Influence of coating on thermal response of composites reinforced with anisotropic fibers
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1 2 j ⌫ 6
[3]
10.
where j 2 is the mean square fluctuation distance and ⌫ is the mean frequency of atomic motion. The mean square fluctuation distance is given by j2 ⫽
3kT 4K
[4]
12.
where k is Boltzmann’s constant and K is the Waser–Pauling force constant.[17] For liquid Sn, the force constant is 33 N/m[17] and at the melting temperature of Sn (505 K), the mean square fluctuation distance calculated from Eq. [4] is j 2 ⫽ 1.58 ⫻ 10⫺22 m2. If a thermally activated process for diffusion via a fluctuation mechanism is assumed[13] and the diffusion coefficient is given by Eq. [1], then the frequency factor, D0, is given by D0 ⫽ gf j 2ve⌬S/R 2
⫺22
[5]
m , and the same values for the Using j ⫽ 1.58 ⫻ 10 other parameters as used* previously, the entropy term is 2
*It is not clear if atom motions resulting from a fluctuation mechanism would be correlated. However, the correlation coefficient would have a value 0.684 ⱕ f ⱕ 1.0, and therefore, its value does not appreciably affect the calculation.
calculated to be ⌬S ⫽ ⫹27.6 J mole⫺1 K⫺1. A positive value for the entropy change resulting from a fluctuation mechanism would be expected for the same reasons as for a hole mechanism and the value of ⫹27.6 J mole⫺1 K⫺1 calculated seems reasonable in that it is similar to values calculated for solid diffusion via a vacancy mechanism.[15] Further, the activation volume for liquid diffusion is very small, ⬇0.05 atomic volumes,[18] and this also favors a fluctuation mechanism. It is concluded that while liquid diffusion via the hole mechanism is improbable, diffusion via a fluctuation mechanism remains feasible.
The financial assistance of NSERC Canada in the form of an operating grant is gratefully acknowledged. REFERENCES 1. J.B. Edwards, E.E. Hucke, and J.J. Martin: Metall. Rev., 1968, vol. 13, pp. 1-28. 2. Mitsuo Shimoji and Toshio Itami: in Diffusion and Defect Data, F.H. Wohlbier, ed., Trans Tech Publications Ltd., Switzerland, 1986, vol. 43, pp. 1-344. 3. Michael Klassen and J.R. Cahoon: Metall. Mater. Trans A, 2000, vol. 31A, pp. 1343-52. 4. J.R. Cahoon: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 583-93. 5. A. Bruson and M. Gerl: Phys. Rev. B, 1980, vol. 21, pp. 5447-54. 6. G. Careri, A. Paoletti, and M. Vincentini: Nuovo Cimento, 1958, Ser. 10, vol. 10, pp. 1088-99. 7. W. Lange, W. Pippel, and H. Opperman: Isotopen-Tech., 1962, vol. 2, p. 132. 8. K.G. Davis and P. Fryzuk: J. Appl. Phys., 1968, vol. 39, pp. 4848-49. 9. U. Soedervall, H. Odelius, A. Lodding, G. Frohberg, K.H. Kraatz, and H. Wever: Proceedings of the Fifth International Conference on SecMETALLURGICAL AND MATERIALS TRANSACTIONS A
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