Crystal Structure, Ionic Conductivity, Dielectric Properties and Electrical Conduction Mechanism of the Wyllieites Na1.5Mn3.5(AsO4)3 and Na1.5Mn3Fe0.5(AsO4)3

Rezgui, Eya; Ouerfelli, Najoua; Gavinho, S. R.; Carvalho, J. P. F.; Graça, M. P. F.; Teixeira, S. Soreto

doi:10.3390/cryst13081251

Open AccessFeature PaperArticle

Crystal Structure, Ionic Conductivity, Dielectric Properties and Electrical Conduction Mechanism of the Wyllieites Na_1.5Mn_3.5(AsO₄)₃ and Na_1.5Mn₃Fe_0.5(AsO₄)₃

by

Eya Rezgui

¹

,

Najoua Ouerfelli

¹,

S. R. Gavinho

²

,

J. P. F. Carvalho

²

,

M. P. F. Graça

²

and

S. Soreto Teixeira

^2,*

¹

Laboratory of Materials, Crystallochemistry and Applied Thermodynamics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis 1068, Tunisia

²

i3N & Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal

^*

Author to whom correspondence should be addressed.

Crystals 2023, 13(8), 1251; https://doi.org/10.3390/cryst13081251

Submission received: 30 June 2023 / Revised: 4 August 2023 / Accepted: 11 August 2023 / Published: 14 August 2023

(This article belongs to the Special Issue Advances in Composite Electrodes Materials)

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Abstract

:

Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ compounds were synthesized via a high-temperature solid-state combustion reaction. The obtained samples were submitted to structural, morphological, and electrical characterizations. X-ray diffraction measurements revealed that both compounds crystallize in the monoclinic system with the space group P2₁/c. The lattice parameters were determined to be a = 6.78344 Å, b = 12.93830 Å, c = 11.22825 Å, and β = 98.5374° for Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃, and a = 6.76723 Å, b = 12.9864 Å, c = 11.256 Å, and β = 98.8636° for Na_1.5Mn²⁺₃Fe³⁺_0.5(AsO₄)₃. The structures consist of octahedral Mn^II and Mn^III or Fe^III ions connected by sharing edges, forming infinite chains. These chains are further connected by AsO₄ tetrahedra, resulting in a three-dimensional anionic framework with tunnels parallel to the a-direction and cavities according to the c-direction. The structural models were validated using bond valence and charge distribution analyses. In addition to the structural characterization, the electric results depended on the crystal structures, indicating the potential of the studied materials for being used in several applications.

Keywords:

X-ray diffraction; tunnel structure; electrical properties; electric modulus

1. Introduction

During the last years, thorough research was performed on phosphate and arsenate metal alkaline materials because of their different properties, such as catalytic and optical characteristics [1,2]. Transition metals, especially iron, played an important role in achieving remarkable magnetic features [3]. Monovalent alkaline ions were responsible for ionic conductivity in open framework structures [4,5,6].

Historically, the mineral wyllieite with the ideal formula Na₂Fe^II₂Al(PO₄)₃ was the first phase described in pegmatites [7]. Later, this type of wyllieite was given the name ferrowyllieiteand. True wyllieite occurs as a Mn^II variety, namely, Na₂Mn^II Fe^IIAl(PO₄)₃ [8]. Its crystal structure has been interpreted as very close to that of Na₂Mn^II (Fe^II Fe^III) [PO₄]₃ [9].

Several minerals of the wyllieite family have been discovered in the last decades. Among them, only three arsenates, Ag_1.09Mn_3.46(AsO₄)₃ [10], Na_0.5K_0.65Mn_3.43(AsO₄)₃ [11], and Na_1.25Co_2.187Al_1.125(AsO₄)₃, were synthesized. The conduction pathway study of Na⁺ in Na_1.25Co_2.187Al_1.125(AsO₄)₃ showed that a 1D migration of Na⁺ is possible, suggesting a poor ionic conductivity [12]. However, wyllieites may become a valuable source of alkaline conductive materials due to their crystalline structure, which has been interpreted as very close to allaudites [9].

In this context, wyllieite materials were investigated by synthesizing crystallized powders of new Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ compounds. Initially, Na⁺ migration pathways were analyzed using the bond valence sum energy (BVSE) model. The dielectric properties were then examined by complex impedance spectroscopy.

2. Materials and Methods

The crystalline powders of Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ (I), and Na_1.5Mn^II₃Fe^III_0.5 (AsO₄)₃ (II) were obtained by a high-temperature solid-state combustion reaction. First, mixtures of NaNO₃, NH₄H₂AsO₄, MnCO₃, and MnC₆H₉O₆.2H₂O for (I) and Fe(NO₃)₃·9H₂O for (II) were taken in 1.5:3:3:0.5 stoichiometry. NH₄H₂AsO₄, the precursor reagent for As(V), was synthesized by heating As₂O₃ in concentrated nitric acid (HNO₃) under reflux conditions for three days, following a procedure described in previous work [13]. The resulting solution was then taken to further heating at 100 °C until the evaporation of most of the water and excess HNO₃. The resulting H₅As₃O₁₀ was calcinated at 300 °C for 12 h to yield As₂O₅. Subsequently, this compound was dissolved in hot water (70 °C) and mixed with an aqueous NH₃ solution to adjust its pH to 4.2. The solid NH₄H₂AsO₄ was isolated and confirmed to be phase pure through X-ray diffraction (XRD) analysis using the JCPDS-775 database [14]. The precursors were supplied by Fisher Scientific with a purity percentage of 99%. An amount of 2 g each of the solid mixtures of (I) and (II) were dissolved in 40 mL of water, 10 mL of nitric acid, and 2 g of citric acid. The solutions were placed on a hot plate (maintained at 120 °C), with constant magnetic stirring, to remove excess water. After complete drying, the solid residues were ground manually using an agate vessel and mortar and brought in alumina crucibles at a temperature of 400 °C to promote combustion and remove volatile components. The obtained mixtures of (I) and (II) were then ground for 2 h and brought to 770 °C and 850 °C, respectively, for 24 h.

The data collection of the two materials, Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃, was carried out by a diffractometer of the Bruker D8 Advance type. The powdered samples were evenly distributed on a sample holder and rotated during the measurement, applying a 2θ step = 0.017° for material (I) and a 2θ step = 0.015° for material (II). The indexing of all peaks of the materials was carried out by the TREOR program included in X’Pert HighScore software.

The FTIR spectra of pellets composed of KBr mixed with the powder of each sample, in a weight ratio of 200:1 mg, were registered in transmission mode, between 400 and 4000 cm⁻¹, on a Nicolet Avatar 360 spectrometer. Micro-Raman spectroscopy, using a Jobi Yvon spectrometer, was performed at room temperature in backscattering geometry, with the microscope objective (50×) focusing the exciting light (λ = 532 nm) onto the sample (spot diameter < 0.8 µm). Plasma lines were removed by a filter.

The bond valence site energy (BVSE) calculations were performed by the SoftBV program using Na⁺ as test ions and 0.1 Å resolution grids [15]. The BVSE isosurfaces were visualized using the VESTA 3 program [16].

To investigate the range of thermal stability of the samples, measurement of thermal gravimetry (TG) and differential thermal analysis (DTA) were performed simultaneously using a Hitachi STA 7300. The measurements were then carried out under a 200 mL/min Nitrogen N50 (99.999%) atmosphere, and the heating rate was set to 10 °C/min [17].

The morphology of the powder grains was observed by scanning electron microscopy (SEM), conducted in a Vega 3 TESCAN SEM microscope. The observed surface of the pellets was previously sputtered with carbon. In order to validate the purity of the two synthesized compounds, the elementary qualitative analysis used an energy dispersion X-ray spectroscopy EDX, using a Bruker system.

In the electrical measurements, the bulk samples had a thickness of 1 mm and a disk shape with a diameter of about 10 mm, prepared by using a steel mold and a uniaxial pressure system applying a pressure of 10 tons for 10 min. The measurements were performed as a function of temperature, in the range of 283 K up to 470 K for the sample Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and 296 K up to 393 K for the sample Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ and frequency (100 Hz up to 1 MHz) using Agilent 4294A impedance analyzer. The measurements were made in a bath cryostat system, and during the measurements, the samples were in a helium atmosphere [18,19,20].

3. Results and Discussion

3.1. Resolution and Structure Refinement

Using X’Pert HighScore, it is possible to see that the new phase obtained crystallizes in the monoclinic system P2₁/c isotype to Ag_1.09Mn_3.46(AsO₄)₃ [11]. This structure is then used as a starting model to refine the structure of Na_1.5Mn₂^IIIMn^III_0.5 (AsO₄)₃, by substituting Mn for Fe and fixing the occupations to 1. Structure determination was performed using the GSAS program [21]. When refining the structure, the background noise was treated as a polynomial equation and the line profile as a pseudo-Voigt equation. In the end, the goodness of the refinement,

χ^{2} = {(\frac{R_{w p}}{R_{e x p}})}^{2} = 1.464

, is higher and close to 1, revealing that the refinement quality is good [22]. All atomic positions and thermal site factors were refined. All parameters were refined:

R_{p}

(or R-factor) = 0.022, which is a measure of the difference between the observed diffraction pattern and the pattern calculated from the refined crystal structure,

R_{w p}

(or weighted R-factor) = 0.029, which is similar to

R_{p}

but takes into account the weighting of the data points based on their measurement uncertainty, and

R_{e x p}

(or expected R-factor) = 0.025, which measures the agreement between the observed and calculated diffraction patterns, normalized by the number of independent data points and R(F2)= 0.044, which is a measure of the agreement between the observed and calculated structure factors, which are derived from the diffraction pattern. A good superposition between the experimental diffractogram and the refined one was obtained while respecting the chemical reality of the structural model (Figure 1).

Since the goal was to synthesize the isotype phase of Na_1.5Mn^II₃Mn^III_0.5 (AsO₄)₃ by substituting Mn^III with Fe^III, this structure was used as a starting model to determine and refine the structure Na_1.5Mn^II₃Fe^III_0.5 (AsO₄)₃. Data collection and profile matching were carried out under the same conditions as those for Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃. The final results of refinement were

χ^{2}

= 1.440,

R_{p}

= 0.083,

R_{w p}

= 0.105,

R_{e x p}

= 0.088, R(F2) = 0.05682 (Figure 2, Table 1).

3.2. Structures Validation by CHARDI and BVS Analyzes

The two structural models were validated by both analyses: the bond valence (BVS) calculation [23] and the charge distribution method CHARDI [24].

The CHARDI validation model confirms the two structural models obtained. The charge distribution (Mn^III/Mn^II) of the Mn cation in material (I) is featured by the dispersion factor on the cationic charges σ_cat = 0.079 (Table 2). For material (II), the dispersion factor on the cationic charges is equal to σ_cat = 0.045 (Table 3). The values of the CHARDI and BVS calculations (Table 4 and Table 5) are in agreement with those observed in the bibliography, presented by the wyllieite Na_1.265Mn^II_2.690Mn^III_0.785(PO₄)₃ [25].

The effective oxidation numbers of Mn(1) (Mn^II) and Mn(3) (Mn^III) in (I) are 1.87 and 2.74, respectively (Table 2). These values have also been observed in the alliaudyte Na_1.72Mn_3.28(AsO₄)₃, where the effective oxidation numbers of Mn^II and Mn^III are equal to 1.80 and 2.69, respectively [26]. Indeed, the deviation of the charges on the cations (Mn^III, Mn^II) in (I) suggests a mixed valence of the trivalent cations Mn^III from where the electrons are delocalized in all the three-dimensional networks. However, material (II) did not show any remarkable charge deviations (Table 3).

3.3. Structures Description and Discussion

The asymmetric unit of each compound contains three octahedra of the divalent cation Mn^II, one octahedron of the trivalent cation M^IIIO₆ (M = Mn or Fe), three tetrahedra AsO₄, and two atoms of Na. The entire group is coordinated by twelve crystallographic independent oxygen atoms.

The three M^IIO₆ octahedra are sharing edges to form the M₃O₁₄ group (Figure 2). These groups are connected by sharing edges to form infinite chains in the direction [5,10]. These infinite chains are linked by the tops of the AsO₄ tetrahedra and the edges of the M^IIO₆ octahedra. This arrangement forms a three-dimensional anionic framework containing tunnels parallel to the a-axis and cavities according to the c-direction, where sodium cations are located (Figure 3).

As shown in Table 6, for Mn (1), Mn (2), and Mn (4) in material (I) and Mn (1), Mn (2), and Mn (3) in (II), the MO₆ takes typical M-O distances from those observed in the bibliography. For material (I), Mn^II-O distances range from 1.9270 (1) Å to 2.334(2) Å compared with 2.19 Å, which is the sum of the Shannon crystal for Mn^II six coordinates (0.97 Å) and O^2- three coordinates (1.22 Å), meaning these distances show slight deviations from Mn^II-O distances, which range from 1.959 (5) Å to 2.256 (6) Å. This distance variation also shows deviations compared with the sum of the Shannon crystal distances (2.08 Å) [27]. These deviations are observed in most wyllieites, especially Na_1.265Mn^II_2.690Mn^III_0.785(PO₄)₃ [25].

Mn^IIIO₆ octahedra in the two studied materials adopt distortions observed previously in Na_1.265Mn^II_2.690Mn^III_0.785(PO₄)₃. The Mn^III-O distances in (I) range from 2.193 (2) to 2.4489 (19), while the sum of the Shannon crystalline rays for the Mn^III six coordinated ions (0.78 Å) and O^2- three coordinated ions (1.22 Å) equals 2.00 Å [27]. The Fe³⁺-O distances in (II) vary from 1.973(2) Å to 2.040(3) Å, while the Shannon Fe³⁺-O distance is equal to 2.012 Å [27]. The distortion of the Mn^III ion is typical of the distortion phenomenon Jahn–Teller observed in the weillyte Na_1.265Mn^II_2.690Mn^III_0.785(PO₄)₃ [25] and the allyaudite Na_1.72Mn_3.28(AsO₄)₃ [28]. The octahedral M^IIIO₆ has four short and two longer M^IIIO distances. The distortion of the M^IIO₆ octahedra and the Jahn–Teller effect of the trivalent cations are consistent with the BVS calculations. This compromise reinforces the mixed valence of Mn^II/Mn^III.

3.4. Infrared Spectroscopy Study

Based on their high intensities and frequencies (Figure 4), the bands around 861 cm⁻¹ and 866 cm⁻¹ can be attributed to the AsO₄ group asymmetric valence vibrations ν3 in materials (I) and (II), respectively. Symmetrical valence vibrations ν3 are observed around 820–750 cm⁻¹ for (I) and around 825–889 cm⁻¹ for (II). The asymmetrical deformation vibrations ν4 of the AsO₄ group were observed at the lowest wavelengths. These bands are translated into a wide band divided around 436–371 for material (II) and a band that divides in two around 456–426 cm⁻¹ for material (I). The divisions observed in ν1 and ν4 show that the AsO₄ tetrahedrons are minimally deformed in the monoclinic network. The Mn-O vibrations are observed around 538–581 cm⁻¹ for (I) and around 583 cm⁻¹ for (II). It is also likely that some M^II-O strain vibration bands are coupled to the ν4 vibration modes (Table 7).

3.5. Raman Spectroscopy Study

The Raman spectra of the two compounds (I) and (II) in the range 100–1400 cm⁻¹ are shown in Figure 5. The Raman spectrum can be understood not only by the determination of the internal vibrations of the AsO₄⁻³ units but also by the determination of the vibrations of the crystalline network. In fact, according to the theory of group factors, a material of space group P2₁/c shows 30 bands: 14 corresponding to the symmetry Ag and 16 corresponding to the symmetry Bg. On the other hand, the detection of all bands is difficult because these bands can overlap or have lower intensities than those of background noise [34].

Each spectrum is dominated by a very clear intense band at 838 and 854 cm⁻¹ for compounds (I) and (II) respectively. This band corresponds to the symmetrical vibration assignment of the

{A s O}_{4}^{- 3}

group (Table 8). The bands observed at 899 and 1000 cm⁻¹ correspond to the asymmetric vibration of the AsO₄⁻³ group (Table 8). For material (I), five bands of Mn trivalent are observed around 313–358 cm⁻¹ and those of divalent are observed around 230–192 cm⁻¹. For material (II), the bands of Fe and Mn are observed around 374 and 256–206 cm⁻¹ (Table 8). The superposition of the two Raman spectra showed the same number of bands in the region ranging from 100 to 1250 cm⁻¹. Toward the highest frequencies, it is noticed the appearance of the two broadbands, around 1360 and 1770 cm⁻¹, on the Raman spectrum of (I). These two bands can be attributed to both the D and G vibrations of carbon. Citric acid used for combustion synthesis is the only source of carbon traces. This phenomenon was observed in the Na₂FePO₄F Raman spectrum, which was prepared by the same synthesis method [34].

3.6. Thermal Analysis

The thermal behaviors of both samples, for Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃, derived from TG and DTA, are illustrated in Figure 6a,b, respectively. The TGA thermograms show that the compounds are very stable up to 770 °C. The slight loss of mass can be attributed to the thermal volatilization of components. The DTA curves show that both compounds have thermally stable crystal structures. No phase transitions were detected in the range of temperature 50–800 °C. Figure 6b shows a sharp endothermic peak that can be related to the decomposition of the material.

3.7. Morphological Analysis

The morphology of the surface of Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ was examined by SEM. The microstructure observation of both materials showed a homogenous powder. Further observations of the powders showed spherical grains (Figure 7).

Table 9 shows the elementary composition analysis performed using EDX in both compounds. For compound (I), EDX analysis showed the presence of the elements Na, Mn, As, and O. However, a low-intensity peak was attributed to traces of silicon. The percentages of the detected elements were also in agreement with the crystal structure determined by XRD (Figure 1). For compound (II), Na, Mn, Fe, As, and O elements were detected by EDX analysis. The proportions of the elements detected were consistent with the crystalline structure determined by previous XRD analysis (Figure 1). The source of silicon in material (I) can be attributed to the grinding process using an agate mortar [37].

3.8. Na⁺ Pathways Transport Simulation

According to the BVSE analysis, this structural study allows for determining the directions of migration. The BVS model is used to verify crystal study suggestions and to determine conduction paths that are not visible during the structural study. Thus, to predict the electrical behavior of both materials, the alkaline migration pathways of Na⁺ were simulated using the BVSE model.

Both structures are characterized by tunnels along the a-axis and smaller windows along the c-direction. The simulation of the sodium ion conduction paths in the ionic frameworks of (I) and (II) showed that Na(1) can migrate infinitely in the direction (100) in ruban with an E_mig= 0.901 eV and 1D with an E_mig= 0.865 eV, respectively. However, Na(2) cannot migrate along (001) direction (Figure 8 and Figure 9). The weilliyte Na_1.25Co_2.187Al_1.125(AsO₄)₃ BVSE analysis also showed that sodium migration is possible only along the a-direction but with higher activation energy of 5.54 eV [12]. In fact, for (I), the diameter of the tunnel sections along the a-direction is equal to 4.699 (5) Å, which is slightly less than 4.82 Å, the sum of the diameters of the O^2- and Na⁺ ions. On the other hand, the section size of the windows according to c (3.329 (3) Å) is much smaller than the latter. For (II), the diameter of the tunnel sections is equal to 4.765 (8) Å, which is slightly less than 4.82 Å and the diameter of the tunnel in (II) at the same time. This can explain the higher migration energy of sodium observed in (I). It is noteworthy to point out that the data collection for material (II) involved a greater number of reflections, which enhanced the accuracy of the derived atomic positions of material (I) compared with material (II). For material (I), Na(1) migrated for a 4.257 Å distance from an inertial site i1 to a crystallographic site Na1. At a 2.37 Å distance, Na⁺ encountered the saddle S3 with migration energy equal to 0.791 eV. A higher migration energy (E_mig = 0.901 eV) was required to enable Na(1) to migrate from its crystallographic site to an interstitial site i1, and only an energy of 0.001 eV was required for the migration of Na(1) from i1 to Na1 sites, which enabled Na(1) to migrate a total distance of 9.701 Å. Figure 8b showed two main bottlenecks for material (II) presented by the two saddles, S1 and S2. In fact, Na(1) traveled first for a 2.146 Å distance from a crystallographic site Na1 to another requiring a migration energy equal to 0.819 eV. Then Na(1) traveled for an 8.691 eV distance encountering the highest migration energy of 0.865 eV arriving at the crystallographic site Na1.

3.9. Electrical Measurements

3.9.1. Impedance Analysis

The impedance spectroscopy technique (IS) is frequently employed in experimentation, to explore the electrical characteristics of the ceramic materials. It offers insights into conductivity, relaxation, and permittivity properties. Figure 9 shows the typical complex impedance spectra obtained on heating for Na_1.5Mn^II₃Mn^III_0.5(AsO₄) and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃. Based on the observed behavior, it can be inferred that there is a correlation between Z’ and the electrical resistance of the sample. As the frequency and temperature increase, the value of Z’ decreases, which is a typical behavior observed in dielectric materials [38]. Additionally, for the Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ sample, as the frequency increases, the Z’ values at various temperatures converge. This behavior indicates that the energy barrier to be overcome by the charge carriers in this specific experimental condition is very high for the electrical space displacement [37] (Figure 10).

Figure 11 describes the behavior of the imaginary part of impedance Z″ as a function of frequency, for both materials under different temperatures. The plot shows a gradual increase in Z″ with increasing frequency until it reaches a maximum, indicating the presence of a relaxation phenomenon. The peak in Z″ shifts to higher frequencies as the temperature increases, indicating that the resistance of the material is decreasing. At higher frequencies, and for the Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ sample, Z″ merges for all temperatures, suggesting an accumulation of space charge (Figure 11b). The plot also shows a single relaxation peak that increases with the rise in the temperature, following an Arrhenius behavior [39]. At lower temperatures, the plot of Z″ as a function of frequency for Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ shows two peaks, which suggests two relaxation processes. The lower-frequency peak can be associated with the bulk resistance of the material, while the higher-frequency peak can be associated with the grain boundary resistance. At low temperatures, the grain boundary resistance dominates, leading to a broad peak in the Z″ spectrum (Figure 11a). For both materials, the maximum value of Z″ decreases with the increase in temperature. These plots further show the spreading of the relaxation time distribution, indicating a temperature-dependent relaxation. The observed broadening of the Z″ peak, with increasing temperature, suggests a thermally activated relaxation process associated with different species, such as electrons or immobile species at lower temperatures and defects at higher temperatures [39].

3.9.2. Modulus Analysis

The inverse of the complex dielectric permittivity, ε*, for Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ is known as the complex electric modulus M*. In order to calculate M*, the impedance data was utilized in the following equation: M* = 1/ε* = M′ + jM″ = (Z″ + Z′ωC)/ωCZ₀, where Z′ and Z″ are the real and imaginary parts of the complex impedance Z*, and M′ and M″ are the real and imaginary parts of the complex modulus M*, respectively. Additionally, C₀ represents the vacuum capacitance of the measuring cell, which is determined by the permittivity of the vacuum (ε₀), the cross-section area (S), and the thickness (L) of the sample.

Figure 12 shows the variation of the real part of the modulus M′ as a function of frequency for both studied materials at different temperatures. As can be seen at low frequencies, M′ remains consistent and is almost zero at all temperatures. This is due to the lack of restoring force leading to long-range transport of load carriers below the applied ac-electric field. At higher frequencies, M′ increases progressively due to the short-range conduction effects of the Na⁺ ions.

As shown in Figure 13a, the imaginary part of the dielectric modulus of Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃, M″, increases continuously with the frequency, indicating that the material has a high capacity for energy storage and low capacity for dissipation. This behavior is due to the ability of the material to undergo molecular rearrangements and deformations in response to the applied electric field. This performance is usually observed in viscoelastic materials, polymers, and ionic liquids [40]. Figure 13b shows the frequency dependence of the imaginary part of the electric modulus M″ of Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃. The M″ curve shows a broad peak that rises as the temperature increases until reaching a maximum at 296 K, for a frequency of f_max ≈ 0.5 × 10⁶ Hz, approximately. For higher temperatures, this maximum shifts to higher frequencies. When the frequency is between 10² and 10⁴ Hz, Na⁺ ions can move across large distances. However, when the frequency is higher than f_max, Na⁺ ions are limited to their potential well. As temperature rises, the mobility of the charge carriers increases, causing a decrease in the relaxation time and a shift of the relaxation peak, toward higher frequencies. This phenomenon indicates a dielectric relaxation process, predominantly governed by a hopping mechanism of the charge carriers, which is thermally activated [41].

3.9.3. AC Conductivity Study

To analyze the conductivity of both samples, Equation (1) was used to calculate the ac conductivity for each temperature:

σ_{a c} = ε_{0} ω ε^{″} = ε_{0} ω \frac{Z^{'}}{C_{0} ω ({Z^{'}}^{2} + {Z^{″}}^{2})} = (\frac{L}{S}) (\frac{Z^{'}}{{Z^{'}}^{2} + {Z^{″}}^{2}})

(1)

The real and imaginary parts of the impedance, Z′ and Z″, were used along with the thickness, L, and cross-section, S, of the sample to derive the conductivity [42,43]. Figure 13 shows the plots of the ac conductivity of Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ as a function of frequency. An almost frequency-independent behavior is observed for the sample Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃. There is a slight dispersion in the higher frequency region, but the most characteristic feature is the increase in the conductivity with the temperature, revealing a thermal activation phenomenon. Figure 14b shows a relaxation phenomenon, which maximally shifts to higher frequencies with the rise of the temperature.

4. Conclusions

The crystal structures of Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ have been successfully determined and refined. Both compounds crystallize in the monoclinic system with the space group P2₁/c. The structural models were validated using bond valence calculations and charge distribution analysis, confirming their accuracy. The analysis revealed that the Mn^II and Mn^III ions exhibit deviations in their charges, indicating a mixed valence and electron delocalization within the three-dimensional network. The obtained structures consist of interconnected chains of Mn^II and Mn^III or Fe^III octahedra, with AsO₄ tetrahedra connecting them, forming a three-dimensional anionic framework. The presence of tunnels and cavities within the structure allows for the localization of Na⁺ cations. The electrical properties were investigated using impedance spectroscopy measurements. The impedance study showed a relaxation phenomenon and a decrease in resistance with increasing temperature. The dielectric modulus (M*) and the AC conductivity were also analyzed, providing insights into the conduction and energy storage properties of the materials.

Author Contributions

Conceptualization, E.R., N.O. and M.P.F.G.; methodology, E.R., S.R.G., J.P.F.C. and S.S.T.; software, E.R. and J.P.F.C.; validation, N.O., M.P.F.G. and S.S.T.; formal analysis, M.P.F.G. and S.S.T.; investigation, E.R., N.O. and M.P.F.G.; resources, M.P.F.G.; data curation, S.R.G. and S.S.T.; writing—original draft preparation, E.R.; writing—review and editing, S.R.G., M.P.F.G. and S.S.T.; visualization, E.R.; supervision, M.P.F.G.; project administration, M.P.F.G.; funding acquisition, N.O. and M.P.F.G. All authors have read and agreed to the published version of the manuscript.

Funding

The authors extend their appreciation to the FEDER funds through the COMPETE 2020 Program and National Funds through FCT—Portuguese Foundation for Science and Technology under the project LISBOA-01-0247-FEDER-039985/POCI-01-0247-FEDER-039985, LA/P/0037/2020, UIDP/50025/2020, and UIDB/50025/2020 of the Associate Laboratory Institute of Nanostructures, Nanomodelling, and Nanofabrication—i3N., UCIBIO (UIDP/04378/2020 and UIDB/04378/2020) and Associate Laboratory i4HB (LA/P/0140/2020). S.R. Gavinho acknowledge FCT—Portuguese Foundation for Science and Technology for the PhD grant (SFRH/BD/148233/2019).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

The authors extend their appreciation to the FEDER funds through the COMPETE 2020 Program and National Funds through FCT—Portuguese Foundation for Science and Technology under the projects LISBOA-01-0247-FEDER-039985/POCI-01-0247-FEDER-039985, LA/P/0037/2020, UIDP/50025/2020, and UIDB/50025/2020 of the Associate Laboratory Institute of Nanostructures, Nanomodelling, and Nanofabrication—i3N. S.R. Gavinho acknowledges FCT—Portuguese Foundation for Science and Technology for the PhD grant (SFRH/BD/148233/2019).

Conflicts of Interest

The authors declare no conflict of interest.

References

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Figure 1. Rietveld plot of the powder X-ray diffraction pattern of (a) Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and (b) Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ samples.

Figure 2. The anionic three-dimensional network formed by octahedral M^IIO₆ and M^IIIO₆.

Figure 3. Projection of the structure (a) showing tunnels according to the a-axis, (b) showing cavities according to the c-direction.

Figure 4. Infrared analysis spectra of compounds (I) and (II).

Figure 5. Raman analysis spectra of compounds (I) and (II).

Figure 6. TG-DTA curves of (a) Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and (b) Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ samples.

Figure 7. SEM micrographs (left figures) and magnifications (right figures) of samples: (a) material (I) and (b) material (II).

Figure 8. (a) Migration paths of Na⁺ cations in (I) at E_mig = 0.901 eV; (b) Migration paths of Na⁺ cations in (II) at E_mig = 0.865 eV.

Figure 9. Traveled distance variation of Na (1) as a function of migration energy: (a) in (I), (b) in (II).

Figure 10. The frequency dependence of the real (Z′) part of the complex electrical impedance at several measurement temperatures for (a) sNa_1.5Mn²⁺₃Mn³⁺_0.5(AsO₄)₃ and (b) Na_1.5Mn²⁺₃Fe³⁺_0.5(AsO₄)₃.

Figure 11. The frequency dependence of the imaginary (Z″) part of the complex electrical impedance at several measurement temperatures of (a) for Na_1.5Mn^III₃Mn^II_0.5(AsO₄)₃ and (b) Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃.

Figure 12. Frequency dependence of the real part of electric modulus (a) for Na_1.5Mn²⁺₃Mn³⁺_0.5(AsO₄)₃ and (b) for Na_1.5Mn²⁺₃Fe³⁺_0.5(AsO₄)₃ at different temperatures.

Figure 13. Frequency dependence of the imaginary part of electric modulus for (a) Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and (b) Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ at different temperatures.

Figure 14. Frequency dependence of the AC conductivity for (a) Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and (b) Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃ at different temperatures.

Table 1. Data collection conditions of Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃ and Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃.

Crystal Data
Formula	Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃	Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃
Molar mass (g/mol)	643.53	643.98
Cristal system, S.G, Z	Monoclinic, P2₁/c, 4
a, b, c (Å) ; β (°)	6.78344 (9), 12.93830 (15), 11.22825 (19); 98.5374 (19)	6.76723 (12), 12.9864 (3), 11.256; 98.8636 (13)
V (Å³)	974.54 (2)	977.46 (4)
D_x (g·cm⁻³)	4.386	4.376
Radiation; λ (Å)	Cu K_α (1.54059)
Data Collection
Temperature (K)	298(2)
Diffractometer	D8 Bruker
Reflection number	4613	1190
2θ (°)	5.028–64.984	5–80
Refinement Results
$R_{p}$	0.022	0.083
$R_{w p}$	0.029	0.105
$R_{e x p}$	0.025	0.088
R(F^²)	0.04407	0.05682
$χ^{2}$	1.464	1.440

Table 2. Fractional atomic coordinates, isotropic or equivalent isotropic displacement parameters (Å ²), and Wyckoff positions of material (I).

Atom	x	y	z	Uiso*/Ueq	Wyckoff Positions
As1	0.5824 (3)	0.11275 (14)	0.22827 (18)	0.0277 (6)*	4 e
As2	0.8817 (3)	0.39458 (14)	0.26305 (18)	0.0313 (6)*	4 e
As3	0.2272 (3)	0.28982 (14)	−0.01591 (18)	0.0114 (6)*	4 e
Mn1	0.4139 (3)	0.35341 (14)	0.26964 (18)	0.0216 (6)*	4 e
Mn2	0.7199 (3)	0.23080 (14)	0.49625 (18)	0.0092 (6)*	4 e
Mn3	0.5	0.0	0.5	0.0491 (6)*	2 d
Mn4	0.0827 (3)	0.16419 (14)	0.20656 (18)	0.0217 (6)*	4 e
Na1	0.7403 (3)	−0.01431 (14)	0.00492 (18)	0.0139 (6)*	4 e
Na2	0.0	0.5	0.0	0.0084 (6)*	2 c
O1	0.5503 (3)	0.00107 (14)	0.15914 (18)	0.0787 (6)*	4 e
O2	0.7718 (3)	0.17622 (14)	0.17308 (18)	0.0301 (6)*	4 e
O3	0.6496 (3)	0.09540 (14)	0.37900 (18)	0.0835 (6)*	4 e
O4	0.3917 (3)	0.18877 (14)	0.19837 (18)	0.0217 (6)*	4 e
O5	0.0884 (3)	0.33029 (14)	0.26194 (18)	0.0381 (6)*	4 e
O6	0.2138 (3)	−0.08500 (14)	0.38092 (18)	0.0405 (6)*	4 e
O7	0.0582 (3)	0.00566 (14)	0.15275 (18)	0.0405 (6)*	4 e
O8	0.7251 (3)	0.34213 (14)	0.35173 (18)	0.0746 (6)*	4 e
O9	0.4129 (3)	0.21657 (14)	−0.04974 (18)	0.0217 (6)*	4 e
O10	0.1149 (3)	0.12330 (14)	0.37710 (18)	0.0884 (6)*	4 e
O11	0.3420 (3)	0.38209 (14)	0.07948 (18)	0.0217 (6)*	4 e
O12	0.0472 (3)	0.21869 (14)	0.04507 (18)	0.0242 (6)*	4 e

Table 3. Fractional atomic coordinates, isotropic or equivalent isotropic displacement parameters (Å ²), and Wyckoff positions of material (II).

Atom	x	y	z	Uiso*/Ueq	Wyckoff Positions
As1	0.5977 (4)	0.1126 (6)	0.2306 (6)	0.0084 (6)	4 e
As2	0.890 (1)	0.3943 (5)	0.2631 (5)	0.0228 (5)	4 e
As3	0.2385 (2)	0.2885 (5)	−0.0033 (1)	0.0138 (1)	4 e
Mn1	0.4150 (3)	0.3469 (3)	0.2808 (1)	0.0043 (1)	4 e
Mn2	0.7426 (2)	0.2310 (1)	0.4986 (2)	0.0117 (1)	4 e
Fe3	0.5	0	0.5	0.07525	2 d
Mn4	0.0797 (8)	0.1575 (5)	0.2096	0.0168 (9)	4 e
Na1	0.7676 (2)	−0.0130 (3)	−0.0003 (6)	0.0094	4 e
Na2	0	0.5	0	0.04998	2 c
O1	0.5563 (4)	0.0035 (5)	0.1576 (7)	0.0502 (4)	4 e
O2	0.7559	0.1705 (6)	0.1537 (4)	0.0816 (5)	4 e
O3	0.6380 (5)	0.0966 (1)	0.387	0.0184 (6)	4 e
O4	0.4055 (6)	0.1882 (8)	0.2151 (4)	0.0092	4 e
O5	0.0942 (6)	0.3214 (8)	0.2731 (1)	0.0336 (5)	4 e
O6	0.2627 (7)	−0.0861 (9)	0.3781 (4)	0.0636 (7)	4 e
O7	0.0497 (3)	−0.0014 (5)	0.1586 (2)	0.0086 (9)	4 e
O8	0.7278 (9)	0.3342 (5)	0.3435 (9)	0.003 (2)	4 e
O9	0.4240 (7)	0.2137 (9)	−0.0331 (4)	0.0242 (6)	4 e
O10	0.1413 (9)	0.1352 (8)	0.3901 (8)	0.0089 (4)	4 e
O11	0.3623 (9)	0.3826 (7)	0.0789 (7)	0.0991 (6)	4 e
O12	0.0632 (9)	0.2151 (9)	0.0513 (6)	0.0015 (2)	4 e

Table 4. CHARDI and BVS analysis for cations in Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃. Notes: q(i) = formal oxidation number; Q(i) = computed charge; sof(i) = site occupation factor; CNs = coordination number; ECoN(i) = number of effective coordination.

	BVS Analysis			CHARDI Analysis
Cation	q(i).sof(i)	Q(i)	CN(i)	ECoN(i)
Na1	1	1.02	5	5.03
Na2	1	1.01	6	5.53
As1	5.00	4.99	4	3.92
As2	5.00	5.21	4	3.92
As3	5.00	4.83	4	3.95
Mn1	2.00	1.87	6	5.81
Mn2	2.00	2.02	6	5.81
Mn3	3.00	2.74	6	5.29
Mn4	2.00	2.18	6	5.43

Table 5. CHARDI and BVS analysis for cations in Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃. Notes: q(i) = formal oxidation number; Q(i) = computed charge; sof(i) = site occupation factor; CNs = coordination number; ECoN(i) = number of effective coordination.

	BVS Analysis			CHARDI Analysis
Cation	q(i).sof(i)	Q(i)	CN(i)	ECoN(i)
Na1	1	0.91	5	5.18
Na2	1	1.04	6	6.39
As1	5.00	4.98	4	3.87
As2	5.00	5.02	4	3.86
As3	5.00	4.92	4	3.94
Fe	3.00	3.19	6	5.72
Mn1	2.00	1.94	6	5.88
Mn2	2.00	1.88	6	5.85
Mn3	2.00	2.22	6	5.28

Table 6. M(II)-O and M(III) example distances encountered in weilleytes and alliaudites.

Formula	S.G	M(II)-O (Å)	M(III)-O (Å)	Ref.
Na_1.5Mn₃Fe_0.5(AsO₄)₃	P2₁/c	1.959 (5)–2.256 (6)	1.973 (2)–2.040 (3)	*
Na_1.265Mn^II_2.690Mn^III_0.785(PO₄)₃		1.893 (2)–2.334 (2)	2.171 (6)–2.648 (5)	[25]
Na_1.5Mn₃Mn_0.5(AsO₄)₃		1.9270 (1)–2.341 (4)	2.193 (2)–2.4489 (19)	*
Na_1.25Co_2.187Al_1.125(AsO₄)₃		1.928–2.151	2.170–2.184	[12]
Na₂Fe₂^IIAl(PO₄)₃		2.089–2.225	1.973	[7]
Ag_1.09Mn_3.46(AsO₄)₃		2.105 (4)–2.413 (5)	1.915 (5)–2.186 (6)	[10]
Na_0.5K_0.65Mn_3.43(AsO₄)₃		2.113 (5)–2.46 (5)	1.954 (5)–2.178 (6)	[11]
NaMn^II_2.5Fe^III_0.5 Al_0.5(PO₄)₃	P2₁/n	2.103–2.245	1.956–2.025	[8]
K_1.5Ni₃ Fe_0.5(PO₄)₃	C2/c	2.0153 (14)–2.2241 (13)	2.016 (2)–2.0490 (13)	[28]
Na_1.72Mn_3.28(AsO₄)₃	C2/c	2.218 (9)–2.360 (8)	1.990 (12)–2.193 (11)	[26]

* This work

Table 7. FTIR vibration frequencies (cm⁻¹) attributed to AsO4 tetrahedrons and M-O bonds of some arsenates found in the literature. * This work.

Compound	Valence Vibrations		Deformation		Vibration M-O	Ref.
Compound	ν₁	ν₃	ν₂	ν₄	Vibration M-O	Ref.
(AsO₄)(III)	837	878	349	463	-	[29]
Na_0.5K_0.65Mn_3.43(AsO₄)₃	822	880	-	443	564; 420; 669	[11]
BiCu₆(AsO₄)₃(OH)₆.3H₂O	848	814; 797	390; 311	553; 529; 494	-	[30]
NaNiFe₂(AsO₄)₃	860; 901	820; 789; 700	447	496; 474		[31]
NaCa₂Mg₂(AsO₄)₃	950; 750		550; 300		-	[32]
Na₃In₂(AsO₄)₃	866	934	342	398		[33]
Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃	820; 750	861	-	456; 426	538; 581	*
Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃	825; 889	767	-	436; 371	583	*

Table 8. Raman vibration frequencies (cm⁻¹) attributed to AsO₄ tetrahedrons and M-O bonds of some arsenates found in the literature (s= symmetric, as = asymmetric).

Compound	ν₁ _s	ν₃ _as	ν₂ _s	ν₄ _as	ν₅ M(III)	ν₅ M(II)	Ref.
Na_1.5Fe_0.5Mn₃(AsO₄)₃	854–848–816	1000	417–496	578–569	(Fe) 374	(Mn) 256–206	*
Na_1.5Mn_3.5(AsO₄)₃	838–867–759	899	403–475	529–580	(Mn) 358–313	(Mn) 230–192	*
Na₇Cu₄(AsO₄)₅	813–880	902	480–485	511–527	(Cu) 403 334	-	[35]
Mn₂As₂O₅	820	900	440	580	-		[36]

* This work.

Table 9. EDS semi-quantification results for the elementary atomic percentages.

Material	Na_1.5Mn^II₃Mn^III_0.5(AsO₄)₃		Na_1.5Mn^II₃Fe^III_0.5(AsO₄)₃
Element	Experimental	Theoretical	Experimental	Theoretical
Manganese	20.27%	17.5%	16.75%	15%
Arsenic	16.34%	15%	17.28%	15%
Silicon	1.38%	-	-	-
Sodium	9.33%	7.5%	8.42%	7.5%
Oxygen	52.67%	60%	54.55%	60%
Iron	-	-	3%	2.5%

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Rezgui, E.; Ouerfelli, N.; Gavinho, S.R.; Carvalho, J.P.F.; Graça, M.P.F.; Teixeira, S.S. Crystal Structure, Ionic Conductivity, Dielectric Properties and Electrical Conduction Mechanism of the Wyllieites Na_1.5Mn_3.5(AsO₄)₃ and Na_1.5Mn₃Fe_0.5(AsO₄)₃. Crystals 2023, 13, 1251. https://doi.org/10.3390/cryst13081251

AMA Style

Rezgui E, Ouerfelli N, Gavinho SR, Carvalho JPF, Graça MPF, Teixeira SS. Crystal Structure, Ionic Conductivity, Dielectric Properties and Electrical Conduction Mechanism of the Wyllieites Na_1.5Mn_3.5(AsO₄)₃ and Na_1.5Mn₃Fe_0.5(AsO₄)₃. Crystals. 2023; 13(8):1251. https://doi.org/10.3390/cryst13081251

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Rezgui, Eya, Najoua Ouerfelli, S. R. Gavinho, J. P. F. Carvalho, M. P. F. Graça, and S. Soreto Teixeira. 2023. "Crystal Structure, Ionic Conductivity, Dielectric Properties and Electrical Conduction Mechanism of the Wyllieites Na_1.5Mn_3.5(AsO₄)₃ and Na_1.5Mn₃Fe_0.5(AsO₄)₃" Crystals 13, no. 8: 1251. https://doi.org/10.3390/cryst13081251

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Crystal Structure, Ionic Conductivity, Dielectric Properties and Electrical Conduction Mechanism of the Wyllieites Na_1.5Mn_3.5(AsO₄)₃ and Na_1.5Mn₃Fe_0.5(AsO₄)₃

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2. Materials and Methods