ME 330 Engineering Materials Lecture 5 Material Structure Crystalline vs. Amorphous Crystals and Crystallographic planes Metallic structures (BCC, FCC, HCP) Single Crystal vs. Polycrystalline Structure Please read Chapter 3

Next Lecture ... Please read Chapter 4 Theoretical Strength Point Defects Linear Defects Planar Defects Volume Defects Microscopy Please read Chapter 4

Atomic Packing Crystalline: Amorphous 3-D arrangement of atoms in which every atom has the same geometrical arrangement of neighbors Long-range, periodic array over large length scales Most solids are crystalline (metals, most ceramics, some polymers) Amorphous Arrangement over which no long range order exists Often clear - not enough order to diffract light Rarely purely amorphous - have regions of crystallinity Many polymers and some ceramics

Crystal Structure Definitions Unit cell: Smallest repeating unit of the crystal. Lattice: 3–D framework of a crystal where atoms are located Lattice parameters: Dimensions (a,b,c) and angles (,,) of the lattice b c a   

Bravais Lattices French Crystallographer Bravais (1848) 7 crystal systems using primitive unit cells Primitive - one lattice point at origin 14 distinguishable point lattices P - simple F - face centered I - body centered C - base centered For now, interested in BCC, FCC, HCP Metallic crystal structures Metallic bond is non-directional No restriction on nearest neighbors Very dense packing First need to collect some definitions Tetragonal FCC Monoclinic Rhombohedral BCC Cubic Hexagonal Orthorhomic Triclinic HCP

Crystallographic Directions Determining direction indices Start vector at crystal axis Draw to any point in the 3-D crystal Project vector on each xyz axes measure a in x-direction measure b in y-direction measure c in z-direction Multiply by common factor to achieve smallest integer value Enclose in [ ] without commas Negative directions indicated with - Family of directions indicated by < > Hexagonal crystals have 4 indices x [100] y [010] z [001] [111] a = 1 b = ½ c = 0 [110] [210] When atoms “touch” this is close packed plane In a cubic crystal, are all in the <100> family.

Crystallographic Planes Determining Miller indices Look at plane in unit cell which does not pass through the origin Determine length of planar intercept with each axes (again, a,b,c) Take reciprocal of a,b,c Reduce to smallest integer value Enclose in ( ) without commas Any parallel planes are equivalent x [100] y [010] z [001] c = 1/3 b = 1/2 a = 1 (123) Bring in unit cells to show packing between HCP and FCC as well as different structures (BCC, FCC, HCP) do in class assignment closely related to a homework problem z z y z x x (012) -1

Crystallographic Planes Important for understanding deformation Important planes to note The direction [hkl] is normal to the plane (hkl) for cubic systems only! Negative directions indicated with - Family of planes indicated by { } x [100] y [010] z [001] (110) (111) (100) x y z {111} family Bring in unit cells to show packing between HCP and FCC as well as different structures (BCC, FCC, HCP) do in class assignment closely related to a homework problem

Crystal Characteristics Cube length (a)- dimension of unit cell Volume of unit cell - Vc= a3 Coordination number (Nc) - number of atoms in contact with a single atom (nearest-neighbors) Atomic Packing Factor (APF) - fraction of solid sphere volume in a unit cell where n = number atoms in a unit cell, R is radius of atom True Density- weight per unit volume

Body Centered Cubic Structure Atoms “touch” along body diagonal <111> Cubic unit cell ( ) n = 2 Nc = 8 APF = 0.68 “ABAB” stacking Iron (RT), Tungsten, Molybdenum, Chromium {110} {110} is the closest packed plane When atoms “touch” this is close packed plane

Face Centered Cubic Structure Atoms “touch” along face diagonal <110> Cubic unit cell ( ) n = 4 Nc = 12 APF = 0.74 A “close-packed” structure “ABCABC” stacking Aluminum, Copper, Gold, Silver, Iron (high temp)* {111} {111} is the close packed plane *Allotropic form- crystal structure depends on temperature and pressure

Hexagonal Close-Packed Structure Hexagonal unit cell n = 6 Nc = 12 APF = 0.74 A “close-packed” structure “ABAB” stacking Cadmium, Magnesium, Titanium, Zinc {001} {0001} is the close packed plane

Stacking of Close-Packed Planes HCP (A-B-A) FCC (A-B-C) Can stack second plane in locations B or C Can stack third plane in locations A or C Difference between FCC and HCP? FCC stacking sequences is ABCABC HCP stacking sequence is ABABAB

Density Definitions Deformation depends on density x [100] y [010] z [001] Deformation depends on density Examples for BCC crystal Linear Density: Fraction of line length filled by atoms. Planar Density: Total area of atoms in given unit plane. Volumetric Density: Total volume of atoms in given unit cell. Same as APF. [111] ao [100] ao (100)

Metals Are Polycrystalline

Macroscopic Packing (Single Crystal vs. Polycrystalline) Though we show only single cube, these are small portion of larger, repeating structure Single crystals can be grown to macroscopic size Si crystals for microchips GaAs wafers for semiconductors Turbine blades for aircraft Polycrystalline metals Much more common than single crystals Solidification from various sites leads to grains Grains: Patches of single crystal material essentially randomly oriented with respect to each other Grain boundary: Atomic mismatch in region between grains