Estructura y Propiedades De Los Cristales

CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
ISSUES TO ADDRESS...
• How do atoms assemble into solid structures? (for now, focus on metals) • How does the density of a material depend on its structure? • When do material properties vary with the sample (i.e., part) orientation?

MECH 221

PM Wood-Adams

Winter 2008 1

Crystal Structure
• Motivation: Many of the properties of materials(especially mechanical) are determined by the arrangement of the atoms. This arrangement is called the material’s crystal structure. • An important distinction… – Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number and probability distributions of the electrons. – Crystal structure pertains to the arrangement of atoms in the crystallinesolid material.

MECH 221

PM Wood-Adams

Winter 2008

• Atoms can be arranged either in a regular, periodic array (i.e., long-range order) or completely disordered (amorphous). • We need a way to specify crystallographic directions and planes. c
To illustrate the concept of crystal structure and lattice systems, we first identify a coordinate system (x, y, z):
a

z x y b

We can’tspecify directions or planes without knowing what the reference system is.
MECH 221 PM Wood-Adams Winter 2008

What is the Unit Cell?
• The unit cell is the smallest group of atoms

which can generate the entire crystal by translation.
Definition: the length of each unit cell axis is called a lattice parameter. – In cubic systems, all three orthogonal lattice parameters are equal • Latticeparameters are typically on the order of a few Angstroms (or a few tenths of a nanometer)
MECH 221 PM Wood-Adams Winter 2008

ENERGY AND PACKING
• Non dense, random packing
Energy typical neighbor bond length typical neighbor bond energy r

• Dense, regular packing

Energy typical neighbor bond length

typical neighbor bond energy

r

Dense, regular-packed structures tend to havelower energy.
MECH 221 PM Wood-Adams Winter 2008 2

MATERIALS AND PACKING
Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics -some polymers

crystalline SiO2
Adapted from Fig. 3.18(a),

Callister 6e.

Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = NoncrystallineMECH 221 PM Wood-Adams

Si

Oxygen

noncrystalline SiO2
Adapted from Fig. 3.18(b),

Callister 6e.

Winter 2008 3

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 bondenergy. • have the simplest crystal structures. We will look at three such structures...
MECH 221 PM Wood-Adams Winter 2008 4

SIMPLE CUBIC STRUCTURE (SC)
• Rare due to poor packing (only Po has this structure) • Close-packed directions are cube edges.

In terms of the hard sphere model we say the atoms are touching in the close-packed directions!

• Coordination # = 6 (# nearest neighbors)(Courtesy P.M. Anderson)

MECH 221

PM Wood-Adams

Winter 2008 5

ATOMIC PACKING FACTOR
APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres

• APF for a simple cubic structure = 0.52

a R=0.5a
close-packed directions contains 8 x 1/8 = 1 atom/unit cell
MECH 221

atoms unit cell APF =

volume atom 4 π (0.5a)3 1 3 a3 volume unit cell
Winter 2008 6Adapted from Fig. 3.19, Callister 6e.

PM Wood-Adams

BODY CENTERED CUBIC STRUCTURE (BCC)
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.

• Coordination # = 8

Adapted from Fig. 3.2,

Callister 6e.

(Courtesy P.M. Anderson)

MECH 221

PM Wood-Adams

Winter 2008

ATOMIC PACKING...