AFOSR 1961 THE U N I V E R S I T Y OF M I C H I G A N COLLEGE OF ENGINEERING Department of Chemical and Metallurgical Engineering Technical Note SINTERING OF ZINC OXIDE L, F. Norris G. Parravano ORA Project 02852 under contract wit-ho UNITED STATES AIR FORCE AIR RESEARCH AND DEVELOPMENT COMMAND AIR FORCE OFFICE OF SCIENTIFIC RESEARCH CONTRACT NOo AF 49(638)-493 PROJECT NO. 9762, TASK NO. 37621 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR March 1962

ABSTRACT Sintering studies have been conducted with single-crystal spheres of zinc oxide in air and at lower oxygen partial pressures and total pressures of 10-3 to 1.0 atmospheres over a temperature range of 1050-1250~Co Quantitative observations on the rate of growth of a neck between the spheres were madeo No change in the distance between the geometrical centers of the spheres was observed. An analysis of the kinetic data shows that sintering was predominantly achieved by distillation through the surrounding gas phase. At higher total pressures there was evidence that diffusion through a hydrodynamic boundary layer above the solid surface was the rate-controlling step, while at lower pressures sintering was determined by the rate of evaporationo Previous studies of the welding together of zinc oxide microspheres in the temperature range 700900~C have emphasized the operation of a bulk diffusional transport process, dependent on the nonstoichiometry of zinc oxide. Additional evidence to support this conclusion was obtained in the present work. The pattern of the prevailing transport mechanisms in zinc oxide from 700 to 1250~C is analyzed, and its application to other solid-state transfer processes is discussedo 111

INTRODUCTION Sintering characteristics of zinc oxide compacts are known to depend on experimental conditions like the stoichiometry of the oxide, chemical composition of the surrounding atmosphere, temperature, and purity of the oxide. Variations in sintering behavior reflect the operation of different transport mechanisms underlying sinteringo Previous studies of the welding together of single crystal microspheres of zinc-rich zinc oxide showed that volume diffusion is responsible for the observed sintering in the temperature range 700~900~C, the driving force for the process being supplied by the oxidation of the excess zinc present. It thus seemed of interest to investigate the extent to which this mechanism would operate under different experimental conditions, and whether the reported variations of sintering characteristics of compacts of zinc oxide also are present in the welding together of singlecrystal microspheres. The results obtained in the temperature range 10500-12500C point to the operation of a transport process which is distinctly different from any which predominates at lower temperatures. EXPERIMENTAL Sintering data were obtained by measuring the growth rate of the neck formed between two contacting microspheres of zinc oxide. The spheres were obtained by crushing clear, single crystals of zinc oxide into smaller crystals which were ground and polished using air-grinding techniques previously discussedo Final diameters of the spheres were in the range of 0o5 mm, The chemical composition and X-ray and spectroscopic analysis of the zinc oxide samples, together with the average value of their electrical conductivity, has already been reported2 Two or more microspheres were placed in a groove cut in a 10 rhodiumplatinum rod which formed the heating element of a totally enclosed hot staged Observations were made through an optically flat quartz window. A creep-test microscope, equipped with a filar eye-piece micrometer, was vertically mounted above the heating rod, enabling measurement of the growth of the bridge between spheres,' Neck width was measured directly at sintering temperatures. Measurements of the distance between a fixed number of spheres were used to check the presence of shrinkage. The electrical circuit controlling the current to the heating rod consisted of a step-down.transformer, variac, and voltage stabilizer. Temperatures were measured with a potentiometer and a Pt-Pt Rh thermocouple welded to the rod directly under the location of the zinc oxide microsphereso Temn1

peratures were kept at a constant value (+ 2~C) by a stepless controller connected to a saturable reactor, Sintering studies were made in air, helium, and in hydrogen and steam mixtures. The latter were prepared by adding hydrogen from an electrolytic cell to a known flow rate of purified helium and saturating the mixture with water vapor. Compositional equilibrium was assured by maintaining a 5~C temperature difference between two saturators through which the hydrogen-helium mixture was passed. For runs made in air a flow rate of approximately 25 cc per minute was maintained. Preliminary runs showed no effect of the flow rate on the rate of sintering within gas flow rates of from 0 to 75 cc per minute. Flow rates at sub-atmospheric pressure were obtained with a vacuum pump and capillary tubings on each side of the hot stage. Pressure was read with a mercury manometer connected to the vacuum system. RESULTS Typical results for sintering in air at 1 atm and temperatures of 10501250~C are shown in Fig, 1. The reproducibility of the data can be gauged from Fig. 2, which includes results from four runs under similar conditions. An incubation period was sometimes observed at low temperatures. During this time, no observable sintering took place. The duration of the period was less random than that observed in previous studies,5 and there was evidence that it was largely due to the inability to resolve a neck width of less than about 0-07 mm with the microscope used. The effect of the total gas pressure on the slope (x3/a) deduced from typical sintering plots (Figs. 1 and 2) is shown in Fig. 3, where x and a are the diameters of the neck and of the spheres, respectively. No effect on the rate of sintering was detected when at constant total pressure and temperature, the oxygen partial pressure of the surrounding gas phase was varied from atmospheric to 6.3 x 10- atm, Long, needle-shaped crystals developed on the surface of the spheres at temperatures > 1150~C. They showed no preferential region of growth on the spheres. At 1250~C crystallite formation posed experimental difficulties by growing across the neck region and obscuring observation. Sometimes a crystallite bridge, produced by interlocking crystallites, was formed before substantial sintering occurred. These facts are reminiscent of similar observations on vanadium pentoxide spheres. In this instance, it was shown that whisker growth between adjacent spheres was the first stage of the sintering process between two spheres of vanadium pentoxide.h Measurements of end-to-end distances for two sintering spheres in air generally showed no change during sintering. Occasionally an increase in the end-toend distance was observed. Metallographic examination of spheres exhibiting this 2

behavior revealed the presence of a whisker embedded in the neck region. The whisker, growing from one sphere, had evidently moved the other sphere until friction with the heating groove halted the motion and allowed the subsequent welding process. DISCUSSION The most significant conclusions which can be derived from the experimental data presented in the previous section are as follows~ (a) Neck growth between single-crystal zinc oxide micro-spheres occurred readily in the temperature range 1050~ to 1250~C. (b) At constant temperature and pressure, the experimental results could be fitted into an equation m = kt (1) (Fig. 1), the average value of m being 3. This value was obtained by averaging the results of about 40 runs, whose maximum deviation never exceeded ~ 0.60 There was a tendency, however, for m to decrease as the temperature decreased, (c) At constant temperature, the rate of neck growth was not affected by the oxygen partial pressure of the surrounding atmosphereO (d) At constant temperature, the rate of neck growth was only slightly dependent on the total pressure, except at higher pressures. In this range the rate was adversely affected by the total pressure (Fig. 3)0 (e) The rate of neck growth varied exponentially with temperature. The temperature coefficient of the rate was not dependent on the total pressure. (f) Over the whole range of experimental conditions investigated, the rate was independent of the flow velocity of the carrier gaso According to previous derivations, results under (b) indicate that the rate of growth of the neck was controlled by distillation of matter from the sphere surfaces to the neck regiono Results under (c) and (d) show that the distillation process is controlled by the rate of evaporation of matter from the zinc oxide surface. At higher total pressures, diffusive effects through a boundary layer adjacent to the solid surface play an increasingly important role. Furthermore, at lower temperatures a different transport mechanism sets ino This is evidenced by the tendency for m to have values > 35 When the rate of evaporation of the sintering spheres is the kinetically controlling factor, the rate of mass transported to the neck area is given by)5 5

5 x 3jtMyp ( M >1/2 a p2RT K2RT t (2) where M is the molecular weight of the solid species, p the equilibrium partial pressure, p the density, t time, and y the surface tension. Comparing Eq. (2) with the empirical expression (1), one obtains m = 30 This is consistent with our findings (Fig. 1). Since nonstoichiometric zinc oxide can be regarded as a solid solution of zinc in zinc oxide, its evaporation is incongruent. Assuming that zinc oxide and zinc are the gaseous species formed, the evaporation reactions are: ZnO(in.ZnxO(g)) = ZnO(g) Zn(in ZnxO(g)) = Zn(g) x where x > 1. In the gas phase, then, the following equilibrium is established: Zn(g) + 1/2 02(g) - ZnO(g) 6 Experimentally, zinc oxide seems to be the predominant gaseous species and, for the purpose of our discussion, the dissociation reaction will be neglected. Equation (2) may be solved for po Taking the value of x, averaged over several runs conducted at total pressures < 1 atm at 1150~C, p = 5o61 gr per cc, and y = 1000 dynes per cm2, it is possible to calculate a value of p = 0.082 mm Hg. This value is in satisfactory agreement with the literature value of 0.062 mm Hgo7 In addition, numerical values for the evaporation rates can be computed from our data. Taking the neck volume equal to cx4/16a, and assuming that all zinc oxide evaporated was condensed in the neck area from runs completed at 1150~C and 2.7 x 10 3atm, the evaporation rate from two spheres can be found equal to 3511 x 10-8gr hr-lo In a study of the rate of formation of zinc aluminate from zinc oxide and alumina, in the same temperature range as used in the present sintering experiments, the rate of evaporation of zinc oxide was found to be: R = 6.3 x 10elxp 95,00-r - r-1 1j xRT cm hr (3) Under the conditions of the present experiments, Eq, (5) gives R = 8,08 x 10-7gr per hro This result is within an order of magnitude of the value calculated from sintering. 4

At total pressures close to 1 atm the rate of neck growth was influenced by the total pressure. This indicates that diffusional transport in the gas phase becomes a controlling factor of the evaporation process. Since the flow rate of the carrier gas did not influence the observed growth rate of the neck, the resistance to the flux of evaporating species can be traced to natural convection through a density gradient in the vapor of zinc oxide adjacent to the solid surface. A calculation of the evaporating flux and sintering rate under these conditions has been performed recently.9 Assuming a mass flow perpendicular to the surface of condensation and the Fuchs model for the evaporation and condensation, the sintering rate was found to be: x = 6rD rM 2 a LPRTJ (4) where 6, D are the thickness of the surface film and the diffusion coefficient for species in the gas phase, respectively. From the value of the mean free path in the gas phase, 8 ^ 10 4cm and D can be calculated to be t 2,0 cm per sec. Using these values in Eq. (4) and our experimental data for runs at 1 atm and 1150~C, a value of p = 0,093 mm Hg is deduced. This value is again in good agreement with that obtained by direct measurements quoted above.7 It should be noted that no agreement in the value of the equilibrium vapor pressure obtains for runs at 1 atm if the model based on the rate of evaporation as controlling step is used. The effect of a change in size of the spheres on the sintering rate for the mechanisms discussed above shows911 that in both cases the ratio between the times required for the growth of similar neck width is the following function of the sphere diameters: At a. 2 1 1 At (5) a 2 Figure 4 compares values of 1. as obtained from observed times for equivalent amounts of sintering with values obtained directly from the sphere radii ratios. Although the range of \ investigated was only 1 to 1.4, it is clear from Figo 4 that relation (5) is satisfactorily obeyedo The activation energy calculated from the experimental data (Fig. 5) is 105-110 k cal/mole. This result should be compared with the value of 95 k cal/mole of Eq. (3)o It is also consistent with the value of the evaporation 5

energy of zinc oxide of 123 k cal/mole.7 The high- and low-pressure data should yield, as was found, the same value of the activation energy for the rate of neck growth, since in the case of diffusional control of the evaporation, the only temperature-dependent factor in the final rate expression is the vapor pressure of zinc oxide. The observation that the center-to-center distance of spheres during sintering remained constant can be taken as further evidence for the operation of the distillation mechanism. Previous studies on the sintering of zinc oxide2 at lower temperatures (700-900~C) have emphasized the role of nonstoichiometric zinc ions in zinc oxide. It was postulated that the differences in excess zinc ion concentration between the surface and the interior of the spheres were responsible for the sintering behavior. Diffusional transfer of the excess zinc through the zinc oxide crystal and subsequent surface oxidation accounted for the increase in sphere diameter and the accompanying formation of a neck between spheres. The mechanism was supported by experimental evidence on the limited extent of sintering possible, since no further neck growth occurred after a given period. This extent is related to the initial amount of excess zinc presento The present studies verified this sintering mechanism. Measurements made on a single sphere at 8009C revealed a diameter increase corresponding to a neck growth x/a = 0.125 for spheres 0.585 mm in diameter. No further increase in neck was observed after the indicated diameter change. CONCLUSION It is instructive to summarize briefly the results of these studies on the transport mechanisms observed during the welding together of zinc oxide single-crystal spheres. At low temperatures a solid-state diffusional transport predominates. The transport is affected by the nonstoichiometric nature of zinc oxide and involves a relatively low activation energy (, 55 k cal/mole). There is strong evidence that the carriers are excess zinc ions. Oxygen partial pressure and impurity content of zinc oxide affect the rate of welding. Furthermore, differences in chemical potential of the zinc ions may arise either as a result of surface oxidation (chemical sintering) or as a consequence of the presence of the small convex neck area (physical sintering)o In both cases the bulk of the spheres is the source of the carriers, but their sink is represented by the surface of the sphere for the former, and by the neck area for the latter case. Between 700-900~C chemical sintering is predominant, while physical sintering through bulk diffusion is appreciable at about 10001100 C. At still higher temperatures, the diffusional transport is greatly overshadowed by the transfer of matter through the surrounding gas phase. Sintering then becomes dependent on the rate of evaporation of zinc oxideo In principle, three cases are possible. The transport through the gas phase may not be slowed down by convective phenomena. The rate of transfer is then controlled by the rate of evaporation and is independent of total pressure 6

and gaseous flow rate, and it involves a rather high activation energy (109 k cal/mole). This mechanism tends to occur at lower total pressures At higher pressures, diffusive control of the rate of evaporation setsin, Sintering becomes dependent on the total pressure (natural convection) and, at high flow velocities, should be proportional to a fractional power of the flow velocity of the carrier gas (forced convection). The high-temperature mechanisms are independent of the oxygen partial pressure of the gas phase. The energy values involved in solid diffusion and evaporation are the factors which determine the type of sintering followed. Possibly the pattern of transport mechanisms emerging from these studies can be expanded to cover different substances and transport phenomena (solid-state reactions). 7

REFERENCES 1o Allsopp, H. J., and J. P. Roberts, Trans. Faraday Soc., 55, 1386 (1959). 20 Lee, V. J., and Go Parravano, J. Appl. Phys., 30, 1735 (1959). 3. O'Bryan, H. M., Jr., and G. Parravano, "Sintering of Titanium Dioxide," in: Powder Metallurgy, Werner Leszynski, Editor, Interscience Publishers, New York (1961). 4. Parravano, G., Gazz. Chin. Ital., 91, 467 (1961). 5. Kingery, W. D., and M. Berg, J. Appl. Phys., 26, 1205 (1955)o 6. Brewer, L., Chem. Rev., 52, 1 (1953). 7. Gmelins Handbuch der Anorganischen Chemie, Zink, Verlag Chemie GMBH, Weinheim/Bergstrasse (1956). 8. Bengtson, B.,-and R. Jagitsch, Arkiv. Kern., Mineral Geol., 24A, No. 18 (1947). 9. Moser, J. B., and D. H. Whitmore, J. Appl. Phys., 31, 488 (1960). 10. Reid, R. C., and T. Ko Sherwood, The Properties of Gases and Liquids, New York (1958). 11o Herring, C., J. Appl. Physo, 21, 301 (1950). 8

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22 2 —20 RUNS 39 AND 20 16 | 14 E X RUNS 63 AND 39 C4J o2 / RUNS | FROM R MIOM _ X/ | COMPRED SLOPE DIAM.RATIO < 6 |/ 1/63,39 1,.17 1.03 4___ //_____39,20 1.65 1.59 x 2'/ 2 4 6 8 10 12 14 16 18 At x 12 (RUNS 39,63) minutes x O12 Fig. 4. Comparison between sphere size and sintering time for equivalent amount of neck growth during sintering of zinc oxide microspheres. 12

I I — u 0. I 6.4 66 s8 7.0 22 74 7.6 78 ___! __ (~KxK 10'4 ) TEMPERATURE Fig. 5. Activation energy for sintering of zinc oxide microspheres, calculated from time to extent of sintering of 0.3. 13 I_ _ 0,.I _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ c LII I ('Kxl0I) I. 5 Ao I o ic 13

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