Fluctuations of Step Positions at KDP Crystal Faces
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Fluctuations of Step Positions at KDP Crystal Faces
Leonid N. Rashkovich, Oleg A. Shustin, Tamara G.Chernevich Physics Department, Moscow State University, Moscow, 119899 Russia. ABSTRACT Applying atomic force microscopy in single string scanning mode, dependence of fluctuations of step shifts on KDP crystal faces on time was determined during crystallization from solution. It was shown that fluctuation amplitude grows proportionally to t1/4. On prism faces fluctuations at dissolving were bigger than at growth and bigger than on bipyramid faces. Amplitude of fluctuations was not dependent on distance between steps. Interpretation of experimental results and computation of elementary parameters of crystallization was done based on theory of V.V.Voronkov. INTRODUCTION Velocity fluctuations of elementary growth layers, related to fluctuations of the number of building units attached from the media during crystallization of inorganic compounds from solutions were not investigated as of yet. Similar research was done only at high temperatures under vacuum on surfaces of metals and semiconductors [1-4]. Theoretical interpretation of these works was based on assumption that building units are delivered to locations of growth due to surface diffusion [5,6]. In condensed media crystal growth may differ substantially from growth in gas phase as surface diffusion of building units to step risers, where they are incorporated into the crystals, will not necessarily play any significant role. Investigation of fluctuations in processes of crystallization seems to be important at least in three aspects. Firstly, comparison of experimental results to microscopic theoretical model allows to make a good judgement of its adequacy to observed process. If the model is selected, it is possible to make an attempt to determine its parameters. In particular, such fundamental parameters like kink density,ρ, frequencies of building units attachment to kinks, ω+, (and detachment from them - ω-), linear free energy of steps, αl , in most cases may be computed only based on fluctuation research. The problem is that direct observation of kinks and building units incorporating into them is only possible when kinks are not numerous, building units are big enough and attachment frequencies are comparatively low. In solutions it is possible only for crystals of macromolecular compounds [7-9]. Secondly, fluctuations may lead to coagulation of elementary steps into bigger ones macrosteps. Fluctuating, a step for some time retains one position periodically retreating from it. This time τf may be determined if dependence of fluctuation amplitude on time (for example, w=(χt)β, where w - average squared shift of step segment, χ and β are constants) and step velocity v are known. Then τf may be found from equation (χτf)β ≈ vτf. If within time τf fluctuation shift reaches half of the distance between steps, then macrosteps will be formed. And thirdly, fluctuations are important from the view of even distribution of impurities encaptured by crystal. Let us as
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