On the Relation between Sintering Velocity and Electrical Conductivity of Sintered Zinc Oxide

Studies on Sintering of Oxide Semi-Conductors

Abstract

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-ρ₀/ρ_t-ρ₀…(1)
dP/dt=K(100-P/100)ⁿ…(2)
Where symbols denote:-
ρ_a=bulk densities of specimens after sintering.
ρ₀=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)^-n
where, 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, 7}
log₁₀K=14.9-1.6×10⁴/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