Structural determination of new solid solutions [Y2-xMx][Sn2-xMx]O7-3x/2 (M = Mg or Zn) by Rietveld method

New [Y2-xMx][Sn2-xMx]O7-3x/2 (0 ≤x≤ 0.30 for M = Mg and 0 ≤x≤ 0.36 for M = Zn) solid solutions with the pyrochlore structure were synthesized via high-temperature solid-state reaction method. Powder X-ray diffraction (PXRD) patterns and Fourier transform infrared (FT-IR) spectra showed that these materials are new non-stoichiometric solid solutions with the pyrochlore type structure. The structural parameters for the solids obtained were successfully determined by Rietveld refinement based on the analysis of the PXRD diagrams. Lattice parameter (a) of these solid solutions decreases when x increases in both series. All samples obtained have the pyrochlore structure Fd-3m, no. 227 (origin at center -3m) with M2+ (M = Mg2+ or Zn2+) cations in Y3+ and Sn4+ sites, thus creating vacancies in the anionic sublattice.


I. Introduction
Synthetic pyrochlore-like solids are ternary metallic oxides with the general formula A 2 B 2 O 7 and structure similar to that of the natural mineral called pyrochlore with chemical formula (NaCa)(NbTa)O 6 F/(OH) [1].The pyrochlore structure can be considered as an ordered, defective fluorite solid solution, as shown in Fig. 1.Cations A and B form a face centered cubic array, additionally ordered in the [110] directions and so A and B cations are eight-and six-coordinated, respectively, by oxygen anions, as described below.
The ideal cubic structure is highly symmetrical, with space group ).The general formula is A 2 B 2 O 6 O', and locating the origin on the B site [2], the ions occupy four crystallographically different sites (using Wyckoff's notation): A at 16d, B at 16c, O at 48f and O' at 8b.There is only one positional parameter, x, which describes the position of the oxygen atoms in the 48f site (x,1/8,1/8).The geometry of both the A and B cations depends on the value of the single variable oxygen positional parameter.The A cations have eight nearest neighbor anions forming a distorted cube; the B cations have six nearest neighbor oxygen ions forming a distorted octahedron.All oxygen ions lie within a tetrahedron of nearest neighbor cations.The 8b site has four A cations and the 48f site has two A and two B cations.The vacant 8a site has a tetrahedron of four B cations.
The cations at the A and B sites in the lattice can be replaced by other cations with different formal charge or different oxidation-reduction abilities, to synthesize various kinds of pyrochlore compounds with different physical or chemical properties.
Ternary tin oxides with the pyrochlore structure, M 2 Sn 2 O 7 (M = rare earth or yttrium), constitute a wellknown series of compounds possessing SnO 6 octahedra.There are two main types of pyrochlore compounds: O 7 structure and is significantly important because of its applications as ionic/ electric conductors and because of its piezoelectricity, dielectric properties and resistance to radiation damage [3,4].These materials have been widely used as catalysts, high-temperature pigment, electrochemical cells for NO x decomposition, etc. [5][6][7][8][9].
Due to their wide variety of compositions, some of the stannate pyrochlores exhibit a high efficiency for the oxidative coupling of methane and can be used as high-temperature gas sensors or fast ion conductors [4].Furthermore, stannate pyrochlores have been used as model compounds in MAS-NMR studies of paramagnetic solids [4].Binary and ternary tin oxides have also been investigated as anode materials for lithium ion batteries (LIB) [10].
The structures of [Eu 2-x M x ][Sn 2-x M x ]O 7-3x/2 (0 ≤ x ≤ 0.40 for M = Mg and 0 ≤ x ≤ 0.45 for M = Zn) solid solutions have been recently refined by Rietveld methods of X-ray diffraction [11,12].Keeping in mind that changes in the composition of these kind of systems can regulate their structure and so their properties, we have synthesized two additional pyrochlore systems, namely [Y 2-x M x ][Sn 2-x M x ]O 7-3x/2 (0 ≤ x ≤ 0.30 for M = Mg and 0 ≤ x ≤ 0.36 for M = Zn).The aim of present work is to study the effect of the substitution of large three or tetravalent cations by smaller divalent ones, Mg 2+ and Zn 2+ , on the pyrochlore structure.The structural study of the X-ray diffraction diagrams of both series has been performed by Rietveld analysis in order to obtain accurate data that are not currently available in the literature.

II. Experimental
.30 for M = Mg and 0 ≤ x ≤ 0.36 for M = Zn) were synthesized using the ceramic method in two steps as described in a previous paper [13].Stoichiometric quantities of the oxides (Y 2 O 3 , SnO 2 , MgO or ZnO, all reagents from Aldrich) were mixed and hand ground, then heated in air at 1000°C for 48 h and finally re-ground and submitted to calcinations at 1400°C for 96 h.The samples were heated at 2°/min and the cooling rate was 10°/min in both cases.

III. Data collection and Rietveld refinement
X-ray powder diffraction patterns were recorded in a Siemens D-500 diffractometer with a DACO-MP microprocessor using CuKα radiation (λ = 1.5405Å).The powder diffraction diagrams were obtained by scanning with counting steps of 6 s from 2θ = 12° to 85° using 0.01° step-intervals.The PXRD obtained were analyzed by Rietveld method using Fullprof software [14], the atomic position set and the space group of the pyrochlore structure .A Pseudo-Voigt function was chosen to generate the line shape of the diffraction peaks.The background was estimated by linear interpolation between points corresponding to regions without reflections.A Rietveld refinement was performed to minimize the function S y = ∑ i w i (y i -y ci ) 2 , where y i and y ci are the observed and calculated intensities at the i th step and w i is the weighting factor (w i = 1/y i ).The following R factors were calculated: the profile factor where I i and I ci are the observed and calculated integrated intensities, respectively.
The Fourier-transformed infrared (FT-IR) spectra were recorded in a Perkin-Elmer FT-IR-1600 spectrometer at a nominal resolution of 4 cm -1 and averaging 16 scans to improve the signal-to-noise ratio.Each sample was diluted in IR-grade potassium bromide and pressed into self-supported discs.

IV. Results and discussion
Table 1 shows the experimental and calculated results from X-ray Rietveld analysis of Y 2 Sn 2 O 7 and Zn).The relative deviation between the experimental and calculated spacing is much lower than 0.9 %.These results confirm that the synthesized compounds are single phases as previously described in literature [13].
Similar compounds with formula Eu 1.78 Sn 1.78 M 0.44 O 6.67 (M = Mg, Zn) showed a cubic pyrochlore structure with Fd-3m symmetry.The M 2+ cations occupied the Eu and Sn sites according to [11,12].Following this previous study, yttri- Rietveld analysis could be applied to any of the compounds here prepared within the compositional domain where a stable, single phase is formed.However, our aim was to find a structural model suitable for all the chemical compositions within the stable structural domain with pure phases.Consequently, we have taken arbitrarily a sample with a given composition (but with a relatively large Mg or Zn content) and have applied our model until a satisfactory result is obtained, and the model is able to describe all solid solutions in the stable domain.
Instrumental parameters were used to describe the profile: the zero-point in 2θ, background parameters, three peak-shape parameters, U, V and W in the formula H 2 = Utan 2 θ+Vtanθ+W to describe a Pseudo-Voigt peak whose full width at half maximum, H, increases with θ i .The structure parameters used were: a scale factor, the lattice constant, the positional coordinate, x, for O(48f), the occupancy factors (Table 2) of all atoms and the isotropic temperature factors.
Y  In all cases, the agreement between the observed and calculated profiles is excellent and the final R factors are satisfactory and good, particularly for R B factors which depend on both the atomic coordinates and the chemical composition.These fits between calculated and observed intensity provided the structural parameters shown in Table 3. Data in Figs. 2  and 3 and Table 3 reveal the characteristic reflections (h k l) for Y 2 Sn 2 O 7 (JCPDS 88-0445), such as ( 111), ( 311), ( 222), ( 400), ( 511), ( 440), ( 622), ( 444), ( 800), ( 662) and ( 840 [18]; hence, the substitution of M 2+ ions for Y 3+ and Sn 4+ ions decreases the lattice parameter.These characteristic diffractions indicate that the M (Mg, Zn) metal cations are well distributed in the pyrochlore structure and a small concentration of the doped ions in the pyrochlores does not change the crystal purity since there is no diffraction maximum related with other crystalline compounds.The formation of the solid solutions corresponds to the substitution of M 2+ (Mg 2+ or Zn 2+ ) for Y 3+ and Sn 4+ ions with the simultaneous developing of anionic vacancies in the 48(f) positions.
It has been observed from Rietveld analysis that when the concentration of M (Mg 2+ or Zn increases, the value of the x parameter of the 48f oxygen changes from 0.3374 (for Y 2 Sn 2 O 7 ) to 0.3364 (for M = Mg) and to 0.3367 (for M = Zn).In the pyrochlore structure, the 8a position is vacant; therefore, the 48f oxygen shifts from its ideal tetrahedral position towards two of its surrounding B cations.The t shift is correlated to the x coordinate of 48f oxygen atoms by the relationship x = 6/16-t.For the solid solution [Y 2-x M x ][Sn 2-x M x ]O 7-3x/2 (M = Mg, Zn) the lower charged cations M 2+ substitute the Y 3+ and Sn 4+ cations; as a consequence, an increase of the t shift and a decrease of the x positional parameter takes place (Table 3).Ideally, in an ordered pyrochlore structure (A 2 B 2 O 6 O'), the oxygen x parameter lies within the limit 0.3125-0.375if taking the origin (0,0,0) at the B cation site [1].The FT-IR spectra were recorded on polycrystalline powders in the form of KBr discs from 4000 to 400 cm -1 .There are seven characteristic absorption bands in the region 1200-100 cm -1 for the pyrochlore compounds with the formula A 2 B 2 O 7 [19] but those below 400 cm -1 cannot be recorded with our instrument.Fig. 4 shows the FT-IR spectra of [Y 2-x M x ][Sn 2-x M x ]O 7-3x/2 (0 ≤ x ≤ 0.30 for M = Mg and 0 ≤ x ≤ 0.36 for M = Zn) in the 800-400 cm -1 range.This figure includes also the spectrum of the sample with x = 0.5 to demonstrate the differences in the spectra when segregation of a new phase (MgO or ZnO) occurs from pyrochlore.The strong band in the region of 750-580 cm -1 can be ascribed to Sn-O stretching vibration [1].All spectra are similar to that of the Y 2 Sn 2 O 7 pyrochlore, no displacements can be observed in the spectra, thus suggesting that the M +2 (M = Mg, Zn) metal cations are well distributed in the pyrochlore structure.

V. Conclusions
A new pyrochlore solid solution with formula [Y 2-x M x ][Sn 2-x M x ]O 7-3x/2 (0 ≤ x ≤ 0.30 for M = Mg and 0 ≤ x ≤ 0.36 for M = Zn) was synthesized by solid-state reaction.The incorporation of M 2+ (Mg 2+ , Zn 2+ ) into the yttrium stannate pyrochlore Y 2 Sn 2 O 7 induced the decrease of lattice parameter with x while remaining the cubic pyrochlore phase.Rietveld refinements achieved for [Y 2-x M x ][Sn 2-x M x ]O 7-3x/2 (x = 0.154, M = Mg, Zn) compounds confirmed an overall Y 2 Sn 2 O 7 cubic pyrochlore structure with M 2+ cations in both Y and Sn sites and simultaneously creation of vacancies in the anionic sublattice.Bands recorded in the infrared spectra of all the compounds are characteristic of the pyrochlore structure.

Figure 1 .
Figure 1.Unit cell of pyrochlore -blue spheres stand for A 3+ cations, yellow ones for B 4+ and red ones for O 2-