Since the internal energy E is a monotonically increasing function of the temperature T, the moment M(T) can be expressed as a function of internal energy E. The corresponding form of E(M) is focused on in this paper. For ferromagnets, the two-dimensional Ising model is used to obtain the exact form of E(M) and this is discussed both near T = 0 and near the critical temperature T,. In three dimensions, we are only able to discuss the forms of E(M) near T = 0 and T = T,. For low temperatures, spin-wave theory readily yields the result that, for insulating ferromagnets, hE = E -E(0) is proportional to (hN)'~with hM = M(0) -M(T) while for the metallic case hE~(hM)"'. Though the theory is much less complete than for ferromagnets, some results are very briefly discussed for pyroelectrics.
This paper explores the application of classical molecular dynamics to the computation of the
heat of transport of Au atoms in a model of solid gold at several elevated temperatures above
the Debye temperature. It is assumed that the solid shows vacancy disorder. The work shows
that to obtain consistent and reliable results it is necessary (a) to use very small time steps
(≈1 fs) in the molecular dynamics integration routine and (b) to take averages over a very large number
of vacancy displacements—a number which varies with temperature but which is of the order of
105.
The results for the reduced heat of transport for the Au atoms show that: (1) it is positive
in sign, i.e. that the diffusion of Au atoms in a temperature gradient is biassed towards the cold
region or equivalently that the vacancies tend to migrate towards the hotter region; (2) it is
predicted to fall as the average temperature increases and that the variation is closely linear in
(1/T); (3) its value
at high T
relative to the energy of activation for vacancy movement is close to the corresponding
ratio of experimental quantities. Analysis of these results indicates that the method and
model may allow reliable predictions for other metals having the face centred cubic
structure.
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