Environmental Engineering Reference
In-Depth Information
4.
Transport of only charged species is considered.
5.
Fulfillment of the charge neutrality condition in the total scale is assumed,
i.e., any section of the growing scale perpendicular to the direction of migrat-
ing species is essentially electrically neutral.
6.
Interfacial space charge effect is neglected.
7.
Lattice diffusion (or volume diffusion) in the product scale is only consid-
ered; no short circuit or easy diffusion paths such as grain boundaries, dislo-
cation pipes, and so on are taken into account.
8.
Absence of associated species or imperfections is assumed, i.e., dilute solu-
tion model has been assumed to be applicable, which means nonexistence
of interactions among ionized imperfection centers for formation of defect
clusters or complexes. The migrating species are free to move.
Keeping in mind the above-mentioned basic assumptions, one can write the
following generalized flux equation for the transport of migrating species in a
compound layer like MX (X stands for oxygen, halogen, sulfur vapor, etc.):
number
m 2
N δµ i
1
Z i e δφ
δξ
J i
C i B i
δξ
(5.58)
s
Such equations can be formulated for the three different migrating species, such
as cations, anions, and electrons or positive holes.
where
C i
concentration of i th species in number per meter cube,
B i
mobility of i th species under unit force in m 2 J 1 s 1 ,
N
Avogadro's number, 6.023
10 23 ,
δµ i /
δξ
chemical potential gradient in J
m 1 ,
δφ
/
δξ
electrical potential gradient in V
m 1 ,
e
charge on the species i in coulombs,
Z i
valence of i th species.
Along with it one has to consider the following charge neutrality relation:
|
J 1 | |
J 2 | |
J 3 |
0
(5.59)
where
|
J 1 |
magnitude of cationic flux,
|
J 2 |
magnitude of anionic flux, and
|
J 3
|
magnitude of electronic flux.
Search WWH ::




Custom Search