Complex Polymorphism and Polytypism of Potassium Metaarsenate

Article pubs.acs.org/crystal

Complex Polymorphism and Polytypism of Potassium Metaarsenate, KAsO3 Berthold Stöger*,† and Michal Dušek‡ †

Institute of Chemical Technologies and Analytics, Department of Structural Chemistry, Vienna University of Technology, Vienna, Austria ‡ Institute of Physics, Department of Structure Analysis, Academy of Sciences, Prague, Czech Republic S Supporting Information *

ABSTRACT: The dehydration of KH2AsO4 to KAsO3 and the complex temperaturedependent polymorphism of KAsO3 were investigated by high-temperature X-ray powder diffraction. Four of the five KAsO3 polymorphs were structurally characterized by single crystal or powder X-ray diffraction and are described with attention to polytypism and structurally related phases. On heating, KH2AsO4 subsequently transforms into γ- (150−200 °C), β- (370− 410 °C) and finally α-KAsO3 (500−510 °C) before melting at 640−650 °C. The dehydration is accompanied by formation of minor amounts of δ- and β-KAsO3. On cooling, α-KAsO3 subsequently transforms into δ-KAsO3 (320−300 °C) and γ-KAsO3 (starting at 270 °C). The α → β transformation was only observed on prolonged heating at 470 °C. The β-KAsO3 phase reversibly transforms into the metastable β′-KAsO3 below 250 °C. β-KAsO3 can be stabilized at lower temperatures by partial substitution of Rb for K. α- and γ-KAsO3 are long-chain polyarsenates with repetition period 2. The crystal structures can be derived from H-MPO3 (M = K, Rb) and the pyroxene orthoenstatite, respectively. The β- and β′-KAsO3 phases feature cyclotriarsenate units with approximately 3m (β-KAsO3) and 2 (β′-KAsO3) symmetry. Both β- and β′-KAsO3, are polytypic order−disorder structures composed of nonpolar layers of one kind. The major polytypes are of a maximum degree of order. Alternative stacking sequences are observed by twinning.

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INTRODUCTION The crystal chemistry of condensed phosphates(V) is multifarious, rivaling the structural richness of silicates. A comprehensive review of the polymorphism of condensed phosphate(V) anions was compiled by Durif.1 A similar complexity can be expected for arsenates(V) with the additional occurrence of octahedral coordination.2 Nevertheless, significantly less structural data are available for the latter [ca. 915 vs 175 entries describing ternary phosphates and arsenates, respectively, in the 2013-2 version of the ICSD3]. Whereas for example the structures of the meta-phosphates of monovalent metals MPO3 have been intensely studied, the crystal chemistry of the corresponding arsenates MAsO3 is much less understood. Only the crystal structures of two polymorphs of LiAsO34,5 and one polymorph of NaAsO36 and AgAsO37 have been determined up to now, whereas the structures of the higher homologues (M = K, Rb, Cs, Tl) are unknown. Structural data of cycloarsenates are particularly rare, since the methatesis reaction from aqueous solution8 which has been fruitfully applied to cyclophosphates1 is not applicable to arsenates due to hydrolysis of the As−OAs bonds. Thilo and Dostál established the thermal stability ranges of three KAsO3 polymorphs, viz., α-, β-, and γ-KAsO3.9 Lacking structural data from single crystal diffraction, the nature of the anionic building blocks of the three polymorphs was determined by astute paper chromatography of solid solutions K(As,P)O3 (the pure As phase cannot be used due to hydrolysis of the As−OAs bonds) and by comparison of © 2014 American Chemical Society

the X-ray powder diffraction patterns (XRPD) with the corresponding phosphates:10 Accordingly, whereas the high and low temperature phases (α- and γ-KAsO3) are long-chain arsenates composed of 1∞[AsO3]− chains, the intermediate βKAsO3 is made up of [As3O9]3− cyclotriarsenate ions. Duquenoy and Josien synthesized two KAsO3 polymorphs,11 which they likewise identify as a long-chain and a cyclotriarsenate by similarity of the diffraction patterns with those of the corresponding phosphates. This remarkable behavior of KAsO3, viz., a long-chain arsenate converting on heating into a cyclotriarsenate and on further heating back into a long-chain arsenate, and the general lack of structural data of cyclotriarsenates made us interested in structural investigations of these KAsO3 polymorphs. A further motivation for the structural characterization of KAsO3 stems from our interest in polytypism. Polytypism is a special kind of polymorphism, whereby polytypes are composed of different stackings of equivalent layers (or, more generally, rods or blocks).12 Polytypes are frequently observed in all classes of compounds ranging from minerals, inorganics, metal−organics and organics to biomacromolecules and are therefore of great technological and theoretical importance. The order−disorder (OD) theory13 was developed in the 1950s to explain the universal occurrence of polytypes and to extend Received: May 20, 2014 Revised: June 16, 2014 Published: August 18, 2014 4640

dx.doi.org/10.1021/cg500733w | Cryst. Growth Des. 2014, 14, 4640−4657

Crystal Growth & Design

Article

Table 1. Crystal Data for β-, β′-, and γ-KAsO3 and β-K0.8Rb0.2AsO3 β-KAsO3 λ/Å T/°C space group, no. formula units Z a/Å b/Å c/Å α/° β/° γ/° V/Å3 formula weight μ/mm−1 Dcalcd /g cm−3 R (Fo, I > 3σ(I)) wR (Fo, all)

β-K0.8Rb0.2AsO3

300 B1,̅ 2 12 9.192(4) 10.285(4) 11.992(3) 105.74(3) 90.00(4) 103.69(4) 1057.7(7) 162.0 10.63 3.051 0.1200 0.1610

67 B1,̅ 2 12 9.0742(17) 10.2593(17) 12.007(4) 105.375(8) 90.02(3) 104.188(8) 1042.4(5) 171.4 13.35 3.275 0.0424 0.0458

γ-KAsO3

27 P21/c, 14 24 8.9748(3) 19.1172(6) 12.1660(3) 90 90.1844(18) 90 2087.35(11) 162.0 10.91 3.131 0.0314 0.0336

−173 Pbcn, 60 8 11.32460(10) 11.4255(4) 4.8816(3) 90 90 90 631.63(5) 162.0 11.87 3.406 0.0257 0.0445

removed from the oven and immediately submerged in perfluorinated oil to avoid rehydration. β-KxRb1−xAsO3 single crystals were grown similarly to β′-KAsO3 by tempering a well ground mixture of 0.855 g (4.75 mmol) of KH2AsO4 and 0.057 g (0.25 mmol) of RbH2AsO4. From the resulting sample, single crystals isotypic with β-KAsO3 and γKAsO3 were isolated, and XRPD measurements confirmed the existence of both phases. Only the former were used for structural elucidation. Single Crystal Diffraction. Crystals were embedded in a quick drying epoxy adhesive and attached to a glass fiber. Generally, the crystals featured arcing of reflections, whereby the situation was worse for γ-KAsO3, with arcing up to 20° (Figure S3). Nevertheless, by testing numerous crystals we were able to obtain tiny fragments featuring sharp diffraction spots with no (β′-KAsO3 and βKxRb1−xAsO3) and little (γ-KAsO3) arcing, which were used for structure elucidation. Diffraction intensities were collected on a Bruker APEX II diffractometer (κ-geometry, Mo Kα̅ radiation) equipped with a CCD detector under a dry stream of nitrogen. Data sets of β′KAsO3 and γ-KAsO3 were collected at −173 °C. Because of inconsistencies of single crystal and powder diffraction data of β′KAsO3 at elevated temperatures, additional data of a β′-KAsO3 crystal were collected at 27 and 177 °C. All three β′-KAsO3 models were virtually equivalent. The 27 °C measurement was used as the basis for the structural description given below. Moreover, data of a βKxRb1−xAsO3 crystal were collected at 76 °C. High temperature single crystal diffraction experiments were performed on an Oxford GEMINI diffractometer (κ-geometry, Mo Kα̅ radiation). β′-KAsO3 crystals were slowly heated to 300 °C, whereby the epoxy glue carbonized. While transforming into β-KAsO3, the crystals fractured and usually featured four or more domains and very weak diffraction intensities. Only after numerous collected data sets, a sample with negligible contribution of secondary domains was found. Despite splitting of reflections and weak intensities, this sample provided the most satisfying structural data, which therefore is the basis of the following discussion. Generally, data were reduced using SAINT-Plus,18 and an absorption correction was applied using the multiscan approach implemented in the SADABS program.18 For β-KAsO3 the CrysAlis RED and CrysAlis PRO software packages19 were used instead. The structures were solved by charge flipping implemented in SUPERFLIP20 and refined against F-values with JANA2006.21 An initial model for β-KxRb1−xAsO3 was generated from the atomic coordinates of the isotypic β-KAsO3. The O atoms in the β′-KAsO3 structure at −173 °C were modeled using isotropic displacement parameters, due to unrealistic anisotropic displacement parameters (ADPs) of two O atoms (a virtually 0 eigenvalue of the ADP tensor). The K and As atoms and all atoms in the remaining structures were refined with

space group symmetry to families of polytypic structures (although not all polytypes can be reasonably described according to the OD formalism). If layers possess higher local symmetry than the overall structure, the stacking of the layers becomes ambiguous. Then an infinity of polytypes exists which are locally geometrically equivalent and as a consequence likewise energetically equivalent if long-range interactions are neglected. In our current line of research, we are investigating the application of OD theory to polytypic structures, to identify its limits and possibly extend it. For example, OD structures of layers with different lattices have received very little consideration, despite examples like KH2AsO4·2H2O.14 Moreover, we have found crystal structures which meet the basic criteria of OD structures, i.e., polytypes with equivalent local symmetry but which do not strictly follow the definition of classic OD theory.15,16 Polytypism of the long-chain silicate wollastonite (CaSiO3) and the isotypic long-chain phosphate NaPO3 (Madrell’s salt) and arsenate NaAsO3 sparked the development of OD theory.17 Therefore, we decided to structurally characterize the isoformular KAsO3 in search of possible OD structures as model compounds. In the present work, we reexamined the temperaturedependent polymorphism of KAsO3 and identified, besides the three polymorphs described by Thilo and Dostál,9 two additional polymorphs. Moreover, we elucidated the structures of four of the five polymorphs by X-ray single crystal and powder diffraction.

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β′-KAsO3 0.71073

EXPERIMENTAL SECTION

KH2AsO4 and RbH2AsO4. A solution of 5 g of 80%wt aq H3AsO4 in 20 mL of H2O was titrated against a ∼20%wt aq KOH solution using a drop of methyl red dissolved in EtOH as an indicator (end point: persistent color change from red to yellow). The solution was evaporated to dryness, and the residue was titurated with EtOH and recrystallized from water to grow large crystals of KH2AsO4 (single phase according to XRPD, Figure S1, Supporting Information). Single phase RbH2AsO4 (Figure S2, Supporting Information) was obtained in a similar way using a concentrated aq RbCO3 solution. β′-, γ-KAsO3, and β-KxRb1−xAsO3 Single Crystals. β′- and γKAsO3 single crystals were grown by prolonged heating of finely ground KH2AsO4 in gold crucibles. β′-KAsO3 was obtained by heating at 580 °C for 4 days followed by 470 °C for 1 week; γ-KAsO3 by heating for 2 weeks at 580 °C. The samples were then quickly 4641



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ADPs. The β′-KAsO3 phase was refined as a twin by pseudomerohedry with a mirror plane normal to [100] as a twin element. For β-KAsO3 and β-KxRb1−xAsO3, the nonstandard B1̅ setting of the P1̅ space group was used to highlight the structural relationship with β′KAsO3, for a clearer description of the OD layers (in the chosen settings two lattice vectors are parallel to the layer planes) and to demonstrate the pseudorectangular metrics of these layers. The chosen setting (a, b, c) is related to the reduced standard setting (ar,br,cr) by

refinement was performed using TOPAS.26 The lattice parameters and the isotropic displacement parameters of all atoms were freely refined. The As−O bond lengths were restrained to 1.66 and 1.77 Å for the terminal and bridging O atoms, respectively. Moreover, the O−O distances were restrained to 2.75 (terminal to bridging and terminal to terminal) and 2.66 Å (bridging to bridging). Details of the refinement are collected in Table 2. A comparison of measured and calculated

Table 2. Crystal Data for α-KAsO3

⎛ 100 ⎞ ⎜ ⎟ (a , b , c) = (a r , br , cr)⎜ 1̅ 0 1̅ ⎟ ⎜ ⎟ ⎝ 010 ⎠

α-KAsO3 λ/Å T/°C space group, no. formula units Z a/Å b/Å c/Å V/Å3 formula weight profile, Rp weighted profile Rwp derived Bragg R-factor, RBobs

Sincedue to the weak intensities and large ADPsthe positions of the O atoms in the β-KAsO3 structure were inaccurately determined, the As−O distances were constrained to approximately those of the β′-KAsO3 refinement (1.760(1) and 1.620(1) Å for bridging and terminal O atoms, respectively). The cationic positions in β-KxRb1−xAsO3 were refined as occupationally disordered with the sum of the occupancies of each position constrained to 1. Since two out of three sites refined to full occupancy of K within the estimated standard uncertainty, these positions were refined using only K in the final refinement cycles. The total stoichiometry of the crystal refined to K0.798(2)Rb0.202(2)AsO3. For simplicity, this solid solution will henceforth be designated as K0.8Rb0.2AsO3. The basic crystal data are compiled in Table 1. The final models and more data collection and refinement details for all data sets, including β′-KAsO3 measured at −173 and 177 °C, are available as Supporting Information in tabular form and as CIFs. Powder Diffraction. High temperature XRPD experiments were performed on a Panalytical X’Pert Pro diffractometer equipped with an Anton Paar HTK-1200N high temperature chamber with Kapton window in Bragg−Brentano geometry using Cu Kα1,2 radiation (λ = 1.540598, 1.544426 Å) and an X’celerator multichannel detector. The sample height adjustment was calibrated using a NIST LaB6 standard, and the temperature control was verified with a thermocouple attached to an empty crucible. A circular Macor sample holder (16 mm diameter, 0.8 mm depth) was filled with finely ground KH2AsO4. For an experiment involving heating above the melting point of KAsO3, a sample holder sputtered with Pt was employed to diminish creeping of the melt. The measurements were performed under atmospheric pressure of air or under a vacuum provided by a two-stage membrane pump (ca. 2 mbar). Unless noted otherwise, the figures and crystallographic data were obtained from measurements performed under a vacuum. Scans were recorded in the 2θ = 10−70° range with 2.122° scan length and 50.165 s exposure time per scan length. They were converted into 0.0167° step-size bins. Between measurements, the samples were heated or cooled with 10 K/min and then kept for 10 min in isothermal regimen. To rule out reaction of the sample with the sample holder, the postmeasurement residue was dissolved in water. In general, practically clear solutions with negligible amounts of insolubles were obtained and only KH2AsO4 could be detected by XRPD after evaporation to dryness. When heating above the melting point of KAsO3, on the other hand, significant amounts of K3Al2As3O1222 and minor amounts of unidentified phases were obtained (Figure S4, Supporting Information). An XRPD pattern of α-KAsO3 was recorded at 470 °C in the 2θ = 10−80° range with an increased exposure time of 200 s per scan length. The pattern was indexed using Monte-Carlo methods with the McMaille software.23 The resulting orthorhombic cell is closely related to the cells of the high temperatures Pbnm phases H-KPO324 and HRbPO3.25 Yet, the (011) and (102) reflections were distinctly observed, precluding the existence of the b- and n-glides. The systematic absences of the 21 screws in all three directions on the other hand were valid, suggesting the maximal subgroup P212121 of Pbnm. Thus, an initial model was generated by reducing the symmetry of HKPO3 to P212121 and replacing the P atom with an As atom. Rietveld

1.540598, 1.544426 470 P212121, 14 4 13.23064(18) 4.69441(6) 6.06492(9) 376.693(9) 162.0 0.0167 0.0280 0.0409

intensities is depicted in Figure 1. The final model and more data collection and refinement details are available as Supporting Information in tabular form and as CIF.

Figure 1. Rietveld refinement of α-KAsO3 at 470 °C. Measured data points are represented by small circles, computed and difference curves by black and gray lines. The calculated positions of the Bragg reflections are represented by blue ticks. Thermogravimetry. KH2AsO4 (20 mg) was subjected to thermogravimetric analysis (TGA) on a NETZSCH Tarsus F3 thermobalance. The sample was heated under a N2/O2 (80:20) atmosphere in an Al2O3 crucible from 30 to 600 °C with a 1 K/min heating rate. Moreover, differential scanning calorimetry measurements were performed on a NETZSCH DSC 200 F3. However, due to the kinetically inhibited phase transitions of KAsO3, the results were inconclusive and will not be expanded upon.

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RESULTS AND DISCUSSION Phase Transitions and Bulk Samples. Overview. The thermal behavior of KAsO3 is complex and marked by kinetically inhibited phase transitions. As mentioned in the introduction, according to Thilo and Dostál three distinct KAsO3 polymorphs exist:9 the low temperature phase γ-KAsO3, stable up to 430 °C; the intermediate phase β-KAsO3, stable up 4642



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Figure 2. Overview of the phase transitions observed in the KH2AsO4/KAsO3 system. Arrows pointing right and left indicate phase transitions on heating and cooling, respectively. Solid arrows indicate phase transitions during the standard heating program (10 K/min) and independent from pressure (vacuum or atmospheric pressure of air). Dashed arrows indicate phase transitions under isothermal regimen, or observed only under either a vacuum or atmospheric pressure of air, as indicated on top of the arrow. The minor amounts of β-KAsO3 obtained on dehydration of KH2AsO4 cannot be differentiated from β′-KAsO3 on the basis of the available data.

to 530 °C and metastable at room temperature; and the high temperature phase α-KAsO3. On heating of the sample, the authors observed the phase transitions α → β → γ. α-KAsO3 transformed into γ-KAsO3 on quenching or into β-KAsO3 on prolonged heating at 430−450 °C. Although we observed two additional polymorphs and a distinctly more complex phase transition behavior, our experiments are consistent with the results of Thilo and Dostál,9 and we will therefore use their nomenclature of the KAsO3 polymorphs. The two additional polymorphs will be denoted as β′- and δ-KAsO3. An overview of the phase transitions according to our high temperature XRPD experiments is given in Figure 2. The diffraction pattern of the β′-KAsO3 polymorph is in good agreement with the powder diffraction data of K3As3O9 reported by Duquenoy and Josien.11 Thus, it is unclear whether the authors indeed obtained, as they supposed, a phase isotypic to the cyclotriphosphate K3P3O9 or the non-isomorphous β′KAsO3 phase. We were unable to assign the diffraction pattern of the KAsO3-β phase with similar d-spacings reported by the same authors to any of the phases that we observed. Dehydration. KH2AsO4 dehydrates in the 150−200 °C temperature range according to KH 2AsO4 → KAsO3 + H 2O

whereby the major product is γ-KAsO3 (Figure 3). Whereas according to thermogravimetry the dehydration starts at ∼130 °C (Figure 4), in XRPD scans the first peaks from phases other than KH2AsO4 are observed at 150 °C. The dehydration proceeds in two distinct steps. At first small peaks of an intermediate phase appear (Figure 3). Because of the weak intensities, the assignment of these peaks is difficult. Nevertheless, they are in good agreement with the diffraction pattern of the δ-KAsO3 polymorph, which we also observed during cooling as described below. The stability of δ-KAsO3 during the dehydration process is dependent on the ambient pressure: under a vacuum δ-KAsO3 slowly transforms into γ-KAsO3 at 180 °C, but minor amounts of the phase exist up to the γ → β phase transition (Figure 3a). Under atmospheric pressure of air, on the other hand, the δ-KAsO3 and the reflections attributed to it quickly vanish (Figure 3b). The first peaks that can be attributed to γ-KAsO3 appear at 170 °C. Simultaneously with γ-KAsO3, traces of β- or β′-KAsO3 are formed, observed by peaks located at 2θ = 25.94, 26.57, and

Figure 3. Dehydration of KH2AsO4 to KAsO3 under (a) vacuum and (b) atmospheric pressure of air. The 13° < 2θ < 24.5° ranges of XRPD scans collected at 10 K intervals from 100 to 300 K are shown. Reflections that were assigned to the KH2AsO4, γ- and δ-KAsO3 phases are marked with *, γ, and δ symbols, respectively. Reflections of KH2AsO4 have been truncated since they are an order of magnitude more intense than the γ- and δ-KAsO3 reflections.

28.12°. A differentiation between β- and β′-KAsO3 is not possible due to a lack of intensity and since the strongest peaks of both phases appear at close 2θ values. In measurements under atmospheric pressure of air, no reflections attributed to KH2AsO4 or δ-KAsO3 can be observed above 190 °C, and thus virtually single phase γ-KAsO3 with 4643



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Heating. γ-KAsO3 and remaining traces of δ-KAsO3 slowly transform into β-KAsO3 during 370−410 °C in a reconstructive phase transition (Figure 6a). The β-KAsO3 phase then

Figure 4. TGA curve of KH2AsO4 in the 100−200 °C range with a heating rate of 1 K/min. The mass loss of 10.0% is higher than the expected value for the KH2AsO4 → KAsO3 + H2O dehydration (8.8%), most likely due to evaporation of adsorbed water.

traces of β- or β′-KAsO3 can be obtained (Figure 5). In contrast, the exact end of the dehydration cannot be

Figure 6. Color mapped plots of XRPD scans of KAsO3 measured at 10 K intervals. Temporally subsequent scans are arranged from bottom to top. (a) Heating from 200 to 580 °C. (b) Cooling from 560 to 100 °C. The scans in (b) have been corrected for a sample height increase of 0.45 mm. Colors vary from yellow over red and blue to black.

Figure 5. Rietveld refinement of γ-KAsO3 and traces of β′-KAsO3 at 300 °C, obtained by heating under atmospheric pressure of air. Atom coordinates were taken from single crystal data collected at −173 °C; the lattice parameters were refined to a = 11.4364(8) Å, b = 11.5740(8) Å, c = 4.9465(3) Å. Measured data points are represented by small circles, computed and difference curves by black and gray lines, respectively. Reflections attributed to β′-KAsO3 are marked by a *. Refining with a structural model of β- instead of β′-KAsO3 led to virtually identical calculated intensities.

transforms abruptly into the α-KAsO3 phase at 500−510 °C. Starting at 470 °C, up to the β → α phase transition an apparent shift of scattering angles toward smaller 2θ values is observed, which is too pronounced to be adequately explained by an enlargement of the unit cell (Figure 6a). Indeed, the shift is persistent after cooling and can therefore be attributed to an increase of the sample height. The effect is accompanied by a sharpening of the reflections (Figure 7, middle curve), hinting toward crystallization processes. The sample height increase was assessed in measurements involving heating above 470 °C by comparison of diffraction patterns of identical phases at identical temperatures on heating and cooling. It varied in the range of ∼0.40−0.70 mm. On further heating, a broad signal of an amorphous phase appears at 640 °C, indicative of melting. At 650 °C, the entire sample is molten, in good agreement with the reported value of 660 °C.9,11 Cooling. On cooling of the melt, the sample spontaneously crystallizes at 580 °C to α-KAsO3. The crystallized sample features extreme texture: virtually only (h00) reflections are in Bragg condition. α-KAsO3 does not readily transform back to β-KAsO3 on further cooling. Indeed, with our standard temperature program, no α → β transition has been observed.

determined for measurements under a vacuum, since the most intense reflections of KH2AsO4 overlap with reflection of δ-KAsO3 or γ-KAsO3. In contrast to for example CsH2PO4, which dehydrates via a Cs2H2P2O7 (=̂ CsPO3·(1/2)H2O)27 intermediate, we could not identify any crystalline intermediate hydrous phase: To our knowledge no structural data of KAsO3·nH2O phases with 0 < n < 1 have been reported up to now, and attempts to relate the peaks that we did not attribute to γ-KAsO3 to the diffraction patterns of the hydrous phosphate phases K2H4P2O728 and K2H4P2O7·H2O29 were unsuccessful. Thermogravimetric analysis confirms the lack of intermediate phases: Even with low heating rates of 1 K/min, we did not observe any steps in the dehydration curve (Figure 4). 4644



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at 100 °C minor amounts of δ-KAsO3 remain (Figure 8b). As opposed to the dehydration process, the stability of the δKAsO3 phase on cooling is not dependent on ambient pressure. Whereas no β-KAsO3 was obtained using our standard temperature program, as already noted by Thilo and Dostál, αKAsO3 converts slowly to β-KAsO3 when heating for a prolonged time slightly below the β → α transition temperature.9 In Figure 9 XRPD measurements of α-KAsO3 at 450 °C

Figure 7. XRPD scans of β-KAsO3 measured at 460 °C (bottom), 500 °C (middle), and after conversion from α-KAsO3 at 450 °C (top) in the 2θ = 12−34° range showing distinct sharpening of reflections on heating. The middle and top scan were corrected for 0.45 mm and 0.65 mm sample height increase and moved along the ordinate for clarity.

Instead, the δ-KAsO3-phase forms at 320−300 °C (Figure 6b). Simultaneously minor amounts of γ-KAsO3 are formed (Figure 8a). δ-KAsO3 slowly transforms into γ-KAsO3 below at 270 °C. Whereas most of the δ-KAsO3 phase has converted at ∼200 °C, the conversion of the remaining δ-KAsO3 is sluggish, and even

Figure 9. 2θ = 12−17° range of XRPD scans of α-KAsO3 heated at 450 °C recorded at 55 min intervals. The scans have been corrected for a sample height increase of 0.65 mm.

performed at 55 min intervals are depicted. Peaks of β-KAsO3 can be observed at t = 3.7 h, and no more α-KAsO3 can be detected after a heating time of t = 13.8 h. The thus-obtained βKAsO3 is of distinctly higher crystallinity than the phase obtained during heating even after the crystallization effect involving sample height increase (Figure 7, top curve). On cooling, β-KAsO3 features a subtle, but distinct and reversible phase transformation into the low temperature phase β′-KAsO3, which is noticeable for example by a vanishing peak at 2θ = 20.6° and a peak appearing at 2θ = 20.1° (Figure 10a). The β- and β′-KAsO3 phases are metastable below the γ → β transition temperature. A direct conversion into the low temperature γ-KAsO3 was not observed in our experiments nor by Thilo and Dostál.9 Whereas the temperature range of the β′ → β transition on heating was consistently located at 250−270 °C (Figure 10b), the reverse β → β′ transition on cooling depends on the crystallinity of the sample: With highly crystalline β-KAsO3 obtained by prolonged heating of α-KAsO3, the phase transition has been observed slightly below the β′ → β transition temperature at 250−240 °C (Figure 10a). A less crystalline sample obtained by heating γ-KAsO3 to 480 °C, on the other hand, featured a strongly depressed phase transition point of 200−160 °C, one by heating to 420 °C converted only at 180−140 °C. To demonstrate the purity and correct structural assignment of the β- and β′-KAsO3 phases, powder data collected at 170 and 320 °C were refined against structural data from single crystals collected at 177 and 300 °C, respectively (Figure 11). No peaks that could not be attributed to the β- and β′-KAsO3 phases were observed. Whereas the fit of β-KAsO3 is convincing, the intensities of the computed and measured patterns of the β′-KAsO3 phase show discrepancies. A slightly improved, albeit still unsatisfactory, model was obtained by modeling the preferred orientation in the [010] direction. We attribute the mismatch of calculated and observed intensities to

Figure 8. XRPD scans of KAsO3 on cooling of the α-phase recorded at (a) 300 °C and (b) 100 °C in the 2θ = 12−42° range. Peaks attributed to γ-KAsO3 are marked by a γ-sign. The unmarked peaks in (a) and the peaks marked by a δ symbol in (b) are attributed to the δ-KAsO3 phase. Both scans have been corrected for a sample height increase of 0.45 mm. 4645



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Figure 11. Rietveld refinements of (a) β-KAsO3 and (b) β′-KAsO3 models from crystal data collected at 300 and 177 °C, against diffractograms collected at 320 and 170 °C, respectively. The lattice parameters were refined to (a) a = 9.2117(5) Å, b = 10.2854(6) Å, c = 7.5676(5) Å, α = 93.378(4)°, β = 52.411(3)°, γ = 76.064(4)° and (b) a = 9.0455(9) Å, b = 19.199(2) Å, c = 12.213(2) Å, β = 90.294(9)°. Minor texture in the [010] directions was modeled for β′-KAsO3 using the March−Dollase function. Measured data points are represented by small circles, computed and difference curves by black and gray lines, respectively.

Figure 10. Color mapped plots of XRPD scans of β- and β′-KAsO3 measured at 10 K intervals. β-KAsO3 was generated by heating αKAsO3 for 9 h at 450 °C. Temporally subsequent scans are arranged from bottom to top. (a) Cooling from 440 to 180 °C. (b) Heating from 190 to 440 °C. The scans were corrected for a sample height increase of 0.65 mm. Colors vary from yellow over red to black.

the polytypic nature of β′-KAsO3 (vide infra): Powder and single crystalline samples of polytypic compounds can feature distinctly different stacking sequences. Most notably, the powder may feature regions of disordered polytypes, and therefore the reflections attributed to ordered stacking sequences may be weaker or even missing.30 Indeed, the very strong reflection at 2θ ≈ 15° is common to all polytypes and thus indicates the existence of disordered polytypes. Nevertheless, attempts to describe the diffraction pattern with the models of various ordered, and disordered polytypes did not result in satisfying fits. Notably the reflection at 2θ = 28° is only explained by the ordered MDO2 and MDO4 polytypes (vide infra). Crystal Structures. Overview. We were able to solve and refine the crystal structures of the α-, β-, β′-, and γ-KAsO3 polymorphs. On the other hand, the powder diffraction pattern of δ-KAsO3 could not be reliably indexed up to now, nor were single crystals obtained. Nevertheless, due to the similarities of the XRPD patterns of α- and δ-KAsO3 as well as the sharp α → δ transition, we conclude that the phases are crystallochemically related. Thus, we were able to confirm the remarkable behavior of KAsO3 described by Grunze et al.:10 On heating, the long-chain arsenate γ-KAsO3 transforms into the cylcotriarsenate βKAsO3, which in turn transforms on further heating back into a long-chain arsenate, α-KAsO3. The chemically different

makeup of the arsenate anions in β- and β′-KAsO3 on one hand and in γ-KAsO3 on the other hand explains why the former are metastable at lower temperatures. Crystal Chemistry of the [AsO3]− Anion. In KAsO3, we observed four distinctly different kinds of anionic [AsO3]− frameworks. To our knowledge, for metaphosphates and -arsenates, such a rich polymorphism of the anionic network was only described for NaPO3, which is known to exhibit chains with period 3 in Madrell’s salt,31 4 in Kurrol’s salt,32,34 and cyclotriphosphate units in Na3P3O9.35 Whereas five long-chain polymorphs of KPO3 have been described,24,36,37 all of them feature the same kind of chain and differ only subtly by desymmetrization. The four kinds of anions in the KAsO3 polymorphs are depicted in Figure 12 with approximate phase transition temperatures: α-KAsO3 and γ-KAsO3 are long-chain arsenates with chain period 2. In the former, the chains are symmetric by a 2-fold screw, and the apical O atoms face alternately in opposite directions (Figure 12, left). Such chains are for example known from the MPO3 (M = K, Rb) family of structures.24,25,36−38 In γ-KAsO3, on the other hand, the chains are symmetric by a glide and the apical O atoms face the same 4646



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Figure 12. Anionic [AsO3] frameworks in the structurally characterized KAsO3 polymorphs. Arrows indicate phase transitions and are marked with approximate transition temperatures. The intermediate δKAsO3 phase was omitted since the nature of its anionic framework was not elucidated up to now.

direction. This kind of chain is for example observed in Zn(PO3)239 and LiAsO3.4 β- and β′-KAsO3 are the first cyclotriarsenates that have been structurally characterized. In β-KAsO3, the [As3O9]3− anion has approximate 3m symmetry (Figure 12, middle top), by far the most common conformation of cyclotriphosphate units,1 as observed for example in Na3P3O935 or K3P3O9.38 In β′-KAsO3, on the other hand, the [As3O9]3− anion is approximately symmetric by 2-fold rotation (Figure 12, middle bottom). This conformation has only be observed in rare cases, like the isopropylammonium40 and potassium ethylenediammonium41 cyclotriphosphates. In these cases the unusual conformation has been explained by stabilization with strong N−H···O hydrogen bonds.40,41 The temperature-dependent switching of both conformations has to our knowledge not been observed for any cyclotriphosphate. In the following paragraphs, the crystal structures of the longchain arsenates α- and γ-KAsO3 will be described in more detail followed by the cyclotriarsenates β- and β′-KAsO3. α-KAsO3. The enantiomorphic α-KAsO3 crystallizes in the space group P212121. It is most likely isotypic to the H′-KPO3 phase reported by Schmahl.37 Yet, since to the best of our knowledge no structural data of the latter have been published, we will discuss α-KAsO3 in relation to the closely related phases H-MPO3 (M = K,24 Rb25) from which it can be derived by a translationengleiche symmetry reduction of index 2 from Pbnm to P212121. Both α-KAsO3 and H-MPO3 are characterized by infinite − 1 [XO ∞ 3] (X = P, As) chains running along [010] (Figure 13) with repetition period 2. Whereas the chains are symmetric by mirroring at (001) in H-MPO3, they are rotated around the propagation direction in α-KAsO3 and thus their symmetry is reduced from Wy b21m to Wy 1211. In H-MPO3, the K atom is coordinated by eight O atoms, viz., six terminal and two bridging O atoms of the 1∞[PO3]− chains (Figure 14a). Four close (K−O bond lengths of 2.75− 2.94 Å; Rb−O: 2.95−3.00 Å) terminal O atoms are located at the corners of a rectangle, and two slightly more remote terminal O atoms (K−O: 3.10 Å; Rb−O: 3.19 Å) are located on the same side of the rectangle. At the opposite side are located two distinctly more remote (K−O: 3.33 Å; Rb−O: 3.48 Å) bridging O atoms. Compared to H-MPO3, the K coordination polyhedron in αKAsO 3 is more irregular (Figure 14b). Three close (2.646(10)−2.809(10) Å) and a more remote O atom (3.329(9) Å) are practically coplanar. Two terminal O atoms coordinate on both sides of this distorted rectangle with K−O

Figure 13. Crystal structures of (a, b) α-KAsO3 and (c, d) the high temperature H-KPO324 polymorph viewed down (a, c) [010] and (b, d) [001]. O and K atoms are represented by red and purple spheres, [XO4] (X = As, P) tetrahedra are in yellow.

Figure 14. Comparison of the [KOx] coordination polyhedra in (a) HKPO324 and (b) α-KAsO3. O and K atoms are represented by spheres of arbitrary radius. Color codes as in Figure 13.

bond lengths of 2.958(6) and 3.485(7) Å, respectively. Moreover, one bridging O atom is located in the coordination sphere of the K atom (K−O bond length 3.061(13) Å). In summary, the coordination polyhedron of the K atom can be described as a strongly distorted octahedron with corners occupied by terminal O atoms and one face capped by a bridging O atom. The correctness of the model is supported by an iterative charge distribution (CD) analysis implemented in CHARDI:42 The charges Q of both cations are distributed in a ratio of 1:5, as expected [K: Q = 1.020, As: Q = 4.980]. γ-KAsO3. The crystal structure of γ-KAsO3 (Figure 15a) is closely related and isopointal43 to orthopyroxenes like protoenstatite MgSiO344 with orthorhombic Pbca symmetry (Figure 15b). Nevertheless, because of the distinctly different 4647



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Figure 15. Crystal structures of (a) γ-KAsO3, (b) protoenstatite MgSiO3,44 and (c) the low temperature modification of Zn(PO3)239 viewed down [010]. Color codes as in Figure 13. Mg and Zn atoms are light blue, [SiO4] tetrahedra yellow.

Figure 16. Anionic layers in (a, b) the low-pyroxene orthoenstatite MgSiO3,47 (c) γ-KAsO3 and (d) Zn(PO3)2.39 (Pseudo)symmetry elements are indicated by the standard graphical symbols.48 The rectangles indicate the standard setting of the unit cell of the crystal structure, not of the layer.

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Figure 17. Coordination polyhedra of the cations in (a) protoenstatite MgSiO3,44 (b) γ-KAsO3, and (c) Zn(PO3)2 projected on (100). Color codes: pink: nearly regular octahedral [MO6]; green: nearly regular cubic [MO8]; yellow: distorted cubic [MO8]; orange: irregular [MO8].

symmetry as Zn(PO3)2, but the [AsO3] layers are distinctly more distorted and have to be considered of the p(1)21/c type. Therefore, the existence of an orthorhombic polytype is less likely in this case. The cations in classic pyroxenes are located on two (chemically) different positions, whereby M is always octahedrally coordinated, and the [MO6] octahedra are connected via edges to chains running along [001] (Figure 17a). M′ features coordination numbers 6−8. In Zn(PO3)2 and LiAsO3, the M atom is likewise octahedrally coordinated (Figure 17c), and the M′ position is unoccupied (Zn(PO3)2) or coordinated by four close (ca. 2 Å) and two more remote (ca. 3 Å) O atoms (LiAsO3). Both Zn(PO3)2 and LiAsO3 can therefore be considered clinopyroxenes with the formula Zn□P2O6 (□ represents an unoccupied position) and Li2As2O6. In γ-KAsO3, on the other hand, M (K2) is coordinated by eight O atoms located at the corners of a close-to-regular cube (K−O distances 2.738(3)−2.834(2) Å) (Figure 18b, Table 3), which are connected via faces to chains

oxo-coordination of the cations it cannot be considered as a classic pyroxene. Of the members of the metaphosphate and -arsenate family, γ-KAsO3 is most closely related to the low temperature phase of Zn(PO3)239 (Figure 15c) and to LiAsO3,4 which can be considered as clino-pyroxenes. Pyroxenes are polytypes which feature a pronounced chemical and geometrical variability of the layers. These kinds of polytypes have also been designated as improper polytypes.12 An OD interpretation of pyroxenes was given by Sedlacek et al.,45 whereby the pyroxenes are classified into two distinct OD families, viz., the high- and the low-pyroxenes. Although this approach is uncommon and has been criticized,12 we will use the nomenclature of high- and low-pyroxenes given by these authors. Pyroxenes have the general formula MM′.46 They are, like γ-KAsO3, made up of an alternating stacking of cationic [MM′] and anionic [XO3] layers. The long chains of a [XO3] layer face alternately “up” and “down” (i.e., the MO bonds of the apical O atoms are directed approximately along a* and −a*). Two kinds of [XO3] layers are observed in pyroxenes: In layers with (idealized) p(b)cm symmetry (the direction lacking translational symmetry is indicated by parentheses13), the [XO4] tetrahedra are virtually symmetric by mirroring at a plane normal to the direction of propagation of the chains (Figure 16a). In lower symmetry p(1)21/c layers, the [XO4] tetrahedra are tilted around the stacking direction [010], whereby the tilting in adjacent chains is in opposite direction (Figure 16b). In high-pyroxenes, all layers are of the p(b)cm variety, whereas in low-pyroxenes the p(b)cm layers alternate with p(1)21/c layers. On the other hand, none of the anionic layers in γ-KAsO3, feature (pseudo)mirror symmetry. In contrast to the p(1)21/c layers of low-pyroxenes, the symmetry of the layers is p(b)c21 due to rotation of all [AsO4] tetrahedra in the same direction (Figure 16c). The mirror symmetry of the p(b)cm layers in pyroxenes is responsible for their OD character45 and consequently the polytypism observed in pyroxenes. Because of the absence of mirror symmetry in the anionic layers of γ-KAsO3, on the other hand, there is no ambiguity in the layer stacking; i.e., in terms of OD theory the structure is f ully ordered.13 Zn(PO3)2 is made uplike high-pyroxenesof p(b)cm layers (Figure 16d) and has therefore to be considered as polytypic. Whereas the polytype described in the literature39 has C2/c symmetry, a different, but locally equivalent, stacking has the same Pbcn space group as γ-KAsO3. This demonstrates the necessity to consider local symmetry when discussing structural relationships. LiAsO3 features the same C2/c

Figure 18. Oxygen coordination environments of (a) K1 and (b) K2 in γ-KAsO3. Ellipsoids are drawn at the 75% probability levels. Color codes as in Figure 13.

Table 3. γ-KAsO3: Selected Interatomic Distances d and the Charges Q Calculated with an Iterative CD Algorithm Implemented in CHARDI42 atoms

d/Å

atoms

d/Å

As1O2 As1O1 K1O1 K1O2 K1O2 K1O3 atom

1.628(3) 1.639(3) 2 × 2.795(3) 2 × 2.746(3) 2 × 3.067(3) 2 × 2.792(3) Q

As1O3 As1O3 K2O1 K2O1 K2O1 K2O2 atoms

1.770(2) 1.771(3) 2 × 2.834(2) 2 × 2.824(2) 2 × 2.793(3) 2 × 2.738(3) Q

K2

0.993

K1 4649

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Figure 19. Crystal structures of (a) protoenstatite MgSiO3,44 (b) γ-KAsO3, and (c) Zn(PO3)2 viewed down [001], showing different relative positions of the [XO3] and [MM′] layers along [010]. Color codes as in Figure 13.

running along [001]. M′ (K1) is likewise coordinated by eight O atoms, though forming a more irregular coordination polyhedron (Figure 18a, Table 3), since two atoms are distinctly more remote (O3; 2 × 3.067(3) Å) than the remaining six (2.746(3)−2.795(3) Å). These [K1O8] polyhedra are connected via faces to the [K2O8] cubes, thus forming infinite ribbons running along [001] (Figure 17b). The charges Q of both K atoms [K1: Q = 1.004, K2: Q = 0.993] calculated by iterative CD are in excellent agreement with the expected value of 1. The difference of the M coordination polyhedra in γ-KAsO3 and classic pyroxenes, Zn(PO3)2 or LiAsO3 is caused by different relative positions of the [XO3] and the [MM′] layers along [010]: In γ-KAsO3, the terminal O atoms of the 1 − ∞[AsO3] chains are aligned with the K atoms in the [100] direction, whereas the corresponding O atoms are located between the M atoms in classic pyroxenes (Figure 19). Thus, as opposed to LiAsO3 and Zn(PO3)2, γ-KAsO3 cannot be considered a member of the pyroxene family. β- and β′-KAsO3. The crystal structures of the β- and β′KAsO3 polymorphs are closely related. The structures of βKAsO3 and β-K0.8Rb0.2AsO3 are isotypic. Since the latter was refined from low temperature (T = 76 °C) data of a nonfragmented crystal, the structural data are more reliable and were used for the figures given below. Unless specified otherwise, if in the following text the term “β-KAsO3” is used, structural features common to both β-KAsO3 and βK0.8Rb0.2AsO3 will be discussed. The basic building blocks of both structure types are [As3O9]3− cyclotriarsenate units made up of three cornersharing [AsO4] tetrahedra (Figure 20). As expected, the As−O bond lengths (Tables 4−6) involving terminal O atoms (βK0.8Rb0.2AsO3: 1.611(5)−1.631(5) Å; β′-KAsO3: 1.624(4)− 1636(4) Å) (the bonds of β-KAsO3 are not listed, since the As−O bond lengths were restrained) are shorter than those involving bridging O atoms (β-K0.8Rb0.2AsO3: 1.750(4)− 1.772(5) Å; β′-KAsO3: 1.737(6)−1.784(4) Å). As stated before, the geometry of the [As3O9]3− units differs in both polymorphs. Detailed views of the groups are given in Figure 20. In β-KAsO 3 the [As 3 O 9 ] 3− units possess approximately 3m symmetry, with all three apical O atoms facing the same direction (Figure 20a,b). In β′-KAsO3 the [As3O9]3− units are virtually symmetric by 2-fold rotation with the axis running along [010] passing through the O3 atom of the [As2O4] tetrahedron (Figure 20d,e). Thus, the apexes of the remaining two [AsO4] tetrahedra face opposite directions.

Figure 20. [As3O9]3− cyclotriarsenate units in (a, b) β-KAsO3 and (c, d) β′-KAsO3 viewed approximately down (a, c) [100] and (b, d) [001]. Color codes as in Figure 13. The atom names are given according to the idealized symmetry of the An layers in β- and β′KAsO3.

Both β- and β′-KAsO 3 are made up of distinct crystallochemical layers parallel to (010) (Figure 21). As is customary in OD theory, these layers will be designated as An, where n is a sequential number and the vector normal to the layer planes with the length of one layer width is designated as b0. Although the arrangement of the [As3O9]3− units and K atoms are very similar in both phases, due to the different geometries of the [As3O9]3− units, these layers feature different symmetry, as schematized in Figure 22: In β-KAsO3, the An layers possess idealized b2/m(1)1 symmetry, whereby the mirror plane coincides with a mirror plane of the [As3O9]3− units. In β′-KAsO3, on the other hand, the layer symmetry can be considered as pc(c)a, whereby the 2-fold rotation axes normal to the layers coincide with the corresponding axes of the [As3O9]3− units. Whereas the point group of the A layers in β-KAsO3 (2/m) is a subgroup of the point group of the A layers in β′-KAsO3 (mmm), the situation is reversed for the translation groups: the translations of the layer lattice of β′KAsO3 are a subgroup of the translations of the I -centered lattice of β-KAsO3. Thus, the layer groups of the A layers in βand β′-KAsO3 are not related by a group−subgroup relationship, and the β ↔ β′ phase transition is reconstructive, explaining the cracking of the crystals when heating above the 4650



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Table 4. β-KAsO3: Selected Interatomic Distances d and the Charges Q Calculated with an Iterative CD Algorithm Implemented in CHARDI42 atoms

atoms a

d/Å a

As1aO2a As1aO1a As1aO4a As1aO3 As1bO1b As1bO2b As1bO3 As1bO4b atoms

1.620(19) 1.620(7)a 1.760(13)a 1.760(6)a 1.620(10)a 1.620(19)a 1.760(8)a 1.760(13)a d/Å

As2O5 As2O6 As2O4b As2O4a

1.620(6) 1.62(2)a 1.760(9)a 1.760(12)a

atoms

d/Å

K1O1a K1O1b K1O5 K1O5 K1O6 K1O6 K1O4b K1O4a

2.71(2) 2.71(3) 2.753(18) 2.87(2) 2.81(2) 2.90(2) 3.092(18) 3.221(16)

K2O2b K2O2a K2O1a K2O1b K2O2b K2O5 K3O2a K3O6 K3O1b K3O1a K3O2a K3O2b K3O3 K3O4b K3O3 K3O4a atoms

2.64(3) 2.64(2) 2.719(18) 2.77(3) 2.77(2) 2.881(19) 2.71(2) 2.79(3) 2.84(3) 2.92(3) 3.62(2) 3.79(2) 3.65(2) 3.723(17) 3.788(14) 3.798(16) Q

Q

atom K1 K3 a

d/Å

0.947 0.909

K2

Table 5. β-K0.8Rb0.2AsO3: Selected Interatomic Distances d and the Charges Q Calculated with an Iterative CD Algorithm Implemented in CHARDI42

1.001

Distance restrained in refinement.

c

(c )

d/Å

atoms

d/Å

As1aO2a As1aO1a As1aO3 As1aO4a As1bO1b As1bO2b As1bO3 As1bO4b

1.611(5) 1.631(5) 1.750(4) 1.760(6) 1.617(5) 1.628(5) 1.757(5) 1.768(5)

As2O5 As2O6 As2O4b As2O4a

1.613(4) 1.614(5) 1.759(4) 1.772(5)

K1O1a K1O1b K1O5 K1O5 K1O6 K1O6 K1O4b K1O4a

2.665(5) 2.695(5) 2.761(5) 2.777(6) 2.880(5) 2.895(5) 3.114(6) 3.189(5)

K2O2b K2O2a K2O1a K2O1b K2O2b K2O5 K3O2a K3O6 K3O1b K3O1a K3O2a K3O2b K3O3 K3O4b K3O3 K3O4a Atoms

2.625(6) 2.664(6) 2.684(5) 2.735(6) 2.795(5) 2.918(5) 2.664(5) 2.732(6) 2.825(5) 2.871(6) 3.369(6) 3.615(6) 3.709(6) 3.756(5) 3.783(6) 3.797(5) Q

atom

Q

K1 K3/RB3

0.946 0.914

K2

0.996

adjacent An+1 layer, where N = |.| = |pc(2)a| = 4 is the order of the group of λ-τ partial operations (POs)13 of An and F = |.n ∩ .n + 1| = |p1(1)1| = 1 is the order of the group of λτ-POs which apply to An and An+1. Z = 4 possible orientations is unusual, and in most OD structures described in the literature there are only Z = 2 equivalent ways of connecting adjacent layers. Since the An and An+1 layers are translationally equivalent, the most convenient way to describe the orientations of An+1 is by the corresponding translation vector: The four possible positions of An+1 can be related to An by a translation along either of t++ = ((r − 1)/2)a + b0 + ((s − 1)/2)c, t−+ = ((1 − r)/2)a + b0 + ((s − 1)/2)c, t+− = ((r − 1)/2)a + b0 − ((s − 1)/2)c or t−− = ((1 − r)/2)a + b0 − ((s − 1)/2)c. These stacking possibilities give rise to an infinity of locally equivalent polytypes, of which four are of a maximum degree of order (MDO):50 MDO1 (...t++t++..., P1̅, b = t++), MDO2 (...t++t−−..., P21/c, b = 2b0), MDO3 (...t++t+−..., P112/b, b = ra + 2b0) and MDO4 (...t++t−+..., P21/b11, b = 2b0+sc). Their symmetry is schematized in Figure 23 by triangles that are red on one side and blue on the other side. Brighter colors indicate translation along c/2. Additional translation in the viewing direction c is indicated to the left. The overlap of all polytypes is the family structure. It plays a special role in the structural elucidation of OD structures, since the reflections corresponding to the family structure are common to all polytypes. The family structure of β′-KAsO3 has Immm symmetry and lattice basis (a/2, 2b0, c/2) (Figure 24).

phase transition temperature. In both cases, the symmetry of the layers is higher than the symmetry of the overall structure. Both phases are therefore OD polytypes. The atoms in the actual structure have been named according to the idealized A layer symmetry. Thus, all atoms K1x, x = a,b,c,d in β′-KAsO3 are equivalent according to the idealized pc(c)a symmetry of the A layers, etc. The OD character of β′-KAsO3 will be discussed first. OD Description of β′-KAsO3. Since the symmetry elements of adjacent An layers in β′-KAsO3 do not coincide, it can be described as a category I13 OD structure composed of nonpolar layers of one kind. The OD groupoid family symbol reads according to the notation of Dornberger-Schiff and GrellNiemann13 as p

atoms

a

{ 2r /n2, s + 1 (2 2 /ns + 1, r + 1) 2s /nr ,2 }

Accordingly, given an An layer, one possible position of the adjacent An+1 layer is is related to An by a 2-fold screw with intrinsic translation ra/2 or equivalently by a screw with intrinsic translation sc/2. Since r,s ∉ , the a- and c-glide planes of adjacent A layers normal to [001] and [100], as well as the 2fold axes parallel to [010] do not coincide. In consequence, given an An layer, there is more than one position of an adjacent An+1 layer leading to geometrically equivalent (An, An+1) pairs. Their number is derived using the NFZ relationship:49 Given an An layer, there are Z = N/F = 4 possible positions of an 4651



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Table 6. β′-KAsO3: Selected Interatomic Distances d and the Charges Q Calculated with an Iterative CD Algorithm Implemented in CHARDI42 atoms

d/Å

atoms

d/Å

As1aO2a As1aO1a As1aO4a As1aO4a As1bO1b As1bO2b As1bO3a As1bO4b As1cO2c As1cO1c As1cO4c As1cO3b

1.629(5) 1.636(4) 1.757(4) 1.762(6) 1.626(4) 1.631(5) 1.758(6) 1.761(4) 1.626(5) 1.630(5) 1.756(4) 1.776(6)

As1dO1d As1dO2d As1dO3b As1dO4d As2aO5a As2aO5b As2aO4a As2aO4b As2bO5c As2bO5d As2bO4c As2bO4d

1.624(4) 1.634(5) 1.737(6) 1.759(4) 1.628(6) 1.632(5) 1.778(4) 1.778(4) 1.624(5) 1.630(5) 1.784(4) 1.784(4)

K2aO1d K2aO2b K2aO5c K2aO2a K2aO1a K2aO2c K2bO1c K2bO2a K2bO5d K2bO2a K2bO2b K2bO1b K2cO1b K2cO2d K2cO5a K2cO2b K2cO2c K2cO1c

2.596(5) 2.674(6) 2.728(6) 2.897(5) 2.915(5) 2.927(6) 2.647(5) 2.674(5) 2.736(6) 2.759(6) 2.909(6) 2.939(5) 2.639(5) 2.652(6) 2.730(6) 2.745(6) 2.832(6) 3.135(5)

K2dO1a K2dO2c K2dO5b K2dO2d K2dO2d K2dO1d K1aO5b K1aO5d K1aO1d K1aO1b K1aO5c K1aO4b K1aO4d K1aO5a K1bO5c K1bO5a K1bO1c K1bO1a K1bO4a K1bO5b K1bO5d K1bO4c atoms

2.591(5) 2.682(6) 2.703(5) 2.820(6) 2.858(6) 3.078(5) 2.747(5) 2.747(5) 2.816(5) 2.868(5) 2.972(5) 2.973(5) 2.988(5) 3.011(5) 2.738(5) 2.748(5) 2.792(5) 2.824(5) 2.972(5) 3.014(5) 3.017(5) 3.019(5) Q

atom

Q

K1a K1b K1c

0.980 0.984 0.987

K1d K2a K2b

operations of the MDO3 and MDO4 polytypes which are not operations of MDO2: 2-fold rotation axes normal to (001) and parallel to [100], and mirror planes normal to [100] and parallel to (001). Ordered polytypes commonly feature desymmetrization with respect to the idealized OD description.52 In the actual MDO2 polytype, it manifests as a deviation from the perfect orthorhombic metrics (β = 90.1844(18)°) and a symmetry reduction of index 4 of the A layer from pc(c)a to p1(c)1. To quantify the desymmetrization, an idealized structure was computed by grouping atoms according to the idealized pc(c)a layer symmetry, averaging their positions and moving atoms close to a Wyckoff position onto the latter. The distances of the idealized to actual atoms (under the assumption of β = 90°) are summarized in Table 7. The idealized structure is virtually identical to the actual structure: The largest deviations are observed for atoms K2c (0.118 Å from the idealized position), O2d (0.118 Å), and O2b (0.100 Å). Indeed, the K2x and O2x atoms are located at the boundary of the A layers, where the largest desymmetrization is expected, since they are located in an environment with different symmetry. All other atoms deviate by less than 0.08 Å, demonstrating the validity of the OD interpretation. On the basis of the idealized structure, the metric parameters were determined as (r, s) = (0.516, 0.500). The parameters are close to 1/2 for crystallochemical reasons: Because of the symmetric connectivity of the K2 atoms with [As3O9] units in adjacent layers, the horizontal origin shifts between the layers are ≈ ± (a/4) ± (c/4) (Figure 21). OD Description of β-KAsO3. An OD interpretation in analogy to β′-KAsO3 leads to the OD groupoid family b

2/m

(1) 1

{ 2r /n2, s ( 1̅ ) 1̅ }

Thus, one possible orientation of An+1 is related to An by a screw with intrinsic translation ra/2 or equivalently a glide with intrinsic translation b0 + sc/2. For OD groupoid families with rectangular layer and monoclinic crystal systems, the b0 vector is often conveniently chosen not normal to the layers to make one of the metric parameters vanish (in this case s).53 In the case at hand, we refrained from doing so to stay consistent with the description of the β′-KAsO3 structure. According to the NFZ relationship there are Z = |bm(1)1|/|b1(1)1| = 2 equivalent positions the An+1 layer can adopt, given an An layer, which are related by the m operation of the An layer. These stacking possibilities give rise to two MDO polytypes: MDO1 (B1,̅ b = b0 + ra/2 + sc/2) and MDO2 (B2/b11, b = 2b0 + sc) as schematized in Figure 25. Actual Structure of β-KAsO3. The crystals under investigation were all of the MDO1 (B1̅) polytype. In these crystals, fragments of the MDO2 polytype result in twinning by mirroring at a plane normal to [100]. Indeed, this twin operation has been observed repeatedly. Yet, an additional twinning by mirroring at a plane normal to [001] was likewise observed. This twinning is not consistent with the given OD interpretation and probably is caused by a cracking of the crystal during the reconstructive phase transition from β′KAsO3 involving a non-group/subgroup symmetry change, as opposed to classic twinning.51 Like β′-KAsO3, the actual structure of β-KAsO3 features desymmetrization: the symmetry of the A layers is reduced by an index of two from b(2/m)11 to b1̅. The resulting deviation

0.988 0.994 0.989

Actual Structure of β′-KAsO3. The bulk of the β′-KAsO3 crystals under investigation were of the MDO2 polytype with P21/c symmetry. A layer triple of MDO1 results in MDO2 domains with same orientation and does therefore not correspond to twinning in the classic sense.51 Thus, the existence of MDO1 fragments cannot be evidenced by routine single-crystal diffraction methods. Fragments of the MDO3 and MDO4 polytypes, on the other hand, result in twinning. (An, An+1, An+2) triples of either polytype result in twinning consistent with the structure refinement. Thus, because of the unusually high Z = 4, whereas OD theory provides a plausible explanation of the twinning and the location of the twin contact plane, the exact nature of the latter (fragments of MDO3 or MDO4) remains unknown. Attempts to describe the diffraction pattern of powdered samples with any of the MDO polytypes, the family structure or partially disordered MDO2 polytypes did not confirm either of the two twin contact planes (vide supra). The four twin elements can be derived from the symmetry 4652



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Figure 21. Crystal structures of (a, b) β-KAsO3 and (c, d) β′-KAsO3, viewed down (a, c) [100] and (b, d) [001]. Color codes as in Figure 13.

Figure 22. Schematic representation of the idealized A layers in (a) β- and (b) β′-KAsO3. The [AsO4] tetrahedra of the [As3O9]3− anions are represented by triangles and squares, K atoms by gray spheres. Symmetry elements of the layers are represented by the standard graphical symbols.48

of the β-angle from the ideal value of 90° is less than the estimated standard uncertainty (β-KAsO3: 90.00(4)°, βK0.8Rb0.2AsO3: 90.01(3)°) and thus is even less pronounced than in β′-KAsO3. An idealized structure with b2/m(1)1 layer symmetry was computed for β-K0.8Rb0.2AsO3 as described above. It is again virtually identical to the actual structure: The largest deviations are observed for the O2a/O2b atoms (0.122 Å from the idealized positions), which are located at the layer boundaries, whereas all other atoms deviate by less than 0.08 Å (Table 8). Since the β-parameter of the actual structure is virtually 90°, the metric parameters of the OD family can be computed as (r, s) = (2b cos γ/a, 2b cos α/c). For β-KAsO3 and K0.8Rb0.2AsO3 (r, s) = (−0.53, −0.47) and (r, s) = (−0.55, −0.45) are

obtained. Thus, the relative position of adjacent layers parallel to the layer plane is approximately ± a/4 − c/4 but deviates more strongly from this ideal values than in the case of β′KAsO3. In the [001] direction, this can be explained by the distinct tilting of the [As3O9]3− units (Figure 21) with respect to the (001) plane. Crystal Chemistry of the Cations. So far, for simplicity, the discussion of the β- and β′-KAsO3 structures was based mainly on the [As3O9]3− anions. Nevertheless, the cations play a significant role in the β ↔ β′-phase transition as is demonstrated by the stabilization of the β-KAsO3 phase at lower temperature on partial substitution of Rb for K. In both β- and β′-KAsO3, the K1x atoms are located at the central plane of the A layers (Figure 21). According to the 4653



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Figure 23. Symmetry of the (a) MDO1, (b) MDO2, (c) MDO3, and (d) MDO4 polytypes of β′-KAsO3 schematized by triangles, which are blue on one side and red on the other side. Brighter colors indicate translation along c/2. Additional translation along c is indicated to the left of the layers. Unit cells of the polytypes, symmetry operations of the layers, and operations relating adjacent layers are indicated using the standard graphical symbols.48

lengths are distributed over the 2.7−3.2 Å range (Tables 4−6) and the calculated charges Q are slightly below the expected value of 1 in β′-KAsO3 (Q = 0.98−0.99) and more pronouncedly in β-KAsO3 and β-K0.8Rb0.2AsO3 (Q = 0.947, 0.946). The coordination chemistry of the K atoms located at the layer interfaces differ in the β- and β′-KAsO3 phases. According to idealized symmetry of the A layers, there is one such atom in β′-KAsO3 (K2) located on a general position, yet two (K2, K3) in β-KAsO3, both located on mirror planes parallel to (100) (Figure 22). The K2x atoms in β- and β′-KAsO3 are chemically very similar. They are coordinated by six O atoms located at the corners of distorted octahedra (Figure 26b,d), with a bond length distribution and comparable to K1x (Tables 4−6). The calculated charges Q according to CD are very close to the expected values of 1 (β-KAsO3: Q = 1.001, β-K0.8Rb0.2AsO3: Q = 0.996, β′-KAsO3: Q = 0.994, 0.989). The K3 atom in β-KAsO3, on the other hand, features a highly unusual coordination polyhedron. Considering bond lengths up to 3.5 Å, it is connected to only five O atoms. Increasing the relevant bond lengths to 3.9 Å, it is coordinated by five additional O atoms located at 3.7−3.9 Å. The coordination polyhedron formed by the 10 atoms is highly irregular and difficult to derive from simple geometric figures (Figure 26e). The calculated charges Q according to iterative CD analysis with CHARDI42 are significantly below the expected value of 1 in unsubstituted β-KAsO3 (Q = 0.909) and only slightly improved in β-K0.8Rb0.2AsO3 (Q = 0.914). In both, the ADPs of the K3 are distinctly enlarged compared to

Figure 24. Family structure of β′-KAsO3 with Immm symmetry, schematized as in Figure 23. Gray triangles are symmetric by mirroring at (001).

idealized symmetry of the A layers, they are located on the 2fold axes parallel to [001] (β′-KAsO3) and [100] (β-KAsO3) (Figure 22). Considering K−O bond lengths up to 3.5 Å as relevant (corresponding to 0.025 valence units according to bond valence calculations), they are coordinated by O atoms of four [As3O9]3− units of a single A layer. The O atoms are located on the corners of irregular [KO8] polyhedra that can be described as a square antiprism (Figure 26a,c). The K−O bond 4654



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Table 7. Distance d of the Actual Atoms in β′-KAsO3 to the Atoms in the Idealized Structure with pc(c)a Layer Symmetrya actual As1a (4 e 1) As1b (4 e 1) As1c (4 e 1) As1d (4 e 1) As2a (4 e 1) As2b (4 e 1) (K1a (4 e 1) K1b (4 e 1) K2a (4 e 1) K2b (4 e 1) K2c (4 e 1) K2d (4 e 1)

idealized

d/Å

actual

As1 (8 d 1)

0.016 0.051 0.020 0.048 0.008 0.026 0.023 0.047 0.076 0.076 0.118 0.075

O1a (4 e 1) O1b (4 e 1) O1c (4 e 1) O1d (4 e 1) O2a (4 e 1) O2b (4 e 1) O2c (4 e 1) O2d (4 e 1) O3a (4 e 1) O3b (4 e 1) O4a (4 e 1) O4b (4 e 1) O4c (4 e 1) O4d (4 e 1) O5a (4 e 1) O5b (4 e 1) O5c (4 e 1) O5d (4 e 1)

As2 (4 b 0.2.) K1 (4 c..2) K2 (8 d 1)

idealized

d/Å

O1 (8 d 1)

0.061 0.065 0.031 0.052 0.045 0.100 0.042 0.118 0.036 0.056 0.014 0.020 0.027 0.022 0.026 0.024 0.035 0.028

O2 (8 d 1)

O3 (4 b 0.2.) O4 (8 d 1)

O5 (8 d 1)

a

Multiplicity, Wyckoff letter, and site symmetry of the atomic position according to the space (actual) and layer (idealized) groups are indicated in parentheses.

Figure 25. Schematized symmetry of the (a) MDO1, (b) MDO2 polytypes of β-KAsO3. Symbols as in Figure 23.

Table 8. Distance d of the Actual Atoms in β-K0.8Rb0.2AsO3 to the Atoms in the Idealized Structure with Perfect b(2/ m)11 Layer Symmetrya actual

idealized

d/Å

As1a/As1b (4 i 1) As2 (4 i 1) K1 (4 i 1) K2 (4 i 1) K3 (4 i 1) O1a/O1b (4 i 1) O2a/O2b (4 i 1) O3 (4 i 1) O4a/O4b (4 i 1) O5 (4 i 1) O6 (4 i 1)

1 (8 f 1) As2 (4 e m) K1 (4 d 2) K2 (4 e m) K3 (4 e m) O1 (8 f 1) O2 (8 f 1) O3 (4 e m) O4 (8 f 1) O6 (4 e m) O6 (4 e m)

0.047 0.036 0.046 0.048 0.015 0.077 0.123 0.017 0.040 0.021 0.042

Figure 26. Two chemically different O coordination environments of K atoms in β′-KAsO3 exemplified by (a) K1a and (b) K2a and (c−e) the three coordination polyhedra in β-K0.8Rb0.2AsO3, viewed down c*. In general, O atoms closer than 3.5 Å were considered as relevant, in (e) more remote O atoms located at 3.7−3.9 Å are indicated by blue rods. Ellipsoids are drawn at the 75% probability levels. Color codes as in Figure 13.

the β-K0.8Rb0.2AsO3 crystal under investigation, substitution with Rb could only be evidenced for this position, whereby 60.7(5)% of the K atoms are substituted with Rb. Since the βK0.8Rb0.2AsO3 phase is stable at low temperatures, the unusually large coordination polyhedron of the K3 position seems to be the prime reason for the instability of the β-KAsO3 phase below ∼250 °C. Thus, like for the cyclotriphosphate anion, the geometry with approximate 2 symmetry is stable only under exceptional circumstances: strong H-bonding40,41 or, in the case of β-KAsO3, underbonding of the cation in the case of the anion with approximate 3m symmetry. Related Alkali Metal Metaarsenates and Phosphates. The relationship of the structurally characterized KAsO3 polymorphs with some condensed phosphates and arsenates was established above. In this section, a more complete overview of the known structures of alkaline metal

a

Multiplicity, Wyckoff letter, and site symmetry of the atomic position according to the space (actual) and layer (idealized) groups are indicated in parentheses.

the other cationic positions, suggesting (in the case of the high temperature β-KAsO3 phase possibly dynamic) disorder. Because of the unusually large K−O distances, Rb substitution is expected mostly at the K3 position. Indeed, in 4655



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Table 9. Comparison of the Structures of Alkali Metal Metaarsenates and Phosphates MXO3a phase

space group

V/Å3

Z

V/Z/Å3

anionic network

period

LiPO3 NaPO3 (Madrell’s salt) NaPO3 (Kurrol’s salt A) NaPO3 (Kurrol’s salt B) NaPO3 (Kurrol’s salt C) Na3P3O9 T-KPO3 Z-KPO3 H′-KPO3 H-KPO3 HT-KPO3 K3P3O9 T-RbPO3 Z-RbPO3 H-RbPO3 HT-RbPO3 LiAsO3 LiAsO3 (high pressure) NaAsO3 α-KAsO3 β-KAsO3 β′-KAsO3 γ-KAsO3

Pn P1̅ P21/n P21/n I41/a Pmcn P21/a P21/a P212121 Pbnm Bbmm P21/n P21/n P21/n Pbnm Bbmm C2/c R3̅ P1̅ P212121 P21/c P21/c Pbcn

1149.4 382.8 524.9 519.9 1031.4 807.5 641.2 665.7 ? 342.3 347.8 952.0 330.2 722.1 367.8 378.1 472.0 284.5 426.3 376.7 1057.7 2087.3 631.6

20 6 8 8 16 12 8 8 4 4 4 12 4 8 4 4 8 6 6 4 12 24 8

57.47 63.80 65.62 64.99 64.46 67.29 80.15 83.21 ? 85.58 86.95 79.33 82.55 90.26 91.95 94.56 59.00 47.42 71.05 94.18 88.14 86.97 78.95

long-chain long-chain long-chain long-chain long-chain cycle long-chain long-chain long-chain long-chain long-chain cycle long-chain long-chain long-chain long-chain long-chain ilmenite sheets long-chain long-chain cycle cycle long-chain

10 3 4 4 4 3 2 2 2 2 2 3 2 2 2 2 2 3 2 3 3 2

ref 54 31 32 33 34 35 24 24 37 24 36 38 25 25 25 25 4 5 6 this this this this

work work work work

Z is given with respect to the MXO3 formula unit even for cyclotriphosphates and -arsenates. The column, “period” lists the period of the chain or the size of the cycle.

a

dimensional heringbone like pattern, separated by the alkali metal ions.

metaphosphates and -arsenates MXO3 (M = Li, Na, Rb, Cs; X = P, As) is given for an improved structural classification of KAsO3 with respect to the chemically related compounds. Numerous structural characterizations of these phases have been published up to now, and in particular the polymorphism of NaPO3, KPO3, and RbPO3 has been extensively investigated. With the exception of a high pressure modification of LiAsO3 which crystallizes in the ilmenite structure type and features sheets of edge sharing [AsO6] octahedra,5 all of the known structures feature either cyclotriphosphate or long-chain phosphate/arsenate anions. An overview of the structures is given in Table 9, listing the type of the anionic network (cycle or chain) and the repetition period or cycle size. Long chain phosphates and arsenates have been described for MPO3 (M = Li, Na, K, R, Cs) and MAsO3 (M = Li, Na). Repetition periods of 2 (KPO3,24,36,37 RbPO325 and LiAsO34), 3 (NaPO331 and NaAsO36), 4 (NaPO332,33), and 10 (LiPO354) have been documented. The KPO3 and RbPO3 polymorphs are related to α-KAsO3 as described above, and LiAsO3 is a clino pyroxene and thus related to γ-KAsO3. The OD character of Kurroll’s salt of type A (NaPO3) has been recognized,55 yet to our knowledge no detailed OD description has been given up to now. The symmetry and the lattice parameters of a CsPO3 analogue of the low temperature T-RbPO3 polymorph have been reported, but no atom coordinates were determined up to now.56 NaPO335 and KPO338 polymorphs with cyclotriphosphate units have been described. The geometry of their cyclotriphosphate anions corresponds to the cyclotriarsenate anions in the high temperature phase β-KAsO3 but is distinctly different from those in β′-KAsO3, as discussed in above. Moreover, as opposed to β- and β′-KAsO3, the M3P3O9 phases do not crystallize as layered structures. Instead, the triphosphate units and the K atoms are arranged in a three-

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ASSOCIATED CONTENT

S Supporting Information *

These contain details of the data collection and refinements as well as the final structure models in tabular form and as CIFs, structure factors as FCFs, a reconstructred precession-image of a γ-KAsO3 crystal demonstrating arcing and XRPD scans of single phase KH 2 AsO 4 and RbH 2 AsO 4 as well as a postmeasurement residue obtained by heating KAsO3 beyond its melting point in a Macor crucible. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +43 (1) 58801 17123. Fax: +43 (1) 58801 17199. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank Werner Artner for performing the high temperature XRPD measurements. The X-ray center of the Vienna University of Technology is acknowledged for providing access to the single crystal and powder diffractometers. The project P204111/0809 of the Grant Agency of the Czech Republic is acknowledged for supporting high temperature single crystal measurements.

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REFERENCES

(1) Durif, A., Ed.; Crystal Chemistry of Phosphates; Plenum Press: New York, 1995. 4656



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(2) Schwendtner, K.; Kolitsch, U. Acta Crystallogr. 2007, B63, 205− 215. (3) Inorganic Crystal Structure Database (ICSD), Karlsruhe F. I. Z., 2013. (4) Hilmer, W.; Dornberger-Schiff, K. Acta Crystallogr. 1956, 9, 87− 88. (5) Driss, A.; Jouini, T. J. Solid State Chem. 1989, 78, 126−129. (6) Liebau, F. Acta Crystallogr. 1956, 9, 811−817. (7) Curda, J.; Peters, E.-M.; Jansen, M. Z. Anorg. Allg. Chem. 2004, 630, 491−494. (8) Boullé, A. C. R. Acad. Sci. 1938, 206, 517−518. (9) Thilo, E.; Dostál, K. Z. Anorg. Allg. Chem. 1959, 298, 100−115. (10) Grunze, I.; Dostál, K.; Thilo, E. Z. Anorg. Allg. Chem. 1959, 302, 221−229. (11) Duquenoy, G.; Josien, F.-A. Rev. Chim. Min. 1978, 15, 169−177. (12) Ferraris, G.; Makovicky, E.; Merlino, S. Crystallography of Modular Materials; IUCr Monographs on Crystallography; Oxford University Press: Oxford, 2004; Vol. 15. (13) Dornberger-Schiff, K.; Grell-Niemann, H. Acta Crystallogr. 1961, 14, 167−177. (14) Stöger, B.; Weil, M.; Zobetz, E. Z. Kristallogr. 2012, 227, 859− 868. (15) Stöger, B.; Weil, M. Mineral. Petrol. 2013, 107, 253−263. (16) Stöger, B.; Kautny, P.; Lumpi, D.; Fröhlich, J. Acta Crystallogr. B 2012, B68, 667−676. (17) Dornberger-Schiff, K.; Liebau, F.; Thilo, E. Acta Crystallogr. 1955, 8, 752−754. (18) SAINT and SADABS; Bruker Analytical X-ray Instruments, Inc.: Madison, WI, USA, 2008. (19) CrysAlis PRO and CrysAlis RED; Oxford Diffraction Ltd, Abingdon, Oxfordshire, England, 2008. (20) Palatinus, L.; Chapuis, G. J. Appl. Crystallogr. 2007, 40, 786− 790. (21) Petříček, V.; Dušek, M.; Palatinus, L. Z. Kristallogr. 2014, 229, 345−352. (22) Stöger, B.; Weil, M. Acta Crystallogr. 2012, E68, i15. (23) Bail, A. L. Powder Diffraction 2004, 19, 249−254. (24) Jost, K. H.; Schulze, H. J. Acta Crystallogr. 1969, B25, 1110− 1118. (25) Holst, C.; Schmahl, W. W.; Fuess, H. Z. Kristallogr. 1994, 209, 322−327. (26) TOPAS-Academic V4.1; Coelho Software: Brisbane, Australia, 2007. (27) Larbot, A.; Norbert, A.; Cot, L. C. R. Acad. Sci. Paris 1979, 288, 185−187. (28) Larbot, A.; Durand, J.; Norbert, A.; Cot, L. Acta Crystallogr. 1983, C39, 6−8. (29) Dumas, Y.; Galigné, J. L.; Falgueirettes, J. Acta Crystallogr. 1973, B29, 2913−2918. (30) Stöger, B.; Weil, M.; Skibsted, J. Dalton Trans. 2013, 42, 11672− 11682. (31) Jost, K. H. Acta Crystallogr. 1963, 16, 428. (32) Jost, K. H.; Schulze, H. J. Acta Crystallogr. 1961, 14, 844−847. (33) Jost, K. H. Acta Crystallogr. 1963, 16, 640−642. (34) Immirzi, A.; Porzio, W. Acta Crystallogr. 1982, B38, 2788−2792. (35) Ondik, H. M. Acta Crystallogr. 1965, 18, 226−232. (36) Jost, K. H.; Schulze, H. J. Acta Crystallogr. 1971, B27, 1345− 1353. (37) Schmahl, W. W. Z. Kristallogr. 1987, 178, 197−198. (38) Bagieu-Beucher, M.; Tordjman, I.; Durif, A.; Guitel, J. C. Acta Crystallogr. 1976, B32, 1427−1430. (39) Averbuch-Pouchot, M. T.; Durif, A.; Bagieu-Beucher, M. Acta Crystallogr. 1983, C39, 25−26. (40) Averbuch-Pouchot, M. T.; Durif, A.; Guitel, J. C. Acta Crystallogr. 1988, C44, 1907−1909. (41) Averbuch-Pouchot, M. T.; Durif, A. Acta Crystallogr. 1988, C44, 1909−1911. (42) Nespolo, M.; Ferraris, G.; Ivaldi, G.; Hoppe, R. Acta Crystallogr. 2001, B57, 652−664.

(43) de Faria, J. L.; Hellner, E.; Liebau, F.; Makovicky, E.; Parth, E. Acta Crystallogr. 1990, A46, 1−11. (44) Smith, J. V. Acta Crystallogr. 1959, 12, 515−519. (45) Sedlacek, P.; Zedler, A.; Reinecke, K. Krist. Technol. 1979, 14, 1055−1062. (46) Liebau, F. Structural Chemistry of Silicates: Structure, Bonding and Classification; Springer-Verlag: Berlin, 1985. (47) Morimoto, N.; Koto, K. Z. Kristallogr. 1969, 129, 65−83. (48) Hahn, T. International Tables For Crystallography; D. Reidel Publishing Company: Dordrecht, The Netherlands, 2006; Vol. A; Chapter Graphical symbols for symmetry elements in one, two and three dimensions, pp 7−11. (49) D̆ urovic̆, S. EMU Notes Mineral. 1997, 1, 3−28. (50) Dornberger-Schiff, K. Acta Crystallogr. 1982, A38, 483−491. (51) Hahn, T. International Tables For Crystallography; D. Reidel Publishing Company: Dordrecht, The Netherlands, 2006; Vol. D; Chapter Twinning of crystals, pp 393−448. (52) D̆ urovic̆, S. Krist. Tech. 1979, 14, 1047−1053. (53) Fichtner, K. Krist. Tech. 1979, 14, 1453−1461. (54) Guitel, J. C.; Tordjman, I. Acta Crystallogr. 1976, B32, 2960− 2966. (55) Dornberger-Schiff, K. Acta Crystallogr. 1966, 21, 311−322. (56) Corbridge, D. E. C. Acta Crystallogr. 1955, 8, 520.

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Complex Polymorphism and Polytypism of Potassium Metaarsenate

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