Lattice statistics in a magnetic field, I. A two-dimensional super-exchange antiferromagnet

Abstract
A calculation of the maximum shear strain under which a two-dimensional close-packed lattice is stable has been carried out in terms of the forces between the lattice components. Two types of force were used; those between floating bubbles, which enabled a comparison with experiments on actual rafts of bubbles to be made, and also the forces derived from a potential V = Ae$^{-\beta r^{2}}$, which form has been frequently proposed as an approximation to the repulsive interaction terms between metal ions. The conclusion reached is that this maximum strain may be considerably less than that deduced from a simple sine law approximation to the shear force versus displacement curve. Detailed consideration is given to edge effects in bubble rafts, and reasonable agreement with experimental results obtained. The overall result is that the formation of dislocations and consequent plastic yielding can occur in an initially perfect lattice only at quite large shear strains. The analogy with metals is discussed, and we conclude that the low strengths of metallic single crystals are explicable only on the assumption that they are not perfect and that dislocations already exist in them and move under very small shear stresses.

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