PAPER www.rsc.org/materials | Journal of Materials Chemistry
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Synthesis, structure and properties of the hexagonal perovskite,h-BaTi1�xHoxO3�x/2
Yang Liu, Emma E. McCabe, Derek C. Sinclair and Anthony R. West
Received 23rd December 2008, Accepted 1st May 2009
First published as an Advance Article on the web 11th June 2009
DOI: 10.1039/b822785c
The crystal structure of hexagonal (h)-BaTi0.85Ho0.15O2.925 has been determined using neutron powder
diffraction data. The structure is derived from that of h-BaTiO3 and contains Ho3+, the largest cation
known to be accommodated by the B site in h-BaTiO3. Ti and Ho are disordered over the B1 octahedral
sites and the structure may be regarded as intermediate between those of h-BaTiO3 and
Ba3Sr(Nb,Ta)2O9. h-BaTi0.85Ho0.15O2.925 forms as a long-lived but metastable, intermediate phase
before transforming, slowly, to the thermodynamically stable cubic polymorph of the same
composition; its formation is an example of Ostwald’s rule of successive reactions. It is an electrical
insulator with relative permittivity of �50.
Introduction
The perovskite BaTiO3 exists in a number of polymorphs, all
related to the cubic ABO3 perovskite structure, also known as the
3C-type perovskite structure.1 This 3C-type structure consists of
close-packed AO3 layers stacked along [001] in a cubic sequence
(i.e. ABCABC) with B cations occupying octahedral sites to form
a lattice of corner-linked BO6 octahedra.2 The tetragonal poly-
morph of BaTiO3, in which the Ti4+ cations are displaced from
the centre of the octahedra towards an apex, has received much
attention as a result of the high permittivity at the tetragonal–
cubic phase transition (3max �10 000, TC �130 �C).3
Undoped BaTiO3 is stable in the 6H hexagonal polymorph at
temperatures above �1460 �C and adopts this structure until it
melts at�1620 �C.4 The structure of the 6H (here also referred to
as h) polymorph of BaTiO3-related materials is composed of 6
close-packed BaO3 layers stacked in the sequence [cch]2, where c
and h refer to cubic and hexagonal stacking, respectively. This
results in two different octahedral sites for the B cations: B(1)
occupies corner-linked octahedra and B(2) is located in face-
shared B(2)2O9 dimers.5 The hexagonal polymorph of undoped
BaTiO3 can be stabilised to room temperature by heating BaTiO3
in reducing conditions, resulting in partial reduction of Ti4+ to
Ti3+ and the creation of oxygen vacancies in O(1) sites in the
hexagonal layers;6 the general formula is BaTi4+1�xTi3+
xO3�x/2.
In addition, a number of B site dopant cations, of comparable
size to Ti4+, can stabilise the 6H polymorph to lower tempera-
tures. For aliovalent substitution of lower valence cations, charge
compensation is again achieved by creation of oxygen vacancies
in the O(1) sites.7–12 The permittivity of doped and undoped
h-BaTiO3 at room temperature is typically in the range 20 # 30 #
100, giving rise to possible microwave dielectric applications.13
Various mechanisms for stabilisation of this 6H polymorph
have been put forward yet it is still not well understood. Dickson
et al. proposed that transition metal cations with partially filled
d orbitals are necessary, with stabilisation driven by the
Department of Engineering Materials, University of Sheffield, MappinStreet, Sheffield, UK S1 3JD
This journal is ª The Royal Society of Chemistry 2009
formation of metal–metal bonds within the B(2)2O9 dimers.7 Ren
et al. proposed that cations such as Mn4+, comparable in size to
Ti4+, are essential.14 Langhammer et al. suggested that Jahn–
Teller active dopants (especially Ti3+, Mn3+ and Cu2+) are
required.15,16 However, stabilisation with p-block cations8,9 such
as Ga3+ also occurs and indicates the need for continued inves-
tigation of the stabilisation mechanism of this high temperature
phase.
Here, we report the structural characterisation of h-BaTiO3
stabilised kinetically by partial substitution of a much larger
cation, Ho3+, in place of Ti4+, together with its electrical prop-
erties. The phase—h-BaTi0.85Ho0.15O2.925—forms as a long-lived
metastable intermediate before formation of the thermodynam-
ically stable cubic (c)-polymorph of the same composition. The
c-polymorph is then stable at all temperatures and, once formed,
does not transform back to the h-polymorph. This work forms
part of a larger study into the phase equilibria, solid solution
mechanisms and electrical properties of Ho-doped BaTiO3, to be
reported elsewhere.17
Experimental procedure
Polycrystalline samples of h-BaTi0.85Ho0.15O2.925 were prepared
by solid state reaction of stoichiometric quantities of dried
BaCO3, TiO2 and Ho2O3. The reagents were intimately ground in
an agate mortar and pestle, heated at 1050 �C for 12 h and then at
1550 �C for 24 h in air in Pt crucibles, with intermittent grinding.
Pellets for electrical characterisation were prepared by heating
the reagents at 1050 �C for 12 h, then at 1450 �C for 12 h, pressed
into pellets using a uniaxial press followed by a cold isostatic
press (CIP) and sintered at 1550 �C for 12 h. This gave pellets
with density of�74% of the theoretical value. It was not possible
to increase the pellet density by firing at higher temperatures
because the structure then changed (slowly) to that of the
c-polymorph. Electrodes were fabricated on opposite pellet faces
using Au paste which was dried, decomposed and hardened by
gradually heating to 800 �C. Impedance spectroscopy (IS)
measurements were carried out using a Hewlett Packard 4192A
Impedance Analyser between room temperature and 500 �C in
J. Mater. Chem., 2009, 19, 5201–5206 | 5201
Table 2 Selected bond lengths and inter-ionic distances in �A
Ba(1)–O(1) 3 � 2.9118(1) Ti/Ho(1)–O(2) 6 � 2.0713(6)Ba(1)–O(1) 3 � 2.9116(1) Ti(2)–O(1) 3 � 2.050(1)Ba(1)–O(2) 6 � 2.9270(6) Ti(2)–O(2) 1 � 1.923 (1)Ba(2)–O(1) 3 � 2.855(1) Ti(2)–O(2) 2 � 1.923(1)Ba(2)–O(2) 2 � 2.9144(1)Ba(2)–O(2) 1 � 2.9143(1) Ti(2)–Ti(2) 2.818(2)Ba(2)–O(2) 2 � 2.9141(1) Ti/Ho(2)–Ba(2) 3.4383(4)Ba(2)–O(2) 1 � 2.9141(1) Ti/Ho(2)–Ba(2) 3.4384(4)Ba(2)–O(2) 3 � 3.0801(9) Ti/Ho(2)–Ba(2) 3.572(1)
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the frequency range 10 Hz to 1 MHz. X-Ray powder diffraction
(XRPD) data were collected at room temperature over a period
of 10 h using a Sto€e STADI P diffractometer operating in
transmission mode with a monochromated Cu Ka1 radiation
source and a position sensitive detector with a step size of 0.01�
2q. Time of flight (TOF) neutron powder diffraction (NPD) data
were collected at room temperature on GEM at ISIS, Oxford,
UK. Rietveld refinements used the GSAS suite of programs.18
Selected area electron diffraction (SAED) patterns were taken
using a Philips EM430 transmission electron microscope, accel-
erating voltage 300 kV.
Results and discussion
Structural characterisation of h-BaTi0.85Ho0.15O2.925
Structural refinement. Both the XRPD and NPD patterns were
indexed on a hexagonal unit cell, a z 5.81 �A and c z 14.31 �A
with space group P63/mmc. A refinement was carried out using
the structure reported by Akimoto et al.5 as a starting model. The
lattice parameters were first refined using the bank 6 data and
were then fixed as subsequent banks of data were added to the
refinement. Background (shifted Chebyshev function), histo-
gram scale factor and peak profiles were refined for each histo-
gram. Atomic coordinates were refined with constraints applied
to the temperature factors and positions of Ti and Ho on the 2a
site. In the initial model, Ti and Ho were distributed statistically
across both B sites but this model did not give a sensible
refinement. Subsequent results showed that the B(2) site was
occupied exclusively by Ti and this distribution was therefore
fixed. The fractional occupancies of both oxygen sites were
initially refined freely giving an overall oxygen content of
2.869(5) per formula unit, with vacancies located predominantly
on the O(1) site in the hexagonal layer. This is somewhat less than
the expected value of 2.925 per formula unit. However, when the
overall oxygen content was fixed to 2.925, there was a negligible
change in agreement between the calculated and observed
patterns. The oxygen content is related directly to the oxidation
states of the cations. The only cation capable of variation in
oxidation state is Ti. However, Ti3+, even in small concentration,
causes the electrical conductivity of titanates to rise dramatically.
Since the present phase is highly insulating (see later), the Ti must
be present as Ti4+ and hence the oxygen content is given directly
by the cation stoichiometry. In the final refinement, the overall
oxygen content was fixed at 2.925 and the occupancies of O(1)
and O(2) refined within this overall constraint. Final parameters
Table 1 Structural parameters from refined room temperature TOF NPD d
Atom Wyckoff site x y
Ba(1) 2b 0 0Ba(2) 4f 1/3 2/3Ti/Ho(1) 2a 0 0Ti/Ho(2) 4f 1/3 2/3O(1) 6h 0.51869(9) 0.0374(1)O(2) 12k 0.83130(7) 0.6626(1)
a a ¼ 5.8112(2) �A, c ¼ 14.2830(8) �A, c2 ¼ 14.89 (81 variables), Rwp ¼ 3.76%
5202 | J. Mater. Chem., 2009, 19, 5201–5206
are given in Table 1, selected bond lengths in Table 2, refinement
profiles in Fig. 1 and the structural model in Fig. 2.
h-BaTi0.85Ho0.15O2.925 adopts a B site ordered 6H structure in
which the face-shared B(2)O6 octahedra are occupied exclusively
by Ti, whilst the B(1)O6 octahedra between the c-stacked BaO3
layers accommodate both Ti and Ho. The O vacancies are
located in both the h-BaO3 layers and the c-BaO3 layers.
P63/mmc vs. P63/m. The ideal (hcc)2 structure has space group
P63/mmc but materials such as Ba3SrNb2O9 and Ba3SrTa2O9
adopt slightly distorted structures with P63/m symmetry. The
lower symmetry is manifested by tilting of the octahedra around
one of their three-fold axes. These two phases show complete
ordering of Sr and Nb/Ta over the two B sites: Sr occupies the
larger cubic B(1) site and Nb/Ta are located in the B(2)2O9 face-
shared octahedra. Due to the substantial difference in size of Sr2+
and Nb5+/Ta5+ (six-coordinate ionic radii 1.18, 0.64 and 0.64 �A,
respectively),19 stacking of the different-sized octahedra is facil-
itated by rotation of the octahedra.20
The structure of these phases shows similarities with
h-BaTi0.85Ho0.15O2.925: both contain relatively large, lower val-
ent cations substituted onto the B(1) sites. The c/a ratio of
2.4578(2) observed for h-BaTi0.85Ho0.15O2.925 is slightly larger
than the accepted maximum of 2.45 for structures of P63/mmc
symmetry, above which distortions resulting in structures of P63/
m symmetry usually occur. A high c/a ratio, 2.47, is also observed
for BaFe0.67Ti0.33O2.664 of P63/mmc symmetry,10 but the oxygen
vacancies may give rise to an expansion which might account for
the large c/a ratio.
Structural refinements for h-BaTi0.85Ho0.15O2.925 were also
carried out using models of P63/m symmetry but no improve-
ment in fit was observed (Rwp of 3.20% with 51 variables,
compared with Rwp of 3.18% for the equivalent model of P63/
mmc symmetry with 48 variables). In the absence of additional
reflections in XRPD, NPD and SAED patterns due to loss of the
ata for h-BaTi0.85Ho0.15O2.925, space group P63/mmca
z Fractional occupancy Uiso � 100/�A2
1/4 1 0.68(3)0.09870(7) 1 1.17(2)0 0.55/0.45 0.22(5)0.8487(1) 1/0 0.87(3)1/4 0.950(2) 1.24(2)0.08307(3) 0.987(1) 1.19(1)
, Rp ¼ 3.37%.
This journal is ª The Royal Society of Chemistry 2009
Fig. 1 Observed (+), calculated (�) and difference (bottom) profiles
from refinement using room temperature TOF NPD data for h-
BaTi0.85Ho0.15O2.925, bank 6 (a), bank 5 (b), bank 4 (c), bank 3 (d) and
bank 2 (e), overall c2 ¼ 14.89, Rwp ¼ 3.76%, Rp ¼ 3.37%.
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c glide plane from P63/mmc, there was no justification for
lowering the symmetry from P63/mmc. The slightly larger
c/a ratio for h-BaTi0.85Ho0.15O2.925 may reflect some local tilting
of the octahedra due to the presence of both large HoO6 and
small TiO6 octahedra in the same set of sites between the cubic
layers, but the long range structure is best described with
P63/mmc symmetry. The Ti/Ho(1) site must exhibit considerable
local deviation from the average size shown by the bond
distances in Table 2 as Ti4+ is much smaller than Ho3+. Never-
theless, we find no evidence of cation order or site distortions
associated with this set of sites.
B cation coordination environments. The presence of dopant
cations exclusively on the cubic B(1) sites is relatively unusual for
substituted h-BaTiO3. In most cases, either a statistical distri-
bution of B site cations is found (as observed for
BaTi1�yGayO3�y/28) or a preference for the B(2) site in the face-
shared octahedra (as found for BaTi0.667Ir0.333O37). The fact that
Ho3+ is not located in the B(2) sites is probably due to its large
ionic radius (0.901 �A);19 location in the B(1) site minimises
cation–cation repulsions which would otherwise be significant if
Ho was located in the face-shared B(2) sites. It also increases
substantially the mean radius of the B(1) site and this ensures
adequate separation of Ba(2) and B(2) ions on the cation sub-
lattice (see later). To the best of our knowledge, Ho3+ is the
largest cation known to substitute onto the B sites in h-BaTiO3,
the next largest being Pt2+ (ref. 7) and In3+ (ref. 21) (with six-
coordinate ionic radii of 0.8 �A).19
The variation in metal–oxygen bond lengths clearly demon-
strates the site preferences of the two different-sized B site
cations; bond lengths of 2.0713(6) �A for Ti/Ho(1)–O represent an
average between expected bond lengths of �1.976 �A for Ti–O
and �2.3 �A for Ho–O. In contrast, the Ti(2)–O bond lengths are
within the range expected for Ti–O bonds. These observations
are consistent with the B(2) site containing exclusively Ti4+
cations whilst Ho is located only on the cubic B(1) site. Inter-
estingly, Ti(2) forms 3 long bonds to O(1) sites and 3 short bonds
to O(2) sites. This difference in bond lengths highlights the
repulsion between the two Ti(2) ions located in the face-sharing
B(2)2O9 dimers, causing the Ti(2) ions to move apart towards the
cubic layers and away from the h-BaO(1)3 layer. This repulsion
may be further enhanced by the occurrence of some O(1)
vacancies which reduces the shielding between Ti(2) ions.
Oxygen vacancy distribution. All models used in Rietveld
refinements were slightly improved when the oxygen vacancies
were not confined to the O(1) site; refinements suggest vacancies
are located on both O(1) and O(2) sites. This is relatively unusual
as recent studies have demonstrated that even for high vacancy
concentrations, in most systems, vacancies are located exclu-
sively on the O(1) site;6 however, other exceptions are reported,
such as BaFeO2.79.22
A and B metal atom array in 6H-ABO3. In an elegant structural
analysis of 6H-Ba(Ti,Fe3+,Fe4+)O3-d Grey et al.11 demonstrated
the significance of considering the metal sublattice of the 6H
structure in an attempt to understand the factors that control its
stability, especially on incorporation of oxygen deficiency. They
noted that the largest variations in interatomic distances were
J. Mater. Chem., 2009, 19, 5201–5206 | 5203
Fig. 2 Unit cell of h-BaTi0.85Ho0.15O2.925 viewed down b axis, with unit
cell axes shown as solid lines in grey, Ba as large grey spheres, Ti/Ho(1)O6
octahedra in black and Ti(2)O6 octahedra in grey.
Fig. 3 Plot of Ba(2)–B(2)0 distances against average B cation ionic
radius, as shown by Grey et al.,11 with BaTi0.85Ho0.15O2.925 shown to be
similar to oxygen stoichiometric 6H materials.
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associated with pairs of B(2) ions and/or Ba(2) ions along [001].
Twinning of the BaB array occurs about the h-Ba(1)O(1)3 layers
and this produces two non-equivalent Ba and B atoms, Fig. 2.
In their solid solution, Grey et al.11 noted a short B(2)–Ba(2)
distance prior to any oxygen deficiency and that this distance was
essentially invariant at 3.40(1) �A on removal of oxygen from the
O(1) site across the solid solution range. This distance was noted
to be shorter than that expected for a BaTi alloy (�3.58 �A) and
therefore resistant to further contraction. The net result of
removal of O(1) atoms is displacement of both Ba(2) and B(2) in
the z-direction; however, this causes a reduction in Ba(2)–B(2)0
distance, Fig. 2. To avoid an unreasonably short Ba(2)–B(2)0
distance (dashed line Fig. 2) adequate separation of the
c-Ba(2)O(2)3 layers is required (see dotted lines). In h-BaTi0.85-
Ho0.15O2.925, this is aided by the presence of a large ion (Ho) on
the B(1) site as it resides in octahedral holes between adjacent
c-Ba(2)O(2)3 layers.
Our results for h-BaTi0.85Ho0.15O2.925 are in excellent agree-
ment with the description provided by Grey et al.11 Oxygen
deficiency is greater from the O(1) site, the Ti(2)–Ti(2) separation
is large (�2.818(2) �A), the Ba(2)–B(2) separation, 3.4384(4) �A is
>3.4 �A. The Ba(2)–B(2)0 separation (3.572(1) �A) is increased due
to the large Ho cation located exclusively on the B(1) site.
Grey et al.11 constructed a plot of Ba(2)–B(2)0 separation
against mean B site ionic radius for selected 6H phases and noted
a linear relationship for stoichiometric ABO3 phases, ranging
from BaCrO3 to Ba3YIr2O9. The Ba(2)–Ba(2)0 distance for
h-BaTi0.85Ho0.15O2.925 lies on this line, Fig. 3.
Thermodynamic considerations. h-BaTi0.85Ho0.15O2.925 is not
thermodynamically stable but forms as a kinetically stable
intermediate during reaction of starting materials:17 on
5204 | J. Mater. Chem., 2009, 19, 5201–5206
prolonged heat treatment, the structure transforms to that of
a cubic BaTiO3 solid solution. Phase diagram studies show that
the high temperature hexagonal phase of BaTiO3 is in fact
destabilised on doping with Ho, as shown by the increase in the
cubic to hexagonal phase transition temperature with increasing
Ho-content.17 As a consequence, the h-polymorph of BaTi0.85-
Ho0.15O2.925 could exist, hypothetically, as a thermodynamically
stable phase at very high temperatures, [1600 �C but this does
not happen in practice as samples melt prior to any possible
phase transition.
Given that h-BaTi0.85Ho0.15O2.925 is not stable thermody-
namically, it is relevant to consider the factors that influence its
formation and, once formed, its kinetic stability. Most phase
transitions are accompanied by an increase in enthalpy, DH, with
increasing temperature and therefore, from the free energy
relationship, DG ¼ DH � TDS, the phase transitions, and the
higher temperature polymorphs, must also have an increase in
entropy, DS. Indeed, high temperature polymorphs are ther-
modynamically stable at high temperatures only because the
magnitude of the �TDS term reduces their free energy to below
that of the low temperature polymorph(s). In the case of
BaTi0.85Ho0.15O2.925, the stable c-polymorph melts before
transforming to the h-polymorph17 and therefore, the magnitude
of T required for the h-polymorph to be thermodynamically
stable is inaccessible in the solid state. The h-polymorph, there-
fore, has both higher DH and higher DS than the c-polymorph at
all realistic temperatures.
Since h-BaTi0.85Ho0.15O2.925 has higher free energy than
c-BaTi0.85Ho0.15O2.925, it is thermodynamically metastable; we
may therefore regard it as a high energy reaction intermediate in
the pathway that leads finally to the thermodynamically stable,
cubic polymorph. It has higher entropy than that of the final
product; once formed, there is a high activation barrier for the
h- to c-transformation and therefore it has considerable kinetic
stability.
There are three aspects to be considered in the formation and
kinetic stability of a metastable phase such as h-BaTi0.85-
Ho0.15O2.925. First, why does the phase form at all? Clearly it
must have a high negative enthalpy of formation, with a high
lattice energy, in order to be kinetically stable at high tempera-
tures. It therefore forms in preference to the final, thermody-
namically stable product, because it has high entropy and in
particular, has an entropy intermediate between that of the
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disordered mixture of ions in the early stages of reaction and that
of the final product with the lowest entropy.
Second, what are the structural features of the metastable
phase that contribute to its high entropy? In the case of
h-BaTi0.85Ho0.15O2.925 the Ti/Ho(1) site must exhibit consider-
able local disorder which probably involves positional disorder
of either or both the cations and the surrounding oxygens, as
well as the occurrence of oxygen vacancies. A rule-of-thumb
guide to stable solid solution formation is that atom sizes
should be within 15% of each other for significant substitution
to occur. Using octahedral ionic radii: Ho3+, 0.901 �A and Ti4+,
0.605 �A,19 the Ho3+ cation is �50% larger than Ti4+; this size
difference is well beyond the limits of what may be regarded as
generally acceptable for Ho and Ti to be disordered over the
same set of crystallographic sites. We therefore identify the
Ti/Ho(1) site, and the surrounding oxygens, as the principal
source of high entropy in the structure. In particular, it seems
highly unlikely that any of the Ti/Ho–O(1) bonds have length
2.071 �A and that instead, this length represents an average of
significantly shorter bonds for Ti–O and much longer bonds
for Ho–O.
Third, why is the transformation to the thermodynamically
stable product slow? In this case, the h- to c-transformation
involves a change in the oxygen stacking sequence and in the
nature of the linkage of the (Ti,Ho)O6 octahedra. It is, therefore,
a major reconstructive transformation which involves the
breaking and reforming of strong Ti–O bonds.
The formation and kinetic stability of h-BaTi0.85Ho0.15O2.925
are an example of Ostwald’s rule of successive reactions, in which
reactions proceed through one or more metastable intermediates
before reaching the equilibrium product.23 In practice, this rule is
a guideline rather than a quantitative and verifiable rule.
Although often not stated explicitly, there are very many
examples in the reactions and formation of inorganic solids
where Ostwald’s rule may be cited. h-BaTi0.85Ho0.15O2.925 is yet
another example.
Fig. 4 (a) Impedance complex plane plot, (b) Z00/M00 combined spec-
troscopic plot and (c) capacitance C0 versus frequency, for h-BaTi0.85-
Ho0.15O2.925 ceramic at 399 �C.
Fig. 5 Arrhenius plot for h-BaTi0.85Ho0.15O2.925: total resistances (-)
and bulk resistances (,) extracted from the Z0 intercepts on Z* plots.
Electrical characterisation of h-BaTi1�xHoxO3�x/2
The electrical properties of h-BaTi0.85Ho0.15O2.925 ceramics
(pellets of �74% theoretical density) were measured using
impedance spectroscopy. Impedance complex plane plots,
Fig. 4a, and combined Z00/M00 spectroscopic plots, Fig. 4b,
indicate the presence of two components. The relative resistances
of the two responses in the complex plane plots did not change
with temperature, suggesting that they have the same activation
energy. The high frequency component has the smaller capaci-
tance value, 7 � 10�12 F cm�1; as it corresponds to the main peak
in the M00 plot, it is attributed to the bulk impedance of the
sample and also has the highest resistance (largest peak in the Z00
plot). The low frequency component has a capacitance of 3 �10�10 F cm�1 at 399 �C and is attributed to a thin layer compo-
nent which, from the similar activation energy of the resistance
values, appears to be associated with a constriction resistance.24
Values for the two resistances as a function of temperature are
presented as Arrhenius plots in Fig. 5.
The impedance data can also be represented as plots of
capacitance against frequency, as shown in Fig. 4c, and the
bulk capacitance value may be readily extracted from the
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frequency-independent high frequency plateau. The bulk
permittivity of h-BaTi0.85Ho0.15O2.925 is relatively high for
a non-ferroelectric compound (30 �50) and is consistent with
literature reports of h-BaTiO3 and other doped h-BaTiO3
phases.13
Conclusions
The crystal structure of h-BaTi0.85Ho0.15O2.925 has been deter-
mined. It is a hexagonal perovskite derived from the structure of
h-BaTiO3 and contains Ho3+, the largest cation known to enter
the h-BaTiO3 structure in the B sites. Smaller dopant cations
generally occupy partially the face-sharing octahedral sites,
whereas Ho is preferentially located on the other set of octahe-
dral sites that are corner-linked. The structure therefore shows
similarities to those of Ba3SrNb2O9 and Ba3SrTa2O9 in which the
larger Sr2+ cation occupies exclusively the corner-sharing octa-
hedral sites; h-BaTi0.85Ho0.15O2.925 may be regarded as an
intermediate between these structures and that of h-BaTiO3.
It is unusual for ions as different in size as Ti4+ and Ho3+ to
replace each other in solid solution formation. In this case, the
resulting phase is thermodynamically metastable and may be
regarded as an entropically stabilised high temperature poly-
morph which forms as an intermediate in the reaction pathway
that yields, eventually, the thermodynamically stable, cubic, Ho-
doped BaTiO3 polymorph. The source of the high entropy of the
h-structure is revealed by the Rietveld refinement results. The Ti/
HoO(1) octahedra contain two very different-sized cations,
whose average bond length to oxygen is either too long or too
short for the individual, cation–oxygen distances. Consequently,
there must be considerable local positional disorder of the atoms
involved, contributing to the high entropy of the structure.
The electrical properties of h-BaTi0.85Ho0.15O2.925 are similar
to those of other doped hexagonal perovskites; the permittivity is
high for a non-ferroelectric material with a value of �50 and the
phase is an electronic insulator with a conductivity of e.g. 2 mS
cm�1 at 600 K. The ceramics were not of high density, in spite of
the high sintering temperatures, as demonstrated by the imped-
ance data which indicated that the samples were electrically
inhomogeneous with bulk and constriction resistance compo-
nents with activation energies in the range 0.6–0.7 eV: constric-
tion resistances are a common feature of poorly sintered
ceramics.
5206 | J. Mater. Chem., 2009, 19, 5201–5206
Acknowledgements
We thank EPSRC for funding, Dr R. Smith for the collection of
NPD data, Dr H. Bagshaw for the collection of SAED patterns
and Prof. A. J. Bell (Leeds) for use of a CIP.
References
1 H. D. Megaw, Proc. Phys. Soc. London, 1946, 58, 133–153.2 R. H. Mitchell., Perovskites Modern and Ancient, Almaz Press,
Thunder Bay, 2002.3 A. v. Hippel, Rev. Mod. Phys., 1950, 22(3), 221–245.4 K. W. Kirby and B. A. Wechsler, J. Am. Ceram. Soc., 1991, 74(8),
1841–1847.5 J. Akimoto, Y. Gotoh and Y. Oosawa, Acta Crystallogr., Sect C:
Cryst. Struct. Commun., 1994, 50, 160–161.6 D. C. Sinclair, J. M. Skakle, F. D. Morrison, R. I. Smith and
T. P. Beales, J. Mater. Chem., 1999, 9, 1327–1331.7 J. G. Dickson, L. Katz and W. Ward, J. Am. Chem. Soc., 1961, 83,
3026–3029.8 A. Feteira, G. M. Keith, M. J. Rampling, C. A. Kirk, I. M. Reaney,
K. Sarma, N. M. Alford and D. C. Sinclair, Cryst. Eng., 2002, 5, 439–448.
9 A. Feteira, D. C. Sinclair and I. M. Reaney, J. Am. Ceram. Soc., 2006,89(7), 2105–2113.
10 I. E. Grey, L. M. D. Cranswick and C. Li, J. Appl. Crystallogr., 1998,31, 692–699.
11 I. E. Grey, C. Li, L. M. D. Cranswick, R. S. Roth andT. A. Vanderah, J. Solid State Chem., 1998, 135, 312–321.
12 G. M. Keith, K. Sarma, N. M. Alford and D. C. Sinclair, J.Electroceram., 2004, 13, 305–309.
13 E. Sawaguchi, Y. Akishige and M Kobayashi, J. Phys. Soc. Jpn.,1985, 54(2), 480–482.
14 F. Ren, S. Ishida and S Mineta, J. Ceram. Soc. Jpn., 1994, 102(1),105–107.
15 H. T. Langhammer, T. Muller, R. Bottcher and H.-P. Abicht, SolidState Sci., 2003, 5, 965–971.
16 H. T. Langhammer, T. Muller, K.-H. Felgner and H.-P. Abicht, J.Am. Ceram. Soc., 2000, 83(3), 605–611.
17 Y. Liu and A. R. West. J. Europ. Ceram. Soc., accepted.18 A. C. Larson, R. B. v. Dreele, Los Alamos National Laboratory
Report: LA-UR-86-748, 1987.19 R. D. Shannon, Acta Crystallogr., 1976, A32, 751–767.20 H. W. Zandbergen and D. J. W. Ijdo, Acta Crystallogr., Sect C: Cryst.
Struct. Commun., 1983, 39, 829–832.21 M. J. Rampling. Synthesis and Characterisation of Undoped and
Doped Hexagonal Barium Titanate. University of Sheffield,Sheffield, 2003.
22 A. J. Jacobson, Acta Crystallogr., Sect. B: Struct. Sci., 1976, 32, 1087.23 T. Threlfall, Org. Process Res. Dev., 2003, 7(6), 1017–1027.24 P. G. Bruce and A. R. West, J. Electrochem. Soc., 1983, 130, 662–669.
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