Synthesis of schafarzikite-type (PbBi)(Fe_1−xMn _x )O₄: a study on structural, spectroscopic and thermogravimetric properties

2.1 Synthesis

Polycrystalline samples of (PbBi)(Fe_1−xMn _x )O₄ (x = 0–1) were synthesized by the conventional solid-state method, grinding respective stoichiometric amounts of PbO (99.9 %, Alfa Aesar), Bi₂O₃ (99 %, Alfa Aesar), Fe₂O₃ (99 %) and Mn₂O₃ (99 %) in a agate mortar. Afterward, the mixture was pressed into pellets and transferred into dried quartz tubes. The tubes were sealed with an internal pressure of about 1.0 Pa followed by heating in a muffle furnace at 923 K for 72 h.

2.2 X-ray powder diffraction

X-ray powder diffraction (XRPD) data were collected on a Bruker D8 Advance diffractometer (Bruker AXS GmbH, Karlsruhe Germany) using a Bragg-Brentano geometry with CuK_α1 radiation and a Johansson monochromator. Measurements were taken at ambient conditions from 10° to 130° 2θ with a step width of 0.0145° and a data collection time of 1.25 s per step. The XRPD data were refined using the Rietveld method (TOPAS V4.2, Bruker AXS). The respective fundamental parameters were calibrated using a LaB₆ standard and used for the profile line-shape. During the refinements general parameters such as sample displacement, scale factor and background parameter (Chebychev polynomial) were optimized. The lattice parameters, atomic coordinates and atomic displacement parameters were also refined. The isotropic atomic displacement parameters (ADP) were constrained between atoms located at the same Wyckoff site (Bi/Pb, Fe/Mn) to avoid unphysical outcomes such as negative ADPs. Besides the heavy elements Pb and Bi, the ADPs of the light oxygen atoms were as well refined constrained to each other. The starting atomic coordinates were taken from the crystal structure data of FeSb₂O₄, where the 8h Wyckoff site was set to co-share between Pb²⁺ and Bi³⁺ with an occupancy of 0.5 each. ²⁵ Since the X-ray scattering factors of Pb²⁺ and Bi³⁺ are similar, the Rietveld refinement cannot distinguish the occupancy parameters between the respective atoms. As such, the nominal compositional occupancy was fixed, which was supported by the EDX results. For the same reason, the occupancy parameter between Fe and Mn were set to their nominal compositions.

2.3 UV/Vis diffuse reflectance spectroscopy

A Shimadzu UV-2600 (Shimadzu, Kyoto, Japan) spectrophotometer, equipped with an ISR-2600 plus two-detector integrating sphere (Pike Technologies, USA), was used for the collection of optical diffuse reflectance spectra at room temperature. Data were recorded in the wavelength range between 190 nm and 950 nm with a step of 1 nm. A BaSO₄ powder sample was used as reference standard for the baseline correction. The Tauc-type ^{26 , 27} band gaps (direct or indirect) were compared with those determined by the DASF method ^{28 , 29} after converting the reflection data to absorption ones using the Kubelka-Munk transformation. ³⁰

2.4 Vibrational spectroscopy

Raman spectra were recorded on a LabRam ARAMIS (Horiba Jobin–Yvon) Micro-Raman spectrometer. A laser of 525 nm providing power of less than 20 mW was focused on the sample surface through a 50× objective (Olympus) with a numerical aperture of 0.75. The focus spot was estimated to be about 1 μm when closing the confocal hole to 200 μm. Using a backscattering geometry each spectrum was recorded between 40 cm⁻¹ and 850 cm⁻¹ with a spectral resolution of approx. 3.2 cm⁻¹ using a grating of 1800 grooves/mm and a thermoelectrically cooled CCD detector (Synapse, 1024 × 256 pixels). Fourier transform infrared (FTIR) spectra were collected in the mid-infrared range from 400 cm⁻¹ to 4000 cm⁻¹ on a Bruker VERTEX 80v spectrometer equipped with a DTGS Detector. Standard KBr pellet method was used for data collection.

2.5 Thermal analysis

Simultaneous thermogravimetric analysis and differential scanning calorimetry (TGA/DSC) measurements were performed on a simultaneous TGA/DSC 3+ STAR e system (Mettler Toledo, Schwerzenbach, Switzerland). Approximately 10 mg of each polycrystalline sample was measured with a heating rate of 10 K/min and a continuous N₂ flow of 20 mL/min from 300 K to 1500 K. An empty corundum crucible was used as reference. Data were normalized to the respective mass and a drift correction was applied based on empty crucible versus empty crucible data.

3.1 Crystal structure

XRPD data Rietveld refinements confirm that each member of the (PbBi)(Fe_1−xMn _x )O₄ solid solution is found to be phase pure and crystallizes in the space group P4₂/mbc. A representative Rietveld plot of (PbBi)(Fe_0.5Mn_0.5)O₄ is shown in Figure 2 and the refined crystal structural parameters of the solid solution (PbBi)(Fe_1−xMn _x )O₄ are given in Table S1 (Supplementary information). The metric parameters (a = b, c and V) are given in Table S2, and the interatomic bond distances and angles in Table S3.

Figure 2:

Rietveld plot of (PbBi)(Fe_0.5Mn_0.5)O₄ schafarzikite-type sample.

Complete substitution of Fe³⁺ with Mn³⁺ in (PbBi)(Fe_1−xMn _x )O₄, leads to a slight elongation (0.3(1) %) of the (a, b)- and a contraction (−0.7(2) %) of the c-lattice parameters. The latter parameter plays the dominant role for almost a negligible cell volume contraction of −0.1(4) % between the endmembers, as depicted in Figure 3. The observed cell volumes of the endmembers (PbBi)FeO₄ (V = 441.35(4)·10⁶ pm³) and (PbBi)MnO₄ (V = 440.76(6)·10⁶ pm³) are in excellent agreement with the reported ones. ^{24 , 31} The slight deviation of each lattice parameter from the Vegard’s rule line can be understood due to these small changes of the metric parameters with respect to the chemical composition. The interplay between the geometric distortion of the MO₆ and LO₃E polyhedra and the stereochemical activities of the associated LEPs should also be considered to explain the slight deviation from the Vegard’s lines. Moreover, the adoption of the high-spin (HS) and low-spin (LS) configurations of the M cations directly influence the respective ionic radii, and the metric parameters as well. Due to Fe³⁺/Mn³ mixed occupancy the average ionic radius of the M cations should consider four different spin configurations: Fe³⁺/Mn³⁺ (LS–LS), Fe³⁺/Mn³⁺ (LS–HS), Fe³⁺/Mn³⁺ (HS–LS) and Fe³⁺/Mn³⁺ (LS–LS). The trends of the metric parameters fit well to the Fe³⁺/Mn³⁺ (LS–HS) configuration (Figure S2).

Figure 3:

Changes of the metric parameters in (PbBi)(Fe_1−xMn _x )O₄ with respect to the x-value of the chemical composition.

The axial Fe–O1 (202.8(11) pm) and equatorial Fe–O2 (203.8(7) pm) bond lengths for the endmember (PbBi)FeO₄ are found to be close (Table S3) to the respective Mn–O1 (200.0(7) pm) and Mn–O2 (200.2(7) pm) bond lengths in (PbBi)MnO₄. Due to mixed occupancy the axial (Fe/Mn)–O1 and the equatorial (Fe/Mn)–O2 bond distances lie close to each other irrespective to the chemical composition, as depicted in Figure 4.

Figure 4:

Fe/Mn–O interatomic bond distances (left), polyhedral volumes (middle) and M–M distances with respect to chemical composition in (PbBi)(Fe_1−xMn _x )O₄. The solid line is for eye guideline.

The gradual decrease of the M–M distance from 305.3(8) pm (Fe–Fe) to 303.1(6) pm (Mn–Mn) in the octahedral chains can be understood from the deviation between the Fe–O and Mn–O distances, which leads to a contraction of the c-lattice parameter. The MO₆ octahedral volume remains almost constant at 10.94(4)·10⁶ pm³ followed by a sharp contraction for x = 1.0(10.42(6)·10⁶ pm³) (Figure 4), indicating a dominant influence of the Fe³⁺ cations in the structure. The underlying geometric consequences should influence the polyhedral distortions. The mixed valence LEP cations (Pb²⁺ and Bi³⁺) on the same atomic position imposes additional distortion to the LO₃E tetrahedra ³² due to the asymmetric distribution of the O–Pb–O–Bi–O distances. Indeed, the bond distortion in the LO₄E polyhedra shows a slight increase, with an insignificant change of the MO₆ polyhedra, for an increasing Mn content in the solid solution (Figure S1).

The bond valence sum of the M- and L-cations are calculated from the M–O and L–O bond distances (Table S3) in the MO₆ and LO₃ polyhedra, respectively, for any given chemical composition. ^{33 , 34} The structural BVS of the L-cation exhibits an over-bonding nature above the average 2.5 v.u., as shown in Figure 5, which is a common finding for stereochemically active LEP containing cations. ^{14 , 15} On the other hand, except for the endmember (PbBi)MnO₄ where Mn shows a BVS of 2.65(4) v.u., the BVS of the M³⁺ cation shows an under-bonding nature below the formal value 3 v.u. with almost a constant deviation of about 0.2 v.u. throughout the solid solution. Such a constant deviation may not be explained due to experimental uncertainty. Since all oxygen atoms of the LO₃E polyhedra are linked to the MO₆ octahedral apexes, the respective BVS deviations in opposite directions can be understood from geometric distortions. The observed absolute value of the WLE parameters (|Φ_i|) of 3.72(2)·10⁻⁵ and 3.43(2)·10⁻⁵ for (PbBi)FeO₄ and (PbBi)MnO₄, respectively, are within the typical range of a stereochemically active Pb²⁺/Bi³⁺ cations in the crystal structures. ¹⁴ Most of the |Φ_i| values lie close to 3.75·10⁻⁵, indicating an asymmetric distribution of the LEP ³⁵ followed by a withdrawal of the positive charge of the nucleus toward the bonding oxygen ligands. Such redistribution leads to an increase in the bonding capacity of an L-cation, which may extend the first coordination sphere ³⁶ along with a higher coordination number. This phenomenological concept can further explain the inclusion of Li⁺ cations into the schafarzikite void channels. ¹¹ According to the Hamani LEP localization model ³⁷ where each L-cation is decomposed into cationic cores (M*) and LEP spatial spheres, as given in Figure 6, allowing for the calculation of the distance between M* and center of the LEP sphere (d _M*-LP ). Irrespective of the chemical composition throughout the solid solution the LEP sphere radius of the Pb²⁺/Bi³⁺ cations is found to be 120(1) pm and the center of the LEP sphere locates 68(1) pm away from the Pb²⁺/Bi³⁺ core which itself possesses a radius of 77(1) pm. Since the shortest interatomic distance between two LEP cations is 375 pm, the estimated corresponding LEP-LEP distance of about 239(1) pm (375 pm − 2*68(1) pm = 239(1) pm) well allows free space in the center of a pseudo-tetrahedron formed by four LEP cations, for a sphere with a radius of ∼80 pm. Such empty space well fits, for instance, to the cationic diameter of lithium of 118 pm. ^{38 , 39}

Figure 5:

Deviations of bond valence sum (BVS) from formal valence (^forV) of the M and L-cations in (PbBi)(Fe_1−xMn _x )O₄ (left), and the correlation between the absolute value of the Wang-Liebau eccentricity parameter (| Φ _i |) and the BVS for Pb/Bi (right).

Figure 6:

Schematic representation for the estimation of effective free space in the (PbBi)FeO₄ schafarzikite structure using Hamani ³⁷ model, where the L-cation is decomposed into a cationic core (M*) and a LEP spatial sphere with radii of r_M* and r _LEP , respectively, and d_M*-LEP is the distance between their centers. The free space sphere with a radius of r_FS is located at the center of a pseudo-tetrahedron formed by four LEP cations, which fits well for small cations such as lithium.

3.2 Vibrational properties

For the room-temperature Raman and FTIR spectra of (PbBi)(Fe_1−xMn _x )O₄, which are given in Figure 7, the factor group analysis predicts 62 vibrational modes (5A_1g + 3A_1u + 7A_2g + 5A_2u + 7B_1g + 5B_1u + 5B_2g + 3B_2u + 13E_u + 9E_g). As listed in Table S4, 26 of them are Raman (5A_1g + 7B_1g + 5B_2g + 9E_g), 16 are infrared (4A_2u + 12E_u) active, 2 are acoustic (A_2u + E_u) and a substantial number of 18 of them are optically silent (3A_1u + 7A_2g+ 5B_1u + 3B_2u). Fitting the resolved Raman spectra requires 19 and 17 pseudo-Voigt peaks for the endmembers (PbBi)FeO₄ and (PbBi)MnO₄, respectively. The vibrational features of each Raman spectrum can be categorized into three spectral regions of low- (<140 cm⁻¹), mid- (140–600 cm⁻¹) and high-frequency (>600 cm⁻¹).

Figure 7:

Stack plots of FTIR (left) and Raman (right) spectra of (PbBi)(Fe_1−xMn _x )O₄.

The low-frequency region is mainly dominated by the L–O–L and O–L–O bending contributions of the LO₄E nido-tetrahedra. The mid-range covers the M–O–M and O–M–O bending of the MO₆ octahedra, and the L–O stretching modes of LO₄E polyhedra. The high-frequency region is purely associated with the M–O symmetric and asymmetric vibrations in the MO₆ octahedra. More details of the vibrational description of the endmember (PbBi)MnO₄ are available elsewhere. ²⁴ The low-frequency Raman modes at 106(1) cm⁻¹ and 134(1) cm⁻¹ of (PbBi)FeO₄ gradually shift to 95(2) cm⁻¹ and 130(1) cm⁻¹, respectively, as shown in Figure S3, which is mainly due to weaking of the associated bending force constant as the average L-O bond distances between the endmembers (Table S3) does not significantly change. Some high-frequency modes show slight blue shifts, indicating to the observed shortening of the M–O bond lengths in the MO₆ octahedra. To better understand the vibrational spectra of the centrosymmetric structures the FTIR spectra of the investigated phases provide complementary information (Figure S4). The compact nature of the FTIR spectra due to merging and the instrumental limitation (>400 cm⁻¹), the shift of the mode frequencies could hardly be followed with changing chemical composition of the solid solution. However, an apparent quasiharmonic trend of each FTIR peak maximum complements the mid- and high-frequency Raman modes.

3.3 Optical band gap

The UV/Vis diffuse reflectance spectra of the endmembers of the (PbBi)(Fe_1−xMn _x )O₄ solid solution are shown in Figure S5 and Figure S6. To determine the optical band-gap transition energy (E _g ) from a given absorption spectra by using the Tauc method, ²⁷ the reflectance data are transformed into the corresponding absorption spectra using the Kubelka-Munk function. ⁴⁰ Absorption data are then recalculated for the use of the Tauc method to calculate a band-gap transition energy assuming a direct (E _d ) or indirect (E _i ) electron transition. Each analysis is performed by plotting a tangent to the baseline at low energies and a second tangent to the slope in the linear region of the absorption onset. ^{41 , 42 , 43} The energy of the band gap can then be estimated by the intersection of these two lines (Figure S5). Since the Tauc method cannot assert the nature of the transition type (E _d or phonon assisted E _i ), the derivative absorption spectra fitting (DASF) method ²⁸ is demonstrated ^{29 , 44} to compare the optical band-gap types. With gradual increase of Mn content in the solid solution the reflectivity becomes noticeably lower, which hampers calculating the band-gap energies using Tauc’s approach. However, data treated with the DASF method appears as peak shape (Figure S5), allowing for calculation of the band-gap energy (E _g ) from the fitted peak-maximum. A comparison between E _d and E _i with the DASF E _g value guides to ascertain the type of transition. In the present, since each band-gap energy obtained by the DASF method (Table S5) agrees well with E _d , each member of the solid solution presumably follows direct transition. Beside the band-gap energy, the FWHM (F _g ) of the DASF line shape essentially describes the edge of the valence and the conduction bands split into different quantized levels based on the distribution of crystallite sizes and available defects. If one assumes the slope of the absorption edge corresponds directly to the sharpness of the transition (the shaper the energy level separation the flatter the valence and/or the conduction bands in the transition region), the F _g of the DASF peak is a direct measure for this behavior. Although the optical band gaps of the schafarzikite family members are not well explored, the experimental E _g of minium Pb₃O₄ (2.1 eV) ⁴⁵ and MnSb₂O₄ (2.65(2) eV) ⁹ are comparable to those of the present compounds. Considering the direct transition (PbBi)FeO₄ holds a band gap of 2.24(3) eV which drops to 1.77(3) eV for x = 0.3. Afterward, a slight linear decrease results in 1.72(3) eV for the endmember (PbBi)MnO₄, as shown in Figure 8.

Figure 8:

Changes of direct (E _d ) and indirect (E _i ) electron transfer to the conduction band and band-gap energy (E _g ) with respect to the chemical composition x in (PbBi)(Fe_1−xMn _x )O₄.

3.4 Thermal properties

The TG and the DSC stack plots of the compounds (PbBi)(Fe_1−xMn _x )O₄, as shown in Figure 9, suggest that samples with higher Mn content exhibit ∼1 % weight loss at around 1080(3) K, 1084(1) K, 1075(3) K, and 1062(1) K, respectively, for x = 0.7, 0.8, 0.9 and 1.0. Such tiny weight loss is most likely associated with the evaporation of Bi-containing amorphous contents. Exothermic signals are observed at 981(1) K and 1000(1) K, respectively, for the endmembers (PbBi)FeO₄ and (PbBi)MnO₄. The other members (0 < x < 0.7) of the solid solution exhibit an exothermic signal at slightly lower temperatures. The onset temperature (first point of inflection) has been taken as the decomposition temperature, which fluctuates around 1360 K within 20 K for any given composition of the solid solution, as shown in Figure S7.

Figure 9:

Thermoanalytic evaluation of (PbBi)(Fe_1−xMn _x )O₄.