Course notes
93
L Transport number t i
The transport number of species i is defined by the relation
t i
t
i
σ
σ
=
The sum of the transport numbers must satisfy the following normalization
condition:
t
1
i
i
=
/
L Nernst-Einstein relation
Considering that the diffusion and migration mechanisms are identical, we have
RT
z F C D
i
i
2 2 i i
σ =
3.2 – Microscopic approach to ionic transport in crystals:
Activated-hopping model
3.2.1 – Electric mobility
The ion, which can move, oscillates in a potential well with a vibrational frequency ν 0 of the order of 10
13
Hz. We allow the ion to hop from one site to a
neighboring site along the x direction only and according to a unique mechanism.
With no external electric field the forward and reverse hopping frequencies ν f
and ν r are equal and are given by
e
f
r
0
RT
G
m
ν
ν
ν
=
=
−
D
where Δ m G is the free enthalpy for the ion to attain the activated state and acts
as a “potential barrier” (fig. 38). R and T have their usual meanings.
93
L Transport number t i
The transport number of species i is defined by the relation
t i
t
i
σ
σ
=
The sum of the transport numbers must satisfy the following normalization
condition:
t
1
i
i
=
/
L Nernst-Einstein relation
Considering that the diffusion and migration mechanisms are identical, we have
RT
z F C D
i
i
2 2 i i
σ =
3.2 – Microscopic approach to ionic transport in crystals:
Activated-hopping model
3.2.1 – Electric mobility
The ion, which can move, oscillates in a potential well with a vibrational frequency ν 0 of the order of 10
13
Hz. We allow the ion to hop from one site to a
neighboring site along the x direction only and according to a unique mechanism.
With no external electric field the forward and reverse hopping frequencies ν f
and ν r are equal and are given by
e
f
r
0
RT
G
m
ν
ν
ν
=
=
−
D
where Δ m G is the free enthalpy for the ion to attain the activated state and acts
as a “potential barrier” (fig. 38). R and T have their usual meanings.