Categories
Disordered Systems Nonequilibrium Pattern Formation

Theoretical Aspects of Polycrystalline Pattern Growth in Al/Ge Films

R. Hilfer

in: Fluctuation Phenomena and Pattern Growth
edited by: H.E. Stanley and N. Ostrowsky
Kluwer Academic Publishing, Dordrecht, 127 (1988)
https://doi.org/10.1007/978-94-009-2653-0_23
ISBN 978-94-009-2653-0, ISBN 978-0-7923-0073-1

submitted on
Friday, July 22, 1988

These notes discuss recent theoretical approaches to polycrystalline fingering during annealing of amorphous Al/Ge thin films, and compare the to experiment.



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Categories
diffusion fluid flow Nonequilibrium Pattern Formation

Pattern Formation at Liquid Interfaces

B. Heidel, C. Knobler, R. Hilfer, R. Bruinsma

Physical Review Letters 60, 2492 (1988)
10.1103/PhysRevLett.60.2492

submitted on
Monday, January 11, 1988

Although many examples of pattern formation resulting from chemical reactions at liquid interfaces are known, few have been studied in detail. We report a quantitative study of patterns formed by the photoproduction of Fe++ and its subsequent reaction to form Turnbull’s Blue. The experiment leads to the postulation of a mechanism in which autocatalysis is enhanced by double diffusion. The phase diagram contains a line of phase transitions whose critical behavior is discussed.



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Categories
Disordered Systems Fractals Nonequilibrium Pattern Formation

Phase Separation by Coupled Single-Crystal Growth and Polycrystalline Fingering in Al/Ge: Theory

S. Alexander, R. Bruinsma, R. Hilfer, G. Deutscher, Y. Lereah

Physical Review Letters 60, 1514 (1988)
10.1103/PhysRevLett.60.1514

submitted on
Tuesday, May 26, 1987

We present a theory for a new mode of phase separation discovered recently in thin layers of amorphous Al-Ge alloys. Phase separation and crystallization occurs in colonies developing from Al nuclei. Their growth is controlled by diffusion of atomic Ge inside crystalline Al, and by the nucleation and growth of Ge crystallites on the Al-Ge interface. We find that the growth velocity is constant as a consequence of the interaction between the ramified Al-Ge interface and the smooth boundary of the colony with the amorphous phase. Diffusion occurs only in a narrow strip controlled by a length scale related to the width of the Ge dendrites. Solution of the growth equations leads to a velocity selection mechanism as long as the Ge concentration is above a critical threshold. The basic length scale is argued to be controlled by a competition between nucleation and growth of the Ge crystallites.



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Categories
Disordered Systems Nonequilibrium Pattern Formation

On Dense Branching Phase Separation

R. Hilfer, S. Alexander, R. Bruinsma

in: Time Dependent Effects in Disordered Materials
edited by: R.Pynn and T. Riste
Plenum Press, New York, 417 (1987)
https://doi.org/10.1007/978-1-4684-7476-3_43
ISBN 978-1-4684-7478-7, ISBN 978-1-4684-7476-3

submitted on
Tuesday, March 31, 1987

Recently Deutscher and Lareah discovered a new mode of phase separation in thin films of Al/Ge alloys. They observe the growth of circular “colonies” whose densely packed appearance has been called “dense branching morphology”. The colonies consist of a highly branched starlike “island” of polycrystalline Ge inside a “lake” of monocrystalline Al which is only slightly larger than the Ge island. Thus the Al forms a thin but essentially uninterrupted rim around the Ge peninsulas. The whole colony is embedded in the amorphous phase having an overall composition of 40 percent Al and 60 percent Ge. As these colonies grow into the metastable amorphous surrounding they preserve their more or less circular shape. This immediately raises the question why on the one hand the Al/Ge-interface shows an instability, while on the other the Al/amorphous boundary does not. We investigate this question first. We then present the theoretical description of the new growth morphology. We outline the solution of our equations and indicate how a unique growth velocity is selected. We finally compare our results with experiment.



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