Phase transformation, reaction kinetics and microwave
characteristics of Bi
2
O
3
–ZnO–Nb
2
O
5
ceramics
San-Yuan Chen
a,*, Shinn-Yih Lee
b, Yih-Jaw Lin
aaDepartment of Materials Science and Engineering, National Chiao-Tung University, Hsinchu, 300, Taiwan, ROC bDepartment of Ceramic and Material Science, National Lien-Ho Institute of Technology, 1 Lien-Kung, Kung-Ching Li,
Miao Li, Taiwan, ROC
Received 28 December 2001; received in revised form 4 June 2002; accepted 16 June 2002
Abstract
Oxide powders of Bi2O3, ZnO and Nb2O5were used to investigate the phase transformation, reaction kinetics and microwave
properties of both Bi2(Zn1/3Nb2/3)2O7 and (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7 phases in the Bi2O3–ZnO–Nb2O5 system. Kinetic studies
indicate that the formation mechanism of Bi2(Zn1/3Nb2/3)2O7phase belongs to diffusion controlled reaction with a zero nucleation
rate. In contrast, (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7phase was interpreted as diffusion controlled reaction with a constant nucleation rate
with either Bi5Nb3O15or BiNbO4phases as the nuclei. Furthermore, a lower activation energy and formation temperature were
observed in the (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7than Bi2(Zn1/3Nb2/3)2O7phase. Additionally, the (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7phase
exhi-bits a higher dielectric constant but a lower Q value as compared with Bi2(Zn1/3Nb2/3)2O7phase.
#2002 Elsevier Science Ltd. All rights reserved.
Keywords:Bi2O3–ZnO–Nb2O5; Microwave characteristics; Phase transformation; Reaction kinetics
1. Introduction
Mobile radio communication networks have been greatly expanded by portable and automobile tele-phones.1,2 The development of multilayer devices for
microwave applications has received wide attraction since these multilayer devices have unique character-istics of smaller size and high volume efficiency.3,4
Although the techniques for the multilayer capacitors have been well developed in the past few years,5 the
requirement in either materials or internal electrodes is more important and urgent. In order to reduce the tan-gent loss, the electrodes with higher conductivity such as silver have to be used in the co-firing process. Therefore, it is imperative to lower the sintering temperature of microwave ceramics in order to co-fire with low loss conductors below 1000C.
Recently, Bi2O3–ZnO–Nb2O5(hereafter designated as
BZN) system has received wide attraction since it does present relatively low sintering temperature (less than
1000C) and excellent microwave properties.69Yan et
al. revealed that these materials based on Bi2(ZnNb2)O9
and Bi3(Ni2Nb)O9 system, when sintered at the
tem-peratures ranging from 880 to 920 C, show large
dielectric constant of 80 to 100, smaller temperature coefficients of < 20106/C, and relatively large Q
values of 2000 to 3000 in the 100 kHz to 3 MHz.7
Swartz et al. disclosed that there are two distinct crys-talline phases with nominal stoichiometries of Bi2(Zn1/3
Nb2/3)2O7 and Bi4/3(Zn2/3Nb4/3)O6 in BZN ceramic.9
Both phases are pyrochlore structure which is one of the oxygen octahedron based families with the general for-mula written as A2B2O7. The A cations are eight
coor-dinated and the B cations are six-coorcoor-dinated.10,11
Bi2(Zn1/3Nb2/3)2O7 (termed as O–BZN) belongs to an
orthorhombic pyrochlore.12On the other hand,
accord-ing to XRD patterns (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7(termed
as C–BZN) instead of Bi4/3(Zn2/3Nb4/3)O6composition
was indexed as a typical pyrochlore with a face-centered cubic cell. The relationship between Bi2(Zn1/3Nb2/3)2O7
and (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7can be indicated using a
common chemical formula.12
Bi3xZn23x
ð ÞðZnxNb2xÞO7 ð0:5 4 x 4 0:66Þ
0955-2219/03/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. P I I : S 0 9 5 5 - 2 2 1 9 ( 0 2 ) 0 0 1 9 9 - 1
www.elsevier.com/locate/jeurceramsoc
* Corresponding author: Fax: +886-3-5725490. E-mail address:sychen@cc.nctu.edu.tw (S.-Y. Chen).
When the x is equal to 0.5, the structure formed is close related to cubic pyrochlore. When x is equal to 0.66, the structure with orthorhombic pyrochlore phase formed. Further, a mixture of orthorhombic and cubic pyrochlores exists in the compositions with x in between 0.5 and 0.66. The related microwave properties of orthorhombic and cubic pyrochlores phases are er 80,
te +200 ppm/C, tand < 0.0002 and er 145, te
360 ppm/C, tand < 0.0002 (100 kHz), respectively.9
Thus, it is possible to control the temperature compen-sation of the dielectric permittivity by adjusting the ratio of positive-te O–BZN and negative-te C–BZN
phases by modifying Bi2O3 content and sintering
con-ditions. However, The undesirable Bi–Nb oxide phases such as BiNbO4and Bi5Nb3O15will be produced during
calcination and makes it difficult to control the ratio of O–BZN and C–BZN phases, which further leads to inferior microwave dielectric behavior. The control in the composition and calcinations temperature plays a very important role in the phase reaction and micro-wave properties.68Therefore, it is imperative to
under-stand the role of Bi-Nb oxide phases in the formation of O–BZN and C–BZN phases. Consequently, the BZN compositions corresponding to orthorhombic Bi2(Zn1/ 3Nb2/3)2O7and cubic (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7 phases
were studied in this work. The formation mechanism and reaction kinetics for both pyrochlore phases will be investigated. A possible reaction mechanism is proposed and discussed in this paper. Furthermore, the relation-ship between the sintering density and microwave properties of BZN ceramics is also presented.
2. Experimental procedure 2.1. Sample preparation
High-purity (more than 99.5%) Bi2O3(R.D.H.,
Ger-many, 1.15 mm), ZnO (Merck 8849 GerGer-many, 1.67 mnd Nb2O5(Mitsui, Japan, 0.95 mm) powders were used to
prepare xBi2O3–ZnO–Nb2O5(0.784x42) multiple-oxide
ceramic systems by a conventional powder-processing technique. Two major compositions—Bi2(Zn1/3Nb2/3)2O7
and (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7—were mainly used in
this work. The weighed oxides in accordance with the compositions were mixed in deionized water with ZrO2
as milling media in polyethylene container. A fixed amount of 1 gm powder sample, extracted from the 100 gm batch, was subjected to calcination at 400–1000Cfor 1 min to 4 h. Each datum appearing on
the calcination temperature/time curves was the average of three test results. The deviation of the data was around 5%. To reduce the influence of heating up and cooling down, calcination was conducted by directly putting the mixture sample into a furnace kept at preset temperatures. The time was measured from the instant
the powder samples reached the preset temperatures, which was generally of the order of 1 min. The samples were pulled out immediately after heat treatment and air-quenched.
2.2. Characterization and microstructure analysis X-ray diffractometer (XRD) was used to determine crystal structure. To study the formation mechanism and reaction kinetics, the relative percentage of the formed phase was calculated according to the equation, Pð%Þ ¼100 Ii
Iiði ¼appearing phasesÞ
ð1Þ
where Iiand Ii represent the individual and summary
integrated intensities of the strongest diffraction peaks of the appearing phases according to ASTM JCPDS, respectively. For example, the (222) and (220) peaks were the strongest peaks in the cubic and orthorhombic pyrochlore phases, respectively. Differential thermal analysis (DTA) was also used to study the possible reactions with a heating rate of 10 C/min. Dielectric
characteristics at microwave frequencies were measured by Hakki and Coleman’s dielectric resonator method,13
as modified and improved by Courtney.14 A
cylin-drically shaped dielectric resonator was positioned between two brass plates. An HP8722D network analy-zer was used for the microwave measurements at 3 GHz.
3. Results and discussion
3.1. Crystal structures and phase evolution
In the Bi2O3–ZnO–Nb2O5 (BZN) system, it was
reported that bismuth content exhibits a strong effect on the formation of pyrochlore phases.12 Five
composi-tions were used in this work as shown in Table 1 where BN1, BN2, BN3, O–BZN and C–BZN are representative of Bi1.7Nb0.3O3.3, Bi5Nb3O15, BiNbO4, orthorhombic
Bi2(Zn1/3Nb2/3)2O7 and cubic (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7
phases, respectively. The ratio of ZnO/Nb2O5was fixed
with changing Bi2O3from 2 to 0.78 in the xBi2O3–ZnO–
Nb2O5 compositions and labeled with A1 to A5,
respectively. Typical XRD patterns of BZN ceramics sintered at 1000 Cfor 1 h were shown in Fig. 1. A
typical orthorhombic Bi2(Zn1/3Nb2/3)2O7 pyrochlore
phase was observed for A2 (1.5 Bi2O3–ZnO–Nb2O5)
composition. If excess Bi2O3 was used in the Bi2O3–
ZnO–Nb2O5system, it was found that not only O–BZN
but also BN2 phases are always observed in the A1 (2Bi2O3–ZnO–Nb2O5) composition. The XRD patterns
in Fig. 1 show that the A3 (1.25 Bi2O3–ZnO–Nb2O5)
O–BZN and cubic C–BZN pyrochlores. With decreas-ing Bi2O3content, the A4 (1 Bi2O3–ZnO–Nb2O5)
com-position tends to form C–BZN. As the Bi2O3content is
further reduced, the Bi2O3-deficient composition such as
A5 (0.78Bi2O3–ZnO–Nb2O5) leads to the formation of a
residual phase ZnNb2O6phase as shown in Fig. 1.
The phase evolution of xBi2O3–ZnO–Nb2O5
compo-sitions with annealing temperatures at 500–900 Cis
summarized in Table 1. At 500C, the BN1 phase was
always first formed irrespective of compositions according to the report of JCPD.15 With raising
tem-perature to 600C, the BN2 phase was subsequently
developed. However, the formation and the stability of BN2 phase are found dependent on the bismuth con-tent. The BN2 phase is always observed along with the formation of O–BZN phase in the bismuth-rich BZN composition such as A1.
For A2 composition, the phase evolution with annealing temperatures was shown in Fig. 2. The XRD patterns indicate that the BN1 phase first develops at the lower temperature below 500 C. With increasing
annealing temperature, the BN1phase gradually dis-appears along with the formation of BN2 phase at 600C. At 750C,the BN3 phase starts to form. Above
800C, the O–BZN phase develops. This indicates that
the formation of O–BZN phase was probably inter-related with the simultaneous existence of BN2 and BN3 phases.
As the Bi2O3 content was further reduced from
Bi2(Zn1/3Nb2/3)2O7 composition, i.e., A3, it was
observed that the phase evolution is more complex. Below 700 C, both BN1 and BN2 phase could be
detected in A3 composition. At 750 C, C–BZN phase
starts to form and BN3 phase is developed, indicating that C–BZN phase is possibly transformed from the mixture phases of BN1 and BN2. Subsequently, at 800 C, the peaks for O–BZN phase are identified. It
reveals that C–BZN phase is more easily developed at
Table 1
Phase evolution of xBi2O3–ZnO–Nb2O5 compositions annealed at various temperatures for 1 h
Composition x 500C600C700C750C800C900C 2 A1 BN1 BN1 BN1 BN1 BN2 BN2 BN2 BN2 O–BZN O–BZN BN3 1.5 A2 BN1 BN1 BN1 BN1 BN2 O–BZN BN2 BN2 BN2 BN3 O–BZN 1.25 A3 BN1 BN1 BN1 BN2 BN2 O–BZN BN2 BN2 BN3 BN3 C–BZN C–BZN C–BZN O–BZN 1 A4 BN1 BN1 BN1 BN2 BN3 C–BZN BN2 BN2 BN3 C–BZN C–BZN 0.78 A5 BN1 BN1 BN1 BN2 BN3 BN3 BN2 BN3 C–BZN C–BZN BN3 C–BZN BN1: Bi1.7Nb0.3O3.3; BN2: Bi5Nb3O1.5; BN3: BiNbO4. O–BZN: orthohombic pyrochiore phase. C–BZN: cubic pyrochotre phase.
Fig. 1. XRD patterns for xBi2O3–ZnO–Nb2O5system with x=0.78– 2.0 compositions annealed at 1000Cfor 1 h; BN2: Bi
5Nb3O15, BN3: BiNbO4; ZN: ZnNb2O6, O: O–BZN, C: C–BZN.
Fig. 2. XRD patterns for O–BZN phase evolution with annealing temperatures.
lower temperature than O–BZN phase. At 900C, even
though both BN2 and BN3 phases disappear, both O– and C–BZN pyrochlore phases remain stable.
For the (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7 composition (A4),
the XRD patterns in Fig. 3 show that at 500 C, only
BN1 intermediate phase was identified and followed by BN2 phase formation at 600C. As the A4 composition
was annealed at 750C, C–BZN phase starts to form.
At 800 C, in contrast to A3 composition, no O–BZN
phase was detectable but only C–BZN phase with smaller BN3 amount was produced. However, we also found that the BN3 phase can be further reduced with increasing sintering temperature. As the Bi2O3 content
was further decreased, although the A5 composition shows the same phase transitions as the A4composition, a single pure C–BZN phase cannot be formed even annealed at higher temperatures.
The Bi–Nb intermediate oxide phases (BN1, BN2 or BN3) depend on the bismuth content in Bi2O3–ZnO–
Nb2O5 composition, which would influence the
sub-sequent formation of pyrochlore phase type; O–BZN or C–BZN. The detailed formation mechanism and domi-nant intermediate phase for O–BZN or C–BZN phases would be discussed in the following.
3.2. Formation mechanism of C–BZN and O–BZN phases
In order to investigate the formation mechanisms for both Bi2(Zn1/3Nb2/3)2O7 (O–BZN) and (Bi1.5Zn0.5)
(Zn0.5Nb1.5)O7(C–BZN) phases, the relative percentage
of formed phases as a function of isothermal soaking time was determined based on the Eq. (1) as shown in Figs. 4 and 5. Fig. 4(a) and (b) shows the relationship between the formed percentage of individual phase and the soaking time at 750Cand 800Cfor A4
composi-tion, respectively. Fig. 4(a) illustrates that, at 750 C,
only both BN1 and BN2 phases can be detected in a very short time, i.e., 2 min. With increasing soak time, the BN1 phase gradually disappears but the amount of the BN2 increases up to a maximum at around 25 min, at which C–BZN phase starts to develop but BN2 phase presents a rapid decrease. We also observe that BN3 phase initiates at about 10 min and then increases with increasing soaking time. This observation might suggest that the BN2 phase has played an important role in the early reaction stage of C–BZN phase formation.
As the annealing temperature increases up to 800C,
as shown in Fig. 4(b), it was found that not only BN1 and BN2 phases but also BN3 phase have already formed in a very short time, i.e. 2 min. However, after soaked more than 10 min, a rapid decrease of BN2 phase is accompanied by the continuous formation of both BN3 and C–BZN phases, indicating that the latter two phases are probably evolved from the former phase. Apparently, in the early stage, the formation of C–BZN is major due to direct evolution from BN2 phase. However, it was noted that after 15 min, although the BN2 phase nearly disappears, the detected amount of
Fig. 3. XRD patterns for C–BZN phase evolution with annealing temperatures. (N: Nb2O5; B: Bi2O3, Z: ZnO).
Fig. 4. Relationship between soaking time and intermediate phase content for A4 composition annealed at (a) 750Cand (b) 800C.
C–BZN phase presents a continuous increasing but the BN3 phase rapidly decreases. The phenomenon reveals that the phase formation of C–BZN could be possibly contributed from BN3 phase. Interestingly, it was found that the transition occurs at 50 65% C–BZN phase content. These results indicate that both BN2 and BN3 phases play equally important roles in C–BZN phase formation. Obviously, the formation of C–BZN phase is dominated by BN2 and BN3 phase at the earlier and later stages, respectively.
On the other hand, the phase evolution of A2 compo-sition shown in Fig. 5(a) indicates that the phase for-mation of BN2 is always accompanied by the reduction of BN1 phase at 750C. Even soaked at a longer time,
i.e., 240 min, only the BN2 phase is detected. Obviously, the annealing temperature of 750Cis not high enough
for promoting the formation of O–BZN phase. At 800 C[Fig. 5(b)], both BN2 and BN3 phases can be
detected in a very short time. The former phase gradu-ally diminished with soaking time but the latter phase reversed. Prior to 10 min, the XRD pattern shows no O–BZN phase, indicating that an incubation time was apparently required for O–BZN phase formation. After 25 min, a rapid increase of O–BZN phase is observed and accompanied with the rapid decrease of BN2 and BN3 phases. These observations might reveal that there
exists a close relationship between BN2/BN3 and O–BZN phases. It can be concluded that both BN2 and BN3 phase instead of either BN2 or BN3 phases as in the case of C–BZN mainly dominate the formation of O–BZN phase.
Even though the chemical reactions for the formation of both C–BZN and O–BZN phases have been reported by Wang et al.12both detailed reaction mechanisms and
the role of Bi-Nb oxides in the pyrochlore formation of C–BZN and O–BZN phases have not been thoroughly studied. According to our results in Table 1, it shows that the type of pyrochlore phase formation, i.e., O–BZN or C–BZN, is strongly dependent on Bi2O3
content in the Bi2O3–ZnO–Nb2O5system and the
reac-tion mechanisms should be different for these pyro-chlore phases. Additionally, Figs. 4 and 5 reveal that the intermediate Bi–Nb–O oxides to dominate the type of pyrochlore phase are also different. As shown in Fig. 4(a), the C–BZN phase can be developed from the BN2 phase without the presence of BN3 phase. How-ever, in the later stage of C–BZN phase formation, although the BN2 phase has exhausted out, the C–BZN phase can be still produced in the presence of BN3 phase. Therefore, it can be postulated that either BN2 or BN3 phases dominate the formation of C–BZN phase. On the other hand, for the phase formation of O–BZN, Fig. 5(a) illustrates that although the BN2 has been formed, no detectable O–BZN phase can be observed even annealing the powder sample at 750 C
for a longer time. However, at 800C, with the presence
of both BN2 and BN3 phases, the O–BZN phase can be developed, indicating that both BN2 and BN3 are simultaneously required for O–BZN phase formation. Therefore, both phase formation mechanisms of (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7(C–BZN) and Bi2(Zn1/3Nb2/3)2
O7(O–BZN) can be summarized as follows:
(a) (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7 (C–BZN) pyrochlore
phase: 5Bi2O3+Nb2O5!6Bi1.7Nb0.33O3.3 400C < T < 600 3Bi1.7Nb0.33O3.3+Nb2O5!Bi5Nb3O15 600C < T < 750C Bi5Nb3O15+Nb2O5!5BiNbO4 750C < T < 800C Bi5Nb3O15+2ZnO!2Cub.(Bi1.5Zn0.5)(Zn0.5Nb1.5)O7+Bi2O3 750C < T < 800C or 3 2BiNbO4+ZnO!Cub.(Bi1.5Zn0.5)(Zn0.5Nb1.5)O7 800C < T < 850C
(b) Bi2(Zn1/3Nb2/3)2O7(O–BZN) pyrochlore phase:
5Bi2O3+Nb2O5!6Bi1.7Nb0.33O3.3 400C < T < 600C 3Bi1.7Nb0.33O3.3+Nb2O5!Bi5Nb3O15 600C < T < 750C Bi5Nb3O15+Nb2O5!5BiNbO4 750C < T < 850C Bi5Nb3O15+BiNbO4+2ZnO!3Bi2(Zn2=3Nb4=3)O7
800C < T < 900C Fig. 5. Relationship between soaking time and intermediate phase
3.3. Reaction kinetics of C–BZN and O–BZN phaseformation
The relative percentage of formed (Bi1.5Zn0.5)
(Zn0.5Nb1.5)O7 (C–BZN) and Bi2(Zn1/3Nb2/3)2O7
(O–BZN) phases under isothermal heat treatment was calculated according to the Eq. (1). Fig. 6 shows that a sigmoid shape, which signifies the existence of an incu-bation time before a measurable phase, characterizes the solid-state reaction of pyrochlore phases. The results indicate that the reaction is a diffusion-controlled mechanism and minimum activation energy is required. It can be seen that the formed pyrochlore content increases with increasing temperature and soaking duration. From Fig. 6(a), as corresponding to afore-mentioned results, the C–BZN phase begins to develop at 750Cafter 25-min incubation. When the calcinaton
temperature was raised to 800 C, the required
incu-bation is very short about 1 2 min, and a complete formation of C–BZN phase required 50 60 min. For a higher calcination temperature, i.e., 850C, it took only
25 min to obtain a maximum content of C–BZN phase. In the other case of O–BZN phase formation, as shown in Fig. 6(b), the starting temperature of O–BZN phase formation is about 800C, which is slight higher
than that of C–BZN phase. An incubation time was still required to nucleate the O–BZN phase embryos. It was
found that the formation rate of O–BZN phase, if based on the same annealing temperature, is slower than that of C–BZN phase. It took more than 100 120 min. to reach a maximum content at 850C. These results
indi-cate that reaction kinetics between C–BZN phase and O–BZN phase formation should be different.
Referring to the DTA results of Fig. 7, it can be observed that the reaction for C–BZN phase is more complex than O–BZN phase. Two smaller exothermic reaction peaks around 700–800Cwere observed in the
(Bi1.5Zn0.5)(Zn0.5Nb1.5)O7(A4) composition for C–BZN
phase formation. Those peaks may be corresponding to the formation of BN3 and Zn-rich C–BZN phases as evidenced from Fig. 4(b). The formation of both BN3 and C–BZN phases was accompanied with the rapid decrease of BN2 due to its reaction with ZnO after a longer soaking time at 750C.
Since the used materials are multiphase, the formation reaction of either C–BZN or O–BZN phase belongs to heterogeneous system. A model used to treat multiphase reaction kinetics was derived by Johnson and Mehl16
and by Avrami17as follows:
ln 1=ð1 yÞ½ ¼ðktÞn
where y is the formation content of BZN pyrochlore phase, k the reaction rate constant, t the reaction time and n the reaction order. This model has been widely and successfully used in multiphase systems for analysis of reaction kinetics.18,19 Further calculation from the
data shown in Fig. 6 can be replotted as ln{ln[1/(1y)]} vs. ln (t) for both C–BZN and O–BZN phase systems, as shown in Fig. 8(a) and (b), respectively. Noted that as the samples were annealed at a lower temperature below 800C, two straight segments can be observed because
of slower reaction kinetics, which can be treated as a two-stage process in the formation of BZN pyrochlore phase. Since the reaction in stage 2 plays a less
impor-Fig. 7. DTA curves of both A2 and A4compositions at a heating rate of 10C/min.
Fig. 6. Isothermal transformation kinetics of (a) A4 and (b) A2com-positions annealed at various temperatures.
tant role, the reaction kinetics occurring in stage 1 will be focused. In this stage, the reaction orders (n values) are 2.47 and 1.65 for C–BZN and O–BZN phase for-mation, respectively. This indicates that the reaction mechanisms and the controlling factors are different.
According to Johnson–Mehl–Avrami model, the n value around 2.5 for the reaction of C–BZN phase pre-sents diffusion controlled growth with constant nuclea-tion rate.17,2022From Fig. 4, it can be observed that the
C–BZN phase formation is not only going through BN2 transition, but also the BN3 phase also makes con-tributions on the C–BZN phase formation. Further-more, as mentioned above, BN3 phase formation possibly results from the transformation of BN2 phase. This fact again demonstrates that BN2 and BN3 phases play an important role in C–BZN phase formation during the calcination. Therefore, a heterogeneous nucleation was promoted since more than these two phases exist in the (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7
composi-tion. Consequently, the formation reaction in the C–BZN phase can be considered as diffusion controlled process with constant nucleation rate.
On the other hand, the n value of 1.5 reveals that the reaction of O–BZN phase is possibly diffusion con-trolled process with zero nucleation rate. This formation behavior of O–BZN phase can be reasonably explained
with the Fig. 5(a) as one can see. Without the BN3 phase, although BN2 phase has been formed, the O–BZN phase can not be produced. In other words, the O–BZN phase formation can be interpreted as due to the simultaneous contribution from the reaction of BN2 and BN3 phases. Therefore, the provided nuclei for O–BZN phase are limited prior to the formation of O–BZN. Consequently, the reaction formation of O–BZN phase could be thought as diffusion controlled process with zero nucleation rates.
The temperature dependence of reaction rate constant kcan be represented by the Arrhenius equation, i.e., k /exp(–Q/RT), where the activation energy (Q) can be obtained from the curve of ln k vs. 1/T. The activation energy (Q= 450 kJ/mol) of C–BZN phase is smaller than that (Q= 602 kJ/mol) of O–BZN phase. This could be confirmed by firing the A2 composition at higher temperature more than 1100 C. The
composi-tion should be corresponding to the formacomposi-tion of O–BZN phase as annealed at 800–850 C. However, it
was found that a mixture of O–BZN and C–BZN pha-ses was detected instead of single O–BZN phase. Once the cubic pyrochlore forms, the transformation of the cubic phase (C–BZN) to pseudo-tetragonal phase (O– BZN) cannot be triggered by heating at lower tempera-ture. The phenomenon suggests that higher activation energy is possible related to crystal structure. Since A sites in the A2B2O7as in Bi2(Zn1/3Nb2/3)2O7pyrochlore
structure are occupied by Bi3+ ions only, the 6s2lone
pair electrons would lead to the distortion of the cell. Therefore, larger activation energy was required for the formation of distorted orthorhombic (O–BZN) phase as compared to cubic C–BZN phase.
3.4. Characteristics and microwave properties
As mentioned before, in Bi2O3–ZnO–Nb2O5 (BZN)
system, it was reported that bismuth content exhibits a great effect on the pyrochlore phase formed. Therefore, the effect of bismuth content on characteristics and microwave properties of BZN ceramics will be further studied to elucidate the role of crystal structure. For comparison, BZN ceramics were sintered at 1000 C
for 1 h. Based on the crystal structure and lattice parameters of BZN phase, the calculated densities were 7.11g and 7.94 g/cm3for C–BZN and O–BZN phases,
respectively.12 Fig. 9 shows that the bulk density of
6.79 g/cm3 for A4 (x=1 in the xBi
2O3–ZnO–Nb2O5
system) composition with single C–BZN phase corre-sponds to the theoretical density of 95.5%. Similarly, under the same sintering condition, A2 (x =1.5) composition with single O–BZN phase gives a bulk density of 7.71 that is about 97.1% theoretical density. The C–BZN or O–BZN phase content in Fig. 9 was calculated based on Eq. (1). The reduction of C–BZN phase content in A5 composition (x=0.78) as
com-Fig. 8. Johnson–Mehl–Avrami plots of the kinetic data for (a) C– BZN and (b) O–BZN phase formation.
pared to A4 composition (x=1) is probably due to ZnNb2O6 phase formation as evidenced from Fig. 1.
Similarly, for the BZN composition with x=2 (A1), the decreased amount of O–BZN phase is partially attributed to the forming of BZN-containing Bi2O3
phase, which is very close to BN2 phase. However, the increase in bulk density was obviously related to BZN Bi2O3-containing BZN phase since Bi2O3 like PbO is
well known to have a lower melting point, which in turn enhances sintering densification, and therefore, a higher density was easily obtained in the bismuth-rich composition. Therefore, as the Bi2O3content increased
from x=1.0 to 1.5, the formed O–BZN phase content makes a jump increase and the bulk density was also enhanced.
Fig. 10 illustrates that C–BZN phase always exhibits a higher dielectric constant than O–BZN phase. This might be related to O–BZN crystal structure, as men-tioned previously, O–BZN phase belongs to a distorted orthorhombic structure. The smaller dielectric constant in O–BZN phase may be attributed to the more dis-torted nature, which generally suppresses the
polariz-ability of ions with increasing the distortion. Therefore, a sharp decrease in dielectric constant corresponding to the phase transition from C–BZN to O–BZN phase is observed. The decrease of dielectric constant in A5 than A4 can be reasonably explained with the formation of ZnNb2O6 phase, in which the dielectric constant is
about 25 and much smaller than C–BZN phase.23 On
the other hand, as compared with A2 composition, the slight increase in dielectric constant in A1 composition can be attributed to its higher bulk density. From Fig. 10, it can be observed that Q values were strongly interrelated with phase structure existed in the compo-sitions. The O–BZN phase gives a larger Q values than C–BZN phase. However, as the composition contains a second phase, the Q value was much reduced. There-fore, even though A1 composition (x=2) has a higher bulk density, the Q value becomes smaller than that of A2 (x=1.5) composition due to the existence of Bi2O3
-containing Bi2O3BZN phase.
4. Conclusions
Some conclusions were drawn from the study of phase transformation and reaction kinetics in the Bi2O3–ZnO–
Nb2O5(BZN) system especially on both Bi2(Zn1/3Nb2/3)2
O7 (O–BZN) and (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7 (C–BZN)
phases.
(1) The Bi2O3content plays a very important role in
crystal structure and phase transformation of BZN ceramics.
(2) Kinetics studies indicate that both BN2 and BN3 phases are simultaneously required for the for-mation of O–BZNphase but the forfor-mation of C–BZN phase can be developed from either BN2 or BN3 phases.
(3) The formation of O–BZN phase belongs to dif-fusion controlled reaction with a zero nucleation rate. On the other hand, C–BZN phase should be diffusion controlled reaction with a constant nucleation rate.
(4) C–BZN phase has a lower activation energy and formation temperature than O–BZNphase. (5) C–BZN phase exhibits a higher dielectric
con-stant but a lower Q value as compared with O–BZNphase.
Acknowledgements
The authors would like to thank the financial sup-port from the National Science Council of the Republic of China under Contract No. NSC89–2213-E-009–080.
Fig. 9. Effect of x(Bi2O3) content on phase content and bulk density of xBi2O3–ZnO–Nb2O5ceramics sintered at 1000Cfor 1 h.
Fig. 10. Effect of x(Bi2O3) content on microwave properties of xBi2O3–ZnO–Nb2O5ceramics sintered at 1000Cfor 1 h.
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