Model for Grain Boundary Diffusion Controlled Growth of Deep Liquid Channels

The penetration of liquid phase along grain boundaries is a very important p ocess in any case including the contacts between liquid and solid metals. In this paper the model is presented of deep grain boundary channels formation based on grain boundary diffusion mechanis m. According to the model the depth of the liquid channel is proportional to the square root of time for “C” re gime and to the fourth root of time for “B” regime of grain boundary diffusion. The estimated depths of channels correlate well with the experimental results for Bi-Cu system . Introduction During the last years the problem of liquid channels formation along grain boundaries (GB) in metals was treated in many papers [1-9]. It is very important for technological applications including the contacts between liquid and solid metals. The analysis of experimental data shows the existence of severa l types of the GB liquid channels [5,10] possessing the significant morphological differences. These differences are defined by many factors: nature of materials, structure of GB, temperature, GB and liquid-solid (LS) tensions, presence of internal mechanical stresses at the channel root, etc. The most important are the GB wetting conditions and the level of internal stresses. The GB wetting conditions are characterized by the value of nondim e sional criterion SL b γ γ 2 , where γb is GB tension, and γSL is LS tension. If 1 2 < SL b γ γ , GB are not wetted, and contrary, if 1 2 > SL b γ γ wetting occurs. To characterize the level of internal stresses we must intr oduce the second nondimensional criterion cr σ σ , where σ is the value of mechanical stresses which appear at the channel root and σcr is the critical stress of crack formation. We shall not discuss here the nature of the stresses, which may be connected with the difference of γb and γSL [1], difference of atomic sizes of solid and liquid metals, misfit [10], etc. It is important to note that we can judge the existence of stress by the etch pits [11] and other data. By the use of these criteria and experimental data one can consid er three fields corresponding to different morphological types of liquid channels (Fig. 1). Field 1: temperature is relatively low, γb < 2γSL, GB are not wetted, internal stresses are lower than critical value; under these conditions so called Mullins groove s ar formed (Fig. 2a), the average rate of channels deepening is usually more than ten micrometers per hour . Defect and Diffusion Forum Online: 2003-02-14 ISSN: 1662-9507, Vols. 216-217, pp 181-188 doi:10.4028/www.scientific.net/DDF.216-217.181 © 2003 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-16/03/20,12:54:19) Fig. 1 Three fields corresponding to different morphological types of liquid channels Field 2: temperature is somewhat higher, γb > 2γSL, GB are wetted, but internal stresses as formerly are lower than critical value; the conditions are favor ble to form deep liquid channels– micrometric films along GB (Fig. 2b), the average rate channels deepening varies in wide range – from several tens micrometers per hour to several parts of millimeter per hour. Field 3: the internal stresses are more than critical value, t he cracks may occur along GB’s; the penetration of the liquid in this case is particularly great, the average rate of channels deepening can reach several millimeters per hour. Sometimes the transparent cha nels are formed. The channels may be full of melt totally or partially, sometimes one can s ee empty channels – cracks (Fig. 2c). The deep channels (cracks) formation in the field 3 is also possible when GB is not we tted (Fig. 2d).