Exchange Interactions in Solid ³He on a Parallel Computer

Citation

Callahan, Sean Macauley (1989) Exchange Interactions in Solid ³He on a Parallel Computer. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4dxb-6t85. https://resolver.caltech.edu/CaltechETD:etd-06072007-135648

Abstract

We have developed a method of calculating the Gruneisen parameter, γ ≡ ∂linJ/∂lnν (J - exchange splitting; ν - molar volume), for energy splittings that are due to atoms exchanging lattice sites in fermionic systems for which the exchange splittings are small compared with the lattice kinetic and potential energies. The method involves making two separate path integral Monte Carlo calculations, one for a path (sequence of particle positions in time) that doesn't involve atoms exchanging lattice sites, and one for a path in which the atoms do exchange lattice sites. The difference between a quantity calculated for the two systems is related to the Gruneisen parameter.

The central results of this thesis are firstly, that there is no significant variation of the Gruneisen parameters for two, three and four particle exchange (γ₂, γ₃ and γ₄, respectively) for solid ³He, in going from 24 cm³/mole, which is near melting, to 22 cm³/mole. This result was extended to 20 cm³/mole for γ₂. Since no significant variation was observed, the values calculated for different molar volumes were combined to give best estimates for the Gruneisen constants, γ₂ = 15.9 ± .8, γ₃ = 16.4 ± 1.4 and γ₄ = 13.8 ± 1.5. The second result is that the magnitudes of the Gruneisen parameters are very similar for the three types of exchange despite their significantly different geometry. Some very limited runs were done for a system of hard spheres. It is interesting that for the hard sphere diameter chosen, the Gruneisen parameters are of the same order as for solid ³He, γ₂ = 21.7 ± .8, γ₃ = 16.8 ± 2.1 and γ₄ = 19.3 ± 1.9 for the small test systems checked. The final result relates to ³He deposited on a graphite surface. The Gruneisen parameter for three particle exchange for a two-dimensional system with a triangular mesh is found to be consistent with γ₃ = 50 ± 5 for a range of nearest-neighbor, lattice spacings from 3.2 Å to 3.6 Å. This is inconsistent with experiment, indicating that three particle exchange confined to two dimensions does not account for the ferromagnetic properties of this system, as was claimed previously.

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