On the structure of the disordered Bi2Te4O 11 phase

Article abstract of DOI:10.1016/j.jssc.2004.03.010

The structure of the disordered metastable Bi₂Te ₄O₁₁ phase has been investigated using both neutron powder diffraction and reverse Monte Carlo (RMC) modelling. The average structure, of fluorite-type (space group Fm3m), is characterized by very high Debye-Waller parameters, especially for oxygen. Whereas the cations form a fairly well-defined FCC lattice, the oxygen sublattice is very disordered. It is shown that the local order is similar to that present in the stable monoclinic Bi₂Te₄O₁₁ phase. Clear differences are observed for the intermediate range order. The present phase is analogous to the anti-glass phases reported by Troemel in other tellurium-based mixed oxides. However, whereas Troemel defines anti-glass as having long range order but no short range order, it is shown here that this phase is best described as an intermediate state between the amorphous and crystalline states, i.e. having short and medium range order similar to that of tellurite glasses and a premise of long range order with the cations only.

Full text of DOI:10.1016/j.jssc.2004.03.010

ARTICLE IN PRESS
Journal of Solid State Chemistry 177 (2004) 2168–2176
On the structure of the disordered Bi2Te4O11 phase
O. Masson,a,* P. Thomas,a O. Durand,a T. Hansen,b J.C. Champarnaud,a
and D. Mercurioa
a
´ ´ ´ ´ ´ ´
Faculte des Sciences, Departement de Chimie, Universite de Limoges, Science des Procedes Ceramiques et de Traitements de Surfaces UMR 6638
CNRS, 123 avenue Albert Thomas, 87060 Limoges Cedex, France
b Institut Laue-Langevin, 6, rue Jules Horowitz BP 156, 38042 Grenoble Cedex 9, France
Received 4 November 2003; received in revised form 27 February 2004; accepted 3 March 2004
Abstract
The structure of the disordered metastable Bi2Te4O11 phase has been investigated using both neutron powder diffraction and
%
reverse Monte Carlo (RMC) modelling. The average structure, of fluorite-type (space group Fm3m), is characterized by very high
Debye-Waller parameters, especially for oxygen. Whereas the cations form a fairly well-defined FCC lattice, the oxygen sublattice is
very disordered. It is shown that the local order is similar to that present in the stable monoclinic Bi2Te4O11 phase. Clear differences
are observed for the intermediate range order. The present phase is analogous to the ‘‘anti-glass’’ phases reported by Tromel in other
tellurium-based mixed oxides. However, whereas Tromel defines anti-glass as having long range order but no short range order, it is
shown here that this phase is best described as an intermediate state between the amorphous and crystalline states, i.e. having short
and medium range order similar to that of tellurite glasses and a premise of long range order with the cations only.
r 2004 Elsevier Inc. All rights reserved.
Keywords: Disordered structure; Neutron diffraction; Reverse Monte Carlo modelling
1. Introduction
first by El Farissi [3] and later by Astaf’ev et al. [4]. It
forms under fast crystallization of the Bi2Te4O11 melt.
Its structure and its phase transition toward the stable
monoclinic form were recently investigated by Szaller
et al. [5] and Lovas et al. [6] using X-ray powder
diffraction and selected area electron diffraction. This
phase is presented as having a nearly perfect oxygen-
Bismuth tellurites are attractive materials from both
fundamental and engineering applications points of
view. This is partly due to the lone electron pairs of
bismuth and tellurium atoms which are generally
stereochemically active and which confer good non-
linear optical properties on the materials. Among the
bismuth tellurites, the Bi2Te4O11 compound, although
well studied, still raises questions; in particular concern-
ing the structure of its cubic polymorph. It is known that
the Bi2Te4O11 compound has two polymorphs. The
stable one (a-Bi2Te4O11) was first studied by Frit et al.
[1]. Its structure was completely determined by Rossel
et al. [2]. It has a monoclinic symmetry (space group
P21=n) and is related to the fluorite structure. More
precisely, it is an anion-deficient superstructure of
fluorite composed of an ordered intergrowth of
Bi2Te2O7 (fluorite-type) and Te2O4 (rutile-type) layers.
The metastable polymorph (b-Bi2Te4O11) was reported
5
%
deficient
fluorite-type
structure
(Fm3mðOhÞ;
a ¼ 5:636 A, Z ¼ 4) with no chemical ordering, i.e.
tellurium and bismuth atoms evenly distributed on the
cation sites. However, there is some inconsistency in
describing the actual structure by the fluorite model. To
our knowledge, there is no precedent of such crystal-
chemistry of Te (IV). Indeed, a fluorite structure with a
cell parameter of 5.636 A requires Te–O bond lengths of
about 2.44 A which is much larger than the usual Te–O
bond lengths found in other crystalline tellurites
(B1.87–2.20 A), and notably in the a-Bi2Te4O11. In
addition, each cation is coordinated by eight anions
whereas in all-known tellurite, Te(IV) is commonly
coordinated by three or four oxide ions. In the paper of
Lovas et al. [6], no mention is made of the presence of
atomic displacement disorder which could account for
*Corresponding author. Fax: +33-5-55-45-72-70.
E-mail address: olivier.masson@unilim.fr (O. Masson).
0022-4596/$ - see front matter r 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2004.03.010

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O. Masson et al. / Journal of Solid State Chemistry 177 (2004) 2168–2176
2169
such a discrepancy. The isotropic displacement para-
meters they obtained by Rietveld refinements are indeed
relatively low. In the same line of thought, the phase
transition toward the stable form is described as a
chemical ordering of the cations and the oxygen
vacancies but no mention is made about the change in
the short and medium range orders that a transition
from a fluorite to the monoclinic structure would
require.
The aim of the present paper is to clarify some of the
aspects discussed above, in particular those concerning
the actual nature of the metastable b-Bi2Te4O11 phase.
A first part is devoted to the study of the average
structure by analyzing the Bragg scattering. This part
already emphasizes important differences with respect to
previous results. The second part deals with a more in-
depth description of the actual structure by analyzing
the total scattering. In particular, we discuss its relation
to the monoclinic one, notably from the short and
intermediate range orders point of view.
data were collected in the 8–125ꢀ 2y range with a step
size of 0.02ꢀ 2y. The Rietveld analysis was performed
with the FullProf [7] program.
Total neutron diffraction experiments were carried
out on the D20 high flux diffractometer at the ILL
(Institut Laue-Langevin). This reactor based instrument
uses a curved position-sensitive detector which covers
153.6ꢀ 2y and operates in a wide range of wavelengths.
A wavelength of 0.7985 A was used, enabling us to
record intensities up to Qmax ¼ 15 AÀ1 (Q ¼ 4p sin y/l).
The powder samples were placed in a thin-walled
(2.5 mm) vanadium container of 6 mm in diameter. The
experiments were performed under vacuum, both at
room and low (10 K) temperatures.
In order to extract the total static structure factor
SðQÞ; the neutron raw data were corrected (for zero and
sample displacement errors, background artifacts, ab-
sorption, inelastic and multiple scattering) and normal-
ized using the program CORRECT [8]. The total pair-
correlation function GðrÞ was derived from SðQÞ with
the following integral equation:
Z
sin Qr
SðQÞ À 1 ¼ r0 4pr2ðGðrÞ À 1Þ
dr;
ð1Þ
2. Experimental
Qr
where r0 is the atomic density of the sample. Inversion
of Eq. (1) was achieved indirectly by using a Monte
Carlo-based inversion method [9], which allows, in
contrast to the conventional direct Fourier transform, to
correctly handle noise, truncation of data and the finite
resolution of the instrument.
2.1. Sample preparation
Polycrystalline samples of the Bi2Te4O11 metastable
compound were synthesized from a mixture of pure
Bi2O3 and TeO2 in stoichiometric (1:4) proportions.
Starting materials were Bi2O3 (Aldrich 99.9%) and TeO2
prepared from thermal decomposition of orthotelluric
acid H6TeO6 (Aldrich 99.9%) at 550ꢀC for 24 h. In order
to prevent from oxidation of tellurium (IV) during
synthesis, the sample was prepared in sealed gold tube.
The oxides mixture was melted at 730ꢀC for 1 h and
quenched to room temperature in water. No change of
weight occurred.
The measured density of the sample is
rexp ¼ 6:84ð1Þ g/cm3 (rth ¼ 6:83 g/cm3). The metastable
modification is thus less dense than the stable a-
Bi2Te4O11 phase (rexp ¼ 7:10ð4Þ g/cm3). Note also that
this sample progressively transforms into the stable
phase at temperatures above 450ꢀC, as previously shown
[5].
2.3. RMC modelling
In simple systems, quantitative information about the
local structure, e.g. the coordination numbers, can be
directly obtained from the peak areas in the total pair-
correlation function. Gaussian functions are for instance
fitted to peaks which have been assigned to particular
bonding pairs. For the three components system
considered here, the total pair-correlation function
contains six partial pair functions. This induces a high
overlap of peaks and thus large uncertainties in the
result.
For this reason, structural information was extracted
using the Reverse Monte Carlo algorithm (RMC) [10].
In this method, experimental data from diffraction or
other techniques are used to generate real space models
of the sample. An initial model is randomly varied until
the best agreement with both data and constraints on
the structure is obtained. Constraints are essential to
severely limit the number of structures that are
consistent with the data. It is indeed well-established
[11] that RMC methods do not produce a unique
solution but instead a three-dimensional structure,
generally the most disordered, which is simply consistent
with the data and constraints.
2.2. Measurement techniques
Because of the metastable nature of this phase, it was
not possible to obtain large single-crystals, so that the
subsequent structural analysis was performed on pow-
der samples.
Preliminary measurements were done by X-ray
diffraction. Patterns were collected at room temperature
using CuKa (l ¼ 1:5418 A) radiation on a Siemens-
Bruker D5000 Bragg-Brentano (y22y) powder diffract-
ometer with graphite secondary monochromator. The

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O. Masson et al. / Journal of Solid State Chemistry 177 (2004) 2168–2176
2170
Table 1
For each atom pair, the closest approach distance Rmin; the maximum
Also given in Table 1 are the Faber-Ziman weighing
coefficients of the different partial structure factors.
They show that neutron diffraction mainly probes the
Te–O, Bi–O and O–O pair-correlations. Preferentially
probing cation-cation pairs would require other kind of
experiment (e.g. X-ray diffraction). In the present study,
we are mainly interested in the cation–anion pair-
correlation, the cation–cation pairs being largely con-
strained by the cationic long range order present in this
phase.
coord
distance for calculating the coordination numbers
R
;
the
and
max
val
max
maximum distance for calculating the bond valence sums R
the Faber-Ziman weighting coefficients used in the RMC model are
given
val
max
Atom
pair
Rmin (A)
Rcmoaoxrd (A)
R
(A)
Neutron weight
Te–Te
Te–O
Te–Bi
O–O
3.08
1.68
3.16
2.40
2.08
3.16
0.04967
0.27333
0.07307
0.37602
0.20104
0.02687
2.44
3.1
3.1
Bi–O
Bi–Bi
3. Results and discussion
val
max
Note that the R
to the valence sum lower than 0.05.
value has been chosen in order to get a contribution
3.1. The average structure—Bragg scattering analysis
The X-ray powder diffraction pattern of the Bi2-
Te4O11 sample is shown in Fig. 1. Only one crystalline
phase is clearly present. The 15 diffraction lines in the
10–125ꢀ 2y range can be unambiguously indexed in the
In the present case, the RMC models were built with
2448 atoms (576 Te, 1584 O and 288 Bi) in a cubic box
(B34 A/side) at the proper density (r0B0.0633 atom/
A3). The RMC modelling of the total pair-correlation
function and the total structure factor were achieved
with the RMCA and RMCPOW [12] programs respec-
tively. Constraints on the approach distances of the
different atom pairs were applied using the minimum
approach values reported in Table 1. These values are
based on those found in other crystalline tellurites and
mixed oxides, in particular in the monoclinic Bi2Te4O11
phase. They are about 10% smaller than the corre-
sponding distances found in other phases to allow
disorder in the bond lengths. We modified the RMCA
program in order to implement individual constraints on
the coordination number and the bond valence sum of
each atom type. These additional constraints enabled to
generate the correct crystal-chemistry for tellurium,
oxygen and bismuth atoms. The coordination number
of tellurium atoms was constrained to 3 or 4, which
corresponds to the usual TeO3 or TeO4 polyhedra found
in tellurites. The coordination number of oxygen atoms
was constrained to 1 or 2 to account for terminal or
bridging oxygen. No constraint was applied for bismuth
atoms as they can have quite variable coordination.
Valence sums were constrained to 4 and 3 for tellurium
and bismuth atoms respectively. The constraints have
been implemented by adding for each constraint a term
to the total w2 (i.e. the criterion minimized during RMC
modelling) as follows:
5
%
Fm3mðOhÞ cubic space group with a ¼ 5:636ð4Þ A,
confirming previous results [5,6]. They do not exhibit
significant extra broadening with respect to the instru-
ment resolution, indicating that the structure has a fairly
well-defined long range order. A Rietveld analysis was
carried out with the chemically disordered fluorite
structural model proposed by Lovas et al. [6] in which
the 4a (000) position is filled with bismuth and tellurium
atoms in 1/3–2/3 ratio and the 8c (1/4,1/4,1/4) positions
are occupied by oxygen with 11/12 site occupancy. The
fit is not perfect as attested by the residuals and the
reliability factors. In addition, the isotropic displace-
ment parameters are very large (BTe ¼ BBi ¼ 4:7 A2,
BO ¼ 14:6 A2), indicative of high displacement disorder,
especially for oxygen. This result seems in contradiction
X
2
w2 ¼ ? þ
ð1 À faÞ =s2;
where the sum is over all constraints, fa is the proportion
of atoms of type a that meet the required coordination
number or bond valence sum and s is a parameter
weighting this constraint relatively to others and the fit
to the data. Valence sums were calculated within the
maximum distances reported in Table 1 using the
exponential law and parameters from [13].
Fig. 1. Rietveld fit of the XRD powder pattern of the b-Bi2Te4O11
sample. Rp=6.8%; Rwp=8.6%; RB=3.4%; GoF=1.4; DW (Durbin-
Watson)=1.2.

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2171
function of the atom positions. Thus, the large
displacement obtained for oxygen in the /111S direc-
tions indicates that whereas its average position is (1/
4,1/4,1/4), few atoms are actually at this location but
many are likely shifted toward the center of the cell or
the middle of the edges.
The experiment carried out at 10 K gives almost the
same results as for room temperature. As it can be seen
from Fig. 2, differences in the diffraction pattern are
indeed hardly noticeable with only a very small increase
of the Bragg peaks intensities in the 5–7 AÀ1 Q range. It
is thus very unlikely that the high oxygen Debye-Waller
parameter be induced by thermal motions of atoms, so
that the disorder present in this phase is certainly of
static nature.
This oxygen displacement disorder induces diffuse
scattering. For non-correlated atom displacement, dis-
tributed with a Gaussian probability density function,
the coherent diffuse scattering can be approximated by
Fig. 2. Rietveld fit (the background signal is not fitted) of the neutron
scattering cross-section for the b-Bi2Te4O11 sample at room tempera-
ture Rp=1.08%; Rwp=1.56%; RB=6.1%; GoF=1.2; DW=1.35.
Diffuse scattering signal (dotted curve) calculated for uncorrelated
Gaussian-distributed atom displacement and Rietveld refined Biso
values. Neutron scattering cross section for the b-Bi2Te4O11 sample at
10 K (upper curve), shifted upward by 5 units for clarity.
[14]
X
2
coh
diff
I
ðQÞ ¼
ckjbkj ð1 À exp½ÀBkQ28p2ŠÞ;
ð2Þ
k
where ck; bk and Bk are the concentration, the scattering
length and the isotropic displacement factor of atomic
species k in the system. By using the Bk s obtained from
with the relatively low oxygen displacement factor
(BO ¼ 4:8 A2) given by Lovas et al. [6], which suggests
that the structure is well-ordered. However, we think
that this low value is doubtful as only a very high BO of
about 15 A2 can account for the (222)/(200) line
intensities ratio observed in the XRD pattern given in
their paper.
The neutron structure factor is shown in Fig. 2. It
contrasts with the XRD pattern. We can see diffraction
lines of the fluorite lattice superimposed on a high
background signal which increases rapidly with increas-
ing Q to finally oscillate about a maximum at large Q
values. The background signal is clearly associated with
the oxygen atoms as the neutron coherent scattering
lengths of the oxygen and tellurium atoms are almost
identical (5.803 versus 5.8 b respectively), whereas for X-
rays, the pattern is dominated by the scattering of
tellurium (and bismuth). As shown below, it is
associated with the displacement disorder of the oxygen
atoms.
0
the Rietveld refinement of the neutron data, we get the
curve also depicted in Fig. 2. This curve scales and
reproduces quite well the main trend of the experimental
diffuse scattering, in particular the rapid increase with
increasing Q: From a scattering point of view, the
diffuse scattering is thus consistent with the decrease of
the Bragg intensities. It is also obvious from Fig. 2 that
the experimental diffuse scattering exhibits features that
are not reproduced with Eq. (2). This indicates that the
oxygen disorder is not fully random but exhibits local
structural correlation.
3.2. The actual structure—total scattering analysis
To study the local structural correlation, one needs to
consider the total structure factor, i.e. both Bragg and
diffuse scattering. All this information is contained in
the pair-correlation function.
The Rietveld refinement of the neutron data obtained
at room temperature gives basically the same results as
with XRD data. In particular, it confirms the large
displacement parameters of cations and oxygen atoms
(BTe=BBi=3.5 A2, BO=18.3 A2). The fit is significantly
improved with a split atom refinement in which
tellurium, bismuth and oxygen atoms fill the 32f
(x,x,x) position. The refined positions are x ¼ 0:035
and 0.312 for Te/Bi and O atoms, respectively, and the
isotropic displacement factors drop to BTe=BBi=0.8 A2
and BO=8.1 A2. Split atom refinements generally enable
to take into account a non-Gaussian probability density
The total pair-correlation function of the sample is
shown in Fig. 3. There are 3 narrow peaks in the
distance range from B1.8 to B3 A and broad peaks
further. Is also depicted for comparison the pair-
correlation function of the monoclinic phase obtained
with isotropic displacement parameters of 0.5 A2 for all
atoms. One can immediately notice the strong analogy,
especially in the low correlation length region, indicating
that the local order of both phases is similar. The first
and highest peak at B1.90 A is unambiguously assigned
to the Te–O correlation lengths whereas the second peak
at B2.35 A corresponds mainly to the Bi–O bond

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O. Masson et al. / Journal of Solid State Chemistry 177 (2004) 2168–2176
2172
guess of the FCC cationic lattice of the disordered
phase.
The relationship of this fluorite subcell (subscript F)
to the monoclinic cell (subscript M) is:
0
1
F A
0
10
A@ M A
1
aF
b
À4
2
0
À3
3
1
1
1
aM
b
1
6
B
@
C
B
@
CB
C
¼
:
cF
2
cM
The initial model was then obtained by first generat-
ing a large monoclinic structural block with slightly
modified cell parameters a ¼ 6:9028; b ¼ 7:9706;
c ¼ 19:524 A and a ¼ b ¼ g ¼ 90ꢀ (monoclinic cell
parameters:
a ¼ 6:9909ð3Þ;
b ¼ 7:9593ð3Þ;
c ¼ 18:8963ð8Þ A, a ¼ g ¼ 90ꢀ and b ¼ 95:176ð3Þꢀ) in
order to get non-distorted fluorite subcells with the
proper cell parameter (a ¼ 5:636 A). A cubic box
consisting of 6 ꢁ 6 ꢁ 6 fluorite subcells was then
extracted and origin was chosen to have bismuth and
tellurium atoms located at the cube origin. The chosen
6 ꢁ 6 ꢁ 6 size (B34 A/side) is adequate for RMC
modelling and enables to match the periodicity of the
monoclinic phase. Next, the Te/Bi long range order
corresponding to that of the monoclinic phase was
partially destroyed by rotating a quarter or half a turn
layers composed of 9 (3 ꢁ 3 ꢁ 1) cubic elements (each
cubic element being composed of 2 ꢁ 2 ꢁ 2 fluorite
subcells) about the x; y and z axis in a sequential and
random fashion (i.e. in the way used with the Rubik’s
cube game). Note that different sequences were used
with no effect on the final result. Few atoms were finally
moved out in such a way that the model fulfils the
closest approach conditions.
The as-obtained model partly matches the local order
of the monoclinic phase and a chemically disordered
FCC cationic lattice. As one can see from Fig. 4, total
neutron scattering calculated from this model agrees
quite well with the experimental data even prior to
RMC fitting. The main features of the pattern are
indeed reproduced. This initial configuration is likely a
simple and consistent description of the real structure
even if it is obvious, from the difference in Bragg and
diffuse intensities, that it is still too much ordered.
The RMC fit of both the total pair-correlation
function in the range 0–17 A and the total structure
factor are shown in Fig. 4. The fit are satisfactory
(although not perfect) with coordination constraints
satisfied at 92% and 91% for tellurium and oxygen
atoms respectively, valence constraints satisfied at 90%
and 92% for tellurium and bismuth atoms with an
average valence sum of 3.9 for tellurium atoms and 2.9
for bismuth atoms. This indicates that the assumptions
made in the RMC model, i.e. the presence of inter-
connected TeO3 or TeO4 structural units as those
usually found in crystalline tellurites, are consistent
with the data. Some differences between the RMC fit
Fig. 3. Total pair-correlation function GðrÞ from neutron diffraction
measurement for the b-Bi2Te4O11 sample (open circles) and for the a-
Bi2Te4O11 phase.
lengths. These preliminary results show that the actual
structure has the typical Te–O bond lengths found in
other crystalline tellurites, and not the 2.44 A as
expected with the fluorite model. Further information
has to be extracted via RMC modelling.
3.2.1. The RMC model
In glass structure modelling, the initial configuration
generally consists of a random arrangement of atoms
within a cubic cell, with constraints on the density, the
closest atomic approaches and the coordination num-
bers. In the present case, although highly disordered, the
phase also exhibits long range order so that the w2
function has numerous deep local minima, which can
rather complicate its minimization. A better initial
configuration can be obtained by using a crystalline
model. The fluorite phase with randomly disordered
bismuth, tellurium atoms and oxygen vacancies has two
main drawbacks. First, as stated above, its local order is
very different from that present in the b-Bi2Te4O11
phase, so that no coordination and valence constraints
are met. Second, it is not easy to control how tellurium,
bismuth atoms and oxygen vacancies are distributed or
similarly to account for some correlations in the position
of bismuth atoms and oxygen vacancies. Random does
not mean uniform and it is likely that the initial model
contains non-realistic clusters of bismuth atoms and
oxygen vacancies. The starting model we used instead
derives from the monoclinic phase, the underlying ideas
being the followings: first, the short range order of the
two phases is similar as discussed above, so that the
chemistry of both tellurium and bismuth are satisfied in
the starting model. Second, this phase has a fluorite
sublattice, although distorted and chemically ordered,
so that a slight modification can allow to get a good

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2173
and the experimental total structure factor can be
noticed in the lower Q region. A short range order peak
at QB1:4 AÀ1 corresponding to correlation length of
B4.5 A in the structure is for example not reproduced
by the model. These subtle differences are not well
explained until now.
The projection of the model along the c-axis and its
average structure, i.e. the projection of all unit cells into
a single one, are given in Fig. 5. The projection of the
monoclinic structure is also depicted for comparison.
These pictures catch some of the main characteristics of
the b-Bi2Te4O11 phase, namely its disordered nature, its
relation to the fluorite structure and its analogy with the
monoclinic phase. In particular, the latter has also a
large apparent displacement of the oxygen atoms with
respect to the fluorite tetrahedral sites. This is necessary
to account for the chemistry of tellurium and bismuth
atoms given that cations form a fairly well-defined FCC
sublattice. The slight distortion of this FCC sublattice
can be interpreted as due to the Bi/Te ordering along a
cubic [111]F direction in one set of {111}F planes.
3.2.2. The short and intermediate range orders
The partial pair-correlation functions obtained from
the RMC model are depicted in Fig. 6. The cation–
cation coordination shells corresponding to a FCC
lattice are fairly well resolved. The peaks are relatively
broad with almost the same width, indicative of an
uncorrelated displacement disorder. In contrast, the O–
O correlation function only exhibits one single peak at
B2.8 A which correspond to the usual O–O distances
found in the TeO3 or TeO4 polyhedra. Further, the
correlation function is almost flat, indicating that the
oxide sublattice is nearly completely disordered (neither
medium nor long range order) similarly to what is found
in tellurite glasses. The Te–O correlation function has an
intense and very sharp maximum at B1.9 A, a weaker
maximum at B2.9 A, and a much broader at B4.5 A.
The next coordination shells are barely resolved. The
sharpness of the first peak indicates that there is no
significant disorder in the Te–O bond lengths. Similar
features are obtained with the Bi–O pair but with a
slightly broader first peak at B2.4 A. The proportion of
TeO3 is almost the same as that of TeO4 for a cut-off
radius of 2.4 A. However, it seems that there is no
clear boundary between TeO3 and TeO4 units as the
Fig. 4. Total neutron structure factor SðQÞ for the b-Bi2Te4O11 phase :
experimental (solid line), RMC fit (dashed line) and calculated from
the initial (i.e. prior to RMC fit) RMC model (short dotted line). Inset:
total pair distribution function GðrÞ from neutron diffraction (open
circles) and RMC fit (solid line).
Fig. 5. Projection along the fluorite c-axis of the a-Bi2Te4O11 phase (left), the b-Bi2Te4O11 RMC model (right) and its average structure (upper right
corner).

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O. Masson et al. / Journal of Solid State Chemistry 177 (2004) 2168–2176
2174
Fig. 6. Partial pair-correlation functions from the b-Bi2Te4O11 RMC model.
Fig. 7. O–Te–O (left) and Te–O–Te (right) bond angle distributions.
proportion depends slightly on the chosen cut-off
radius. This contrasts with the monoclinic phase in
which the local tellurium environment is clearly made of
TeO3 and TeO4 in the 3:1 ratio. For bismuth atoms, the
obtained coordination numbers are 8, 7 and 6 in the
20%, 50% and 22% proportions, respectively, and a
small amount of less-realistic coordination numbers
(o6). For the a-Bi2Te4O11 phase, bismuth atoms are 7
or 8-fold coordinated in the same amount.
peaks, indicating that disorder affects mainly the bond
valence angles. For the O–Te–O distribution, the peaks
occur close to the internal angles of the TeO3 and TeO4
polyhedra found in the monoclinic phase and in pure
tellurite polymorphs: for TeO3 units, the angles lie
between 85ꢀ and 100ꢀ and for TeO4 units, bond angles
are B96ꢀ for the equatorial oxygen and B178ꢀ for the
axial one.
Concerning the Te–O–Te angle distribution, the peak
is close to 120ꢀ and is clearly smaller than the 140–144ꢀ
values found in the monoclinic phase. The Te–O–Te
The O–Te–O and Te–O–Te bond angle distributions
are given in Fig. 7. They are characterized by broad

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2175
angle distribution is characteristic of how the TeO3 and
TeO4 polyhedra are linked together. It is thus indicative
of the intermediate range order in the structure. As one
can see in Fig. 8, the structure of the monoclinic phase
can be described as an ordered sequence of tellurium-
only layer and a mixed double layer containing equal
numbers of bismuth and tellurium atoms (of composi-
tion Bi2Te2O7). The composite double layer contains
only isolated TeO3 units. In the tellurium-only layers,
TeO3 and TeO4 units are linked together by a single
oxygen bridge to form parallel infinite long sinusoidal
chains. Identical chains are present in the paratellurite a-
TeO2 phase [15]. In these chains, the Te–O–Te angles lie
between 140ꢀ and 144ꢀ. The lower value found with the
RMC model suggests that these sinusoidal chains do not
form in the b-Bi2Te4O11 phase. This could indicate that
these chains can only form in tellurium-only layers, i.e.
in the paratellurite a-TeO2 phase or in the a-Bi2Te4O11
phase. The bond angle found in the present case are
rather indicative of other type of linkage as for instance
the zigzag chains found in the g-TeO2 phase [16] or the
double oxygen bridge present in the tellurite b-TeO2
phase [17]. A close inspection of the structure of the
RMC model reveals that there are mainly long cooked
and branched chains, rings and few double oxygen
bridges. Rings are interesting features as they are usually
found in tellurite glasses, for example in sodium tellurite
glasses [18] but not in the a-Bi2Te4O11 phase. The ring
distribution found in the model is given in Fig. 8. T he
maximum populated are the smallest, i.e. three-fold,
rings. Are also present 4-, 5-, 6-membered and larger
rings with a decreasing population. In many respects,
the Te–O polyhedra linkage found in this phase seems
closer to those found in tellurite glasses than those
found in the a-Bi2Te4O11 phase. This clear difference of
intermediate range order with respect to the monoclinic
phase may partly explain the relative stability of the b-
Bi2Te4O11 phase with respect to its transformation
toward the a-Bi2Te4O11 phase. A very substantial
rearrangement is indeed required to break the small
rings and generate long sinusoidal chains.
4. Concluding remarks
To conclude, whereas the b-Bi2Te4O11 phase exhibits
a fluorite-type average structure with quite well-defined
long range order, it is shown that only the cations form
a crystalline (FCC) lattice. The anions exhibit a large
displacement disorder with respect to the tetrahedral
sites in order to fulfil the crystal-chemistry of both
bismuth and tellurium atoms. It is worth noting that
similar phases have been observed in other chemical
tellurium-oxide-based systems by Tromel [19]. Even if
no structural details were given, their XRD pattern are
typical of the fluorite structure and their Raman spectra
are similar to that of tellurite glasses (the same kind of
Raman spectra has been obtained for the present phase
but it is not presented in this paper). These phases have
been denominated by Tromel ‘‘antiglass’’ phases in
order to account for what he defines as structure having
long-range order but no short-range order. According to
the present study, it appears that these phase are
certainly best described as being an intermediate state
between the glass and crystalline states in which the
short range order is present and the cationic network
has already formed as the premise of crystallization.
Fig. 8. Up: Typical features of the a-Bi2Te4O11 structure: alternate
sequence of tellurium-only and Bi/Te mixed layers. The composite
double layer contains only isolated TeO3 units and the tellurium-only
layers are formed of parallel infinite long sinusoidal chains of TeO3
and TeO4 units linked together by a single oxygen bridge. Bottom:
typical features of the b-Bi2Te4O11 RMC model: projection along the
c-axis of a single (distorted) FCC unit cell showing a part of a Te–O
chain containing a 3-fold tellurium ring and a double oxygen bridge
(the isolated smaller atoms are the other Te and Bi atoms of the FCC
unit cell which are not involved in this chain). Also given is the
tellurium rings distribution.

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This phase is certainly a first stage of the crystallization
of the stable a-Bi2Te4O11 phase.
[5] Zs. Szaller, L. Poppl, Gy. Lovas, I. Dodo
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[7] J. Rodriguez-Carvajal, FULLPROF program, See www-
llb.cea.fr/fullweb/fp2k/fp2k.htm
Acknowledgments
[8] M.A. Howe, R.L. McGreevy, P. Zetterstrom, CORRECT
program, See ftp://studsvik.uu.se/pub
We would like to acknowledge the ILL staff for
experimental support. One of us, O. Durand, is grateful
to the Conseil Regional du Limousin for financial
´
[9] M.A. Howe, R.L. McGreevy, L. Pusztai, MCGR program, See
ftp://studsvik.uu.se/pub
[10] R.L. McGreevy, L. Pusztai, Mol. Simul. 1 (1988) 359.
[11] R.L. McGreevy, P. Zetterstrom, J. Non-Cryst. Solids 293–295
(2001) 297.
support. The authors would also like to acknowledge
Prof. B. Frit for fruitful and stimulating discussions on
the present work.
[12] R.L. McGreevy, A. Mellegard, See ftp://studsvik.uu.se/pub
[13] N.E. Brese, M. O’Keeffe, Acta Crystallogr. B 47 (1991) 192.
[14] B.E. Warren, X-ray Diffraction, Addison-Wesley, Reading, MA,
1969.
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