Apart from the specific difficulties with Morse and LJ potentials, there are other general difficulties that are common to all pair potentials, which make them unsuitable for radiation damage studies.

Expanding the energy as a sum of pairwise inter­actions introduces some constraints on what data can be fitted, even in principle. It is important to distin­guish this problem from a situation where a particular parameterization does not reproduce a feature of a material. There are many features of real materials that cannot be reproduced by pair potential whatever the functional form or parameterization used.

1.10.4.2.1 Outward surface relaxation

For a single-minimum pair potential, the nearest neigh­bors repel one another, while longer ranged neighbors attract. When a surface is formed, more long-range bonds are cut than short-range bonds, so there is an overall additional repulsion. Hence, the surface layer is pushed outward. But in almost all metals, the surface atoms relax toward the bulk, because the bonds at the surface are strengthened. Similarly, pair potentials

Figure 2 Pressure versus temperature phase diagram for the crystalline region of the Lennard-Jones system in reduced units where p is pressure and p is density. The equilibrium density is at ps3 = 1.0915. Filled squares are the harmonic free energy integrated to the thermodynamic limit from Salsburg, Z. W.; Huckaby, D. A. J. Comput Phys. 1971, 7, 489-502. All other points are from lattice-switch Monte Carlo simulations with N atoms, lines showing the phase boundary deduced from the Clausius-Clapeyron equation, from Jackson, A. N. Ph. D. Thesis, University of Edinburgh, 2001; Jackson, A. N.; Bruce, A. D.; Ackland, G. J. Phys. Rev. E 2002, 65, 036710.

give too large a ratio of surface to cohesive energy, again consistent with the failure to describe the strengthening of the surface bonds.

1.10.4.2.2 Melting points

With LJ, the relation between cohesive energy and melting is Ec/kBTm « 13, other pair potentials being similar. Real metals are relatively easier to melt, with values around 30. One can fit the numerical value of the e parameter to the melting point, and accept the discrepancy as a poor description of the free atom.