The relation between sintering mechanism and electrical conductivity of zinc oxide, a typical representative of oxide semi-conductor, was studied from a view point of rate-process. On the degree of sintering
P and velocity equation of sintering, expressions (1) and (2) were examined.
P=ρ
a-ρ
0/ρ
t-ρ
0…(1)
dP/
dt=
K(100-
P/100)
n…(2)
Where symbols denote:-
ρ
a=bulk densities of specimens after sintering.
ρ
0=bulk densities of specimens before sintering
ρ
t=true density of specimens
K=velocity constant
n=order of reaction
t=duration of sintering
Now it was established that the expressions (6) and (7) are valid between
n and
K as functions of φ and ψ which are indentically equal to values of log (100-
P) when the reaction velocity (
dP/
dt) becomes unity or 100, respectively. (Fig. 4)
n=2/(ψ-φ)…(6)
log
K=
n(2-φ)…(7)
For simple one component system such as metallic oxides, to which zinc oxide used in the experiment also belongs, or metal and glass powders., order the of reaction
n will be constant over the range of sintering temperature. In the case of zinc oxide,
n was found to be 5.7 in a range of 800-1250°C, while the value of φ was expressed as a certain function of temperature. In two or more components system,
n is not a constant but a function of temperature. For instance, it was found with powdered clayey raw material for electric insulating porcelain that value of
n decreases lineally with temperature.
As expressed in equation (8), the velocity constant
K, has a physical meaning of reciprocal of
n′th power of
q0, “degree of not-sintering” which is equal to the percentage of remainder of sintering.
K=(
q0)
-nwhere,
q0=(100-
P0)/100…(8)
Result of experiments with zinc oxide show their activation Energy
E to be 74.6kcal/mol. in case of firing at 800-1250°C in common air atomosphere and its sintering process can be expressed as follows
dP/
dt=
K(100-
P/100)
5, 7log
10K=14.9-1.6×10
4/
T}………………………………(9)
The electrical resistivity of zinc oxide is predominantly determined by diffusion of zinc atom librated by dissociation of ZnO in oxide lattice. Electrical resistivity, ρ decreases with increase of sintering time as expressed by the equation, ρ=
At-B, obtained experimentally, where
A and
B are constants depending on sintering temperature. But the resistivity attains finally at a saturation value after some time of firing, necessary duration of which is also some function of temperature. (Fig. 7) The logarithm of saturation value is found to be a linear function of the ratio, (γ) of sintering and melting temperature as shown in equation (11).
log ρ
sat.=15.4-20.3γ……………………………………(11)
Then the relation between velocity constant
K and the saturated value of electrical conductivity, σ
sat. is expressed as
σ
sat.=4.47×10
-6[
K]
1.15…………………………………(12)
In this equation, it is seen that σ
sat. is nearly proportional to
K. This means that amounts of intersticial zinc atom diffused in oxide
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