Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory
Abstract
We study the Kolmogorov-Johnson-Mehl-Avrami theory of phase conversion in finite volumes. For the conversion time we find the relationship τcon=τnu[1+fd(q)]. Here d is the space dimension, τnu the nucleation time in the volume V, and fd(q) a scaling function. Its dimensionless argument is q=τex/τnu, where τex is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate fd(q) in one, two, and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for fd(q).
- Publication:
-
Physical Review Letters
- Pub Date:
- April 2008
- DOI:
- 10.1103/PhysRevLett.100.165702
- arXiv:
- arXiv:0802.0535
- Bibcode:
- 2008PhRvL.100p5702B
- Keywords:
-
- 64.60.Q-;
- 64.75.-g;
- 81.30.-t;
- Nucleation;
- Phase equilibria;
- Phase diagrams and microstructures developed by solidification and solid-solid phase transformations;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Materials Science;
- High Energy Physics - Lattice
- E-Print:
- 4 pages, 4 figures. Additions after referee reports: Scaling of the variable q is proven. Additional references are added