Chemistry and thermodynamics of the twin charge-ordering transitions in RBaFe2O5+w series

Article abstract of DOI:10.1016/j.jssc.2003.08.011

Thermal and volume parameters of the twin charge-ordering Verwey transitions in RBaFe₂O_5+w (R=a rare-earth element) are summarized as a function of R and w. Their determination is exemplified for case R = Dy, for which also synthesis conditions, phase relations, and refined crystal-structure data for the valence-mixed (Fe^2.5+) and charge-ordered (Fe²⁺ and Fe³⁺) phases are reported. Data for the R=Nd, Sm, Eu and Gd variants with wide ranges of oxygen non-stoichiometry suggest that increasing w decreases ΔS and the temperature of the transition in a manner that is similar to a behavior under increasing concentration of an ideal solution of RBaFe₂O₆ in RBaFe₂O₅. Thermal parameters of the transition for the ideal mixed-valence composition RBaFe₂O_5.000 are estimated from such compositional dependences, varying reasonably smoothly as a function of R (radius, electronegativity, polarizability). Parameter ΔV is the only one that follows the structural discontinuity between the charge-ordered R = Nd and variants with smaller trivalent R ions. The ordering of the d_xz orbitals of the Fe²⁺ ions is thus being achieved at a cost of lowering the symmetry when the R size becomes unfavorably large. A definition of the Verwey transition as a first-order orbital ordering of a valence-mixed phase is suggested.

Full text of DOI:10.1016/j.jssc.2003.08.011

ARTICLE IN PRESS
Journal of Solid State Chemistry 177 (2004) 281–292
Chemistry and thermodynamics of the twin charge-ordering
transitions in RBaFe O
series
2
5þw
Ã
P. Karen
Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern N-0315 Oslo, Norway
Received 19 May 2003; received in revised form 25 July 2003; accepted 7 August 2003
Abstract
Thermal and volume parameters of the twin charge-ordering Verwey transitions in RBaFe2O5þw (R ¼ a rare-earth element) are
summarized as a function of R and w: Their determination is exemplified for case R = Dy, for which also synthesis conditions,
2:5þ
2þ
3þ
phase relations, and refined crystal-structure data for the valence-mixed (Fe ) and charge-ordered (Fe and Fe ) phases are
reported. Data for the R ¼ Nd; Sm, Eu and Gd variants with wide ranges of oxygen non-stoichiometry suggest that increasing w
decreases DS and the temperature of the transition in a manner that is similar to a behavior under increasing concentration of an
ideal solution of RBaFe2O6 in RBaFe2O5: Thermal parameters of the transition for the ideal mixed-valence composition
RBaFe2O5:000 are estimated from such compositional dependences, varying reasonably smoothly as a function of R (radius,
electronegativity, polarizability). Parameter DV is the only one that follows the structural discontinuity between the charge-ordered
2
þ
R = Nd and variants with smaller trivalent R ions. The ordering of the dxz orbitals of the Fe ions is thus being achieved at a cost
of lowering the symmetry when the R size becomes unfavorably large. A definition of the Verwey transition as a first-order orbital
ordering of a valence-mixed phase is suggested.
r 2003 Elsevier Inc. All rights reserved.
Keywords: Mixed-valence classes; Verwey-transition thermodynamics; Depression of charge-freezing point by non-stoichiometry; Synchrotron
X-ray diffraction; Charge-ordering superstructure; Rare-earth barium iron oxides
1
. Introduction
associated with alignment of the antiferromagnetic
moments in a direction perpendicular to the tetragonal
four-fold axis (viz., along b) [4]. Given the typical shape
of the dxz orbitals, the magnetostrictive contraction
along b offers, together with the corresponding expan-
sion along a; an opportunity for ordering of these
orbitals [3], minimizing their energy and allowing them
There are thousands of compounds that fulfill one of
the Day–Robin definitions [1] of the three classes of
mixed valence. As noted by Mott [2], only a few of them
change from one class to another as a function of
temperature. To date there is only one structural type
that makes the metamorphosis through all three
Day–Robin classes, via two first-order phase transitions
6
to be doubly occupied in case of a high-spin d ion, such
¨
as Fe : Mossbauer spectroscopy has shown [3] that at a
certain temperature below TN a premonition of the full
2þ
[3,4]. It is RBaFe2O5; a double-cell perovskite in which
the small size of the trivalent rare-earth ion R
3þ
charge ordering occurs within this minor orthorhombic
2
:5þ
(
R ¼ Nd–Ho and Y) stabilizes an oxygen vacancy, and
distortion, when the single valence-mixed state Fe
separates into two states Fe
2:5Àe
2:5þe
and Fe ; correspond-
the divalence of the large barium ion introduces the
charge imbalance that forces the semi-integer valence
upon iron.
ing to the Day–Robin class-II mixed valence. This
premonitory charge-ordering transition is manifested by
a relatively small caloric effect and a small increase in
electrical resistivity. No structural changes are detected
by either synchrotron X-ray or neutron powder diffrac-
tion [4,5]. Upon further cooling, a full separation into
integer charges of the class-I mixed valence occurs at a
temperature TV referring to the Verwey transition
observed first [6] in magnetite. The ensuing ordering of
As a class-III mixed-valence paramagnetic conductor
above TNE430 K; the phase has a tetragonal structure
´
of the P4=mmm symmetry. Below the Neel temperature,
an increasing orthorhombic distortion appears (Pmmm),
Ã
Fax: +47-22-85-54-41.
E-mail address: pavel.karen@kjemi.uio.no.
0022-4596/$ - see front matter r 2003 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2003.08.011

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
282
di-and trivalent iron is accompanied by a huge increase
in orthorhombic distortion that minimizes the energy of
and barium carbonate (0.1% Sr, Merck) by liquid
mixing in a citrate melt. The procedure is described in
detail in Ref. [8]. Calcination was performed at 860 C
in an atmosphere of Ar, H2 and H2O having
2þ
ꢀ
the doubly occupied dxz orbitals of Fe : The long-range
charge-ordered structure below the transition tempera-
ture TV thus features alternate chains of di-and trivalent
iron running along b; instead of their alternating in all
three dimensions, as dictated [7] for point charges. The
localization of the ionic charges is manifested by a two-
orders-of-magnitude increase in electrical resistivity, an
increase in volume and a decrease in entropy causing a
proportionally stronger caloric effect than that observed
at the premonitory charge-ordering transition. The
magnitudes of these changes, as well as the transition
temperatures TV are strongly influenced by the type of
the R atom (R ¼ Nd [8], Sm [8], Eu [9], Gd [10], Tb [3],
Y [4] and Ho [5]) that seemingly have little to do with the
charge-ordering process of the iron atoms. This is not
uncommon. Also in iron molecular complexes, moieties
that are not coordinated to iron exhibit influence over
the stability of the charge-ordered state [11].
logðpO =barÞE À 16; yielding a single-phase powder.
2
The master sample material was sintered in the form of
2
cylinders (cold pressed at 150 kg=cm ) at 1000 C under
ꢀ
logðp =barÞE À 15:2: The oxygen non-stoichiometry
O2
(w) was controlled by high-temperature equilibration
and quenching in similar atmospheres with partial
pressures of oxygen defined by the humidity of the gas
(measured by an Endress–Hauser MMY150 hygro-
meter). The equilibrated samples were quenched into a
metal container filled with high-purity Ar (o2 ppm O ;
2
dried over a P O desiccant). A thin surface layer was
2
5
removed before further characterizations, and samples
were stored under argon. The oxygen content was
determined by a cerimetric method described in detail in
Ref. [14]. The standard deviations of the titration may
be judged from data presented in Section 3.1. For a
typical distribution of the oxygen content across such
quenched samples; see Ref. [10].
For obvious reasons, the transition parameters are
also strongly influenced by any departure from the ideal
ratio of the integer iron valences caused by oxygen non-
stoichiometry [8,12] or aliovalent doping [13]. The
In an attempt to further improve the oxygen-content
homogeneity, a sintered cylinder of DyBaFe O
was
sealed in an evacuated quartz tube, annealed for 3
2
5:006
oxygen non-stoichiometry is of the RBaFe O
2
type
5þw
ꢀ
with w40; and the additional oxygen is accommodated
at the vacant perovskite site situated in the R layer.
Accordingly, the achievable occupancy of this site varies
with the size of the R atom: from w ¼ 0:03 for R ¼ Ho
months at 250 C and gradually cooled down to ambient
temperature over a 1-month period. The comparison of
the thus obtained sample (new oxygen-content para-
meter w ¼ 0:013) with a sample that has not been
annealed (w ¼ À0:004) is in Section 3.4.
3
4
up to some filling for the largest compatible R ¼ Nd at
ambient oxygen pressures. This gives a wide range for
the control of the average oxidation state of iron, from
2.2. Phase-content determinations
2
.5 for w ¼ 0 to 3 for w ¼ 0:5; and higher up. The most
important effect of the oxygen non-stoichiometry is the
progressive decrease of the concentration of the valence-
mixed Fe
All samples were characterized by conventional X-ray
¨
powder diffraction (XPD) with Guinier–Hagg camera,
2
:5þ
state as seen by Mo
¨
ssbauer spectrometry.
CuKa1 radiation, using Si as an internal standard.
Contents of crystalline phases were estimated from
comparisons of calculated and observed intensities of
prominent Bragg peaks fitted as Lorentzian profiles. All
phase contents are listed in molar fractions x that refer
to formula units where non-oxygen atoms are normal-
ized to unity. This corresponds to expressing the
composition in terms of coordinates in the subsolidus
Dy(O)–Ba(O)–Fe(O) phase diagram.
This decrease has been described by a probability model
of pairing of neighboring integer ionic charges [12].
In this paper, thermodynamic description of Verwey
transitions in RBaFe O
2
is attempted experimentally
5þw
in terms of variables of thermal (DH; DS; T ) and
c
structural (DV) origin, which are summarized and
analyzed as a function of R and w: For R ¼ Dy as an
example, determination of these variables is reported in
detail, together with synthesis, phase relation data, and
crystal structure refinements of the charge-ordered
superstructure.
2.3. Synchrotron powder X-ray diffraction (SXPD)
Data on DyBaFe O
2
were collected at the powder
5þw
diffractometer with He cryostat installed on the BM1B
beamline at the ESRF Grenoble in following sequences:
2
. Experimental
(1) High-resolution, high-counting-statistics data collec-
2
.1. Syntheses and oxygen-content control
tion for Rietveld refinement in the GSAS programme
suite [15] of the long-range charge-ordered superstruc-
ture of the class-I mixed-valence phase at 100 or 200 K:
(2) Isothermal scans upon warming through the Verwey
transition over the 020-type Bragg peaks; for unit-cell
Amorphous precursor for synthesis of DyBaFe O5þw
2
was obtained from standardized Dy O (99.9%, Stan-
ford Materials), metallic iron (99.95%, Koch–Light)
2
3

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
283
data from Lorentzian profile fits. (3) High-resolution
data for Rietveld refinement of the class-III mixed-
valence phase at 330 K: Data for Rietveld refinements
were binned from all six Si-crystal analyzers of the
diffracted beam currently installed at the diffractometer.
For short scans only that analyzer was used whose
angular position is directly calibrated. Samples were
sealed in glass capillaries of 0:25 mm in diameter
-
13
Oxidative decomposition
Single phase
Reductive decomposition
5
.046
5.045
-14
5
.031
5
.000
-15
(
calculated absorption mRo1), spinning in the mono-
5.006
2
chromatic X-ray beam of a cross-section of 1 Â 5 mm
4.998
˚
and wavelength lE0:5 A calibrated with a NIST
5.005
5.013
.021
5.027
standard silicon. According to Ref. [10], the Bragg-line
asymmetry observed for these phases arises from
convolutions of the nearly Lorentzian instrumental
profile with compositional distributions of unit-cell
parameters. As such, it was modeled by releasing the
linear strain coefficients Shkl of Stephens [16] in the
profile function based on the pseudo-Voigt function of
Thompson et al. [17]. Although not all nuances of the
unit-cell-parameter distributions can be contoured in
this manner, the important peak/background resolution
of the extremely weak superstructure peaks at the
foothills of the strong peaks is good.
-16
5.344
5
4
.920
-17
4.986
4.969
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er
Fig. 1. Limits in partial pressures of oxygen for formation of
ꢀ
RBaFe2O5þw at 1000 C; as seen after 4 days of equilibration. Oxygen
content per the nominal formula unit is listed for samples with
majority phase RBaFe2O5þw:
Table 1
2
.4. Differential scanning calorimetry (DSC)
a
ꢀ
Decomposition products upon oxidation of DyBaFe O5þw at 1000 C:
Parameters estimated by molar balance are in italics
2
A liquid-nitrogen operated Perkin–Elmer Pyris 1
Oxygen content
DyFeO3
Ba1ÀyDy FeO3Àw0
y
instrument was used to monitor thermal-flux curves
upon heating (10 K=min) between 160 and 360 K:
Aluminum pans (50 mL) were used to seal the coarsely
powdered samples. Temperatures were corrected to the
zero sample-weight based on a peak-temperature
dependence measured in a separate calibration series
0
˚
a/A
x
x
y
w
5.306(1)
5.424(4)
0.21
0.22
0.79
0.78
0.37
0.36
0.44
0.37
3.9210(7)
3.9211(5)
a
For definition of the phase content x see Section 2.2.
(
the correction was rarely larger than 1 K). The
temperature scale was calibrated on cyclopentane,
cyclohexane, n-octane, n-decane, n-dodecane, m-nitro-
toluene and p-nitrotoluene standards of 499:7% purity
and found linear. Enthalpy was standardized on melting
of the Perkin–Elmer standard indium as well as on the
low-temperature phase transitions of cyclohexane.
Standard deviations of these runs were typically 71%
of the value. Both the transition enthalpy and entropy
were determined by integration of the heat-flow peaks,
as described in Ref. [10].
perovskite-type structure, and R ¼ Er; which does not
form a perovskite. It is seen that changing R varies
dramatically the homogeneity limits of RBaFe2O5þw:
Oxidation in pure oxygen of phases with R down to
Gd does not cross the upper homogeneity limit at
ꢀ
1000 C: The stability window narrows substantially for
variants with smaller R; as these phases become stable
only in reducing atmospheres. Their oxidation upon
gradually increasing partial pressure of oxygen proceeds
sharply into multiphase products exemplified in Table 1
for R ¼ Dy:
3
. Results and discussion
Reductive decomposition as a function of decreasing
ꢀ
partial pressure of oxygen proceeds at 1000 C over an
3
.1. Formation of RBaFe O
2
intermediate pseudo-equilibrium range into a dark-
green product where iron has oxidation state close to
þ2 (by cerimetry; the phase identity was not ascer-
tained). By correcting the redox conditions, the green
product can be oxidized back to a single-phase double-
cell perovskite. The intermediate range (Fig. 1) is
approximately 0:2 bar wide in terms of oxygen partial
pressure; about twice the estimated effect of the
5þw
In order to obtain a comprehensive picture of the
redox stability of RBaFe2O5þw; a series of oxygen-
control equilibrations has been performed at 1000 C on
all R variants. In Fig. 1, partial pressures of oxygen that
limit the formation of RBaFe O
ꢀ
are plotted as a
2
5þw
function of R; including R ¼ La; which forms a single-

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
284
Table 2
Syntheses and characterizations of nominal DyBaFe O5þw samples
2
Oxygen
Double-cell perovskite, XPD
˚
logðp=barÞ
a
b
ꢀ
˚
b=A
˚
c=A
content
x
a=A
Ar : H2
H2O
O2
t= C
t/days
Not det.
0.31
0.57
3.9464(11)
3.9437(4)
3.9442(8)
3.9426(7)
3.9440(5)
3.9440(4)
3.9438(8)
3.9441(5)
3.9442(4)
3.9426(5)
—
3.9186(11)
3.9187(4)
3.9175(6)
3.9180(7)
3.9181(5)
3.9175(3)
3.9185(8)
3.9177(4)
3.9186(3)
3.9192(4)
—
7.5647(20)
7.5664(7)
7.5660(16)
7.5654(13)
7.5626(10)
7.5639(9)
7.5668(14)
7.5644(10)
7.5665(9)
7.5717(11)
—
8.78
8.78
À4.35
À4.35
À4.35
À4.35
À3.99
À1.62
À4.35
À1.65
À1.76
À1.70
À1.74
À1.70
À28.54(1)
À28.84(1)
À29.15(1)
À29.46(1)
À29.36(1)
À15.71(2)
À29.78(1)
À15.17(3)
À14.11(3)
À13.63(3)
À13.28(4)
À12.75(6)
660
650
6
6
6
6
5
4
5
4
3
3
3
3
4.732(1)
4.888(4)
4.988(2)
4.996(1)
5.006(1)
5.008(1)
5.020(1)
5.030(1)
5.045(3)
5.306(1)
5.424(4)
0.65
1
0.992
8.78
8.78
640
630
c
9.19
8.52
610
1
1
1
1
1
0
0
1000
620
8.78
18.2(1)
82(2)
123(3)
198(6)
332(18)
1000
1000
1000
1000
1000
—
—
—
a
Overall cerimetric oxygen content per nominal formula DyBaFe2O5þw:
By volume; standard error refers to variations over time.
According to SXPD; see Section 2.2 for definition of x:
b
c
variations in the composition of the flowing gas and the
temperature of the wetting solution.
Table 3
Kinetic limitation of reductive decomposition of DyBaFe O5þw
samples
2
a
According to Fig. 1, single-phase RBaFe O
2
is
5þw
formed over a w range that is narrowing towards smaller
R ions and approaching simultaneously the ideal mixed-
valence composition w ¼ 0:000: In the particular case
Oxygen tE6 days DyBaFe O BaðDy; CÞO3
Dy O3 Fe
2
2
5
ꢀ
˚
a=A
content t= C
x
x
x
x
4
.888(4) 640
0.65
0.57
0.31
0.07
0.11
0.22
4.216
4.214
4.209
0.04
0.04
0.07
0.24
0.28
0.40
of DyBaFe O5þw; single-phase compositions down to
2
ꢀ
4.732(1) 650
Not det. 660
w ¼ 0:006 are obtained at 1000 C (Table 2). However
small, such compositional nuances are important for the
three-dimensional long-range charge ordering to be
detectable, the detection limit being wE0:02 [8].
t=days
ꢀ
ðt ¼ 650 CÞ
4
.732(1)
6
0.57
0.25
0.13
0.00
0.11
0.24
0.27
0.31
4.214
4.216
0.04
0.08
0.11
0.12
0.28
0.43
0.49
0.57
The ideal mixed-valence composition DyBaFe O
2
5:000
Not det. 12
Not det. 18
Not det. 24
appears better achievable when the oxygen-content
control procedure is performed at temperatures below
4.212
4.212(1)
ꢀ
7
00 C: Decomposition under increasingly reducing
a
For other details on these samples see first three lines of Table 2.
See also Section 2.2 for definition of x:
conditions then proceeds with no apparent discontinuity
in the overall (cerimetric) oxygen contents; as though
ꢀ
the range of sluggish kinetics observed at 1000 C were
much broader. Indeed, decomposition products gradu-
ally and clearly emerge and prevail as a function of
increasing temperature when the reaction atmosphere
and time are kept constant. While the overall oxygen
contents of such mixtures decrease, unit-cell parameters
of the original phase (Table 2) and of the decomposition
products (Table 3) do not change. This is not compatible
with thermodynamic equilibrium among these phases.
The implied kinetic limitation was verified by investigat-
Intensities of the observed 1 1 0, 2 0 0, 2 1 1 Bragg
reflections matched reasonably well with a solid-solution
phase of composition related to Ba Y CO [18,19]. The
conjecture is that the triple-perovskite superstructure of
the oxide-carbonate phase is not developed at these
relatively low temperatures and only the disordered
cubic-perovskite diffraction pattern is seen.
3
2
8
3.2. Structure of the valence-mixed DyBaFe O
2
5
ꢀ
ing the deoxidation process isothermally at 650 C as a
function of time (Table 3), in which the extent of
decomposition increased steadily with time. Table 3
further lists concentrations of the decomposition pro-
SXPD data were collected at 330 K on
DyBaFe O5:013; the sample that had been annealed for
2
several months in order to standardize the oxygen-
content distribution (see Section 2). Small amounts of
two other phases were identified: Fe [x ¼ 0:0069; cubic,
ducts, which are metallic Fe, Dy O3 and a cubic
2
perovskite-type phase. Identification of the latter phase
was attempted from Dy(O)–Ba(O)–Fe(O) phase-dia-
gram considerations that dictate a composition with
somewhat higher molar fraction of Ba than of Dy.
˚
a ¼ 2:8687ð16Þ A] and Dy O3 [x ¼ 0:0014; cubic,
2
˚
a ¼ 10:6532ð22Þ A]. The refined pattern is shown in
Fig. 2. For both impurity phases, only one strongest

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
285
0
10
12
14
16
18
20
22
24
2θ/°
1
2
1
20
Fig. 2. Detail of the refined pattern ( of angular and of intensity ranges) for DyBaFe O5:013 at 330 K: The vertical bars denote Bragg reflections
2
˚
(
l ¼ 0:49981 A) for Fe (top), Dy O3 (middle) and the Pmmm DyBaFe O5:013 (bottom).
2
2
Table 4
Valence-mixed DyBaFe O5 at 330 K; refined structure data
Table 5
Charge-ordered DyBaFe O5:013 at 100 K and DyBaFe O4:996 at 200 K
2
2
2
(
in italics); refined structure data
Unit-cell parameters
Refinement statistics
Unit-cell parameters
Space group
Refinement statistics
Space group
˚
Pmmm
Rwp
Rp
0.0562
0.0443
0.0275
644
a=A
3.93855(1)
3.92433(1)
7.57344(1)
117.056(0)
Pmma
Rwp
0.0900
0.0849
0.0692
0.0613
0.0307
0.0231
784
˚
b=A
2
RðF Þ
˚
c=A
˚
V=A
˚
a=A
Nobs
8.03833(4)
8.04527(3)
3.84648(2)
Rp
3
Nvars
33
˚
b=A
2
RðF Þ
3
.85127(1)
Atom
Site
n
x
y
z
100Uiso
˚
c=A
7.54026(4)
7.54680(3)
233.139(2)
233.834(1)
Nobs
Dy
Ba
Fe
1c
1a
2t
2t
1f
2s
2r
2r
1
1
1
1
1
1
1
0
0
1/2
0
0.52(1)
0.52(1)
0.51(1)
0.51(1)
0.92(4)
0.92(4)
0.92(4)
0.92(4)
584
3
0
0
˚
V=A
Nvars
38
36
1/2
1/2
1/2
1/2
0
1/2
1/2
1/2
0
0.2652(1)
0.25
0
Fe
O(1)
O(2)
O(3)
O(4)
0
Atom
Dy
Site
n
x
y
z
100Uiso
0.3101(3)
0.3101(3)
1/2
1/2
1/2
2c
1
0
0
1/2
0.19(2)
0.33(4)
0.16(3)
0.013
1/2
Ba
2a
2f
2f
2f
2e
2e
4j
1
0
0
0
0
Constraints: Uiso: Dy ꢁ Ba; Fe ꢁ Fe ; OðiÞ ꢁ OðjÞ; z: Oð2Þ ꢁ Oð3Þ;
0
.34(4)
0
Fe fixed.
Fe(1)
Fe(2)
O(1)
O(2a)
O(2b)
O(3)
O(4)
1
1/4
1/2
1/2
1/2
0
0.2547(7)
0.23(2)
0.26(4)
0.23(2)
0.26(4)
0.12(8)
0.40(12)
0.12(8)
0.40(12)
0.12(8)
0.40(12)
0.12(8)
0.40(12)
0.12(8)
0
.2545(9)
0.2683(6)
.2692(7)
À0.001(5)
.002(7)
Bragg peak is identifiable in the diffraction pattern. Also
other cubic sesquioxide formers, R ¼ Ho and Y, yield
the same phase composition under analogous synthesis
conditions. The cerimetrically determined content of the
added oxygens, w ¼ 0:013; is taken under consideration
in the Rietveld refinements by introducing a split site for
1
3/4
0
1
1/4
0
1
3/4
0.318(4)
0.314(6)
0.308(4)
1
1/4
0
0
0
.314(6)
iron, Fe ; corresponding to the fraction of irons that are
0
1
0.0152(13)
0
1/2
1/2
0.3098(6)
0.3114(7)
1/2
in contact with the added oxygens. These Fe atoms
.0149(9)
have the z coordinate fixed to 0.25, which is believed to
conform better with the local octahedral coordination.
The refined data for the main phase are listed in Table 4.
2f
0.013
1/4
Constraints: Uiso: Feð1Þ ꢁ Feð2Þ; OðiÞ ꢁ OðjÞ; nOð4Þ fixed.
3
.3. Structure of the charge-ordered DyBaFe O5
2
quenched DyBaFe O4:996; and a pattern at 100 K of
2
the long-term annealed DyBaFe O5:013: The results of
2
Two sets of SXPD data were collected at two different
occasions, viz., a pattern at 200 K of the directly
the Rietveld refinements of the charge-ordered super-
structure in these two samples are combined in Table 5.

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
286
The refinement itself is not straightforward because the
Bragg superstructure intensities are extremely weak.
Several such peaks are marked in a detail of the refined
pattern shown in Fig. 3 (see Ref. [10] for a typical full
pattern). None of them coincides with any calculated
Bragg line of the two impurity phases. Only one
other forming a locally enhanced background. A
pseudo-multiphase model was used in Ref. [10] for
refinements of this type of enhanced background. Given
that none of important superstructure Bragg intensities
is directly affected by this feature, the pseudo-multi-
phase refinement was not used in the present study
because it has the undesirable effect of causing refine-
ment instabilities and creating false minima. However,
two of six superstructure-related coordinates proved
somewhat unstable, viz., the z coordinates of O(2a) and
O(2b) that also differ most between the two cases of the
charge-ordered superstructure refinement reported here.
Assuming that random variations in the collected
pattern are likely to affect the extremely weak super-
structure intensities, taking an average of atomic
coordinates from these two refinements appears as the
best solution to arrive at values representative of the
charge-ordered structure.
impurity Bragg reflection (the strongest of Dy O ) is
3
2
identifiable in these low-temperature patterns. This is
because the Fe 1 1 0 Bragg peak seen in the high-
temperature pattern is hidden in one of the strong peaks
of the main phase (cf. Fig. 2).
As established in Ref. [10], a distribution of the
oxygen contents in the sample is responsible for the
specific asymmetry of the Bragg peaks in these phases.
In Ref. [10] such a distribution is estimated for
GdBaFe O
2
via. deconvolution of suitable Bragg-
5þw%
peak profiles with the instrument-width profile accord-
ing to dependence of the unit-cell parameters on w: This
approach is not fully applicable in the present case,
because unit-cell parameters cannot be established over
a sufficiently wide range of w: Nevertheless, peak
profiles for R ¼ Gd and Dy show both the same type
and magnitude of the asymmetrical peak broadening:
The Bragg-profile tailing in Figs. 2 and 3 is of the same
orientation in both the charge-ordered and valence-
mixed states, and this correlates with the orthorhombic
distortion diminishing and c increasing as a function of
w: The asymmetry is best observed for the 4 0 0, 0 2 0,
The averaged atomic coordinates from Table 5 were
used to calculate bond distances and bond valence
sums (BVS) for DyBaFe O5 within the 200 K unit-cell
2
dimensions (Table 6). Single-bond lengths by Brown [20]
2
þ
are used for metal ions, of which Fe
at the Fe(2) site and Fe
is located
þ
at the Fe(1) site, by
3
comparison of bond distances. It is seen that these
distances are close to those obtained by neutron powder
diffraction for the R ¼ Tb [3], Y [4] and Ho [5] version,
but differ from data obtained for R ¼ Gd [10] that
are based on a single SXPD pattern collected with
a less good statistics and refined with the pseudo-
multiphase model. Somewhat surprisingly, the bond-
distance errors cancel when BVS are calculated, and
also BVS for R ¼ Gd are consistent with data for the
other R variants, as shown in Fig. 4 for the case of iron
atoms.
0
1
0 4 Bragg peaks, which are situated between 13.5 and
ꢀ
5 2y (Fig. 3). Because the orthorhombic distortion for
the low-temperature charge-ordered phase is much
larger than for the high-temperature valence-mixed
phase, the asymmetry effect is enhanced, in particular
between the orthorhombically split peaks of the h00 and
h
0
0 type, whose asymmetry is directed against each
2
314
122
112
302
104
114
304
322
0
10
12
14
16
18
20
22
24
2θ/°
Fig. 3. Detail of the refined pattern (0.616 of angular and 1 of intensity ranges) for class-I (charge-ordered) DyBaFe O4:996 at 200 K: The vertical
20
2
˚
bars denote Bragg reflections (l ¼ 0:48572 A) for Dy O3 (top) and the Pmma DyBaFe O5:013 (bottom). Superstructure Bragg reflections are
2
2
marked with their hkl values where visually resolved on this scale.

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
287
Table 6
Bond distances (in A) and bond valence sums (BVS) for charge-ordered DyBaFe O5 at 200 K
˚
2
Atom
Dy
Ba
Fe(1)
Fe(2)
Oxygen BVS
O(1)
4 Â 2:7845ð1Þ
2 Â 3:120ð35Þ
2 Â 3:091ð34Þ
4 Â 3:036ð4Þ
1 Â 1:921ð60Þ
1 Â 2:029ð58Þ
2 Â 1:958ð9Þ
2.13(17)
1.96(9)
1.98(10)
1.95(3)
O(2a)
O(2b)
O(3)
2 Â 2:444ð26Þ
2 Â 2:466ð26Þ
4 Â 2:401ð3Þ
2 Â 1:972ð11Þ
2 Â 1:937ð5Þ
2 Â 2:155ð9Þ
Metal BVS
2.78(10)
2.00(5)
3.00(16)
2.18(11)
Averaged atomic coordinates from Table 5 are used, see also Supporting information. Oð4Þ ðꢁ wÞ is neglected.
3.0
2.8
2.6
2.4
2.2
2.0
4.00
3.95
3.90
3.85
3.80
a
3
+
Fe(1) (≡Fe )
b
2+
Fe(2) (≡Fe )
2
00 220 240 260 280 300 320 340
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
T
/K
R
Fig. 5. Evolution of the SXPD-based dimensions per a single-
perovskite-type cell across the Verwey transition in DyBaFe O4:996
upon warming.
Fig. 4. Bond-valence sums for the two crystallographically different
iron atoms calculated from structure data [3,5,10] for charge-ordered
RBaFe2O5 at various low temperatures.
2
3.4. Characteristics of the Verwey transition
in DyBaFe O5
1
.0
.8
DSC heat-flow curve, normalized
xVM and its least-squares fit
above fit, differentiated
2
0
Evolution of the unit-cell parameters, volume, phase
contents, and of the thermal effect upon warming
through the mixed-valence class I–II transition and
class II–III transition is illustrated on the example of R
0.6
0.4
=
Dy. The unit-cell data for DyBaFe O
2
(quenched)
4:996
in Fig. 5 reveal a discontinuous change at the main
Verwey transition (class I–II) whereas no discontinuity
at the weak class II–III transition.
The gradual increase in the content of the valence-
mixed phase, appearing at the expense of the charge-
ordered phase upon warming through the main Verwey
0
.2
.0
0
260
270
280
/K
290
300
transition, is illustrated in Fig. 6 for the DyBaFe O
2
5:013
T
(
annealed) sample. The appropriate DSC heat-flow peak
Fig. 6. Mole fraction xVM of the valence-mixed phase DyBaFe O5:013
2
is drawn for comparison. When differentiated, the
formation of the valence-mixed phase contours the
shape of the DSC peak, confirming that the oxygen-
content distribution in the sample contributes to the
DSC peak width. Determination of the volume change is
upon warming through the main Verwey transition; according to
SXPD. DSC trace drawn for comparison.
meters are listed in comparison with other R variants in
Section 3.6.
illustrated in Fig. 7 for DyBaFe O4:996: Note the lack of
2
any observed volume change at the weak class II–III
transition. Transition temperatures and thermal para-
DSC traces in Figs. 6 and 7 refer the two different
samples that were quenched at first, but one of them was

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
288
solution. When RBaFe O is taken as the solvent and
2
5
RBaFe2O6 as the solute (the solute concentration is w),
the transition temperature TV decreases as a function of
w in the manner that is consistent with the freezing-point
depression by the thus defined solute. Assuming zero
solubility in the solid solvent, the equality of chemical
potentials for the pure solvent in both phases yields a
simple expression for the composition dependence of TV
when the latent heat of fusion of the pure solvent is
considered independent of temperature:
58.60
58.55
58.50
58.45
DHð0Þ
TVðwÞ ¼
:
ð1Þ
DSð0Þ À R lnð1 À wÞ
2
00 220 240 260 280 300 320 340
T
/K
The parameters DHð0Þ and DSð0Þ refer to the pure
solvent (w ¼ 0). The analogy with the latent heat
suggests that the transition enthalpy should decrease
linearly with increasing concentration of the solute,
Fig. 7. Determination of the volume per single-perovskite-type cell of
DyBaFe O4:996 upon warming through the main Verwey transition;
according to SXPD. DSC trace is used to localize TV:
2
ꢀ
ꢁ
w
DHðwÞ ¼ DHð0Þ 1 À
ð2Þ
wð0Þ
subsequently thermally equilibrated and then slowly
ꢀ
cooled in a closed system (at 250 C; see Section 2 for
as it can be imagined that each added oxygen atom takes
away several unit cells from the pool of the valence-
mixed/charge-ordered states, decreasing thus the
amount of the solution that freezes discontinuously.
Given that
details). Comparison of the DSC traces shows that both
have practically identical shape. When the sigmoid
curves for the evolution of the valence-mixed phase,
such as that shown in Fig. 6, are compared in a similar
manner, a slightly broader temperature range is seen for
the equilibrated sample than for the sample that was
only quenched. Together with the same pattern of
Bragg-peak broadening for these two samples, this
suggests that no improvement in sharpness of the
oxygen-content distribution across the bulk is achieved
during a subsequent thermal equilibration of once
quenched sample.
DHðwÞ
TVðwÞ ¼
;
ð3Þ
DSðwÞ
the composition dependence of the transition entropy,
DSðwÞ; is expressed by substitution of TVðwÞ in Eq. (1)
from Eqs. (3) and (2) and used together with Eq. (2) to
fit simultaneously, by least squares, the experimental
composition dependences DSðwÞ and DHðwÞ: The three
free parameters of such fits were chosen to be the fusion
enthalpy and entropy of the pure ‘solvent’, DHð0Þ and
DSð0Þ; and the non-stoichiometry wð0Þ where the former
two values become zero.
3
.5. Oxygen non-stoichiometry and thermodynamics
of Verwey transition in RBaFe2O5þw
As noted in Section 1, 57Fe Mo
has been used [12] to account for the valence-mixed and
ssbauer spectroscopy
The fits of the above model to the experimental
thermal data of the main Verwey transition in
¨
charge-ordered states of iron in RBaFe O ; regardless
2
RBaFe O
2
are shown in Fig. 8. For phases with wide
5þw
5þw
of the disorder caused by the added oxygen w and
whether or not their transition is discontinuous. Despite
the progressive decay of these states with increasing w;
traces of the valence-mixed state are still detected at
non-stoichiometry levels as high as w ¼ 0:35 [12].
However, as manifested by DSC on the enthalpy change
and by diffraction methods on the volume change, the
ranges of oxygen non-stoichiometry (R ¼ Nd [8], Sm [8],
Eu [9] and Gd [10]), all three parameters are refined
(Table 7), for the other phases (R ¼ Tb [3], Dy, Y [4]
and Ho [5]) the parameter wð0Þ has been fixed to 0.25.
The reason for this is apparent from Fig. 8 where the
wð0Þ values vary only moderately for R ¼ Sm; Eu and
Gd, and the increases in DHð0Þ are compensated by the
slope of DHðwÞ being steeper. Notably, R ¼ Nd deviates
from the other variants by having DHð0Þ; DSð0Þ; and
wð0Þ distinctly smaller. This discontinuity correlates
with the change in symmetry of the charge-ordered
structure, from Pmma to P21ma for NdBaFe2O5 [5,8].
2
electron localization is discontinuous only to some of
such a range. Along this interval in w; the changes in
3
enthalpy, entropy, and volume across the main Verwey
(
class I–II) transition become zero, from a maximum
seen at w ¼ 0:
1
In line with the analogy between charge ordering and
freezing of water, Ref. [10] considered the Verwey
transition enthalpy of non-stoichiometric RBaFe O
The wð0Þ values, being close to ; may imply that one
4
added oxygen atom takes away four unit cells (formula
units) from the long-range charge (and orbital) order.
This appears reasonable, considering that one oxygen
2
5þw
being analogous to the latent heat of a freezing/thawing

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
289
Table 7
Fit parameters of the depression of freezing point model for
RBaFe2O5þw to the experimental DSðwÞ and DHðwÞ data points for
the main Verwey transition (Fig. 8)
5
0
R
= Nd
Sm
R
DHð0Þ
DSð0Þ
wð0Þ
ÀDHð0Þ=wð0Þ
kJ/mol
J=ðmol KÞ
kJ/mol
Nd
Sm
Eu
Gd
1.14(5)
1.83(14)
1.98(4)
2.16(6)
5.38(7)
7.86(16)
7.79(5)
8.08(6)
0.151(4)
0.234(5)
0.234(3)
0.242(4)
À7.54(45)
À7.84(66)
À8.48(22)
À8.92(29)
5
0
Y
Gd
Eu
Sm
Nd
300
250
200
150
5
0
Ho
Dy
Tb
Eu
5
0
Gd
Tb
5
0
0.00
0.05
0.10
0.15
0.20
0.25
w
Fig. 9. Experimental TV values for RBaFe2O5þw compared with
TVðwÞ curves calculated from Eq. (1) and parameters (Table 7) fitted
to the DSðwÞ and DHðwÞ functions (Fig. 8).
5
0
Dy
Y
charge ordering. Macroscopically, the action of the
added oxygens w is gradual; first the long-range three-
dimensional order is destroyed, manifested by disap-
pearance of the superstructure Bragg reflections. Then
the remaining sequences of the one-dimensional order
along b direction are being removed and disappear at
wE0:25; and this is manifested by disappearance of the
orthorhombic distortion.
5
0
Considering the error margins of the DSC method,
the fits of the freezing-point-depression model to the
main Verwey transition enthalpy and entropy functions
of the non-stoichiometry parameter w are good. How-
ever, only a qualitative agreement with experimental TV
values is seen in Fig. 9, where the TVðwÞ curves derived
from the freezing-point-depression model [Eq. (1)] are
plotted together with the DSC-based values. The
5
0
Ho
0.00
0.05
0.10
0.15
0.20
0.25
w
Fig. 8. Experimental DSðwÞ and DHðwÞ data for the main Verwey
transition in RBaFe2O5þw and their fits according to the model for
depression of the freezing point (see text for details).
experimental T values at w ¼ 0 are always higher than
V
those derived from the model, but this is owing to the
fact that the experimental data are read from the DSC-
peak tops whereas temperatures derived from thermal
data refer to the peak centers of gravity. The more
significant difference is that the model follows only
atom oxidizes two divalent iron atoms into trivalent,
and assuming that the unit cells facing these newly
oxidized trivalent irons across the R structural layer may
not be able to participate in the valence mixing and
partially the trend of a steeper decrease in T ðwÞ
V
towards R ¼ Nd, and the experimental T ðwÞ data are
V

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
290
more concave, even showing a trend to increase close to
the situation when the Verwey transition ceases to be
discontinuous. No better fit is obtained when the
freezing-point-depression model allows DHð0Þ to
change as a function of T according to heat capacities
of the solid and melted pure solvent being different, but
independent of temperature. First when one considers
that the difference of these heat capacities is a linear
function of temperature, a better curvature can be
obtained. It is however doubtful whether such fitted
parameters are real or not. It is interesting to note that
neither the model nor the experimental data indicate
that TVðwÞ is linear. The only thermal parameter that
appears to be linear as a function of the non-
stoichiometry parameter w is DH:
3.6. Thermodynamic parameters of Verwey transition
in RBaFe O
5
2
The ideal mixed-valence composition RBaFe2O5 is an
important reference point. Fig. 10 illustrates that
temperatures and caloric effects of the main charge-
ordering Verwey transition in samples approaching such
composition vary strongly as a function of R; and
obtaining good reference thermal data is essential.
Given the error margins in both oxygen-content
analyses and thermal values (cf. Fig. 8) such thermal
parameters are best obtained from compositional
dependences, not from selected individual samples.
Moreover, as illustrated in Section 3.1, not all R
variants can reach the ideal composition with w ¼ 0:
A conservative approach is to fit the thermal data as a
function of w with a Gauss curve centered at w ¼ 0: This
approach has its backing in the probability model of
formation of the valence-mixed state suggested in
Ref. [12]. Data from such Gaussian fits are available
for R ¼ Nd [8], Sm [8], Eu [9], Gd [10], Tb [3], Dy (this
work), Ho [5] and Y [4]. Alternatively, thermodynamic
parameters for w ¼ 0 are extrapolated according to the
0
0
0
0
.15
.10
.05
.00
Ho
Dy
Tb
Gd
Eu
Sm
Pm
Nd
R
200
250
/K
300
T
Fig. 10. DSC caloric effects of Verwey transition in RBaFe2O5 upon
w
warming. Selected samples with non-stoichiometry parameter
ranging from w ¼ À0:001 (R ¼ Sm) to 0.012 (R ¼ Tb).
Table 8
Thermodynamics of the twin Verwey transitions between the Day–Robin mixed-valence classes in RBaFe2O5
a
Class I–II
Peak TV
K
Class II–III
Peak T
K
b
c
d
b
Mean T Refs.
R
DH
DS
Mean TV
DV
dP=dTV
bar/K
DH
DS
kJ/mol
J=ðmol KÞ
K
J=ðmol barÞ
À0.0235(6)
kJ/mol
J=ðmol KÞ
K
Nd 216.1(3)
Sm 238.8(2)
Eu 256.3(4)
Gd 270.3(10)
Tb 285.1(9)
Dy 293.5(12)
Ho 295.7(10)
1.07(4)
5.00(15)
5.38(7)
7.26(8)
7.86(16)
7.44(13)
7.79(5)
7.72(8)
8.08(6)
8.69(9)
8.82(8)
8.44(10)
8.66(6)
8.48(27)
8.66(9)
8.51(9)
9.19(7)
214(14)
À211(4)
286.3(13)
0.222(26) 0.79(9)
281(67)
294(24)
294(23)
302(39)
305(16)
309(38)
319(51)
330(35)
[8]
1
.14(5)
1.68(2)
.83(14)
1.88(4)
.98(4)
2.06(3)
.16(6)
2.45(2)
.50(8)
2.45(3)
.56(6)
2.48(7)
.56(9)
2.62(3)
.88(7)
232(6)
252(9)
267(7)
282(5)
290(7)
293(17)
307(6)
À0.0373(10)
À0.0352(10)
À0.0336(122)
À0.0250(8)
À0.0236(8)
À0.0218(15)
À0.0181(30)
À189(2)
295.3(10)
298.8(40)
307.3(15)
308.5(7)
316.4(7)
324.5(5)
334.2(3)
0.168(7)
0.191(7)
0.57(2)
0.65(2)
[8]
1
À208(13)
À226(77)
À345(8)
[9]
1
0.162(10) 0.54(3)
[10]
[3]
2
0.173(4)
0.129(8)
0.57(2)
0.42(3)
2
À355(17)
À386(39)
À465(43)
Here
[5]
2
0.180(15) 0.56(4)
0.150(8) 0.45(2)
2
Y
309.5(3)
[4]
2
a
Conservative estimates for ideal RBaFe2O5 (w ¼ 0) compositions, obtained from Gaussian-curve fits to the w dependences. Data from the
freezing-point-decrease model are in italics.
b
As given by DH=T ¼ DS:
c
SXPD data for a sample close to w ¼ 0; except for R = Gd, which originates from a w dependence.
d
According to Clapeyron equation, dP=dTV ¼ DS=DV:

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
291
model of the freezing-point depression of the charge
liquid (Section 3.5). Transition enthalpies and entropies
obtained in such manner are larger than those from the
first method and can be considered maximum estimates.
Parameters of the transitions between the Day–Robin
mixed-valence classes I–II and II–III are summarized
in Table 8 referring to the standard direction of
warming up.
compatible with accommodation of the characteristic
shape of the doubly occupied dxz orbital of the divalent
iron that requires an orthorhombic distortion of the
lattice [5]. However, when the ionic size alone is
considered, an anomalously high stability of the
charge-ordered state is observed for R ¼ Y: It can be
speculated that a higher atomic polarizability of yttrium
is behind this, but the correlation also improves when
Allred–Rochow electronegativities [22] are used instead
of the ionic radii.
Within the lanthanoid subseries of RBaFe2O5; ther-
mal parameters of the main Verwey transition vary
smoothly across the discontinuity in symmetry [5,8]
between the long-range charge-ordered variants of
R ¼ Sm and Nd. The only parameter that follows this
discontinuity is DV (Fig. 13 bottom) whereas the slope
It is seen that enthalpies and transition temperatures
of the main transition increase reasonably smoothly
across the lanthanoid series as a function of decreasing
3
þ
R
ionic size (Figs. 11 and 12). Why the ‘spectator’ R
atom exercises such an influence? The likely reason is
that lanthanoids are substantially less deformable than
Ba. An increasing size of R then becomes less and less
of the phase boundary dP=dT ¼ DS=DV (Fig. 13 top)
V
remains approximately constant. It appears that when
the energy balance associated with charge ordering can
no longer support the even higher volume increase
projected for R ¼ Nd, structural deformation occurs for
the R ¼ Nd variant allowing it to keep a high level of the
9
8
7
6
2
þ
d
xz
Fe
orbital ordering (Fig. 4).
5
Y
Why the thermal parameters of the premonitory
charge-ordering transition vary so little with R? One
reason is that this transition appears to proceed under
no volume change. It utilizes the existing small
magnetostrictive orthorhombic distortion to perform a
similar orbital ordering as the main transition, only in a
much smaller extent [3]. It proceeds without any
detectable long-range ordering [4], hence between any
two iron neighbors along the longer a axis, by increasing
the bond-valence sum for one of them at the expense
of the other. Since the strength of the magnetic
3
2
2
1
1
.0
.5
.0
.5
.0
Ho Dy
Tb
Gd
Eu
Sm
Nd
1.15
1.20
1.25
CN8
rR
/Å
(III)
Fig. 11. Enthalpies and entropies of the main Verwey transition in
RBaFe2O5; obtained from the freezing-point-depression model, as a
function of Shannon [21] ‘CR’ radii for R3
interactions can be measured in terms of the Ne
temperature TN; and TN is constant across the R series
´
el
þ
:
[
5], the temperature of the premonitory charge-ordering
340
320
300
280
260
240
220
200
-100
-
200
-300
400
Y
Ho
Dy
Tb
-
Gd
Y
Ho
Eu
-0.020
Dy
Nd
Tb
Sm
-
-
-
0.025
0.030
0.035
Gd
Nd
Eu
Sm
1.15
1.20
1.25
1.15
1.20
1.25
CN8
(III)
rR
/Å
CN8
rR
/Å
(III)
Fig. 12. Premonitory (open symbols) and main (closed symbols)
transition temperatures as a function of Shannon [21] ‘CR’ radii for
R3 in RBaFe2O5:
þ
Fig. 13. Volume parameters of Verwey transition in RBaFe2O5 as a
3þ
function of Shannon [21] ‘CR’ radii for R
:

ARTICLE IN PRESS
P. Karen / Journal of Solid State Chemistry 177 (2004) 281–292
292
transition varies less as a function of R than does the
main transition temperature TV:
doubly or two sole singly occupied nearly degenerated
orbitals, these may also order, but their thermally
induced mixing would proceed gradually and the
transition would not be of the first order. That is the
case of YBaCo2O5:
4
. Conclusion
Key aspects of the twin charge-ordering transitions in
RBaFe O can be understood by considering conditions
2
5
Acknowledgments
for ordering of the (nearly) degenerated doubly occupied
dxz orbitals of divalent iron as the primary cause of
disproportionation of the thermally induced valence-
Experimental assistance from the staff of the Swiss-
Norwegian Beam Lines at ESRF is gratefully acknowl-
edged.
2
:5þ
mixed Fe
states. The effect of other structural and
compositional variables depends on their compatibility
with the symmetry of the spatial electrostatic interac-
tions defined by the shape of the dxz charge as opposed
to a point-charge model. The ‘spectator’ ions with
approximately spherical symmetry influence the charge
ordering via their variable size and deformability.
Magnetic interactions appear to have their say, via the
magnetostrictive effect, which is essential in defining the
direction of the symmetry breakings under the subse-
quent charge-ordering transitions.
Supporting information: CIF files can be obtained
from the Fachinformationszentrum Karlsruhe, 76344
Eggenstein-Leopoldshafen, Germany, (fax: (49)7247-
8
08-666; e-mail: crysdata@fiz-karlsruhe.de) on quoting
the depository number CSD 413169 for charge-ordered
DyBaFe O at 200 K and CSD 413170 for valence-
2
5
mixed DyBaFe O at 330 K:
5
2
References
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very simple RBaFe O5 model, a definition of the
2
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These attributes comply with the original Verwey
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2
[
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þ
3þ
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þ
4
5þ
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3þ
´
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[
[
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4þ
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4þ
(
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3þ
Re ; Re couples.
[
˚
g, A. Kjekshus, in: AMSAHTS
When both prospective charge-ordered ions possess
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mutual ordering, thermal energy may not be sufficient
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1
[
[
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