Lecture 3 - Crystal Bonds

1 Chapter 3 - Crystal structure Contents Chapter 3 - Crystal structure ........................................................................................................... 1 What is the difference between short range and long range order? ............................................ 3 What are the 2 sorts of packing, and how do their energy differ? .............................................. 3 What are the differences between the 2 types of materials? ....................................................... 3 What is the crystal structure? ...................................................................................................... 3 Crystalline or amorphous? Metals, ceramics, glasses, polymers ................................................ 3 What are space lattices? .............................................................................................................. 3 What are unit cells? ..................................................................................................................... 3 Define metallic crystal structures ................................................................................................ 4 Define some structures ................................................................................................................ 4 Stacking sequence? ..................................................................................................................... 4 What is polymorphism/allotropy? ............................................................................................... 5 What is the rule of thumb for the densities of different material classes? .................................. 5 How do we group crystals? ......................................................................................................... 5 Name a few different crystal systems ......................................................................................... 6 How to name them! ..................................................................................................................... 7 Single crystals vs polycrystals .................................................................................................... 7 Anisotropic vs isotropic .............................................................................................................. 7 What is X-ray diffraction pattern used for? ................................................................................ 8 Amorphous materials .................................................................................................................. 8 Definitions: ..................................................................................................................................... 9 Close packed plane ..................................................................................................................... 9 Coordination number .................................................................................................................. 9 Atomic packing ........................................................................................................................... 9 Linear atomic density .................................................................................................................. 9 Planar atomic densities ............................................................................................................... 9 Grain boundary ........................................................................................................................... 9 Polycrystalline ............................................................................................................................. 9 Math: ............................................................................................................................................. 10 Atomic packing factor ............................................................................................................... 10 Crystal density ........................................................................................................................... 11

2 Linear density ............................................................................................................................. 11 Planar density ............................................................................................................................. 11 FINDING OUT THE TYPE OF CRYSTAL STRUCTURE USING X-RAY DIFFRATION ... 11

4 Define metallic crystal structures Very densely packed because: - Usu, only 1 element, so all atomic radii the same - Non directional - Dist. Between atoms are small in order to lower BE - e - clouds shield cores from each other. They have the simplest crystal structures They are separated into 1 of 3 densely packed structures: 1. Body centered cubic (BCC) 2. Face centered cubic (FCC) 3. Hexagonal (close packed) (HCP) Define some structures Name Some facts Picture Simple cubic structure (SC) Rare because it is poor packing Coordination number = 6 Body centered cubic structure (BCC) APF = 0.68 Face centered cubic structure (FCC) 5 atoms in unit cell ABCABC stacking sequence APF = 0.74 Stacking sequence: Hexagonal close packed structure (HCP) ABAB stacking sequence 6 atoms/cell APF= 0.74 Stacking sequence: Stacking sequence?

5 What is polymorphism/allotropy? It Is the property where some elements can exist in multiple crystal forms. This usually necessitates change in temperature or pressure. Ex : graphite (LP) can become diamonds in HP Polymorphism can also result in change of volume because packing and APF will be changing What is the rule of thumb for the densities of different material classes? p metals > p ceramics > p polymers this is because, metals have close packing because of metallic bonding, and large atomic masses Ceramics have less dense packing, lighter elements Polymers have low packing density (usually amorphous) and lighter elements. Composites have intermediate values How do we group crystals? We group them into crystal systems, Depending on the shape of the unit cell. This is done using: Where x y z are the axes of lattice Alpha beta gamma are the angles that separate the axes

7 How to name them! Funfacts To describe 1 cube, we use a family of directions <100> = [100], [010], [001], [1̅ 00], [01̅ 0]…etc Similarly, we have a family of planes {100} Particularity of cubic systems: [111] direction is perpendicular to the (111) plane Single crystals vs polycrystals Single crystals: made up of 1 crystal, all the unit cell have the same orientation Polycrystals: many small crystals (grains) with different orientations joined together. Anisotropic vs isotropic In general, properties vary with the direction of the crystal. Its basically vectors No fractions, always whole numbers Written between square brackets, no commas For negatives, bar. Describes the plane Uses rounded brackets NOT coordinates, if it intercepts an axe, then you get a number, if not, infinity. 1. Make sure that the plane does NOT pass through the origin 2. Determine where the plane intercepts axes 3. Take the reciprocal

8 If property varies with direction – anisotropic If not – isotropic Single crystals: - anisotropic Polycrystals: the effect is resulted in the average value of all directions. - If grains randomly oriented : isotropic - If grains textured: anisotropic What is X-ray diffraction pattern used for? It is used to find out the type of crystal structure. X-Rays are diffracted off atoms and constructively or destructively interfere Amorphous materials Non crystalline, no long range order, only short range order

10 Math: Atomic packing factor Example:

11 Crystal density Linear density *has to be whole atoms. But, it works if on the line, you have ½ a radius, 1 diameter, ½ a radius, cuz that is equal to 2 atoms (2 radiuses = 1 atom) * trick: count the number of radiuses Planar density FINDING OUT THE TYPE OF CRYSTAL STRUCTURE USING X-RAY DIFFRATION