Alan R. Allnatt
Professor Emeritus
B.Sc. (University of London)
Ph.D. (University of London)
Physics and Astronomy 224b
Phone: 519 661-2111 ext 86316
Statistical Mechanics and Thermodynamics
Current Research Programs:
Since retirement I no longer support a research
group of my own but I still collaborate with other research groups
where possible. My current interests are mostly in the applications of
statistical mechanics to models of the matter transport and
thermodynamic properties of solids. I am pursuing essentially
analytical methods and leaving full scale computer simulations to
others! Theories of matter transport in solids are
usually based on "stochastic models” . These are defined in terms of
atom and point defect concentrations and interaction energies, plus the
jump frequencies of elementary atom movements, e.g. atom-vacancy
exchanges. A central problem is to express the Onsager phenomenological
coefficients in terms of these model parameters. Such expressions are
used in the interpretation of measured transport coefficients such as
diffusion coefficients, mobilities etc. and as input by those who model
complex processes, such as matter transport in irradiated alloys and
demixing of alloys in chemical potential gradients. The book referenced
below summarizes some of the systems and methods of interest. My
current work on dilute alloys is focused on the enhancement of
diffusion coefficients of solvent and solute due to vacancy-solute
interactions. Other developments for dilute alloys of the linear
response theory described in the book include extensions to anisotropic
crystals and a new route to the evaluation of mechanical relaxation
modes. For concentrated alloys we continue the exploitation and
further development of the self-consistent kinetic theory for random
mixing alloys devised by Moleko, Allnatt and Allnatt. Atomic transport in solids induced by a
temperature gradient (thermotransport) is characterized by the heat of
transport parameters defined in non-equilibrium thermodynamics. Despite
many experimental studies, sometimes motivated by the use of
engineering components in extreme temperature gradients, there is
little fundamental understanding or reliable intuition about these
parameters. Atomistic theories require calculations of either the
perturbation of vacancy and interstitial jump frequencies by the
temperature gradient, or of the heat flux associated with isothermal
jumps. I recently completed a new formulation of time correlation
function expressions for these quantities and have now turned to the
much harder problem of establishing approximate analytical methods for
their evaluation using lattice dynamics and developments in the
statistical mechanics of phonon scattering.
Selected Publications:
A.R. Allnatt and A.B. Lidiard (1993). Atomic Transport in Solids. Cambridge University Press, Cambridge. A.R. Allnatt (2001). Time correlation formula
for the heat of transport associated with atom-vacancy exchange in a
crystal. J. Phys. A: Math. Gen. 34, 7741-7458. I.V. Belova, A.R Allnatt and G.E. Murch (2002).
Collective and tracer diffusion kinetics in the ternary random alloy.
J. Phys. Condens. Matter 14, 6897-6907. A.R. Allnatt, I.V. Belova and G.E. Murch (2006).
Atom Transport in random two sublattice structures: analogue of the
random alloy sum rule. Phil. Mag. 86, 5837-5846. I.V. Belova, A.R Allnatt and G.E. Murch (2007).
Interdiffusion in strongly ionic insulating materials: the
Nernst-Planck equation. Phil. Mag. 87, 4169-4180.
