Grain Growth in Cao.16Zro.8401.84 by T. Y. TlEN and E. C. SUBBARAO

Westinghouse Research laboratories, Pittsburgh, Pennsylvania

Isothermal grain growth in Ca0.16Zr0.8~0~.84, a cubic solid solution of the fluorite type, was studied between 1600’ and 20OO0C. The grain size increased as the 0.4 power of time. The growth rate was found to be slower than in metals. The activation energy for grain-bound- ary migration was about 80 kcal per mole. The influence of sintering atmosphere on grain

growth is shown.

1. Introduction HE grain growth in metal systems has been studied ex- tensively and excellent reviews of the subject are avail- able.’ The general concept of this process is that the

grain boundaries in polycrystalline specimens tend to migrate toward their centers of curvature. The driving force for boundary migration in grain growth is generally accepted to be the reduction of the total surface free energy due to grain boundaries by decreasing the total boundary area. In this process, some grains grow at the expense of others and the average size of the remaining grains increases. The rate of growth is a function of temperature and time. From the analogy to cell growth in a bubble froth, Turnbul12 suggested the lollowing relation :

D 2 - Do2 = K y V t (1)

T

D = average diameter a t time t . DO = average original grain diamctcr a t zero timc. y = average intcrfacial energy. 17 = gram-atomic volume. I< = it rate constant which is temperature dependent.

However, many metals studied do not follow this law. et nL. proposed that

Beck

D = (Kt)“ (2)

when the initial grain size is negligible. Several investigators found that the time exponent, n, has values less than l/2.

For example, Bolling and Winegard4 in studying the grain growth in zone-refined lead found that the time exponent, ?z, is 0.4 for pure lead.

Presentcd at the Sixty-Fifth Annual Meeting, The American Ceramic Society, Pittsburgh, Pa., April 30, 1963 (Basic Science IXvision, No. 16-B-63).

This work was supported by the Advanced Research Projects Agency through the Office of Naval Research.

The writers are, respectively, engineer, Metallurgical and Ceramic Technology, and Research engineer, Solid State Phe- nomena Department, Westinghouse Research Laboratories.

‘ ( a ) J. E. Burke and D. Turnbull, “Recrystallization and Grain Growth”; pp. 220-92 in Progress in Metal Physics, Vol. 111 (edited by Brucc Chalmers). I’ergamon Press, London, 1952. 331 pp

( b ) 1’ A. Beck, “Annealing of Cold-Worked Metals,” Advan.

(c) R. L. Fullman, “Boundary Migration During Grain Growth”. pp. 179-207 in Metal Interfaces. American Society for Metais, Cleveland, Ohio, 1952.

David Turnbull, “Theory of Grain-Boundary Migration Rates,” J . Metals, 3 ; Trans. AIME, 191 [8] 661-65 (1951).

P. A. Beck, J. C. Kremer, L. J. Demer, and M. L. Holz- worth, “Grain Growth in High-Purity Aluminum and in an Aluminum-Magnesium Alloy,” Metals Technol., 14 IS] 23 pp.

Received March 8, 1963.

Phys., 3 [ l l ] 245-324 (1954).

335 pp.

(1947); T ~ U K S . AIME, 175,372-94 (1948).

It may be expected that the grain-growth laws observed for metallic systems will hold broadly for nonmetallic systems as well. Systematic studies of grain growth in oxides are, however, scarce. The early observations in oxide systems were ably summarized by Burke,b who also pointed out the need for further work. The recent experiments of CobleG on A1203 and of Daniels et d7 on MgO and CaO represent the first detailed reports on oxides. Equation (2) was found to be applicable to these oxides with time exponents of ‘/2 in the case of AlzOs and

The present investigation was undertaken to p rovide additional data on grain growth in oxide systems. Cao~6- 2r0.8401.84 was chosen for this study because of the availability of diverse experimental data on this material and because of its usefulness as a refractory and as a solid electrolyte in galvanic8 and fuelQ cells. Microstructure may well have an important bearing on the measured properties of the ma- terial. This study forms a part of a broader examination of the transport properties of nonstoichiometric oxides.

Cubic Cao.16Zro 8401.8c has a defect fluorite-type structure. E-Iund10 proved, by means of density measurements, that the Ca2+ and Zr4+ ions fill the cation sites and that electrical neutrality is preserved by the creation of oxygen ion vacan- cies. The unusually high oxygen ion mobility found in this material by Kingery et aL.“ was attributed to the anioc vacancies and was correlated with electrical conductivity data. The cation diffusion rates, recently determined by

for MgO and CaO.

(a) G. F. Bolling and W. C. Winegard, “Grain Growth in Zone-Refined Lead,” Acta Met., 6 [4] 283-87 (1958) (in English).

( b ) G. F. Bolling and W. C. Winegard, “Some Effects of Im- purities on Grain Growth in Zone-Refined Lead,” ibid., pp. 288-92 (in English).

6 ( ~ ) J. E. Burke, “Recrystallization and Sintering in Ce- ramics”; Chapter 15, pp. 120-31, in Ceramic Fabrication Processes (W. D. Kingery, editor). Technology Press of Massachusetts Institute of Technology, Cambridge, and John Wiley & Sons, Inc., New York, 1958. 235 pp.; Ceram. Abstr., 1958, May, p. 123h.

( b ) J. E. Burke, “Grain Growth in Ceramics”; Chapter 16, pp. 109-16, in Kinetics of High-Temperature Processes-Report of Eiidicott House Conference on Kinetics of High-Temperature Proccsses, June 1958 (W. D. Kingery, editor). Technology Press of Massachusetts Institute of Technology, Cambridge, and John Wiley & Sons, Inc., New York, 1959. 326 pp.; Ceram. Abstr., 1960, October, p. 246.1..

8 R. L. Coble, “Sintering Crystalline Solids: 11, Experimental Test of Diffusion Models in Powder Compacts,” J . Appl. Phys., 32 151 793-99 (1961).

A. U. Daniels, Jr., R. C. Lowrie, Jr., R . L. Gibby, and I. B. Cutler, “Observations on Normal Grain Growth of Magnesia and Calcia.” J . Am. Ceram. Soc.. 45 I61 282-85 (1962).

8 Kalevi Kiukkola and ’Cari Wagner, ‘“Measurements on Galvanic Cells Involving Solid Electrolytes,” J . Electrochem. Soc.,

9 J. Weissbart and R. Ruka, “A Solid Electrolyte Fuel Cell,” J . Electrochem. Sac., 109 [8] 723-27 (1962).

1oF. Hund. “Die Fluoritahase im System ZrOg-CaO: Ihre

104 [6] 379-87 (1957).

Fehlordnung . und das Aiftreten elektrischer Leitfahigkeit” (Fluorite Phase in the System ZrO2-CaO; Its Defect Structure and Electrical Conductivity), 2. Physik. Chem., 199 [l-31 142-51 (1952).

11W. D. Kingery, J. Pappis, M. E. Doty, and D. C. Hill, “Oxygen Ion Mobility in Cubic Zro.86Ca~.1~0~.8~r” J . Am. Ceram. Sac., 42 [8] 393-98 (1959).

489

490 Journal of The American Ceramic Society Tien and Subbarao Vol. 46, No. 10

Fig. 1 . Typical microstructure of sintered Cao.lsZr0.~01.s4 (a) fired at 1400°C for ‘/4 hour, 40% porosity; (b) fired at 1 7OO0C for 2 hours, 10% porosity; (c) fired at 1900°C for 2 hours, 8% porosity; (d) fired at 20OO0C for 8 hours, 670 porosity.

Rhodes and Cartcr,12 were found to be several orders of magnitude lower than that for the oxygen ion. The activa- tion energy for self-diffusion was found to be 30 kcal per mole for oxygen ions and 109 kcal per mole for Ca2+ and Zr4+ ions.

I I . Experimental The ZrOz used in this study was supplied by the National

Lead Company. It contained 99.8y0 ZrOz and the highest impurity present was 0.15% SOs. The 5r02 powder was mixed with cp CaC03 to give a composition of Cao.16Zro.84- 0 1 8 4 after firing. The mixing was carried out in a water medium in a rubber-lined ball mill with (commercial) calcia- stabilized zirconia pebbles. The mixture was dried and re- acted at 135OoC for 24 hours and was then ball milled to a finer particle size to pass a 360-mesh screen. Cylindrical specimens ( l /2 in. in diameter and in. high) were pressed with 1% of Carbowax as binder and the binder was removed by heating to 140OoC for I5 minutes. The grain size after this treatment was negligible compared with the final grain size. The photomicrograph of this starting material is shown in Fig l ( a ) . The X-ray diffraction pattern showed that it was a well-crystallized single-phase material with a cubic cell edge of 5.132 A. The density computed from these data was 5.525 g per emu3.

The final sintering was carried out in an oxygen atmosphere at different temperatures for various periods of time as given in the results. A 60Pt40Rh wire-wound furnace13 was used for temperatures in the range 1600° to 180OoC and a pro- pane-oxygen pot furnace for the 1900OC and the 2000°C firings.

Sintered specimens were polished using usual metallo- graphic techniques and were then etched with a mixture of 15 ml HN03, 30 ml HCI, and 20 ml HF for 10 minutes. The grain-size measurements were made by using the intercept (or Heyn) p r ~ c e d u r e . ~ ~ The data presented were an average

r l l - I l i I I

-3.0 3.6 3.8 4.0 4.2 4 .4 4.6 4 .8

Lcq Time ( s e d

Fig. 2. Log-log plot of average grain diameter vs. time.

of 15 or more of such counts. graphs are shown in Fig. 1. versus time (t) are plotted in Fig. 2 on a log-log scale.

A few typical photomicro- The observed grain diameter (D)

l2 W. H. Rhodes and R. E. Carter, “Ionic Self-Diffusion in Calcia-Stabilized Zirconia” ; presented at the Sixty-Fourth Annual Meeting, The American Ceramic Society, New York, April 30, 1962 (Symposium on Kinetics of Ceramic Reactions, No. 1-2s-63); for abstract see Am. Ceram. SOC. Bull., 41 [4] 283 (1962).

l 3 P. D. S. St. Pierre, “Internally Wound Platinum-Rhodium Furnace for Use in Air up to 1900°C,” Am. Ceram. SOC. Bull., 39

l4 “Tentative Method for Determining the Average Grain Size of Metals,” ASTM Designation E 112-55 T. 1955 Book of ASTM Standards, Part 1, pp. 1435-44. American Society for Testing Materials, Philadelphia, Pa.

[5] 264-66 (1960).

October 1963 Grain Growth in Cao.16 Zro.84 01.84 49 1

I I I I I I I 20 30 40 50 60 70 80

Time f ~ e c ) ” ~

Fig. 3. Isothermal grain growth.

111. Results and Discussion The simple grain-growth laws, equations (1) and (2), have

been found to have only limited application. One reason for this is because inclusions or pores inhibit grain growth, as shown by Smith.I5 He used a suggestion by Zener that grain growth should stop a t an average grain size, D , when

D f = d/f (3) d = average diameter of inclusions or pores. f = volume fraction of inclusions or pores.

Burke and Turnbull’@) have considered the influence of D, on the rate of grain growth in metals, when D, is independent of temperature and time.

Oxide systems present complications that are not present in metals, since polycrystalline oxide compacts contain pores which change in size and in volume fraction with time and temperature. In the early stages of sintering, the pores, which form rather a large volume fraction, lie on the grain boundaries and hinder grain growth. As sintering proceeds, the volume fraction of pores decreases while the pores grow in size, thus increasing the limiting grain size, D,. The in- fluence of porosity on grain growth therefore decreases with the progress of sintering. The porosity of the present speci- mens ranged from 12% for the specimen heated at 1600°C for 2 hours to 6% for the specimen heated a t 20OO0C for 8 hours. The gradual increase of pore size with time and temperature is apparent from Fig. 1. The rate of grain growth in this case may be described by an equation of the form

(4)

where k is a constant and Df gradually increases in value with time or temperature; no proper solution could be found for this formula. Qualitatively, it could be seen that with increasing sintering D, increased and therefore the rate of grain growth increased. In the absence of an explicit solu- tion for equation (4), attempts were made to fit the present data to equations (1) and (2).

The observed data can be described quite well by equation (2) with n approximately equal to 0.4 (Fig. 3). A best-fit analysis of the measured values, however, indicates that n decreased monotonically from 0.41 a t lGOO°C to 0.32 a t 2000°C.

The rate constant, K, of equation (2) varies with absolute temperature ( T ) as

I< = KO exp - (Q/RT) (5)

Here Q is the activation energy in the Arrhenius sense, R is the gas constant, and Ro is a rate constant which is indepen- dent of temperature. Slopes from Fig. 3, which are pro-

4 - 4 . 6 r 4.2 4.4 4.6 4.8 5.0 5. 2

~ O ~ / T P K I

Fig. 4. Temperature dependence of grain growth.

portional to the rate of grain growth, are plotted against reciprocal absolute temperature (Fig. 4) to obtain an activa- tion energy of about 80 kcal per mole. If the variation of n with temperature is taken into account in determining the rate of grain growth, then an activation energy of about 91 kcal per mole was obtained.

The data presented here confirm that the rate laws govern- ing grain growth in metals are generally applicable to CQ.16- 2ro.8401.84. The observed values of the time exponent, n, in equation (2) are within the range reported for metal and oxide systems. The rate of grain growth encountered here is, however, one or more orders of magnitude smaller than that in high-purity metal system~.4(a) The rates in oxides appear to be comparable to those of alloy systems such as alpha and to those of impure metals4cb) The slow rate effected by soluble impurities has been attributed by McLeanlG to a different diffusion rate a t the grain boundaries. Bollingl’ has recently proposed nonuniform solute distribution as a possible hindrance to boundary migration. It is not clear whether the slow rates found in Cao.l~Zro.8401.~4 should be attributed to the fact that it consisted of three species (Ca2+, Zr4+, and 02-), similar to alloys, or to the presence of impurities. Grain-growth studies on purer oxides and also on Zr02-Ca0 solid solutions with varying amounts of calcia should shed light on this problem.

(I) Time Exponent, n The value of n has been found to decrease with increasing

temperature. It has already been pointed out that the de- creasing pore fraction and increasing pore size which ac- company sintering a t higher temperatures tend to increase the rate of grain growth or to decrease n, although no explicit expression for this relation is available a t present. Alterna- tively, Coble18 suggested that the photomicrographs indicate

C. S. Smith, “Grains, Phases, and Interfaces; An Interpreta- tion of Microstructure,” Metals Technol., 15 [4] ; Trans. AIME, 175, 15-51 (1948).

18 D. McLean, Grain Boundaries in Metals, p. 242. Oxford University Press, New York, 1957.

1’ G. F. Bolling, “Grain-Boundary Migration,” Trans. AIME, 224 [lo] 1075 (1962).

l* R. L. Coble, private communication.

346 pp.

492 Journal of The American Ceramic Society-Tien and Subbarao Vol. 46, No. 10

Fig. 5. Effect of sintering otmosphere on grain growth of Cao.1sZro.s4Ol.s~ (a) fired in oxygen at 1 800°C for 2 hours, 9% porosity, and (b) fired in hydrogen at 1 800°C for 305 hours, 9% porosity

the presence of a liquid phase a t the grain boundaries. The amount of the siliceous liquid (chemical analysis showed 0.15yo SOz) increased with increasing temperature. The presence of a liquid in which the matrix grains are soluble may facilitate mass transfer by a solution-precipitation mechanism, thus increasing the rate of grain growth with in- creasing temperature.

(2) Effect of Atmosphere A specimen fired in oxygen at 18OO0C for 2 hours had a

porosity of 9% and an average grain diameter of about 2 5 ~ whereas a similar specimen fired in hydrogen a t 180OoC for a long period (30.5 hours) had essentially the same porosity but very small grain size (Fig. 5 ) . In this case, it is possible that the smaller pore size inhibited grain growth in the manner suggested by Zener. The rapid removal of pores in specimens fired in oxygen was no doubt due to high oxygen ion mobility in this material. CobleIg found that the solubility of a gas influenced the sintering of A1203 in a given gas atmosphere.

(3) Activation Energy The activation energy for grain-boundary migration in

high-purity metals has been found to be comparable to that for boundary self-diffusion, which in turn is smaller than that for bulk or lattice self-diffusion. No data are available on boundary self-diffusion in oxide systems. The available data on activation energies for Cao 16Zro 8 4 0 1 84, A1203, and

R. L. Coble, “Sintering Alumina: Effect of Atmospheres,’ J . Am. Cevam. Soc., 45 [3] 123-27 (1962).

Table 1. Activation Energies

Activation (kcal/mole) energy reference Footnote

Species and system

Diffusion of Ca2+ in Cao.1eZro.a401 84 109 12 Diffusion of Zr4+ in Cao.l&ro.saOl.sr 109 12 Diffusion of 02- in Cao.lsZro.szOl.se 29.8 11 Grain growth in Cai1.16Zro.8401 .a4 80 Present study Mg2+ in MgO 79 * Oa-in MgO 62.4 t Grain growth in MgO 60 7 A13+ in A1203 0 2 - in A1203 single crystal 02- in A1203 polycrystal Grain growth in A1201

114 152 125 153

i § § 6 - - .

* Roland Lindner and G. D. Parfitt. “Diffusion of Radioactive Magnesium in Magnesium Oxide Cr$stals,” J . Chem. Phys., 26

t Y . Oishi and W. D. Kingery, “Oxygen Diffusion in Periclase Crystals.” ibid.. 33 131 905-906 (1960); Ceram. Abstr., 1961,

[l] 182-85 (1957).

. _ . April, p. 103j. I’ A. E. Paladin0 and W. D. Kineerv. “Aluminum-Ion Diffusion

in Aluminum Oxide,” J . Chem. P%yL,’37 [5] 957-62 (1962). OY. Oishi and W. D. Kingery, “Self-Diffusion of Oxygen in

Single-Crystal and Polycrystalline Aluminum Oxide,” ibid., 33 [2] 480-86 (1960).

MgO are compiled in Table I. Additional data are needed before the effect of impurities and of boundary diffusion is understood in the case of oxides.

Acknowledgments

R. L. Coble for helpful discussions. The writers are grateful to G. F. Bolling, R. B. Grekila, and