Step bunching in potassium dihydrogen phosphate crystal growth: Phenomenology
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A.A. Chernov Universities Space Research Association, 4950 Corporate Drive, Suite 100, Huntsville, Alabama 35806
P.G. Vekilov Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4004 (Received 4 December 2001; accepted 28 May 2002)
We have developed a real-time phase-shifting interferometer capable of imaging interfacial morphology with a depth resolution of approximately 25 Å, with a lateral resolution of approximately 0.5 m across a field of view of 2 × 2 mm2, and with time resolution of 0.1 s. The method is applied in situ to the (101) face of potassium dihydrogen phosphate crystals growing from an aqueous solution. We image the formation and evolution of solution-flow-induced step bunches and determine their characteristic wavelength to be c ⳱ 45 m. This wavelength is within the range predicted by a stability theory on the basis of the balance between the diffusion interaction between steps and capillarity. The value of c suggests that step–step interactions are the likely major factor for instability.
I. INTRODUCTION
Morphological stability of crystal interfaces during growth largely determines the structure and perfection of the resulting crystals.1–5 Smooth surfaces that grow by the generation of new layers and their lateral spreading (step flow growth mode) lose stability due to bunching of the growth steps. The formation of step bunches, or macrosteps, may cause striations via the differential trapping of impurities and defects, as well as the formation of inclusions. Hence, understanding and control of step bunching is important for fields ranging from corrosion, through electrochemistry, and to protein and semiconductor crystal growth.6 –12 Despite the extensive discussions of the step bunches and their consequences, in the case of growth of crystals from solution neither the onset nor the evolution of step bunching has thus far been addressed in quantitative experiments. Here we report features of our experimental setup and first results of an ongoing investigation aimed at quantitative insight into the step bunching during growth of crystals from solution. In this first study, we determine the spectrum of the wavelengths present on the growing interface on which bunching is developed.
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Address all correspondence to this author. e-mail: [email protected] J. Mater. Res., Vol. 17, No. 8, Aug 2002
This spectrum includes as its major component the typical wavelength at which loss of morphological stability occurs. As a model system, we chose potassium dihydrogen phosphate (KDP). This is a well-studied salt– water system,13 and the solubility, viscosity, refractive index, and other relevant properties are known in a broad range of parameters. Furthermore, KDP crystals as large as 65 cm are needed as frequency multipliers for the controlled nuclear fusion projects carried out at Lawrence Livermore National Laboratory.14,15 The efforts to grow such crystals revealed that the main difficulty stems from the formation of step bunches along the pathway of growth steps.14 –
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