Solid state reaction of zirconia with carbon

Solid State Ionics 104 (1997) 109–122

Solid state reaction of zirconia with carbon Alexandre Maitre, Pierre Lefort* ´ Laboratoire de Ceramiques Nouvelles, ESA CNRS 6015, 123, Avenue Albert-Thomas, 87060 Limoges cedex, France Received 24 March 1997; accepted 15 July 1997

Abstract The solid–solid reaction between zirconia and carbon under flowing argon produces zirconium carbide via the intermediate formation of an oxycarbide ZrC 0.84 O 0.06 . In the temperature range 1623–1823 K, its final transformation into carbide is slow. The reaction producing the oxycarbide obeys the kinetic law between the degree of conversion a and time: F(a ) 5 1 2 (1 2 a )1 / 3 5 K e 2E / RT t, associated with an activation energy of 208615 kJ?mol 21 . This reaction occurs via two solid–gas reactions: ZrO 2 1 0.84 CO 5 ZrC 0.84 O 0.06 1 1.39 O 2 and 2.78 C 1 1.39 O 2 5 2.78 CO. The oxycarbide appears on the surface of the oxide whose grain shape is not modified. Keywords: Kinetics; Zirconia; Zirconium Carbide; Carbon; Synthesis

1. Introduction The most common industrial process for synthesizing zirconium carbide is the carbothermal reduction of zirconia by: ZrO 2 1 3 C 5 ZrC 1 2 CO.

(1)

It provides powders of sufficient purity for the different uses of this material, which is well known for its physical properties (high melting point: 3693 K [1], high mechanical properties: high Vickers’s hardness Hv 527 GPa [1,2] and high Young’s modulus E5355 GPa [1,3]). Zirconium carbide is used as a refractory material for crucibles [2], in the nuclear industry [4], in electric and electronic devices [5] or simply for cutting tools [2]. As a result, its sintering process has *Corresponding author.

been studied both for monolithic massive pieces [6,7] and for composites materials [8]. In fact zirconium carbide is not among the most studied materials and hardly any papers have been devoted to it during the last ten years. In particular, its synthesis following Eq. (1) is, perhaps wrongly, considered to be well known, in so far as no recent work concerns the mechanism of this reaction, whereas in fact very little information is available on this topic. The oldest papers [9–11] have shown that a cubic oxycarbide appears during the reaction under vacuum. Its lattice parameter [12–18] and its physico-chemical properties [12,15] depend on its composition. The role of carbon monoxide as a vehicle for carburizing the oxide has been evidenced by kinetical and thermodynamical studies [19,20] but the kinetics of carbothermal reduction in the most usual conditions, i.e. under inert gas without addition of carbon monoxide, have never been presented. This is the aim of the present work.

0167-2738 / 97 / $17.00  1997 Elsevier Science B.V. All rights reserved. PII S0167-2738( 97 )00398-6

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2. Thermodynamics A synthetical presentation of the phases in the system Zr / O / C, using a thermodynamical approach, consists in drawing its volatility diagram, as already published for other systems [21,22]. The equilibrium constants necessary for calculations were taken from the JANAF tables [23]. Fig. 1 presents these diagrams for two temperatures, 1600 K and 1800 K, taking the partial pressure of oxygen as a reference. They are simple because only two solid

phases and three gases are known in this system. It can be noticed that the highest equilibrium gaseous pressure reaches a value of only 10 26.352 Pa for ZrO and the stability domain of ZrC moves towards high oxygen pressures with increasing temperature. The same diagram drawn as a function of the carbon monoxide partial pressure shows (cf. Fig. 2) that a pressure lower than only 10 3.185 Pa is sufficient for obtaining the carbide at 1600 K (10 4.367 Pa at 1800 K).

Fig. 1. Volatility diagram for the system Zr / O / C at 1600 and 1800 K as a function of partial pressure of oxygen.

Fig. 2. Volatility diagram for the system Zr / O / C at 1600 K and 1800 K as a function of partial pressure of carbon monoxide.

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Table 1 Main characteristics of the powders Powder (Supplier)

Variety

Particle size (mm)

ZrO 2 (S.E.P.R) C (Prolabo)

Monoclinic

3.1

Carbon black

0.2–0.3

3. Materials and experimental procedures The main characteristics of the starting powders and their suppliers are summarized in Table 1. Particle sizes and purities are provided by the suppliers and the specific areas were measured by B.E.T. Powders were mixed in an agate mortar in small batches of 6 g following the stoichiometric proportions of Eq. (1) i.e. 77.4 wt.% of zirconia and 22.6 wt.% of carbon. After mixing, the batch was put in a vitreous carbon crucible and dipped into a furnace (V.A.S., Suresnes, France) with a graphite heating element. After degassing at 600 K, flowing argon (quality U, Prodair S.A.) was introduced (30 l?h 21 ). The heating rate was fixed at 20 K?min 21 . When the chosen temperature was reached, the sample was maintained for the required time from 30 min to 24 h. After cooling (30 K?min 21 ) the

Specific area (m 2 g 21 ) 2 35

Purity (%) 98 Ashes ,0.75

powders were analysed by X-ray diffraction (XRD)(Siemens D5000 diffractometer) to determine the phases and their lattice parameters and then observed by scanning electron microscopy (SEM) (Phillips XL 30).

4. Results

4.1. Kinetics Isotherms obtained between 1623 and 1823 K are presented in Fig. 3, showing the relative weight loss as a function of time. Each point corresponds to one test, the sample being heated only once. The curves decelerated continuously with an initial maximum rate. By the end of the reaction (Dm /m 0 ¯ 32%) the rate became very weak, particularly at the highest

Fig. 3. Reaction kinetics of ZrO 2 / C mixtures under flowing argon.

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temperatures. Even for the longest times at the maximum temperature, the measured relative weight loss Dm /m 0 never exceeds the theoretical maximum expected on the basis of Eq. (1), i.e. 35.17%, which proves that there is no significant volatile phase lost during reaction, except carbon monoxide.

4.2. Morphological observations Fig. 4 shows the aspect of starting powders of zirconia (Fig. 4a) and carbon black (Fig. 4b). Their markedly different particle sizes, allows the two powders to be easily distinguished after mixing. The aspect of the zirconia grains is not affected by their

Fig. 4. SEM micrographs of the powders of zirconia (a) and carbon (b) before reaction.

conversion into carbide during the reaction, whatever the temperature or duration. The surface of the grains remains smooth and even, the only change observed being a light sintering with the formation of some necks (Fig. 5a). The only real indicator of the reaction advancement is the progressive disappearance of the small carbon grains which vanish quite completely by the end of the reaction (Fig. 5b).

4.3. Phase analysis During the reaction, the XRD peaks of monoclinic zirconia (JCPDS file nr 37-1484) regularly decrease

Fig. 5. SEM micrographs of ZrO 2 / C mixtures partially reacted at 1733 K for 3 h with Dm /m 0 50.183 (a) and at 1693 K for 20 h with Dm /m 0 50.327 (b).

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Fig. 6. X-ray diffraction patterns of ZrO 2 / C mixtures heated at 1733 K for 0.5 h (a), 1 h (b), 3 h (c), 6 h (d) and 12 h (e) respectively.

Fig. 7. Lattice parameter of the oxycarbide product as a function of the relative weight loss in the reaction.

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till Dm /m 0 ¯ 0.32 where they completely disappear. The peaks of cubic zirconium carbide (JCPDS file nr 35-0784) are visible from the beginning of the reaction, but they are always shifted towards the large angles and they grow correlatively with the disappearance of those of zirconia, as can be seen in Fig. 6. The carbide lattice parameter at different temperatures and progress of the reaction remains constant (Fig. 7) up to Dm /m 0 ¯ 32% at a value of a ¯0.4688 nm which is markedly smaller than that of pure zirconium carbide (0.4693 nm) [24]. This is generally considered [25] as characteristic of the presence of oxygen in the carbide lattice, forming a cubic oxycarbide ZrO x C y . The constant value of the lattice parameter means that this oxycarbide, formed during the reaction, is the same from its beginning up to near its end. It is only for Dm /m 0 .32% that the lattice parameter suddenly grows towards the value corresponding to stoichiometric carbide.

reaction three phases coexist: zirconia, carbon and zirconium oxycarbide. They cannot be separated by a classical physical method. In such a case a differential oxidation of carbon and oxycarbide may be attempted, if their temperature ranges of oxidation are different [26]. Fig. 8 presents the reaction in air of a mixture previously heated at 1693 K for 20 h (Dm /m 0 ¯ 0.327) with a linear increase of temperature (180 K?h 21 ). It shows that the oxycarbide oxidation begins at around 3008C, accompanied by a weight increase, the carbon oxidation becoming predominant only after 5208C. Unfortunately, the oxycarbide oxidation leads to an oxide phase which partially retains free carbon in its structure by [27– 29]:

S

D

x ZrO x C y 1 (1 1 z) O 2 5 ZrO 2 1 y 2 z 2 ] C free 2 x 1 z 1 ] CO 2 , (2) 2

S

D

followed by the oxidation of the free carbon: 5. Discussion

C free 1 O 2 5 CO 2 .

(3)

5.1. Oxycarbide phase The obtained oxycarbide phase has a well-defined composition since its lattice parameter remains constant during almost all the reaction time. Firstly, it is interesting to determine its composition. During the

This last reaction coexists with the oxidation of the carbon remaining from the incomplete reaction (1), so that they cannot be distinguished. Hence it is impossible to determine the oxycarbide composition by this way. The only method usable without very

Fig. 8. Oxidation in air of a ZrO 2 / C mixture partially reacted at 1693 K for 20 hours.

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important means of analysis is to measure the lattice parameter of this phase and to compare it with previous results. Fig. 9 summarizes the results published by other authors. By comparing the measurements presented in Fig. 7 with those in Fig. 9, it appears that the oxycarbide obtained for Dm /m 0 , 32% has the composition ZrC 0.84 O 0.06 , and therefore corresponds to the reaction: ZrO 2 1 2.78 C 5 ZrC 0.84 O 0.06 1 1.94 CO.

(4)

Then, the rapid increase of the lattice parameter seen in Fig. 7 for Dm /m 0 .32% can be assumed to be related to the transformation of the oxycarbide into carbide according to: ZrC 0.84 O 0.06 1 0.22 C 5 ZrC 1 0.06 CO.

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considered as the result of the successive reactions (4) and (5). Nevertheless, there remains a question about the conditions of the oxycarbide formation which is not forecast by thermodynamics, that allows two hypotheses, without any respect to the reaction mechanism. Either the oxycarbide is the early product of the reaction by the direct reaction (4), or it is the result of a solid–solid reaction between the only thermodynamically stable phase ZrC, initially formed according to reaction (1), and zirconia according to: 0.22 2.78 0.26 ]] ZrO 2 1 ]] ZrC 5 ZrC 0.84 O 0.06 1 ]] CO. 3 3 3 (6)

(5)

Considering the weight loss of the overall reaction (1), the beginning of reaction (5) should correspond to a relative weight loss of 34.1 wt.%, higher than observed on the basis of the evolution of the lattice parameter (Dm /m 0 ¯32%). This can be explained by the grain size distribution of the starting zirconia, the smallest grains being converted before the biggest ones. Therefore the global reaction (1) can be

This last possibility can be dismissed because this reaction is said not to be quantitative before 16008C [15], so we must calculate the thermodynamic conditions for the existence of the oxycarbide phase ZrC 0.84 O 0.06 from the constants K1 and K7 given by the JANAF tables [21] for the equilibrium (1) and the following reaction: ZrO 2 1 2 C 5 Zr 1 2 CO,

Fig. 9. Influence of the oxygen and carbon contents in the zirconium phase on its lattice parameter.

(7)

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respectively. From a thermodynamical point of view, ZrC 0.84 O 0.06 is the sum of the three components Zr, ZrC and ZrO 2 according to: 0.13 Zr 1 0.84 ZrC 1 0.03 ZrO 2 5 ZrC 0.84 O 0.06

change of the oxide grains has been observed during the reaction. So, zirconia having a cubic structure, it is possible that mechanical stresses at the interface ZrO 2 / ZrC, inside the original zirconia grains, induce the retention of some oxygen in the lattice, minimizing the local strains, as is sometimes observed.

(8)

The corresponding equilibrium constant K4 of the reaction in Eq. (4) is then calculated by:

5.2. Kinetical exploitation

Log K4 5 Log K7 1 0.84 Log Kf(ZrC )

The only part of the kinetic study which can be exploited is that corresponding to the zirconia conversion into oxycarbide, described by Eq. (4), the number of points available being too restricted to accurately define the last stage of the reaction, above Dm /m 0 [32%. For the first reaction a degree of conversion a is defined from Dm /m 0 , the relative weight loss of the samples by:

1 0.03 Log Kf( ZrO 2 ) 2 0.06 Log Kf( CO ) , (9) where Kf (ZrC ) , Kf( ZrO 2 ) and Kf ( CO ) are the formation constants of these products. Hence, the corresponding values of the constant K5 of equilibrium (5) can be deduced by the following relation: Log K5 5 Log K1 2 Log K4 .

(Dm /m 0 ) Dm a 5 1.03]]]] 5 2.93], m0 (Dm /m 0 ) max

(10)

(11)

where Dm /m 0 is expressed in %, (Dm /m 0 ) max being the theoretical maximum weight loss for Eq. (1) (0.352) and the coefficient 1.03 representing the ratio of the theoretical weight loss in reaction (1) to that in reaction (4). Otherwise, we note that the time considered here corresponds to the temperature plateau. In so far as the reaction rate is weak for the lowest temperature, this time is a good approximation of that of the reaction. For the highest temperatures, however, the time of the reaction becomes markedly longer than that of the isothermal treatment. A more exact value is obtained by adding to the isothermal time the duration of heating and cooling between the lowest temperature (1623 K) and the considered temperature. Thus, Fig. 10 presents the kinetics of reaction (4) defined by the

Table 2 provides the useful values and the calculated partial pressure of carbon monoxide PCOe in the conditions of thermodynamical equilibrium. This shows that a very high pressure of carbon monoxide is required to make the oxycarbide stable beside the carbide. In the present conditions, PCO is always smaller than 10 4 Pa [22], the oxycarbide phase obtained is thus metastable and there is no obvious reason enabling the justification of its presence. Nevertheless, we can notice that the density of zirconium oxycarbide varies with its composition [15] and is minimal for the composition ZrO 0.03 C 0.88 close to that of our product. Now, morphological observations have evidenced that the oxycarbide appears on the original zirconia since no significant

Table 2 Thermodynamics constants of formation of ZrC, ZrO 2 , CO, Eqs. (1), (7), (4), (5) and equilibrium partial pressures of carbon monoxide for Eq. (5) T (K) 1600 1800

Kf ( ZrC ) 5.98 5.27

Kf( ZrO 2 ) 26.08 22.16

Kf ( CO ) 8.23 7.81

K1

K7 23.64

10 10 21.27

K4 29.62

10 10 26.54

K5 24.30

10 10 21.92

Pco e (Pa) 0.66

10 10 0.65

10 16 10 15.83

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Fig. 10. Kinetics of formation of oxycarbide.

couples (a, t c ), a being calculated by (11) and t c representing the corrected time in accordance with the proposed protocol. The classical direct treatment of the curves by the method of reduced time [30] shows that, for conversion degrees between 0 and 1 and temperatures between 1623 and 1803 K, each curve obeys the

same kinetic law and can be deduced from, for instance, that obtained at 1693 K, by multiplying time by a factor A (affinity coefficient) independent of a and a function of temperature only (Fig. 11). The curve for T51823 K, defined only by two points, has not been taken into account. It can be deduced that, in the explored temperature range, only

Fig. 11. Superimposition of the experimental points by affinity on time.

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one mechanism for the conversion of zirconia into zirconium oxycarbide ZrC 0.84 O 0.06 [30] is to be considered. The value of E5219619 kJ?mol 21 for the activation energy E of the reaction is calculated by plotting Log A versus 1 /T (Fig. 12).

5.3. Reaction mechanism Several data are available for outlining a reaction mechanism. The existence of two successive reactions leads at once to present a model for the first one, that is the conversion of zirconia into zirconium oxycarbide. In this model, we consider that the product appears on the surface of zirconia and does not actually modify the morphology of grains, although the volume expansion coefficient D (the ratio between the molar volumes of oxycarbide and zirconia) only reaches D 50.78. This last value is calculated from the lattice parameters of cubic zirconia (a o 50.509 nm [31]) and zirconium oxycarbide and their molar weights. In the proposed mechanism a diffusional process as a limiting step is excluded because of the shape of the kinetic curves. In these conditions, let us examine three possible hypotheses.

5.3.1. Solid–solid reaction between carbon and zirconia In this model (Fig. 13a) carbon diffuses into zirconia through direct contact points between solids, and oxycarbide is growing from these points. Nevertheless, this model is obviously incompatible with the morphological and kinetical features as the grains have not been pressed in the powder bed so that a large fraction of the carbon grains are never in contact with zirconia. As a consequence, during carbon consumption, the number of contact points should decrease very quickly, accompanied by a significant slowing down of the reaction which should be complete only with a great excess of carbon with respect to stoichiometry. Therefore this mechanism cannot be considered. 5.3.2. Solid–gas reaction with a gaseous phase ex zirconia According to the volatility diagram in Fig. 1, two gases can thermodynamically exist in the presence of zirconium carbide: metallic zirconium and zirconium monoxide. They may diffuse towards carbon and react with it as shown in Fig. 13b. But the oxycarbide phase, which is very difficult to justify if the

Fig. 12. Arrhenius diagram using the method of reduced time (s) and the function F(a ) (♦).

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Fig. 13. Schematic illustration of the possible reaction mechanisms: (a) solid–solid model; (b) with a gas ex-zirconia; (c) with a gas ex-zirconia and carbon monoxide; (d) with carbon monoxide only.

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gas is metallic zirconium, should appear on the carbon grains. That is not observed. The so-formed oxycarbide would cover the carbon grains (D ¯2.7) and the zirconia grains would slowly disappear while oxycarbide and carbide would keep the morphology of the initial carbon grains more or less sintered. All this has nothing to do with the microscopic observations of Fig. 5 and such a model is not likely.

5.3.3. Gas–gas reaction The reaction providing a gas phase issued from carbon is obviously its oxidation, providing mainly carbon monoxide in the temperature range considered. Thus, carbon monoxide may react with gaseous zirconium or zirconium monoxide according to: 1 Zr 1 CO 5 ZrC 1 ]O 2 2

5.3.4. Gas–solid reaction with a gaseous phase ex carbon In this hypothesis, carbon monoxide reacts with zirconia according to: 3 ZrO 2 1 CO 5 ZrC 1 ]O 2 . 2

(14)

Carbide is hence formed on the zirconia as observed. Instead of carbide, oxycarbide may be formed following the same reaction in the conditions explained above (see Section 5.1) by: ZrO 2 1 0.84 CO 5 ZrC 0.84 O 0.06 1 1.39 O 2 .

(15)

(12)

or ZrO 1 CO 5 ZrC 1 O 2

unlikely at the temperatures considered. This reaction mechanism is therefore rather improbable.

(13)

as illustrated in Fig. 13c. However, the product should be pure zirconium carbide, or some well-defined phase such as Ti 2 OC in the TiO 2 / C reactive system [32]. Then a secondary reaction has to be assumed between the solids ZrO 2 and ZrC but, as shown above, this reaction is

As the volume of the oxycarbide formed on the zirconia grains is much smaller than that of the oxide consumed, it can be considered that the product does not cover and protect the reagent making possible carbon monoxide to penetrate to zirconia. But, even if some atomic rearrangement or migration occurs (as attested by slight sintering), allowing oxycarbide to be covered, the reaction (15) can result from several steps such as sorption of carbon monoxide at the external surface of the oxycarbide, inwards

Fig. 14. Plots of F(a ) versus corrected reaction time for the data given in Fig. 10.

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diffusion of carbon and outwards diffusion of oxygen through the oxycarbide. Anyway, whether there is a continuous oxycarbide layer on the oxide grains or not, oxygen given off by reaction (15) diffuses in the gaseous phase towards carbon where it reacts according to: 1.39 O 2 1 2.78 C 5 2.78 CO

so-formed CO, itself giving off oxygen necessary for oxidizing carbon. Each of these reactions is certainly complex, not elementary and it is not possible to determine which is limiting. Otherwise, the opposite gaseous diffusion of oxygen and carbon monoxide has no kinetical effect.

(16)

with or without intermediate formation of carbon dioxide. The sum of Eqs. (15) and (16) actually gives Eq. (4) representative of the overall reaction. On a kinetical point of view, the classical model sometimes called ‘contracting sphere model’, describes the results from the classical equation: F(a ) 5 1 2 (1 2 a )1 / 3 5 K0 e 2E / RT t,

121

(17)

where K0 is a constant. Fig. 14 confirms that reaction (4) obeys well this equation leading to the values of 25.6 s 21 and 208615 kJ?mol 21 for the K0 factor and the activation energy respectively (Fig. 12). This last value is in good agreement with that directly obtained by the method of reduced time and very close to that of the free enthalpy of formation of the oxycarbide ZrC 0.84 O 0.06 (202 kJ?mol 21 at 1823 K [20]) but it has no significance in terms of the mechanism. The validation of this model proves that the limiting step of the reaction is located either on the surface of the grains of carbon black during their oxidation by (16) or on the zirconia grains (at the interface ZrO 2 / oxycarbide). The available results do not allow a conclusion on this point.

6. Conclusion This study allows the mechanism of the solid-state reaction between zirconia and carbon to be approached. It concerns mainly the formation of the intermediate oxycarbide ZrC 0.84 O 0.06 . The final transformation of this oxycarbide into carbide has not been elucidated. In fact, the solid–solid reaction ZrO 2 / C actually hides two solid–gas reactions which are linked together: the carbon oxidation providing CO and the carburizing of zirconia by

References [1] H. Pastor, Ind. Ceram. 709 (1977) 573. [2] L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York–London, 1971, pp. 141–184. [3] G.E. Hollox, Mater. Sci. Eng. 3 (1968) 121. [4] T. Ogawa, K. Ikawa, J. Nucl. Mater. 105 (1982) 331. [5] G. Montel, A. Lebugle, H. Pastor, Rev. Int. Htes Temp. Refract. 16 (1979) 95. [6] P. Barnier, C. Brodhag, F. Thevenot, J. Mater. Sci. 21 (1986) 2547. [7] A.G. Lanin, E.V. Marchev, S.A. Pritchin, Ceram. Int. 17 (1991) 301. [8] P. Barnier, F. Thevenot, Silicates Industriels 53 (1988) 133. [9] C.H. Prescott, J. Am. Chem. Soc. 48 (1926) 2534. [10] G.A. Meerson, G.V. Samsonov, J. Appl. Chem. USSR 25 (1952) 287. [11] V.S. Kutsev, B.F. Ormont, V.A. Epel’baum, Doklady Akad. Nauk USSR 104 (1955) 567. [12] E.K. Storms, The Refractory Carbides, Academic Press, New York, 1967, pp. 18–34. [13] V.D. Luybimov, G.P. Shveikin, Z.K. Askarova, S.I. Alyamovskii, Y.G. Zainulin, Ivz. Akad. Nauk USSR 12 (1975) 1765. [14] Y.G. Zainulin, S.I. Alyamovskii, G.P. Shveikin, P.V. Gel’d, Teplfizika Vysokikh Temperatur 9(3) (1971) 546. [15] P. Barnier, F. Thevenot, Eur. J. Solid State Inorg. Chem. 25(5–6) (1989) 495. [16] J. Hensey, J.W.S. Jones, in: Proc. of the Symposium held by the British Ceramic Research Association, Academic Press, London, 1965, p. 35. [17] K. Constant, R. Kieffer, P. Ettmayer, Monatshefte fur Chemie 106 (1975) 823. [18] S.I. Alyamovskii, Y.G. Zainulin, G.P. Schveikin, P.V. Gel’d, Russian J. Inorg. Chem. 16(1) (1971) 3. [19] A. Ouensanga, A. Pialoux, M. Dode, Rev. Int. Htes Temp. Refract. 11 (1974) 289. [20] A. Ouensanga, M. Dode, J. Nucl. Mater. 59 (1976) 49. [21] A.H. Heuer, V.L.K. Lou, J. Am. Ceram. Soc. 73(10) (1990) 2789. [22] P. Lefort, D. Tetard, P. Tristant, J. Eur. Ceram. Soc. 12 (1993) 123. [23] M.W. Chase, C.A. Davies, J.R. Donney, D.J. Frurip, R.A. McDonald, A.N. Syrerud, JANAF Thermochemical Tables, Am. Ceram. Soc. and Am. Inst. of Physics for the NBS, New York, 1986.

122

A. Maitre, P. Lefort / Solid State Ionics 104 (1997) 109 – 122

[24] A. Van Arkel, Phys. Neder. Tijd. Natuur. 4 (1924) 286. [25] F. Leprince-Ringuet, A.M. Lejus, R. Collongues, C.R. Acad. Sc. Fr. 258 (1964) 221. [26] P. Lefort, F. Marty, G. Ado, M. Billy, Rev. Chim. Min. 22 (1985) 534. [27] L.C. Dufour, J. Simon, P. Barret, C.R. Acad. Sc. Fr. 265 (1967) 71. [28] G.A. Ramao Rao, V. Venugupal, J. Alloys Comp. 206 (1994) 237.

[29] S. Shimada, T. Ishii, J. Am. Ceram. Soc. 73(10) (1990) 2804. [30] P. Barret, in: Techniques de l’ingenieur, Vol. J-1161, pp. 18–19. [31] J. Katz, J. Am. Ceram. Soc. 54 (1971) 531. [32] P. Tristant, P. Lefort, J. Alloys Comp. 196 (1993) 137.