Question

4 (a) Derive a relation for the oxygen pressure dependence of electrical conductivity in NiO.

      (b) Discuss the effects of Cr₂O₃ additions on the electrical conductivity of NiO, giving equations describing the temperature at which the conductivity changes from intrinsic to extrinsic in relation to the impurity concentration.  

Answer 1

A)

• In the various oxygen pressures, we investigated the temperature dependency of the electrical conductivity (σ) of NiO. It changes from the form A exp (-E/kT) to A' exp (-E/2kT) with the increase of oxygen pressure (P:10^-3~760 mmHg).
• From this change we can determine the unique value of the activation evergy E. E=1.25 eV. The dependency upon the oxygen pressure at a definite temperature can be expressed generally,by the formula, σ ∞ P^x1.
• If we assume, as usual, that when the oxygen pressure increases,the nickel ions moves towards the surface to react with oxygen and extend the lattice of NiO, leaving vacant lattice points on the nickel lattice of NiO, and that such vacant lattice points form the impurity levels, then we can obtain the relation σ ∞ P⁴¹.
• Experimental value of x is 3.7 at 1000°,almost in accord with the above-mentioed result. But at lower temperatures we gain the smaller value of x,until finally it reaches to the relation σ ∞ P. And with such assumption,we cannot explain the change of the temperature dependence of the conductivity in the different oxygen pressures.
• So,we assume that the nickel ions which left the normal lattice points,partially extend the lattice NiO at the surface,and partially occupies the interstitial positions. Then, thenumber of the vacant lattice points (N_h) is proportional to √P,and the number of the interstitial nickel ions (N_f) is inversely proportional to√P.
• So the number of electrons at the imprurity levels,and of positive holes in the full band varies depending upon the oxygen pressure. Using these relations,we can derive the theory which may account for the experimental data.

From our data,we get a constant δ=N_f/h ~ 2 × 10^-3 at 1000°, P=760 mmHg, in which n denotes the number of free positive holes. This value of δ is very small, nevertheless the effect of this small value is very serious

B)

• The electrical conductivity of single crystals of α-Al2O3 doped with Cr2O3 (0.03–2.5 wt%), NiO (0.75 wt%) plus Cr2O3 (0.03–0.15 wt%), and NiO (0.75 wt%) has been measured under 1 MeV electron irradiation at 300 K to investigate the effects of the concentration of impurity and of the depth of impurity levels in forbidden bands on the radiation induced conductivity (RIC).
• The RIC of Cr2O3 and/or NiO doped α-Al2O3 decreases with increasing concentration of Cr2O3 and/or NiO dopants. The electrical conductivity of 2.5 wt% Cr2O3doped α-Al2O3 is smaller than any other doped materials tested.
• The dose rate exponent for Cr2O3 doped α-Al2O3 is smaller than that for NiO plus Cr2O3 doped material, due to deeper trapping centers of Cr (5.8 eV from the conduction band) than those of Ni (2.0 eV). Doping impurities with deep trapping centers are most effective for suppressing RIC.