Evidence for a short range three body interaction in copper

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Abstract
Conventional volume dependent interactions describing the behaviour of the conduction electrons are incapable of accounting for the four observed Cauchy discrepancies in the second and third order elastic constants of copper: C12-C44, C112-C155, C123-C144, and C144-C456. A satisfactory solution to this problem is obtained if it is assumed that triplets of mutually nearest neighbours interact through a potential of the form phi (r1,r2,r3)= phi 0 exp (-(r1+r2+r3-3r0)/ rho ) where r1, r2, and r3 are the particle separations, r0 the nearest neighbour distance, rho a range parameter and phi 0 the energy per triplet at equilibrium. All four discrepancies can be accounted for simultaneously if rho and phi 0 are in the region of 0.291*10-10 m and 9.25*10-22 J per triplet respectively.