Crystal Growth & Surface Energies
Just about the only thing we know without doubt about crystal growth is that crystals do, in fact, grow. They grow from solution, from the melt, from gas via sublimation, from seeds and have many, many growth regimes. All the stuff in the middle, between going from solution/gas phase to a small crystal (e.g. nucleation, growth) is, to say the least, complex but that doesn't stop us introducting some approximations to hopefully help guide us in the pursuit of controlling the overall growth and resulting properties of crystals!
Introduction to Crystal Morphology
The morphology of a crystal is its external shape - which faces appear and their relative sises. Understanding and predicting crystal morphology is crucial for:
- Pharmaceuticals - Crystal shape affects dissolution, flowability, compaction
- Materials - Morphology influences optical, electronic, mechanical properties
- Process optimisation - Control crystallisation to get desired shapes
At equilibrium, the resulting crystal shape is in-principle determined by surface energies: lower energy faces grow slower and appear larger in the final crystal. Solvents can dramatically affect morphology by stabilizing certain faces more than others. This is effectively the same thing as surface tension, but liquids are basically isotropic/lack distinct facets - unlike nicely ordered crystals.
Input Structure
We'll continue with the urea crystal structure from the previous tutorial:
Viewer shows the asymmetric unit only
Crystal Growth Calculation
Let's assume the free energies that dictate crystal growth can be expressed as the sum of neighbouring interactions (a big assumption), to get there we can compute interaction energies within the crystal, and break up the solvation surface into chunks representative of the solvation/desolvation that must happen as part of the growth/dissolution process. The below calculation (see paper) automatically computes the gas-phase molecule wavefunction(s), solvated wavefunction(s) and all the corresponding energies and partition and prints out a handle table/writes some convenient output files
Parameters:
--radius 3.8- Neighbour cutoff for bulk lattice energy calculations (Å)--cg-radius 3.8- Neighbour cutoff for surface energy calculations (Å)--solvent water- Solvent for solvated morphology (also calculates vacuum automatically)--surface-energies 10- Calculate surface energies for top 10 crystal facets (ordered by interplanar spacing/)
Default energy model: CE-B3LYP (can be changed with --model flag)
Understanding the Output
Solvent Accessible Surface
The calculation generates a detailed point cloud representation of the solvent-accessible surface, partitioned into regions (CDS - Charge Density Surface and Coulomb contributions). Each point has an associated area and energy contribution:
Color modes:
- Uniform: Solid color (blue for CDS, orange for Coulomb)
- Energy: Viridis colormap showing energy per surface point (blue/purple = low energy, yellow = high energy)
- Neighbor: Each neighboring molecule gets a distinct color, showing which dimer (neighboring molecule pair, not just symmetry-unique dimers) is closest to each part of the surface
Surface types:
- CDS (blue): Cavitation/Dispersion/repulsion Surface - represents the non-electrostatic (cavity formation, dispersion, exchange-repulsion) surface partition
- Coulomb (orange): Electrostatic surface partition
- Both: Shows both surfaces simultaneously
The point cloud shows where solvation stabilization occurs around the molecule. The Neighbor mode is particularly useful for understanding how the surface is partitioned among all neighboring molecules in the crystal packing.
Free Energy Summary
Neighbour Interactions
Surface Energies
Visualizing Crystal Morphology
The calculations generate .ply files containing the predicted 3D crystal shapes. You can visualise these directly:
The visualisation shows the Wulff construction based on calculated surface energies. Faces with lower energies appear larger. Toggle between vacuum and water morphologies to see how the solvent changes the crystal shape!
Physical Interpretation
Why Surface Energy Matters
Low surface energy face:
- Molecules nearly as stable at surface as in bulk
- Low driving force to grow
- Grows slowly → remains large in final crystal
High surface energy face:
- Molecules less stable at surface than bulk
- High driving force to add more molecules
- Grows quickly → disappears (grows out of existence)
Solvent Effects
Solvents affect crystal faces differently because:
- Face-specific chemistry: Different faces expose different functional groups
- Solvent-surface interactions: Polar solvents stabilise polar faces more
- Dielectric screening: Reduces electrostatic interactions differently per face
Result: Relative surface energies change → morphology changes
Next Steps
You now understand how to predict crystal shapes and solvent effects! Continue to the next tutorial to explore more advanced topics.