By G. Müller (auth.)
1 The content material ofthis article is predicated on a German ebook model ) which seemed on the finish of the 12 months 1986. the writer attempted to include - so far as attainable - new vital effects released within the final 12 months. however the literature within the box of "convection and inhomogeneities in crystal progress from the soften" has elevated rather a lot meanwhile that the reader and the collegues may still make allowance for any incompleteness, additionally within the case that their vital contributions haven't been stated. this may for instance carry for difficulties relating to the Czochralski development. yet specifically for this subject the reader could be refered to the coming near near quantity of this sequence, which includes targeted contributions on "Surface stress pushed circulation in Crystal development Melts" via D. Schwabe and on "Convection in Czochralski Melts" by means of M. Mihelcic, W. Uelhoff, H. Wenzl and okay. Wingerath. The education of this manuscript has been supported through numerous girls whose assistance is gratefully said through the autor: Mrs. Gisela Neuner for the kind writing, Mrs. Abigail Sanders, Mrs. Fiona Eels and particularly Prof. Nancy Haegel for his or her assist in questions of the English language and Mrs. Christa Weber for examining corrections. additionally the great cooperation with the Springer Verlag, particularly Mrs. Bohlen and with the coping with editor of Crystals, Prof. H. C. Freyhardt, who severely learn the manuscript, is acknowledged.
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Extra info for Crystal Growth from the Melt
Which has been defined in Eq. (27). 3,74) and the extended Jackson and Hunt modeC7). , which have been evaluated according t073 , 74), demonstrating the convective influence on the fiber spacing. The interesting finding of this investigation is that the results cannot be explained by segregation, if the composition of the melt is assumed to be exactly eutectic. If this is the case the longitudinal extension of the concentration profile of several micrometers is much too small to be influenced greatly by buoyancy convection.
This result is depicted in Fig. 18 for different values of ko. An experimental confirmation of this relation is given in Fig. 19. It should be noted that, strictly speaking, ko in Eq. (19) represents the value of k extrapolated to the velocity R = 0, which is not necessarily an equilibrium value. In the following section a simple model for the description of segregation of a finite volume will be discussed by assuming a constant value of the effective segregation coefficient. 2 Longitudinal Segregation During Directional Solidification Scheil67 ) and later Pfann 23 ,68) have given the distribution of the concentration Cs of an impurity for the directional solidification of a finite melt volume.
2 (compare Fig. 29). A maximum radial inhomogeneity is also found for medium values of Ra44). This is in qualitative agreement to the results of Chang and Brown (Fig. 46). 53 Macroscopic Inhomogeneity 1. t::. o. s::: o. 5 radius r 1 . 0 ,------------, N ..... s::: o. 5 Raw = 2x 10 4 Ra= 0 Fig. 44. 7) in a cylindrical container with isothermal boundaries according to Fig. 12 for hid = 1 and various values of Ra and Raw48) 54 Lateral Segregation 1 . 0 , - - -- - - - - - ---, I I I / I ...... r:::.