Reaction kinetics and mechanism of BaPbO
3
formation
M.C. Chang
a,∗, J.M. Wu
a, S.Y. Cheng
b, S.Y. Chen
caDepartment of Materials Science and Engineering, National Tsing Hua University, Hsinchu, Taiwan bMaterials Research Laboratories, Industrial Technology Research Institute, Chutung, Hsinchu, Taiwan
cDepartment of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan Received 8 July 1999; received in revised form 10 December 1999; accepted 15 December 1999
Abstract
The influence of starting materials on the formation of BaPbO3is studied. The reaction kinetics of perovskite BaPbO3phase formation
depends greatly on the phase of lead oxide raw materials. Kinetics of BaPbO3formation is analyzed by the Johnson–Mehl–Avrami model.
The experimental results reveals that the reaction of BaCO3–PbO2raw materials has a reaction order of n=5/2, and the reaction is controlled
by diffusion. On the other hand, in the case of BaCO3–PbO system, the reaction order n is equal to 1. The formation is controlled by the
interface reaction. In the final stage of both systems, the reaction orders are the same of about 0.5. The phases left in the final stage are BaPbO3and BaCO3. © 2000 Elsevier Science S.A. All rights reserved.
Keywords: BaPbO3; Kinetics; Perovskite; Johnson–Mehl–Avrami model
1. Introduction
The crystal structure of BaPbO3is pseudocubic perovskite at room temperature. Each cell unit contains one BaPbO3 [1]. The perovskite BaPbO3is a well-known metallic con-ducting oxide [1]. Due to its structure and high electronic conductivity, BaPbO3was used as a substrate for the depo-sition of Pb(Ni1/3Nb2/3)O3thin film by sol–gel techniques [2]. The use of BaPbO3as substrates is to provide not only the stable formation of perovskite-type Pb(Ni1/3Nb2/3)O3, but also high electronic conductivity of BaPbO3as electrode. This approach is expected to be effective in the development of other perovskite-type thin films, such as Pb(Zr,Ti)O3, (Ba,Sr)TiO3 and Pb(Mn,Nb)O3. In the past, extensive ex-perimental and theoretical investigations had been devoted to BaPb1−xBixO3, since the discovery of superconductivity in the composition range 0.055x50.30, with a maximum Tc of 12 K [3–6]. This superconducting oxide system attracts great interest because of potential applications. One tion is as stable Josephson junctions [7], another is applica-tion in new cryoelectronic devices [8–10]. However, studies of BaPbO3formation are relatively rare. Understanding the reaction kinetics and mechanism of BaPbO3formation is of great help in fabricating BaPbO3 ceramics for the
applica-∗Corresponding author.
E-mail address: 781032@mrl.itri.org.tw (M.C. Chang)
tion in thick film resistor and preparing the sputtering target for the thin film processing.
In our studies, we found that the formation of BaPbO3 depends greatly on the starting raw materials of lead ox-ides. There are two simple lead oxide forms: PbO and PbO2, where lead is di-valent and tetra-valent, respectively. A num-ber of intermediate oxides also exist in which both oxida-tion states are present together. Lead monoxide occurs in two polymorphic forms. The tetragonal form, litharge, is sta-ble up to 489◦C, the orthorhombic form, massicot, is stable above this temperature. Fig. 1 illustrates the crystal structure of litharge. The unit cell contains two PbO groups [11–13]. Massicot is metastable at room temperature [14] and trans-forms readily to litharge by mechanical forces [15,16], al-though the additions of small impurities can stabilize the massicot form and prevent its transformation to litharge at room temperature [17].
Lead dioxide is a brownish black crystalline powder which decomposes rather easily into lower oxides and oxy-gen. Lead dioxide has two crystal forms. The common form,-PbO2, the mineral plattnerite, has the rutile struc-ture which is shown in Fig. 2. The orthorhombic dioxide,
␣-PbO2, has the columbite structure, which is essentially a hexagonal close-packed assembly of oxygen ions in which one-half of the octahedral holes are occupied by lead ions. The composition of alpha and beta lead dioxide is not always stoichiometric. Density studies indicate that non-stoichiometric compositions result from the presence of 0254-0584/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved.
Fig. 1. Crystal structure of litharge.
vacancies in the crystal structure, probably in the ratio of four missing oxygen atoms to one of lead.
In the present investigation, we will report the reaction kinetics and mechanisms of BaPbO3 formation with dif-ferent raw material systems including BaCO3–PbO and BaCO3–PbO2.
2. Experimental procedures
The characteristics of the raw materials, consisting of PbO, PbO2 and BaCO3, are given in Table 1. The pow-ders of BaCO3–PbO and BaCO3–PbO2with a composition equivalent to BaPbO3were ball-milled in a polyethylene jar with ZrO2as the grinding media and alcohol solvent as the mixing agent for 20 h. After mixing and drying, samples of 0.1 g powder mixture were extracted from the 200 g batch and were subjected to heat treatment at 600–750◦C for 1 min to 3 h in Pt crucibles. Each datum appearing on the heat treatment temperature–time curves was the average of three test results. To reduce the influence of the heating and cool-ing periods of the heat treatment, the powder mixture sam-ples were put directly into a furnace kept at the preset tem-peratures. The temperature was measured with a Pt-Pt10Rh thermocouple in contact with the Pt crucible. The time was measured from the instant the powder samples reached the heat treatment temperature, which was generally of the
or-Fig. 2. Crystal structure of plattnerite.
der of 1 min. The samples were pulled out immediately after heat treatment and air-quenched.
The relative amount of the BaPbO3perovskite phase was determined by the integrated intensities of the (1 1 0) peak of the perovskite phase, the (1 0 1) peak of the litharge and the (1 1 1) peaks of the massicot and the BaCO3from X-ray powder diffraction (XRD)1 patterns of heat treated samples, as described by Klug and Alexander [18]. The percentage of formed BaPbO3 perovskite phase was calculated by the following equation:
% perovskite= 100 ×PIpero
Ii (i = appearing phases)
where Ipero and Ii represent the integrated intensities of peaks for perovskite and appearing phases, respectively. Differential thermal analysis/Thermogravimetry2 of the BaCO3–PbO and BaCO3–PbO2 mixture was conducted from 25 to 1100◦C. The heating rate was 5◦C min−1. To identify the peaks occurred in DTA analysis, powders heat treated to temperatures lower than the peak temperatures were characterized by XRD.
3. Results and discussion
3.1. DTA and TG analyses
Both DTA/TG data of BaCO3–PbO and BaCO3–PbO2 are shown in Fig. 3. In BaCO3–PbO system (Fig. 3(a)), decomposition of BaCO3starts at temperature about 800◦C where weight loss increases obviously. Endothermic peaks are found at 798 and 847◦C. To prevent the peak occurring at 847◦C, DTA was conducted from 25 to 825◦C. The powder put in the DTA crucible was identified by XRD after DTA finished the run at 825◦C. The diffraction pattern is shown in Fig. 4(a). Not only the product phase (BaPbO3) but also the raw materials (PbO and BaCO3) were found in that powder. The sample was obviously divided into two parts in color: the upper part was black and the lower part was yellow. When DTA was conducted above 850◦C, only black color appeared and pure BaPbO3was formed which is identified by XRD analysis (Fig. 4(b)). Endothermic peaks found at 798 and 847◦C are resulted from the formation of BaPbO3 phase. The double peaks are considered to be the effect of rod-shape Al2O3crucible of DTA, which derives 798◦C peak for upper part and 847◦C peak from lower part reaction. Because lead ion needs to be oxidized more in the formation of BaPbO3, the upper part of crucible is liable to get oxygen from air and presents reaction peak at lower temperature.
In BaCO3–PbO2 system (Fig. 3(b)), reaction is quite similar to that of BaCO3–PbO system when temperature is higher than 700◦C. However, the weight loss starts from lower temperature of 350◦C, which is considered to be
1 PW 1700, Philips Electronic Instruments, Eindhoven, Netherlands. 2 Model STA 409, Netzsch, Exton, PA.
Table 1
Characteristic properties of raw materials
Powder Purity (%) Particle size (m) Phase Maker
PbO 99.89 7.5 Litharge Mitsui Lot No. 30520
PbO2 >99 4.2 Plattnerite Merck Art. 7406
BaCO3 >99 1.8 Witherite Merck Art. 1714
the decomposition point of PbO2. According to Fig. 3(b), PbO2 is gradually decomposed from 350 to 600◦C. Phase change in this temperature range is identified by X-ray powder diffraction. PbO2 phase finally changes into PbO
Fig. 3. DTA/TG curves of: (a) BaCO3–PbO powder and (b) BaCO3–PbO2 powder.
Fig. 4. XRD results of the BaCO3–PbO powder mixtures which were heated in DTA and stop: (a) at 825◦C and (b) above 850◦C.
phase through PbO1.57 and Pb3O4intermediate phases. The corresponding weight loss of phase change was calculated and shown in Table 2 which confirms the phase change sequence. Weigh loss continues to increase at temperature higher than 600◦C. The BaPbO3phase is formed at temper-atures of 780 and 831◦C. This behavior is the same as that of BaCO3–PbO system. However, formation temperature of BaPbO3 phase in BaCO3–PbO2 system is a little lower than that in BaCO3–PbO system. It indicates that reaction mechanism may be different for these two systems. Since PbO2 phase has decomposed to PbO before reacting with BaCO3, the PbO phase should play a main role in the for-mation of BaPbO3phase. The only difference one can see from Fig. 3 is that the formation temperature of BaPbO3 phase in BaCO3–PbO2 system is lower. It implies that the reaction rate is a little fast in BaCO3–PbO2system.
3.2. Reaction kinetics of BaPbO3formation
The formed BaPbO3phase percentage under isothermal heat treatment is shown in Fig. 5. The duration of 0 means sample is withdrawn directly from oven when the temper-ature reaches set value. In BaCO3–PbO system, BaPbO3 phase gets 80% at 600◦C/60 min, 97% at 700◦C/20 min and higher than 97% for 750◦C/10 min (Fig. 5(a)). The forma-tion rate is faster in BaCO3–PbO2system as shown in Fig. 5(b). It took only a few minutes to obtain complete formation of BaPbO3phase at temperature higher than 650◦C. Even at 600◦C, only about 30 min was sufficient for the process. Formation rate can be obtained by differentiating the wt% of BaPbO3with time. The results are shown in Fig. 6. Reaction mechanism should be different in these two systems accord-ing to results shown in Fig. 6. Formation rate decreases with increasing time in BaCO3–PbO system (Fig. 6(a)). There are maximum formation rates (peaks) in BaCO3–PbO2 system (Fig. 6(b)). The peaks shift toward shorter time when the temperature increases. Therefore, the difference in reaction
Table 2
The reaction sequence from PbO2 to PbO
Region Reaction Weight loss (%)
(Oloss/(BaCO3+PbO2))
1 PbO2→PbO1.57 1.58
2 PbO1.57→Pb3O4 2.45
3 Pb3O4 2.45
Fig. 5. Influence of calcination time on the obtained BaPbO3 content at various temperatures in: (a) BaCO3–PbO system and (b) BaCO3–PbO2 system.
kinetics for both BaCO3–PbO and BaCO3–PbO2system is obvious.
In this investigation, the formation reaction of perovskite BaPbO3 phase is heterogeneous and raw materials are multiphases. A model used to treat multiphase reaction kinetics was derived by Johnson and Mehl [19] and by Avrami [20,21]. This model was also used to analyze the Pb[(Zn,Mg)1/3Nb2/3]O3 successfully [22]. Reaction equa-tion is presented as follows:
ln 1 1− y = (kt)n
where y is the formation content of BaPbO3 phase; k, the reaction rate constant; t, the reaction time and n, the reaction order. Relationship of ln [ln [1/(1−y)]] versus ln t is shown in Fig. 7, where two straight segments are found. The reaction is treated as a two-stage process and two different reaction kinetics are considered to be existent. Both BaCO3–PbO and BaCO3–PbO2 systems show the same trend although the slope of each line is different. Besides, the slope of each line or the reaction order n is independent of the reaction temperature. The n value for each segment is calculated and listed in Table 3. Different n values are found in Stage 1, while they are approximately the same in Stage 2.
The reaction rate constant k can be represented by equation
Fig. 6. Formation rate of BaPbO3phase as a function of temperature and time in: (a) BaCO3–PbO system and (b) BaCO3–PbO2 system.
Fig. 7. Reaction kinetics fitted by the Johnson–Mehl–Avrami equation for: (a) BaCO3–PbO system and (b) BaCO3–PbO2 system.
Table 3
Reaction order and activation energy of BaPbO3 formation
System Stage 1 Stage 2
E (kJ mol−1) n E (kJ mol−1) n BaCO3–PbO 132 1 177 0.4 BaCO3–PbO2 148 5/2 169 0.5 k = A exp −E RT
where E is the activation energy; R, the gas constant; T, the absolute temperature and A, is a constant. Curves of ln k ver-sus 1/T are plotted in Fig. 8. In the investigated temperature range, straight lines are found for both BaCO3–PbO and BaCO3–PbO2 systems. The activation energies are calcu-lated from the slopes and are shown in Table 3. The E values are higher in Stage 2 even though n values are only about 0.5 for both systems. In Stage 1, BaCO3–PbO and BaCO3–PbO2 systems have n values of 1 and 5/2, respectively. This in-dicates that the reaction mechanisms and the controlling factors are different. According to Johnson–Mehl–Avrami model, n value of 1 means that the reaction is a surface nu-cleation mode [23]. The n value of 5/2 reveals that reaction is controlled by random diffusion with constant nucleation rate after the model of Marotta and Buri [24]. Therefore, reaction kinetics for both BaCO3–PbO and BaCO3–PbO2
Fig. 8. Activation energy of BaPbO3formation in: (a) BaCO3–PbO system and (b) BaCO3–PbO2system derived by fitting to the Arrhenius equation.
systems are controlled by different mechanisms in Stage 1. The n value of 0.5 in Stage 2 explains that the reaction is bimolecular reaction control [25]. No matter what raw ma-terials used, reaction kinetics in Stage 2 are the same for both systems.
3.3. Mechanism of BaPbO3phase formation
The content of each raw material and BaPbO3 under isothermal reaction are shown for BaCO3–PbO2 system in Fig. 9, while those for BaCO3–PbO system are shown in Fig. 10. In Fig. 9(a), PbO2 has decomposed into litharge PbO phase at 600◦C. BaPbO3 phase is completely formed after 25 min soaking at 600◦C. PbO2 phase disappears through-out the reaction and should take no reaction with BaCO3 phase. This result is consistent with DTA/TG result shown in Fig. 3. Litharge PbO phase generally changes into mas-sicot phase at temperatures higher than 500◦C. However, no massicot PbO phase was found in BaCO3–PbO2system. Litharge PbO phase exists even at temperature as high as 750◦C, which is quite different from that of BaCO3–PbO system (Fig. 10). It is believed that the litharge PbO phase causes different reaction kinetics as mentioned above. Com-paring with Fig. 3(b), weight loss of BaCO3 phase occurs continuously before the formation of BaPbO3 phase. That means BaCO3 changes into BaO by releasing CO2. XRD analysis, which shows no BaO phase detected, indicates that the introduction of BaO into PbO litharge phase to form an intermediate solid solution phase (Pb,Ba)O is very possible. This may also explain why litharge PbO phase can be found
Fig. 9. The amounts of BaPbO3and raw materials as a function of time at: (a) 600◦C and (b) 750◦C in BaCO3–PbO2 system.
Fig. 10. The amounts of BaPbO3and raw materials as a function of time at: (a) 600◦C and (b) 750◦C in BaCO3–PbO system.
at high temperature. The BaPbO3 phase is nucleated from the solid solution phase through the dissolving BaO.
In BaCO3–PbO system, Fig. 10(a) shows that litharge PbO phase coexists with massicot PbO phase at 600◦C while Fig. 10(b) shows that at 750◦C litharge PbO phase changes completely into massicot PbO phase. The content of massi-cot PbO phase increases with the PbO transformation from litharge and decreases with the BaPbO3 phase formation. This explains that massicot PbO phase increases initially then decreases afterward (Fig. 10(a)). Phase transformation proceeds sharply at temperature 750◦C as seen in Fig. 10(b). According to the results, BaPbO3phase is formed by reac-tion of BaCO3and massicot PbO phase directly. No litharge solid solution was found in BaCO3–PbO system.
According to the data listed in Table 3, both BaCO3–PbO and BaCO3–PbO2 present a two-stage reaction with the same reaction order at second stage. In Stage 2, BaPbO3 and BaCO3 are main phases as shown in Figs. 9 and 10. The incorporation of BaO into BaPbO3dominates reaction in this stage. Consequently, both systems present the same behavior in Stage 2.
The overall reaction of BaPbO3phase formation can be presented as follows.
In BaCO3–PbO2system: Stage 1 (n=5/2)
BaCO3+PbO2⇒ BaPbO3+(Pb, Ba)O + CO2↑ +BaCO3 Stage 2 (n=0.5)
BaPbO3+BaCO3+(Pb, Ba)O(little)⇒ BaPbO3+CO2↑
In BaCO3–PbO system: Stage 1 (n=1)
BaCO3+PbO(m)⇒ BaPbO3+PbO(m)+CO2↑ +BaCO3 Stage 2 (n=0.4)
BaPbO3+BaCO3+PbO(m)(little)⇒ BaPbO3+CO2↑
4. Conclusions
Reaction kinetics and formation mechanisms of BaPbO3 are different in BaCO3–PbO and BaCO3–PbO2systems. The intermediate phases of solid solution litharge and massicot PbO phase play a main role in the BaPbO3 formation in BaCO3–PbO2and BaCO3–PbO systems, respectively. In the BaCO3–PbO system, surface nucleation model with reaction order n=1 and activation energy E=132 kJ mol−1was found for the first reaction stage. The diffusion controlled crys-tal growth with n=5/2 and E=148 kJ mol−1 was proposed in the first reaction stage for the BaCO3–PbO2 system. In the second reaction stage, both systems show similar reac-tion behavior and the bimolecular reacreac-tion is the dominant mechanism.
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