Structural study by X-ray diffraction, magnetic susceptibility and Mössbauer spectroscopy of the Na2Mn2(1 − x)Cd2xFe(PO4)3 (0 ≤ x ≤ 1) solid solution

Mourad Hidouri; Alain Wattiaux; Léopold Fournés; Jacques Darriet; Mongi B. Amara

doi:10.1016/j.crci.2011.04.002

Résumé

Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (0 ≤ x ≤ 1) phosphates were prepared by solid state reaction and characterized by powder X-ray diffraction, magnetic susceptibility and Mössbauer spectroscopy. The X-ray diffraction patterns indicated the formation of a continuous solid solution which crystallizes in the alluaudite structural type characterized by the general formula X(2)X(1)M(1)M(2)₂(PO₄)₃. The cation distribution, deduced from a structure refinement of the x = 0, 0.5 and 1 compositions, is ordered in the X(2) sites and disordered in the remaining X(1), M(1) and M(2) sites. The magnetic susceptibility study revealed an antiferromagnetic behaviour of the studied compounds. The ⁵⁷Fe Mössbauer spectroscopy confirmed the structural results and proved the exclusive presence of Fe³⁺ ions.

1 Introduction

The term alluaudite designates a large family of mineral phosphates and arsenates either natural or synthetic. The alluaudite type structure was described by Moore who proposed the general formula X(2)X(1)M(1)M(2)₂(PO₄)₃ where X(2), X(1), M(1) and M(2) are cationic sites arranged in decreasing size [1]. Its main structural feature is the occurrence of M(2)₂O₁₀ dimmers of edge-sharing M(2)O₆ octahedra which are alternated by M(1)O₆ octahedra that form infinite zig-zag chains in the [1 0 1] direction. These chains are connected by P(2)O₄ tetrahedra to form what have been described as “pleated sheets” perpendicular to the [0 1 0] direction. The linkage of these sheets is ensured by the P(1)O₄ groups leads to a three-dimensional framework with two sets of tunnels where the X(2) and X(1) sites are located (Fig. 1). The cohesion of the structure is ensured by attractive electrostatic interaction between negative anionic sheets and positive X(1) and X(2) sites. The great flexibility of these sites, demonstrated by their capacity to accommodate a variety of cations with different sizes and charges, leads to the synthesis of a great number of isostructural compounds with different chemical compositions.

Fig. 1
Polyhedral representation of the alluaudite structure as viewed along the [0 0 1] direction. The M(1)O₆ and M(2)O₆ octahedra are represented by clear and dark polyhydra, and PO₄ by crossed ones.

As a part of a continuing exploratory study of the A₃PO₄-M₃(PO₄)₂-FePO₄ systems where A is an alkali metal and M is a divalent cation, we report here the synthesis and structural study, by powder X-ray diffraction, magnetic susceptibility and Mössbauer spectroscopy of the new alluaudite-like solid solution Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (0 ≤ x ≤ 1).

2 Experimental

Polycrystalline samples of the Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (0 ≤ x ≤ 1) phosphates were synthesized by conventional solid state reaction starting from stoichiometric mixtures of Na₂CO₃, MnO, Cd(NO₃)₂·4H₂O, Fe(NO₃)₃·9H₂O and (NH₄)₂HPO₄. Each of these mixtures was firstly dissolved in diluted nitric acid and the resulting solution was slowly evaporated at 353 K. The dry residue was ground, placed in a platinum crucible and heated in stages to 473 K, 673 K, 873 K for 24 h at each stage, and to 1173 K for 48 h with intervening grinding. The phase purity of the materials was tested by X-ray powder diffraction. X-ray powder diffraction patterns of the Na₂Mn₂Fe(PO₄)₃ (x = 0), Na₂MnCdFe(PO₄)₃ (x = 0.5) and Na₂Cd₂Fe(PO₄)₃ (x = 1) compositions chosen for the structural refinements were recorded with a Philips PW 1050 diffractometer using graphite monochromatized CuK_α radiation (λ = 1.5406 Å) and operating in Bragg-Brentano geometry. Refinements were carried out using the Rietveld method [2] and the Fullprof program [3]. The initial atomic coordinates were those of the alluaudite type structure of Na_1.79Mg_1.79Fe_1.21(PO₄)₃ [4]. A preliminary examination of the patterns evidenced some additional reflections in that of Na₂MnCdFe(PO₄)₃ which indicates small amounts of a secondary phase in the sample. Attempts to identify this phase were unsuccessful. A pseudo-Voigt function was used to describe individual line profiles. The parameters refined include the scale factor, zero point shift, six background parameters, cell parameters and atomic positions. Subsequent refinements of the isotropic thermal displacement parameters (B_iso) shown that those of the X(1) and X(2) sites converge to extraordinarily large values which by far exceed those usually obtained in alluaudite-like compounds. Alternative refinements in which these parameters were fixed to the reasonable value 1.0 were undertaken and shown to be successful in view of the resulting R (reliability factors) values. Crystal data and refinement conditions are summarized in Table 1. Final atomic coordinates and thermal displacement parameters are given in Table 2. Observed, calculated and difference profiles are plotted in Fig. 2. The magnetic measurements were done using a Super Conducting Quantum Interference Device (SQUID) MPMS-5S magnetometer. Measurements were carried out at a constant applied magnetic field of 0.5 T in the 2-305 K temperature range. The ⁵⁷Fe Mössbauer spectra were recorded with a constant acceleration HALDER-type spectrometer using ⁵⁷Co source (Rh matrix) in the transmission geometry. The polycrystalline absorbers containing about 10 mg.cm⁻² of iron were used to avoid the experimental widening of the peaks. The velocity was calibrated using pure iron metal as a standard material. All isomer shifts were made in reference to α-Fe.

	Na₂Mn₂Fe(PO₄)₃	Na₂MnCdFe(PO₄)₃	Na₂Cd₂Fe(PO₄)₃
Space group	C2/c	C2/c	C2/c
Formula units/cell (Z)	4	4	4
a (Å)	12.039(3)	12.169(4)	12.297(4)
b (Å)	12.625(3)	12.692(4)	12.799(4)
c (Å)	6.511(2)	6.530(2)	6.562(2)
β (°)	114.54(2)	114.56(2)	114.85(2)
Volume	900.21(4)	917.58(5)	937.06(2)
Temperature (K)	298	298	298
Angular range	(10° ≤ 2θ≤ 120°)	(10° ≤ 2θ≤ 120°)	(10° ≤ 2θ≤ 120°)
Step scan increment	0.02°	0.02°	0.02°
Zeropoint (2θ)	0.022(2)	−0.015(2)	0.019(2)
Pseudo-Voigt function
$[P V = η L + (1 - η) G]$	η = 0.40(2)	η = 0.47(3)	η = 0.43(3)
No. of refined parameters	56	56	59
Asymmetry parameter	0.03(1)°	0.06(1)	0.06(1)
Pref. orientation parameter	0.99(1)	0.97(4)	0.99(2)
R_p	0.11	0.13	0.09
R_wp	0.15	0.16	0.13
R_exp	0.12	0.11	0.10
χ²	1.5	2.0	1.7
R_B	0.06	0.09	0.07
R_F	0.04	0.06	0.04

Na₂Mn₂Fe(PO₄)₃
Site	Atom	x	y	z	B(Å²)
X(2)	Na	0	0.019(2)	3/4	1.0
X(1)	0.8 Na + 0.2 Mn	1/2	0	0	1.0
M(1)	0.8 Mn + 0.2 Na	0	0.269(1)	1/4	0.5(1)
M(2)	0.5 Fe + 0.5 Mn	0.221(2)	0.155(1)	0.139(1)	0.3(1)
P(1)	P	0	0.286(1)	3/4	0.4(2)
P(2)	P	0.237(1)	−0.106(1)	0.130(1)	1.0(2)
O(11)	O	0.043(1)	0.211(1)	0.961(2)	1.0(2)
O(12)	O	0.095(1)	0.363(1)	0.737(2)	1.0(2)
O(21)	O	0.372(1)	−0.092(1)	0.172(2)	1.0(2)
O(22)	O	0.172(1)	−0.001(1)	0.119(2)	1.0(2)
O(23)	O	0.163(1)	−0.160(1)	0.896(2)	1.0(2)
O(24)	O	0.225(1)	−0.174(1)	0.317(2)	1.0(2)
Na₂MnCdFe(PO₄)₃
Site	Atom	x	y	z	B(Å²)
X(2)	Na	0	0.022(2)	3/4	1.0
X(1)	0.8 Na + 0.2 Cd	1/2	0	0	1.0
M(1)	0.8 Cd + 0.2 Na	0	0.269(1)	1/4	0.8(1)
M(2)	0.5 Fe + 0.5 Mn	0.224(1)	0.154(1)	0.141(1)	0.5(1)
P(1)	P	0	0.277(1)	3/4	0.5(2)
P(2)	P	0.234(1)	−0.105(1)	0.136(1)	0.5(2)
O(11)	O	0.053(1)	0.202(1)	0.965(2)	0.7(2)
O(12)	O	0.102(1)	0.354(1)	0.745(2)	0.7(2)
O(21)	O	0.365(1)	−0.080(1)	0.172(2)	0.7(2)
O(22)	O	0.172(1)	0.002(1)	0.116(2)	0.7(2)
O(23)	O	0.173(1)	−0.155(1)	0.912(2)	0.7(2)
O(24)	O	0.221(1)	−0.172(1)	0.312(2)	0.7(2)
Na₂Cd₂Fe(PO₄)₃
Site	Atom	x	y	z	B(Å²)
X(2)	Na	0	0.023(2)	3/4	1.0
X(1)	0.8 Na + 0.2 Cd	1/2	0	0	1.0
M(1)	0.2 Na + 0.8 Cd	0	0.270(1)	1/4	0.4(1)
M(2)	0.5 Fe + 0.5 Cd	0.226(1)	0.152(1)	0.147(1)	0.5(1)
P(1)	P	0	0.282(1)	3/4	0.5(2)
P(2)	P	0.236(1)	−0.104(1)	0.134(1)	0.5(2)
O(11)	O	0.046(1)	0.206(1)	0.958(2)	0.7(2)
O(12)	O	0.093(1)	0.359(1)	0.734(2)	0.7(2)
O(21)	O	0.366(1)	−0.085(1)	0.174(2)	0.7(2)
O(22)	O	0.172(1)	−0.001(1)	0.119(2)	0.7(2)
O(23)	O	0.165(1)	−0.158(1)	0.906(2)	0.7(2)
O(24)	O	0.228(1)	−0.168(1)	0.316(2)	0.7(2)

Fig. 2
Observed (crosses), calculated (full lines) and difference (bottom) X-ray powder diffraction patterns for the Na₂Mn_{2(1 − x)}Cd_2xFe_1 + x(PO₄)₃ (x = 0; 0.5; 1) compounds.

3 Results

3.1 X-ray diffraction

The X-ray diffraction patterns of the Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ compounds are close to that of the alluaudite indicating the formation of a continuous solid solution with the same structure type. The cell parameters a, b, c and β as well as the cell volume V are found to increase with increasing Cd content, in accordance with a larger ionic radius of Cd²⁺ (r_i = 0.95 Å) compared to that of Mn²⁺ (r_i = 0.80 Å) for an octahedral environment [5]. The identification and quantification of the cation distribution in the alluaudite type structures is usually not a straightforward task because the X(2), X(1), M(1) and M(2) sites are known to be so flexible that they can accommodate a variety of cations with different sizes and charges. Moreover, the X(1) and X(2) sites can be occupied or left vacant with no significant effect on the structure [1,6]. For the title solid solution, several distributions were envisaged. They include a totally ordered distribution, an ordered distribution in some sites and disorder in the others, and a totally disordered distribution. The best agreements between the calculated and observed patterns resulting in reasonable R values were obtained for the distribution specified in Table 2. In terms of the general formula of the alluaudite, this distribution is given by [(Na)^X(2)][(Na_0.8M_0.2)^X(1)][Na_0.2M_0.8)^M(1)][(M_0.5Fe_0.5)^M(2)]₂(PO₄)₃. It shows that the title solid solution is formed by cationic substitutions of Mn²⁺ to Cd²⁺ according to: Mn²⁺→Cd²⁺. These substitutions occurred in the M(2) sites. Main interatomic distances and angles are listed in Table 3. The X(2) site is fully occupied by Na⁺ ions. As often occurs for alkali ions, the environment of this site exhibits a wide range of bond lengths and it is difficult to separate bonding and non-bonding contacts. One of the simplest criteria is to consider all distances which are shorter than the shortest Na⁺ to next cation. The X(2) environment then consists of eight oxygen atoms which form a gable disphenoid similar to that observed in Na₄CaFe₄(PO₄)₆ [7]. Contrary to X(2), the X(1) site features a statistical distribution of Na⁺ and M²⁺ (M = Mn or Cd) in an atomic ratio of approximately 4:1. Considering the same criteria used for X(2), this site is also surrounded by eight oxygen atoms which form a highly distorted cube. The M(1) site is occupied by Mn²⁺ and Cd²⁺ while that of the M(2) type contains a disordered distribution of Fe³⁺, Mn²⁺ and Cd²⁺. The contents of the Fe³⁺ and Mn²⁺ ions within the M(2) site were fixed to their theoretical values since these ions cannot be distinguished by X-ray Rietveld refinement. As suggested by the M(1)-O and M(2)-O bond lengths, the octahedral geometry of these sites is strongly distorted. Similar deformation is common in the alluaudite-like structures and it is in part due to the edge-sharing between the M(1)O₆ and M(2)O₆ octahedra. The two crystallographically distinct PO₄ contained in the structure have P-O bond lengths in the range 1.489(2)–1.600(2) Å. Their overall average of 1.550 Å is comparable to those frequently reported for anhydrous monophosphates.

	Na₂Mn₂Fe(PO₄)₃	Na₂MnCdFe(PO₄)₃	Na₂Cd₂Fe(PO₄)₃
M(1)-O(11) × 2	2.271(1)	2.371(2)	2.361(2)
M(1)-O(21) × 2	2.234(1)	2.425(2)	2.385(2)
M(1)-O(23) × 2	2.264(1)	2.403(2)	2.341(2)
<M(1)-O>	2.256	2.399	2.362

M(2)-O(11)	2.091(1)	2.005(2)	2.150(2)
M(2)-O(12)	2.023(1)	1.930(2)	2.014(2)
M(2)-O(22)	2.004(1)	2.035(2)	2.042(2)
M(2)-O(23)	2.063(1)	2.106(2)	2.132(2)
M(2)-O(24)	2.126(1)	2.135(2)	2.190(2)
M(2)-O(24)’	2.217(1)	2.272(2)	2.345(2)
<M(2)-O>	2.087	2.080	2.145

P(1)-O(11) × 2	1.566(1)	1.600(2)	1.578(2)
P(1)-O(12) × 2	1.532(1)	1.588(2)	1.550(2)
<P(1)-O>	1.549	1.594	1.564

P(2)-O(21)	1.539(1)	1.549(2)	1.526(2)
P(2)-O(22)	1.553(1)	1.535(2)	1.538(2)
P(2)-O(23)	1.565(1)	1.486(2)	1.544(2)
P(2)-O(24)	1.547(1)	1.500(2)	1.489(2)
<P(2)-O>	1.551	1.518	1.524

X(1)-O(12) × 2	2.281(1)	2.420(2)	2.331(2)
X(1)-O(21) × 2	2.359(1)	2.324(2)	2.345(2)
X(1)-O(21)’ × 2	2.537(2)	2.547(2)	2.604(2)
X(1)-O(12)’ × 2	2.979(2)	3.123(2)	3.049(2)
<X(1)-O>	2.539	2.590	2.582

X(2)-O(11) × 2	2.740(2)	2.608(2)	2.651(2)
X(2)-O(22) × 2	2.433(1)	2.453(2)	2.478(2)
X(2)-O(22)’ × 2	2.608(1)	2.599(2)	2.617(2)
X(2)-O(23) × 2	2.893(2)	2.961(2)	2.976(2)
<X(2)-O>	2.668	2.655	2.680

3.2 Magnetic susceptibility

The temperature dependencies of the inverse molar magnetic susceptibility χ⁻¹ for the Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (x = 0, 0.5, 1) compounds are illustrated in Fig. 3 and the magnetic characteristics are summarized in Table 4. The curves are similar and they indicate a transition from paramagnetic to antiferromagnetic state at T_N = 17(1), 15(1) and 12(1) K for x = 0, 0.5 and 1, respectively. Above T_N, the Curie-Weiss law is obeyed. The Curie constant and the effective magnetic moment are in accordance with the theoretical spin only values for high spin Mn²⁺/Fe³⁺ ions (C = 4.375 emu.mol⁻¹.K and μ = 5.92 μ_B). The Curie temperature θ_P, determined through a linear least squares extrapolation to zero is negative indicating that the exchange interactions which occur at low temperatures are predominantly antiferromagnetic. The θ_P values and subsequently the magnetic interactions are decreased when the paramagnetic Mn²⁺ ions are substituted by the diamagnetic Cd²⁺ ones. The antiferromagnetic character of the title solid solution is supported by the plots of the χ.T products (Fig. 4) which decrease with decreasing temperature. However, a careful examination of the plot for Na₂Mn₂Fe(PO₄)₃ shows a significant increase of the χ.T product at the Néel temperature. A similar behaviour has already been observed for the phosphates Ag₂Mn₂Fe(PO₄)₃ [8] and KMn₄(PO₄)₃ [9] and it was attributed to a possible magnetic phase transition occurring at critical temperature.

Fig. 3
The inverse molar magnetic susceptibility x⁻¹ as function of temperature for the Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (x = 0; 0.5; 1) compounds.

Compound	Na₂Mn₂Fe(PO₄)₃	Na₂MnCdFe(PO₄)₃	Na₂Cd₂Fe(PO₄)₃
Behaviour	Antiferromagnetic	Antiferromagnetic	Antiferromagnetic
T_N (K)	17	15	12
C (emu.mol⁻¹.K)	4.14	4.42	4.40
μ_eff (μ_B)	5.76	5.95	5.93

Fig. 4
Thermal variation of the χ.T product for Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (x = 0; 0.5; 1).

3.3 Mössbauer spectroscopy

The room temperature Mössbauer spectra for the Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (x = 0, 0.5, 1) compounds are shown in Fig. 5. They exhibit two resonance absorption lines with large line widths, resulting from a superposition of many iron site environments. The spectra were refined using lorantzian profile lines and the best results were obtained by considering two doublets assigned to two different iron sites. The hyperfine parameters deduced from the refinements are given are in Table 5. The isomer shifts (0.42(2) mm/s < δ < 0.44(2) mm/s) are close to those usually observed for Fe³⁺ in octahedral environment [10]. According to the structure refinements, iron occupies statistically 50% of the M(2) sites and the remaining 50% of the sites are occupied by a distribution of M²⁺ cations (M = Mn or Cd). The iron environments within the M(2)₂O₁₀ dimmers are then split in two types, namely Fe₂O₁₀ and (Fe, M)₂O₁₀ and which have the same probability of existence. Effectively, the Mössbauer spectroscopy shows two iron sites Fe(1) and Fe(2) with very similar isomer shifts and quasi-identical populations. From a comparison of the quadrupole splitting values for Fe(1) and Fe(2), one can deduce that the Fe(2) environment (ΔEQ₂ = 0.60(1) mm.s⁻¹) is more regular than that of Fe(1) (ΔEQ₁ = 0.90(1) mm.s⁻¹). Thus, the Fe(2) site can be attributed to the Fe₂O₁₀ type environment and the Fe(1) to that of (Fe, M)₂O₁₀ type. The strong distortion of the latter environment is due to the difference between the ionic radii of the M²⁺ and Fe³⁺ ions.

Fig. 5
The Mössbauer spectra of Na₂Mn_{2(1 − x)}Cd_2xFe_1 + x(PO₄)₃ (x = 0; 0.5; 1) at 293 K.

Compound	Site	δ (mm.s⁻¹)	<Δ> (mm.s⁻¹)	Γ (mm.s⁻¹)	% population
Na₂Mn₂Fe(PO₄)₃	Fe(1)	0.420(10)	0.925(10)	0.311(8)	46.5
Fe(2)	0.430(8)	0.619(8)	0.295(6)	53.5

Na₂MnCdFe(PO₄)₃	Fe(1)	0.425(10)	0.885(10)	0.317(9)	44.10
Fe(2)	0.433(7)	0.574(7)	0.298(6)	55.90

Na₂Cd₂Fe(PO₄)₃	Fe(1)	0.421(9)	0.931(9)	0.331(9)	47.00
Fe(2)	0.434(7)	0.587(7)	0.304(6)	53.00

4 Conclusion

A new solid solution Na₂Mn_{2(1 − x)}Cd_2xFe(PO₄)₃ (0 ≤ x ≤ 1) has been prepared and shown to be of the alluaudite type. According to the X(2)X(1)M(1)M(2)₂(PO₄)₃ general formula of the alluaudite structure, the cation distribution can be summarized by: [(Na)^X(2)][(Na_0.8M_0.2)^X(1)][Na_0.2M_0.8)^M(1)][(M_0.5Fe_0.5)^M(2)]₂(PO₄)₃ where M is Mn or Cd. This solid solution is then formed by cationic substitutions within the M(2) sites according to: Mn²⁺→Cd²⁺. Magnetic susceptibility measurements indicated an antiferromagnetic behaviour of the studied compounds with Néel temperatures of 17(1), 15(1) and 12(1) K, for x = 0, 0.5 and 1, respectively. The Mössbauer spectroscopy results were consistent with the structures and confirmed exclusive presence of octahedral Fe³⁺ ions.