• Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but properties are generally non-directional • crystal structure = FCC: 4 atoms/unit cell • atomic weight = 63.55 g/mol (1 amu = 1 g/mol) • atomic radius R = 0.128 nm (1 nm = 10-7 cm) Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3 Compare to actual: ρCu = 8.94 g/cm3 Result: theoretical ρCu = 8.89 g/cm3 2D repeat unit . Crystal Structure FCC BCC HCP Rhomb HCP FCC BCC BCC HCP FCC Ortho. Note that there are two possible positions for a proper stacking of layer B. 8. 2. 2. Dia. Primary Metallic Crystalline Structures (BCC, FCC, HCP) There are 14 different types of crystal unit cell structures or lattices are found in nature. 265 o .125 o .125 O. b 1 b 2 b 3 A A A A A A C B C C B B Face Centered Cubic Slip Systems FCC (eg. Crystal Structure FCC BCC HCP Rhomb HCP FCC BCC BCC HCP FCC Ortho. 71 5 85 34 65 55 25 87 o .143 o. • We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP). However most metals and many other solids have unit cell structures described as body center cubic (bcc), face centered cubic (fcc) or Hexagonal Close Packed (hcp). the repeating bcc structure, equivalent to many adja-cent unit cells (Part (c) courtesy of Molecular Simu- lations, Inc.). HCP STRUCTURE •ideal ratio c/a of 8/3 1.633 •unit cell is a simple hexagonal lattice with a two-point basis (0,0,0) (2/3,1/3,1/2) a a Plan view •{0002} planes are close packed •ranks in importance with FCC and BCC Bravais lattices 72 Resolved Shear Stress What do we need to move dislocations? Dia. 071 o. 265 o .125 o .125 O. For packing, we identify the atoms that belong to a close packed framework with either BCC, FCC(CCP) or HCP. • We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP). For packing, we identify the atoms that belong to a close packed framework with either BCC, FCC(CCP) or HCP. • for uniform crystal materials, all parallel directions have the same properties • negative index: a bar over the index However most metals and many other solids have unit cell structures described as body center cubic (bcc), face centered cubic (fcc) or Hexagonal Close Packed (hcp). 217 o .114 o .149 o .197 o. 217 o .114 o .149 o .197 o. PDF | A large database of experimentally observed structures in unary and binary systems is searched for bcc, fcc, and hcp superstructures. amorphous structures. cubic FCC Atomic radius (nm) Symbol (amu) (g/cm3) Adapted from Table, "Charac- teristics of Selected Elements", inside front cover, Callister 6e. 2. Solution: At T < 912°C iron has the BCC structure. [100],[010],[001] in simple cubic are same. 8. MatSci 193/203: Atomic Arrangements in Solids Hexagonal close-packed, face-centered cubic, stacking faults, and body-centered cubic 3. cubic FCC Atomic radius (nm) Symbol (amu) (g/cm3) Adapted from Table, "Charac- teristics of Selected Elements", inside front cover, Callister 6e. 3. 071 o. A Shear Stress! Close-Packed Structures Both the HCP and FCC crystal structures are close-packed structure. BCC and HCP Metals Introduction The majority of common metals have either a Face Center Cubic Structure, fig la, a Body Centered Cubic Structure, fig.lb or an Hexagonal Close Packed structure fig.lc. 3.2(c), Callister 7e. 2 Crystallographic directions (continue) • denote the direction by [uvw] • family direction , defined by transformation • material properties along any direction in a family are the same, e.g. 2. 2. Layer B. Layer A Place the next layer on top of the first. FCC. 71 5 85 34 65 55 25 87 o .143 o. FCC {111} <110> 12 α-Fe, W, Mo BCC {110} <111> 12 α-Fe, W {211} <111> 12 α-Fe, K {321} <111> 24 Cd, Zn, Mg, Ti, Be HCP {0001} <1120> 3 Ti, Mg, Zr {1010} <1120> 3 Ti, Mg {1011} <1120> 6. 2. Primary Metallic Crystalline Structures (BCC, FCC, HCP) As pointed out on the previous page, there are 14 different types of crystal unit cell structures or lattices are found in nature. Classifying Crystal Structures •We will classify a large number of crystal structures using a small number of common characteristics, namely packing, compositional ordering, and filling of interstitial sites. Classifying Crystal Structures •We will classify a large number of crystal structures using a small number of common characteristics, namely packing, compositional ordering, and filling of interstitial sites. 1. • Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but properties are … amorphous structures. 1. The major These are usually abbreviated to FCC, BCC or HCP structures respectively. Cu, Ag, Au, Al, and Ni) Slip Planes {111} Slip Directions [110] The shortest lattice vectors are ½[110] and [001] According to Frank’s rule, the energy of a dislocation is proportional to the square of the (100) Adapted from Fig. Consider the atoms as spheres: Place one layer of atoms (2 Dimensional solid). View 2_hcp_fcc_bcc.pdf from MATSCI 193 at Stanford University.