Crystal Structures & X-ray Crystal Structures & X-ray DiffractionDiffraction

Chemistry 123Spring 2008

Dr. Woodward

CrystalsCrystals

Crystalline SolidsCrystalline Solids

• Crystal Lattice – A 3D 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.

CaFCaF22 Unit Cell Unit Cell

3D Crystal 3D Crystal Systems Systems

(7)(7)CubicCubic

TetragonalTetragonalHexagonalHexagonal

RhombohedrRhombohedralal

OrthorhombicOrthorhombicMonoclinicMonoclinic

TriclinicTriclinic

14 Bravais 14 Bravais LatticesLattices

Cubic

The crystal systems each have distinctive

symmetry and unit cell dimensions

X-ray DiffractionX-ray Diffraction

Diffraction Diffraction DemoDemo

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 LawBragg’s Law

The extra path length traveled by wave B (shown in red) is equal to 2d sin , where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple

of the wavelength (n). When we use Bragg’s Law we When we use Bragg’s Law we generally set n=1.generally set n=1.

AA

BB

dd

Symmetric StructuresSimple X-ray PatternEx. Gold – Face centered cubic structure

Low symmetry Structures

Complex X-ray Pattern

Ex. CuSO4 5H2O (triclinic structure)

(a) CsCl (b) NaCl (c) Zinc blende

Simple Cubic Crystal StructuresSimple Cubic Crystal Structures

Decreasing coordination number

20 30 40 50 60 702Theta

0

50

100

150

200

250

300

350

Int.

X-Ray Powder Diffraction Pattern X-Ray Powder Diffraction Pattern (Ex. Magnesium Sulfide, MgS)(Ex. Magnesium Sulfide, MgS)

Each peak corresponds to scattering from a different set of lattice planes. Two planes are

shown above for MgS, which has the same structure as NaCl.

020 planes

220 planes

MgS with the NaCl structure

ZnS with the Zinc Blende structure

Two Component Phase Two Component Phase DiagramDiagram

Mole % ZnS

0 25 50 75 100

Liquid

2-phase region

MgS (ss) + ZnS (ss)

MgS (ss) + Liquid ZnS (ss) +

LiquidMgS (ss)

ZnS (ss)

Tem

pera

ture

(C

)

Pure ZnSPure MgS

A

B

C

Eutectic Point

D

Mole %

0 25 50 75 100

Liquid

2-phase region

(ss) + (ss)

(ss) + Liquid (ss) +

Liquid(ss)

Tem

pera

ture

(C

)

Pure Pure

Eutectic Point

Rock salt type Mg1-xZnxS

Zinc Blende type Zn1-xMgxS

X-ray Powder Diffraction Pattern

X-ray Powder Diffraction Pattern

X-ray Powder Diffraction Pattern

Microscopic View

Region AMgS-type solid

solution

Region BZnS-type solid

solution

Region CTwo-phase region

Microscopic View Microscopic View