II. EXPERIMENTAL

The new K₂FeF₅ forms are the products of monohydrate thermolysis, which was reported by Bentrup (Reference Bentrup1991) to lead to an orthorhombic form at 135 °C. It is shown here that this orthorhombic form (noted III) is not the high-temperature solid-state one (Le Bail et al., Reference Le Bail, Desert and Fourquet1990a) belonging to the Pbcn space group (noted form-I), nor the hydrothermally synthesized form (Fourquet and Duroy, Reference Fourquet and Duroy1993) crystallizing in the Pbam space group (noted form-II), both these known phases being characterized from single crystal data. Moreover, a phase transition from form-III to a fourth form is observed at 412 °C, which finally undergoes a phase transition to the normal Pbcn HT form-I at 580 °C. The powder diffraction patterns of K₂FeF₅ forms III and IV could be recorded at room temperature. Note that form-II transforms at 190 °C irreversibly to K₃FeF₆ + KFeF₄ (Fourquet and Duroy, Reference Fourquet and Duroy1993).

III. INDEXING, STRUCTURE DETERMINATIONS, AND RIETVELD REFINEMENTS

A. K₂FeF₅ form-III

At the identification stage by search-match procedures applied to the powder diffraction pattern recorded at room temperature, by using the ICDD-PDF database, the best match was from K₂VO₂F₃ (see PDF entry 04-009-3298; PDF, 2012) (Ryan et al., Reference Ryan, Mastin and Reisfeld1971). Rb₂CrF₅ (Jacoboni et al., Reference Jacoboni, De Pape, Poulain, Le Marouille and Grandjean1974) belongs to the same crystal structure type. Thus, the Rietveld (Reference Rietveld1969) refinement, using the FULLPROF software (Rodriguez-Carvajal, Reference Rodriguez-Carvajal1993) was made starting from the Rb₂CrF₅ atomic coordinates (Pnma space group), and readily converged to satisfy R values. In order to improve the sample crystallinity, it was maintained at 400 °C just before the form-III → form-IV transition, nevertheless, a small amount of form-IV had to be considered in the final Rietveld refinement (Figure 1), with fixed atomic coordinates, after the form-IV structure was solved. The Rietveld refinement details, the atomic coordinates, selected geometric parameters, and X-ray diffraction data are shown in Tables I–IV, respectively.

Figure 1.

(Color online) Rietveld plot for K₂FeF₅ form-III (CuKα). The second phase corresponds to a 6.1(2)% contribution of form-IV starting to appear. A third phase remains unidentified, showing a main peak at 23.2° (2θ).

Table I.

Experimental and Rietveld refinement details for the K₂FeF₅ forms III and IV.

Table II.

Fractional atomic coordinates and isotropic displacement parameters (Ų) at 23 °C for K₂FeF₅ forms III and IV in the Pnma and C2/m space groups, respectively; BV is the bond-valence calculated according to Brese and O'Keefe (Reference Brese and O'Keefe1991).

Table III.

Selected interatomic distances (Å) and angles (°) for the K₂FeF₅ forms III and IV at 23 °C.

Symmetry codes – Form-III : (i) −x+1, y + 1/2, and −z + 1; (ii) x − 1/2, −y + 1/2, and −z + 1/2; (iii) −x + 1, y − 1/2, and −z + 1; (iv) x − 1, y, and z; (v) x − 1, −y + 1/2, and z; (vi) x − 1/2, −y + 1/2, and −z + 3/2; (vii) −x + 3/2, −y, and z + 3/2; (viii) x + 1/2, y, and −z + 1/2; (ix) −x + 3/2, −y − 1, and z + 3/2; Form-IV : (i) x, −y, and z; (ii) −x + 1/2, y − 1/2, and −z + 1; (iii) −x + 1/2, y + 1/2, and −z + 1; (iv) −x + 1, y, and −z + 1; (v) x + 1/2, y − 1/2, and z + 1; (vi) −x, y, and −z + 1; (vii) x, y, and z + 1; (x) x, −y, and z + 1.

Table IV.

X-ray diffraction data for K₂FeF₅ form-III at 23 °C (CuK α1).

B. K₂FeF₅ form-IV

The search-match process was negative for that sample quenched at 500 °C. Indexing was realized by using the McMaille software (Le Bail, Reference Le Bail2004), leading to a C-centered monoclinic cell. The Figures of Merit (FoMs) were M ₂₀ = 55.9 (de Wolff, Reference de Wolff1968), F ₂₀ = 79.5 (0.0043, 58) (Smith and Snyder, Reference Smith and Snyder1979), and McM ₂₀ = 169.9 (Le Bail, Reference Le Bail, Clearfield, Reibenspies and Bhuvanesh2008). The cell volume was similar to that of form-III. On using Le Bail fitting (Le Bail, Reference Le Bail2005) for evaluating the reliability of the indexing and for intensity extraction, the C2/m, C2, or Cm space groups were found to be the most probable. The structure solution was carried out in direct space by using the ESPOIR software (Le Bail, Reference Le Bail2001), moving in the cell the appropriate number of K, Fe, and F atoms by a Monte Carlo process. A satisfying solution allowing us to recognize [FeF₆] octahedra was obtained in the C2/m space group, which was confirmed by a Rietveld refinement using FULLPROF (Figure 2). Traces of KFeF₃ were identified indicating some Fe³⁺ → Fe²⁺ disproportionation; another impurity in a very small proportion could not be defined. The Rietveld refinement details, the atomic coordinates, and selected geometric parameters are shown in Tables I–III, respectively, and the X-ray diffraction data are in Table V.

Figure 2.

(Color online) Rietveld plot for K₂FeF₅ form-IV (CuKα). The second phase corresponds to 3.4(1)% of the cubic KFeF₃ phase. A third phase remains unidentified, showing weak reflections between ~15° and 20° (2θ).

Table V.

X-ray diffraction data for K₂FeF₅ form-IV at 23 °C (CuK α1).

IV. STRUCTURE DESCRIPTION AND CORRELATIONS WITH RELATED COMPOUNDS

The form-III structure (Figure 3) is very common since it is adopted by Rb₂ M ^IIIF₅ (M ^III = Cr, Fe, and Ga) and Cs₂FeF₅, as well as by some oxyfluoride compounds. MF₆ octahedra are connected by cis-corners to form infinite (FeF₅) _n ²ⁿ⁻ zigzag chains. Calculated bond valences reported in Table II for both forms III and IV are close to the expected values (maximum difference attaining 12%), indicating that the unrestrained Rietveld refinements from laboratory powder data have led to medium quality results. The bridging Fe–F distance (2.029 Å in form-III and 2.011 Å in form-IV) is longer than the terminal ones 1.864 < Fe–F_term < 1.960 Å in form-III and 1.831 < Fe-F_term < 1.909 Å in form-IV; the bridging Fe–F–Fe angle is 180° in both forms. The same cis-chains of the FeF₆ octahedra are the characteristic of K₂FeF₅ form-II hydrothermally synthesized (Fourquet and Duroy, Reference Fourquet and Duroy1993) but the mutual orientation of the chains is different leading to a doubling of the longer axis (b _II = 23.0897 Å ~2 × c _III = 11.544 Å), the two other cell parameters being very similar (Table VI). All of the potassium ions are tenfold coordinated in both forms II and III, with a clear cut of the K–F distances. In form-IV all of the potassium ions are also tenfold coordinated (they have coordination 9, 10, and 11 in form-I) and the same zigzag cis-connected (FeF₅) _n ²ⁿ⁻ chains (Figure 4) appear to present again a different mutual orientation (Figure 5). A topotactic reaction hypothesis looks highly plausible to explain the form-III → IV transition : it is sufficient to rotate half the chains accompanied by the potassium ions nearest neighbors by 90° along the b-axis (arrows in Figure 5), and to translate the chains by 1/2 b in order to make form-III appear back from form-IV (but since the reaction is irreversible, the inverse moves have to be considered). Polymorphic transitions were also proposed to be topotactic and a similar displacive mechanism was suggested for the α, β, and γ-BaAlF₅ phases characterized by the same cis-connected octahedral chains, some of these structures being also solved from the powder data (Le Bail et al., Reference Le Bail, Férey, Mercier, De Kozak and Samouël1990b). K₂FeF₅ form-II (Figure 6) may be described as containing kink-folded blocks related to form-IV, and if the junction zone between these blocks is examined, one recognizes similarities with form-III (Figure 3). All of the four K₂FeF₅ forms are characterized by cis-connected octahedral chains, and their V/Z ratios at room temperature (Table VI) are almost identical. The periodicity is of N = 2 octahedra for forms II, III, and IV, corresponding to the shortest cell parameter close to 5.7 Å (Table VI), whereas form-I shows N = 8 (Figure 7) so that the phase transition IV → I at 580 °C looks to require a much larger atomic displacement amplitude than for the III → IV transition. A different organization with N = 4 was established for α-(NH₄)₂FeF₅ (Fourquet et al., Reference Fourquet, Le Bail, Duroy and Moron1989), also produced by dehydration and solved from the powder data, so that the current number of structure types for the A₂MF₅ compounds presenting cis-connected octahedral chains is five. Concerning K₂FeF₅, only form-I is yet characterized magnetically, however the three other forms should logically share the same characteristic one-dimensional antiferromagnetic model (Chelkowski and Wijn, Reference Chelkowski and Wijn1995). Other A₂ MF₅ structural types not considered here, characterized by trans-connections leading to linear octahedral chains, are described elsewhere (Babel and Tressaud, Reference Babel, Tressaud and Hagenmuller1985).

Figure 3.

(Color online) Projection along the short b-axis of the structure of K₂FeF₅ form-III.

Figure 4.

(Color online) View of the structure of K₂FeF₅ form-IV along the c axis, showing the infinite cis-connected octahedral chains. A view of form-III along its a-axis would be quite similar.

Figure 5.

(Color online) Projection of the structure of K₂FeF₅ form-IV along the b axis, to be compared to Figure 3 in order to recognize how the rotation of half of the chains (see the arrows) and their translation of 1/2 b would allow us to rebuild the form-III structure (thin lines).

Figure 6.

(Color online) Projection of the structure of K₂FeF₅ form-II along the c axis, to be compared to Figure 5 in order to recognize kink folded blocks of the form-IV monoclinic cell (thin lines) which reproduce also the form-III arrangement at their junctions.

Figure 7.

(Color online) Projection of the structure of K₂FeF₅ form-I along the a axis, showing a N = 8 periodicity along the octahedral chains, to be compared to Figure 4 showing N = 2 for form-III (and also for forms II and IV).

Table VI.

Summary of the crystallographic details of the four K₂FeF₅ forms.