An optical method for determining the surface orientation of crystals
- PDF / 2,022,795 Bytes
- 2 Pages / 598 x 778 pts Page_size
- 54 Downloads / 250 Views
,n
- -}--
REFERENCES
eoJ
[8]
where D,.o-,l,y~'~2 B
--
-
-
krm
Here, D, is the interface diffusivity, ~81 is the interface energy of the rod, y is the atoms per unit area of the interface which can diffuse, f~ is the atomic volume, and Tm is the monotectic temperature. In order to pinch off, this time must he less than the time the rod phase remains liquid. Thus, combining Eqs. [7] and [8], we get a criterion for the droplet formation of Ro < ( S ) '/4
[9]
where S-
BAT
1. J.D. Livingstone and H.E. Cline: TMS-AIME, 1969, vol. 245, pp. 35157. 2. A. Kamio, S. Kumai, and H. Tenzuka: Mater. Sci. Eng., 1991, vol. A146, pp. 105-21. 3. R.N. Grugel and A. Hellawell: Metall. Trans. A, 1982, vol. 13A, pp. 493-95. 4. R.A. Parr and M.H. Johnston: MetalL Trans. A, 1978, vol. 9A, pp. 1825-28. 5. C. Schafer, M.H. Johnston, and R.A. Parr: Acta Metall., 1983, vol. 31, pp. 1221-1224. 6. B. Majumdar: Ph.D. Thesis, Indian Institute of Science, Bangalore, 1995. 7. Lord Rayleigh: Proc. London Math. Soc., 1878, vol. 10, p. 4. 8. S. Chandrasekbar: Hydrodynamics and Hydromagnetic Stability, Oxford University Press, Oxford, United Kingdom, 1961, pp. 515-76. 9. S.R. Coriel and S.C. Hardy: J. Appl. Phys., 1969, vol. 40, pp. 165255. 10. F.A. Nichols and W.W. Mullins: TMS-AIME, 1965, vol. 233, pp. 1840-48. 11. R.F. Sekerka and T.F. Marinis: Proc. Solid-Solid Phase Transformation, TMS, Warrendale, PA, 1982, pp. 67-84. 12. B. Derby, D. Camel, and J.J. Favier: J. Cryst. Growth, 1983, vol. 65, pp. 280-85.
4G In x ~ The expression in Eq. [9] is nonlinear and difficult to evaluate due to the uncertainties of the initial amplitude. However, it is a relatively weak function of Ro/eo. Figure 5 gives a plot of Ro vs V for two Ro/~o ratios of 5 and 60, which represent a realistic range for the case of Zn-Bi monotectic growth. The curves for all the intermediate values are contained in the preceding envelope. The shift in the curve toward the origin for the increasing Ro/eo value is maximum for the values ranging from 5 to 10. These represent high values of initial amplitude, which are less likely in actual experimental conditions. Beyond the Ro/~o value of 20, the shift gets progressively smaller, and beyond 60, it is negligible. These curves separate the region of stable rod growth from the region where rod will break down to yield rows of droplet morphology. The R0 as a function of V estimated from the experimental inter-rod spacings using Eq. [6] is also included in the figure. The changeover from rod to droplet morphology takes place within the range of growth velocity between 0.18 and 0.47 • 10 _6 m/s for the corresponding Ro/eo range of 5 to 60. Thus, it is clear that the experimental conditions adopted by us (lowest growth velocity = 3 • 10 -6 m / s ) are expected to yield only rows of droplets. It is also possible to estimate the effect of temperature gradient and volume fraction of the rod phase on the stability of the rod morphology. The increases in both the temperature gradient and the volume fraction result in an expansion of the
Data Loading...
