Last Modified 17 December 1999

If spherical balls are packed together as tightly as possible into a crystal they can form one of two structures:

1. The face centered cubic (fcc) lattice,

   

2. or the hexagonal close packed (hcp) lattice.

The two forms differ by the way they stack. A triangular plane of balls has two sites where another layer of balls can sit, close-packed, above it. If we label these sites B and C, and the site of the original plane A, then the fcc lattice stacks in the sequence ABCABCABC, while the hcp lattice stacks in the sequence ABABABAB.

In a system of hard spheres there are actually many other close packed structures that can form. One example is the alpha-Samarium structure, where the stacking is ABCBCACAB. This structure alternates between fcc style stacking (ABC, BCA, CAB) and hcp-like stacking (BCB, CAC).

Real systems are not hard spheres, but many atoms form in the fcc phase (e.g. Aluminum, Copper, Gold) or the hcp phase (Titanium, Zinc, Zirconium). In these phases the difference between the fcc and hcp structures is usually quite small, though not zero as in the hard sphere example. Since the energy is so small, occasionally a stacking fault occurs. In gold, the stacking fault might look something like this:

ABCABCABCBCABCABCA

The last blue C should be followed by an A atom, but instead it is followed by the hcp-like B layer, after which the fcc stacking order resumes. The transition between the blue and red ordering is known as the stacking fault, and the energy difference between a structure without a stacking fault and a structure with a stacking fault is known as the stacking fault energy.

The stacking fault energy is correlated with the ductility of a metal. If the metal has a low stacking fault energy, then in general it will be ductile, since any shear on the crystal will tend to form stacking faults rather than breaking the crystal.

Actually, the above is not quite correct. Usually there is a barrier between the perfect crystal and the stacking fault. In this case it takes more energy to to form the stacking fault then the stacking fault energy would indicate. This maximum height of the barrier is known as the anti-stacking fault energy, and this is what should be correlated with ductility.

The purpose of this test, then, is to determine the stacking fault and anti-stacking fault energy in Gold, a system where we have found excellent tight binding parameters.

Look at other examples.

Get other parameters from the Tight-binding periodic table.

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