Hostname: page-component-7857688df4-jkt97 Total loading time: 0 Render date: 2025-11-13T23:34:58.418Z Has data issue: false hasContentIssue false
  • English
  • Français

The Grain Size Distribution in Crystallization Processes With Anisotropic Growth Rate

Published online by Cambridge University Press:  01 February 2011

Kimberly S. Lokovic ,
Ralf B. Bergmann  and
Andreas Bill
Kimberly S. Lokovic
Affiliation:
klokovic@gmail.com, California State University Long Beach, Physics & Astronomy, 90840, California, United States
Ralf B. Bergmann
Affiliation:
bergmann@bias.de, Bremen Institute for Applied Beam Technology, Bremen, Germany
Andreas Bill
Affiliation:
abill@csulb.edu, California State University Long Beach, Physics & Astronomy, 1250 Bellflower Blvd., Long Beach, California, 90840, United States, 5629858616, 5629857924
Get access

Abstract

The grain size distribution allows characterizing quantitatively the microstructure at different stages of crystallization of an amorphous solid. We propose a generalization of the theory we established for spherical grains, to the case of grains with ellipsoidal shape. We discuss different anisotropic growth mechanisms of the grains in thin films. An analytical expression of the grain size distribution is obtained for the case where grains grow through a change of volume while keeping their shape invariant. The resulting normalized grain size distribution is shown to be affected by anisotropy through the time-decay of the effective growth rate.

Keywords

nucleation & growththin filmgrain size

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1 Bergmann, R.B. and Bill, A., J. Cryst. Growth 310, 3135 (2008).Google Scholar
2 Teran, A.V., Bergmann, R.B. and Bill, A., Mater. Res. Soc. Symp. Proc. 1153, A05–03 (2009).Google Scholar
3 Teran, A.V., Bergmann, R.B. and Bill, A., Phys. Rev. B 81, 075319 (2010).Google Scholar
4 Kolmogorov, A.N., Akad. Nauk SSSR, Izv. Ser. Matem. 1, 355 (1937).Google Scholar
5 Avrami, M., J. Chem. Phys. 7, 1103 (1939); ibid., 8, 212 (1940).Google Scholar
6 Johnson, W. and Mehl, R., Trans AIME 135, 416 (1939); W. Anderson and R. Mehl, ibid., 161, 140 (1945).Google Scholar
7 Kumomi, H. and Yonehara, T., Jpn. J. Appl. Phys. 36, 1383 (1997)Google Scholar
8 Kumomi, H., in Growth, Characterization and Electronic Applications of Si-based Thin Films, edited by Bergmann, R. B. (Research Signpost, Trivandrum, India, 2002).Google Scholar
9 Oriented Crystallization on Amorphous Substrates Givargizov, E.I. (Springer Verlag, 1991).Google Scholar
10 Gentry, K.P., Gredig, T. and Schuller, I.K., Phys. Rev. B 80, 174118 (2009).Google Scholar