CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
[Pages:15]CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
Metallic Crystals
? tend to be densely packed.
? have several reasons for dense packing: -Typically, only one element is present, so all atomic radii are the same. -Metallic bonding is not directional. -Nearest neighbor distances tend to be small in order to lower bond energy.
? have the simplest crystal structures.
We will look at three such structures...
Cubic Unit Cells
a
2R
SIMPLE CUBIC STRUCTURE (SC)
BODY CENTERED CUBIC STRUCTURE (BCC)
FACE CENTERED CUBIC STRUCTURE (FCC)
Simple Cubic (SC) Structure
? Coordination number is the number of nearest neighbors ? Linear density (LD) is the number of atoms per unit length
along a specific crystallographic direction
. a3
a1 . .a2
Coordination number = 6
LD110 = 1 atoms/22 R LD100= 1 atoms/2R
? Rare due to poor packing (only Po [84] has this structure) ? Close-packed directions are cube edges.
Atomic Packing Factor (APF)
? APF for a simple cubic structure = 0.52
Body Centered Cubic (BCC) Structure
R a
? Coordination number = 8 ? Close packed directions are cube
diagonals:
LD110= 1 atom/(4R(2/3))=1/(2R8/3) LD001 = 1 atom/(4R/3))= 1/(2R 4/3) LD111 = 2 atoms/4R = 1/(2R)
? Unit cell contains: 1 + 8 x 1/8 = 2 atoms/unit cell
? APF = 0.68:
8
Face-Centered Cubic (FCC) Structure
? Coordination number = 12
? Close packed directions are face
diagonals:
LD110= 2 atom/(4R)= 1/2R LD001 = 1 atom/(2R2))= 1/(2R 2) LD111 = 1 atoms/4R = 1/(2R 6 )
? Unit cell contains:
a
6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell
? APF = 0.74
Hexagonal Close-Packed (HCP) Structure
? ABAB... Stacking Sequence
? 3D Projection
? 2D Projection
A sites
B sites
A sites
? Coordination number = ? ? APF = ?
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