The polyhedral representations of KNaNbOF₅ and KNaMO₂F₄ (M = Mo⁶+, W⁶⁺) are shown in Figure 2. These three-dimensional structures can be described as an ordered rock-salt double perovskite with the general formula ABB′X₆ with ordered A-site layers where K⁺ occupies half the A-sites and Na⁺ and Nb⁵⁺ or M⁶⁺ occupy the B and B′ sites, respectively. X represents one O^2- and five F^- in KNaNbOF₅ and two O^2- and four F^- in KNaMO₂F₄. Note that throughout the following discussion M corresponds to either molybdenum or tungsten atoms.

In KNaNbOF₅, the Na⁺ and Nb⁵⁺ ions occupy ordered corner-shared octahedra (no tilt, a⁰a⁰a⁰) as in the ReO₃ structure type. The Nb⁵⁺ ions form short Nb=O bonds and one long Nb–F bond trans to the oxide (Table 1) resulting in a distorted octahedron, as seen in previously reported d⁰ transition metal anionic units [19,20]. Mid-IR confirms the presence of the Nb=O bond with a peak at ν_s 975 cm^-1 [21]. The Nb–O–Na and Nb–F2–Na bond angles are 180° along the c-axis (Table 1), consistent with corner sharing octahedra with no tilt. The Nb–F3–Na bond angle is 162.50(4)°.

In KNaMO2F4, the oxide ion and its trans fluoride are ordered. The second oxide ion is disordered among the other three fluorides in the equatorial positions. Although this partial ordering occurs between the oxide and fluoride ions, the A- and B-site cations are both ordered. The B-site cations, Na⁺ and M⁶⁺, form corner-sharing octahedra (no tilt, a⁰a⁰a⁰). The M⁶⁺ ions form one short M=O and one long M–F bond trans to the oxide (Table 1) and, as a result, distort toward the corners of the octahedra as opposed to the edges [22,23]. Mid-IR confirms the presence of the M=O bond with peaks at ν_s 969 cm^-1 and ν_as 916 cm^-1 for Mo and ν_s 991 cm^-1 and ν_as 923 cm^-1 for W [21]. Again, the M–O–Na and M–F2–Na bond angles are 180° along the c-axis consistent with corner-shared octahedra with no tilt. The M–X3–Na bond angle is 164.03(5)° and 162.11(8)° for Mo and W, respectively.

The A-site K⁺ cations occupy half of the positions in an ordered array. Along the c-axis, the K⁺ cations are 12-coordinated to the F^- in the A-site layer. In the adjacent layer, where the axial oxides are located, the A-site is vacant. The unique ABB′X₆ structure can be described as repeating AX layers of KF, BX₂ layers of Na_1/2Nb_1/2F_4/2, X layers of O, BX₂ layers of Na_1/2Nb_1/2F_4/2, etc (Figure 2a) for KNaNbOF₅. KNaMO₂F₄ can be described as repeating AX layers of KF, BX₂ layers of Na_1/2M_1/2(O/F)_4/2, X layers of O, BX₂ layers of Na_1/2M_1/2(O/F)_4/2, etc. (Figure 2b).

Electronic potentials and chemical hardness cooperatively influence the long-range order of the [NbOF₅]^2- anionic unit [20,23]. Oxide and fluoride order can be understood in the context of Pauling's second crystal rule (PSCR) which states that anions with the largest negative potentials will occupy sites having the largest positive potentials [24]. The assessment of the positive potential in the crystal frameworks, carried out by calculating the PSCR (bond strength) sum [25] and bond valence sum [24,26] around each anionic position, should match as closely as possible to the assessment of the negative potentials of each oxide and fluoride ion (Tables 2 and 3). The central Nb⁵⁺ ion has been excluded from the PCSR calculations because we are only interested in the oxide and fluoride interactions with the extended bond network.

In a purely inorganic bond network, the oxide and fluoride ligands in the [NbOF₅]^2- anionic unit with the largest residual negative charge will make the most and strongest contacts to the coordination environment [20]. In KNaNbOF₅, the F2 fluorides, which occupy positions in contact with one six-coordinate Na⁺ and four twelve-coordinate K⁺ (1/6 + 4 × 1/12 = 0.5 PSCR sum and bond valence sums of 0.46 vu), retain the most negative potentials (0.58 vu) (Table 3). The four remaining fluorides, F3, have less negative potentials (0.29 vu). They are each three-coordinate (one Na⁺ and two K⁺) with lower bond valence sums of 0.40 vu and PSCR sums of 0.33.

The observation that the O1 site in KNaNbOF₅ makes one cationic contact to Na⁺ in the extended bond network is understandable when other crystal chemistry factors are considered. The polarizability of the oxide (6.49 ų) and fluoride (1.57 ų) ions [29] also influences their interactions with the extended bond network. For instance, the “harder” (relative to oxide) F2 trans fluoride interacts with one Na⁺ (2.3501(14) Å) and four K⁺ (2.9586(9) Å) cations (Tables 2 and 3). Although there are fewer Na–F bonds compared to K–F, the Na–F interactions are much stronger, as seen by their shorter bond lengths and higher bond valences. Thus, the Na⁺ cation is significantly over bonded (1.22 vu) with respect to K⁺ (1.08 vu). The K⁺ cation is softer than Na⁺, therefore it needs to make more contacts to the fluorides in order to satisfy PSCR. At the same time, the Nb⁵⁺ ion displaces away from the trans fluoride toward the “softer” oxide which has the lowest PSCR sum and bond valence sum of 0.17 and 0.26, respectively. As a result, the oxide attracts one Na⁺ in the extended bond network at 2.2961(16) Å and is under bonded.

KNaNbOF₅ has a noncentrosymmetric polymorph [20]. The results discussed here on the noncentrosymmetric polymorph can be found in [20]. The different local coordination environments around the centrosymmetric (CS) and noncentrosymmetric (NCS) [NbOF₅]^2- structures are illustrated in Figure 3. In the NCS polymorph the two fluorides F1 and F3 contain the largest residual negative charge (0.48 and 0.23 vu, respectively) and make three contacts with two eight-coordinate K⁺ and one six-coordinate Na⁺. In the CS polymorph, one fluoride, F1, has the largest residual negative charge (0.58 vu) and makes four contacts with four twelve-coordinate K⁺ and one six-coordinate Na⁺. Although there are fewer Na–F interactions than K–F in both the NCS and CS polymorphs, the Na–F interactions are stronger, as seen by their shorter bond lengths and higher bond valences. As a result, in the CS polymorph the Na⁺ cation is slightly more over bonded (1.22 vu) compared to K⁺ (1.08 vu).

The oxides in both the NCS and CS polymorph are under bonded. In the NCS polymorph, the oxide is three-coordinate with one K⁺ and one Na⁺ contact and a Nb=O bond at 1.745(5) Å. In the CS polymorph, the oxide is two-coordinate and makes one Na⁺ contact and as expected there is a shorter Nb=O bond distance of 1.7179(14) Å. Conversely, the extra K⁺ contact in the NCS polymorph results in a longer Nb=O bond.

In a perovskite with B-site rock-salt ordering the A-site cations prefer to order in a layered arrangement which is stabilized by the presence of a second order Jahn Teller displacement of at least one d⁰ transition metal at the B-site [10,11]. In NaLnMnWO₆ and NaLnMgWO₆ with a trivalent and monovalent A-site cation, the oxides coordinated to the Na⁺ are under bonded while the oxides coordinated to the Ln³⁺ are over bonded. To compensate, the d⁰ transition metal, W⁶⁺, at the B-site will shift towards the oxide coordinated to the smaller cation (Na⁺) and away from the larger cation (Ln³⁺) to alleviate the lattice strain arising from the size mismatch (Figure 4a). A similar comparison can be made to KNaNbOF₅. Instead of having two A-site cations, there is an occupied and unoccupied A-site. As a result, the oxide in the same layer as the unoccupied A-site is under bonded. To compensate, the Nb⁵⁺ at the B-site shifts toward the oxide and away from the trans fluoride (Figure 4b). Thus, the long range ordering of the KNaNbOF₅ structure results in a centrosymmetric arrangement of the anionic units.

In KNaMO₂F₄ (M = Mo⁶⁺, W⁶⁺), the oxide and its trans fluoride are ordered while the second oxide is disordered along with the other three fluorides at the equatorial positions. Despite the partial ordering of the oxide and fluoride, the A- and B-site cations are ordered. The partial ordering of the anionic unit has been reported previously, where Mo/W distorts towards the corner as opposed to the edge [22,23]. The partial ordering of the oxide and fluoride is due to the symmetric environment around the equatorial positions. In KNaNbOF₅, the bond network at the oxide differs from the trans fluoride; therefore, the oxide can be identified based on bond lengths. When two oxides are present as in KNaMO₂F₄, one oxide is ordered (Figure 5). The bond lengths of the oxide and the trans fluoride at the axial positions are different, which we use to identify the oxide and fluoride sites. However, at the equatorial positions, the bond length is the average of the four bonds from the second oxide and three fluorides, therefore the second oxide and three fluorides are not differentiated. In addition, bond valence sums cannot be accurately calculated because it is dependent on the observed bond lengths.

Single crystal X-ray diffraction data of KNaNbOF₅, KNaMoO₂F₄ and KNaWO₂F₄ were collected with Mo-Kα radiation (0.71073 Å) on a Bruker APEX2 CCD diffractometer and integrated with the SAINT-Plus program [35]. The structures were solved by direct methods and refined against F² by full-matrix least-squares techniques with SHELX. A face-indexed absorption correction was performed numerically using the program XPREP. All structures were checked for missing symmetry elements with PLATON [36]. The final refinement includes anisotropic displacement parameters. Further details of the crystal structure investigations may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, http://www.fiz-karlsruhe.de/request_for_deposited_data.html) on quoting the 422708 (KNaNbOF₅), 422707 (KNaMoO₂F₄) and 422709 (KNaWO₂F₄) CSD numbers. Crystallographic data for KNaNbOF₅ and KNaMO₂F₄, (M = Mo⁶⁺, W⁶⁺) are given in Table 4.

Mid-infrared (600–4000 cm^-1) spectra of KNaNbOF₅, KNaMoO₂F₄ and KNaWO₂F₄ were collected using a Bruker 37 Tensor FTIR spectrometer equipped with an ATR germanium cell attachment operating at a resolution of 2 cm^-1.