Superplastic flow in a non-stoichiometric ceramic: Magnesium aluminate spinel

Acta metall, mater. Vol. 41, No. 4, pp. 1229-1235, 1993

0956-7151/93 $6.00+ 0.00 Copyright © 1993Pergamon Press Ltd

Printed in Great Britain. All rights reserved

SUPERPLASTIC FLOW IN A NON-STOICHIOMETRIC CERAMIC: MAGNESIUM ALUMINATE SPINEL R. LAPPALAINEN~', A. PANNIKKAT and R. RAJ:~ Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853-1501, U.S.A. (Received 3 July 1992)

A~traet--Tensile superplastic deformation of ceramics is often limited by their susceptibility to intergranular cavitation. However, we find that fine grained magnesium aluminate spinel exhibits unusual superplastic ductility at strain rates of up to 5 x 10-4s -t and at temperatures below 1280°C. The ductility is all the more remarkable because the flow stress of the spinel was in the range of several hundred MPa. We propose that the unusual cavitation resistance of interfaces in spinel is related to its non-stoichiometry. We further propose that the non-linear threshold stress like rheology which we have measured is related to an electrical double (barrier) layer which is postulated to form to compensate the net charge at interfaces of non-stoichiometric ceramics. We estimate that a boundary double layer potential, ~kb,of 5-50 mV can account for this threshold stress. The phenomenological characteristics of superplastic flow in the spinel are shared by other non-stoichiometric ceramics such as yttria stabilized zirconia, hydroxyapatite and zinc sulphide.

1. INTRODUCTION The superplastic ductility of metals may be limited either by the strain rate sensitivity of the flow stress or by intergranular fracture§. But the superplastic deformation of ceramics is nearly always controlled by intergranular cavitation¶. Thus while alumina [4] can be deformed in compression, it has practically no ductility in tension. However, by doping with yttria [5] it can be deformed to significant elongations albeit at slow strain rates ( < 1 0 - 5 s - t ) . The addition of 1 mol% zirconia, or hafnia, also enhances the cavitation resistance of alumina [6, 7]. Some ceramics, however, are remarkably ductile in tension. Wakai [8] has demonstrated that yttria stabilized zirconia can be deformed by 200% at strain rates > 1 0 - 4 s -1. Interestingly, he points out that pure zirconia, without the addition of yttria or ceria, is brittle [9]. tPresent address: University of Helsinki, Department of Physics, Siltavuorenpenger 20 M, 00170 Helsinki, Finland. :~Presently on leave at Max Planck Institut fiir Metallforschung, Seestrasse 92, Stuttgart 1, Germany. §For example in alloys of titanium [1] superplasticity is exhibited in the regime where the strain rate sensitivity, m, is greater than about 0.5, and the failure mechanism is strain localization, but in aluminum alloys the ductility can be lower than in titanium alloys even though the strain rate sensitivity is higher, because intergranular cavitation limits the strain to failure [2, 3]. ¶This is because whereas metals can deform by a variety of mechanisms leading to a wide range of strain rate sensitivities, large deformation in most fine grained ceramics is often sustainable only by the diffusional creep mechanism. However, ceramics have also been successfully deformed by dislocation mechanisms at very high homologous temperatures.

The above results suggest that the ductility of ceramics may be related to their non-stoichiometry. The unusual ductility of spinel, reported here, is also attributed to non-stoichiometry. (Ceramics that contain very small amounts of a liquid phase can be deformed in tension because the enhanced diffusivity through the fluid layer lowers the flow stress to such an extent that intergranular cavitation is preempted [10, 11]. The procedures used for the preparation of the spinel specimens, however, preclude the possibility that a silicate liquid may have been responsible for its superplastic behavior.) The superplastic behavior of non-stoichiometric ceramics is different in one other way. While stoichiometric ceramics and ceramics with a glass phase exhibit linear viscous superplastic behavior, in nonstoichiometric ceramics the strain rate increases non-linearly with stress. This non-linearity is also observed when the interfaces in stoichiometric oxides are rendered non-stoichiometric by doping with rare earth and transition metal oxides (for example, when alumina is doped with yttria, titania, zirconia or hafnia [6]). Here, as in the earlier paper [6] we characterize such non-linear behavior in terms of a threshold stress. In more recent work, two other non-stoichiometric ceramics, hydroxyapatite and lead-titanate [12], both of which are functional (as opposed to structural) ceramics, have been shown to be easily superplastic in tension. In the following sections detailed results for superplastic deformation of MgO.xAl203 are presented and compared to the superplastic behavior of ZrO: (Y203). Then a new conceptual model for interface controlled diffusional flow is described. It is based upon interfaces having a net charge and an adjacent

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LAPPALAINEN et al.: SUPERPLASTIC FLOW IN A CERAMIC

compensating electrical double layer. The strength of the interface charge is represented by a boundary potential, fib, that is equal to the electrical potential difference between the interface and the remote grain interior. The mechanical threshold stress, described above, is then expressed in terms of ~bb. 2. EXPERIMENTAL 2. I. Specimen preparation and testing Specimens for tensile testing were prepared by a powder free process described in detail elsewhere [13]. In this process thin films of the material are deposited from the vapor phase in a vacuum of 0.1-1 mPa where the source materials are heated by electron beams (in the present set of experiments the source materials consisted of slightly sintered pellets of high purity A1203, MgO, MgO.A1203, and the metal Pt). The typical deposition rate in our process is 1 nm/s. Two source materials may be evaporated simultaneously to control the composition of the films. The substrate temperature during deposition is below 130°C. The deposition rates are measured with previously calibrated thickness monitors. The film thickness and its density is measured by a combination of techniques that include Rutherford Backscattering Spectroscopy (RBS), profilometer, ellipsometer, and SEM. The composition of the films is obtained by RBS and microprobe. The grain size and the presence of second phases in the films is characterized

Fig. I. A TEM micrograph of a MgO.1.7AI203 specimen, made without platinum. The large grains are u-alumina and

the small grains are spinel. Note that cavities form more frequently at the u-alumina grain boundaries.

by X-ray diffraction and transmission electron microscopy. From these films microtensile specimens having a gage section of 50/z wide, about 1.0/~m thick and 4 mm long are prepared by lithographic techniques described in detail in Ref. [13]. Tensile tests on these specimens were carried out in a small screw driven machine built specially for this purpose. This machine is fitted with an in-line load cell, has a wide range of displacement rates, and is equipped with a furnace that can operate at temperatures up to 1400°C. The set-up is computer interfaced for displacement control as well as data acquisition. The above process for specimen preparation has the following advantages: (a) it is a one-step process for making ceramic materials of controlled compositions and purity, (b) the composition can be easily changed to study the influence of chemistry on mechanical properties, (c) nearly 1000 tensile specimens of exactly the same dimensions are obtained in one process cycle, (d) the grain size of the ceramic can be controlled by heat treatment and the use of dopants since the material may be deposited in the amorphous state--for example, we have been able to obtain nanocrystalline specimens by this procedure, and (e) the thin film specimens are eminently suitable for characterization by TEM. 2.2. Materials and microstructure The as deposited MgO. 1.25A1203 films were found to be amorphous. As expected from the phase diagram, these specimens phase separated into spinel and a-Al203 when annealed at 1000-1280°C. These annealed specimens had a bimodal grain structure consisting of small, 99 nm sized grains of spinel and 1300nm sized grains of ~-A1203 (at 1200°C). This material was not superplastic, failing at 3% tensile strain at a strain rate of 1 x 10 -s s -t at 1200°C. The low failure strain is attributed to the weak interfaces of alumina in this material. Figure 1 shows a micrograph of a MgO.1.7AI203 specimen which has a typical bimodal grain size distribution. The large grains in the picture are of s-alumina. Note that cavities have formed at the interfaces of several large grains. To obtain equiaxed, fine grained specimens of spinel, the magnesium aluminate was doped with platinum. The platinum served as a nucleating agent for the spinel crystallites and suppressed the nucleation of ~t-A1203; thus, a single phase material (except for the dispersion of platinum precipitates) was obtained. More than 1 wt% Pt was required to obtain a nanocrystalline single phase spinel material. In the platinum doped compositions crystallization occurred at the deposition temperature which was below 130°C. The as deposited films had a grain size of less than 10 nm. The relative density of the as deposited samples was determined to be 74%. Subsequent annealing procedures led to near theoretical density at temperatures above 1000°C. Some grain

LAPPALAINEN et al.:

1231

SUPERPLASTIC FLOW IN A CERAMIC 2:6 150

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Fig. 2. A TEM micrograph of a 8 wt% Pt/MgO.1.25A1203 specimen. A very uniform, and single phase spinel grain structure is obtained. The average grain size is 88 nm. growth was observed during high temperature annealing. The annealing procedure for the specimens was established to stabilize the grain size during superplastic deformation. The specimens were annealed in situ. First, they were heated to 800°C at a heating rate of 15°C/min, and then to 1100°C at 2-10°C/min. The 8 2so

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specimens were held at 1100°C for 1 h and then at the testing temperature for several hours before mechanical testing. The grain size was measured after the completion of the mechanical test from TEM micrographs. The fine grained structure of a 8 wt% Pt/MgO.xAi203 specimen is shown by the micrograph in Fig. 2. The grain size of this specimen is 88 nm. 3. RESULTS

Typical stress/strain curves for 8 wt% Pt/spinel at ll00, 1200 and 1280°C are given in Fig. 3. The present data is compared with similar results for yttria stabilized zirconia from earlier work [13], which is reproduced in Fig. 4. Both materials exhibit unusual tensile ductility despite the high value of the flow stress, which is greater than 200 MPa at 1100°C in the case of spinel. Interestingly, the strain rates in spinel are about one order of magnitude greater than in zirconia, probably because the grain size in ZrO 2 (Y203) was 100-300 nm, as compared to 38-88 nm for the MgO.1.25A1203. Two other features of these curves are special: (i) both materials show essentially no strain hardening which suggests that there is little if any dynamic grain growth during superplastic deformation, and (ii) the stress/strain curves are serrated; this, as discussed in detail in Ref. [13], is attributed to bursts of strain in superplastic deformation which have been observed in the present experiments due to the small specimen size (relative to the grain size). The non-linearity of the stress/strain rate behavior in both MgO.l.25A1203 and ZrO 2 (Y203) is shown by the data in Fig. 5. The data suggest threshold stresslike behavior. Estimates of the threshold stress are as follows: in the range 5-7 MPa for ZrO2 (2.6-8.4 mol% Y203) at 1280°C, and in the range 40-50 MPa

1232

LAPPALAINEN et al.:

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zirconia and (b) spinel showing the non-linear behavior. We interpret this non-linearity in terms of an apparent threshold stress. at 1280°C, 85-115 MPa at 1200°C, and 150-190 MPa at I100°C for MgO. (x = 0.9-1.9)A1203(3.5-8 wt% Pt). We are surprised that the apparent threshold stress is relatively independent of stoichiometry; however, this is consistent with the measurements of Chiang and Kingery [14] who found the ratio of A1/Mg in the grain boundary regions of spinels to be relatively insensitive to stoichiometry. The insensitivity of the superplastic flow parm e t e r s to the composition of the spinel is further illustrated by the data in Fig. 6 which shows the stress/strain rate data for MgO.xAl203 (3.5 wt% Pt) where x = 1.0-1.8, at 1200°C. The grain size of all these specimens was nearly the same, falling in the range 98-121 nm. The effect of grain size on flow behavior was measured by annealing samples at different temperatures above the test temperature. Figure 7 shows the results for 8 wt% Pt/MgO. 1.25A1203 with three grain sizes, 38, 70 and 90 nm, tested at 1100°C. These data suggest that the rheology does not follow Coble creep which predicts that the strain rate changes as d -3. Instead the data suggest a weaker dependence of the

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grain size, either d -j or d -2, which is expected in interface or lattice diffusion controlled creep. Platinum concentration had an anomalous effect on the flow stress. Its effect was negligible as long as the platinum content was less than 8 wt%. However, at 14 wt% the flow stress decreased by an order of magnitude, as shown by the two sets of graphs in Fig. 8 which show the difference in the stress/ strain-rate behavior, plotted here on a logarithmic scale. This effect was seen at 1200°C but not at I I00°C. The grain size differences are insignificant in comparison to the change in the flow stress, and go the wrong way since the 14% sample had the larger grain size at 1200°C. The TEM specimens for the 8 and 14% Pt samples tested at 1200°C showed the Pt precipitates to be more finely dispersed in the 14% sample. We are unable to offer an explanation for this unusual result, except to suggest that the electronic structure of interfaces in spinel may change abruptly with Pt concentration and temperature. .10-5

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LAPPALAINEN et al.:

SUPERPLASTIC FLOW IN A CERAMIC

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1234

LAPPALAINEN et al.: SUPERPLASTIC FLOW IN A CERAMIC

The activation energy for the creep mechanism was obtained by fitting the data to the equation: = .4 (an/kT) e x p ( - E / R T ) , where the strain rate and the grain size were held constant. First the strain rate and flow stress data, at a given grain size and temperature were plotted on a logarithmic plot to determine the power law exponent, n, and then data from different temperatures, but the same grain size and strain rate were plotted in the manner shown in Fig. 9 to determine the activation energy E. The results give a value E = 8 0 0 - 1 0 0 0 k J mol -~, for a wide range of Pt content. Such large values for the activation energy cannot be accounted for simply by the diffusivity of the ionic species. The high values suggest that concentration of the ionic species in the interface layer to be significantly different from the concentration within the grain interior, the two concentrations being related exponentially through an enthalpy. The measured activation energy then becomes the sum of this enthalpy and the activation barrier for ionic diffusion along the interface.

nickel the electrons are delocalized and therefore provide cohesive strength across the interface; however, the presence of sulphur localizes the electrons toward one side, thus weakening the interfacial bond [15]. Non-stoichiometric ceramics are so defined because they form charged defects more easily than do stoichiometric ceramics. Thus, it is possible that these ceramics have more complex and varied ionization states at the interface that lead to stronger electronic bonding. The presence of a net charge at the interface will create a counter charge in the adjacent lattice. This double layer may be described by a characteristic width and a potential difference between the interface and the remote grain interior. We call this potential difference the boundary double layer potential, or #b" A consequence of the electrical potential is that the chemical potential, #j, of charged species j in the material must be replaced by the electrochemical potential, rb, such that tb = #j + Z j F $ b

4. DISCUSSION Superplastic properties of magnesium aluminate spinel have been found to be similar to yttria stabilized zirconia. Both materials show an unusual resistance to intergranular cavitation, and both can be deformed to large elongations at high strain rate. Furthermore, both ZrO 2 (Y203) and MgO.xA1203 exhibit a non-linear stress/strain rate rbeology having the appearance of a threshold stress. It is interesting that both materials, although classified as structural ceramics, are highly nonstoichiometric. Functional ceramics, which are nearly always non-stoichiometric, for example, hydroxyapatite and lead-titanate, have also been shown to be highly superplastic in tensile deformation. We would like to propose that the electronic structure of grain boundaries in non-stoichiometric ceramics is the underlying cause of their unusual superplastic behavior. Next, we discuss the question of how nonstoichiometry can lead to greater intergranular cohesion, and how it can give rise to a threshold stress in diffusional deformation. Here, the measurements of the A1/Mg ratios near interfaces in spinels by Chiang and Kingery [14] provide some insight. They report an excess concentration of aluminum in the interface region. Assuming the ionization state of the aluminum and magnesium atoms to be 3 + and 2 + , Chiang and Kingery's results lead to the inference that the interfaces in spinel contain a net charge. The reasoning for a net charge at the interface does not explain why these interfaces may be mechanically stronger. The cohesive strength of interfaces can be understood from ab initio calculations of the electron structure of interfaces. In metals, this approach has successfully explained why grain boundaries in nickel are embrittled by the presence of sulphur; in pure

(1)

where Z is the charge, F the Faraday constant and Sb is the local potential. The apparent threshold stress, fro, discussed in this paper, may then be expressed in terms of Sb, as follows 0" o ~

Zj, F~kb [~j,

(2)

where j ' , refers to the charged species which control the rate of mass transport. An idea of the magnitude of ~'b is obtained by considering a threshold stress of 100 MPa. We substitute Z = 2, and use the molar volume of equimolar spinel for ~)= 0.066 nm3; this leads to Sb = 20 mV. 5. SUMMARY The main theme of this paper is that magnesium aluminate spinel displays unusual superplastic ductility. It can be deformed at very high rates and despite its high flow stress it resists intergranular fracture. In many respects, its deformation pattern is similar to that of yttria stabilized zirconia. This pattern is different from the superplasticity of ceramics, such as fl-spodumene and silicon-nitride, that contain a liquid phase at grain interfaces. While zirconia and spinel exhibit a non-linear stress/strain rate behavior and a high flow stress, liquid phase containing systems exhibit a linear stress/strain rate behavior and can be deformed only at very high temperatures where the flow stress becomes too small to nucleate cavities. The grain size dependence of the strain rate is also weaker in the zirconia and spinel systems than in the liquid phase systems. Ceramic materials are often separated into structural ceramics and functional ceramics. In general, structural ceramics are nearly stoichiometric and functional ceramics are non-stoichiometric.

LAPPALAINEN et al.: SUPERPLASTIC FLOW IN A CERAMIC The materials described here, ZrO2(Y203) and MgO.xAl203, are exceptions to these guidelines since they have structural applications but are also non-stoichiometric. We propose that their unusual superplastic behavior is related to this nonstoichiometry. In contrast, functional ceramics are often nonstoichiometric. So far, all such ceramics (examples include hydroxyapatite, lead-titanate and zinc sulphide [16]) that have been tested have been found to be easily superplastic. These results lead us to the conclusion that (i) the grain interfaces in nonstoichiometric ceramics have greater resistance to intergranular cavitation, and (ii) superplastic flow in these ceramics has the appearance of a threshold stress, and that, quite possibly, it is interface reaction controlled. In this paper we have proposed that the unusual properties of interfaces in non-stoichiometric ceramics arise from the electronic structure of these interfaces leading to a net charge. The charged double layer forms adjacent to the interface in response to this effective charge. The idea of a boundary double layer potential for solid state interfaces is introduced. It is estimated that ¢'b of few tens of millivolts can account for the measured values of the threshold stress. These concepts can be developed further both theoretically and experimentally. If correct, they point out the importance of impurities and electrical effects in influencing and controlling the basic mechanical properties of structural ceramic materials. Acknowledgements--This research has been supported by the Department of Energy under Grant No: DE-FG02-87-

ER45303. Support was also received from the National Science Foundation through the use of the facilities of the

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Materials Science Center at Comell University. Extensive use was made of the facilities of the National Nanofabrication Facility at Cornell University. This facility is supported by the NSF under Grant No: ECS-8619049. Raj wishes to thank the Max-Planck-Institut for Metallforschung in Stuttgart for hosting his visit to Germany under the sponsorship of the Alexander yon Humboldt Foundation, and Dr R. Kirchheim at that Institute for pointing out to him the importance of the electrochemical potential. REFERENCES

1. C. H. Hamilton, Proc. of the M R S Int. Meeting on Advanced Materials, Vol. 7 (edited by M. Kobayashi and F. Wakai), p. 59. MRS, Pittsburgh, Pa (1989). 2. C. C. Bampton and J. W. Edington, Metall. Trans. 13A, 1721 (1982). 3. C. C. Bampton, M. W. Mahoney, C. H. Hamilton, A. K. Ghosh and R. Raj, Metall. Trans. 14A, 1583 (1983). 4. K. R. Venkatachari and R. Raj, J, Am. Ceram. Soc. 69, 135 (1986). 5. P. Gruffel, C. Carry and A. Mocellin, Sci. Ceram. 14, 587 (1988). 6. J. Wang and R. Raj, Acta metall, mater. 39, 2909 (1991). 7. F. Wakai and H. Kato, Adv. Ceram. Mater. 3, 71 (1988). 8. F. Wakai, S. Sakaguchi and Y. Matsuno, Adv. Ceram. Mater. 1, 259 (1986). 9. F. Wakai, private communication. 10. J.-G. Wang and R. Raj, 3". Am. Ceram. Soc. 67, 399 (1984). l 1. F. Wakai, Y. Kodama, S. Sakaguchi, N. Murayama, K. Izaki and K. Nihara, Nature 344, 421 (1990). 12. F. Wakai, Y. Kodama and S. Sakaguchi, J. Am. Ceram. Soc. 73, 457 (1990). 13. R. Lappalainen and R. Raj, Acta metall, mater. 39, 3125 (1991). 14. Y.-M. Chiang and W. D. Kingery, J. Am. Ceram. 73, 1153 (1990). 15. R. P. Messmer and C. L. Briant, Acta metall. 30, 457 0982). 16. L. A. Xue and R. Raj, J. Am. Ceram. Soc. 72, 1792 (1989).