Olfa Labidi

Michel Drache
email: michel.drache@ensc-lille.fr

Pascal Roussel

Jean-Pierre Wignacourt

Crystal structures and Conductivity properties of MBi 6 V 2 O 15 family type compounds (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 )

A family of compounds was prepared as powder samples with nominal formulas MBi 6 V 2 O 15 (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ), as well as single crystals with closely related compositions. Single crystal structure determinations were realized using X-ray diffraction.

Each sample crystallizes in a monoclinic cell related to the δ-Bi 2 O 3 fluorite type cell, through the relationship:

With M=Na 0.5 Bi 0.5 , the non-centrosymetric C2 space group was selected, while for M=Pb-Cd, the structures were determined in the centrosymetric space group C2/c. Whatever the M element, a non-stoichiometric phase can be obtained. For M= Sr, Ca and Cd, mixed sites were observed; from their refined M/Bi occupancy factors, a determination method of Pb/Bi ratios has been proposed. These phases adopt a layer like structural model related to the δ-Bi 2 O 3 fluorite structure, built from stacking slab units of cationic triple layers [(Bi, V) / (Bi, Bi/M) / (Bi, V)] where the vanadium atoms are located in the two external layers. Oxygen atoms are trapped either in cationic tetrahedrons (OBi 4 , O(Bi/M) 4 ) for those within the slabs, or in VO 4 vanadates for those in the inter-slab spaces, thus limiting the materials oxide conductivity.

Key words

-alkaline-earth bismuth vanadium based mixed oxide.

-lead bismuth vanadium based mixed oxide.

-cadmium bismuth vanadium based mixed oxide.

-sodium bismuth vanadium based mixed oxide -single crystal structure refinement.

-electrical conductivity properties -structure-conductivity properties correlation

Introduction

The δ-Bi 2 O 3 variety, which crystallizes in a fluorite-type structure, is known to date to be the best oxide anion conducting material at high temperature; for a review, see [1]. This interesting conductivity property [2] has been attributed to the defective and disordered characters of the oxide sub-lattice, associated to the high polarizability of Bi 3+ cations [3].

With the aim of obtaining structurally related phases, keeping the interestingly high conducting properties, or reaching even better ones at temperatures as low as possible, numerous investigations of bismuth rich domains in binary systems [4][5][6][7][8][9][10][11][12][13][14], ternary systems [15] or quaternary ones [16] were carried out. Many δ-related phases could be stabilized at room temperature. Their conductivity performances are unfortunately poorer than that of the high temperature δ-Bi 2 O 3 variety, due to the ordering of the oxygen network. The oxide mobility appears to be linked to the polarizability of cationic sub-network; the higher the bismuth content, the higher is the materials conductivity.

The ternary systems PbO-Bi 2 O 3 -P 2 O 5 /As 2 O 5 /V 2 O 5 are among the most investigated systems; the existence of PbBi 6 X 2 O 15 (X=V, P, As) was established by Jie [17]. For PbBi 6 V 2 O 15 , he identified an orthorhombic cell with a=11.970Å, b=11.023Å, c=17.324Å. Lee [START_REF] Lee | Solid State Ionics : Trends in the new millennium[END_REF], proposed another unit cell from indexing the powder X-ray data, i.e.: a= 23.983(18) Å, b=17.172 (13) Å, c=11.092 (11) Å. Hitherto, to our knowledge, the structure has not been solved. The various authors agree that this compound derives structurally from the fluorite-type cubic form of δ-Bi 2 O 3 . Complete P or As for V substitutions in PbBi 6 V 2 O 15 produce solid solutions: PbBi 6 V 2-x P x O 15 and PbBi 6 V 2-x As x O 15 [START_REF] Lee | Solid State Ionics : Trends in the new millennium[END_REF][START_REF] Lee | [END_REF]. On the other hand, two domains of limited solid solutions PbBi 6 P 2-x As x O 15 are obtained with a two-phase area for x compositions ranging between 0.30 and 1.55; another solid solution Pb 1-x Sr x Bi 6 V 2 O 15 is also observed. Lee concludes that the materials PbBi 6 X 2 O 15 (X=V, P, As) and SrBi 6 V 2 O 15 are isomorphous. The conductivities measured on these materials decrease in the order: SrBi 6 V 2 O 15 > PbBi 6 V 2 O 15 > PbBi 6 As 2 O 15 > PbBi 6 P 2 O 15 [START_REF] Lee | Solid State Ionics : Trends in the new millennium[END_REF]. New investigations, reported in this paper, were realized with the aim of basically determining the crystal structures of several members of this family, then correlating the structures to the fluorite-type δ-Bi 2 O 3 , as well as the structural modifications to the evolution of the conductivity performances.

Experimental.

Syntheses.

Powder samples of MBi 6 V 2 O 15 (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ) were prepared by solid state reaction of stoechiometric amounts of the starting reagents: Bi 2 O 3 (Aldrich, 99.9%) and V 2 O 5 (Aldrich, 99.6%), while introduction of the appropriate "divalent cation" was realized using PbO (Riedel de Haën, 99%), CdO, strontium or calcium carbonate, and a mixture of Na 2 CO 3 and Bi 2 O 3 in Na/Bi equimolar proportions. Reagents were weighed, mixed in an agate mortar and then fired at temperatures between 600°C and 800°C for a week, with intermediate regrindings in order to obtain the desired phase.

Single crystals were obtained from powder sample melting at 1000°C, followed by slow cooling at 1°C/h until 840°C, and then furnace disconnection. The selection of good quality crystals was based upon the sharpness of the observed diffraction spots.

Characterizations

Polycrystalline samples were investigated using various techniques. X-ray powder diffraction data were collected at room temperature using a D8 Advance Bruker. The pattern reflections were indexed from the crystalline cell identified on single crystals. The high temperature X-ray diffraction diagrams were explored using a Guinier-Lenné diffraction system with CuKα1 radiation to investigate whether any phase transitions exist; these observations were corroborated by thermal studies (differential thermal analysis DTA) performed on a Linseis L62 instrument. For investigation of electrical properties, sintered pellets (diameter and thickness around 5 mm) were elaborated from materials sintering at 850°C for 48h. The relative density of the sintered samples was nearly 85%. Gold electrodes were then sputtered on both flat faces of the pellets and measurements were done by impedance spectrometry in the range 1-10 6 Hz using a Schlumberger 1170 frequency response analyzer. Each set of values was recorded after 1 h stabilization stage.

None of the thermal studies indicated a phase transformation between the sintering temperature and the ambient one. A structural characterization on single crystal using the Bruker X8 CCD 4K diffractometer was realized for each composition at room temperature.

Structural Investigation

Single crystals were obtained from the melts of various nominal compositions MBi 6 V 2 O 15 (M=Pb, Sr, Cd, Ca, Na 0.5 Bi 0.5 ), generally in the form of rectangular plates; in each case, a crystal was selected for the collection of the diffracted intensities. The SAINT 7.12 Software [START_REF]Bruker Analytical X-ray system[END_REF] was used to extract reflection intensities from the collected frames and the SADABS 2006/1 program [START_REF] Sheldrick | SADABS, Bruker-Siemens Area Detector Absorption and Other Correction[END_REF] was used to correct data from absorption effects using a semiempirical method based on redundancy. The crystal structures were solved by direct methods using the software SIR97 [START_REF] Altomare | SIR 97[END_REF] which readily established the heavy atoms positions (Pb, Bi, V). Oxygen atoms were localized from difference Fourier maps. The last cycles of refinement included atomic positions, anisotropic displacement parameters for all non-oxygen atoms, and isotropic displacement parameters for oxygen atoms. Full-matrix least squares structure refinements against F were carried out using JANA2000 [23]. In the structural refinement procedure, VO 4 tetrahedrons were treated as rigid "molecular" groups. The rigidity of the molecule was determined by a number of common parameters for all atoms of the molecule.

Each position of the molecular model was defined by 3 rotations (Ф, χ, ψ) and 3 translations (xtrans, ytrans, ztrans). The main results of the refinement stages are regrouped in Table I. Hereafter, as an example, the structural resolution is presented for the calcium based sample, particularly representative in the series Pb-Ca. An orthorhombic F cell was initially identified with the parameters: a=11.546(2)Å, b=19.934(4)Å, c=52.231(2)Å. The high Rint=0.637 value highlighted a possible error on symmetry. The structure fits in fact in a monoclinic C cell: a=19.7711(6) Å, b=11.5481(3) Å, c=27.6881(8) Å, β=110.773(4)° (Rint=0.0830 after absorption correction). The most intense reflections characterize a sub-cell of the standard mother structure: a fluorite δ-Bi 2 O 3 . The matrix relationship between this monoclinic cell and the cubic δ fluorite-type cell is:

δ                     - - =           c b a c b a 4 2 2 0 3 2 3 2 3 2 3 2 3
Taking into account the systematic extinctions, the space group is either C2/c or Cc.

The centrosymmetrical space group C2/c was retained after refinement. The 144 heavy atoms within the unit cell are distributed as 14 general positions for bismuth and 4 general positions for vanadium (Fig. 1-a). The Bi11, Bi12, Bi13 and Bi14 sites are partially occupied by calcium and bismuth. Vanadium atoms were regarded in their close oxygen environment as VO 4 tetrahedral rigid groups and refined as such (Fig. 1-b). In the case of the calcium based sample two tetrahedral configurations V(1d)O 4 and V(1e)O 4 are identified, indicating an oxygen disorder (Fig. 2). The atomic coordinates and isotropic/equivalent* parameters are given in Table II, and the atomic displacement parameters are regrouped in Table III. Structural refinements on single crystal led to a non-stoichiometric formulation [Ca 1.966(3) Bi 12.034(3) ]V 4 O 30 , characteristic of a sample belonging to a solid solution. Three similar homologous phosphates (Bi 6 TP 2 O 15+x ≡ T 2 Bi 12 P 4 O 30+2x ) were recently reported [24].

In each of these, the non-stoichiometry was proposed from the existence of mixed cationic sites, and also a partially occupied oxygen site. For the three reported samples (T=Fe, Ni, Zn) the oxygen content has been evaluated from the occupancy refinement of the related oxide site, which was in agreement with the calculated formula using the usual oxidation number of the non oxygen elements. In our work, the structural investigation did not permitted identification of any supplementary oxygen site in agreement with the Bi 3+ for Ca 2+ substitution in Ca 2 Bi 12 V 4 O 30 identified from the refinement. However, in the Ca based sample, taking into account the usual oxidation states of the (Ca 2+ , Bi 3+ , V 5 + ) cations, the neutral formulation of the sample would be [Ca 1.966(3) Bi 12.034(3) ]V 4 O 30.017 .

The structural resolution was similar for related materials containing lead, strontium or cadmium, but was somewhat different for the Na containing material, which was refined in a C2 non-centrosymmetrical space group (i.e. determination of 36 heavy atom positions). In the case of strontium, cadmium or Na containing sample, the non-stoichiometric formulation was unambiguously identified from the structural resolution; the corresponding charge balanced space group; in the case of "PbBi 6 V 2 O 15 " refinement, which has been conducted in the same space group, the existence of similar mixed sites can be presumed. From the experimental data reported in Table I, and using the Shannon and Prewitt tables [25,26], we have calculated the "mean radius" (VI coordinence) of the "mixed cationic species" present in sites 11, 12, 13 and 14, which are mixed sites in the Sr, Cd and Ca-samples. For these sites, this "radius" exhibits a quasi-linear dependence versus the unit cell volume. Each curve is calculated from a least square regression method, and a good R 2 correlation factor: 0.849(1), 0.906(1), 0.990(1) and 0.999(1) respectively for sites 11, 12, 13 or 14 (Fig. 3) is observed. Using these calibration graphs, the "mean" cationic radius in each "PbBi II regroups the significant values of this study at 500°C (conductivity: σ, and activation energy: Ea) and 800°C (σ). The conducting properties of the lead or strontium containing samples are similar to those obtained by Lee [START_REF] Lee | Solid State Ionics : Trends in the new millennium[END_REF].

The Arrhenius plots underline some features: only the Sr containing material exhibits a linear domain over the whole investigated temperature range. Each of the other samples, less conducting, displays a curved domain of evolution. This is a typical behaviour of ionic solid conductors, in which the number of charge carriers, rather low at room temperature, increases significantly with the temperature. While preponderant oxide ion mobility can be reasonably presumed for Pb, Sr, Ca and Cd based materials, in the case of the Na based family member, a Na + cationic conductivity contribution cannot be excluded, and could even become preponderant. The specific high temperature behaviour of Na based sample, with the rapid increase of σ versus temperature in the range 775-850°C, also shows that this sample cannot be considered with the other materials for the comparison of conductivity performances.

Over the whole investigated range, at a given temperature, the conductivity level decrease in the order Sr, Cd, Pb and Ca (Fig. 4). SrBi 6 V 2 O 15 sample, presents the weakest energy of activation, clearly distinct from the three other samples at low temperature (Table IV): at 300°C, the Sr based sample is nearly 10 times more conductive than all other samples.

Discussion and conclusion.

The fluorite type structures reported in this paper display a cationic organization of layer triplets, in which vanadium with its close oxygen environment is considered as VO 4

tetrahedrons, and can be distinguished as systematically located in the outer cationic layers, (Fig. 5-a). These triplets will be hereafter labelled "slabs". Averaged distances between cationic layers are higher in inter-slab spaces (≈3. [START_REF]Bruker Analytical X-ray system[END_REF] [27], can be used also in Bi 46 X 8 O 89 (X=P, V) [28] or Pb 5 Bi 18 P 4 O 42 [29]. According to Lee [START_REF] Lee | Solid State Ionics : Trends in the new millennium[END_REF], PbBi 6 V 2 O 15 and SrBi 6 V 2 O 15 conductivities do not show any evolution, when the atmosphere evolutes from air (PO 2 ≈0.2atm) to nitrogen; the electronic contribution to conductivity is negligible. Consequently these materials can be considered as pure ionic conductors. On the basis of the slab model in rhombohedral Bi-Sr-O type phases, the conductivity of MBi 6 V 2 O 15 -type materials might result from oxide ions moving into the inter-slab spaces. The oxygen evidenced in these spaces is trapped in VO 4 tetrahedrons. In each cationic layer (central or lateral/external layer of the slab), the crushing of the fluorite structure led to a spacing of the cations compared to their relative location in the cubic lattice.

The higher the crushing, the higher is the possibility for the oxygen atoms to move, between the cations, from inside the slabs towards the inter-slab spaces, and consequently, the higher is the oxide conductivity. This is in good agreement with the best conductivity performance noted for the Sr based material. [27][28][29]. The limited conductivity of the MBi 6 V 2 O 15 -type materials is likely related to the trapping of the oxygen atoms of the inter-slabs space in VO 4 tetrahedral units.

Supplementary material.

Crystal Structure Data for the various phases gathered in Table I

collected -27≤ h ≤33 -19≤ k ≤15 -46≤ l ≤42 -35≤ h ≤35 -19≤ k ≤20 -49≤ l ≤49 -34≤ h ≤34 -19≤ k ≤19 -32≤ l ≤46 -35≤ h ≤34 -20≤ k ≤21 -45≤ l ≤50 -33≤ h ≤33 -17≤ k ≤19 -47≤ l ≤47 No. of

Figure 1 :

 1 Figure 1: (010) projection of MBi 6 V 2 O 15 related structures (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ): Ca based sample. Viewing of related fluorite cell (a), and VO 4 tetrahedrons (b).

Figure 2 :

 2 Figure 2: disordered VO 4 in Ca based MBi 6 V 2 O 15 related sample.

4 )

 4 Bi 12.57(4) ]V 4 O 30.285 , [Cd 1.838(5) Bi 12.162(5) ]V 4 O 30.081 , [Na 0.834(3) Bi 13.166(3) ]V 4 O 30.166 .A similar oxygen environment around the Bi, Sr, Cd or Ca cations, characterized by 3 types of polyhedron, with a coordinence ranging from 6 (distorted octahedron) to 8 (distorted cube), is observed for the various samples. The effect of the 6s 2 lone pair is clearly enlighted by the distorted geometry of these polyhedrons. The structures of MBi 6 V 2 O 15 (M=Pb, Sr, Cd, Ca, Na 0.5 Bi 0.5 ) family compounds can be described either by the stacking of 6 cationic layers along the a axis (Fig.1-a), or 8 cationic layers along the c axis. Note that the M atoms are only located in one out of three cationic layers parallel to the (100) crystallographic plane.Hitherto, PbBi 6 V 2 O 15 and SrBi 6 V 2 O 15 seemed to correspond to definite compounds[START_REF] Lee | [END_REF]. The structural determinations carried out in this work on the MBi 6 V 2 O 15 type family (M=Sr, Cd, Ca, Na 0.5 Bi 0.5 ), evidence several mixed M-Bi sites, showing the existence of solid solutions domains. For M = Sr, Cd and Ca, the refinements have been realized in the C2/c

Figure 3 .

 3 Figure 3. Dependence of the "mean cationic radius" versus Unit Cell volume, in the (Bi, M) mixed sites 11, 12, 13, 14 for MBi 6 V 2 O 15 -type family.

4 .

 4 However, these values have to be considered carefully, keeping in mind that, in fluorite related structures, cations have a cubic anionic environment of eight sites, which are statistically occupied by six oxygen atoms. Then using the ionic radius values in coordinence eight, instead of six, leads to slightly different Pb/Bi occupancy ratios and to a somewhat different formula: site 11 is still only occupied by bismuth atoms, however the decrease of the bismuth/lead ratio from site 12 to site 14 is no longer monotonous, as observed for the Pb sample (using r VI values), and for Sr, Cd or Ca samples.The experimental powder X-ray patterns of the four MBi 6 V 2 O 15 materials correspond to the theoretical patterns calculated from the results of the structure determinations. For Sr based material which exhibits the largest discrepancy between the nominal composition and the composition refined from the single crystal X-ray data, we have realized a complete indexing of the powder X-ray pattern for the nominal composition SrBi 6 V 2 O 15 . The refined cell parameters are: a=19.8466(7)Å, b=11.6092(4)Å, c=27.843(1)Å, β=110.645(2)°. The parameters evolution versus the composition variation of the solid solution is then very slight. Conductivity properties.Conductivity measurements were carried out on ceramic pellets of nominal compositions MBi 6 V 2 O 15 , and the temperature dependence of the conductivity was evidenced from Arrhenius plots log (σT) = f (1/T). Representation of the 1 st cooling (800-300°C) and of 2 nd heating (300-850°C) runs overlap, and only the 2 nd heating runs are presented for clarity of the figure. Table

Figure 4 :

 4 Figure 4: Conductivity Arrhenius plots of MBi 6 V 2 O 15 materials (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ).

Figure 5 :

 5 Figure 5: MBi 6 V 2 O 15 related structure (M=Pb, Sr, Cd, Ca, Na 0.5 Bi 0.5 ) viewed as cationic layers (a) or OBi 4, O(Bi, M) 4 and VO 4 tetrahedron layers arrangements (b).

Figure 6 :

 6 Figure 6: MBi 6 V 2 O 15 -type materials (M=Pb, Sr, Ca, Cd): Evolution of « slab+interslab » thickness (observed distorted lattice), and of theoretical cubic fluorite cell diagonal, versus r VI (M 2+ ).

Fig. 1 -Fig. 2 -Fig. 3 -Fig. 4 -Fig. 5 -

 12345 Fig. 1-(010) projection of MBi 6 V 2 O 15 related structures (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ): Ca based sample. Viewing of related fluorite cell (a), and VO 4 tetrahedrons (b).

Fig. 6 -

 6 Fig. 6-MBi 6 V 2 O 15 -type materials (M=Pb, Sr, Ca, Cd): Evolution of « slab+interslab » thickness (observed distorted lattice), and of theoretical cubic fluorite cell diagonal, versus r VI (M 2+ ).

table ( r

 ( VI (Pb 2+ )=1.18 Å and r VI (Bi 3+ )=1.02 Å). It can then be proposed that site 11 is only occupied by bismuth, whereas the three other sites are Pb/Bi mixed sites. The Pb/Bi occupancy ratios determined from the cationic radii in the mixed sites and from the Pb 2+ and

	Bi 3+ radii are 0.175/0.825, 0.343/0.657 and 0.703/0.297, respectively for site 12, site 13 and
	site 14. Therefore, the charge balanced formula corresponding to the refined structure can be
	written: Pb (0.175+0.343+0.703) Bi (10+1+0.825+0.657+0.297) V 4 O 30 . 391 ≡ Pb 1.218 Bi 12.782 V 4 O 30.391 . It is worth

6 V 2 O 15 " corresponding site has been estimated from the cell volume. It leads to _ r VI ≈1.019, 1.048, 1.075, 1.132Å for sites 11, 12, 13 and 14 respectively. The occupancy ratios of Bi 3+ and Pb 2+ , within each site, have thus been deduced using the values given in the Shannon and Prewitt to note that the occupancy of site 11, only by bismuth, is also observed in the case of the Sr based sample, likely due to the chemical similarity of Pb 2+ and Sr 2+ cations.

  Bi 14 P 4 O 31 [Bi 12 P 6 O 33 , Bi 18 O 27 ] or in Bi 50 V 4 O 85

	Å); for this later case, no evident correlation with the alkaline-earth cation size can be
	observed.
	Another possible structural representation consists in considering OBi 4 and O(Bi,M) 4
	anti-tetrahedral units (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ) and VO 4 tetrahedral ones. It is so possible
	to identify cationic slabs made up of three "layers": [(OBi 4 , O(Bi/M) 4 , VO 4 ); (OBi 4 ,
	O(Bi/M) 4 ); (OBi 4 , O(Bi/M) 4 , VO 4 )] in the various samples (Fig. 5-b). Thus, no supplementary
	oxygen atom is observed in the inter-slab space. This stacking design, similar to that
	considered in
	-3.21 Å) than within the slabs (≈3.02-3.06

  Bi 50 V 4 O 85 , Bi 46 X 8 O 89 (X=V, P), Pb 5 Bi 18 P 4 O 42 , Bi 14 P 4 O 31

The cationic model of layer triplets [(Bi, V) / (Bi, Bi/M) / (Bi, V)] where the vanadium atoms are placed in the external layers, is well adapted to the compounds highlighted in this work, but fits also with the other vanadates / phosphates fluorite type structures reported in the literature:

  , have been sent to the

	Fachinformationzentrum	Karlsruhe,	76344	Eggenstein-Leopoldshafen,	Germany
	(fax: (+49)7247-808-666; e-mail: crystaldata@fiz-karlsruhe.de;
	http://www.fiz-karlsruhe.de/ecid/Internet/en/icsd/depot_anforderung.html),
	as supplementary material CSD Nos. 391414 (PbBi 6 V 2 O 15 ), 391415 (SrBi 6 V 2 O 15 ), 391416
	(CaBi 6 V 2 O 15 ), 391417 (CdBi 6 V 2 O 15 ), 391418 (Na 0.5 Bi 6.5 V 2 O 15 ). Copies of this information
	can be obtained by contacting the FIZ (quoting the article details and the corresponding CSD
	number).

Table I : Crystal data and structure refinements for MBi 6 V 2 O 15 (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 )

 I

	Nominal formula	PbBi 6 V 2 O 15 ≡ Pb 2 Bi 12 V 4 O 30	SrBi 6 V 2 O 15 ≡ Sr 2 Bi 12 V 4 O 30	CdBi 6 V 2 O 15 ≡ Cd 2 Bi 12 V 4 O 30	CaBi 6 V 2 O 15 ≡ Ca 2 Bi 12 V 4 O 30	Na 0.5 Bi 6.5 V 2 O 15 ≡ NaBi 13 V 4 O 30
	Refined formula	Bi14V4O30	[Sr1.43(4)Bi12.57(4)]V4O30	[Cd1.838(5)Bi12.162(5)]V4O30	[Ca1.966(3)Bi12.034(3)]V4O30	[Na0.834(3)Bi13.166(3)]V4O30
		a=19.9345(3)	a=19.9112(9)	a=19.6969(6)	a=19.7711(6)	a=19.8603(5)
		b=11.5464(2)	b=11.5916(6)	b=11.5315(3)	b=11.5481(3)	b=11.5096(2)
	Cell parameters (Å)	c=27.9515(4) β=110.8813(9)	c=27.911(1) β=110.872(2)°	c=27.7679(8) β=110.993(1)°	c=27.6881(8) β=110.773(4)°	c=27.8321(5) β=111.172(3)°
		°
	Cell volume (Å 3 )	6011.1(2)	6015.3(5)	5888.4(3)	5910.7(4)	5932.6
	Crystal system	←		Monoclinic		→
	Space group	←	C 2/c (N o 15)	→	C 121(N o 5)
	Z	←		8		→
	F000	11947	11432	11433	10957	11467
			Intensity collection
	Wavelength (Å)	0.71073 (MoKα)	0.71073 (MoKα)	0.71073 (MoKα)	0.71073 (MoKα)	0.71073 (MoKα)
	θ range (°)	1.56-36.63	1.56-39.39	1.57-37.93	1.57-40.32	1.57-37.52
	Data

Table II : Atomic occupancy factors, coordinates and isotropic/equivalent* parameters (Å 2 ) for CaBi 6 V 2 O 15 . **Somme of occupancies for Bi/Ca mixed sites or atoms of the VO 4 disordered tetrahedron was fixed to 1.

 II

	Atoms		Occ.	x	y		z	Ueq*/Uiso
	Bi1		1	0.25104(2)	0.68636(4)	0.190912(17)	0.01539(13)*
	Bi2		1	0.23046(3)	0.03790(5)	0.18434(2)	0.02743(18)*
	Bi3		1	0.58097(2)	0.83374(4)	0.05134(2)	0.02117(15)*
	Bi4		1	0.40434(2)	0.99040(4)	0.064020(16)	0.01435(12)*
	Bi5		1	0.08697(2)	0.19455(5)	-0.06291(2)	0.02252(15)*
	Bi6		1	0.09811(2)	0.31063(4)	-0.185964(16)	0.01591(13)*
	Bi7		1	0.58059(2)	0.02089(4)	0.186134(16)	0.01392(12)*
	Bi8		1	0.41055(2)	0.51736(4)	0.188537(18)	0.01759(13)*
	Bi9		1	0.57536(2)	0.70077(4)	0.181704(17)	0.01336(12)*
	Bi10		1	-0.08261(2)	0.01231(4)	0.435004(17)	0.01491(12)*
	Bi11		0.717(2) **	0.23790(3)	0.84345(5)	0.05772(2)	0.01618(19)*
	Ca11		0.283**	0.2379	0.8435		0.0577	0.01618(19)*
	Bi12		0.695(2)**	0.25453(3)	0.48361(6)	0.06033(3)	0.0222(2)*
	Ca12		0.305**	0.2545	0.4836		0.0603	0.0222(2)*
	Bi13		0.412(3)**	0.24382(5)	0.35768(9)	0.17808(4)	0.0257(3)*
	Ca13		0.588**	0.2438	0.3577		0.1781	0.0257(3)*
	Bi14		0.210(3)**	0.24210(7)	0.16748(13)	0.05791(6)	0.0282(6)*
	Ca14		0.790**	0.2421	0.1675		0.0579	0.0282(6)*
	O1		1	0.2827(4)	0.1698(6)	0.1611(3)	0.0163(15)
	O2		1	0.6125(4)	0.8608(7)	0.1641(3)	0.0167(15)
	O3		1	0.2974(4)	0.5409(7)	0.1671(3)	0.0228(18)
	O4		1	0.1140(4)	0.3529(7)	-0.1086(3)	0.0185(16)
	O5		1	0.1999(4)	0.1668(6)	-0.0353(3)	0.0167(15)
	O6		1	0.6091(4)	0.6643(7)	0.0282(3)	0.0167(15)
	O7		1	0.6259(5)	0.6215(8)	0.1332(4)	0.034(2)
	O8		1	0.6911(5)	0.6737(8)	0.2248(4)	0.029(2)
	O9		1	0.6976(4)	0.8558(7)	0.0890(3)	0.0253(19)
	O10		1	0.2879(4)	0.9879(7)	0.0277(3)	0.0240(18)
	O11		1	0.6001(5)	0.8554(8)	-0.0211(4)	0.029(2)
	O12		1	-0.1950(4)	-0.0186(7)	0.4090(3)	0.0230(17)
	O13		1	0.1925(5)	0.5507(8)	0.2081(4)	0.031(2)
	O14		1	0.1267(7)	0.1438(11)	-0.1589(5)	0.064(4)
	Atoms of tetrahedral rigid molecule
	V1		1	0.08634(9)	0.85609(15)	0.19785(7)	0.0121(3)*
	O15		1	0.0724(5)	0.9841(7)	0.2244(4)	0.071(2)
	O16		1	0.1628(5)	0.7998(9)	0.2348(4)	0.093(3)
	O17		1	0.0181(5)	0.7640(8)	0.1900(4)	0.083(2)
	O18		1	0.0895(6)	0.8836(9)	0.1390(3)	0.076(2)
	Molecular rigid groups
	Positions		Φ	χ	ψ	xtrans	ytrans	ztrans
	Tetra 1		0	0	0	0	0	0
	Tetra 2		-24.3(4)	14.0(4)	113.0(4)	0.31793(9)	-0.20938(16)	-0.13718(7)
	Tetra 3		150.8(4)	1.2(4)	1.5(4)	0.31233(9)	0.00689(15)	-0.00983(7)
	Tetra 4		161.0(15)	63.6(7)	19.4(14)	0.5022(2)	-0.7043(4)	-0.13472(17)
	Tetra 5		146(2)	40.9(19)	9(2)	0.4995(7)	-0.6865(13)	-0.1341(5)
	Atomic coordinates :
		Atoms	Occ.	x	y		z	Ueq*/Uiso
		V1a	1	0.08634(9)	0.85609(15)	0.19784(7)	0.0121(3)*
		O15a	1	0.0727(6)	0.9841(7)		0.2244(4)	0.071(2)
	Tetra 1	O16a	1	0.1630(5)	0.7998(10)	0.2349(4)	0.093(3)
		O17a	1	0.0183(5)	0.7640(8)		0.1900(4)	0.083(2)
		O18a	1	0.0897(6)	0.8836(9)		0.1390(3)	0.076(2)
		V1b	1	0.40406(9)	0.64671(16)	0.06065(6)	0.0121(3)*
		O15b	1	0.3900(7)	0.5601(8)		0.1065(3)	0.071(2)
	Tetra 2	O16b	1	0.4082(7)	0.5656(8)		0.0135(4)	0.093(3)
		O17b	1	0.3390(7)	0.7460(8)		0.0387(4)	0.083(2)
		O18b	1	0.4830(6)	0.7176(8)		0.0879(4)	0.076(2)
		V1c	1	0.39846(9)	0.86298(15)	0.18800(6)	0.0121(3)*
		O15c	1	0.3994(7)	0.7308(8)		0.2165(4)	0.071(2)
	Tetra 3	O16c	1	0.3810(7)	0.9634(10)	0.2234(4)	0.093(3)
		O17c	1	0.4768(6)	0.8893(9)		0.1801(4)	0.083(2)
		O18c	1	0.3333(7)	0.8617(10)	0.1290(3)	0.076(2)
		V1d	0.74(3)**	0.5883(2)	0.1515(4)		0.06311(17)	0.0121(3)*
		O15d	0.74**	0.5503(5)	0.0782(9)		0.1010(5)	0.071(2)
	Tetra 4	O16d	0.74**	0.5358(5)	0.2595(10)	0.0350(5)	0.093(3)
		O17d	0.74**	0.6711(5)	0.1986(10)	0.0977(5)	0.083(2)
		O18d	0.74**	0.5961(6)	0.0599(9)		0.0180(5)	0.076(2)
		V1e	0.26**	0.5857(7)	0.1697(13)	0.0637(5)	0.0121(3)*
		O15e	0.26**	0.5587(9)	0.0836(15)	0.1040(7)	0.071(2)
	Tetra 5	O16e	0.26**	0.5466(9)	0.2960(15)	0.0587(7)	0.093(3)
		O17e	0.26**	0.6754(8)	0.1839(15)	0.0851(7)	0.083(2)
		O18e	0.26**	0.5603(9)	0.1063(15)	0.0052(6)	0.076(2)

Table III : Atomic displacement parameters (Å 2 ) for CaBi 6 V 2 O 15

 III

	Atome	U 11	U 22	U 33	U 12	U 13	U 23
	Bi1	0.01484(18)	0.01283(19)	0.01820(19)	-0.00112(15) 0.00550(15)	-0.00154(17)
	Bi2	0.0291(3)	0.0221(3)	0.0373(3)	-0.0017(2)	0.0195(2)	0.0058(2)
	Bi3	0.0152(2)	0.0270(3)	0.0245(2)	-0.00076(17) 0.01081(17)	-0.00499(20)
	Bi4	0.01466(18)	0.0133(2)	0.01520(18)	0.00389(14)	0.00540(15)	0.00246(16)
	Bi5	0.01435(19)	0.0190(2)	0.0310(3)	-0.00142(16) 0.00396(18)	-0.0059(2)
	Bi6	0.01631(19)	0.0180(2)	0.01218(17)	-0.00235(16) 0.00356(14)	-0.00236(16)
	Bi7	0.01596(18)	0.01161(18)	0.01610(18)	0.00135(14)	0.00802(15)	-0.00021(15)
	Bi8	0.01331(18)	0.0142(2)	0.0210(2)	-0.00045(15) 0.00085(16)	-0.00272(17)
	Bi9	0.01169(17)	0.01281(19)	0.01743(19)	-0.00150(14) 0.00745(14)	0.00071(16)
	Bi10	0.01173(17)	0.0164(2)	0.01725(19)		0.00597(15)	0.00060(17)
	Bi11	0.0224(3)	0.0105(3)	0.0159(3)	-0.0028(2)	0.0071(2)	-0.0016(2)
	Ca11	0.0224(3)	0.0105(3)	0.0159(3)	-0.0028(2)	0.0071(2)	-0.0016(2)
	Bi12	0.0263(3)	0.0202(4)	0.0240(3)	-0.0047(2)	0.0137(3)	-0.0014(3)
	Ca12	0.0263(3)	0.0202(4)	0.0240(3)	-0.0047(2)	0.0137(3)	-0.0014(3)
	Bi13	0.0314(5)	0.0294(6)	0.0138(4)	-0.0081(4)	0.0049(4)	-0.0013(4)
	Ca13	0.0314(5)	0.0294(6)	0.0138(4)	-0.0081(4)	0.0049(4)	-0.0013(4)
	Bi14	0.0224(7)	0.0290(9)	0.0353(9)	0.0030(5)	0.0127(6)	0.0035(6)
	Ca14	0.0224(7)	0.0290(9)	0.0353(9)	0.0030(5)	0.0127(6)	0.0035(6)
	V1a	0.0139(4)	0.0105(4)	0.0127(4)	-0.0001(3)	0.0057(4)	-0.0003(3)
	V1b	0.0110(7)	0.0101(3)	0.0084(4)	-0.0015(3)	0.0019(4)	0.0015(3)
	V1c	0.0117(6)	0.0091(4)	0.0092(4)	-0.0024(4)	0.0027(4)	0.0006(3)
	V1d	0.0119(4)	0.0086(4)	0.0123(7)	-0.0016(3)	0.0067(4)	-0.0008(4)
	V1e	0.0122(5)	0.0096(4)	0.0103(7)	-0.0028(3)	0.0056(5)	-0.0011(4)

Table IV : Ea activation energies (eV) and σ conductivities (S.cm -1 ) of MBi 6 V 2 O 15 (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ).

 IV

	R(M 2+) VI	Material	σ (S.cm -1 )	Ea (eV)	σ (S.cm -1 )
	coordinence		at 500°C		at 800°C
	1,18	PbBi 6 V 2 O 15	3,36.10 -6	1.19	1,13.10 -3
	1,16	SrBi 6 V 2 O 15	3,54.10 -5	0.91	1,78.10 -3
	1,00	CaBi 6 V 2 O 15	2,28.10 -6	1.17	5,98.10 -4
	0.95	CdBi 6 V 2 O 15	4,07.10 -6	1.21	1,15.10 -3
	1.02	Na 0.5 Bi 6.5 V 2 O 15	2.89.10 -6	0.96	2.103.10 -3


Olfa Labidi

Michel Drache
email: michel.drache@ensc-lille.fr

Pascal Roussel

Jean-Pierre Wignacourt

(MBi) 46 V 8 O y -Family type (M=Pb; Sr; Ca; Cd; Na 0.5 Bi 0.5 ) : Syntheses, crystal structures and conductivity properties

Cd; Na 0.5 Bi 0.

Introduction

Because of its excellent ionic conduction properties, the cubic fluorite type ( F ) δ-Bi 2 O 3 (approximately 1 S.cm -1 at 750°C) [1], and its related phases were very largely studied. Many bismuth containing mixed oxides adopt structure types closely connected to this variety [2][3][4][5][6][7][8][9][10][11][12][13][14].

In 1997, Watanabe identified the Bi 23 V 84 O 44.5 phase (≡Bi 46 V 8 O 89 ) with a triclinic lattice [15]. According to Darriet [16], this phase is characterized by a monoclinic cell: a=20.0100(4)Å, b=11.6445(4)Å, c=20.4136(4)Å and β=107. [START_REF] Shannon | [END_REF](3)°, space group P21/c. The structure can be described by the stacking along the c axis, of 6 atomic layers with twice the sequence: 2 layers [Bi 14 V 4 O 31 ] + 1 layer [Bi 18 O 27 ]. In 1983, another vanadate Bi 14 V 4 O 31 (≡Bi 42 V 12 O 93 ) [17] was observed with a monoclinic cell a=19.720Å, b=11.459Å, c=80.160Å and β=90.50° and either C2, Cm or C2/m space group. The structure determination did not succeed, but the cell is also related to the fluorite structural type. In 2005, Bi 50 V 4 O 85 was deferred in the binary diagram Bi 2 O 3 -V 2 O 5 [18]; it is also monoclinic (I2/m space group) with the lattice parameters a=11.8123(3)Å, b=11.7425(2)Å, c=16.5396(2)Å, β=90.14(1)°. To stabilize this phase, an air quenching from 920°C to room temperature is necessary. Under a low temperature annealing, it transforms into a mixture of sillenite type [19,20] and fluorite type phases. The poor quality of Bi 50 V 4 O 85 crystals, due to the thermal instability of this compound, did not allow a reliable structural determination. Nevertheless, Darriet succeeded in locating the heavy atoms, making it possible to propose the sequence: 1 layer [Bi 14 V 4 O 31 ] + 2 layers [Bi 18 O 27 ]. In fact, these phases (Bi 14 V 4 O 31 , Bi 46 V 8 O 89, Bi 50 V 4 O 85 ) constitute 3 members of a general family type Bi 18-4m X 4m O 27+4m (X=V, P), where m is the ratio of the number of [Bi 14 X 4 O 31 ] layers to the total number of layers yielding the definition of the phase.

According to this model, the structure of Bi 14 P 4 O 31 (m=1) results from the repetition of 16x On the other hand, Pb 5 Bi 18 P 4 O 42 was identified and characterized [21] as a phase with a fluorite-type structure. Its structure was determined by synchrotron single-crystal X-ray diffraction in a monoclinic cell (I2/m S.G.; a ≅3/2 * 2 * a F , b≅3/2 * 2 * a F , c≅3 * a F , β≈90°).

The structure was described by the sequence of lead atoms and disordered phosphates constituting a two-dimensional assembly parallel to the (a,c) plane. Between these layers, Bi-O layers are located to form a three-dimensional array. However, this structure can also be considered as a stacking of 2 Bi 12 Pb 2 P 4 O 30 layers sandwiching a single Bi 12 Pb 6 O 24 layer. For the vanadate, refinements of the powder pattern yielded the cell parameters a=12.009(4)Å, b=11.711(5)Å, c=16.143 (7)Å and β=90.11(2)°. Isomorphous Pb 5 Bi 18 X 4 O 42 homologues (X=V or As) were characterized [22] by powder X ray diffraction. Very similar overall compositions Pb 5 Bi 17 X 5 O 43 (X=P, V, As) were also identified [23]. Thus, it appeared interesting to investigate the pseudo-binary system Pb 5 Bi 18 V 4 O 42 -Bi 46 V 8 O 89 in order to prepare new original phases, with a possible attracting conductivity property resulting from an optimal Pb 2+ for Bi 3+ substitution rate. This substitution could enhance the conductivity due to the increase of the mobile oxide ion number, and increase the structural stability in relation to the decrease of the vacancy ratio. The presence of a nonbonding 6s 2 lone pair induces a high polarisability for both cations which facilitates the mobility of the oxide ions. In such a material, the coexistence of Pb 2+ and Bi 3+ isoelectronic ions, cannot be identified from X-ray diffraction crystal structure. For this reason, the structural investigations which have been realized, could not be used to consider any accurate structure-conductivity property correlations. In order to dodge this handicap to identify the location of Pb 2+ , we have also examined the possibility of substituting this cation in Pb 5 Bi 18 V 4 O 42 , by other divalent M 2+ (Sr 2+ , Ca 2+ , Cd 2+ ) or mixed equivalent ones (Bi 3+ 0.5 Na + 0.5 ), which can be easily differentiated from bismuth, assuming they will be located in crystallographic sites equivalent to the lead ones; the obtained structural results, which were used to evaluate the formula(s) of the lead containing sample(s), will be (firstly) described in this paper.

Experimental.

Syntheses.

M 10(1-x) Bi 36+10x V 8 O 84+5x powder samples for different compositions (M=Sr, Ca, Cd, Na 0.5 Bi 0.5 with x=0; M=Pb with x varying from 0 to 1, by x step of 0.1) were prepared by solid state reaction. Bi 2 O 3 (Aldrich, 99.9%) and V 2 O 5 (Aldrich, 99.6%) were used as the main starting materials; "divalent cations" were introduced into the achieved different phases from SrCO 3 (Aldrich, 98.0%), CaCO 3 (Aldrich, 99.0%), CdO (Carlo Erba, 99.0%), a mixture Na 2 CO 3 (Aldrich, 99.5%)-Bi 2 O 3 in Na/Bi equimol proportions, or PbO (Riedel de Haën, 99%) with their correct stoichiometric amounts. For each composition, the reagents were weighed, placed in an agate mortar, and thoroughly grinded and homogenized. These mixtures were deposited in gold boats and heated in static air atmosphere for five 15 hrs treatments. Each one, ended by an air quenching, was followed by a regrinding. The treatment temperatures ranged between 600 and 800°C with a step temperature 50°C. Completion of the reaction was indicated by the reproducibility of the X-ray patterns after the two last treatments.

Single crystals were obtained from the powder sample melting at 1000°C, followed by slow cooling at 1°C/h until 840°C and then furnace disconnection; the cooling process was so uncontrolled. The selection of good quality crystals was based upon the sharpness of the diffraction spots.

The characterizations of the produced phases

A Bruker X8 CCD 4K diffractometer was used for the crystallographic characterization of the single crystals, which were made for all M compositions at ambient temperature. The crystal structures were solved using SIR97 software [START_REF] Altomare | SIR 97[END_REF], and refined with the JANA2000 program [25]. In the structural refinements, VO 4 tetrahedra were regarded as rigid molecular groups. The rigidity of the vanadate group was determined by a number of common parameters for all the constituting atoms. Each position of the rigid group was defined by 3 swing angles (Ф, χ, ψ) and a translation vector (xtrans, ytrans, ztrans). The conditions of data collection are gathered in Tables I andII. Atomic positions and thermal parameters are available as supplementary materials.

Sintered pellets (diameter and thickness about 5 mm) were elaborated from materials sintering at 850°C for 48h, for investigating their electrical conductivity properties. The relative density of the sintered samples was nearly 85%. Gold electrodes were then sputtered on both flat faces of the pellets and measurements were done by impedance spectrometry in the range 1-10 6 Hz using a Schlumberger 1170 frequency response analyzer. Conductivity measurements were realized in static air atmosphere between 300 and 840°C (temperature step: 10°C). Each set of values was recorded after 1 h stabilization stage.

Guinier Lenné X-ray diffraction camera (gold grid sample holder; heating rate ≈20°C.h -1 ) as well as differential thermal analysis (DTA Linseis L62; platinum crucibles; heating cooling rate 300°C.h -1 ) were used to investigate the thermal behaviour of all samples in air, corroborating the conductivity properties investigation.

Results and discussion

3.1. Crystal structures in the (M , Bi) 46 V 8 O y family (M=Sr, Ca, Cd, Bi 0.5 Na 0.5 ).

As an example for this family, the crystal structure determination process of the Sr based sample is presented in order to show the complexity of each stage. The investigation was initially undertaken in the most symmetrical proposed orthorhombic lattice, i.e. in the Immm space group, after merging the equivalent reflections (R(F²) int =0.063 after absorption correction [21]). At this stage, the structural resolution did not succeed either by direct method, nor by Patterson interpretation. A reinvestigation was undertaken in a cell of lower symmetry, (monoclinic I) and yielded a R(F²) int factor of about 0.057 with absorption correction. The structural refinement was thus conducted in the monoclinic I cell (a=11.9411(5)Å, b=11.7063(5)Å, c=16.3652(7)Å, β=90.059(3)°). The tested space groups were respectively I2/m, I2 and Im. In the two first cases, the refinements were not conclusive.

The best structural refinement was found in the Im non-centrosymetric space group. Fourteen heavy atom positions (including 6 mixed sites Sr/Bi) were identifed and refined. Ten oxygen atoms were located by successive Fourier difference syntheses. At this point, the vanadium atomic environments were incomplete. Refinement of the anisotropic thermal coefficients of of bismuth, strontium and vanadium atoms, lead to the reliability factor 0.0609.In place of monoclinic Im S.G, the Platon software [Spek 1990] suggested to use the orthorhombic symmetry, with a non-centrosymetric Imm2 space group. Using these characteristics, a structural refinement was realized without introducing oxygen around vanadium atoms. The reliability factor converged towards 0.0642 with 93 refined parameters instead of 154 previously. The Platon software, used a second time, proposed the centro-symetric Immm space group. Six bismuth atoms positions, with one mixed site Sr1/Bi1b and one site fully occupied by strontium (Sr2) were thus refined. Oxygen atoms were introduced from examination of Fourier difference maps around the two vanadium atoms (V1 and V2). The oxygen site occupancies were constrained in order to form two VO 4 tetrahedral entities.

Residual peaks are still observed around vanadium atoms while the suggested model is thus an idealized model. The distances between V1 and O7, O8 and O9, and those between V2 and O10, O11 and O12 were also soft-constrained to the "ideal" value 1.65(2) Å. A last refinement cycle yielded a reliability value of 0.0596. In summary, it was impossible to solve the structure using the Immm space group, even if in fine, this space group is the actual one and thus used in the refinement process. The crystallographic characteristics, conditions of data collection and various refinement parameters are gathered in Table I-first column. The atomic coordinates and isotropic/equivalent* parameters and the atomic displacement parameters are given as supplementary materials.

Samples containing calcium or cadmium crystallise in analogous cells. Each structure determination has been undertaken using the non-centrosymetric Pn2n space group. With a careful examination of the atomic positions, the Pnmn space group was finally selected. For calcium containing crystal, this element was distributed over a unique position and two Ca/Bi mixed sites. On the other hand, in the case of the cadmium based sample, Cd atoms occupy 3 mixed sites Cd/Bi with different occupancy rates. With M=Bi 0.5 Na 0.5 , the structure was finally refined in I2/m space group and Na was distributed over two Na/Bi mixed sites. The crystallographic characteristics of the three structures (M=Ca, Cd, Bi 0.5 Na 0.5 ), the conditions of data collection and various refinement parameters are gathered in Table I-columns 2-4.

Each structure consists in a stacking of 6 cationic layers closely related to the cubic fluorite-type lattice (Fig. 1-a). The M atoms are distributed in the layers in Bi/M mixed sites for all the compositions but, except for the Sr based sample, where one Sr atom lies in a distinct site. The vanadium atoms are located in two out of three layers. Their oxygen environment determines tetrahedral VO 4 entities (Fig. 1-b) which are disordered over two positions. (Fig. 2). The cationic environment of the remaining oxygen atoms determines a long range sub-lattice of closely linked OM 4 anti-tetrahedrons (Fig. 1c).

Relationship with δ-Bi2O3 cell δ                     - =           c b a c b a 3 0 0 0 0 2 3 2 3 2 3 2 3 Z 2 2 2 2
Density calculated (g.cm -3 ) Surprisingly, the Pb 6 Bi 40 -1 crystal obtained from the Pb richest nominal composition, displays a unit cell similar to Bi 46 V 8 O 89 [16], i.e. for the lead free composition. As in the (M , Bi) 46 V 8 O y family (M=Sr, Ca, Cd, Bi 0.5 Na 0.5 ) reported in the precedent paragraph, the three crystal structures can be described as a stacking of 2 types of cationic layers containing either bismuth/lead/vanadium, or bismuth/lead. Vanadium is located in two third of the layers; a "slab" structural model can be seen from a stacking of triple layer blocks, where the vanadium is systematically located in both "external" layers. A sequence of 6 layers in Pb 3 Bi 43 or Pb 6 Bi 40 -1 (Fig. 4) and 9 layers in Pb 6 Bi 40 -2 (Fig. 5) can be identified along the c axis, corresponding respectively to a stacking of 2 slabs and 3 slabs, thus describing each structure from a common structural feature. As previously indicated, the lead atom cannot be distinguished from bismuth by X-ray diffraction when using Mo Kα radiation. In order to try to the lead site, a tentative comparison of the crystal structures of M [21,23], where Pb and Bi atoms were unambiguously identified, was undertaken. with the already known fluorite type structure was undertaken with the aim of understanding their similarities and differences, and to identify a general layer like structural model.

Relationship with δ-Bi2O3 cell δ                     - - - =           c b a c b a 0 3 3 0 3 2 3 2 3 2 3 2 3 δ                     - - =           c b a c b a 4 0 3 2 5 2 5 2 3 2 3 2 3 2 3 δ                     - =           c b a c b a 3 0 0 0 0 2 3
collected -33≤ h ≤36 -20≤ k ≤17 -36≤ l ≤38 -35≤ h ≤35 -20≤ k ≤19 -48≤ l ≤52 -13≤ h ≤23 -22≤ k ≤23 -30≤ l ≤28 No. of

The electrical conductivity properties.

Investigation of materials conductivity was undertaken for M 10 Bi 36 V 8 O 15 (M=Pb, Sr, Ca, Cd, Na 0.5 Bi 0.5 ) nominal compositions. While preponderant oxide ion mobility can be reasonably presumed for Pb, Sr, Ca and Cd based materials, a Na + cationic conductivity component cannot be excluded in the Na based family member, and could even become preponderant. For this latter Na sample we could not prepare a pellet with stable dimensions, going through the necessary sintering process; this thermal instability is probably related to the high sodium content of the material which yields a significant hygroscopicity.

Conductivity measurements were carried out on ceramic pellets of the other materials;

the temperature dependence of the conductivity was evidenced from Arrhenius plots log (σT) = f (10 3 T -1 ). Representation of the 1 st cooling (800-300°C) and of 2 nd heating (300-840°C) runs overlap, and only the 2 nd heating data are represented for clarity of the figure (Fig. 6).

Table III regroups the significant values of this study for σ conductivity (500 and 800°C) and for Ea activation energy (500°C).

The manufactured materials display an Arrhenius type electrical conduction behaviour, i.e. a linear relationship between log (σT) and 1/T. The absence of any break or jump in each graph (300-840°C) is in good agreement with the absence of any event occurring during the thermal behaviour samples examination (Guinier Lenné diffraction and differential thermal analyses). Only one phase is stable within the whole investigated temperature range. For a given temperature above 550°C, the conductivity level decreases in the order Pb, Sr, Ca and Cd. The Ca 10 Bi 36 V 8 O 84 sample presents the weakest activation energy, clearly distinct from the three other samples at low temperature. At 300°C, the Ca and Pb based samples exhibit similar conductivity performances.

Discussion

In a previous paper about the MBi 6 V 2 O 15 -family type [START_REF] Labidi | Solid State Sciences[END_REF], we have described three isomorphous members (M=Sr, Ca and Cd), in the same space group C2/c. A methodology, based on structural results, allowed us to plot for the different (Bi, M) mixed site compositions, the mean cationic radius versus the unit cell volume. The dependence between the mean cationic radius and the cell volume for this series permitted us to construct a calibration curve that we used as a "standard chart", and consequently, we were able to evaluate the Pb/Bi radii for the corresponding mixed sites of the isostructural lead containing sample. From these radii, the Bi/Pb occupancy factors were estimated and a chemical formula was proposed. The same approach was tried for the materials reported in the present paper, i.e. the (M,Bi) 46 V 8 O y family, which crystallizes with closely related structures, but with various space groups. Unfortunately, no correlation between the mixed site cationic radii could be evidenced.

Examining successively the various members of the series (M,Bi) 42 V 12 O y independently of the changes of space group (respectively C2, Cm ou C2/m for Bi 42 V 12 O 93 [17], C2/c or C121 for (M,Bi) 42 V 12 O y with M=Pb, Sr, Ca, Cd or Na 0.5 Bi 0.5 ) a linear correlation can be identified between the cell volume and the ions volume for the corresponding formula units (calculated from M 2+ , Bi 3+ , V 5+ and O 2-ionic radii (VI) [START_REF] Shannon | [END_REF]28]-Fig. 7; correlation factor r 2 =0.94). M for Bi substitution, even when rM 2+ >rBi 3+ (M=Sr, Pb), leads to a decrease of the cell volume. This tendency is resulting from the decrease of the oxygen content when compared to Bi 42 V 12 O 93 . An analogous cell contraction is observed for (M,Bi) 46 V 8 O y crystalline materials obtained from substitutions in Bi 46 V 8 O 89 using smaller elements than bismuth (Na 0.5 Bi 0.5 , Ca, Cd; linear correlation factor r 2 =0.91), whereas a dilatation of the lattice is observed with Sr. The organization in cationic layer triplets (hereafter slabs) is a common structural character to numerous phases in this system. The mixed oxide phases with the rhombohedral Bi-Sr-O-type [29], containing bismuth -alkaline-earth, or bismuth -rare earth can be so described. In this case, the number of slabs is specific to each variety: a single slab determines the ε-variety, whereas a stacking of three slabs is necessary to describe β 2 or β 1 variety.

The cationic planes correspond to (111) crystallographic planes of a distorted cubic standard fluorite cell. In the M 6 Bi 36 V 12 O 90 series [START_REF] Altomare | SIR 97[END_REF], it consists of a crushing of the fluorite type lattice perpendicularly to these planes, thus leading, in each plane, to increased inter cationic distances compared to their initial location in a truly cubic cell. This type of crushing is also observed for the rhomboedral Bi-Sr-O type structures [29]. In the (M,Bi It is worth to note that the conductivity performances of M 10 Bi 36 V 8 O 84 materials in the high temperature domain increase in the order Cd→Ca→Sr→Pb. This order corresponds to the regular increase of the unit cell volume and to decrease of the inter layer distances within the slab therefore producing an expansion of the interlab space. This space can be reasonably presumed as the host sublattice for the mobile ions, considering the analogy of these structures with the rhombohedral Bi-Sr-O type conductors [29]. The latter as well as the This high stretching rate is likely responsible of the opening of migration pathways for the oxide ions, and consequently to a decrease of the activation energy.

M

Conclusion

The cationic slab model built out of [(Bi/M, V) / Bi/M /(Bi/M, V)] triple layers where the vanadium atoms are systematically located in the external layers, appears to be adapted to the whole family of phases highlighted in this work, but fits also other fluorite related structural types, i.e. vanadates or phosphates reported in the literature: Bi 50 V 4 O 85 [18],

Bi 46 X 8 O 89 (X=V, P) [16] shown the existence of two kinds of triple layer stacking (6 cationic layers organized in 2 slabs, or 9 cationic layers in 3 slabs). The lead atoms could not be located and specifically identified from Bi.

Figure captions

  Pb 5 Bi 17 P 5 O 43 crystallizes with a superstructure of δ-Bi 2 O 3 form. Its structure was solved using synchrotron radiation in the cell: a=11.341(2)Å, b=16.604(3)Å, c=11.432(2)Å, β=93.73(3)° and Im space group. A combination with powder neutron diffraction allowed the localization of heavy atoms (Bi and Pb) implied in the formula, as well as the oxygen atoms. The structure can be described as a succession of layers (Bi 10 Pb 6 P 2 O 26 , Bi 14 P 4 O 31 , Bi 10 Pb 4 P 4 O 29 ). In a quasi-general manner, in such a series of homologous materials, the conductivity increases from the phosphate to arsenate and the vanadate derivative. For the vanadium based materials, the reported conductivity Arrhenius plots show a decrease of the σ performances from Bi 46 V 8 O 89 to Pb 5 Bi 18 V 4 O 42 and then Pb 5 Bi 17 V 5 O 43 . Due to the analogy of each structure to the δ-Bi 2 O 3 fluorite type, they are assumed to be oxide ion conductors.

Figure 1 :

 1 Figure 1: (010) projections of Sr 10 Bi 36 V 8 O 84 related structure: cationic arrangement, crystalline cell and related fluorite sub-cell (a); viewing of VO 4 tetrahedrons (b); long range network from VO 4 and O(Bi,M) 4 assembly (c).

Figure 2 : 3 . 2 .Fig. 3 : 7 ,

 23237 Figure 2: Evidence of VO 4 disordering in Sr 10 Bi 36 V 8 O 84 related structure.

Figure 4 :

 4 Figure 4: (010) projections of Pb 6 Bi 40 -1 structure: cationic arrangement, crystalline cell and related fluorite sub-cell (a); viewing of VO 4 tetrahedrons and two slabs stacking (b); long range network from VO 4 and O(Bi,M) 4 assembly (c).

Figure 5 :

 5 Figure 5: (010) projections of Pb 6 Bi 40 -2 structure: cationic arrangement, crystalline cell and related fluorite sub-cell (a); viewing of VO 4 tetrahedrons and three slabs stacking (b); long range network from VO 4 and O(Bi,M) 4 assembly (c).

Figure 6 :

 6 Figure 6: Conductivity Arrhenius plots of M 10 Bi 36 V 8 O 84 materials (M=Pb, Sr, Ca, Cd).

Figure 7 :

 7 Figure 7: Cell volume -ions volume correlation for (MBi) 46 V 8 O y and (MBi) 42 V 12 O y families.

  ) 46 V 8 O y series considered in the present paper, the fluorite lattice is stretched. The reference thickness unit, i.e. "slab + inter-slab", which corresponds in all cases to the main diagonal (a F √3) of a standard fluorite cell, is here longer than the diagonal of a truly cubic fluorite cell (maximum of inequality for Ca based sample).Another representation of these structures consists in layer like arrangements of O(Bi,M) 4 anti-tetrahedrons (M=Pb, Bi, Sr, Ca, Cd, Bi 0.5 Na 0.5 ) and VO 4 tetrahedrons, as presented in the MBi 6 V 2 O 15 -type family[START_REF] Altomare | SIR 97[END_REF] where a stacking of disconnected slabs has been identified; on the contrary, the slabs of (M,Bi) 46 V 8 O y materials are linked by O(Bi,M) 4 antitetrahedrons. There exists a relationship between the number of oxygen of the lateral slab layers and the inter-slab distance, since a slight dilatation of inter-slab space is observed between Bi 50 V 4 O 85 and Bi 46 V 8 O 89 : as 4 vanadium atoms substitute for bismuth atoms, a contraction of the layers should appear (bismuth ionic radius being larger than the vanadium one); however, this is negligible compared to dilatation. The influence of the cationic size is thus counterbalanced by the major influence of introduced oxygen atoms. On the other hand, increasing the vanadium content ratio (from (M,Bi) 46 V 8 O y materials to MBi 36 V 12 O 90 ≡ MBi 6 V 2 O 15 ) induces the trapping of interslab oxygen atoms, towards the slabs, to form vanadate anions. So the slabs are more easily distinguished. The presence of the oxygen ratio in the interslab spaces leads to the formation of "bridging" O(Bi,M) 4 entities between the slabs.

Fig. 1 :Fig. 2 :Fig. 3 :

 123 Fig. 1: (010) projections of Sr 10 Bi 36 V 8 O 84 related structure: cationic arrangement, crystalline cell and related fluorite sub-cell (a); viewing of VO 4 tetrahedrons (b); long range network from VO 4 and O(Bi,M) 4 assembly (c). For clarity, only one configuration of tetrahedrons is presented.

Fig. 4 :

 4 Fig. 4: (010) projections of Pb 6 Bi 40 -1 structure: cationic arrangement, crystalline cell and related fluorite sub-cell (a); viewing of VO 4 tetrahedrons and two slabs stacking (b); long range network from VO 4 and O(Bi,M) 4 assembly (c). For clarity, only one configuration of tetrahedrons is presented.

Fig. 5 :Fig. 6 :Fig. 7 :

 567 Fig. 5: (010) projections of Pb 6 Bi 40 -2 structure: cationic arrangement, crystalline cell and related fluorite sub-cell (a); viewing of VO 4 tetrahedrons and three slabs stacking (b); long range network from VO 4 and O(Bi,M) 4 assembly (c). For clarity, only one configuration of tetrahedrons is presented.

  Bi 14 P 4 O 31 layers parallel to the (001) plane; Bi 46 X 8 O 89 (X=V, P and m=2/3) is formed from the stacking of [Bi 14 X 4 O 31 , Bi 18 O 27 , Bi 14 X 4 O 31 ] successive layers, while Bi 50 V 4 O 85 (m=1/3) results from [Bi 14 V 4 O 31 , Bi 18 O 27 , Bi 18 O 27 ] layers.

Table I : Principal characteristics of M 10 Bi 36 V 8 O 84 (M=Sr, Cd, Ca, Na 0.5 Bi 0.5 ) structure determinations on the X-ray single crystal diffractometer.

 I

			Crystallographic data
	Nominal formula	Sr10Bi36V8O84	Ca10Bi36V8O84	Cd10Bi36V8O84	Na5Bi41V8O84
	Refined formula	Sr3.59(5)Bi19.41(5)V4O42	Ca4.207(4)Bi18.793(4)V4O42	Cd3.573(7)Bi19.427(7)V4O42	Na1.533(6)Bi21.467(6)V4O42
	Symmetry	Orthorhombic	Orthorhombic	Orthorhombic	Monoclinic
	Space group	I mmm (N°71)	P nmn (N°58)	P nmn (N°58)	I 2/m (N°12)
	Cell parameters (Å)	a=11.9411(5)	a=11.9584(2)	a=11.9529(7)	a=12.0352(3)
		b=11.7063(5)	b=11.5275(2)	b=11.4873(3)	b=11.5748(4)
	Cell volume (Å 3 )	c=16.3652(7) 2287.6(2)	c=16.0738(3) 2215.77(8)	c=15.965(1) 2192.2(2)	c=16.0686(5) β=90.115(2)° 2238.4(1)

Table II : Principal characteristics of Pb 6 Bi 40 V 8 O 86 -1, Pb 6 Bi 40 V 8 O 86 -2 and Pb 3 Bi 43 V 8 O 87.5 structure determinations on the X-ray single crystal diffractometer.

 II

		Crystallographic data
	Nominal formula	Pb10(1-x)Bi36+10xV8O84+5x (x=0.4)	Pb10(1-x)Bi36+10xV8O84+5x (x=0.7)
		≡ ≡ ≡ ≡ Pb6Bi40V8O86	≡ ≡ ≡ ≡ Pb3Bi43V8O87.5
	Sample identification	Pb6Bi40V8O86 -1	Pb6Bi40V8O86 -2
	Refined formula	Bi23V4O45	Bi23V4O44	Bi23V4O44
	Symmetry	Monoclinic	Monoclinic	Orthorhombic
	Space group	C 2/m (N°12)	C 2/m (N°12)	I mmm(N°71)
	Cell parameters (Å)	a=20.0822(4)	a=20.0874(4)	a=12.1371(4)
		b=11.6351(2)	b=11.6841(2)	b=11.6935(4)
		c=21.0878(5) β=111.678(1)°	c=29.5629(6) β=98.816(1)°	c=16.0191(6)
	Cell volume (Å 3 )	4578.8(2)	6856.5(2)	2273.5(1)

  10 Bi 36 V 8 O 84 (M=Sr, Ca, Cd) and the structures of Pb 10 Bi 36 P 8 O 84 (≡Pb 5 Bi 18 P 4 O 42 ) and Pb 10 Bi 34 P 10 O 86 (≡Pb 5 Bi 17 P 5 O 43 )

Table III

 III

	: σ σ σ σ total conductivity (

ohm.cm) -1 at 500 and 800°C and Ea activation energy (eV) for M 10 Bi 36 V 8 O 84 (M=Pb, Sr, Cd, Ca) samples.

	Ionic radii of M 2+	(VIII) (Å)	Sample	σ (ohm.cm) -1	Ea (eV)
				500°C	800°C	500°C
	1.29		Pb 10 Bi 36 V 8 O 84	8,91.10 -5	4,57.10 -3	0,92
	2.26		Sr 10 Bi 36 V 8 O 84	3,75.10 -5	1,87.10 -3	1,01
	1.12		Ca 10 Bi 36 V 8 O 84	3,73.10 -5	1,05.10 -3	0,79
	1.10		Cd 10 Bi 36 V 8 O 84	4,27.10 -6	2,52.10 -4	0,93

  10 Bi 36 V 8 O 84 materials are slightly more conductive than the MBi 6 V 2 O 15 (≡M 6 Bi 36 V 12 O 90 ) family. It is difficult to identify the parameters responsible for these better conductivity properties: both the ionic compactness of the structure and the oxide ions number are lower for M 10 Bi 36 V 8 O 84 , and when the first characteristic favours the conductivity, the second one would diminish it. In fact M 10 Bi 36 V 8 O 84 series, contrarily to MBi 6 V 2 O 15 -one, exhibits oxygen ions in the interslab space, with OBi 4 and O(Bi,M) 4 environments. It is reasonable to think that these ions are responsible for the conductivity enhancement.On the other hand, to the Ca 10 Bi 36 V 8 O 84 material which exhibits the lowest activation energy, is associated the structure characterized by the most stretched fluorite type lattice.

  , Pb 10 Bi 36 P 8 O 84 (≡Pb 5 Bi 18 P 4 O 42 ) [21], Bi 42 P 12 O 93 (≡Bi 14 P 4 O 31 ) [18]. The crystal structure investigation of Pb 10(1-x) Bi 36+10x V 8 O 84+5x solid solution samples has

Supplementary material.

Crystal Structure Data for the various phases gathered in Table I