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Crystallogenesis and Mineralogy
Saint Petersburg, Russia
30 September-4 October 2007
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Conferences & Meetings 2nd International Conference "Crystallogenesis and Mineralogy"
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Step bunching at crystal growth from solutions

RMS-DPI code:  2007-1-3-1
Scientific session:  Session 1. Fundamental problems of crystallogenesis
Author listing:  Bredikhin V.I., Galushkina G.L., Kulagin A.A., Kuznetsov S.P., Malshakova O.A.
Principal author:  Bredikhin Vladimir I.
Language:  English
Abstract - Summary 
(short description):
The problem of step bunching in crystal growth is important both for comprehension of processes at the crystal-solution boundary and for achievement of high quality of growing crystals. The present report deals with results of in situ experimental and theoretical investigations of step bunching. The experimental investigations were mainly carried out on the KDP crystal grown from solution. The investigations were performed in growth by a single (101) or (100) face in a shaping optical cell with forced feed. In particular, it has been found out that:
1. The basic factor determining step bunching is hydrodynamics of feed.
2. Step bunches are formations of uncoupled steps with increased density of elementary steps. These formations are reversible, they may vanish leaving no visible defects under favorable hydrodynamic conditions. Under unfavorable conditions step bunches may transfer into uncontrollable structures leading to capture of the solution and occurrence of striations.
3. Step bunches form at some distance from the generating growth center. This distance depends on the hydrodynamic conditions.
4. As a rule, step bunches form traveling quasi-periodic waves. Their amplitude, propagation velocity and wavelength depend on the hydrodynamic conditions.
5. Solitary step bunches are possible.
6. An excess of the growth rate over the optimal one under the same hydrodynamic conditions also results in step bunching.
The theoretical study has demonstrated that the basic properties of step bunches are adequately described in the model of non-stationary diffusion boundary layer. Nonlinear differential equations for the relative supersaturation s on the surface and the density n of elementary steps are obtained by solving the boundary problem for the non-stationary two-dimensional diffusion equation at the assigned thickness of the diffusion layer d, the equation of motion for the density n of elementary steps and the third-kind boundary condition binding them on the growing surface. The set of equations was studied numerically for two cases: traveling coupled periodic waves and quasi-soliton waves for n and s. It is shown that periodic wave bunches occur at deviation of growth parameters from the equilibrium ones. The amplitude, the period and the propagation velocity of waves depend on the degree of this deviation. The obtained parameters of waves and quasi-soliton steps satisfactorily agree with the parameter found from the experimental data. The suggested model is applicable for crystal growth from solutions, including gels, and can be developed to growth from melts.
RMS-DPI code:  2007-1-3-1
Proceeedings volume 
in the RMS catalogue:
Crystallogenesis and Mineralogy
Pages:  39-40
File of proceedings 
 258 K
Status:  printed
Accepted:  23/05/2007
Published on-line:  21/12/2007
Permanent address of publication:  http://www.minsoc.ru/2007-1-3-1/
Contact author(s):  Bredikhin, Vladimir I.
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