Proefschrift Reinier Grimbergen

From Crystal Structure to Morphology

Gepromoveerd 25 mei 1998 KU te Nijmegen

Promotor Prof.Dr. P.Bennema

Copromotor Dr. H.L.M. Meekes

The work in this thesis can be divided into two parts:

Theory: chapter 2-5

Experiments and interpretation: chapter 5-10

In **chapter 2** the Hartman-Perdok theory is reconsidered and an F-face is redefined as a crystal face having a roughening transition temperature larger than zero Kelvin (> 0). It is demonstrated that a crystallographic orientation (*hkl*) which contains more than one connected net (i.e. surface configuration) may have a zero step free energy. When a pair of symmetry related connected nets gives rise to a zero step energy this is called *symmetry roughening*. The results of a connected net nalysis are linked to the results of simple statistical thermodynamical surface models as described in literature. Finally, it is shown that the presence of multiple connected nets can have important implications for the prediction of the theoretical equilibrium and growth morphology.

In **chapter 3** all symmetry relations between connected nets are categorized and their implications regarding symmetry roughening are discussed. It is shown that the cases of symmetry roughening are in a sense complementary to the classical BFDH law. Moreover, a distinction is made between microscopic and macroscopic symmetry roughening. Microscopic roughening is, like macroscopic roughening, caused by a symmetry related pair of connected nets, but does not give rise to a macroscopic roughening of the face.

The growth and equilibrium behaviour of crystal faces containing (symmetry) related multiple connected nets is studied in **chapter 4**. The results of a connected net analysis are compared with the results of Monte Carlo (MC) simulations. Apart from the well-known flat and rough surface phases also disordered flat (DOF) were identified for specific surface bonding structures. These surface phases may influence the growth behaviour of a crystal face dramatically. This is illustrated by calculation of the relative growth rates of crystal faces (*hkl*) as a function of supersaturation by MC simulations. Specific crystal faces containing multiple connected nets can show anomalous growth behaviour due to (pseudo) symmetry roughening. Moreover, it is demontrated that the classical recipes µ
** **and µ
** **fail completely for these types of face. Using the relative growth rates of the MC simulations it is possible to predict the growth morphology as a function of supersaturation.

In **chapter 5** the phase diagram for the {011} faces of naphthalene is derived from a simplified restricted SOS model. The phase diagram consists of a flat, DOF and rough region. The DOF phase is separated from the flat phase by a preroughening transition line. MC simulations confirm the result of the statistical thermodynamical surface model and show a maximum in the specific heat at . At the preroughening temperature the effective step energy decreases drastically which causes a significant lowering of the nucleation barrier. Therefore, the growth rate of a face in the DOF phase will be relatively high at low supersaturation. However, MC simulations indicate that such a face still grows by a layer-by-layer growth mechanism.

Experimental evidence for the presence of a preroughening transition is presented in **chapter 6**. Vapour growth experiments of naphthalene and anthracene were done and anomalous growth behaviour was found for the {011} faces of naphthalene. These faces could be observed at very low supersaturations at 283 K. On increasing the supersaturation, the faces disappeared very rapidly already at very low supersaturation due to a sudden increase in growth rate. This behaviour is explained by the presence of a DOF phase.

**Chapter 7** describes the results of a rigorous connected net analysis for orthorhombic n-paraffins. The complete set of connected nets is treated and all symmetry relations are analyzed. As a result it is found that the side face structure of n-paraffin crystals may, apart from the {110} faces, also show {100}, {010} and {111} faces.

The experimentally observed morphology of orthorhombic n-paraffin crystals grown from solution, melt and the vapour are compared with the theoretical prediction in **chapter 8**. For the first time flat {010}, {100} and {111} faces were observed on crystals grown from the vapour. The large aspect ratio of crystals grown from solution is explained in terms of the step free energy of those faces.

In **chapter 9** the theoretical morphology of the industrially very important compound e
-capro-lactam (a precursor for nylon-6) is derived. Due to the presence of hydrogen-bonded pairs of molecules in the crystal lattice the connected net analysis was done assuming both monomers and hydrogen-bonded dimers as growth units. The results of the two analyses are very similar. It is argued that, due to the presence of two stacked connected nets, the {110} faces may grow with half layers with a thickness *d _{220}* dependent on the growth conditions. Experimen-tal data from literature show that the presence of these faces depends on the solvent from which the e
-caprolactam crystals are grown.

The experimentally observed dependence of the supersaturation of the morphology of the protein lysozyme is explained in **chapter 10**. The crystals are bounded by {110} and {101} faces. At low supersaturations needles (along the c-axis) are observed, whereas at higher supersaturations block-like crystals are found which is in agreement with the attachment energy prediction. A detailed connected net analysis based on the crystal graph which contains only three bonds *X*, *Y* and *Z* predicts that pseudo symmetry roughening may occur for a certain bond ratio *X:Y:Z*. Based on the step energies of the three F-faces {110}, {101} and {111} it is possible to understand the depen-dence of the morphology on the supersaturation. The results are in agreement with previously published MC simulation data and the experimentally observed surface structure. There are strong indications that, depending on the temperature, DOF surface phases might occur for the face of lysozyme.

**Chapter 11** treats the growth morphology of a series of cesium halides (CsF, CsCl, CsBr and CsI). Vapour growth experiments show a very distinct transition from a cubic ({001}, high temperature) to a dodecahedral ({110}, low temperature) morphology as a function of temperature and super-saturation. It is shown that the temperature is the critical parameter which determines whether the transition is observed. Moreover, the transition temperature depends on the halide. A connected net analysis yields the {001}, {110} and {111} faces as F-forms when only first nearest neighbour bonds are taken into account. In principle the connected nets found for {001} and {111} faces would cause symmetry roughening. However, when (repulsive) next nearest neighbour bonds are considered, it becomes clear that the {001} faces are stabilized by a c2x2 reconstruction. The relative growth rates of the {001} and {110} faces as a function of temperature were determined by MC simulations at a fixed supersaturation. The simulation results confirm the experimentally observed transition from a cubic into a dodecahedral morphology when the temperature is increased. Moreover, our MC results are in agreement with the Ising transition temperatures as given by the phase diagram of the statistical thermodynamical staggered BCSOS model. It is concluded that the observed dependence of the temperature is a result of a phase transition of the {001} faces from a reconstructed c2x2 into a deconstructed rough or DOF phase dependent on the anisotropy.