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By Wilhelm U. Oster

This e-book presents updated learn at the box computational fabrics. This box of research involves the development of mathematical types and numerical answer ideas with using desktops to examine and resolve medical, social medical and engineering difficulties.

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ACF for two values of p (solid curves) and as a function of p . its Gauss approximation for p = 1 / 3 (broken curve). As figure 12 demonstrates, computed ACF may be rather well approximated by a Gauss function 18 Vladimir I. 8 , (38) hence the roughness spectrum (Fourier transform of ACF) ( ) g (k ) = πσ 2 Λ2 exp − k 2 Λ2 / 4 , (39) where k = 2π / L is the roughness vector modulus, or spatial frequency and L the spatial period. These results may directly be compared with experimental data of Ref.

79) and (80) we obtain ( ξ λ (τ ) = 1 − exp − K λ ⋅ τ n ) (89) where K λ = λ , n = 3 for CN-VIC and K λ = 3λ / 4 , n = 2 for IN-VIC. The existence of analytic asymptotes (88) and (89) suggests that the crystallization kinetics for a film of arbitrary thickness may be approximated by a generalized KJMA equation ( ξ λ (τ ) = 1 − exp − K λ ⋅ τ n(λ ) ) (90) with parameters depending on a film thickness. This is confirmed by plots in figure 32, clearly demonstrating that the CN-VIC kinetic curves are well straightened in the appropriate to (90) coordinates ln[− ln(1 − ξ )] against ln τ , and table 1, indicating that parameters, founded from here, in limiting cases of extremely thin and thick film converge to their KJMA values.

Nauk SSSR, Ser. Mathem. No. 1 (1937) 355. W. A. Jonson and R. F. Mehl, Trans. Am. Inst. Min. Metall. Eng. 135 (1939) 416. M. Avrami, J. Chem. Phys. 7 (1939) 1103; 8 (1940) 212; 9 (1941) 177. Belen’kii, Geometric-probabilistic models of crystallization: phenomenological approach, Nauka, Moscow, 1980, in Russian. Rep. 8 (1953) 270. I. Trofimov, Thin Solid Films 428 (2003) 56. G. Rasigni, F. Varnier, M. , Surface Sci. 162 (1985) 985, J. Vac. Sci. Technol. A10 (1992) 2869. I. S. Park, Appl. Surface Sci.

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