1. Andrew Dougherty Franklin Stinner (‘11) Physics Department Lafayette College, Easton PA http://sites.lafayette.edu/doughera Sidebranching in the Dendritic Crystal Growth of Ammonium Chloride

2. Experiments NH 4 Cl growing in aqueous solution Growth cell: 40 x 10 x 2 mm 3 Obtain an approximately spherical seed. Lower temperature  T (~1 o C) to initiate slow growth.

3. Apparatus

4. Growth from a Nearly Spherical Seed

6. Apparent tip oscillations – note the regular sidebranches close to the tip. However – such patterns are only rarely seen in this experiment, and we have not found any way to repeat them.

7. Typical sidebranches—note the long smooth tip and the slightly irregular branches.

9. Noise-induced Sidebranch Amplitude w ave (z) = average shape of the dendrite.

10. Determining Materials Constants d 0 : Capillary length: Measure the very slow growth and dissolution of an initially spherical seed. v,  and   : Measure the tip of steady-state growing dendrites.

11. Finding d 0 : Modeling the initial growth Assume quasi-static, diffusion-limited, spherically-symmetric growth: Increasing supersaturation  increases growth rate. Growth rate proportional to local concentration gradient. Surface tension limits sharpness Unstable equilibrium at R c, the critical radius for nucleation. 2d 0/ /R term is very small; need to optimize the experimental protocol to determine d 0

12. Slow Growth of a Spherical Crystal

13. Modeling the initial growth

14. Fitting the Dendrite Tip First, model the tip, then look for sidebranches as deviations from the initially smooth tip. Approximate model for tip shape: (A 4  -0.002) Measure tip position to determine v.

15. Preliminary Results for Materials Constants d0d0 (2.2 + 0.1)x10 -4  m d  /dT 0.0043 + 0.0001/ o C v2v2 12.1 + 0.1  m 2 /s ** 0.093 + 0.008

16. Noise-induced Sidebranch Amplitude w ave (z) = average shape of the dendrite.

17. Average Shape: No single simple shape – Different Scaling Regimes: Near tip, w ~ z 1/2 Very far back, w ~ z 1 Intermediate region: w ~ z 3/5 ? Actual scaling varies more continuously.

18. Average shape for 3 growth velocities. w ~ z 0.6~0.8

21. Modeling Initial Sidebranches Approximate model for initial sidebranches (all distances are scaled by  :

25. Aggregated Fits for RMS Sidebranch Amplitude

27. Preliminary Fit Results for Noise Amplitude S 0 (expt)~5 x 10 -4 S 0 (theory)~1 x 10 -4

28. Conclusions: No velocity oscillations were observed during normal steady-state growth. The functional form of the sidebranch amplitude is reasonably-well described by the noise-driven scenario. The amplitude of the sidebranches is slightly larger, but of the same order of magnitude as predicted by the noise-driven scenario. Limitations: The most important limitations are precise characterizations of both w ave and actual sidebranch amplitudes.