Nuclear spin lattice relaxation and electric field gradient in liquid indium

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Abstract
We have measured the nuclear spin lattice relaxation time in liquid indium from 130°C to 300°C to be: 1/T 1=(1.98 × 0.0082T) × 103 sec-1. The relaxation rate consists of two significant parts: (1/T 1) K from the nuclear magnetic hyperfine interaction, and (1/T 1) Q from the nuclear quadrupole interaction. We calculate (1/T 1) K from the the modified Korringa relation using a correction factor of order unity for electron-electron interactions. The hyperfine term is linear in T and accounts for the second term in 1/T 1. Within experimental error the remaining rate, (1/T 1) Q , is temperature independent, and theoretically varies as the product of the square of the electric field gradient, q, and τc, a typical time between field gradient fluctuations. Making use of the x-ray RDF, we construct a simple model for liquid indium and calculate the ionic and electronic contributions, q I and q E, to the electric field gradient, to be q I=1.4 × 1024/cm3 and q E=8.5 × 1024/cm3. The calculation of q E assumes covalent bonding between nearest neighbours. Taking q I and q E to be of opposite sign, we find that the correlation time τc is 1.6 × 10-13 sec. When we further identify τ c with the correlation time for diffusion in a three-dimensional random walk, we are able to calculate the r.m.s. jump distance, Δr D, involved in self-diffusion, Δr D=0.38 Å. This value is consistent with the x-ray peak width of 0.38 Å which we used earlier to calculate the electric field gradient.

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