The driving force for chemically induced migration of molten ni films between w grains
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[2]
where M is the dislocation mobility for climb and 1"s is the line tension of the dislocations contained in the subgrain boundaries. Equation [2] assumes that the mechanisms of coalescence of subgrain boundaries and boundary migration both occur simultaneously. 3 The calculation of a theoretical value of K involves the following three equations: "'s = (C,. b2)/3.5 Os = D~ e x p ( - Q / R T ) M = (Ds" b ) / ( k . T)
[3] [4] [5]
where G = shear modulus = 2.618 • 101~N / m 2 b = Burgers vector = 2.86 x 10 l~ k = Boltzmann constant = 13.8 • l 0 -24 J / K T = annealing temperature = 523 K R = universal gas constant = 8.31 J/mole 9 K Q = activation energy for self diffusion = 127 k J/mole DO = constant = 10 5 m2/sec The appropriate values of the terms involved in Eqs. 131, [41, and [5] are shown above which results in ~-~ = 6.12 • 10 -~~ N / m 2 = line tension of the dislocation lines D~ = 2.038 • 10 ~s m2/sec = self diffusion coefficient M = 8.078 x 10~ m2/N 9 sec = dislocation mobility for climb The calculated value of K is thus 5.44 • 10 ~6 m 2 per second and the observed value is greater than this by a factor of only 1.09 or approximately nine percent. This is considered to be an excellent correlation between theoretical results and experimental observations even though the authors do realize that more experimental data in Figure 1 are required to establish fully the validity of Sandstrom's model for parabolic subgrain growth in pure aluminum during static annealing, it will be of great interest to determine whether or not K values are dependent on the extent of dynamic recovery experienced by aluminum during cold working for similar subgrain sizes. Kreisler and Doherty 6 have pointed out that the mechanism of coalescence would be dominating if the misorientation angles for the subgrains are large while boundary migration should prevail if the distribution of subgrain sizes shows large non-uniformity based on the driving force required in each case. Thus, aluminum samples with similar cell sizes but having large misorientation angles should provide good starting material to identify the subgrain growth mechanism more precisely. REFERENCES 1. R. Sandstrom: Acta Metall., 1977, vol. 25, p. 897. 2. R. Sandstrom: Acta Metall., 1977, vol. 25, p. 905. METALLURGICAL TRANSACTIONS A
3. R. Sandstrom, B. Lehtinen, E. Hedman, I. Groza, and S. Karlsson: J. Mat. Sci., 1978, vol. 13, p. 1229. 4. S.K. Varma and B.G. LeFevre: Metall. Trans. A, 1980, vol. l l A , p. 935. 5. J. Howard: Scripta Met., 1976, vol. 10, p. 441. 6. A. Kreisler and R.K. Doherty: Metal Sci., December 1978, p. 560.
The Driving Force for Chemically Induced Migration of Molten Ni Films between W Grains YOUNG-DUH SONG and DUK N. YOON Recently, Yoon and Huppmann 1 observed that spherical W grains separated by molten Ni films grew into their neighbors during liquid phase sintering at 1640 ~ The driving force was attributed to the composition difference between the pure parent W and the W-Ni alloy precipitated on the growing grains, but the boundary migration r
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