MSE_442_Lecture_20_Nov 8 2013

G two spheres a sphere on a plate or two wires or the

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Unformatted text preview: form of the neck growth equaKons indicates that a plot of log(X /a ) versus log t yields a straight line with a slope equal to 1/m , so by fi[ng the theoreKcal predicKons to experimental data, the value of m can be found. q༇  A similar procedure can be applied to the analysis of shrinkage if it occurs during sintering. q༇  Data for validaKng the models are commonly obtained by measuring the neck growth in simple systems (e.g., two spheres, a sphere on a plate, or two wires) or the shrinkage in a compacted mass of spherical parKcles. q༇  Since m is dependent on the mechanism of sintering, at first sight it may seem that the measurement of m would provide informaKon on the mechanism of sintering. 8 The Initial Stage - Limitations q༇  However, the basic assumpKon in the models of a single dominant mass transport mechanism is not valid in most powder systems. q༇  When more than one mechanism operates simultaneously, the measured exponent may correspond to an enKrely different mechanism. q༇  As an example consider the iniKal sintering of copper. Kingery and Berg showed that the neck growth and shrinkage data of copper spheres gave exponents characterisKc of la[ce diffusion as the dominant mechanism. Later analysis showed that surface diffusion was the dominant mechanism with a significant contribuKon from la[ce diffusion (which gave shrinkage). 9 Idealized Models for The 3 Stages of Sintering a.  Ini*al stage: Model structure represented by spheres in tangen*al contact. b.  Near the end of the ini*al stage: Spheres have begun to coalesce. The neck growth illustrated is for center- to- center shrinkage of 4%. c.  Intermediate stage: Dark grains have adopted the shape of a tetrakaidecahedron, enclosing white...
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