(145b) A Pseudo-Quantum Description of Classical Vacancy Diffusion in Crystals
AIChE Annual Meeting
2012
2012 AIChE Annual Meeting
Engineering Sciences and Fundamentals
In Honor of Keith Gubbins' 75th Birthday III: Fundamentals & Model Development
Monday, October 29, 2012 - 3:45pm to 4:05pm
We introduce an observable field to describe the
dynamics of a single vacancy in a crystal. This field is the
probability density ρ(x | r) to find the vacancy pseudo-particle at
the point x when the atoms are in a configuration r. We considered
the case of a classical and a "quantum" pseudo-particle, to
which correspond a classical (Boltzman-like) and a ground state
"quantum" density, respectively. These densities are
obtained assuming that the vacancy pseudo-particle is subject to the
potential energy field generated by the atoms in the sample.
In our description, the fictitious inverse temperature β*
and the coefficient α of the quantum kinetic energy term are tunable parameters that
make the classical/"quantum" density localized in the
regions of relevant minima of the potential energy field. We show
that the classical density is unsatisfactory. In fact, at finite
temperature this density results multimodal (see Fig. 1/A)
and is, therefore, difficult to use it to identify the vacancy
position. On the contrary, the "quantum" density is well
behaving: localized in the relevant minima of the potential and
smooth (Fig. 1/B). We use the "quantum"
ρ (x | r) in rare event simulations to investigate vacancy diffusion
paths in a 2D crystal.
Further progresses to study vacancy related phenomena
at high temperature, where vacancy formation and annihilation must be
taken into account, could come from "quantum" statistics.
In conclusion, we have shown how a ground state
quantum description of a vacancy allows to identify the dynamics
of point defects in solids.
Figure 1: Classical (A) and "quantum" (B)
ρ(x | r) in a configuration along a local vacancy migration path at
T = 2.5 ε/kB.
See more of this Session: In Honor of Keith Gubbins' 75th Birthday III: Fundamentals & Model Development
See more of this Group/Topical: Engineering Sciences and Fundamentals
See more of this Group/Topical: Engineering Sciences and Fundamentals