Crystal structures, phase stability, and dielectric properties of (1-x) Bi3/2MgNb3/2O7-x Bi2Zn 2/3Nb4/3O7 ceramics

Article abstract of DOI:10.1016/j.jallcom.2014.07.002

The preparation, crystal structures, phase stability and dielectric properties of the (1-x) Bi_3/2MgNb_3/2O₇-x Bi₂Zn_2/3Nb_4/3O₇ (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) ceramics were investigated systematically. The sol-gel process was employed to produce crystalline, single-phase Bi_1.5Mg _1.0Nb_1.5O₇ (BMN) and Bi₂(Zn _2/3Nb_4/3)O₇ (β-BZN) pre-nanopowders for the synthesis of the ceramics. X-ray diffraction data indicated that these ceramics presented a phase transition for Bi³⁺ and Zn ²⁺-rich specimens (x ≥ 0.6), from cubic pyrochlore to orthorhombic zirconolite-like structure. The tolerance factor (t) combined with r _A/r_B value and the lattice energy (U) were employed to provide an indication of the structural stability of the (1-x) BMN-x β-BZN cubic pyrochlores (x ≤ 0.4). The tolerance factor (t) calculation contain more structural information, which gives further insight into the details of the structural stability features in the (1-x) BMN-x β-BZN cubic pyrochlores. The relationships between the crystal structures and dielectric properties of the ceramics were determined, and the dielectric loss was related to the phase stability of the system. It is suggested that the dielectric properties are mainly determined by the phase structure, composition and stability in the (1-x) BMN-x β-BZN system.

Full text of DOI:10.1016/j.jallcom.2014.07.002

Journal of Alloys and Compounds 615 (2014) 433–439
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Crystal structures, phase stability, and dielectric properties of (1ꢀx)
Bi MgNb O ꢀx Bi Zn Nb O ceramics
3
/2
3/2
7
2
2/3
4/3 7
⇑
H.L. Dong, L.X. Li , Y.X. Jin, S.H. Yu, D. Xu
School of Electronic and Information Engineering, Tianjin University, Tianjin 300072, China
a r t i c l e i n f o
a b s t r a c t
Article history:
The preparation, crystal structures, phase stability and dielectric properties of the (1ꢀx) Bi3/2MgNb3/2
Received 5 March 2014
Received in revised form 29 April 2014
Accepted 1 July 2014
7
O ꢀx Bi
2 7
Zn2/3Nb4/3O (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) ceramics were investigated systematically. The
sol–gel process was employed to produce crystalline, single-phase Bi1.5Mg1.0Nb1.5
Zn2/3Nb4/3)O (b_BZN) pre-nanopowders for the synthesis of the ceramics. X-ray diffraction data indi-
cated that these ceramics presented a phase transition for Bi and Zn -rich specimens (x P 0.6), from
cubic pyrochlore to orthorhombic zirconolite-like structure. The tolerance factor (t) combined with r
value and the lattice energy (U) were employed to provide an indication of the structural stability of
7 2
O (BMN) and Bi
(
7
Available online 7 July 2014
3
+
2+
A
/
Keywords:
Ceramics
r
B
the (1ꢀx) BMN–x b_BZN cubic pyrochlores (x 6 0.4). The tolerance factor (t) calculation contain more
structural information, which gives further insight into the details of the structural stability features in
the (1ꢀx) BMN–x b_BZN cubic pyrochlores. The relationships between the crystal structures and dielec-
tric properties of the ceramics were determined, and the dielectric loss was related to the phase stability
of the system. It is suggested that the dielectric properties are mainly determined by the phase structure,
composition and stability in the (1ꢀx) BMN–x b_BZN system.
Sol–gel processes
Crystal structure
Phase transitions
Stability
Dielectric properties
Ó 2014 Elsevier B.V. All rights reserved.
1
. Introduction
Members of Bi
2
O
3
–MO–Nb
_BZN), Bi
(BMN), have received the most particularly attention
[14–16]. The crystal structure of the Bi1.5Zn1.0Nb1.5 _BZN)
and Bi1.5Mg1.0Nb1.5 (BMN) pyrochlores are cubic structure with
space group Fd-3 m, while it adopts an orthorhombic distorted
pyrochlores structure in the Bi (b_BZN) ceramics
[11,17]. Because these two phase pyrochlores have opposite signal
of the temperature coefficient of the capacitance ( ): negative and
2
O
5
(M = Mg, Zn) pyrochlores family,
Bi1.5Zn1.0Nb1.5
O
7
(a
(Zn2/3Nb4/3)O (b_BZN), Bi1.5Mg1.0
2 7
The pyrochlores family with the general formula, A
2
B
2
O
7
, is
Nb1.5O
7
fascinating for the A- and B-sites can be occupied by a broad range
of elements that can give rise to a great variety of physical proper-
ties, [1] which allow a diverse useful technological applications,
such as high frequency dielectric microwave materials for LTCC
technique, the electrolyte in solid-oxide fuel cells, host materials
for the immobilization of fission products, catalysis, piezoelectric-
ity, ferro- and ferri-magnetism, luminescence, giant magneto
resistance, and thermal barrier coatings [2–9].
7
O (a
O
7
2
(Zn2/3Nb4/3)O
7
s
c
positive, respectively, a temperature stable ceramics can be fabri-
cated by mixed in different stoichiometric proportions sintered
at suitable temperatures.
Bi-based A
–MO–Nb
2
B
O
2
O
7
-types ternary metallic oxides pyrochlores,
(M = Mg, Zn), have received wide attraction for
Bi
2
O
3
2
5
Research efforts have been focused on composition, stability,
their potential use for multilayer capacitor, electric-field tunable
dielectric thin films materials and integrated device applications
due to their outstanding dielectric properties, i.e. high dielectric
and processing windows of the main phases in the Bi
Nb (M = Mg, Zn) systems [18–20]. In particular, Wang et al.
[15] reported the phase stability of the orthorhombic and cubic
pyrochlores in the Bi –ZnO–Nb (BZN) system. Nino et al.
[18] investigated the Bi solubility in Bi –ZnO–Nb pyroch-
lores system. Based on the results of previous work, excess Bi
with respect to the base formulation of the cubic pyrochlores phase
in the Bi –ZnO–Nb and Bi –MgO–Nb system was
2 3
O –MO–
2 5
O
constants (
e
) as well as electric-field tunable, relatively low dielec-
2
O
3
2 5
O
tric losses over a considerable frequency range around room tem-
perature, and compositionally tunable temperature coefficients of
2
O
3
2
O
3
2 5
O
2 3
O
c
capacitance (s ) combined with low sintering temperatures which
enable the possibility of co-firing with Ag electrodes [10–14].
2
O
3
2
O
5
2
O
3
2 5
O
performed. The differences of the phase stability behavior between
these systems were discussed by Nino and co-workers [21]. How-
ever, because of the immense flexibility of chemical composition in
⇑
Corresponding author. Tel./fax: +86 22 27402838.
E-mail address: lilingxia66@hotmail.com (L.X. Li).
http://dx.doi.org/10.1016/j.jallcom.2014.07.002
925-8388/Ó 2014 Elsevier B.V. All rights reserved.
0

4
34
H.L. Dong et al. / Journal of Alloys and Compounds 615 (2014) 433–439
and ethylene glycol (99.00%) were used as a chelating agent and reaction medium,
respectively. The experimental procedure for preparing the nanopowders is shown
in Fig. 1. Firstly, stoichiometric Nb was dissolved in the appropriate amount of
the Bi
questions still remain to be answered about the phase stability in
these systems. In addition, it notes that unlike Bi –ZnO–Nb
system, there is no stable orthorhombic phase in Bi –MgO–
system, although Mg2 and Zn have similar ionic radii
0.72 and 0.74) in six coordination as well as similar electronega-
tivity ( Mg = 1.31, Zn = 1.65) according to the crystal chemistry
22]. Therefore, the determination of the phase stability of the
orthorhombic and cubic pyrochlores in the Bi –ZnO–MgO–
Nb system are theoretical and technical important.
To expand the knowledge on the processing windows and solu-
bility limits of Bi-based pyrochlores ceramics, single cubic Bi1.5
(BMN) and Bi (Zn2/3Nb4/3)O (b_BZN) orthorhombic
pyrochlores phase powders were synthesized separately by the
sol–gel process, and compositions of the full range (1ꢀx) BMN–x
b_BZN (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) between BMN and b_BZN were
produced by mixing different amounts of the two ceramics. For
these ceramics, the crystal structures and phase stability have
not been investigated yet. In this work, for the first time, the toler-
2 3 2 5
O –MO–Nb O (M = Mg, Zn) pyrochlores system, many
2 5
O
2
O
3
2 5
O
HF at 80 °C for 20 h, and then ammonia water was added into the above solutions
2
O
3
to form chemical precipitate of niobic acid [Nb(OH) ]. The precipitates were filtered
5
+
2+
+
+
Nb
(
2
O
5
off and washed with distilled water to remove the H and F ions. The Nb(OH)
cipitates were dissolved completely in citric acid water solution under stirring at
0 °C. Subsequently, stoichiometric amounts of Mg(NO ꢁ6H O, Zn(NO ꢁ6H
and Bi(NO O were added to the niobium citrate solution heated at 60 °C to
ꢁ5H
5
pre-
8
3
)
2
2
)
3 2
2
O
v
v
3
)
3
2
[
form the (Bi, Mg, Nb) and (Bi, Zn, Nb) complex precursors, respectively. The
solutions was kept under stirring at 60 °C, resulting in clear pale yellow solutions.
Ethylene glycol was added to those solutions to promote polymerization of the
mixed citrate. By heating in a water bath at 80–90 °C, viscous gels were obtained.
Finally, the gels was dried at 200 °C and then calcined at 650 °C in air for 2 h,
respectively. Ceramics of the full range (1ꢀx) BMN–x b_BZN (x = 0.0, 0.2, 0.4, 0.6,
0.8, 1.0) between BMN and b_BZN were produced by mixing different amounts of
the two ceramics. The samples were uniaxially pressed at 10 MPa and sintered in
air at 960 °C, for 4 h.
2 3
O
2 5
O
Mg1.0Nb1.5
O
7
2
7
Powder X-ray diffraction analysis (Rigaku, D/MAX-2500, Tokyo, Japan) was used
to analyze the crystal structure of sintered ceramics. A Hewlett-Packard 4278A
capacitance meter was used to test capacitance (C) and dielectric loss (tand) at
1 MHz. The dielectric constant (er) was calculated by the equation er = (14.4Cd)/
2
D , where D and d are the average diameter and the thickness of the sample, respec-
tively. The temperature coefficient of the capacitance (
equation
= (C85–C25)/60ꢂC25, where C85 and C25 are the capacitances of the sam-
ples at 85 and 25 °C, respectively. Archimedes’ principle was used to test the bulk
density ( ) of all the samples using the equation = (m /m water, where
ꢀm
, m , and m are the weight after drying, the weight in the air, and the weight
in water, respectively.
c
s ) was calculated by the
A B
ance factor (t) combined with r /r value (the ratio of the ionic
s
c
radius of A-site over the ionic radius of B-site) and the lattice
energy (U) are employed to provide an indication of the structural
stability of the (1ꢀx) BMN–x b_BZN cubic pyrochlores. The rela-
tionship between the crystal structures, stability, and dielectric
properties of the (1ꢀx) BMN–x b_BZN ceramics are determined.
q
v
q
v
0
1
2
) q
m
0
1
2
2
.2. Theory development
A B
The tolerance factor (t) combined with r /r value (the ratio of the ionic radius
of A-site over the ionic radius of B-site) and the lattice energy (U) are employed to
provide an indication of the structural stability of the (1ꢀx) BMN–x b_BZN ceramics.
2
. Experiment and theory
2.1. Experimental methods
Bi1.5Mg1.0Nb1.5
O
7
(BMN) and Bi
thesized by the sol–gel process. For preparation of the precursor solution, analyti-
cally pure (AR) Bi(NO O (99.00%), Mg(NO ꢁ6H O (99.00%), Zn(NO ꢁ6H
ꢁ5H
99.00%) and Nb (99.99%) were used as the raw materials. Citric acid (99.00%)
2
(Zn2/3Nb4/3)O
7
(b_BZN) nanopowders were syn-
2.2.1. The tolerance factor (t)
It is reported that the tolerance factor is an useful tool to determine the stability
field of the ceramics [23]. The tolerance factor (t) concept was introduced to analyze
structure–property relations of ceramics with the perovskite crystal structure
)
3 3
2
3
)
2
2
)
3 2
2
O
(
2 5
O
Fig. 1. Flow chart for preparing the (1ꢀx) BMN–x b_BZN ceramics by the sol–gel process.

H.L. Dong et al. / Journal of Alloys and Compounds 615 (2014) 433–439
435
(
ABO
es structure(A
determined the tolerance factor to be: [25]
3
) [24]. Isupov firstly introduced the tolerance factor concept to the pyrochlor-
Kk
B cosðhÞ
d ¼
ð7Þ
2
B
2
O
7
) on the assumption that the BO
6
were perfect octahedra, and
r
r
A
þ r
þ r
0
t ¼ 0:866
ð1Þ
where d, k, B, and h are crystallite size, Cu K
a
wavelength, full width
B
0
at half-maximum intensity (FWHM) in radians, and Bragg’s
diffraction angle, respectively. The average crystallite sizes of
BMN and b_BZN powders, calculated from the main diffraction
peaks of BMN (222) and b_BZN (220), are 27.4 nm and 25.8 nm,
respectively.
Recently, Cai et al. [23] developed a new set of tolerance factors for pyrochlores
that took into account the complete pyrochlores crystallography. The first tolerance
factor t was defined as:
1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
À
Á
2
0
1
4
1
x ꢀ
þ
rA þ r
32
0
0
t
t
1
2
¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2Þ
À
Á
2
1
2
1
32
r
B
þ r
0
x ꢀ
þ
The second tolerance factor was defined as:
3.2. Crystal structure evolution
pffiffiffi
3
3
¼
a
ð3Þ
The XRD patterns of the (1ꢀx) Bi3/2MgNb3/2O (BMN)–x Bi Zn
7
2
2/3
8
ðr
A
þ r
0
Þ
7
Nb4/3O (b_BZN) (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) ceramics sintered at
0
where r
A
, r
B
, r
O
are ionic radii of A, B, and oxygen ions, respectively. The variable x in
9
60 °C for 4 h are shown in Fig. 3.
There are three types of phases in the (1ꢀx) BMN–x b_BZN
t
1
is the atom position parameter of oxygen ions which are located at Wyckoff posi-
0
tion 48f (x , 1/8, 1/8). In this study, the stability field of (1ꢀx) BMN–x b_BZN ceramics
ceramics according to the XRD patterns, including cubic pyrochlor-
es, orthorhombic zirconolite-like, and their mixture phase. The
reflections of cubic pyrochlores and orthorhombic zirconolite-like
phase are indexed according to the JCPDS cards (Joint Committee
on Powder Diffraction Standard) Nos. 52-1770 and 54-0972,
respectively. The main phase of the specimens with x 6 0.6 is cubic
pyrochlores. The BMN specimen shows peaks of the second phase:
1
is determined by t because its calculations contain more structural information.
2
.2.2. Lattice energy (U)
The conception of the lattice energy was defined as the heat of dissociation of
one mole of solid into its structural components, which can be applied to evaluate
the stability of a structure [26]. Volume parameter method is used to calculate the
lattice energy in this study. The lattice energy is defined as: [27]
1
=3
U ¼ AIð2I=V
m
Þ
ð4Þ
ð5Þ
Magnesium niobate oxide, which is indexed as MgNb O6 with
JCPDS card No. 33-0875. Single cubic pyrochlores phase solid
2
X
2
2
I ¼
n
i
Zi
solutions are formed in the range, 0.2 6 x 6 0.4. It is well known
i
that the Bi
2 3 2 5
O –ZnO–Nb O system is less refractory than the
Bi –MgO–Nb O system, and therefore single cubic pyrochlores
2
O
3
2 5
V
m
¼ Vcell=Z
ð6Þ
phase form in (1ꢀx) BMN–x b_BZN (0.2 6 x 6 0.4) ceramics at a
relatively lower sintering temperatures than BMN specimen [21].
The 0.4BMN–0.6b_BZN ceramics shows peaks of the second phase:
where I is the ionic strength, n
ith ion, Vcell is the unit cell volume, and A = 121.4, respectively.
i
is the ionic molality and Z
i
units is the charge on the
A B
In addition, many researches have confirmed that the r /r value could be used
5 3
Bismuth niobate oxide, which are indexed as Bi Nb O15 with JCPDS
to define the stability region of pyrochlores [28–32].
card No. 16-0293. Orthorhombic phase appears in the specimen
with x = 0.6, and cubic and orthorhombic phase coexist in the spec-
imen with x = 0.8. Single orthorhombic zirconolite-like phase
ceramics is found in the b_BZN specimen. The XRD characteriza-
tion reveals the occurrence of the phase evolution with the x
increasing.
3
. Results and discussion
3.1. The BMN and b_BZN pre-nanopowders
The XRD patterns of the BMN and b_BZN powders calcined at
50 °C for 2 h are shown in Fig. 2.
In order to investigate the phase evolution mechanisms for the
6
(
1ꢀx) BMN–x b_BZN system, two reported ceramics systems, the
Bi –ZnO–Nb [15] and Bi –MgO–Nb [17,21], are quoted
for comparison in this study. The phase structure evolution of
Bi –ZnO–Nb , Bi –MgO–Nb
and (1ꢀx) BMN–x b_BZN
systems are summarized in Table 1.
Single cubic and orthorhombic pyrochlores phases are obtained
2
O
3
2
O
5
2
O
3
2 5
O
and indexed according to the JCPDS cards (Joint Committee on
Powder Diffraction Standard) Nos. 52-1770 and 54-0972,
respectively. The average crystallite sizes are calculated using the
Scherrer formula:
2
O
3
2
O
5
2
O
3
2 5
O
Fig. 2. The XRD patterns of the BMN and b_BZN powders calcined at 650 °C for 2 h.
Fig. 3. The XRD patterns of the (1ꢀx) BMN–x b_BZN ceramics, at 960 °C.

4
36
H.L. Dong et al. / Journal of Alloys and Compounds 615 (2014) 433–439
Table 1
Phase structure evolution of Bi
2
O
3
–ZnO–Nb
2
O
5
, Bi
2
O
3
–MgO–Nb
2
O
5
and (1ꢀx) BMN–x b_BZN systems.
System
Struc. formula
Composition range
Phases
Bi
2
O
3
–ZnO–Nb
2
O
5
(Ref. [15])
(Bi3aZn2ꢀ3a)(Zn
a
Nb2ꢀa)O
7
0.5 6 a < 0.55
Cub.a
0
0
–
–
.55 6 a 6 0.64
Cub.a & Orth.b
b
.64 < a 6 0.67
Orth.
Bi
2
O
3
–MgO–Nb
2
O
5
(Bi1.5Mg0.5)(ꢀMg0.5Nb1.5)O
7
Cub.a
(
(
Refs. [17,21])
1ꢀx) BMN–x b_BZN
Bi
–
2
Mg2/3Nb4/3
O
7
Cub.a
0.0 6 x 6 0.4
Cub.a
0
0
.6 6 x 6 0.8
.8 < x 6 1.0
Cub.a & Orth.b
Orth.b
a
Cubic.
Orthorhombic.
b
In contrasting phase structure evolution of Bi
–MgO–Nb
and (1ꢀx) BMN–x b_BZN systems with various
composition range, discussions regarding the stability of the Bi-
based pyrochlores are raised. Unlike Bi –ZnO–Nb
and (1ꢀx)
BMN–x b_BZN system, there is no stable orthorhombic phase in
2 3 2 5
O –ZnO–Nb O ,
Bi
2
O
3
2 5
O
O
2 3
2 5
O
3
+
2 3 2 5
Bi O –MgO–Nb O system [21]. It has been reported that Bi con-
tent exhibits a strong effect on the phase evolution in the Bi-based
pyrochlores, and the distorted orthorhombic phase is suggested to
2
result from the long-range coupling of the 6s lone-pair electrons
3
+
of Bi on the A-site position, which can be affected by the charac-
ter of B site ions [15]. Compared to Bi –MgO–Nb system,
however, the Zn (with its 3d orbits) in the Bi –ZnO–Nb
O
2 3
2 5
O
2
+
10
2
O
3
2 5
O
system can establish energetically stable asymmetric crystal field
potentials that can sustain a distorted octahedral bond field
according to crystal field theory [33–35]. Since Mg2+ cannot estab-
lish a distorted coordination, which is requiredthe stabilization of
the orthorhombic structure, the monoclinic phase analogous to
that in Bi
be formed in the Bi
compared with the Bi
2
O
3
–ZnO–Nb
2
O
5
and (1ꢀx) BMN–x b_BZN systems cannot
–MgO–Nb ceramics [21]. In addition, as
–ZnO–Nb system, the substitution of
2
O
3
2 5
O
O
2 5
2
O
3
2
+
2+
Mg on the Zn site makes the crystal chemistry in the (1ꢀx)
Fig. 4. The dependence of the phase evolution of the (1ꢀx) BMN–x b_BZN ceramics
on the stoichiometric of Bi3 content and Zn /Mg ratio.
+
2+
2+
BMN–x b_BZN system become complex. Studies of the cation dis-
3
+
tribution in the Bi-based pyrochlores have revealed that the Bi
occupy A-site and the divalent cations of Zn2+ or Mg occupy both
the A- and B-sites [36]. The known limits of structural stability for
the ideal cubic pyrochlores structure type suggest that it should
2+
structural stability of the (1ꢀx) BMN–x b_BZN cubic pyrochlores.
For the tolerance factor is derived and calculated based on the ideal
pyrochlores structure, it is important to recall previous studies on
the pyrochlores structure. The ideal cubic pyrochlores structure is
not be possible for the smaller Zn2 and Mg to occupy the A site
without significant local structural distortion [1,36]. Based on the
discussion above, the stability of the cubic pyrochlores and ortho-
rhombic phase in the (1ꢀx) BMN–x b_BZN system are dependent
+
2+
highly symmetrical, which has four distinct sites occupied by the A
0
(
site 16d), B (site 16c), O (site 48f) and O (site 8b) ions. Because of
high symmetry, the positions of all ions except O ion are fixed. The
O ions in 48f sites have a single variable parameter along the x-
direction [36]. It is assumed that this variable equals to 0.3196 in
all initial models for (1ꢀx) BMN–x b_BZN cubic pyrochlores
3
+
on the Bi content as well as the distribution and variety of
2+
2+
divalent cations, such as Zn /Mg ratio. The dependence of the
phase evolution of the (1ꢀx) BMN–x b_BZN ceramics on the stoi-
3
+
2+
2+
chiometric of Bi and Zn /Mg ratio are shown in Fig. 4.
Phase transformation, from cubic pyrochlores to orthorhombic
(
x 6 0.4). However, the actual parameter will alter imaginably
3+ 2+ 2+
along with the change of Bi content and Zn /Mg ratio in the
3+
2+
zirconolite-like structure, occurs with the Bi content and Zn
/
(
1ꢀx) BMN–x b_BZN cubic pyrochlores (x 6 0.4). In addition, this
2
+
Mg ratio increasing. The phase structure is cubic pyrochlores in
the specimens with x 6 0.4. Reflections of orthorhombic peaks
appear in the specimen with x = 0.4, however, the main phase is
cubic pyrochlores, which indicate that the crystal structure have
been distorted while the orthorhombic phase have not been
formed. Mixture phase coexist in the specimen with x = 0.8. The
phase structure is orthorhombic zirconolite-like when the x value
is close to 1. The stability field of cubic and orthorhombic phase
in the (1ꢀx) BMN–x b_BZN ceramics are shown in Table 2. Further
study is needed to determine the detail stability field of the (1ꢀx)
BMN–x b_BZN ceramics.
variable is expected to be a significant fact or for the properties
of (1ꢀx) BMN–x b_BZN ceramics. So how to determine this param-
eter was a primary factor before calculate the tolerance factor of
the (1ꢀx) BMN–x b_BZN ceramics. In this study, the Rietveld struc-
ture refinement method was introduced to solve this difficulty.
Table 2
Phase stability field of the cubic and orthorhombic in the (1ꢀx) BMN–x b_BZN
ceramics.
Phases
x
Bi content
Zn2+/Mg2+ ratio
Cub.a
0–0.4
0.6
0.8
1
1.5–1.7
1.8
1.9
0–0.4445
1
2.6665
>2.6665
a
Distorted Cub.
Cub. & Orth.b
Orth.b
a
3.3. The tolerance factor (t) determine the stability field
2
a
The tolerance factor (t) combined with r
lattice energy (U) are employed to provide an indication of the
A
/r
B
value and the
Cubic.
Orthorhombic.
b

H.L. Dong et al. / Journal of Alloys and Compounds 615 (2014) 433–439
437
The previous reports about Fd-3 m average cubic pyrochlores
A B
It is suggested that the tolerance factor (t) as well as the r /r
0
structure of (Bi1.5Zn0.42)(Zn0.5Nb1.5)O
6
O
0.92 is employed as the
value and lattice energies (U) can provide an indication of the
structural stability of the (1ꢀx) BMN–x b_BZN pyrochlores
initial structural model for the Rietveld refinement [36]. For the
purposes of the following calculations of the tolerance factor (t),
the 4% vacancy concentration reported for the A site and the 8%
A B
(x 6 0.4). The tolerance factor (t) and the r /r for the cubic pyroch-
lores are derived from the geometrical aspects, and similar results
are obtained from these two different parameters calculations. The
0
vacancy concentration reported for the O site were ignored i.e.,
0
the stoichiometry of the (1ꢀx) BMN–x b_BZN cubic pyrochlores
positional parameter x has been taken into account in the toler-
are effectively assumed as (Bi1.5+0.5x
M
0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6
)
ance factor (t) calculation, which gives further insight into the
details of the structural stability features in the (1ꢀx) BMN–x
b_BZN cubic pyrochlores.
0
O
6
O
1
(M = Mg & Zn). Considering the divalent cation distribution
2+
2+
in the Bi-based pyrochlores, i.e. the Zn and Mg occupy both
the A- and B-sites, the proposed chemical formula for structure
refinement with different cation distributions in A- and B-sites of
0
the (Bi1.5+0.5x
M
0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6)O
6
O
1
(M = Mg, Zn) cubic
/r
B
3.4. Correlation of crystal structure, phase stability and dielectric
properties
pyrochlores (x 6 0.4) and their corresponding relative
values are listed in Table 3. The initial atoms position for
r
A
0
(
Bi1.5+0.5xM0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6)O
6
O
1
(M = Mg, Zn) pyrochlores
r
Fig. 6 present the variations of the dielectric constants (e ) and
(
x 6 0.4) based on their proposed chemical formula are shown in
apparent densities of (1ꢀx) BMN–x b_BZN ceramics as a function
Table 4.
The Rietveld refinement of the structure is carried out using the
of b_BZN content.
r
The dielectric constant (e ) of the specimen increases to a max-
program Fullprof suite toolbar. The results of the structural infor-
imum value and thereafter it decreases with the x increasing, as
mation refined by Rietveld method are shown in Table 5.where a
is the lattice parameter, V is the unit cell volume, x is the variable
shown in Fig. 6. According to the variation trend of the dielectric
0
constant (
regions are distinguished, i.e. (1) 0 6 x 6 0.4, cubic pyrochlores
region, the dielectric constant ( ) increases with increasing x and
reached the maximum at x = 0.4; (2) 0.6 6 x < 1, mixture phase
region, the dielectric constant ( ) decreases with increasing x.
r
e ) and phase structure evolution of the specimens, two
atom position parameter of the oxygen which located at Wyckoff
0
position 48f (x , 1/8, 1/8), t is the tolerance factor and U is the lattice
e
r
energies, respectively.
0
The x parameter shows a decrease trend as increasing b_BZN
e
r
0
content, and different x value can be obtained based on different
Allowing for the XRD results, phase transformation occurs at
x > 0.6. The phase structure is cubic pyrochlores in the specimens
0
chemical formula models. The variation of the x parameter indi-
cates the distortion of the unit cell, and the distortion due to the
difference of the ionic size and distribution between A and B-site
would be determined and correlated to the stability of the struc-
ture. The tolerance factor (t) and lattice energies (U) are also shown
in Table 5. The results show that both the tolerance factor (t) and
lattice energy (U) present decrease trend as increasing b_BZN con-
with x 6 0.4. The dielectric constant (
cubic pyrochlores (x 6 0.4) increases with x increasing, and the lar-
ger dielectric constant ( ) of the cubic Bi-rich pyrochlores is
e
r
) of (1ꢀx) BMN–x b_BZN
e
r
expected. Given that the expected dielectric polarizability per vol-
0
ume unit for (Bi1.5+0.5x
M
0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6)O
6
O
1
(M = Mg &
Zn, x 6 0.4) , which is calculated using the empirical ion polariz-
abilities that were derived by Shannon, [37] is significantly higher
0
tent, which is consist with the trend of the x parameter. Fig. 5
shows the variation of the tolerance factor (t) calculated based
than that for (Bi1.5Mg0.5)(Mg0.5Nb1.5)O (BMN). However, the
7
on different chemical formula models as a function of r
of the (1ꢀx) BMN–x b_BZN cubic pyrochlores (x 6 0.4).
A
/r
B
values
decreasing trend of dielectric constant (e ) in the specimens with
r
x P 0.6 is unexpected from the ion polarizabilities consideration.
Allowing for the phase structure evolution of the (1ꢀx) BMN–x
b_BZN ceramics, it can be inferred that the orthorhombic distortion
reduces the overall ionic polarizability.
The apparent densities shows increasing trend in its values as a
function of x, as shown in Fig. 6. It is well known that higher
density would lead to higher dielectric constant owing to lower
A B
With the r /r values increasing, the tolerance factor (t) shows a
decreasing trend, from 0.8882 to 0.8069. It is well known that the
tolerance factor (t) is 1.0 for the ideal structure, and the closer
tolerance factor (t) is to unity, the greater the stability of the
structure. The decrease of the tolerance factor (t) indicates that
the stability of the phase structure became weak. Furthermore,
the decrease of the phase stability indicates the distortion of the
crystal structure, which is due to the distribution and variety of
divalent cations in the A-and B-site. The lattice energies (U) versus
the b_BZN content are also presented in Fig. 5. The lattice energy
decreases with the b_BZN content increasing, from 66608.12 to
porosity. The variation of dielectric constant (
x 6 0.4, cubic pyrochlores region, is consistent with that of the den-
sity. However, the variation of dielectric constant ( ) of specimens
with x P 0.6, mixture phase region, shows reverse trend with that
of the density. It is suggested that the dielectric constant ( ) of the
r
e ) of specimens with
e
r
e
r
6
6132.35. It is interesting to note that the trend of the tolerance
(1ꢀx) BMN–x b_BZN ceramics is mainly determined by the intrin-
sic fact, i.e. phase structure, when compare to the extrinsic fact
such as apparent densities.
factor (t) versus the r /r values is consist with that of the lattice
A
B
energies (U), which further verified the decline of the stability of
the phase structure in the (1ꢀx) BMN–x b_BZN cubic pyrochlores
Fig. 7 presents the variations of dielectric loss and
f
s values of
(x 6 0.4).
(1ꢀx) BMN–x b_BZN ceramics as a function of b_BZN content.
Table 3
0
The proposed chemical formula for structure refinement with different cation distributions in A- and B-sites of the (Bi1.5+0.5x
M0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6)O
6
O
1
(M = Mg, Zn)
pyrochlores (x 6 0.4).
BMN–b_BZN
0.8 BMN–0.2b_BZN
0.6 BMN–0.4b_BZN
Model 1a
(Bi1.5Mg0.5) (Mg0.5Nb1.5)O
(Bi1.6Mg0.4) (Mg0.4Zn0.1333Nb1.4667)O
(Bi1.7Mg0.3) (Mg0.3Zn0.2667Nb1.4333)O
7
7
7
b
Model 2
–
–
(Bi1.6Mg0.32Zn0.08) (Mg0.48Zn0.0533Nb1.4667)O
(Bi1.6Mg0.2667Zn0.1333) (Mg0.5333Nb1.4667)O
7
(Bi1.7Mg0.18Zn0.12) (Mg0.42Zn0.1467Nb1.4333)O
(Bi1.7Mg0.0333Zn0.2667) (Mg0.5667Nb1.4333)O
7
Model 3c
7
c
7
c
a
a
b
a
b
r
A
/r
B
1.5
1.5211
1.5242
1.5265
1.5421
1.5467
1.5523
a
b
c
3+
2+
Bi and Mg co-occupy the A-site.
3+
2+
2+
Bi , Mg and Zn co-occupy the A-site at the same time.
2+
Zn only occupy the A-site.

4
38
H.L. Dong et al. / Journal of Alloys and Compounds 615 (2014) 433–439
Table 4
0
Initial atoms position for the (Bi1.5+0.5x
M0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6)O
6
O
1
(M = Mg, Zn) pyrochlores (x 6 0.4).
Atom
Wyckoff position
x
y
z
Occupancy
Bi, M (A-site)
Nb, M(B-site)
O
16d
16c
48f
8b
0.5
0
0.3196 (x )
0.5
0
0.125
0.375
0.5
0
0.125
0.375
(0.75+0.25x), (0.25ꢀ0.25x)
(0.75ꢀx/12), (0.25+x/12)
0
1
1
0
O
0.375
Table 5
0
0
1
The structure parameters (a, V and x ), the tolerance factor (t) and the lattice energies (U) for the (Bi1.5+0.5x
M0.5ꢀ0.5x)(M0.5+x/6Nb1.5ꢀx/6)O
6
O
(M = Mg, Zn) pyrochlores (x 6 0.4).
BMN
0.8 BMN–0.2 b_BZN
0.6 BMN–0.4 b_BZN
Model 1
Model 2
Model 3
Model 1
Model 2
Model 3
a (Å)
10.5580
1176.92
0.32271
0.8882
10.5515
1174.74
0.31665
0.8684
10.5515
1174.74
0.31511
0.8626
10.5515
1174.74
0.31423
0.8593
10.5657
1179.49
0.30113
0.8148
10.5657
1179.49
0.29860
0.8069
10.5657
1179.49
0.31086
0.8205
3
V (Å )
0
x
t
U (kJ/mol)
66608.12
66435.24
66435.24
66435.24
66132.35
66132.35
66132.35
Fig. 7. Dielectric loss and
b_BZN content.
f
s values of (1ꢀx) BMN– xb_BZN ceramics as a function of
A B
Fig. 5. Tolerance factor (t) as a function of r /r (black part) and the lattice energy as
a function of b_BZN content (blue part). (For interpretation of the references to
colour in this figure legend, the reader is referred to the web version of this article.)
and thereafter it decreases with x increasing, as shown in Fig. 7.
It is worthy noted that the values of the dielectric loss around
the endpoints, x = 0.0, 0.2 and 1.0, are smaller compare with that
of the middle points, x = 0.4, 0.6 and 0.8. Combine with the XRD
results and the stability analysis, the variation of dielectric loss
was mainly related to its phase composition and stability. The
specimens with x = 0.2 and 1.0 present relative low loss due to
their single phase together with the high phase stability. The large
dielectric loss of the ceramics with x = 0.4, 0.6 and 0.8 are mainly
due to the weak phase stability, and the dielectric loss of the
ceramics with x = 0.6 reaches the maximum value company with
the phase transformation. The temperature coefficient of permit-
tivity (
s
f
) of (1ꢀx) BMN–x b_BZN ceramics tend to be shifted to
positive region, from ꢀ404.67 ppm/°C to 173.84 ppm/°C , with x
increasing, and near zero
It is well known that the
s
f
obtains at x = 0.8, as shown in Fig. 6.
s
f
value is governed by the composition,
the additive, and the second phase of the materials [38]. There
are two main phases in the (1ꢀx) BMN–x b_BZN system: cubic
7
pyrochlores phase Bi3/2ZnNb3/2O with temperature coefficient of
capacitance approximately ꢀ400 ppm/°C and monoclinic zircono-
r
Fig. 6. Dielectric constants (e ) and apparent densities of (1ꢀx) BMN–x b_BZN
lite-like phase Bi with temperature coefficient of
2
Zn2/3Nb4/3O
7
ceramics as a function of b_BZN content.
capacitance approximately 200 ppm/°C. Therefore, a temperature
stable material is obtained by mix the two phase composite with
negative or positive in a certain stoichiometric proportion, and
almost zero temperature coefficient of capacitance (NP0) charac-
teristics (±15 ppm/°C between ꢀ55 and 125 °C) is attainable within
The variation trend of the dielectric loss is similar to that of the
dielectric constant (
r
e ). The loss of the specimen slightly decrease
when x 6 0.2, then it increases to a maximum value at x = 0.6

H.L. Dong et al. / Journal of Alloys and Compounds 615 (2014) 433–439
439
the system. The results are consistent with the Lichtenecker loga-
rithmic mixing rule [39]. From the results of the analysis above,
it is verified that the dielectric properties are mainly determined
by the phase structure, composition and stability in the (1ꢀx)
BMN–x b_BZN ceramics system.
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This work was supported by Program for New Century Excellent
Talents in University (NCET) and 863 program (2007AA03Z423)
and China Postdoctoral Science Foundation.
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