The Avrami Equation

When materials are heated or cooled, their structure often changes. This is called a phase transformation. Phase transformations are used extensively to modify and control the final microstructure and properties of a material during manufacturing into its final product form. The Avrami equation describes the sigmoidal (S-shaped) way in which the amount of a new phase evolves, initially accelerating as particles of the new phase nucleate and grow, and then decelerating as the old phase becomes progressively exhausted. This chapter explains the development of new phases by nucleation and growth, the mechanisms of precipitation, eutectoid and martensite reactions, and the use of time–temperature–transformation curves to understand and control transformation behaviour. The Avrami equation was derived independently in the mid-20th century by Melvin Avrami at Columbia University, Robert Mehl and his student W. Johnson at Carnegie Tech, and Andrei Kolmogorov at Moscow State University. Avrami was horrified by the development of the atomic bomb at the end of the Second World War and dropped out of society to work as a caretaker on Orcas Island off the West Coast of America, before changing his name and returning as a physicist some years later; Mehl is known as one of the father figures of metallurgical science in the United States; and Kolmogorov made important advances in fields such as trigonometry, probability, topology, turbulence and genetics.