Diffusion of the 65 Zn Radiotracer in ZnO Polycrystalline Ceramics

Zinc self-diffusion coefficients were measured in polycrystalline ZnO of high density (>99% of the theoretical density) and of high purity (> 99.999%). The diffusion experiments were performed from 1006 to 1377 °C, in oxygen atmosphere, for times between 16 and 574 h. The diffusion profiles were established by means of Residual Activity Method using the Zn radioactive isotope as zinc tracer. In our experimental conditions, the zinc volume diffusion coefficients can be described by the following Arrhenius relationship: D(cm/s) = 1.57×10 exp[(-2.66 ± 0.26) eV/ kT]. In the same experimental conditions, the grain-boundary diffusion coefficients are approximately 4 orders of magnitude greater than the volume diffusion coefficients, and can be described by the Arrhenius relation: D’δ (cm/s) = 1.59×10 exp[(-2.44 ± 0.45) eV/kT], where D’ is the grain-boundary diffusion coefficient and δ is the grain boundary width.


Introduction
The transport properties and the defect chemistry of zinc oxide have been intensivelly studied in the last decades due to, principally, the utilization of this material in ZnO-based varistors.
The non-linear current-voltage characteristics of ZnO varistors, as well as its degradation in operation (loss of its varistor property) are grain-boundary phenomena involving interaction between point defects and ionic diffusion 1,2 .The understanding and the modelling of these phenomena demand the knowledge of the defect structure and of the diffusional processes in ZnO.
In spite of numerous previous studies about diffusion and defect in ZnO, there is still lack of reliable defect and diffusion data as shown by Tomlins et al. 3,4 .
The present work is part of a wide project concerned with the study of diffusion and defects in ZnO 5 , and deals with the study of the zinc diffusion in ZnO.
While previous works 4,6,7 about zinc diffusion in ZnO were performed in single crystalline samples, this work is dedicated to the determination of zinc diffusion in impurity content was less than 10 ppm (elements detected: 0.1 ppm Fe and 1 ppm Pb).The powder was cold pressed and sintered at 1400 °C, for 4 h in oxygen atmosphere.No additive was used as powder agglomerant in the sintering experiments.
The sintered ZnO had high density (> 99% of the value of the theoretical density) and grain size of 20 µm.These samples were resintered for 72 h at 1393 °C, in oxygen atmosphere, in order to increase the grain size above 80 µm.
A typical microstructure of the ZnO samples used in this work, after thermal etching at 1150 °C, for 1 h, in air, is shown in Fig. 1.
For the diffusion experiments, samples of dimensions 17 mm × 17 mm × 3 mm, were polished with diamond paste, and submitted to pre-annealing in order to equilibrate the samples with the temperature and atmosphere to be used in the diffusion annealings.

Preparation of the 65 Zn radioactive tracer
The zinc tracer used in this work was the radioactive isotope 65 Zn.This isotope has a half-life of 244.1 days and decays emitting the radiations γ (1.1154 and 0.820 MeV) and β + ( 0.324 MeV).

Deposition of the tracer
A drop of the irradiated ZnCl 2 was deposited on the polished surface of the sample, previously thermodinamically equilibrated.The drop was carefully spread on the surface, slowly dried, and then oxidized at 500 °C, for 2 h, in air.

Diffusion experiments
The diffusion experiments were performed from 1006 to 1377 °C, in oxygen atmosphere, for times between 16 and 574 h.These diffusion treatments were performed in a tubular furnace of super kanthal resistance.
In order to minimise the evaporation of the tracer and of the ZnO samples, which is significative above 1100 °C, the samples were placed in a ZnO crucible for the diffusion annealings.

Determination of the 65 Zn diffusion profiles
After the diffusion annealings, about 1 mm in thickness of material was removed from each lateral face and back.This operation was performed to remove 65 Zn tracer eventually diffused along the lateral surface, followed by diffusion into volume, where it would be counted.
The diffusion profiles of 65 Zn were determined by means of the Gruzin's Method or Residual Activity Method 8 .
In this method, sections of the sample are removed, and the activity remaining in the sample after each sectioning is measured.The sectioning was performed by mechanical abrasion using a high precision grinder.The thickness of the removed section was determined by measuring the mass of the sample before and after the sectioning.
The diffusion profiles of 65 Zn were established by plotting the residual activity (I), after each sectioning, versus the depth (x) of the sectioning.
The residual activity method is applicable if the radiation used is absorbed exponentially, with a linear absorption coefficient µ.If I is the residual activity after the n th section, it can be show that 8 : (1) whatever the functional form of C(x).This equation can be simplified if the used radiation is only slightly absorbed, as in the case of the γ radiation used in this work.The simplified equation is given by: (2)

65 Zn volume diffusion
Figure 2 shows a typical diffusion profile after diffusion of the 65 Zn at 1300 °C, in oxygen atmosphere, for 29 h.The diffusion profile shows two regions.
The first part of the profile, of high gradient dI/dx, corresponds to the volume diffusion and the second part of profile of low gradient dI/dx, ie, the tail of the profile, is a characteristic of the diffusion along the grain-boundaries 8 .
In our experimental conditions, diffusion from an instantaneous source, Eq. ( 2) has the following form 8 .
(3) Resolving Eq. ( 3), it is obtained the following relationship for I as a function of x 9 : where the erfc function is given by The fit of Eq.4 to the first region of the diffusion profile, as shown in Fig. 2, gives the value of the volume diffusion coefficient (D). Figure 3 shows the dependence on temperature of the diffusion coefficients determined in this work, which can be described by an Arrhenius equation given by: (5) Further experiments of zinc diffusion as function of the oxygen pressure have been performed in order to determine the zinc diffusion mechanism (vacancy or insterstitial mechanism) in ZnO, and will be the subject of another paper.

65 Zn grain-boundary diffusion
According to Harrison's conditions 10 , our 65 Zn intergranular diffusion experiments are of B-type: where δ is the grain-boundary width, D is the volume diffusion coefficient and Φ is the grain size.For B-type intergranular diffusion, it is possible to determine the product D'δ, where D' is the grain-boundary diffusion coefficient.For the experimental conditions used in this work, the product D'δ is calculated by using the Suzuoka's model 11 through the relationship:   (7)   where the parameter β is given by: (8) The gradient is calculated from the tail of the diffusion profile in a plot of ln(-dI/dx) versus x 6/5 as shown in Fig. 4.
The experimental conditions used and the results obtained for the grain-boundary diffusion are listed in Table 1.
The dependence on temperature for the product D'δ can be described by the following Arrhenius equation: Assuming for δ the usual value 12 of 1 nm, the 65 Zn grainboundary diffusion coefficient can be estimated from Eq. 10.

Figure 1 .
Figure 1.Typical microstructure of polycrystalline ZnO used in this work, after thermal etching at 1150 °C, for 1 h, in air.

Figure 3
Figure 3 also shows the comparison of the results of the present work with those previously published 6-8 .Our results and those recently determined by Tomlins et al. show good agreement for the volume diffusion coefficients values.Further experiments of zinc diffusion as function of the oxygen pressure have been performed in order to determine the zinc diffusion mechanism (vacancy or insterstitial mechanism) in ZnO, and will be the subject of another paper.3.2 65 Zn grain-boundary diffusionAccording to Harrison's conditions 10 , our 65 Zn intergranular diffusion experiments are of B-type:

Figure 2 .
Figure 2. Diffusion profile for the isotope 65 Zn in ZnO polycrystal at 1300 °C.

Figure 3 .
Figure 3.Comparison of volume diffusion coefficients obtained in this work with those available in the literature.

1 .
Zinc volume diffusion coefficients and zinc grainboundary diffusion coefficients in ZnO were measured by means of the residual activity method using the 65 Zn as zinc tracer.The diffusion coefficients were studied as a function of the temperature under an oxygen pressure of 10 5 Pa.The product D'δ for the

Figure 5 .
Figure 5.Comparison of volume diffusion coefficients (D) and grain-boundary diffusion coefficients (D') obtained in the same experimental conditions.

Table 1 .
Experimental conditions and results for zinc diffusion in polycrystalline ZnO