R EPORTS of correlation functions yield coefficient of determi- where ⌫ is the gamma function, defined as ⌫(n) ϭ References and Notes 2 ͐ ϱ Ϫx nϪ1 1. C. A. Angell, K. L. Ngai, G. B. McKenna, P. F. McMillan, nation R values greater than 0.99 in most cases. 0 e x dx. S. W. Martin, J. Appl. Phys. 88, 3113 (2000). Standard errors for the fitting parameters tend to be 36. The orientational transient can be calculated from 5 2. M. D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000). extremely small (1 part in 10 ) but provide little the polarized fluorescence data with 3. H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999). meaningful basis for comparison because of the large ͑ ͒ ␤ ␶ Ϫ // t covariance of and . A useful measure of this error ␪͑t͒ ϭ tan 1ͫͱ ͬ 4. M. D. Ediger, C. A. Angell, S. R. Nagel, J. Phys. Chem. ␤ Ќ͑t͒ 100, 13200 (1996). determines that a 1% variation in or a 5% variation in ␶ is sufficient to reduce the R2 value from 0.99 to Molecules were determined to have exchanged environ- 5. J. T. Fourkas, D. Kivelson, U. Mohanty, K. A. Nelson, ␶ Eds., Supercooled Liquids: Advances and Novel Appli- 0.98. The rotational correlation time C is defined as ments when the average angle jump changes by more cations, vol. 676 of ACS Symposium Series (American the integral from zero to infinity of the correlation than 2 SD from the previous average angle jump. Chemical Society, Washington, DC, 1997). function, but for a stretched exponential function, 37. C. Bennemann, C. Donati, J. Baschnagel, S. C. Glotzer, this integral can be conveniently written in terms of Nature 399, 246 (1999). 6. G. Harrison, The Dynamic Properties of Supercooled ␶ ␤ Liquids (Academic Press, New York, 1976). the and parameters as 38. D.A.V.B. is a Research Corporation Cottrell Scholar and a Camille and Henry Dreyfus Foundation New 7. T. Gleim, W. Kob, K. Binder, Phys. Rev. Lett. 81, 4404 ϱ Faculty Awardee. This work is supported by grants (1998). ␶ 1 8. D. B. Hall, A. Dhinojwala, J. M. Torkelson, Phys. Rev. ␶ ϭ ͵ ͑ ͒ ϭ KWW ⌫ ͩ ͪ from the Research Corporation. C C t dt ␤ ␤ Lett. 79, 103 (1997). KWW KWW 9. G. Adam, J. H. Gibbs, J. Chem. Phys 43, 139 (1965). 0 10 October 2000; accepted 28 February 2001 10. H. Wendt, R. Richert, Phys. Rev. E. 61, 1722 (2000). 11. E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, D. A. Weitz, Science 287, 627 (2000). 12. C.-Y. Wang, M. D. Ediger, J. Phys. Chem. B 104, 1724 (2000). 13. I. Chang, H. Sillescu, J. Phys. Chem. B 101, 8794 Real-Space Imaging of (1997). 14. K. L. Ngai, J. Phys. Chem. B 103, 10684 (1999). 15. R. Richert, J. Phys. Chem. B 101, 6323 (1997). Nucleation and Growth in 16. E. V. Russell, N. E. Israeloff, Nature 408, 695 (2000). 17. W. E. Moerner, Science 265, 46 (1994). 18. P. F. Barbara, W. E. Moerner, Acc. Chem. Res. 29, 561 Colloidal Crystallization (1996). 1 1 2 2 19. H. P. Lu, X. S. Xie, Nature 385, 143 (1997). U. Gasser, * Eric R. Weeks, † Andrew Schofield, P. N. Pusey, 20. S. Nie, D. T. Chiu, R. N. Zare, Science 266, 1018 D. A. Weitz1 (1994). 21. D. A. Vanden Bout et al., Science 277, 1074 (1997). 22. R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, Crystallization of concentrated colloidal suspensions was studied in real space Nature 388, 355 (1997). with laser scanning confocal microscopy. Direct imaging in three dimensions 23. T. Basche, S. Kummer, C. Braeuchle, Nature 373, 132 (1995). allowed identification and observation of both nucleation and growth of crys- 24. The single-molecule environment is probe depen- talline regions, providing an experimental measure of properties of the nucle- dent, with its size determined by the dye used. ating crystallites. By following their evolution, we identified critical nuclei, 25. J. J. Macklin, J. K. Trautman, T. D. Harris, L. E. Brus, determined nucleation rates, and measured the average surface tension of the Science 272, 255 (1996). 26. The sample is held atop a closed loop piezo scanning crystal-liquid interface. The structure of the nuclei was the same as the bulk stage and illuminated with the second harmonic of a solid phase, random hexagonal close-packed, and their average shape was rather Nd:yttrium-aluminum-garnet laser through a 1.25 nu- nonspherical, with rough rather than faceted surfaces. merical aperture (NA) oil immersion objective in the epi configuration. By scanning the sample in the focus of a laser beam, we can observe the fluorescence from in- The study of the structure, growth, and prop- the surface energy and bulk energy is reflect- dividual molecules. The fluorescence signal from the erties of crystals is one of the most important ed in the free energy for a spherical crystallite molecules is passed through a dichroic beam splitter to areas of solid state physics (1). Although a remove excitation light and split into two orthogonal 4␲ 2 3 polarizations, which are imaged onto the front of two great deal is known about the behavior of ⌬G ϭ 4␲r ␥ Ϫ r ⌬␮n (1) single-photon-counting avalanche photodiodes. For bulk crystals, considerably less is known 3 temperature-dependent data, the sample was held at about their earliest stage, when they nucleate where r is the radius, ␥ is the free energy of constant temperature in an Oxford Microstat-N cryo- and grow from a liquid. Homogeneous nucle- the crystal-liquid interface per unit area, ⌬␮ stat, and the fluorescence was excited and collected through a 0.6-NA long working distance air objective. ation occurs when small crystalline regions is the difference between the liquid and solid All other aspects of the experiment remain unchanged. form from structural fluctuations in a liquid chemical potentials, and n is the number den- 27. The Tg of the polymer was measured by differential cooled below its freezing point. The growth sity of particles in the crystallite (2). The size scanning calorimetry. ϭ ␥ ⌬␮ 28. T. Ha, T. A. Laurence, D. S. Chemla, S. Weiss, J. Phys. of these regions depends on a competition of the critical nucleus is rc 2 /( n), Chem. B. 103, 6839 (1999). between a decrease in bulk energy, which corresponding to the maximum of ⌬G (Eq. 29. R. M. Dickson, A. P. Bartko, J. Phys. Chem. B. 103, favors growth, and an increase in surface 1). Despite its crucial role, very little is 3053 (1999). 30. R. M. Dickson, D. J. Norris, Y.-L. Tzeng, W. E. Moerner, energy, which favors shrinkage. The smallest known about this nucleation process, primar- Science 274, 966 (1996). crystals continually form by fluctuations but ily because of the difficulty of directly ob- 31. Measurement of the full three-dimensional orientation then typically shrink away because of the serving the nuclei in real space. (27, 28) is not required because the dynamics are high surface energy. Growth becomes ener- No experiment has ever directly measured isotropic in three dimensions and thus revealed fully in the fluctuations of the dichroism. Additionally, the use getically favorable only when the crystallites the size of the critical nucleus. It cannot be of a high NA objective (NA ϭ 1.25) leads to a slight reach a critical size. The competition between determined theoretically—even the surface contamination of the dichroism signal due to the out- tension is unknown. Furthermore, an addi- of-plane component of the fluorescence that manifests itself as an additional background but does not adverse- 1Department of Physics and Division of Engineering tional important yet unresolved question in- ly affect the measured dynamics (28). and Applied Sciences, Harvard University, Cambridge, volves the internal structure of critical nuclei, 32. J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. MA 02138, USA. 2Department of Physics and Astron- because nucleation need not occur via the van Hulst, Phys. Rev. Lett. 83, 2155 (1999). omy, University of Edinburgh, Edinburgh, Scotland stable bulk phase (3). General arguments 33. T. Ha, J. Glass, T. Enderle, D. S. Chemla, S. Weiss, Phys. EH9 3JZ, UK. Rev. Lett. 80, 2093 (1998). based on symmetry suggest that nucleation 34. G. E. P. Box, G. M. Jenkins, Time Series Analysis Forecast- *To whom correspondence should be addressed. E- may proceed by a body-centered cubic (bcc) ing and Control (Holden-Day, San Francisco, 1976). mail: [email protected] 35. For all correlation functions, the first point containing †Present address: Physics Department, Emory Univer- structure as an intermediate phase, with the the noise is not shown and not included in the fit. Fits sity, Atlanta, GA 30322, USA. final equilibrium solid phase having a differ- 258 13 APRIL 2001 VOL 292 SCIENCE www.sciencemag.org R EPORTS ent symmetry (4). Computer simulations of a manner, but the boundaries of the phase dia- the sample before observation. Heterogeneous Lennard-Jones system found critical nuclei gram are shifted to slightly lower ␾ values (11). nucleation at the walls of the sample chamber with a face-centered cubic (fcc) core and a Colloidal (6–8, 13–16) and protein (17) sys- was suppressed by fusing colloidal particles of predominantly bcc surface layer (5). Howev- tems have been valuable for studying crystal a smaller size onto the walls before adding the er, light-scattering measurements from hard nucleation, but these studies did not directly colloidal samples. Further, we focused at least 8 spheres (6–8), which provide an average visualize the critical nuclei and thus were un- and typically 15 particle diameters from the over crystalline regions of all sizes, suggest able to directly observe their properties.