A. The Solid State 1. 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 Solids2011 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 Solids 1. Diffraction = scattering of light by a crystals 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 Xrays 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. Braggs awarded 1915 Nobel Prize for crystallography iii. Example: find d if n = 1, = 1.54 , = 19.3o 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, H 2O 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 Crystals 1. Growing crystals is an art as much as a science a. You have to try to grow crystals in order to grow crystalshard 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 Data 1. 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 What you dont want to see Examples courtesy of the Smith group and the U. of Cincinnati Typical Hardware Low Temperature
Detect or Camera Goniometer Sampl e
Source(s) Crystal Examination Initial Diffraction pattern What we expect to see: 3. Calculate the Unit Cell
a. Only a small amount of data is needed (a,b,c and ) b. If the computer cant 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 datahow much depends on the kind of Bravais Lattice a. Poor crystalswant more data b. Great crystalsrequire less data G. Solving the Structure
1. Computer picks space group 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. a. Sometimes it is wrong and has to be corrected by the crystallographer b. Picking the right space group can dramatically improve the results 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 dont have much difference c. Hydrogens usually dont 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)
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