Lecture 3 - Structure of Metals (I) PDF

MCEN30017 Mechanics and Materials
Lecture 3: The structure of metals (i) – bonding, crystals and grains
To understand the origin of mechanical properties, we need to focus on

1. the forces that hold atoms together,
2. the way that atoms are packed to form a crystal, and
3. the way that crystals are packed together in a solid.
At small separation distances, two isolated atoms exert a force on each other that is the sum of
attractive and repulsive components. When the net force is zero, the energy is at a minimum, a state
of equilibrium exists and the atoms remain separated by the equilibrium spacing, r o . The bond
energy corresponds to the minimum energy.
There are five kinds of interatomic bonding:

1. Primary Bonds
1.1. Ionic (electrostatic attraction between positive and negative charges)
1.2. Covalent (electrons are shared between atoms in new orbitals)
1.3. Metallic (high energy electrons shared in a “sea” of freely wandering electrons)
2. Secondary Bonds
2.1. Van der Waals (dipolar attraction between uncharged atoms)
2.2. Hydrogen (attraction between adjacent polar molecules, specifically H and O, F or N)
Crystal Structures
Amorphous materials do not crystallise and may exhibit short range order, where a specific atomic
arrangement only extends to the nearest neighbours. Examples include silica glass, where each
silicon atom is in the centre of a tetrahedron of four oxygen atoms but these tetrahedra are
arranged randomly through space. A crystalline material is one in which the atoms are arranged in a
periodic array that repeats over large atomic distances – there is long range order. Many of the
properties of crystalline solids depends on the crystal structure.
Because of the nature of the metallic bond, metal atoms can be visualised as hard spheres and the
forces between them are isotropic. The atoms are arranged in a space lattice, which is a 3D
collection of points, where each point in the lattice is identical to every other point in the lattice.
The lattice is described by the unit cell, which is the smallest repeating unit in the lattice. In some
metals, atoms pack closely together in planes and the planes are packed on top of each other in
layers. In metals, the stacking sequence is repeated every 2 or 3 layers. Each atom has 12 nearest
neighbours, 6 in its plane and 3 each in the planes above and below it. When the close packed
planes repeat every third layer, the atoms are arranged in a face centred cubic (fcc) lattice. The unit
cell is a cube with a lattice site (here an atom) on each corner and in the centre of each face of the
cube. Examples include Cu, Ni, Al and Fe at temperatures above 912oC. When the planes repeat
every 2nd layer, the atoms lie on a hexagonally close packed (hcp) lattice. Examples include Mg, Ti
and Zn. The third common lattice found in metals is body centred cubic (bcc). This is not a close
packed structure. The unit cell is a cube with lattice sites at each corner and one in the middle (the
body centre) of the cube. Examples include Cr, W and Fe at temperatures below 912oC.
Crystallographic planes and directions

Miller indices are a system of describing planes and directions in a lattice without having to build or
draw scale models. The Miller indices of a plane are the reciprocals of the intercepts the plane
makes with the three axes that define the edges of the unit cell, reduced to the smallest integers.
The Miller indices of a direction are the components of a vector (not reciprocals) that starts from the
origin, along the direction, reduced to the smallest integer set.
Direction indices for identifying crystal directions,

Miller indices for identifying crystal showing how the [1 6 6] direction is defined. The lower
planes, showing how the (1 3 1) plane part of the figure shows the family of 〈111〉 directions.
and the (1 1 0) planes are defined.
The lower part of the figure shows the
family of {1 0 0} and of {1 1 0} planes.
Density
The density of materials reflect the mass and diameter of the constituent atoms and the efficiency
with which they are packed to fill space. Most metals have high densities because the atoms are
heavy and closely packed, whereas polymers are much less dense because they are made from light
atoms (C, H, O, N) and the structures are not close packed.
Microstructure
The mechanical properties of a crystalline material are also controlled by the size of the crystals and
the way they are arranged in space. This crystal arrangement (the size, shape, spatial distribution
and relative orientation) is called the microstructure. Crystals (grains) vary from < 100 nm to >10
mm in size; they are generally resolvable using an electron or a light microscope. Polycrystalline
materials are those made from many crystals. The interfaces between crystals (grain boundaries)
are a very important microstructural feature.

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MCEN30017 Mechanics and Materials

Lecture 3: The structure of metals (i) – bonding, crystals and grains

To understand the origin of mechanical properties, we need to focus on

There are five kinds of interatomic bonding:

Crystallographic planes and directions

Direction indices for identifying crystal directions,

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