Microstructure-PropertiesIITheKJMAEquation.ppt

Microstructure-Properties: II The KJMA Equation 27-302 Lecture 5 Fall, 2002 Prof. A. D. Rollett Materials Tetrahedron Objective The objective of this lecture is to introduce the concept of phase transformation kinetics as described by the Kolmogorov-Johnson-Mehl-Avrami equation. Part of the motivation for this lecture is to prepare the class for a Lab on the crystallization of glass-ceramics. References Phase transformations in metals and alloys, D.A. Porter, K.E. Easterling,Chapman Hall, 0-412-45030-5, 669.94 P84P2: page 289. Kolmogorov, A. (1937). “A statistical theory for the recrystallization of metals.” Akad. nauk SSSR, Izv., Ser. Matem. 1: 355. Johnson, W. and R. Mehl (1939). “Reaction kinetics in processes of nucleation and growth.” Trans AIME 135: 416. Avrami, M. (1939). “Kinetics of Phase Change. I: General Theory.” J. Chem. Phys. 7: 1103. Avrami, M. (1940). “Kinetics of Phase Change. II: Transformation-Time relations for random distribution of nuclei.” J. Chem. Phys. 8: 212. Avrami, M. (1941). “Kinetics of Phase Change. III: Granulation, Phase Change an Microstructures.” J. Chem. Phys. 9: 177. Anderson, W. and R. Mehl (1945). “Recrystallization of Al in terms of the rate of nucleation and growth.” Trans. AIME 161: 140. Transformation Kinetics The kinetics of transformation are typically described by a standard equation known as the Kolmogorov-Johnson-Mehl-Avrami equation, named after the individuals who derived it. The characteristic of the kinetics is that of the “S-curve”, i.e. slow at first, then accelerating, then decelerating. Transformation kinetics are universal The kinetics of transformation are universal. Consider this example of the kinetics of cell growth. High-Throughput Assay System for the Discovery Of Anti-Bacterial Drugs1J. Bruce Pitner, 2Mark R. Timmins, 2Maurice Kashdan, 3Mandar Nagar, and 3David T. Stitt, 1BD Technologies 21 Davis Drive, Research Triangle Park, NC 27709, 2BD Biosciences, Two Oak Park, Bedford, MA 01730, 3BD Bioscien