Crystal structure of brownmillerite Ba2InGaO5

Journal of Solid State Chemistry 218 (2014) 38–43

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Crystal structure of brownmillerite Ba2InGaO5 Christophe Didier, John Claridge, Matthew Rosseinsky n Department of Chemistry, University of Liverpool, Crown Street, Liverpool L69 7ZD, UK

art ic l e i nf o

a b s t r a c t

Article history: Received 10 April 2014 Received in revised form 2 June 2014 Accepted 8 June 2014 Available online 16 June 2014

Ba2InGaO5 was prepared by high-temperature solid-state reaction. This compound adopts a brownmillerite structure below 1200 1C, which was not found in past studies of Ba2(In1
xGax)2O5. Combined structure refinements against neutron and X-ray powder diffraction data show that this material adopts a layered ordering of In and Ga. This is one of a few examples of such an ordering in the brownmillerite structure solely due to size difference between the B cations. This ordering further stabilizes the brownmillerite crystal structure compared to other compositions at smaller Ga contents (x o0.5), for which the transition to a disordered cubic perovskite occurs at a much lower temperature. As could be expected, such stronger ordering is detrimental to ionic conductivity. & 2014 Published by Elsevier Inc.

Keywords: Ba2In2O5 Brownmillerite Structure refinement Conductivity

1. Introduction Perovskites represent one of the most important structures in the field of solid-state chemistry, as its flexibility lends to large compositional variety, as well as a tolerance for ionic defects, which gives rise to much structural diversity, of prime interest to the solid-state crystallographer. Such diversity enables compounds with perovskite-related structures to display a wide range of physical properties, many of which find practical applications. High oxide ion conductivity for solid-oxide fuel cells (SOFC) is one of such property of interest. The cubic perovskite LaGaO3 co-doped with Sr and Mg, or LSGM, is currently one of the best oxygen ion conducting electrolytes [1]. Chemists have attempted to improve the conductivity of these oxides through various doping and one strategy is to increase the number of oxygen vacancies. In this aspect, compounds with the brownmillerite structure, of general formula A2B2O5, possess a perovskite-related structure with a large number of oxygen vacancies. These vacancies are fully ordered in this structure and it can be described as layers alternating between corner-sharing octahedra and tetrahedra. The most studied brownmillerite as an electrolyte for SOFC is Ba2In2O5 [2]. When the brownmillerite structure is retained, the material ends up being an average oxide ion conductor since the ordering of oxygen ions greatly reduces their mobility. However a transition to a cubic perovskite occurs at higher temperatures, in which vacancies become disordered, leading to greatly improved oxygenion conductivity (0.1 S/cm at 900 1C). It is possible to stabilize the cubic form at lower temperatures through the introduction of n

Corresponding author. Tel.: þ 44 151 794 3499. E-mail address: [email protected] (M. Rosseinsky).

http://dx.doi.org/10.1016/j.jssc.2014.06.011 0022-4596/& 2014 Published by Elsevier Inc.

disorder onto the A site or the B site [3], with such materials showing appreciable performance, though there are other problems such as CO2 instability and partial electronic conductivity. Hydrogen ion conductivity has also been reported in these materials [4–7]. Many elemental substitutions have been attempted in order to improve the conductivity of Ba2In2O5. Solid solutions of Ba2(In1
xGax)2O5 with 0o xo 0.5 have been reported [8,9]. The structure is an orthorhombic brownmillerite for xo0.3, which disorders at high temperatures, and a cubic perovskite for 0.3 ox o0.5. Understanding the conditions necessary for the order–disorder transition to occur is important if one wants to use such materials in SOFC. The aim of this paper is to complete past work on structural determination and relative stability of different structures in Ba2(In1
xGax)2O5 for x ¼0.5 which, from our results, only showed a partial view of the system.

2. Materials and methods Samples of Ba2InGaO5 were prepared by traditional solid-state chemistry using a stoichiometric mixture of BaCO3 (Alpha-Aesar 99.997%), Ga2O3 (Alpha-Aesar 99.999%) and In2O3 (Alpha-Aesar 99.995%), following the reaction: 2BaCO3(s) þ 12 Ga2O3(s) þ 12 In2O3(s)-Ba2InGaO5(s) þ 2CO2(g) Powders were dried overnight before being weighed. The mixture was ground with a mortar and pestle and pressed into a pellet. The pellet was placed in an alumina boat lined with platinum foil and fired for 12 h at either 1100 1C, 1200 1C or 1300 1C under ambient air. The heating and cooling rates were

3. Results 3.1. Phase identification The powder XRD patterns of Ba2InGaO5 obtained in the 1100– 1300 1C range are represented in Fig. 1. The pattern for T¼ 1300 1C can be indexed with a cubic cell of parameter aP ¼4.1539(9) Å. This corresponds to the cubic perovskite phase Ba2(In1
xGax)2O5 with x¼0.5 already reported [8,9]. At T¼1100 1C, the pattern can be indexed using an orthorhombic unit cell with parameters a¼6.11239 (4) Å, b¼15.56492(9) Å and c¼5.92212(3) Å (parameters are from the refinement of the CoKα1 data). For the intermediate temperature T¼1200 1C, a biphasic mixture is obtained. The orthorhombic phase was not reported in previous studies of Ba2(In1
xGax)2O5 and was probably overlooked due to the synthesis temperature being in the stability range where only the cubic phase forms. The transition between the two phases is reversible with temperature, but very sluggish when going from the cubic to the orthorhombic phase; several overnight annealings at 1100 1C, below the transition temperature, are required which explains why it eluded past work. The powder of the brownmillerite phase has a white colour, as is expected for purely ionic compounds with no unpaired electron, however the powder of the cubic perovskite phase has a pink/red colour; this aspect is currently under investigation. 3.2. Structure refinement of brownmillerite Ba2InGaO5 The cell parameters of the orthorhombic phase obtained at T ¼1100 1C are close to √2aP  4aP  √2aP and comparison with

341 143

280 082

080

222

161

240 042

202

200 002 150

101

130

020

a) 1100ºC

10

20

002

30

102

111

c) 1300ºC

112

101

b) 1200ºC

001

Intensity (A. U.)

5 1C/min. Obtained samples were ground, pelletized and annealed a second time in the same conditions. After the second annealing, XRD patterns confirmed the complete disappearance of starting reactants. Phase identification was made by powder X-ray diffraction (XRD) in transmission geometry, on a Bruker D8 advance using CuKα1 radiation (λ ¼1.5406 Å). For the lattice parameters determination and structure refinement of brownmillerite Ba2InGaO5, high quality XRD was measured in Bragg–Brentano reflection geometry on a Panalytical X’Pert Pro diffractometer using CoKα1 radiation (λ ¼1.7890 Å). Time-of-flight (TOF) neutron diffraction data were collected for the same sample on the HRPD beamline at the ISIS Rutherford Appleton Laboratory (Oxford, UK). Structure refinements were done using the Rietveld method [10] with the JANA2006 software [11]. The calculated absorption coefficient of the involved elements is high therefore an absorption correction is necessary and was applied to the data. Estimated standard deviations have been multiplied by Berar’s factor (4990.106) for more realistic values [12]. For Alternating Current (AC) impedance measurements, Ba2InGaO5 powder was uniaxially pressed into pellets who were then isostatically pressed at 200 MPa using an Autoclave Engineers Cold Isostatic Press before being sintered in air at 1100 1C for 24 h. The density of pellets obtained this way was 83% of the theoretical density. Gold paste was applied on each side of the pellets, and contacts were made of gold gauze and wire. The completed electrochemical cell was cured at 800 1C before measurement. AC impedance measurements were done using a Solartron 1255B frequency response analyser coupled to a Solartron 1287 electrochemical interface, over the frequency range from 102 to 107 Hz, with a modulation potential of 100 mV. Data were recorded on cooling over the temperature range 350–800 1C under either dry or wet argon. The dry condition was obtained with purchased dry-grade gas (P H2 O o3 ppm) and the wet condition involved having the inlet gas bubbling through water at room temperature (P H2 O  0:03 atm). Equivalent circuit modelling was performed using ZView (Scribner Associates).

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C. Didier et al. / Journal of Solid State Chemistry 218 (2014) 38–43

40

50

60

2θCu,Kα (º) Fig. 1. Powder XRD pattern of Ba2InGaO5 after annealing at: (a) 1100 1C, the indexation corresponds to the orthorhombic phase; (b) 1200 1C, arrows show visible peaks of the cubic phase; and (c) 1300 1C, indexation corresponds to the cubic phase.

related compounds suggest a brownmillerite structure. As this composition was unreported as a brownmillerite, a refinement of the structure has been undertaken. It is well known that the tetrahedra chains can adopt different orientations in the brownmillerite structure, and the relative orientation of these layers results in a specific symmetry of the unit-cell. Two ordered structures can be obtained, one having space-group Ibm2 (bac setting of Ima2) as in Ca2FeAlO5 [13], or Pcmn (cba setting of Pnma) as in Ca2Fe2O5 [14]. Additionally, a complete disorder between these two orientations can be described with an average model of space-group Icmm (cba setting of Imma), as in Sr2MnGaO5 [15]. In this model, the crystallographic site for the B cation in tetrahedral coordination is split, as well as one of the equatorial oxygen positions of the tetrahedra. From the experimental diffraction pattern, the hþk þl ¼2n reflection condition is observed; this suggests an I-centred Bravais lattice, which leaves either Ibm2 or Icmm as possible space-groups. It is not possible to distinguish between these two space-groups from extinction conditions, thus both models have been attempted in the structure refinement. Since the scattering of oxygen is very weak in XRD compared to the other heavy elements present in the structure, neutron diffraction is required to identify the correct tetrahedral ordering. When the combined refinement (X-rays þ neutrons) is carried out using the Icmm space-group, the atomic positions that were split in the average model end up very close to each other; this suggests that these atoms are actually not split in Ba2InGaO5. Moreover, slightly better reliability factors are obtained when the refinement is carried out in Ibm2, which is thus the correct space-group. Additionally in Ba2InGaO5, both indium and gallium atoms can occupy the B sites hence the occupancies of these atoms have to be taken into account. Two crystallographic sites are available; one corresponds to the octahedral sites and the other to the tetrahedral sites. A free refinement of the occupancies leads to 0.96(5) In in octahedra and 0.94(4) Ga in tetrahedra. Thus a fully ordered model has been considered with full occupation of the indium ions in octahedra and gallium ions in tetrahedra. The best structural model obtained from the combined Rietveld refinement is represented in Fig. 2a. The profiles of the calculated and observed diffraction patterns from the combined Rietveld refinement are shown in Fig. 3. Details of the conditions used for data collection, as well as reliability factors for each data bank, are

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C. Didier et al. / Journal of Solid State Chemistry 218 (2014) 38–43

c

Ba 2InGaO5

a 6.11239(4) Å

2.965(10) Å

5.92212(3) Å

Ba2 In 2 O5

c b 6.0833(10) Å

b

3.44(6) Å

a 5.9563(10) Å Fig. 2. (a) Representation of the structure obtained from the refinement of brownmillerite Ba2InGaO5. (b) And (c) represent the tetrahedral layers perpendicular to the stacking axis in (b) Ba2InGaO5 and (c) parent compound Ba2In2O5. The structural parameters for Ba2In2O5 are taken from Ref. [19].

summarized in Table 1. A list of atomic parameters is given in Table 2 and selected interatomic distances are given in Table 3. All isotropic atomic displacement parameters are within reasonable values and average interatomic distances (dBa-O ¼2.878(5) Å, dInO ¼2.194(7) Å, dGa-O ¼1.829(5) Å) are close to the ones determined by Shannon [16]. The calculated Bond Valence Sum (BVS) [17,18] of each ion is given in Table 1 with values close to the expected valence state of each ion. A finer examination of the pattern reveals that some discrepancies still remain between the observed and calculated intensities (Fig. 3), which do not improve after a Le Bail refinement; this is reflected by the close Rwp values between Rietveld and Le Bail refinements as seen in Table 1, hence excluding problems originating from the structural model. These discrepancies are due to an asymmetry of some of the peaks which cannot be corrected using instrumental asymmetry corrections. It is known that stacking faults can occur in brownmillerites [21,22], which could be at the origin of the peak asymmetry. No correction was attempted to model this asymmetry. Nevertheless the agreement between the observed and calculated intensities is satisfying and the final structural model appears to be correct from the crystal-chemical point of view.

3.3. AC impedance measurement Fig. 4 shows data from AC impedance measurements on brownmillerite Ba2InGaO5. The complex impedance spectrum consists of a single broad semi-circle (Fig. 4a). The capacitance associated with these arcs, calculated using the usual relationship [23] ωRC¼1 at the top of the arc, is close to C ¼ 1  1012 F, which indicates bulk contribution [24]. This bulk resistivity was modelled with an equivalent circuit made of a resistor (Rb) in parallel with a constant phase element (CPE). A second resistor (RΩ) was added in series to model ohmic losses originating from the setup. The complete equivalent circuit as used in fitting of the data is drawn

in Fig. 4a. The obtained values for the bulk resistivity are reported on the Arrhenius plot in Fig. 4b. Under dry conditions, reported values are assumed to be related to oxygen conductivity. Two activation domains can be observed: one with an activation energy of 1.38 eV (133 kJ/mol) for the 800-600 1C range and 0.81 eV (78 kJ/mol) for the 600-350 1C range. These are of the usual range of values for oxide ion conductivity [25]. As could be expected, the conductivity for the brownmillerite Ba2InGaO5 is lower than its cubic counterpart ( 10
4 S/cm at 800 1C for cubic Ba2InGaO5, from Ref. [8]). Under wet conditions, the conductivity increases below 550 1C, which suggests the presence of proton conductivity, as observed in Ba2In2O5 [4]. The pure protonic conduction σH can be determined from the difference between the dry and wet conductivities. In brownmillerite Ba2InGaO5, σH E 10
7 S/cm at 450 1C, which is lower than in undoped Ba2In2O5 (  10
5 S/cm at 450 1C) [4].

4. Discussion 4.1. Crystal structure The refined structural model consists of a brownmillerite structure with Ibm2 space-group and an ordering of the B cations along the stacking direction, with In in octahedra and Ga in tetrahedra. Such an ordering was also observed in Sr2ScGaO5 [26] and Sr2In0.9Ga1.1O5 [27], and was attributed to the size difference of involved B cations. As shown in Table 2, the InO6 octahedra are elongated along the stacking axis, while the interatomic distances are shorter along this direction in the GaO4 tetrahedra. As both ions are spherical, this distortion could be ascribed to the fact that Ga3 þ is more polarizing than In3 þ . This might contribute to the underbonding of the In3 þ ions as revealed by the BVS value smaller than 3 (Table 1). The tilting of the octahedra is a usual feature of brownmillerite structures, which allows accommodation of the smaller tetrahedra in the perovskite-

C. Didier et al. / Journal of Solid State Chemistry 218 (2014) 38–43

related network. This results in a shift of the atomic position O2 in the (a,c) plane, which could explain the observed underbonding (Table 1) for this atom. A comparison of the atomic organization within the tetrahedral layers between Ba2InGaO5 and parent Ba2In2O5 is represented in Fig. 2b and c. The unit-cell parameters perpendicular to the

41

stacking axis are close between these two compounds as they are mainly determined by the size of the Ba2 þ ions and the In3 þ ions in octahedra. However, since GaO4 tetrahedra are smaller than InO4 tetrahedra, the pattern of the chains is different between the two compounds. As represented in Fig. 2, the shorter distance between the equatorial oxygen ions (O3-O3) means the angles between these bonds are more important in Ba2InGaO5 (αO3–O3– O3 ¼ 1741) compared to Ba2In2O5 (αO3–O3–O3 ¼1201). The position of the O3 oxygen ions in Ba2InGaO5 is close to the one expected for an ideal perovskite.

Intensity (A. U.)

4.2. Order–disorder transition

48

10

20

30

40

50

50

60

52

70

54

80

90

56

100

The transition from a brownmillerite to a cubic perovskite at higher temperatures is a classical example of an order–disorder transition as occurs in parent Ba2In2O5 [2]. The ordered brownmillerite phase is the thermodynamically stable phase at low temperatures, with higher crystal density (ρ ¼6.35 g/cm3 for

58

110

120

130

2θCo,Kα (º)

Experimental Calculated

Intensity (A. U.)

Difference

86

88

90

92

94

96

98

Table 2 Atomic coordinates, isotropic atomic displacement parameters (Biso) and Bond Valence Sum (BVS) obtained from the Rietveld refinement of brownmillerite Ba2InGaO5. The space-group is Ibm2 (no. 46 bac setting) and the unit-cell parameters are a¼ 6.11239(4) Å, b¼ 15.56492(9) Å and c¼ 5.92212(3) Å, with volume 563.42(1) Å3 (Z¼ 4). Numbers in parentheses are the estimated standard deviations. Atom

x

y

z

Biso (Å2)

BVS

Ba In Ga O1 O2 O3

0.00654(12) 0 0.93445(16) 0.2516(8) 0.06835(16) 0.7373(9)

0.11878(4) 0 1/4 0.98944(7) 0.14622(5) 1/4

0.4798(5)
0.0169(9) 0.9823(12) 0.2353(13)
0.0073(9) 0.7464(12)

0.43(2) 0.45(3) 0.45(2) 0.67(3) 0.90(3) 0.93(4)

1.956(8) 2.79(2) 3.00(2) 2.03(2) 1.802(4) 2.04(2)

100

Table 3 Selected bond lengths obtained from the Rietveld refinement of brownmillerite Ba2InGaO5. The equatorial direction refers to bonds in the (a,c) plane while the apical direction refers to bonds along to the stacking axis b. The Ba ions are 9-coordinated and the Ba–O bond lengths range from 2.6344(12) Å to 3.091(6) Å.

30

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50

60

70

80

90

100

110

Bond

120

TOF (ms) Fig. 3. Diffraction patterns for the combined Rietveld refinement of brownmillerite Ba2InGaO5. The databanks are (a) X-ray diffraction (CoKα1) and (b) neutron diffraction (backscattered bank from HRPD). Additional neutron diffraction banks were used in the refinement and are included in the Supplementary Information (Fig. S1).

Ga–O2 Ga–O3 Ga–O3 In–O1 In–O1 In–O2

2 1 1 2 2 2

Distance (Å)

Direction

1.8120(10) 1.845(9) 1.884(9) 2.118(7) 2.150(7) 2.3146(8)

Apical Equatorial Equatorial Equatorial Equatorial Apical

Table 1 Diffraction data collection conditions and refinement data for the combined refinement of brownmillerite Ba2InGaO5 using the Rietveld method. Reliability factors are included, according to calculations and notations as given in [20]. The weighted profile reliability factor from the Le Bail refinement, Rwp(LeBail), is included for comparison. Instrument Radiation d-Range (Å) Data points Observed reflections Refined variablesa Rwp (%) Rexp (%) χ2 RF (%) Rwp(LeBail) (%)

Panalytical X’Pert Pro X-rays CoKα1 (λ¼ 1.7890 Å) 10.259–0.987 15,001 348 15þ21 11.54 8.53 1.83 3.43 10.61

HRPD, backscattered bank Neutron TOF 2.589–0.650 4610 1100 12þ 21 6.62 4.84 1.87 2.86 5.46

HRPD, 901 angle bank Neutron TOF 3.821–0.895 2077 422 12þ 21 5.09 2.78 3.35 1.53 3.59

HRPD, low angle bank Neutron TOF 7.233–2.697 823 16 13 þ21 9.88 9.13 1.17 4.29 9.07

a Refined variables are referred to as (1)þ (2) with (1) the number of profile parameters (background, 2θ shift, lattice parameters, peak shape) and (2) the number of structural parameters (scale, atomic positions, isotropic displacement parameters). Crystal structure parameters (unit-cell, atomic positions and isotropic displacement parameters) are common for all the diffraction banks.

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Temperature (ºC) 800

-4

R 5

4.6 × 104 Hz

Zimaginary ( Ω)

-8.0x10

500

400

Dry

CPE

5

-6.0x10

5

-4.0x10

600

Rb

2

10 Hz

log σ ( σ in S/cm)

6

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700

Wet

-5

-6

-7 5

-2.0x10

7

10 Hz 0.0

-8 5.0x105

0.0

1.0x106

1.5x106

2.0x106

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1000/T (K-1)

Zreal ( Ω)

Fig. 4. (a) Typical Nyquist plot obtained from AC impedance measurements on brownmillerite Ba2InGaO5. The plot featured here was obtained at 600 1C under dry condition. (See the experimental section for details on dry and wet conditions.) The line shows the fit of the semi-circle by the equivalent circuit as drawn in the inset. (b) Arrhenius plot of the bulk conductivity determined from the AC impedance data measured under dry or wet conditions. Lines indicate the two identified domains of activation energy under dry condition.

1300

Temperature (ºC)

1200 Brownmillerite (cations ordered)

1100 Cubic perovskite 1000

900

Brownmillerite

cations seems to further stabilize the brownmillerite structure, which is reflected by the anomalously larger transition temperature at this composition (Fig. 5). If disordering of the B cations is required for the cubic phase to be formed in Ba2InGaO5, as opposed to only the oxygen ions in Ba2In2O5, one would expect a higher disordering temperature and slower kinetics for the ordering transition, which are both experimentally observed. From the point of view of application as an SOFC electrolyte, this ordering is detrimental to the ionic conductivity, as a stronger ordering of oxygen vacancies effectively renders them less mobile. This is confirmed by the low values obtained for the conductivity of brownmillerite Ba2InGaO5.

800 0.0

0.1

0.2

0.3

0.4

0.5

x in Ba2 (In1-x Gax) 2O5

Fig. 5. Transition temperature between cubic perovskite and brownmillerite for the Ba2(In1
xGax)O5 solid solution for 0o x o0.5. Values for x o0.5 are from Ref. [8]. Annotations show the observed structure in each corresponding temperature/ composition range.

Ba2InGaO5) while the disordered cubic phase (ρ ¼6.24 g/cm3) is more stable at high temperatures, but can nevertheless be obtained metastable at room temperature. One cannot exclude that, at room temperature, the cubic phase might actually present brownmillerite microdomains at a local range, as TEM studies [28,29] on Ba2(In1
xGax)2O5 suggest, even though it appears cubic at long range in powder diffraction. Fig. 5 shows the temperature at which the transition between the orthorhombic brownmillerite and cubic perovskite occurs in Ba2(In1
xGax)2O5 for 0 o xo0.5. For Ba2InGaO5 (x ¼0.5), this transition occurs between 1100 1C and 1300 1C, which is higher than in undoped Ba2In2O5 (1030 1C), or the solid solution Ba2(In1
xGax)2O5 with xo 0.5 [8]. In this doping series, the transition temperature decreases as the Ga content increases. This is consistent with an increase of the intrinsic disorder due to the mixing of two cations on the B-site. One cannot exclude the possibility that the cubic phase observed at all temperatures for 0.2 ox o0.5 is actually metastable at lower temperatures but the kinetics are too slow for the brownmillerite phase to be formed under used synthesis conditions. The x ¼0.5 composition, as in Ba2InGaO5, is a special case where the B cations can become fully ordered into layers, as determined from the Rietveld refinement. This layered ordering of the B

5. Conclusion This study completes older literature of Ba2(In1
xGax)2O5 which overlooked the ordering into a brownmillerite structure when the ratio between In and Ga is 1:1. At this composition, the B cations are ordered into layers, with indium ions in octahedral sites and gallium ions in tetrahedral sites. Thus Ba2InGaO5 is an example of a brownmillerite where an ordering occurs due to the size difference between the B cations. Unfortunately this also reinforces the ordering of oxygen anions which is detrimental to ionic conductivity. Such an ordering stabilizes the brownmillerite structure, increasing the temperature required to transform into a disordered cubic perovskite, while other rates of gallium substitution had the opposite effect. This stabilization of the brownmillerite structure when the B-cation ratio is 1:1 was already proposed by Antipov et al. [30]. This added stabilization might help obtain compounds which were not possible to obtain as a perovskite-like structure in the first place. Sr2(In1
xGax)2O5 might be such an example, for which no successful Ga doping was reported, but Antipov et al. have recently shown that it can be obtained as a cation-ordered brownmillerite when the composition is Sr2In0.9Ga1.1O5 [27].

Acknowledgements This work is funded by the Engineering and Physical Sciences Research Council (EPSRC Grant agreement EP/H000925/1). It was carried out with the support of ISIS (Grant No. RB1281003). We

C. Didier et al. / Journal of Solid State Chemistry 218 (2014) 38–43

thank A. Daoud-Aladine for assistance in using the High Resolution Powder Diffractometer (HRPD, ISIS). M.J.R. is a Royal Society Research Professor. Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jssc.2014.06.011. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

[25] [26]

[27]

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