I. INTRODUCTION
Lithium-ion batteries are used as portable power sources and are still in the focus of current scientific research. In these devices, LiCoO2 and LiFePO4 still have a wide-spread application as cathode materials although these compounds have already been proposed as cathode material in the 80s and 90s (Mizushima et al., Reference Mizushima, Jones, Wiseman and Goodenough1980; Padhi et al., Reference Padhi, Nanjundaswamy and Goodenough1997). In the past couple of years, research into sodium-ion batteries (SIB) has gained increasing interest. For portable applications like electronic devices (smartphones, tablets, notebooks) Li with its smaller size, lighter weight, and higher energy density is preferred, whereas large-scale stationary applications such as energy storage for power plants and photovoltaic cells might be better served with Na. SIB are considered a good alternative because of similar chemistry, higher abundance, lower toxicity, and lower costs of Na compared with Li (Palomares et al., Reference Palomares, Serras, Villaluenga, Hueso, Carretero-Gonzalez and Rojo2012).
Alkaline-containing transition metal phosphates of the general formula AM’PO4 (A = Li, Na; M′ = Mn, Fe, Co, Ni) crystallize in two distinct polymorphs: triphylite and maricite. For A = Li in high temperature solid-state reactions (ssr) the triphylite structure is thermodynamically favoured, while for A = Na the maricite structure is preferred. Since the maricite structure seems to be electrochemically less active (Prosini et al., Reference Prosini, Cento, Masci and Carewska2014) different synthesis routes have to be applied to achieve potential cathode materials for SIB based on triphylite-type compounds.
Mixed transition metal phosphates LiM x Fe1−x PO4 (M = Mn, Co) can be synthesized via ssr (Giner et al., Reference Giner, Roddatis, López and Kubiak2016; Strobridge et al., Reference Strobridge, Liu, Leskes, Borkiewicz, Wiaderek, Chupas, Chapman and Grey2016) as well as via a hydrothermal treatment at 200 °C followed by annealing at 600 °C (Drozhzhin et al., Reference Drozhzhin, Sumanov, Karakulina, Abakumov, Hadermann, Baranov, Stevenson and Antipov2016). Furthermore, Drozhzhin et al. (Reference Drozhzhin, Sumanov, Karakulina, Abakumov, Hadermann, Baranov, Stevenson and Antipov2016) describe the occurrence of an extra phase Li1−x Mn0.5Fe0.5PO4 during electrochemical extraction of Li in addition to the educt (x = 0) and final product (x = 1). For the mid-charge compound (x = 0.5) lattice parameters were determined by electron diffraction tomography (EDT). For LiCo0.5Fe0.5PO4 a complex mechanism of the electrochemical delithiation is discussed (Strobridge et al., Reference Strobridge, Liu, Leskes, Borkiewicz, Wiaderek, Chupas, Chapman and Grey2016). Higher Li contents than the mid-charge compound Li0.5Co0.5Fe0.5PO4 showed cell voltages of about 3.5 V, lower Li contents caused higher cell voltages of about 4.8 V. These values are close to the standard redox potentials of 3.8 V vs. Li+/Li for Fe3+/Fe2+ or 4.9 V vs. Li+/Li for Co3+/Co2+ (Bratsch, Reference Bratsch1989).
NaMn x Fe1−x PO4 (x = 0 and x = 0.5) can be obtained in the triphylite structure via a molten salt reaction of dittmarite-type compounds NH4Mn x Fe1−x PO4·H2O with an excess of NaOAc·3H2O at temperatures between 65 and 100 °C. Moreover, chemical desodiation with NO2BF4 in acetonitrile enabled the formation of Na0.5Mn0.5Fe0.5PO4 (Lee et al., Reference Lee, Ramesh, Nan, Botton and Nazar2011).
The electrochemical processes of lithiation, delithiation, sodiation, and desodiation of triphylite-related phases AM′PO4 (A = Li, Na; M′ = Mn, Fe, Co, Ni) are often described in literature (Oh et al., Reference Oh, Myung, Hassoun, Scrosati and Sun2012; Kaus et al., Reference Kaus, Issac, Heinzmann, Doyle, Mangold, Hahn, Chakravadhanula, Kübel, Ehrenberg and Indris2014). However, chemical delithiation and sodiation especially for LiFePO4 is examined, too. Multiple oxidation agents such as H2O2 (Lepage et al., Reference Lepage, Michot, Liang, Gauthier and Schougaard2011), Br2 (Avdeev et al., Reference Avdeev, Mohamed, Ling, Lu, Tamaru, Yamada and Barpanda2013), and NO2BF4 (Delacourt et al., Reference Delacourt, Laffont, Bouchet, Wurm, Leriche, Morcrette, Tarascon and Masquelier2005) are used to extract Li from the triphylite-type compound. The chemical sodiation of FePO4 with an excess of NaI in acetone is reported by Avdeev et al. (Reference Avdeev, Mohamed, Ling, Lu, Tamaru, Yamada and Barpanda2013). Li2S (Chaloner-Gill et al., Reference Chaloner-Gill, Shackle and Andersen2000) and Na2S (Haberkorn et al., Reference Haberkorn, Bauer and Kickelbick2014) are mentioned as reducing agents for compounds like LiV3O8 and V2O5.
Triphylite-type mixed transition metal phosphates like NaM 0.5Fe0.5PO4 may be considered as potential cathode materials, but may not be synthesized via high-temperature ssr. In this work. triphylite-type LiM 0.5Fe0.5PO4 was used as starting material in cyclic low-temperature oxidation and reduction processes to yield Na-rich triphylite-type compounds. Ex-situ PXRD studies of the obtained materials to investigate state and reactivity of the intermediate and final products were of interest, too. Triphylite-type Na z Co0.5Fe0.5PO4 (0 ≤ z < 1) is not known in literature and was therefore of special interest.
For Rietveld refinement most often phases with known structure and discrete composition are used. The composition may be known or assumed and otherwise may be determined via refinement. Beck et al. (Reference Beck, Douiheche, Haberkorn and Kohlmann2006) describe modelling of a single phase with lattice parameter fluctuations in chloro-vanadato-apatites by special constraints of asymmetric line shapes or three highly constrained fractions of the same phase with similar but different lattice parameters. Furthermore, Haberkorn et al. (Reference Haberkorn, Bauer and Kickelbick2014) carried out Rietveld refinements using a model of 34 fractions describing a single phase of Na x V2O5 but a broad, variable shaped distribution of different alkaline contents. The lattice parameters of each fraction were constrained by linear interpolation between the lattice parameters of distinct reference phases. Such a parameterization works as a model of a continuous distribution of coexisting compositions covering the complete range of potential compositions. A similar approach was applied in this work to evaluate the obtained powder X-ray diffraction (PXRD) data.
II. EXPERIMENTAL
A. Sample
Prior to all solid-state syntheses, the mixtures of the starting materials were ball milled for 1 h at a rotational speed of approximately 475 rpm using agate grinding bowls (25 ml), ten agate balls (10 mm diameter), and an additive of 10 ml n-pentane in a Fritsch Pulverisette 7 planetary mill.
Co3(PO4)2, Mn3(PO4)2, and Li3PO4 were synthesized by calcinating stoichiometric amounts of the corresponding carbonate (CoCO3, 99%, Alfa Aesar; Li2CO3, p.a., Merck) or oxide (MnO, 99%, Alfa Aesar) and (NH4)2HPO4 (98%, Alfa Aesar) at 650 °C [Co3(PO4)2], 800 °C (Li3PO4) or 900 °C [Mn3(PO4)2] for several hours in a platinum crucible in air. For the synthesis of Fe3(PO4)2 first FePO4 was yielded by heating stoichiometric amounts of FeC2O4·2H2O (99%+, Riedel-de Haën) and (NH4)2HPO4 slowly to 200 °C for 2 h and slowly to 900 °C for 10 h in a platinum crucible in air. In a second step, FePO4 was reacted with stoichiometric amounts of Fe (p.a., Merck) at 800 °C for 6 h in a porcelain crucible in a tube furnace under Ar flow. LiM 0.5Fe0.5PO4 (M = Mn, Co) was synthesized by heating stoichiometric amounts of Li3PO4, M 3(PO4)2 and Fe3(PO4)2 to 800 °C for 16 h in a platinum crucible in a tube furnace under Ar flow.
The compounds LiM 0.5Fe0.5PO4 were subjected to a cyclic process of chemical oxidation and reduction. A schematic synthesis route is shown in Figure 1. In the oxidation processes, the solid and an excess of bromine in acetonitrile were stirred at room temperature for 18 h. In the reduction processes, the solid was reacted with an excess of dried Na2S in absolute acetonitrile (drying process according to Haberkorn et al., Reference Haberkorn, Bauer and Kickelbick2014) under inert conditions (Ar) at reflux for 24 h. The products were filtered in air and washed thoroughly with acetonitrile or ethanol.
Schematic, theoretical synthesis route of NaM 0.5Fe0.5PO4 via chemical oxidation and chemical reduction.
As references for Rietveld refinements NaMn0.5Fe0.5PO4 and Na0.5Mn0.5Fe0.5PO4 were synthesized similar to Lee et al. (Reference Lee, Ramesh, Nan, Botton and Nazar2011) via a molten salt reaction and subsequent chemical desodiation with Br2 in acetonitrile.
B. XRD measurements
PXRD patterns were collected on a D8 Advance diffractometer (supplier Bruker AXS, Karlsruhe, Germany) with focussing Bragg–Brentano geometry and a fine focus X-ray tube with Cu anode. The goniometer radius was 275 mm, the instrument power was 40 kV and 40 mA. CuKα radiation was used for data collection and no α 2 stripping was performed. The scans were carried out using a 2θ range of 7°–120° with a scan time of 2 h at room temperature, a step size of 0.013° and 0.825 s count time per step. No monochromator was attached but low energy radiation was removed by discriminating the detector and a Ni foil (12 µm), working as a K β filter, was mounted on the primary site. A fast Lynxeye detector and variable divergence slits were used.
The structure data of LiFePO4 in the space group Pnma (Maccario et al., Reference Maccario, Croguennec, Le Cras and Delmas2008) were used as starting values for the refinement of other triphylite-type phases.
The powder patterns were evaluated with TOPAS V5 (Bruker AXS, 2014) using the Rietveld method (Rietveld, Reference Rietveld1967) and the fundamental parameter approach (Cheary et al., Reference Cheary, Coelho and Cline2004). The instrumental function was determined empirically with LaB6 as reference material.
III. RESULTS AND DISCUSSION
A. Multi-fraction models
Triphylite-type compounds with different alkaline content could be achieved via a cyclic chemical oxidation and reduction process. The seven step synthesis (in case of M = Co) and five step synthesis (in case of M = Mn) yielded products with sharp reflections in the first two steps, specifically the compounds LiM 0.5Fe0.5PO4 and Li0.5 M 0.5Fe0.5PO4. The patterns could be evaluated by using a single-phase model. In the following steps, powder patterns with broadened reflections were obtained. This peak broadening was owing to the presence of a distribution of different alkaline contents of the type Li(1−y)·z Na y·z M 0.5Fe0.5PO4. Instead of a continuous distribution a set of multiple triphylite-type phases with different alkaline contents was used for Rietveld refinements. We prefer to call this a multi-fraction state instead of a multi-phase state because all phases are of the same structure type and only show minor differences in their composition as well as their crystallographic properties. They may be understood as a continuum of different compositions of the same phase represented by selected fractions. Depending on the complexity of the composition a multi-fraction model with up to 121 fractions was used to interpret the XRD pattern and to calculate an average molecular formula for the synthesized compounds. In the following sections, three different multi-fraction models (with 11, 36, and 121 fractions) will be presented and the application onto the yielded compounds will be discussed. The models with 36 or 121 fractions support simultaneous modelling of the total alkaline content z and the relative Na content y. These models are even more complex than the model of Haberkorn et al. (Reference Haberkorn, Bauer and Kickelbick2014) parameterizing a single variable x of the composition of Na x V2O5.
If the product of a reaction is of a molecular formula Li(1−y)·z Na y·z M 0.5Fe0.5PO4 with either z = 0.5 or z = 1 a model of 11 equidistant fractions can be used to satisfactorily evaluate the PXRD data. For example, Li1−y Na y M 0.5Fe0.5PO4 (i.e. z = 1) was modelled by 11 equidistant fractions with y = 0, 0.1,…, 1. In the case of a variable z, more complex models were required. The more general composition Li(1−y)·z Na y·z M 0.5Fe0.5PO4 with 0.5 ≤ z ≤ 1 and 0 ≤ y ≤ 1 was set up with 6 or 11 equidistant steps in z and y, forming models with 36 and 121 different fractions. A graphical representation of the fractions supported by the three models is given in Figure 2.
Fractions of Li(1−y)·z Na y·z M 0.5Fe0.5PO4 (0 ≤ y ≤ 1) with different alkaline contents supported by (a) the 11 fraction model with z = 1, (b) the 11 fraction model with z = 0.5, (c) the 36 fraction model, and (d) the 121 fraction model.
All three models use reference phases and multiple fractions of the target phase of which the crystallographic parameters are linearly interpolated between those of the references. LiM 0.5Fe0.5PO4, Li0.5 M 0.5Fe0.5PO4, NaM 0.5Fe0.5PO4, and Na0.5 M 0.5Fe0.5PO4 (M = Mn, Co) were employed as references. But prior to be used as a reference in a multi-fraction model, the crystallographic parameters of these compounds had to be determined. For some compounds (LiM 0.5Fe0.5PO4, Li0.5 M 0.5Fe0.5PO4, NaMn0.5Fe0.5PO4, Na0.5Mn0.5Fe0.5PO4) the crystallographic parameters could be refined from pristine self-prepared samples by Rietveld analysis. In the case of Na0.5Co0.5Fe0.5PO4 and NaCo0.5Fe0.5PO4, no pure compounds could be prepared within this work and no crystallographic structures of the corresponding triphylite-type phases are described in literature. Therefore, the crystallographic data for those two references could not be determined exactly. Starting values of the lattice parameters were estimated from those of LiCo0.5Fe0.5PO4 and differences of the metric parameters in the triphylite-type system LiFePO4–FePO4–NaFePO4. The starting values of the atomic positions were taken from the Li analogues. Samples with a composition as close as possible to the desired composition were used to optimize the lattice parameters and to refine the atomic positions. The crystallographic data of the references are given in the supplemental data (see online Tables SI-I–SI-VIII).
The same references were used in all the three models. These reference phases represent the corners (y = 0 or y = 1; z = 0.5 or z = 1) of the possible composition range (0 ≤ y ≤ 1; 0.5 ≤ z ≤ 1). The metric parameters and atomic positions of these references were fixed and the scaling factors were set to zero, their metric parameters and atomic positions were not refined in the Rietveld analysis when using a multi-fraction model.
In the case of 11 or 36 fractions the fractions’ scaling factors were refined individually, in the case of the 121 fraction model the scaling factors s tot were constrained with a bimodal bivariate normality (sum of two Gaussian functions).
$$\eqalign{s_{{\rm tot}} & = \sum\limits_{i = 1}^2 {s_i \cdot} \cr & \quad \exp \left( { - \displaystyle{\matrix{(y - y_{0,i})^2/\sigma _{y,i}^2 + ({z}^{\prime} - z_{0,i}^{\prime} )^2/\sigma _{z^{\prime},i}^2 \hfill \cr + \,2 \cdot (\rho _i \cdot (y - y_{0,i}) \cdot ({z}^{\prime} - z_{0,i}^{\prime} )/\sigma _{y,i} \cdot \sigma _{z^{\prime},i}) \hfill} \over {2 \cdot (1 - \rho _i^2 )}}} \right)}$$
In Eq. (1) z′ with z′ = 2·z−1 and 0 ≤ z < 1 is used. The factors s 1 and s 2 scale the i th Gaussian function, the coordinates y 0 and z 0 are the position of a Gaussian function in the y–z-plane. The variance parameters σ i and the correlation coefficients ρ i provide the width and shape of the distribution function. A normalization factor, as it is commonly used in normal distributions, was omitted here because of the vividness of the constraints within the Rietveld refinement. Not all 12 refinables of this distribution function were refined each time. In many cases, s 2 or ρ i could be fixed to s 2 = 0 or ρ i = 1 without significant loss of fit quality.
For graphical representations of the results of the 121 fraction model the parameters of the bimodal bivariate normality were used to provide a smooth contour plot. This was achieved by using the program MATLAB (MATLAB, 2014).
For the different fractions the metric parameters and the atomic positions were linearly interpolated between two references (Li z M 0.5Fe0.5PO4 and Na z M 0.5Fe0.5PO4 with z = 1 or z = 0.5) in case of the 11 fraction model or between all four references (z = 1 and 0.5) in case of the other two models. The thermal vibration factors, the microstructural parameters and a preferred orientation along (1 0 0), described by a March Dollase equation, were constrained to the same values for all fractions and refined. An overview of the parameterization in the Rietveld refinements is given in the supplemental data (see online Table SI-IX).
The complexity of the model attributes to the poor refinement result of simpler approaches in respect to all measurements regarded. The effect of using one triphylite-type phase with isotropic or anisotropic line broadening and a double-Voigt model for microstructural parameters in comparison with the 121 fraction model is demonstrated on one example in the supplemental data (see online Figure SI-1). Despite of just modelling strain by line width parameters, this sophisticated model also provides a deeper physical meaning.
B. The compounds A z Co0.5Fe0.5PO4
All steps of oxidation or reduction result in a triphylite-type compound. As mentioned before, the distinct diffraction peaks from the first two steps broaden significantly throughout later stages of the synthesis (Figure 3). Via ssr pristine LiCo0.5Fe0.5PO4 was achieved. The derived metric parameters are in agreement with roughly estimated values extracted from a figure by Strobridge et al. (Reference Strobridge, Liu, Leskes, Borkiewicz, Wiaderek, Chupas, Chapman and Grey2016) (Table I). The mean molecular formulae of the multi-fraction phases given in this work were calculated from the results of the 121 fraction model.
(Colour online) Part of the PXRD patterns of the different synthesis steps: LiCo0.5Fe0.5PO4 (step 1), Li0.5Co0.5Fe0.5PO4 (step 2), Li0.47Na0.53Co0.5Fe0.5PO4 (step 3), Li0.25Na0.28Co0.5Fe0.5PO4 (step 4), Li0.26Na0.74Co0.5Fe0.5PO4 (step 5), Li0.25Na0.51Co0.5Fe0.5PO4 (step 6), Li0.24Na0.76Co0.5Fe0.5PO4 (step 7), and hkl-markers of LiCo0.5Fe0.5PO4.
Metric parameters of LiCo0.5Fe0.5PO4 and Li0.5Co0.5Fe0.5PO4. Estimated from Strobridge et al. (Reference Strobridge, Liu, Leskes, Borkiewicz, Wiaderek, Chupas, Chapman and Grey2016).
Delithiation of LiCo0.5Fe0.5PO4 with bromine results in Li0.5Co0.5Fe0.5PO4. Owing to the higher redox potential of Co3+/Co2+ in comparison with Fe3+/Fe2+ only Fe is oxidized leading to the deintercalation of only half of the Li. This is equivalent to the change of the cell voltage for z = 0.5 reported by Strobridge et al. (Reference Strobridge, Liu, Leskes, Borkiewicz, Wiaderek, Chupas, Chapman and Grey2016). Figures 4(a) and 4(b) illustrate the weight fractions (wt-%) of the triphylite-type fractions with different alkaline contents according to the Rietveld refinement. It can be seen that in the case of the first synthesis step (ssr) solely a single fraction (more precisely: wt-% > 98%) with one Li [y = 0 and z = 1 in Li(1−y)·z Na y·z Co0.5Fe0.5PO4] is determined by the fraction model, while for the second synthesis step (delithiation) only a fraction with half a Li (y = 0; z = 0.5) is yielded. Upon sodiation of the semi-delithiated compound with Na2S the formerly narrow reflections broaden. In contrast to the previous compounds, the XRD data of the new compound (step 3) could not be interpreted with a single-fraction phase. A model of various fractions with different Li-to-Na-ratios was necessary to fit the data properly. All fractions seem to be saturated with alkaline (z = 1) but differ in Li- and Na-content (0 ≤ y ≤ 1). Figures 4(c) and 5(a) show that there is a maximum of the weight fraction around the composition Li0.5Na0.5Co0.5Fe0.5PO4, resulting in a compound with the mean molecular formula Li0.47Na0.53Co0.5Fe0.5PO4. A possible explanation for these broad reflections might be diffusion problems because of the particle size since the educt for those oxidation and reduction processes is LiCo0.5Fe0.5PO4 obtained via a high-temperature ssr. In step 4 [Figure 4(d)], a compound with the composition Li0.25Na0.28Co0.5Fe0.5PO4 was obtained instead of the target-composition Na0.5Co0.5Fe0.5PO4 (Figure 1). In contrast to the theoretical synthesis route, Li was not exclusively deintercalated, but the alkaline ions were extracted rather unselectively. However, it can be seen that within the accuracy of the model half of the alkaline was deintercalated and therefore all of the Fe was oxidized. The sodiation in step 5 yielded Li0.26Na0.74Co0.5Fe0.5PO4 [Figure 4(e)] reducing Fe again. However, despite of an excess of Na2S, it was not possible to displace Li from the compound (e.g. through ion exchange). In order to increase the Na content in the triphylite-type compound, another oxidation and reduction step was conducted. As can be seen in Figure 4(f), it was not possible to oxidize the Fe completely anymore, resulting in a compound of the composition Li0.25Na0.51Co0.5Fe0.5PO4 instead. Containing more than half of an alkaline but less than one alkaline, the 11 fraction model was not suitable anymore. Therefore, the 36 fraction model and ultimately the 121 fraction model allowing an even higher resolution was used to refine the PXRD data. It is noteworthy that beside the fact that not all of the Fe was oxidized, Na was deintercalated rather selectively in this step. A possible explanation might be that because of diffusion problems the intercalated Na builds up a shell-like barrier around a core of Li-rich fractions, blocking diffusion paths for smaller ions and leading to a preferred deintercalation of Na if the compound is Na-rich. Because of this blockade in step 7 [Figure 4(g)], the Na content could not be further increased resulting in a composition similar to the fifth reaction step, Li0.24Na0.76Co0.5Fe0.5PO4. The compounds of step 1 to step 5 could be refined with similar results for all three models. But the product in step 6 made it necessary to use a model that provides fractions with an alkaline content between 0.5 and 1. The model with 36 fractions provides such fractions but enables a lower resolution than the 121 fraction model [Figures 5(b) and 5(c)]. A model with higher resolution without constraining the individual scaling factors (as this is the case for the 36 fraction model) would cause overparameterization and no stable refinement. Therefore, the scaling factors were constrained by a bimodal bivariate normality in the 121 fraction model and the compositions of the triphylite-type phases were calculated by the 121 fraction model as described above. The Rietveld plots of two of the reaction steps are shown exemplary in online Figure SI-2 and SI-3 in the supplemental data.
(Colour online) Distribution of Li- and Na-contents of the triphylite-type compounds Li(1−y)·z Na y·z Co0.5Fe0.5PO4 based on the refinements obtained from the 121 fraction model for (a) step 1, (b) step 2, (c) step 3, (d) step 4, (e) step 5, (f) step 6, and (g) step 7.
(Colour online) (a) Distribution of weight fractions of step 3 according to the 11 fraction model and comparison of results of step 6 according to (b) the 36 fraction model, and (c) the 121 fraction model.
C. The compounds A z Mn0.5Fe0.5PO4
In contrast to NaCo0.5Fe0.5PO4 triphylite-type NaMn0.5Fe0.5PO4 could be synthesized as a reference material according to Lee et al. (Reference Lee, Ramesh, Nan, Botton and Nazar2011). Desodiation of this molten salt product with bromine in acetonitrile yielded Na0.5Mn0.5Fe0.5PO4, another reference material for the multi-fraction model. LiMn0.5Fe0.5PO4 prepared via an ssr was used as a starting material for the cyclic chemical oxidation and reduction process. In accordance with the previous results, all five steps of the cyclic synthesis route yielded triphylite-type compounds Li(1−y)·z Na y·z Mn0.5Fe0.5PO4 with sharp reflections in the first two steps and peak broadening in the later steps (Figure 6). The first two steps led to a single-fraction phase with one Li [y = 0; z = 1; Figure 7(a)] and a single-fraction phase with half a Li [y = 0; z = 0.5; Figure 7(b)]. Mn2+ seemed not to be oxidized with bromine in this coarse-grained sample. A comparison of the metric parameters of those two compounds with data from literature is given in Table II. The differences might be because of a slightly different ratio of transition metals. The large ionic radius of Mn compared with Fe leads to an increase in lattice parameters with higher amounts of Mn. Analogous to the Co-containing compound, sodiation of the semi-delithiated compound yielded a product with different fractions with a distribution of alkaline contents [z = 1; 0 ≤ y ≤ 1; Figure 7(c)] resulting in the average molecular formula Li0.48Na0.51Mn0.5Fe0.5PO4. It is noteworthy that the larger Mn2+ did not enable a smaller distribution width. In contrast to the Co-containing compounds, step 4 already led to an alkaline content z between 0.5 and 1 (Li0.50Na0.23Mn0.5Fe0.5PO4) with a broad distribution of different triphylite-type fractions [Figure 7(d)]. The product from a low-temperature molten salt reaction (enabling the desodiation to Na0.5Mn0.5Fe0.5PO4) had smaller grains [crystallite size according to the Rietveld refinement: L vol = 47(2) nm] and therefore shorter diffusion paths than a sample yielded by a high-temperature ssr [L vol = 188(4) nm]. Although crystallite size L vol and grain size D are different properties, a correlation between both properties may be assumed. The length of the diffusion paths might be the reason for the passivation by Na in the ssr-sample. Na is deintercalated exclusively (step 4) resulting in a similar composition [Li0.49Na0.51Mn0.5Fe0.5PO4; Figure 7(e); Rietveld plot see online Figure SI-4 in the supplemental data] after a new sodiation process (step 5) as for step 3. The main difference between the samples of steps 3 and 5 is a differentiation to a more Li-rich and a more Na-rich group of fractions in step 5. Probably the passivation because of Na was preventing the synthesis of a compound with a higher Na content via this route using coarse-grained material.
(Colour online) Part of the PXRD patterns of the different synthesis steps: LiMn0.5Fe0.5PO4 (step 1), Li0.5Mn0.5Fe0.5PO4 (step 2), Li0.48Na0.53Mn0.51Fe0.5PO4 (step 3), Li0.50Na0.23Mn0.5Fe0.5PO4 (step 4), Li0.47Na0.53Mn0.5Fe0.5PO4 (step 5), and hkl-markers of LiMn0.5Fe0.5PO4.
(Colour online) Distribution of Li- and Na-contents of the triphylite-type compounds Li(1−y)·z Na y·z Mn0.5Fe0.5PO4 based on the refinements obtained from the 121 fraction model for: (a) step 1, (b) step 2, (c) step 3, (d) step 4, and (e) step 5.
Metric parameters of LiMn0.5Fe0.5PO4 and Li0.5Mn0.5Fe0.5PO4.
According to Shannon (Reference Shannon1976) the ionic radius for high spin Mn2+ with r(VIMn2+) = 0.830 Å is higher than the radius of the equivalent Co2+ ion with r(VICo2+) = 0.745 Å. Accordingly the volume of the unit cell of LiMn0.5Fe0.5PO4 is about 10 Å3 higher than for LiCo0.5Fe0.5PO4. Because of the higher ionic radius of Mn2+, also a higher diffusion of alkaline ions might be expected in the steps after step 3. However, the opposite was observed and future research may resolve this contrariety.
IV. CONCLUSION
The synthesis of Na-containing triphylite-type compounds via a cyclic synthesis route of chemical oxidation and reduction starting from LiM 0.5Fe0.5PO4 prepared via solid-state synthesis (M = Mn, Co) was achieved. Intercalation of Na into Li0.5 M 0.5Fe0.5PO4 and the following Li- and Na-containing triphylite-type compounds led to a peak broadening, caused by the presence of a distribution of phases of the type Li(1−y)·z Na y·z M 0.5Fe0.5PO4 with different alkaline contents. The term “fraction” instead of “phase” may be preferred because a continuum of states with the same structure-type exists. Multi-fraction models were developed and enhanced to evaluate the XRD data. If the alkaline content z was z = 0.5 or 1 an 11 fraction model with individually refined scaling factors for the 11 fractions proved to be suitable. For complex distributions of the alkaline content and Li-to-Na ratios a model of 121 fractions with constraining the scaling factors by a bimodal bivariate normality provided reliable results.
Because of the unselective deintercalation of alkaline ions a passivation by Na-rich shells in the grains of the coarse-grained material may be assumed. The synthesis of Li-free triphylite-type NaM 0.5Fe0.5PO4 was not possible by this route. The triphylite-type phase with the highest Na content achieved by cyclic chemical redox reactions yielded phases showing the mean compositions Li0.24Na0.76Co0.5Fe0.5PO4 and Li0.49Na0.51Mn0.50Fe0.5PO4. The passivation by Na possibly may be minimized by using fine-grained precursors instead of coarse-grained materials synthesized via high temperature ssr.
SUPPLEMENTARY MATERIAL
The supplementary material for this article can be found at https://doi.org/10.1017/S0885715617000355.
ACKNOWLEDGEMENTS
The authors thank the Graduiertenförderung der Universität des Saarlandes for financial support and Jonas N. Becker (Universität des Saarlandes) for support in preparing the MATLAB figures.
