Chapter 3
Transport in ionic solids
Course notes
The displacement of ions in an ionic crystal can be described phenomenologically
by following the approach developed by electrochemists, or microscopically
by following the approach developed, in particular, by physicists.
3.1 – Phenomenological approach to ionic transport
in ionic crystals
3.1.1 – Electrochemical mobility and flux density
Consider a chemical species i subject to a driving force F m resulting from the
action of an electrochemical potential gradient d μ
~ i
F m
i
dμ
= − u
with
z F
i
i
i
μ μ
ϕ
= +
u
where μ i and z i represent respectively the chemical potential and the charge
number of species i, and φ is the electrical potential of the phase. Opposing this
driving force is a friction force |F |
v
i
i
α
=
and an inertial force |F | m dv dt
i
i
i
=
where m i and α denote respectively the particle mass and the friction coefficient.
In the steady state, the forces sum to zero. We show that the particle rapidly
attains a limiting speed v i,t given by the expression v i,t
i
d μ α
= u
. We use the
following definitions:
2 the limiting speed per unit force is the electrochemical mobility
u
v
1
i
i
i,t
d μ
α
= −
=
u
u
© Springer Nature Switzerland AG 2020
A. Hammou and S. Georges, Solid-State Electrochemistry,
https://doi.org/10.1007/978-3-030-39659-6_3
91