Glue models atoms seek to have as many neighbors as possible; therefore, when a material is cleaved, the surface atoms tend to relax inward toward the bulk to increase cohesion. This effect also arises because of

the longer range of the repulsive part of the potential: at a surface, the further-away atoms are absent. This is in contrast to pair potentials and in agreement with real materials.

1.10.7.2 Cauchy Relations

The functional form of the glue model places fewer restrictions on the elastic constants of materials than pair potentials do; for example, the Cauchy pressure for a cubic metal is as follows20:

-2

Ef,(r 2И2

. j

If the ‘embedding function’ F (minus square root in FS case) has positive curvature, the Cauchy pressure must be positive, as it is for most metals. A minority of metals have negative Cauchy pressure. It is debatable whether this indicates negative curvature ofthe embed­ding function, or a breakdown of the glue model.

There are also some Cauchy-style constraints on the third-order elastic constants. But in general, ‘glue’ type models can fit the full anisotropic linear elastic­ity of a crystal structure.

1.10.7.3 Vacancy Formation

In a near-neighbor second-moment model for fcc, breaking one of twelve bonds reduces the cohesive energy of each atom adjacent to the vacancy by a factor of (1 — J 11/12) = 4.25%. Other glue models give a similar result. Meanwhile, the pairwise (repul­sive) energy is reduced by a full 1/12 = 8.3%. Thus, energy cost to form a vacancy is lower in glue-type models than in pairwise ones. For actual parameterizations, it tends to be less than half the cohesive energy.

1.10.7.4 Alloys

To make alloy potentials in the glue formalism, one needs to consider both repulsive and cohesive terms.

Thinking of the repulsive part as the NFE pair potential, it becomes clear that the long-range behav­ior depends on the Fermi energy. This is composition dependent — the number of valence electrons is criti­cal, so it cannot be directly related to the individual elements. The short-ranged part should reflect the core radii and can be taken from the elements. Despite this obvious flaw, in practice, the pairwise part is usually concentration-independent and is refitted for the ‘cross’ heterospecies interaction.

In the EAM, the function Fj depends on the atom i being embedded, while the charge density JT fj(rij) into which it is embedded depends on the species and position of neighboring atoms. By contrast for FS poten­tials, the function F is a given (square root), while f(rij) is the squared hopping integral, which depends on both atoms. There is no obvious way to relate this heteroatomic hopping integral to the homoatomic ones, but a practical approach is to take a geometric mean21: one might expect this form from considering overlap of exponential tails of wavefunctions.