Crystal Structures X-ray Diffraction Chemistry 123 Spring

Crystal Structures & X-ray Diffraction Chemistry 123 Spring 2008 Dr. Woodward

Crystals

Crystalline Solids Ca. F 2 Unit Cell • Crystal Lattice – A 3 D array of points where each point has an identical environment. • Unit Cell – The repeating unit (a unit cell is to a crystal, like a “brick” is in a house). In a given crystal all unit cells are identical.

Cubic 3 D Crystal Systems (7) Cubic Tetragonal Hexagonal Rhombohedral Orthorhombic Monoclinic Triclinic 14 Bravais Lattices The crystal systems each have distinctive symmetry and unit cell dimensions

X-ray Diffraction

Diffraction Demo Take home message • The diffraction pattern is related but not equal to the grid pattern • Diffraction is most effective for monochromatic light whose wavelength is similar to the spacing of “slits” • For crystals X-rays have a wavelength comparable to spacings of atoms

Bragg’s Law A B d The extra path length traveled by wave B (shown in red) is equal to 2 d sin q, where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple of the wavelength (nl). When we use Bragg’s Law we generally set n=1.

Symmetric Structures Simple X-ray Pattern Ex. Gold – Face centered cubic structure Low symmetry Structures Complex X-ray Pattern Ex. Cu. SO 4 5 H 2 O (triclinic structure)

Simple Cubic Crystal Structures (a) Cs. Cl (b) Na. Cl (c) Zinc blende Decreasing coordination number

X-Ray Powder Diffraction Pattern (Ex. Magnesium Sulfide, Mg. S) 020 planes 220 planes Each peak corresponds to scattering from a different set of lattice planes. Two planes are shown above for Mg. S, which has the same structure as Na. Cl.

Mg. S with the Na. Cl structure Zn. S with the Zinc Blende structure

Two Component Phase Diagram D ° Temperature ( C) Liquid Eutectic Point A Mg. S (ss) + Liquid Zn. S (ss) + Liquid Mg. S (ss) C Zn. S (ss) 2 -phase region Mg. S (ss) + Zn. S (ss) B 0 25 50 75 100 Mole % Zn. S Pure Mg. S Pure Zn. S

Region A Region C Region B Mg. S-type solid solution Two-phase region Zn. S-type solid solution X-ray Powder Diffraction Pattern Microscopic View Rock salt type Mg 1 -x. Znx. S Microscopic View Zinc Blende type Zn 1 -x. Mgx. S