A. The Solid State1. Classification of Solid Structures

a. Crystalline Solids = regular arrangement of components in 3 dimensions

b. Amorphous Solids = disordered arrangement of components

i. Will not be the focus of this chapter

ii. Glasses = “frozen solutions” are disordered, amorphous solids

c. Quasicrystalline Solids—2011 Nobel Prize

2. Crystal Structure Basics

a. Crystal = a piece of a crystalline solid

b. Lattice = 3-dimensional system of designating where components are

c. Unit cell = smallest repeating unit of the lattice

d. Examples: simple cubic, body-centered cubic, face-centered cubic

Three different cubic unit cells and lattices

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

C. X-Ray Analysis of Crystalline Solids1. 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

c. Destructive interference occurs elsewhere

b. Diffractometer = computerized system to rotate crystal while shining X-rays at them and to record the diffraction data produced

c. Diffraction pattern tells us about how far apart the components are

d. Bragg Equation: n = 2dsin

i. Lets us calculate the distance between crystal components

ii. Bragg’s awarded 1915 Nobel Prize for crystallography

iii. Example: find d if n = 1, = 1.54 Å, = 19.3o

D. Types of Crystalline Solids1. 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

E. Growing Crystals1. Growing crystals is an art as much as a science

a. You have to try to grow crystals in order to grow crystals—hard work

b. You can develop skills

c. You have to have a certain amount of luck

2. There are many methods for growing crystals

a. For transition metal complexes, simple methods are often successful

b. Slow Evaporation

c. Diffusion of an insoluble solvent into a solution

d. Demonstration

F. Collecting X-Ray Diffraction Data1. Select a good crystal

a. Well-defined shape with flat faces

b. Needs to be single; not a clump or “tree”

c. Needs to be large enough (0.1mm x 0.1mm x 0.1mm)

2. Mount the crystal on the Diffractometer

1. Glass (amorphous) fiber

2. Use viscous oil or epoxy glue to attach the crystal

3. Calculate the Unit Cell

a. Only a small amount of data is needed (a,b,c and )

b. If the computer can’t do it, the crystal is not good enough

c. Can also tell if crystal is duplicate of known if unit cell is same

4. Collect more data—how much depends on the kind of Bravais Lattice

a. Poor crystals—want more data

b. Great crystals—require less data

G. Solving the Structure1. Computer picks space group

a. Sometimes it is wrong and has to be corrected by the crystallographer

b. 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.

2. Computer gives an initial “solve” where it assigns “peaks” of electron density to atoms in the formula you input

a. Heavy atoms (Metals, S, P) are easy to assign

b. C, N, O don’t have much difference

c. Hydrogens usually don’t show up at all and are calculated in at the end

d. Usually quite a few “peaks” and “holes” unaccounted for (and atoms)

e. Simple Organics often give almost complete solves by computer

3. Experienced crystallographer finishes the solve = “refinement”

a. Assigns atoms to the peaks and “resolves”

b. Indicators either get better or worse

c. Keep working at this until you get an acceptable solve

d. R1 < 0.10 (data used); wR2 < 0.20 (all data)