DIFFUSIONOF IRON IN SINGLE-CRYSTAL NICKELOXIDE
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Diffusion of Iron in Single-Crystal Nickel Oxide
by K. J. Richards and F. E. Wagstaff Metallurgy and Ceramics Reeearch Laboratory, Aerospace Research Laboratories, Wright-Patterson A i r Force Base, Ohio (Received November 1.8, 1966)
The diffusion of FeS6in nickel oxide, NiO, has been studied in air in the temperature range 1000 to 1400O, utilizing a decrease in surface activity method. The measured diffusion exp(-44.5 kcal/RT) cm2 sec-l. Over coefficients can be expressed as D = 1.81 X the temperature range investigated the diffusivity of iron was appreciably greater than the reported values for nickel self-diffusion, but the temperature dependence of the diffusion coefficients was essentially the same.
Introduction A considerable amount of study has been devoted to the various physical properties of NiO and the other monoxides of the iron-group transition metal oxides, primarily because of the variable-valence property of the cations which permits these compounds to behave as intrinsic nonstoichiometric semiconductors when equilibrated with an oxidizing atmosphere. The detailed nature of the lattice point defects in these materials is still, however, a matter of conjecture, as are the diffusion mechanisms. We have chosen to study the effect of ion properties on the diffusion behavior of substitutional impurities in order to gain further insight into the predominant transport processes in NiO. The experimental approach has been to measure in pure nickel oxide the diffusivity of iron impurity which is present in extremely small concentrations, using the radioactive tracer, FeS5. Because of the low concentrations, interaction effects between impurity ions are negligible, resulting in the simplest type of chemical diffusion. Such diffusion measurements are free from the complications often accompanying the more frequently employed type of chemical diffusion experiment which employs very much larger concentration gradients than are needed with tracers. The results of such experiments are thus more amenable to theoretical interpretation.
Experimental Section The decrease in surrace activity method was used to measure the diffusion coefficient for Fe66in NiO. When applicable, this technique offers some definite experimental advantages over the more frequently used
sectioning methods. Experimentally, in the decrease in surface activity method, a vanishingly thin deposit of radioactive tracer is made on a flat surface of a semiinfinite specimen. The decrease in the intensity of the radiation from this “active” face due to the diffusion of the tracer into the specimen is then measured by counting the “active” surface before and after a diffusion anneal. Under these experimental conditions, the appropriate solution to the diffusion equation for the distribution of radioactivity in the specimen after a diffusion anneal is
C
= Q(?rDt)-’/’ exp( -x2/4Dt)
(1)
where C is the concentration of tracer at a depth, x, from the initial radioactive deposit, Q is the number of tracer atoms per unit area initially deposited, and D and t are, respectively, the diffusion coefficient and the diffusion time. Owing to absorption of radiation by the specimen, the activity measured at the “active” surface decreases as the tracer diffuses into the crystal. If the absorption of radiation follows Lambert’s law, it has been shown’ that the ratio of the surface activity after and before a diffusion anneal is
A/&
= eerfc(pZDt)l’*
(2)
where eerfc(y) = exp(y2) [l-erf(y)]. erf(y) is the Gaussian error integral and p is the linear absorption coefficient for the tracer radiation in the diffusion specimen. D can therefore be evaluated by measuring (1) J. Steigman, W. Shockley, and F. C . Nix, Phys. Rev., 56, 13 (1939).
Volume 70, Number 6 M a y 1066
K. J. RICHARDS AND F. E. WAGSTAFF
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the decrease in surface activity as a function of time a t a particular temperature. An additional experimental convenience of this method which is implicit in (2) but which does not seem to have been generally recognized or applied is that a single sample can be used for diffusion measurements at more than one temperature. Since a unique value of the activity ratio is determined for a particular product, Dt, a constant time, 7 , can be chosen to represent the entire previous thermal history of the sample, and eq 2 can be rewritten as
A / A o = eerfc(p2D[7
+ t])”’
(3)
If A . is known, only a single diffusion anneal is needed to evaluate D. If neither A . or 7 are known, D can still be determined by measuring the activity after consecutive diffusion anneals at the same temperature. It should be remembered that for eq 3 to be applicable, the distribution of tracer in the specimen must be accurately described by eq 1. This has been shown to be the case over the temperature range covered in this study for previous studies of self-diffusion in NiO2Pa and the related systems of COOand Fe0.4 In addition, the results of this study show the diffusivity to be time independent, which is a requirement of the applicability of eq 2. The diffusion measurements were made on a single crystal of NiO which was supplied by the Air Force Cambridge Research Laboratories. The crystal was grown by the flame-fusion method from powder of unspecified purity. Emission spectrographic analysis of this crystal showed the following cation impurity concentrations: A1 (10 ppm), Na (10 ppm), K (50 ppm), Li (
