Avrami is a surname most prominently associated with Melvin Avrami (1913–2014), an American physicist, and the Avrami equation (also known as the Johnson–Mehl–Avrami–Kolmogorov or JMAK equation), a mathematical model describing phase transformation kinetics in materials.
Melvin Avrami (Mael Avrami Melvin)
Melvin Avrami was born in Palestine in 1913 to American parents. He studied theoretical physics at the University of Chicago, earning a B.S. (1933), M.S. (1935), and Ph.D. (1938). During his doctoral studies, he worked as a metallurgist at U.S. Steel's Gary Works. He joined Columbia University as a faculty member in 1938, working in the physics and metallurgy departments. After World War II, he left science for a period and changed his name to Mael Avrami Melvin. He later held professorships at Florida State University (from 1952) and Temple University (1966 until retirement). He was elected a Fellow of the American Physical Society and died on October 1, 2014, in Santa Barbara, California.
The Avrami Equation
The Avrami equation describes how solids transform from one phase to another at constant temperature, particularly the kinetics of crystallization. It produces a characteristic sigmoidal (S-shaped) curve where transformation rates are low at the beginning and end but rapid in between. The equation is expressed as:
$$ Y = 1 - \exp(-K t^n) $$
where $Y$ is the volume fraction of transformed material, $t$ is time, $K$ is a temperature-dependent kinetic constant, and $n$ is the Avrami exponent (originally an integer from 1 to 4 reflecting the dimensionality of growth and nucleation type, though now often treated as an adjustable parameter).
The equation was independently derived by:
- Melvin Avrami in a series of three papers in the Journal of Chemical Physics (1939–1941): "Kinetics of Phase Change. I. General Theory" (1939), "Kinetics of Phase Change. II. Transformation-Time Relations for Random Distribution of Nuclei" (1940), and "Kinetics of Phase Change. III. Granulation, Phase Change, and Microstructure" (1941).
- Wade Johnson and Robert Mehl at Carnegie Institute of Technology (1939).
- Andrey Kolmogorov at Moscow State University (1937), who treated the statistical crystallization of a solid.
Applications
The Avrami equation is widely used in:
- Materials science and metallurgy: Describing crystallization, recrystallization, precipitation, and other solid-state phase transformations.
- Polymer science: Modeling polymer crystallization kinetics.
- Biophysics: Modeling tumor growth kinetics and carcinogenesis as phase-transition processes, where the Avrami constant $n$ has been found to range between 4 and 5 for certain cancers, suggesting fractal geometry in carcinogenic dynamics.
- Ecology: Occasionally applied to analyze ecological systems.
Key assumptions of the simplest derivation include: nucleation occurs randomly and homogeneously, the growth rate is constant and independent of transformation extent, and growth is isotropic.
