%0 Journal Article %1 axe1986scaling %A Axe, J. D. %A Yamada, Y. %D 1986 %I American Physical Society %J Phys. Rev. B %K Johnson-Mehl crystalization parallel_adaptation particle_systems spatial_patterns %N 3 %P 1599--1606 %R 10.1103/PhysRevB.34.1599 %T Scaling relations for grain autocorrelation functions during nucleation and growth %U https://link.aps.org/doi/10.1103/PhysRevB.34.1599 %V 34 %X The kinetics of grain growth associated with a first-order phase transformation is studied with use of the Kolmogorov model (constant nucleation rate within the metastable phase; constant growth rate of the nucleated grains) in one and two dimensions (d =1 and 2). The tine-dependent grain- function and grain autocorrelation function, G, (r, t), are calculated exactly for d = 1. For d = 2, G, (r, t) is estimated by Monte Carlo simulation. Scaling relations, G, (r, t)=F(r/R(t)), using forms for I'(x) which are exact for t~o are investigated. It is found that while such scaling relations are no longer exact in late stages of growth, they continue to pro- vide accurate simple approximations.

@article{axe1986scaling, abstract = {The kinetics of grain growth associated with a first-order phase transformation is studied with use of the Kolmogorov model (constant nucleation rate within the metastable phase; constant growth rate of the nucleated grains) in one and two dimensions (d =1 and 2). The tine-dependent grain- function and grain autocorrelation function, G, (r, t), are calculated exactly for d = 1. For d = 2, G, (r, t) is estimated by Monte Carlo simulation. Scaling relations, G, (r, t)=F(r/R(t)), using forms for I'(x) which are exact for t~o are investigated. It is found that while such scaling relations are no longer exact in late stages of growth, they continue to pro- vide accurate simple approximations.}, added-at = {2018-06-20T01:13:59.000+0200}, author = {Axe, J. D. and Yamada, Y.}, biburl = {https://www.bibsonomy.org/bibtex/29d335bdc2dbc4ee45c51dbe5f6d4de6e/peter.ralph}, doi = {10.1103/PhysRevB.34.1599}, interhash = {876e0fc1db63ad1e858d88127e3e6c7a}, intrahash = {9d335bdc2dbc4ee45c51dbe5f6d4de6e}, journal = {Phys. Rev. B}, keywords = {Johnson-Mehl crystalization parallel_adaptation particle_systems spatial_patterns}, month = aug, number = 3, numpages = {0}, pages = {1599--1606}, publisher = {American Physical Society}, timestamp = {2018-06-20T01:13:59.000+0200}, title = {Scaling relations for grain autocorrelation functions during nucleation and growth}, url = {https://link.aps.org/doi/10.1103/PhysRevB.34.1599}, volume = 34, year = 1986 }