductor layers and represents one of the most highly controlled ways of studying crystal growth. Important aspects of chemistry and materials science have been overlooked and the entire treatment is mathematical and very selective in its cited bibliography. This is not to say that we cannot learn from the results of their analysis, indeed there is some excellent conceptual material here, but the balance will not suit everyone.

A concept that comes across particularly well is that of "noise" in growth processes, that is, the randomness of the resultant crystal surface. This comes about because of the stochastic nature of the arriving atoms and the activated character of the surface diffusion. The contribution to the "noise" from each of these origins is clearly described and has application in other fields. The authors have clearly recognised throughout that a problem area in one field can offer valuable insight into another, a feature that makes this work very interesting. The remaining sections are more theoretical and look at extensions to the existing framework.

The book's main shortcoming is the apparent neglect of the original literature on crystal growth and the detailed underlying science. This is a worrying trend in computational modelling generally. Nevertheless, this book is highly recommended to all scientists involved in random crystal or material growth problems. It is interesting and stimulating and would be an excellent text, especially if combined with a bit more physics and chemistry.

Peter Dobson is a lecturer, department of engineering science, University of Oxford.

Fractal Concepts in Surface Growth

Author - Albert-Laszlo Barabasi and Eugene Stanley
ISBN - 0521 48308 5 and 48318 2
Publisher - Cambridge University Press
Price - £45.00 and £16.95
Pages - 366

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