Acceptor doping of Ln2Ti2O7 (Ln = Dy, Ho, Yb) pyrochlores with divalent cations (Mg, Ca, Sr, Zn)

Article abstract of DOI:10.1016/j.materresbull.2009.04.013

New LANTIOX high-temperature conductors with the pyrochlore structure, (Ln_1-xA_x)₂Ti₂O_7-δ (Ln = Dy, Ho, Yb; A = Ca, Mg, Zn; x = 0, 0.01, 0.02, 0.04, 0.07, 0.1), have been prepared at 1400-1600 °C usin

Full text of DOI:10.1016/j.materresbull.2009.04.013

Materials Research Bulletin 44 (2009) 1613–1620
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Acceptor doping of Ln2Ti2O7 (Ln = Dy, Ho, Yb) pyrochlores with divalent
cations (Mg, Ca, Sr, Zn)
a
b
a
D.A. Belov a, A.V. Shlyakhtina b, , S.Yu. Stefanovich , I.V. Kolbanev , Yu.A. Belousov ,
*
O.K. Karyagina c, L.G. Shcherbakova b
a Faculty of Chemistry, Moscow State University, Leninskie gory, Moscow 119991, Russia
b Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow 119991, Russia
c Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow 119991, Russia
A R T I C L E I N F O
A B S T R A C T
Article history:
New LANTIOX high-temperature conductors with the pyrochlore structure, (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy,
d
Received 5 February 2009
Received in revised form 22 April 2009
Accepted 30 April 2009
Available online 6 May 2009
Ho, Yb; A = Ca, Mg, Zn; x = 0, 0.01, 0.02, 0.04, 0.07, 0.1), have been prepared at 1400–1600 8C using
mechanical activation, co-precipitation and solid-state reactions. Acceptor doping in the lanthanide
sublattice of Ln2Ti2O7 (Ln = Dy, Ho, Yb) with Ca2+, Mg2+ and Zn2+ increases the conductivity of the
titanates except in the (Ho1ꢂxCax)2Ti2O7ꢂ system, where the conductivity decreases slightly at low
d
doping levels, x = 0.01–0.02. The highest conductivity in the (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb; A = Ca,
d
Keywords:
Mg, Zn) systems is offered by the (Ln0.9A0.1)2Ti2O7ꢂ and attains maximum value for (Yb0.9Ca0.1)2Ti2O6.9
d
B. Ionic conductivity
C. Impedance spectroscopy
and (Yb0.9Mg0.1)2Ti2O6.9 solid solutions:ꢀ2 ꢁ 10ꢂ2 and 9 ꢁ 10ꢂ3 S cmꢂ1 at 750 8C, respectively. Ca and
Mg are best dopants for Ln2Ti2O7 (Ln = Dy, Ho, Yb) pyrochlores. Using impedance spectroscopy data, we
have determined the activation energies for bulk and grain-boundary conduction in most of the
(Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho; A = Ca, Mg, Zn) materials. The values obtained, 0.7–1.05 and 1–1.4 eV,
d
respectively, are typical of oxygen ion conductors. We have also evaluated defect formation energies in
the systems studied.
ß 2009 Elsevier Ltd. All rights reserved.
1. Introduction
reduce its ionic conductivity, promoting oxygen vacancy-dopant
association [6]. There is also substantial evidence that the
A number of oxygen-ion-conducting rare-earth titanate pyro-
chlores (LANTIOX family) have recently been shown to be good solid
electrolytes, some surpassing YSZ in electrical conductivity [1–5]. In
particular, Ca doping of Yb2Ti2O7 on the Yb site was found to ensure
formation of such defect complexes is favoured by considerable
size mismatches between the dopant cation and Zr4+ [7–11].
Experimental data on doping of R2Ti2O7 (R = Y, Sm, Gd) with
divalent cations (Mg2+, Ca2+, Sr2+) demonstrate that Ca is the most
efficient dopant [12]. According to atomistic simulations [13], Sr-
doped pyrochlore oxides have a low Sr0A–VOꢃꢃ binding energy and
hence a low activation energy for oxygen migration, which is
however in contradiction with experimental data [12]. Mg2+
proved the least efficient dopant for R2Ti2O7 with R = Y, Sm and Gd
[12].
The effect of cation disorder on oxygen transport in the materials
in question is still the subject of controversy. TiLn anti-site defects
may influence the degree of divalent-cation substitution on
the lanthanide site [14]. This led us to examine divalent-cation
doping of heavy-lanthanide titanates (using Yb2Ti2O7 as a model
system), which have the strongest tendency toward anti-structure
pair formation (cation disordering) [15], and intermediate-lantha-
nide titanates (Ln = Dy, Ho), in which this tendency is less
pronounced.
high conductivity of (Yb0.9Ca0.1)2Ti2O6.9
:
ꢀ2 ꢁ 10ꢂ2 S cmꢂ1 at
740 8C and ꢀ0.2 S cmꢂ1 at 1000 8C [5].
Among the Ln2O3–TiO2 systems containing pyrochlore-like
compounds and solid solutions with high oxygen ion conductivity
(LANTIOX), the Ho2O3–TiO2 and Dy2O3–TiO2 systems remain the
least explored. By analogy with (Yb1ꢂxCax)2Ti2O6.9, the highest
ionic conductivity in these systems would be expected to result
from aliovalent Ln-site substitutions.
Studies aimed at optimizing the concentration of R2O3 oxides as
acceptor dopants stabilizing the high-temperature, oxygen-ion-
conducting phase of ZrO2 have shown that cubic zirconia has the
highest conductivity at the lowest possible stabilizer concentra-
tions: 8–11 mol% Y2O3 and 9–11 mol% Sc2O3. Higher doping levels
Our main purposes were to study the effect of Group IIA and IIB
(Mg2+, Ca2+, Sr2+, Zn2+) cation substitutions in the lanthanide
* Corresponding author. Tel.: +7 499 1378303; fax: +7 499 2420253.
E-mail addresses: annash@chph.ras.ru, annashl@inbox.ru (A.V. Shlyakhtina).
0025-5408/$ – see front matter ß 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.materresbull.2009.04.013

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D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
Table 1
Preparation conditions and phase composition of the samples.
Composition
Ho2Ti2O7
Sample No.
x
Method and firing conditions
Phase composition
1
2
0
Solid-state reaction; 1600 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Pyrochlore
0
Pyrochlore
(Ho1ꢂxMgx)2Ti2O7ꢂ
(Ho1ꢂxZnx)2Ti2O7ꢂ
3
0.04
0.1
0.04
0.07
0.1
0.01
0.01
0.02
0.04
0.04
0.1
0.1
0
Solid-state reaction; 1600 8C, 4 h
Solid-state reaction; 1600 8C, 4 h
Solid-state reaction; 1600 8C, 4 h
Solid-state reaction; 1600 8C, 4 h
Solid-state reaction; 1400 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Solid-state reaction; 1400 8C, 4 h
Solid-state reaction; 1600 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Pyrochlore
d
4
Pyrochlore
5
Pyrochlore
d
6
Pyrochlore
7
Solidified melt
Pyrochlore
(Ho1ꢂxCax)2Ti2O7ꢂ
8
d
9
Pyrochlore
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Pyrochlore
Pyrochlore
Pyrochlore
Pyrochlore
Pyrochlore
Dy2Ti2O7
Pyrochlore + TiO2
Pyrochlore
0
0
Pyrochlore
0
Co-precipitation; 1600 8C, 4 h
Solid-state reaction, 1050 8C, 10 h, 1400 8C, 4 h, 1500 8C, 4 h
Pyrochlore
(Dy1ꢂxSrx)2Ti2O7ꢂ
0.04
0.1
0.1
0.02
0.02
0.04
0.04
0.04
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Pyrochlore + SrTiO3(tr)
Pyrochlore + SrTiO3
Pyrochlore + SrTiO3
Pyrochlore
d
Mechanical activation + firing; 1400 8C, 4 h + 1500 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Solid-state reaction; 1600 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Solid-state reaction; 1400 8C, 4 h
Solid-state reaction; 1600 8C, 4 h
Mechanical activation + firing; 1400 8C, 4 h
Co-precipitation; 1400 8C, 4 h
Co-precipitation; 1600 8C, 4 h
Mechanical activation + firing; 1400 8C, 4 h
Mechanical activation + firing; 1400 8C, 4 h
(Dy1ꢂxCax)2Ti2O7ꢂ
d
Pyrochlore
Pyrochlore
Pyrochlore
Pyrochlore
Pyrochlore
Solidified melt
Pyrochlore
Pyrochlore
Pyrochlore
(Yb0.9Ca0.1)2Ti2O6.9
(Yb0.9Mg0.1)2Ti2O6.9
Pyrochlore
Pyrochlore
sublattice of the Ln2Ti2O7 (Ln = Dy, Ho, Yb) titanate pyrochlores on
the total, bulk and grain-boundary conductivities of these solid
electrolytes and to establish appropriate dopants for Ln2Ti2O7
(Ln = Dy, Ho, Yb) and optimize conditions for achieving high
with hot water and then centrifuged until the ammonia smell
was very weak. After air drying at 100 8C for 24 h, the powder was
ground and prefired at 650 8C for 2 h. Next, the powder was
pressed into discs, which were sintered in a muffle furnace at 1400
and 1600 8C.
conductivity in (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb; A = Ca, Mg, Zn)
d
oxygen ion conductors.
2.2. Characterization techniques
2. Experimental
The samples were characterized by X-ray diffraction (XRD) at
room temperature and by impedance spectroscopy at tempera-
tures from 300 to 1000 8C and frequencies from 10 mHz to 3 MHz
under atmospheric oxygen partial pressure.
2.1. Synthesis of polycrystalline (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb;
A = Mg, Ca, Sr, Zn)
d
A number of samples were prepared by solid-state reactions
using as-purchased chemicals: CaCO3, Sr(NO3)2, ZnO, MgO, TiO2,
Dy2O3, Ho2O3 and Yb2O3. Appropriate powder mixtures were
ground in acetone and pressed into discs, which were then placed
in alundum crucibles and fired in air at 1400–1600 8C for 4–8 h.
After firing, all the samples were furnace-cooled (130 8C hꢂ1). The
sample compositions and firing temperatures are listed in Table 1.
(Ln0.9Ca0.1)2Ti2O6.9 (Ln = Dy, Yb), (Yb0.9Mg0.1)2Ti2O6.9 and
(Dy0.9Sr0.1)2Ti2O6.9 were synthesized by firing oxide mixtures
mechanically activated in an Aronov eccentric vibratory mill
[5,16].
2.2.1. XRD examination
Data were collected on a DRON-3 M diffractometer (Cu K
˚
l = 1.5418 A, Bragg–Brentano geometry, 35 kV, 28 mA,
a
radiation,
2u = 13–658, scan step of 0.028 or 0.058). Phase compositions were
determined using JCPDS-ICDD PCPDFWIN v. 2.3 data. In determin-
ing lattice parameters and analysing the samples for phase purity,
we used WinXPow software and the ICDD PDF database.
2.2.2. Impedance spectroscopy
In electrical measurements, we used disc-shaped polycrystal-
line samples 6–12 mm in diameter and 1–5 mm in thickness.
Contacts to the sample faces were made by firing ChemPur C3605
paste, containing colloidal platinum, at 950–1000 8C. The resis-
tance of the contacts was within several ohms.
Measurements were performed by a two-probe method in the
frequency range 10 mHz to 3 MHz at 13 fixed temperatures from
300 to 1000 8C and an applied sinusoidal voltage of 0.5 V peak,
using a Novocontrol Beta-N impedance analyser and a NorECs
ProboStat ceramic cell fitted with platinum electrodes and a Pt/Pt–
Rh thermocouple.
In addition, (Ln1ꢂxCax)2Ti2O7ꢂ (Ln = Dy, Ho) samples were
d
produced through co-precipitation. The DyCl3 and HoCl3 solutions
used were prepared by dissolving Dy2O3 and Ho2O3 in 15% HCl
while heating the mixture. The H2TiCl6 solution was prepared by
dissolving anhydrous TiCl4 in concentrated HCl. The solution
concentrations were determined gravimetrically. An appropriate
mixture of the H2TiCl6, LnCl3 and Ca(NO3)2 solutions was added
dropwise to a vigorously stirred mixture of concentrated aqueous
ammonia (50%), concentrated ammonium bicarbonate solution
(25%) and water (25%). The precipitate was washed four times

D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
1615
Table 2
Eight-coordinate ionic radii of lanthanides, R(LnCN=83+), and dopants, R(ACN=82+), and the lanthanide–dopant size mismatch
DR
in some of the (Ln0.9A0.1)2Ti2O6.9 (Ln = Dy, Ho, Yb; A = Mg, Ca, Sr, Zn) solid solutions studied.
3+
R(ACN=82+) [19]
D
R (A)
˚
˚
Composition
R(LnCN=8 )(A) [19]
(Yb0.9Ca0.1)2Ti2O6.9
(Dy0.9Ca0.1)2Ti2O6.9
(Yb0.9Mg0.1)2Ti2O6.9
(Ho0.9Ca0.1)2Ti2O6.9
(Dy0.9Sr0.1)2Ti2O6.9
(Ho0.9Zn0.1)2Ti2O6.9
(Ho0.9Mg0.1)2Ti2O6.9
Yb, 0.985
Dy, 1.027
Yb, 0.985
Ho, 1.015
Dy, 1.027
Ho, 1.015
Ho, 1.015
Ca, 1.12
Ca, 1.12
Mg, 0.89
Ca, 1.12
Sr, 1.26
Zn, 0.9
0.135
0.093
0.095
0.105
0.233
0.115
0.125
Mg, 0.89
3. Results and discussion
Doping with Zn and Mg (Fig. 1b, curves 1 and 2), which have
markedly smaller ionic radii, reduces the lattice parameter for
3.1. Structure evolution of (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb; A = Ca,
Mg, Zn; x = 0–0.1)
x ꢄ 0.07 in the (Ho1ꢂxZnx)2Ti2O7ꢂ system and for x ꢄ 0.04 in
d
d
(Ho1ꢂxMgx)2Ti2O7ꢂ . At Mg contents above x = 0.04, the lattice
d
parameter remains constant to within experimental uncertainty.
All our samples (Table 1) had a pyrochlore-like structure. Fig. 1
shows plots of the lattice parameter versus dopant concentration
for the seven series of samples studied. These data demonstrate
that, for x ꢄ 0.04, the incorporation of Ca2+, the largest dopant
cation (Table 2), into the lanthanide (Dy, Ho, Yb) sublattice
increases the lattice parameter (Fig. 1a), except for the
3.2. Analysis of impedance spectra
Fig. 2a–d shows the impedance spectra of four different
samples obtained in this study. The spectra are well resolved,
which enables the bulk (intragranular), grain-boundary and
electrode components of conductivity to be separately assessed
(Fig. 3).
(Ho1ꢂxCax)2Ti2O7ꢂ series prepared via co-precipitation followed
d
by firing at 1400 8C (Fig. 1b). At higher Ca contents, the lattice
parameter increases in the (Yb1ꢂxCax)2Ti2O7ꢂ (x = 0, 0.05, 0.1)
For all the samples, independent on the preparation method,
the semicircles in the impedance spectra are better resolved at low
temperatures than at high temperatures (T > 700 8C). The reason
for this is that, with increasing temperature and diffusion rate, the
properties of grain boundaries approach those of the bulk because
of the rise in conductivity.
d
(Fig. 1a, curve 1), (Dy1ꢂxCax)2Ti2O7ꢂ (x = 0, 0.02, 0.04, 0.1) (Fig. 1a,
d
curve 3) and (Ho1ꢂxCax)2Ti2O7ꢂ (Fig. 1b, curve 4) systems and
d
varies very little in the (Ho1ꢂxCax)2Ti2O7ꢂ series from x = 0.04 to
d
x = 0.1 (Fig. 1b, curve 3). (Ho0.99Ca0.01)2Ti2O7ꢂ sample shows the
d
lowest parameter in this series.
The present impedance data are well represented by the
frequency response of the equivalent circuit proposed by Boukamp
[17] for solid electrolytes (Fig. 4, Table 3), which comprises three
(occasionally two) series connected elements, each composed of a
parallel connected resistor and constant phase element (with an
impedance Z = 1/a(iv
)b, where 0 < b < 1). This provides indirect
evidence that the conduction in the materials studied is
predominantly ionic.
3.3.3. Acceptor doping Yb2Ti2O7 with Ca and Mg: (Yb1ꢂxAx)2Ti2O7ꢂ
d
(A = Ca, Mg; x = 0.1)
3.3.1. Acceptor doping Dy2Ti2O7 with Ca and Sr: (Dy1ꢂxAx)2Ti2O7ꢂ
d
(A = Ca, Sr; x = 0, 0.02, 0.04, 0.1)
Fig. 5 shows Arrhenius plots of total, bulk and grain-boundary
conductivities for (Dy1ꢂxCax)2Ti2O7ꢂ synthesized via co-pre-
d
cipitation followed by firing at 1600 8C. The conductivity of the
doped materials for the most part exceeds that of Dy2Ti2O7,
which lends support to a vacancy mechanism of conduction in
the Ln2Ti2O7 pyrochlores [12]. Note that the conductivity rises
markedly at low doping levels, with a much more gradual
increase at x near 0.1. Similar behaviour was reported for other
oxygen ion conductors [18]. The total high-temperature con-
ductivity is seen to slightly increase as the synthesis temperature
changes from 1400 to 1600 8C (Fig. 6). Only at low temperatures
and high doping levels does the opposite relationship hold,
as illustrated by the conductivity–composition–temperature
diagram in Fig. 6.
Fig. 7 shows Arrhenius plots of conductivity for Ca- and Sr-
substituted Dy2Ti2O7 prepared by solid-state reactions. The
Fig. 1. Lattice parameter as a function of dopant concentration for the solid
solutions studied: (a) (1) (Yb1ꢂxCax)2Ti2O7ꢂ (mechanical activation, firing at
conductivity of (Dy1ꢂxCax)2Ti2O7ꢂ increases with Ca content,
d
d
1400 8C), (2) (Dy1ꢂxCax)2Ti2O7ꢂ (co-precipitation, firing at 1400 8C), (3)
d
while (Dy0.96Sr0.04)2Ti2O6.96, which was found to contain trace
levels of SrTiO3, is close in conductivity to undoped Dy2Ti2O7.
The data in Fig. 8 demonstrate that the conductivity of the
(Dy0.9Ca0.1)2Ti2O6.9 samples prepared via co-precipitation and
(Dy1ꢂxCax)2Ti2O7ꢂ
(co-precipitation, firing at 1600 8C) and (b) (1)
d
(Ho1ꢂxZnx)2Ti2O7ꢂ (solid-state reaction at 1600 8C), (2) (Ho1ꢂxMgx)2Ti2O7ꢂ
d
d
(solid-state reaction at 1600 8C), (3) (Ho1ꢂxCax)2Ti2O7ꢂ (co-precipitation, firing
d
at 1400 8C), (4) (Ho1ꢂxCax)2Ti2O7ꢂ (co-precipitation, firing at 1600 8C).
d

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D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
Fig. 2. (a) Impedance spectra of sample 18 (Dy2Ti2O7, co-precipitation). (b) Impedance spectra of sample 14 ((Ho0.9Ca0.1)2Ti2O6.9, co-precipitation). (c) Impedance spectra of
sample 29 ((Dy0.9Ca0.1)2Ti2O6.9, mechanically activated starting mixture). (d) Impedance spectra of sample 27 ((Dy0.9Ca0.1)2Ti2O6.9, solid-state reaction).
Fig. 3. Evaluation of different contributions to total conductivity as exemplified by the 400 8C impedance spectrum of sample 19 ((Dy0.96Sr0.04)2Ti2O6.96).
Table 3
Equivalent circuit parameters for (Ho0.96Zn0.04)2Ti2O6.96 (see Fig. 4).
Parameter
Value (
V
)
Parameter
Value (F)
Parameter
Value
R1
R2
R3
2.83 ꢁ 105
2.16 ꢁ 105
2.13 ꢁ 106
CPE1-T
CPE2-T
CPE3-T
1.22 ꢁ 10ꢂ11
2.16 ꢁ 10ꢂ8
1.31 ꢁ 10ꢂ6
CPE1-P
CPE2-P
CPE3-P
0.95
0.76
0.50

D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
1617
ceramic grains. The data for the samples prepared by solid-state
reactions exhibit deviations from Arrhenius behaviour (Fig. 7):
their grain-boundary conductivity is
a stronger function of
temperature compared to the Arrhenius equation. One possible
reason for this is the presence of an intergranular amorphous
phase, which cannot be detected by XRD.
3.3.2. Acceptor doping Ho2Ti2O7 with Ca, Mg and Zn:
(Ho1ꢂxAx)2Ti2O7ꢂ (A = Ca, Mg, Zn; x = 0, 0.02, 0.04, 0.1)
d
Fig. 9 shows Arrhenius plots of total, bulk and grain-boundary
Fig. 4. 400 8C impedance spectrum of sample
equivalent circuit fit. ZCPE = 1/T(iv P
(the equivalent circuit parameters are listed in
Table 3).
5 ((Ho0.96Zn0.04)2Ti2O6.96) and
conductivities for (Ho1ꢂxCax)2Ti2O7ꢂ synthesized via co-precipi-
)
d
tation followed by firing at 1600 8C. The behaviour of conductivity
differs somewhat from that in the Dy system. At low doping levels
from mechanically activated oxides (Table 1, sample Nos. 22 and
29) is a factor of 5 higher than that of the xCa = 0.1 material
prepared by solid-state reaction at the same temperature (1400 8E)
(Table 1 sample No. 27). It seems likely that the first two
procedures ensure a more even dopant distribution over the
(x = 0.01–0.02), the conductivity of (Ho1ꢂxCax)2Ti2O7ꢂ is below
d
Fig. 5. Arrhenius plots of total, bulk and grain-boundary conductivities for
Fig. 6. Conductivity–composition–temperature diagram for the (Dy1ꢂxCax)2Ti2O7ꢂ
(Dy1ꢂxCax)2Ti2O7ꢂ prepared via co-precipitation followed by firing at 1600 8C
d
d
samples prepared via co-precipitation followed by firing at 1400 and 1600 8C.
(samples 18, 23, 26, 31).

1618
D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
Fig. 8. Arrhenius plots of bulk conductivity for (Dy0.9Ca0.1)2Ti2O6.9 synthesized at
1400 8C using (1) mechanical activation, (2) co-precipitation and (3) solid-state
reaction.
Fig. 7. Arrhenius plots of total, bulk and grain-boundary conductivities for
(Dy1ꢂxCax)2Ti2O7ꢂ and (Dy1ꢂxSrx)2Ti2O7ꢂ prepared by solid-state reactions at
d
d
1500–1600 8C (samples 16, 19, 24, 28).
that of Ho2Ti2O7 (Fig. 9), primarily because of the increase in the
resistance of the intergranular phase.
In the range x = 0.04–0.1, the conductivity of the pyrochlore-
like (Ho1ꢂxCax)2Ti2O7ꢂ increases with Ca content like in
d
(Dy1ꢂxCax)2Ti2O7ꢂ (x = 0–0.1) samples. The bulk and grain-
d
boundary components of conductivity in these materials (Fig. 9)
show insignificant deviations from Arrhenius behaviour. Together
with the observed activation energies, typical of oxygen ion
conductors (Table 4), the Arrhenius behaviour points to pre-
dominantly ionic conduction in the solid solutions studied.
Fig. 10 shows Arrhenius plots of total, bulk and grain-boundary
conductivities for (Ho1ꢂxMgx)2Ti2O7ꢂ (x = 0, 0.04, 0.07, 0.1) and
d
(Ho1ꢂxZnx)2Ti2O7ꢂ (x = 0, 0.04, 0.07) prepared by solid-state
d
reactions at 1600 8C. The conductivity of (Ho1ꢂxAx)2Ti2O7ꢂ
d
(A = Mg, Zn; x = 0–0.1) increases with dopant (A = Mg, Zn) content
like in the (Ho1ꢂxCax)2Ti2O7ꢂ (x = 0.04–0.1) series. Clearly, Mg is
d
Fig. 9. Arrhenius plots of total, bulk and grain-boundary conductivities for
better dopant then Zn. The total and bulk conductivities are seen to
(Ho1ꢂxCax)2Ti2O7ꢂ prepared via co-precipitation followed by firing at 1600 8C
d
exhibit nearly Arrhenius behaviour, whereas the grain-boundary
(samples 2, 9, 10, 12, 14).

D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
1619
Fig. 11. Arrhenius plots of bulk conductivity for (1) (Yb0.9Ca0.1)2Ti2O6.9
, (2)
(Yb0.9Mg0.1)2Ti2O6.9 (3) (Dy0.9Ca0.1)2Ti2O6.9 (co-precipitation, 1600 8C), (4)
,
(Dy0.9Ca0.1)2Ti2O6.9 (co-precipitation, 1400 8C), (5) (Ho0.9Ca0.1)2Ti2O6.9 (co-
precipitation, 1600 8C), (6) (Ho0.9Ca0.1)2Ti2O6.9 (co-precipitation, 1400 8C), (7)
(Ho0.9Mg0.1)2Ti2O6.9 (solid-state reaction, 1600 8C) and (8) (Dy0.9Ca0.1)2Ti2O6.9
(solid-state method, 1600 8C).
component is a stronger function of temperature. Such behaviour
of grain-boundary conductivity, very typical of ceramics produced
by solid-state reactions, suggests the presence of an intergranular
amorphous phase, like in (Dy1ꢂxCax)2Ti2O7ꢂ prepared by solid-
d
state reactions.
3.3.3. Acceptor doping Yb2Ti2O7 with Ca and Mg: (Yb1ꢂxAx)2Ti2O7ꢂ
d
(A = Ca, Mg; x = 0.1)
Fig. 11 shows Arrhenius plots of bulk conductivity for
(Yb0.9Ca0.1)2Ti2O6.9 (Fig. 11, curve 1) and (Yb0.9Mg0.1)2Ti2O6.9
(Fig. 11, curve 2) prepared using mechanical activation at
1400 8C. The conductivity of Ca-doped sample is higher then
Mg-doped.
3.3.4. Lanthanide effect on the conductivity of titanates
(Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb; A = Ca, Mg; x = 0.1). Comparative
study
d
Fig. 10. Arrhenius plots of total, bulk and grain-boundary conductivities for
(Ho1ꢂxMgx)2Ti2O7ꢂ and (Ho1ꢂxZnx)2Ti2O7ꢂ prepared by solid-state reactions at
d
d
In this study, following Kramer et al. [12] we used divalent
dopants: Mg, Ca, Sr (Group IIA) and Zn (Group IIB).
We failed to obtain phase-pure (Dy0.9Sr0.1)2Ti2O6.9 by any of the
procedures used (Table 1), probably because of the large ionic
1600 8C (samples 1, 3–6).
2+
3+
radius of Sr2+ (for CN = 8: Sr2+, 1.26 A; Ca , 1.12 A; Dy , 1.027 A
Table 4
˚
˚
˚
0
Activation energy for oxygen hopping (Ea
) and the difference between the
[19]). (Dy0.96Sr0.04)2Ti2O6.96 also contained SrTiO3 (trace levels).
activation energy for ionic conduction and that for oxygen hopping (g) in some of
In an earlier study of (Yb1ꢂxCax)2Ti2O7ꢂ (x = 0, 0.05, 0.1) [5], the
d
the materials studied.
highest conductivity was achieved at x = 0.1. Fig. 11 compares the
bulk conductivity data for most of the (Ln0.9A0.1)2Ti2O6.9 (A = Ca,
0
Sample No.
Composition
Ea (eV)
g (eV)
Mg) samples synthesized in this work. The data in Fig.
8
1
3
Ho2Ti2O7
0.78
0.85
0.88
0.77
0.74
0.75
0.69
0.83
0.88
0.87
0.75
0.80
0.77
0.76
0.83
0.19
0.11
0.14
0.16
0.22
0.23
0.18
0.12
0.07
0.12
0.19
0.10
0.18
0.21
0.18
(Ho0.96Mg0.04)2Ti2O6.96
(Ho0.9Mg0.1)2Ti2O6.9
(Ho0.96Zn0.04)2Ti2O6.96
(Ho0.93Zn0.07)2Ti2O6.93
Dy2Ti2O7
demonstrate that the (Dy0.9Ca0.1)2Ti2O6.9 ceramics prepared via
mechanical activation and co-precipitation, followed by firing at
the same temperature are close in conductivity. Therefore, the
conductivity data for materials prepared by these procedures can
be analysed together. The highest conductivity is offered by
(Yb0.9Ca0.1)2Ti2O6.9 (Fig. 11, curve 1). The 750 8C bulk conductivity
of (Yb0.9Mg0.1)2Ti2O6.9, (Dy0.9Ca0.1)2Ti2O6.9, (Ho0.9Ca0.1)2Ti2O6.9 is
close to each other (Fig. 11, curves 2–5). It is interesting that
conductivity of (Ho0.9Mg0.1)2Ti2O6.9, synthesized at 1600 8C from
oxides mixture using solid-state method (Fig. 11, curve 7) is close
4
5
6
16
18
23
26
31
2
Dy2Ti2O7
(Dy0.98Ca0.02)2Ti2O6.98
(Dy0.96Ca0.04)2Ti2O6.96
(Dy0.9Ca0.1)2Ti2O6.9
Ho2Ti2O7
9
(Ho0.99Ca0.01)2Ti2O6.99
(Ho0.98Ca0.02)2Ti2O6.98
(Ho0.96Ca0.04)2Ti2O6.96
(Ho0.9Ca0.1)2Ti2O6.9
10
12
14
to the bulk conductivity of (Yb0.9Mg0.1)2Ti2O6.9, (Dy0.9Ca0.1 2-
)
Ti2O6.9 (Ho0.9Ca0.1)2Ti2O6.9 prepared at lower temperature
,

1620
D.A. Belov et al. / Materials Research Bulletin 44 (2009) 1613–1620
(1400 8C) using more homogeneous techniques (mechanical
activation and co-precipitation) (Fig. 11, curves 2, 4, 5). At first
we have supposed that the highest conductivity of Yb- and Dy-
contained samples is related to the presence of Dy and Yb in two
oxidation states 2+ and 3+, whereas Ho is known to have only one
oxidation state. But according to data presented at Fig. 11 the bulk
conductivity of (Ho0.9Ca0.1)2Ti2O6.9 (co-precipitation, 1600 8C),
(Fig. 11, curve 5) is practically the same as for (Dy0.9Ca0.1)2Ti2O6.9
(co-precipitation, 1600 8C) (Fig. 11, curve 3).
The highest conductivity in the (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho,
d
Yb; A = Ca, Mg, Zn) systems is offered by (Yb0.9Ca0.1)2Ti2O6.9. The
conductions of (Yb0.9Mg0.1)2Ti2O6.9, (Dy0.9Ca0.1)2Ti2O6.9 (mechan-
ical activation, 1400 8C), (Ho0.9Ca0.1)2Ti2O6.9 (co-precipitation,
1400 and 1600 8C), (Dy0.9Ca0.1)2Ti2O6.9 (co-precipitation, 1600 8C)
are close to each other. The conductivity of (Ho0.9Mg0.1)2Ti2O6.9
,
synthesized by solid-state reaction at 1600 8C, is slightly lower. Ca
and Mg are the best dopants for Ln2Ti2O7 (Ln = Dy, Ho, Yb).
The conductivity of the ceramics prepared via co-precipitation
and from mechanically activated oxides exceeds that of the
samples prepared by solid-state reactions at the same tempera-
ture, owing to a more even dopant distribution over the ceramic
grains. The solid-state method can, in principle, provide the close
doping distribution but only at the higher synthesis temperatures.
However the grain-boundary conductivity component is seen to
have non-Arrhenius behaviour in the samples synthesized by
solid-state method.
3.4. Conduction mechanism in pyrochlore-like (Ln1ꢂxAx)2Ti2O7ꢂ
d
(Ln = Dy, Ho, Yb; A = Ca, Mg, Zn)
The present conductivity versus frequency and temperature
data can be used to evaluate the activation energy for oxygen
0
hopping (Ea ) and the difference between the activation energy for
0
ionic conduction (Ea) and that for oxygen hopping (g = Ea ꢂ Ea ) in
the (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb; A = Ca, Mg, Zn) solid
The activation energy for conduction depends little on the
sample composition and preparation procedure, with a tendency
to rise upon A2+ substitution for Ln3+
.
d
electrolytes.
As shown by Almond and West [20], the real part of
conductivity can, to some approximation, be written in the form
g
Re
s(
v) =
sdc(1+(v
/v
h) ), where sdc is the dc conductivity, and
v
Acknowledgements
and vh are the angular frequencies of the applied field and ion
hopping, respectively. If the part of an impedance spectrum
corresponding to bulk conduction can be fitted with the frequency
response of an equivalent circuit composed of a parallel connected
This work was supported by the Presidium of the Russian
Academy of Sciences (program Synthesis of Inorganic Substances
with Controlled Properties and Fabrication of Related Functional
Materials, Grant No. 8/2008), the Russian Foundation for Basic
Research (Grant No. 07-03-00716), by the Department of Materials
Sciences of the Russian Academy of Sciences (program of the Basic
Investigations of New Metal, Ceramic, Glass- and Composite-
Materials, Grant No. 2009).
resistor and constant phase element,
the parameters of the circuit: h = (Ra cos(b
the resistance, and a and b are the parameters of the constant phase
element (with an impedance Z = 1/a(i
)b) (Table 3).
From
for hopping, Ea , using the equation vh
gives a linear relation between log
v
h can be expressed through
v
p
/2))ꢂ1/b, where R is
v
v
h(T) data, one can easily evaluate the activation energy
0
0
=
v
0exp(ꢂEa /KT), which
v
h and Tꢂ1. The results for some
References
of our samples are presented in Table 4. A literature search
revealed no data that could be used to assess the accuracy of these
estimates.
On the whole, the data in Table 4 are consistent with the notion
that acceptor doping in the cation sublattice reduces the formation
energy of oxygen vacancies, thereby raising their concentration
compared to the unsubstituted titanates.
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d
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d
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and revealed basic trends in their oxygen ion conductivity as a
function of composition and temperature.
The conductivity of (Ln1ꢂxAx)2Ti2O7ꢂ (Ln = Dy, Ho, Yb; A = Ca,
d
Mg, Zn) increases mainly with A2+ content in the range x = 0–0.1
and attains the maximum value for x = 0.1.
The bulk high-temperature conductivity of (Ln1ꢂxAx)2Ti2O7ꢂ
(Ln = Dy, Ho, Yb; A = Ca, Mg, Zn) series increases with reduction of
d
[18] J.A. Kilner, Solid State Ionics 129 (2000) 13.
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