Crystallization kinetics and microstructure

Due to their softness, colloidal crystals are easily shear molten, simply by shaking the sample. They, however readily re-crystallize on the convenient time scale of seconds to hours. Time resolved static light scattering and various forms of microscopy are applied to study phase behaviour including meta-stable transients, crystallization coupled to phase separation, kinetic coefficients for homogeneous and heterogeneous nucleation and possibilities to control crystal formation by applied external shear fields.

Melt structure and dynamics

Metastable and equilibrium melts

Does a meta-stable melt behave like an equilibrium liquid? It seems no!
Static structure factors of concentrated charged sphere suspensions show a split in the second peak (see below). The collective dynamics in hard sphere fluids show a singularity coincident with the freezing transition. The stretching exponent of the current-current correlator measured in dynamic light scattering vanishes, so does its characteristic time while the amplitude diverges. Above melting, the formation of density fluctuations before the onset of crystal formation is seen in both static light scattering and multi-speckle correlation techniques.

Crystal nucleation and growth

Structure factor

We have been measuring quantitative nucleation and growth kinetics for quite some time (J. Phys.: Condens. Matter 11, R323 - R360 (1999)) employing direct video microscopic observation (J. Chem. Phys. 123, 174902 (2005)), post solidification grain size analysis (Crystal Growth and Design 10, 2258 – 2266 (2010)) or time resolved static light scattering (Soft Matter 7, 11274-11276 (2011)) and USAXS (J. Phys.: Condens. Matter 22, 153101 (2009)).

Growth measurements interpreted in terms of Wilson-Fenkel reaction limited growth allow to determine the melt meta-stability (Phys. Rev. E 52; 6415-6423 (1995)). This Δµ (or for hard spheres Δµ taken from theory) is subsequently used to interpret crystallization data in the framework of classical nucleation theory (Phys. Rev. E 75, 051405 (1-12) (2007)). In hard sphere systems we could demonstrate a two step nucleation scenario which later was confirmed in computer simulations (Phys. Rev. Lett. 105, 025701, (2010))

Heterogeneous nucleation and homogeneous nucleation scenarios and their competition were compared for both hard spheres and charged spheres. Charged spheres were observed to show a wetting transition with increased meta-stability of the melt (Soft Matter 7, 5685-5690 (2011)), while hard spheres always wet the container walls (Soft Matter 7, 11274-11276 (2011)).

Turnbull coefficient

Recently we performed a first determination of the Turnbull coefficient for an experimental system crystallizing into a body centred cubic structure. The melt crystal equilibrium interfacial fee energy, σ0, is proportional to the enthalpy of fusion ΔHf with a proportionality constant (Turnbull coefficient) of about 0.3 in good agreement with suggestions from computer simulation for bcc metals. The bcc value is significantly smaller than the values found for fcc crystallizing material.

Crystal microstructure

Crystallization at seed

Crystal microstructure determines largely the dynamic and elastic properties of a polycrystalline solid. We are interested in ways to manipulate the microstructure by external fields or prescribe it via heterogeneous nucleation at deliberately positioned seeds. Single crystal of micron sized charged spheres can be grown in the presence of an attractive seed. Conditions can be altered such that the particles are either repelled from touching the seed surface and hence arrange on equilibrium positions (left) rather than molding the seed and generating a polycrystalline domain with many faults (right).

Crystallization in different environments

In metallic systems the microstructure is often fine tuned by additives inducing inoculation. In colloidal systems this may be copied by adding large spherical impurities at low concentration to a meta-stable shear melt of sub-micron charged colloidal spheres. The polycrystalline microstructure of an aqueous 70nm charged sphere suspension after adding increasing amounts of 15µm spheres as inoculant. The average grain size first increases slightly then decreases drastically, demonstrating both poisoning of nucleation and grain refinement. (Soft Matter 8, 11034–11037 (2012))

Microstructure of eutectic mixture

Eutectic mixtures show characteristic microstructures due to simultaneous demixing and crystallization, which may couple in a feed-back cycle and produce intriguing intercalated patterns. The example shows a mixture of 96% small with 4% large charged spheres. Upon formation of a crystal of small spheres, the large ones are expelled, but also crystallize when their freezing concentration is exceeded. Interestingly, the small particle crystals are below the roughening transition, while the large particle crystals are above.

Do crystals melt from their surface or from their interior? In colloidal systems this is governed by the rate of contamination and the gradient steepness. For vanishing gradients and very low contamination rates, fluid “nucleates” faults and defects in the crystal interior and a swiss cheese pattern emerges (Phil. Mag. 89, 1695 (2009); see also H. Yoshida et al., Langmuir 15, 2684-2702 (1999)).

Swiss cheese pattern A Swiss cheese pattern B