1. A. The Solid State Classification of Solid Structures
Crystalline Solids = regular arrangement of components in 3 dimensions
Amorphous Solids = disordered arrangement of components
i. Will not be the focus of this chapter
Glasses = “frozen solutions” are disordered, amorphous solids
Quasicrystalline Solids—2011 Nobel Prize
Crystal Structure Basics
Crystal = a piece of a crystalline solid
Lattice = 3-dimensional system of designating where components are
Unit cell = smallest repeating unit of the lattice
Examples: simple cubic, body-centered cubic, face-centered cubic

2. Three different cubic unit cells and lattices

3. B. Bravais Lattices = 14 possible basic crystal structure unit cell types

5. C. X-Ray Analysis of Crystalline Solids
1. Diffraction = scattering of light by a crystal’s regular array of components
a. Wavelength of light must be about the same as the spacing of units
b. Constructive interference occurs when different distances traveled by the same wavelength of light is an integer multiple of l
c. Destructive interference occurs elsewhere

6. Diffractometer = computerized system to rotate crystal while shining X-rays at them and to record the diffraction data produced
Diffraction pattern tells us about how far apart the components are
Bragg Equation: nl = 2dsinq
Lets us calculate the distance between crystal components
Bragg’s awarded 1915 Nobel Prize for crystallography
Example: find d if n = 1, l = 1.54 Å, q = 19.3o

7. D. Types of Crystalline Solids
1. Ionic = ions at lattice points, held together by Coulombic attractions, NaCl
2. Molecular = molecules at lattice point, intermolecular forces, H2O
3. Atomic = atoms at lattice points
a. Metallic Solids = non-directional covalent bonding, Copper metal
b. Network Solids = strong, directional, covalent bonds, Diamond
c. Group 8A Solids = noble gases in solid state, London forces only

8. E. Growing Crystals Growing crystals is an art as much as a science
You have to try to grow crystals in order to grow crystals—hard work
You can develop skills
You have to have a certain amount of luck
There are many methods for growing crystals
For transition metal complexes, simple methods are often successful
Slow Evaporation
Diffusion of an insoluble solvent into a solution
Demonstration

9. F. Collecting X-Ray Diffraction Data
Select a good crystal
Well-defined shape with flat faces
Needs to be single; not a clump or “tree”
Needs to be large enough (0.1mm x 0.1mm x 0.1mm)
Mount the crystal on the Diffractometer
Glass (amorphous) fiber
Use viscous oil or epoxy glue to attach the crystal

10. What you don’t want to see
Examples courtesy of the Smith group and the U. of Cincinnati

11. Typical Hardware Camera Low Temperature Goniometer Detector Sample
Source(s)

12. Crystal Examination

14. Initial Diffraction pattern
What we expect to see:

15. G. Solving the Structure
Calculate the Unit Cell
Only a small amount of data is needed (a,b,c and a,b,g)
If the computer can’t do it, the crystal is not good enough
Can also tell if crystal is duplicate of known if unit cell is same
Collect more data—how much depends on the kind of Bravais Lattice
Poor crystals—want more data
Great crystals—require less data
G. Solving the Structure
1. Computer picks space group
Sometimes it is wrong and has to be corrected by the crystallographer
Picking the right space group can dramatically improve the results
The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices which belong to one of 7 crystal systems. This results in a space group being some combination of the translational symmetry of a unit cell including lattice centering, and the point group symmetry operations of reflection, rotation and improper rotation (also called rotoinversion). Furthermore one must consider the screw axis and glide plane symmetry operations. These are called compound symmetry operations and are combinations of a rotation or reflection with a translation less than the unit cell size. The combination of all these symmetry operations results in a total of 230 unique space groups describing all possible crystal symmetries.

16. Computer gives an initial “solve” where it assigns “peaks” of electron density to atoms in the formula you input
Heavy atoms (Metals, S, P) are easy to assign
C, N, O don’t have much difference
Hydrogens usually don’t show up at all and are calculated in at the end
Usually quite a few “peaks” and “holes” unaccounted for (and atoms)
Simple Organics often give almost complete solves by computer
Experienced crystallographer finishes the solve = “refinement”
Assigns atoms to the peaks and “resolves”
Indicators either get better or worse
Keep working at this until you get an acceptable solve
R1 < 0.10 (data used); wR2 < 0.20 (all data)