Barium oxides: equilibrium and decomposition of BaO2

Journal of Alloys and Compounds 327 (2001) 167–177

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Barium oxides: equilibrium and decomposition of BaO 2 a, b J.L. Jorda *, T.K. Jondo a

University Savoie, Laiman, 9 rue de l’ arc-en-ciel, BP240 F-74942 Annecy-Le Vieux, France b University of Benin, Lome´ , Togo Received 1 March 2001; accepted 11 April 2001

Abstract The stability and decomposition of the barium peroxide BaO 2 have been investigated by means of high temperature X-ray diffraction and differential thermal analysis coupled with thermogravimetry in argon and oxygen atmospheres. Isoconversional methods have been used to determine the activation energies. It was found that either in argon or in oxygen, the decomposition of the barium peroxide follows three different steps implying the terminal solid solutions and an invariant peritectic reaction. The phase relations between the monoxide and peroxide are presented.  2001 Elsevier Science B.V. All rights reserved. Keywords: Barium peroxide; Decomposition

1. Introduction In the past 10 years, a new interest in alkaline-earth oxides and peroxides is related to the study of hightemperature superconducting cuprates. In these complex systems the superconducting properties depend on the phase purity, on the nature of the residual impurities, on the grain-growth, grain-size and orientation . . . , and the knowledge of the path for the formation of the relevant phase is essential to obtain reproducible results after a given process. In our studies of the thallium cuprates [1–5], we have been aware of these problems and decided to reinvestigate the low-ordered systems, including some element-oxides. Amongst them barium peroxide is particularly interesting when used as a precursor in the preparation of high-temperature superconductors, due to its decreased sensitivity to atmospheric moisture compared to BaO and, moreover, because it is assumed to avoid the presence of poisoning carbon in the superconducting phases. The more recent experimental studies of the decomposition of BaO 2 are due to Mayorova et al. [6] and to Tribelhorn and Brown [7]. From combined differential thermal analysis and thermogravimetry (DTA–TG) under different oxygen pressure conditions, Mayorova confirmed that both BaO 2 and BaO are not stoichiometric oxides, *Corresponding author. E-mail address: [email protected] (J.L. Jorda).

fixing the solubility limits at BaO 1.62 for the BaO 2 phase and BaO 1.12 for the BaO phase at T51112 K and PO 2 5 1.5 atm. Taking into account these non-stoichiometries, and assuming a first-order kinetic reaction, Mayorova obtained an activation energy for the decomposition of BaO 2 , Ea 5 360620 kJ mol 21 , which is twice the value found by Tribelhorn and Brown from both isothermal and non-isothermal methods in nitrogen. From a thermodynamic viewpoint, the existence of solid solutions is well established [6,8–10] but the formation of BaO 2 from the melt is still under question. For Roth et al. [8] the phase is congruent, melting at 1073 K while Zimmermann et al. [9] in their recent assessment of the Ba–O system computed a peritectic formation: BaO(s)1 liquid→BaO 2 at 1350 K. In this paper we present results on the kinetics of decomposition of BaO 2 in argon and oxygen atmospheres. A modification of the phase equilibrium between BaO and BaO 2 is proposed.

2. Experimental The BaO 2 powder used for this work was provided by Prolabo. It is 95% pure and contains 5 mass% of BaCO 3 . Our starting material is very similar to that used by Mayorova et al. [6] whose carbonate content was 9.4(1) mass%. Kinetic studies were based on thermogravimetry, taking

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into account the amount of BaCO 3 present in the peroxide. Complete transformation from BaO 2 to BaO corresponded to 9.37% mass % losses measured in a simultaneous differential thermal analysis–thermogravimetry (DTA– TG92 from Setaram) apparatus. In order to avoid buoyancy corrections, the starting point for the weight measurement was selected at the onset of the mass-temperature deviation curve. The samples with a mass of the order of 50 mg were placed into alumina crucibles. The reference for DTA was an empty crucible. The experiments were performed in a controlled flow of 1 l / h of argon or oxygen with five heating rates: 1, 2, 6, 10, 15 and 20 K min 21 . The thermal analyses were complemented by high temperature X-ray diffraction (XRD) either in vacuum (10 22 mbar) or in 1 bar of oxygen, using an INEL arrangement. In argon, strong absorption of the X-ray beam did not allowed significant measurement due to the necessity of a long time exposure. The temperature of the furnace was increased step by step and the data were acquired during isothermal anneals for 15–30 min. The melting point of gold found at 10598C was used as calibration. Some parasitic lines due to the sensitivity of the detector were observed in the temperature range 650– 975 K, essentially when operating in vacuum. Unambiguously identified they have not been removed from the data presented in this paper.

3. Theory The theoretical support for kinetic analysis may be found in numerous reviews, for instance Mittemeijer [11], Carrasco [12], Vyazovkin and Wight [13] for more recent ones. Due to the increase of the accuracy of the mass (or heat) evolution measurements, non isothermal experiments are presently the most used methods to obtain the reaction rate (da / dt) of the decomposition of solids. This quantity is usually expressed as a product of two functions: (da / dt) 5 f(a ) ? k(T ) • f(a ) depends solely on the proportion (a ) of transformed phase and describes the kinetic model for the decomposition • k(T ), usually set as an Arrhenius-type function k(T ) 5 k 0 ? exp (2Eact /RT ) is temperature dependent and related to the frequency factor k 0 and the activation energy Eact of the transformation. The thermogravimetric curve of a DTA–TG experiment is, after transformation, a measurement of a (t), from which efficient computer programs allow the determination of the instantaneous reaction rate (da / dt). The data are then used to obtain f(a ) and Eact . In a classification of possible models for solid state reactions by Sestak and Berggren [14], it is proposed that, for the majority of processes, f(a ) 5 a n ? (1 2 a )m ? [2ln (1 2 a )] p , with at least one of

the exponents (n, m, or p) being zero. This expression is a generalisation of the well-known Johnson–Mehl–Avrami model [15] describing diffusion and nucleus growth in metals and alloys and for which n50 and m 5 1 and p 5 1 / 2. In a simplified option, with n 5 p 5 0, Phadnis and Deshpande [16] described the decomposition of CdCO 3 from a simple DTA curve. With this model, the activation energy Eact is first expressed as a function of T max and amax at the maximum rate of conversion (da / dT ) max . Then, from a plot of ln (da / dT ) vs. 1 /T plot, the ‘reaction order’ m can be determined. A refinement of Eact is then carried out in a selected temperature range. We have extended this method to TG curves for BaO 2 , in order to compare our results with those reported by Mayorova et al. [6] who assumed a reaction order m 5 1 for the decomposition of BaO 2 . However, as a general feature, heterogeneous reactions in solids are not described by a unique rate limiting process, so that m and Eact are expected to change as the reaction progresses. For this reason, isoconversional methods have been developed [17–20]. They are based on the fact that for a given a value, the reaction rate is a temperature dependent function still assumed to be of an Arrhenius type. Then Eact can be determined for each a value and, by the fit of a normalised function Y(a ) 5 C(da / dt) ? exp (Eact /RT ), the associated models can then be determined. In Table 1 we have summarised the equations used for some of the isoconversional methods employed in our study to find the activation energy for the decomposition of BaO 2 and to derive possible models. In Table 1 Ci is related to f(a ) [or g(a ) 5 eda / f(a )] and to the pre-exponential factor k 0 ; Ta is the temperature for which the proportion of the transformed phase is a, R is the ideal gas constant and b is the heating rate. Note that, except for the Friedman method which is based on the differential form of the reaction rate, all others relations are derived from integral approximations of g(a ).

4. Results and discussions

4.1. Barium carbonate impurity The barium peroxide powder used in this work contained 5 mass% of barium carbonate, not observed by XRD at room temperature, due to poor crystallisation, but clearly identified above 650 K. As a preliminary for our experiments, we first wanted to ensure that BaCO 3 does Table 1 Basic relations for isoconversional treatment of reaction kinetics Method Kissinger Friedman Ozawa Lyon

Equation

Ref.

2 a

[17] [18] [19] [20]

ln ( b /T ) 5 C3 2 Eact /RTa ln (da / dt) 5 C1 2 Eact /RTa ln b 5 C2 2 1.052Eact /RTa Eact 5 2 R[(d lnb / d1 /Ta ) 1 2Ta ]

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Fig. 1. Comparative decomposition of barium peroxide and carbonate in argon; heating rate b 56 K min 21 .

not influence the decomposition of BaO 2 . In Fig. 1 we present the comparative curves, with a heating rate of 6 K min 21 , for the decomposition in flowing argon of pure BaCO 3 and of our original BaO 2 batch. It may be observed that • the carbonate begins to decompose at 1237 K, which is also the temperature at which the crystallographic change from hexagonal to cubic-type structure occurs • the change from orthorhombic to hexagonal BaCO 3 at 1073 K may be discerned in the DTA signal of BaO 2 . It is not large enough, however, to permit quantitative analysis • decomposition of BaCO 3 is complete at 1650 K • the peroxide BaO 2 is completely decomposed at 1150 K • there is a discontinuity in the decomposition curve of BaO 2 but, as we will discuss later, it is related to the BaO 2 –BaO phase equilibrium diagram and not to the presence of barium carbonate. These observations are strong indications that BaCO 3 does not interfere with the BaO 2 decomposition. In fact the carbonate reacts with the monoxide BaO, once formed, above 1200 K and a eutectic reaction liquid→(BaO)1 (BaCO 3 ) could be unambiguously detected in argon at 1303 K in mixtures of the two components for peroxide samples with 10 mass% of BaCO 3 added. The related endotherm could not be distinguished in the DTA curve for the barium monoxide resulting from the decomposition of our BaO 2 specimen. Similar behaviour was observed in experiments carried out in flowing oxygen. As final remark concerning the decomposition of BaCO 3 we found, using the Phadnis and Deshpande method, an activation energy

EA 5 302(5) kJ mol 21 , which compares well with the 284 kJ mol 21 determined by Judd and Pope [21].

4.2. Nonisothermal decomposition of BaO2 in argon Fig. 2 shows the a (T ) curves for the decomposition of barium peroxide in argon with different heating rates b. The mass losses begin at temperatures which increase with b from T5720 K for b 51 K min 21 to T5920 K for b 520 K min 21 . For the low heating rates ( b 51 K min 21 and b 52 K min 21 ) a continuous sigmoid curve is observed. For higher values of b, a discontinuity in the a (T ) representation appears, better revealed in the plot of [ln (da / dt) vs. 1 /T ] plot in Fig. 3. This discontinuity occurring in the temperature range 900–1000 K, is not related to the change of the activation energy at 770 K observed by Tribelhorn and Brown [7] in isothermal experiments. Obviously, from results in Fig. 3 a simple mechanism cannot be expected for the decomposition of BaO 2 , but using the Phadnis–Deshpande formalism [16], the ‘reaction order’ m and Eact have been determined for each heating rate b, in regions for which ln (da / dT ) varies linearly with 1 /T. The results are summarised in Table 2 which shows that the major inconvenience of the use of a reaction order model is its limitation to a values ,50%. In addition, except for b 51 K min 21 , the ‘reaction order’ is found to decrease when the heating rate increases and, moreover, the pre-exponential factor, k 0 , which is expected to remain constant, is found to change by four orders of magnitude. The mean apparent activation energy is 120616 kJ mol 21 a much lower value than that found by Mayorova et al. [6] and Triblehorn and Brown [7] but approaches that

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Fig. 2. Decomposition of BaO 2 in flowing argon with various heating rates.

Fig. 3. Logarithmic test for the decomposition of BaO 2 in argon.

Table 2 Reaction order model for the decomposition of barium peroxide in argon

b (K min 21 )

a range

m

Eact (kJ mol 21 )

k0 (SI)

1 2 6 10 15 20

0.01–0.36 0.01–0.22 0.01–0.36 0.01–0.33 0.01–0.39 0.01–0.5

0.75 3 1.75 1.38 1.32 0.84

9460.5 13160.6 14160.8 11660.7 12360.7 11360.5

51.4 2.6310 4 1.3310 5 3.5310 3 8.9310 3 2.9310 3

estimated by the latter for the initial rate process and by earlier studies. In fact, a careful analysis of the results in Fig. 3 reveals that it is possible to distinguish three regions in the decomposition of BaO 2 which are supposed to correspond to different rate limiting mechanisms • initial stage for a (0.05, T , 775 K and E1 (130 kJ mol 21 • intermediate stage for a ,0.36, 775 K,T ,980 K depending on b, E2 (180 kJ mol 21

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• a final stage with an activation energy E3 5150 kJ mol 21 The change of the rate-limiting mechanisms as the reaction proceeds suggested the use of isoconversional analyses, which were thus undertaken on the basis of the methods described in the preceding section and for which an example is given in Fig. 4 for the generalised Kissinger (Fig. 4a) and Friedman (Fig. 4b) treatments. From the latter which represents ln (da / dt) as a function of the

171

inverse temperature for different a from 0.02 to 0.8 and all b values, very dispersed results are observed for a .0.25. The deduced activation energies from all methods are reported as a function of a in Fig. 5. The different stages suggested by the reaction order model are now clearly separated. In the initial stage, the activation energy increases from 140 to |170 kJ mol 21 indicating that the kinetics are not governed by a simple mechanism. Experiments performed in flowing argon gave 21% change of Ea which is not

Fig. 4. (a) Kissinger isoconversional analysis for BaO 2 in argon. (b) Generalised Friedmann isoconversional analysis of BaO 2 in argon. Note the disperse results corresponding to a .0.25.

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Fig. 5. Dependence on the proportion of transformed phase a of the activation energy for the decomposition of BaO 2 in argon.

expected to be due to the reverse reaction. It may be understood considering the phase diagram proposed by Zimmermann et al. [9] which shows • BaO 2 formed by peritectic reaction from BaO and the liquid • a (BaO 2 ) solid solution with phase boundaries depending on temperature. As a consequence of this a liquid phase may appear on heating at a relatively low temperature in the oxygen-rich limit. The oxygen evolved from the barium peroxide is thus related to the equilibrium between the solid and liquid phases. More precisely, the composition of the solid phase follows the solidus line, shifted towards low oxygen contents when the temperature is increased. The formation of a liquid phase could not be satisfactory observed from high-temperature XRD ought to the small quantities of liquid involved, but a tendency of the background of the diffraction pattern to be increased and shrinkage of the samples at temperatures as low as 700 K supports this assumption. The activation energy for this stage is an apparent activation energy which does not take into account the temperature dependence of the solid–liquid equilibrium (for a detailed description see, for instance, [22,23]). The compositions BaO 22x with x.0.05, from temperatures 775 K,T ,860 K for 1, b ,20 K min 21 , respectively, lie into the (BaO 2 ) solid solution. This is illustrated in Fig. 6 representing the XRD pattern of BaO 2 at 825 K in vacuum. BaO 2 is apparent (indexed diffraction lines in

the figure) with the recrystallised impurity BaCO 3 . Some of the diffraction lines due to the carbonate (the multiple peaks at 2u (28, 38 and 418) are artificially enlarged and increased by parasitic response of the detector. The decomposition does not imply crystallisation of stable or metastable BaO y phases, and may be rate-limited either by bond-breaking, vacancy formation, oxygen diffusion, molecular oxygen formation at the surface of the sample . . . . For a simple mechanism, the activation energy is expected to remain at constant value. This behaviour is found up to approximately a 50.25 (840 K,T ,953 K) with Eact 5 16864 kJ mol 21 , which compares well with 160–173 kJ mol 21 obtained by Triblehorn and Brown [7] for a values up to 0.6, i.e considerably higher than the solid solution limit, in experiments performed in N 2 with b 520 K min 21 . However, we were unable to confirm the associated three-dimensional Ginstling–Brounshtein diffusion model proposed. The range 0.25, a ,0.7 is a disturbed region assumed to be due to a change in the mechanism of decomposition, with activation energies of about 200 kJ mol 21 . This change occurs between 853 and 1053 K. It corresponds to the discontinuities observed in the [a 2 T ] or [ln (da / dt) 2 1 /T ] plots (Figs. 2 and 3) and to the endothermic reaction revealed by DTA. It may be attributed to the crossing of either a monovariant line between the (BaO 2 ) and (BaO) solid solutions or the invariant peritectic plateau. In both cases, the decomposition of the peroxide may imply simultaneous monoxide nucleation and growth and oxygen diffusion. The possibility of competitive mechanisms is a reasonable explanation for the observed

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Fig. 6. High temperature (T 5 823 K) XRD pattern of BaO 2 in vacuum. The diffraction lines of the peroxide are indexed; *, recrystallised carbonate.

behaviour. Therefore, at T5853 K for b 51 K min 21 , BaO 1.75 appears to be the maximum limit for the peroxide solid solution in argon. This non-stoichiometry of the peroxide at high temperature is in good agreement with the results of Roth et al. [8] for samples quenched in air from 953 K and with the recent structural works of VerNooy ¨ [24] and Konigstein [25] who determined for BaO 22x an oxygen deficiency up to x50.24 and x50.28, respectively. Indeed, the compositional range 0.25, a ,0.7 readily corresponds to the decomposition of BaO 2 for which Mayorova et al. [6] have estimated an activation energy of 360 kJ mol 21 for a first-order reaction rate. The final stage of the BaO 2 decomposition, for a .0.7, is characterised by an activation energy slowly increasing with a. The behaviour here is assumed to be due, as is the case in the initial stage, to a temperature dependent equilibrium of a (BaO) solid solution with the liquid. Mass losses have been measured up to a (0.9 for which the carbonate impurity changes from orthorhombic to hexagonal type structure and is dissolved in the monoxide. In Fig. 7 the diffraction pattern of a sample at 1125 K in vacuum shows pure BaO with a cubic lattice cell a5 ˚ which results more from thermal dilation than 5.590(1) A, oxygen non-stoichiometry if we refer to a value of a5 ˚ measured after cooling at 625 K, without any 5.535(2) A loss of mass. As a concluding remark for this section, it is interesting to note that only (BaO 2 ), (BaO) and recrystallized BaCO 3

have been identified by high-temperature XRD during the decomposition of the barium peroxide. Thus, as already mentioned, the formation of metastable BaO y phases is not observed when operating in argon. They have, however, been suggested by Mayorova et al. [6] and moreover, observed in an oxygen flow, after quenching from high temperature in previous experiments [26]. The high-temperature evolution of the material due to thermal expansion and / or oxygen departure has to be considered for complete analysis. For the monoxide, we pointed out the thermal expansion effect. For the peroxide, only a decrease of the c parameter of the tetragonal cell was observed at high temperature. It is a strong indication of the major effect of oxygen evolution compared to thermal expansion. For instance, for the sample at 823 K (Fig. 6), using the I4 /mmm space group [24,25] for the tetragonal-type ˚ and c56.723(9) A, ˚ structure, we found a53.808(3) A ˚ c56.822(3) A ˚ measured at compared with a53.806(1) A, ¨ 298 K. From the work of Konigstein [25], our hightemperature c value corresponds to an oxygen deficiency of 0.18 in the (BaO 22 a ) solid solution, which is precisely the value of a deduced from the a (T ) analysis in Fig. 2 for b 51 K min 21 . Such behaviour supports, at least partially, a possible decomposition via transient ‘symmetry-controlled transformations’ as proposed by de La Croix et al. [27] in a lattice-energy model for the decomposition of solids. One option of this model postulates the formation of a compressed cell of BaO 2, previous oxygen removal

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Fig. 7. XRD pattern at 1125 K. The peroxide has been completely transformed into BaO; 1, a parasitic response of the detector.

and recrystallisation unto cubic BaO, with an activation energy of 114 kJ mol 21 . As a result of the compression of the c axis, the XRD pattern is strongly modified and may induce confusion with the formation of new crystallographic structures.

4.3. Nonisothermal decomposition in oxygen Due to the possibility of reverse reaction when operating in flowing oxygen, the decomposition of BaO 2 is expected

to be different to that in inert gas, argon in this work or nitrogen in Ref. [7]. The effect of the oxygen may be observed in a (T ) curves (Fig. 8) which summarises results from Mayorova et al. [6] and this work with a heating rate b 51 K min 21 . Under a pressure of 1 atm of oxygen, for which direct comparison with Ref. [6] is possible, the two a (T ) behaviours may be practically superimposed. In addition, the large temperature range (|200 K) for the initial stage in oxygen compared to argon, is significant of the change of the mechanisms of decomposition.

Fig. 8. Effect of the oxygen pressure on the decomposition of BaO 2 with a heating rate of b 51 K min 21 .

J.L. Jorda, T.K. Jondo / Journal of Alloys and Compounds 327 (2001) 167 – 177 Table 3 Power law f(a ) 5 (1 2 a )m for the decomposition of BaO 2 in oxygen

b (K min 21 )

a range

m

Eact (kJ mol 21 )

k0 (SI)

1 2 6 10 20 30

0.54 0.2 0.2 0.23 0.13 0.37

0.1 0.37 0.32 0.6 1.2 1.2

93(1) 108(2) 128(1) 150(1) 169(8) 195(2)

1 22 210 1.2310 4 1.93 10 5 5.9310 6

In oxygen flow, BaO 2 starts to decompose at 900–950 K, a temperature approximately 200 K higher than in argon. The maximum decomposition rate is observed at |1100 K. As for experiments in argon, the product of the decomposition of BaO 2 in oxygen is, at about 1120 K, BaO 11x (0.1,x,0.3), from which stoichiometric BaO is obtained at 1350 K. Attempts to describe the decomposition by simple power law f(a ) 5 (1 2 a )m resulted in inconsistent reaction orders and activation energies dependent on the heating rate as summarised in Table 3, which shows also a limited range of linearity (represented in Table 3 by the a -range column) for a [ln (da / dt) 2 1 /T ] plot. From isoconversional methods we found, as in argon, that three stages were necessary to describe the decomposition of the barium peroxide in an oxygen flow. The corresponding activation energies deduced from Friedman, Kissinger and Ozawa treatments are reported in Fig. 9. In the first stage, up to a (0.2, which corresponds approximately to the range of linearity in a power law representation, the activation energy increases with a from 220 to 650 kJ mol 21 . In this compositional range, oxygen

175

desorption and absorption have been found to be reversible. From high-temperature XRD (Fig. 10), the highest limit for the peroxide solid solution at 1050 K is BaO 1.8 ˚ c56.69(2) A, ˚ but with lattice parameters a53.82(1) A, this limit corresponds to the monovariant equilibrium BaO 2 –BaO, the monoxide being also present in large quantities in the diffraction pattern. In our opinion, this behaviour reveals the role of the surface reactions in experiments near equilibrium conditions. From a kinetic viewpoint however, for high heating rates, the first stage of the decomposition of the peroxide in flowing oxygen occurs in the solid solution but reversibility crudely modifies the kinetic parameters. The dependence of Eact on a has been claimed to be characteristic of a process involving competitive reactions [28]. In the present case it could be due to the change of the equilibrium composition with temperature in the solid solution. In the range 0.2, a ,0.5, the monoxide is formed from complex reactions involving simultaneous melting, recrystallization and diffusion. The same arguments we gave for experiments in argon apply here and this stage of the reaction is related to the peritectic decomposition of BaO 2 at 1080 K (Fig. 10). The activation energies for this concentration range reach values of more 1 MJ mol 21 . Obviously such high activation energies reflect the importance of the solid–gas interface in the decomposition. In the present case, the oxygen environment of the sample not only favours the possibility of reversible reaction but also influences the formation of molecular oxygen from atomic species 2O→O 2 (g) at the surface of the sample. For a .0.5, nearly constant but not very accurate values for Eact were measured. Reversibility of the reaction and the influence of the decomposition of the carbonate over

Fig. 9. Activation energies from isoconversional analyses in oxygen.

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176

Fig. 10. XRD pattern of barium in oxygen. At 1050 K the two oxides coexist whereas the monoxide is observed at 1080 K.

the high-temperature range are thought to be responsible for such disperse results. In addition, we encounter here a case for which the calculated activation energy depended on the method used for the analysis: 220612 kJ mol 21 from the differential-based Friedmann method and 540690 kJ mol 21 from the Ozawa and Kissinger treatment suggesting a limited validity of the approximations usually accepted in integral methods.

4.4. Equilibrium Considering that equilibrium may be continuously accessed when operating with a low heating rate ( b 51 K min 21 ) in an oxygen atmosphere, it is possible to evaluate the thermodynamic functions relative to the (BaO 2 ) solid solution and to define the BaO 2 –BaO phase equilibrium diagram. For example the change of the standard Gibbs energy of the [O 222 ]⇔[O 22 ]11 / 2O 2 re22 22 action, in which [O 2 ] and [O ] are the activities of molecular and atomic ionic oxygen species in the peroxide solid solution (BaO 22x ), respectively, may be obtained from our data. Here x has a value similar to that of aeq obtained from thermogravimetry. The equilibrium constant of the decomposition reaction may be written K 5 ( pO 2 )1 / 2 ?[O 22 ] / [O 22 2 ] with p O 2 5 1 bar when operating in oxygen flow. If we now consider the solid solution to be regular [6,10,24] with an excess Gibbs energy of the Redlish–Kister type: G xs 5 x(1 2 x)V, we easily get the standard Gibbs energy of the solid solution 2 DG 0 /RT 5 ln K 5 [(1 2 aeq ) /aeq ] 2 1 ln [aeq /(1 2 aeq )], from which DH 0 5 121.22(5) kJ mol 21 and DS 0 5 103.32(5) 21 21 J mol K may be deduced.

In addition, for T51080 K the (BaO 22x1 ) and (BaO 11x2 ) solid solutions coexist at equilibrium with x 1 5 0.27 and x 2 50.14. The interaction parameter, V, may be calculated from the common tangent relation. We found V 521291 J mol 21 which compares well with values reported in previous works [9,10]. Finally, a careful analysis of the endothermic DTA signals, as well as the drastic changes of kinetics parameters, and the fact that the high-temperature XRD pattern never revealed the presence of the peroxide above the invariant temperature, convinces us that, in agreement with the calculated diagram of Zimmermann et al. [9], the decomposition of barium peroxide is peritectic rather than eutectic [8]. The phase equilibrium diagram in oxygen has been drawn in Fig. 11 with a peritectic temperature of 1080 K. The phase limits for the solid phases at this invariant equilibrium are BaO 1.73 and BaO 1.14 . For the monoxide solid solution our result is very similar to that of Mayorova et al. [6] for which x 2 50.89 but their extent of (BaO 22x1 ) solution is up to x 1 50.39 determined from the inflexion point, taken as monovariant equilibrium, of the x(T ) curve for (BaO x ). This explains the discrepancy with our value which was deduced from the value of a at the onset of the DTA curve.

5. Conclusion In this paper we have shown from complementary DTA–TG and high-temperature XRD that the decomposition of the barium peroxide either in argon or oxygen flows cannot be described by a simple reaction order model in all

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177

Fig. 11. Phase equilibria in the BaO–BaO 2 system (? ? ?). The a 2 T analysis (—) at a heating rate of b 51 K min 21 .

the compositional field BaO 2 –BaO. From isoconversional methods we have found three characteristic activation energies as reaction proceeds, related to the terminal solution ranges and the invariant equilibrium between BaO 2 , BaO and the liquid phase. In flowing oxygen reversibility was found to drastically change the order of magnitude of Eact compared with argon, but the steps for the decomposition remain the same. Using a low heating rate, the equilibrium state may be described. We have determined the standard Gibbs energy of the of the peroxide solid solution on the basis of a regular solution. Our kinetic and thermodynamic analyses are consistent with a peritectic decomposition of BaO 2 at 1080 K in 1 atm of oxygen.

Acknowledgements The authors want to acknowledge J.C. Marty for technical assistance. We are also grateful to CIES for financial support which allowed T.K. Jondo to visit the LAIMAN.

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