NaMn₆(P₂O₇)₂(P₃O₁₀) and KCd₆(P₂O₇)₂(P₃O₁₀)

The crystal structures of two new diphosphates, sodium hexamanganese bis­(diphosphate) triphosphate, NaMn₆(P₂O₇)₂(P₃O₁₀), and potassium hexacadmium bis­(diphosphate) triphosphate, KCd₆(P₂O₇)₂(P₃O₁₀), confirm the rigidity of the M₆(P₂O₇)₂(P₃O₁₀) matrix (M is Mn or Cd) and the relatively fixed dimensions of the tunnels extending in the a direction of the unit cell. The compounds are isomorphous; the P₂O₇^4- anion and the alkali metal cations lie on mirror planes. Bond-valence analysis of the bonding details of the atoms found within the tunnels permits a prediction of the conductivity.

S1. Comment

Extending our studies of transition metal phosphate complexes (Bennazha et al., 1999; Erragh et al., 1998a,b; Eddahby et al., 1997; Amroussi et al., 1997) of the formula ABP₂O₇ into stoichiometries of greater complexity, we have recently reported the single-crystal X-ray structures of two compounds of stoichiometry A^IB^II₆(P₂O₇)₂(P₃O₁₀), with A = K and B = Mn, and A = Ag and B = Mn (Bennazha et al., 2001), a family of compounds previously observed only with A = NH₄⁺ [(NH₄)Cd₆(P₂O₇)₂(P₃O₁₀); Ivanov et al., 1978]. We have now identified two further members of the family, NaMn₆(P₂O₇)₂(P₃O₁₀), (I), and KCd₆(P₂O₇)₂(P₃O₁₀), (II). \sch

These two complexes contain a mixture of the phosphate moieties P₂O₇ and P₃O₁₀, which is highly unusual (Durif, 1995). There are only two other examples of triphosphate, P₃O₁₀^-5, and diphosphate, P₂O₇^-4, existing in the same unit cell, namely Na₇Y₂(P₂O₇)₂(P₃O₁₀) (Hamady & Jouini, 1996) and Ca₃(NH₄)₄H₃(P₂O₇)₂(P₃O₁₀) (Actina et al., 1989).

Structures (I) and (II) are isostructural with those of the previously reported A^IB^II₆(P₂O₇)₂(P₃O₁₀) compounds, with A = K and B = Mn, and A = Ag and B = Mn (Bennazha et al., 2001), and with (NH₄)Cd₆(P₂O₇)₂(P₃O₁₀) (Ivanov et al., 1978). Members of this family crystallize with layers of P₂O₇^-4 groups alternating with P₃O₁₀^-5 layers along the b axis (Fig. 1). The A atoms (K, Na or Ag) are found in between P₃O₁₀ groups, and the Mn or Cd atoms are seen within and at the edges of the P₂O₇ layers. The A atom is located on a mirror plane and displays tenfold coordination geometry. It is seen to occupy a tunnel extending parallel to the shortest cell dimension.

Knowledge of these two additional structures provides the opportunity to make several comparisons. Firstly, one can examine the structures of the A^IMn^II₆(P₂O₇)₂(P₃O₁₀) series, with A = K, Ag or Na, to ascertain the influence of a difference in the size of A upon the structure as a whole. In this series, the ionic radii decrease in the following order: K 1.59, Ag 1.28 and Na 1.24 Å (Shannon, 1976). The cell volumes show an irregular decrease in the order 925.1 (9), 928 (2) and 891.1 (3) ų. Within the series, the calculated densities, 3.481, 3.716 and 3.553 Mg m^-3, and the average A—O distances for the ten-coordinate A atom, 3.027 (3), 2.997 (9) and 2.955 (6) Å, differ only marginally. Thus, one asks how the other atoms accommodate the change in the radius of the A atom. Potentially, changes might be observed in the conformation of the phosphate groups or in the Mn bonding.

The P₂O₇ groups show no change in conformation: the O—P···P—O torsion angles are, respectively, 60.0, 59.5 and 60.0°. The P—O—P angles are 150.3 (2), 151.4 (6) and 153.1 (3)°, respectively. Similarly, the P₃O₁₀ groups are identical within experimental error: the P—P—P angles are 93.7 (2), 93.2 (7) and 93.8 (3)°, and the O—P—P—O torsion angles have averages of 3.26, 4.36 and 3.3°, respectively. The details of the Mn bonding are similar; the pseudo-octahedral Mn has average Mn—O distances of 2.22 (3), 2.22 (8) and 2.195 (4) Å in the three structures, respectively.

While previous work has led us to the idea that differences in the ratios of the ionic radii of the A and B atoms lead to very clear differences in structure in A^IB^IIP₂O₇-type diphosphate structures (Elmarzouki, 2002), this appears not to be the case in A^IB^II₆(P₂O₇)₂(P₃O₁₀) structures. One concludes that the Mn₆(P₂O₇)₂(P₃O₁₀) matrix is rigid and provides a rigid host matrix into which has been inserted the K, Ag or Na cation. The Mn₆(P₂O₇)₂(P₃O₁₀) matrix is analogous to the zeolite-type matrices, which are rigid and resist conformational changes due to the presence of guest atoms or molecules in their cavities. Indeed, a projection view of NaMn₆(P₂O₇)₂(P₃O₁₀) down the shortest axis (a) clearly shows that the A atoms lie in the tunnel (Fig. 1).

Bond-valence analysis (Brown, 1981) is usually applied to verify the identity of an atom in a structure, the charge resident on an atom or the quality of a structure determination. However, in our hands, it has proved a useful means of identifying potential atomic movement or conductivity. Cations which are well fixed in their sites will display bond-valence totals approximately equal to their oxidation states. Atoms which are potentially mobile will have lesser totals, indicating their lesser degree of interaction with their neighbours and thus their mobility. The totals for the ten-coordinate A atoms, K, Ag and Na, are 1.015, 0.670 and 0.699, respectively. These large deviations from 1.0 may be interpreted in two ways. One suspects that the Ag and Na structures will show significant conductivity in the a direction as the A atoms move in that direction along the tunnels. Secondly, the Mn₆(P₂O₇)₂(P₃O₁₀) matrix has not collapsed or adapted itself in any significant way to permit higher degrees of interaction with the A atom. This attests to the rigidity of this structure, in which the A atom is a guest.

The preparation of KCd₆(P₂O₇)₂(P₃O₁₀) provides the opportunity to make the comparison between KMn₆ and KCd₆, to see what difference the change in the identity of B makes in the rigidity of the structure formed by B₆(P₂O₇)₂(P₃O₁₀). The ionic radius of Cd is slightly larger than that of Mn (Mn 0.67 Å and Cd 0.95 Å). Details of the B₆(P₂O₇)₂(P₃O₁₀) framework of the two structures, with A = K and B = Mn or Cd, are nearly identical within experimental error: the avearge B—O distances for the two structures are 2.22 (3) and 2.283 (4) Å, respectively. In the P₂O₇ groups, the O—P—P—O torsion angles average 60.0 and 59.2°, respectively, with P—O—P angles of 150.3 (2) and 154.1 (6)°, respectively. The P₃O₁₀ groups display O—P—P—O torsion angles of 3.26 and 4.5°, respectively, with P—P—P angles of 93.7 (2) and 92.6 (2)°, respectively. Furthermore, the average K—O bond distances for ten-coordinate K are 3.027 (3) and 3.061 (5) Å, with bond-valence totals of 1.015 and 1.177, respectively. Thus the substitution of Cd for Mn in the B₆(P₂O₇)₂(P₃O₁₀) framework has made little difference in the structural details of the framework and in the environment experienced by the guest K ion.

S2. Experimental

The starting materials Na₂CO₃ [for (I)] or KNO₃ [for (II)], MnCO₃ (or CdCO₃) and (NH₄)₂HPO₄ were mixed in a stoichiometry expected to lead to the preparation of A₂B₃(P₂O₇)₂, with A = Na and B = Mn for (I), and A = K and B = Cd for (II), according to the following reactions: Na₂CO₃ + 3MnCO₃ + 4(NH₄)₂HPO₄ → Na₂Mn₃(P₂O₇)₂ + 4CO₂ + 8NH₃ + 6H₂O and 2KNO₃ + 3 CdCO₃ + 4(NH₄)₂HPO₄ → K₂Cd₃(P₂O₇)₂ + 2NO₂ + 3CO₂ + 8NH₃ + 6H₂O. The starting mixture was heated slowly to 873 K to eliminate NH₃, CO₂ [or NO₂ in (II)] and H₂O, followed by heating to 1223 K [for (I)] or 1023 K [for (II)] and slow cooling (6 K h^-1) to 673 K, whereupon the furnace was allowed to cool to ambient temperature without control. Colourless solids were produced, which were found to be crystalline (I) and (II).

Computing details

For both compounds, data collection: XSCANS (Siemens, 1991); cell refinement: XSCANS; data reduction: XSCANS; program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: Please provide missing details.

Figures

Fig. 1. A projection view of NaMn6(P2O7)2(P3O10) down the a axis. Displacement ellipsoids are shown at the 50% probability level. The KCd6(P2O7)2(P3O10) compound is isostructural. Please check added text.

(I) Sodium hexamanganese bis(diphosphate) triphosphate

Crystal data

Mn6NaO24P7	F(000) = 916
Mr = 953.42	Dx = 3.553 Mg m^−3
Monoclinic, P21/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yb	Cell parameters from 27 reflections
a = 5.345 (1) Å	θ = 7.5–10.2°
b = 26.620 (4) Å	µ = 4.91 mm^−1
c = 6.559 (1) Å	T = 293 K
β = 107.28 (1)°	Chunk, colourless
V = 891.1 (3) Å^3	0.1 × 0.1 × 0.1 mm
Z = 2

Data collection

Syntex P4 four-circle diffractometer	1822 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.051
Graphite monochromator	θmax = 30.0°, θmin = 3.1°
θ/2θ scans	h = −1→7
Absorption correction: ψ scan (XEMP; Siemens, 1991)	k = −1→37
Tmin = 0.582, Tmax = 0.612	l = −9→9
3530 measured reflections	3 standard reflections every 97 reflections
2645 independent reflections	intensity decay: none

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.050	w = 1/[σ^2(Fo^2) + (0.0065P)^2] where P = (Fo^2 + 2F^c)/3
wR(F^2) = 0.088	(Δ/σ)max < 0.001
S = 1.03	Δρmax = 0.08 e Å^−3
2645 reflections	Δρmin = −0.10 e Å^−3
179 parameters	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0016 (3)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles. Correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Mn1	0.20992 (17)	0.40187 (3)	0.08608 (12)	0.00971 (18)
Mn3	−0.18455 (17)	0.45574 (3)	0.31467 (12)	0.01020 (18)
Na1	0.2440 (9)	0.2500	0.4154 (6)	0.0386 (11)
Mn2	−0.12293 (16)	0.31663 (3)	−0.27988 (12)	0.00919 (18)
P1	−0.5428 (4)	0.2500	−0.0895 (3)	0.0075 (4)
O11	−0.8256 (10)	0.2500	−0.2121 (8)	0.0103 (11)
O13	−0.3548 (10)	0.2500	−0.2206 (8)	0.0108 (11)
O14	−0.4968 (7)	0.29644 (14)	0.0641 (5)	0.0107 (7)
P2	−0.2492 (3)	0.33186 (5)	0.19269 (19)	0.0074 (3)
O21	−0.0646 (7)	0.33425 (14)	0.0545 (5)	0.0121 (8)
O22	−0.3882 (7)	0.38029 (13)	0.2080 (5)	0.0112 (8)
O23	−0.1241 (7)	0.30570 (13)	0.3996 (5)	0.0123 (8)
P3	0.6841 (3)	0.60991 (5)	0.3844 (2)	0.0080 (3)
O31	0.8570 (7)	0.59547 (14)	0.6035 (5)	0.0087 (7)
O32	0.8450 (7)	0.62221 (14)	0.2346 (5)	0.0104 (8)
O33	0.4896 (8)	0.65004 (16)	0.3883 (6)	0.0207 (10)
O34	0.5394 (8)	0.55848 (15)	0.2919 (6)	0.0220 (10)
P4	0.2898 (3)	0.52468 (5)	0.2045 (2)	0.0072 (3)
O41	0.1278 (7)	0.54792 (14)	−0.0028 (5)	0.0098 (7)
O42	0.4115 (7)	0.47443 (14)	0.1743 (6)	0.0117 (8)
O43	0.1410 (8)	0.52105 (14)	0.3676 (5)	0.0124 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn1	0.0092 (4)	0.0107 (4)	0.0089 (3)	0.0006 (3)	0.0021 (3)	−0.0005 (3)
Mn3	0.0089 (4)	0.0133 (4)	0.0077 (3)	0.0021 (3)	0.0016 (3)	−0.0003 (3)
Na1	0.026 (2)	0.054 (3)	0.027 (2)	0.000	−0.0044 (18)	0.000
Mn2	0.0095 (4)	0.0092 (4)	0.0090 (3)	−0.0005 (3)	0.0030 (3)	−0.0006 (3)
P1	0.0071 (9)	0.0086 (9)	0.0058 (8)	0.000	0.0006 (7)	0.000
O11	0.006 (3)	0.007 (2)	0.016 (2)	0.000	−0.001 (2)	0.000
O13	0.009 (3)	0.011 (3)	0.014 (2)	0.000	0.005 (2)	0.000
O14	0.0079 (18)	0.0090 (17)	0.0147 (16)	−0.0038 (15)	0.0029 (15)	−0.0053 (14)
P2	0.0074 (6)	0.0078 (6)	0.0070 (6)	−0.0001 (5)	0.0024 (5)	−0.0004 (4)
O21	0.0119 (19)	0.015 (2)	0.0099 (16)	−0.0043 (16)	0.0041 (15)	−0.0003 (14)
O22	0.0102 (19)	0.0094 (18)	0.0144 (17)	−0.0012 (16)	0.0044 (16)	−0.0007 (14)
O23	0.017 (2)	0.0105 (19)	0.0101 (15)	0.0028 (16)	0.0048 (16)	0.0016 (14)
P3	0.0057 (6)	0.0109 (6)	0.0064 (6)	−0.0002 (5)	0.0005 (5)	0.0014 (5)
O31	0.0108 (19)	0.0104 (17)	0.0047 (15)	0.0022 (15)	0.0022 (15)	0.0001 (13)
O32	0.0117 (19)	0.0133 (18)	0.0069 (15)	−0.0029 (16)	0.0036 (15)	0.0008 (14)
O33	0.023 (2)	0.023 (2)	0.0177 (19)	0.014 (2)	0.0084 (19)	0.0082 (17)
O34	0.018 (2)	0.020 (2)	0.023 (2)	−0.0129 (19)	−0.0021 (19)	−0.0029 (17)
P4	0.0062 (6)	0.0081 (6)	0.0067 (6)	−0.0008 (5)	0.0007 (5)	0.0001 (5)
O41	0.0101 (18)	0.0113 (18)	0.0092 (16)	0.0011 (16)	0.0047 (15)	0.0015 (14)
O42	0.0090 (19)	0.0111 (18)	0.0147 (17)	−0.0005 (15)	0.0032 (15)	−0.0033 (14)
O43	0.015 (2)	0.0125 (19)	0.0091 (16)	0.0024 (16)	0.0023 (16)	0.0003 (14)

Geometric parameters (Å, º)

Na1—O23	2.441 (5)	Mn3—O43^x	2.119 (4)
Na1—O23^i	2.441 (5)	Mn3—O42^xi	2.139 (4)
Na1—O33^ii	3.111 (5)	Mn3—O31^ii	2.157 (4)
Na1—O33^iii	3.111 (5)	Mn3—O41^viii	2.158 (3)
Na1—O14^iv	3.264 (5)	Mn3—O22	2.293 (4)
Na1—O14^v	3.264 (5)	Mn3—O43	2.411 (4)
Na1—O21	3.322 (5)	P1—O11	1.487 (5)
Na1—O21^i	3.322 (5)	P1—O13	1.504 (5)
Na1—O13^vi	2.694 (6)	P1—O14	1.567 (4)
Na1—O11^vi	2.579 (6)	P1—O14^i	1.567 (4)
Mn1—O32^vii	2.134 (3)	O14—P2	1.640 (4)
Mn1—O22^iv	2.136 (4)	P2—O23	1.495 (4)
Mn1—O31^ii	2.171 (3)	P2—O22	1.506 (4)
Mn1—O41^viii	2.181 (4)	P2—O21	1.527 (4)
Mn1—O42	2.204 (4)	P3—O33	1.496 (4)
Mn1—O21	2.293 (4)	P3—O31	1.509 (3)
Mn2—O33^viii	2.075 (4)	P3—O32	1.521 (4)
Mn2—O23^ix	2.120 (3)	P3—O34	1.600 (4)
Mn2—O32^vii	2.164 (4)	O34—P4	1.570 (4)
Mn2—O21	2.173 (3)	P4—O41	1.511 (4)
Mn2—O13	2.263 (3)	P4—O43	1.513 (4)
Mn2—O11^iv	2.334 (4)	P4—O42	1.526 (4)
O23—Na1—O23^i	74.8 (2)	O41^viii—Mn1—O21	89.92 (14)
O23—Na1—O33^ii	76.2 (2)	O42—Mn1—O21	164.12 (14)
O23—Na1—O33^iii	143.2 (2)	O33^viii—Mn2—O23^ix	89.68 (15)
O23—Na1—O14^iv	104.2 (2)	O33^viii—Mn2—O32^vii	105.37 (16)
O23—Na1—O14^v	134.9 (2)	O23^ix—Mn2—O32^vii	92.23 (14)
O23—Na1—O21	48.4 (2)	O33^viii—Mn2—O21	95.24 (15)
O23—Na1—O21^i	99.0 (2)	O23^ix—Mn2—O21	170.98 (15)
O23—Na1—O13^vi	117.2 (2)	O32^vii—Mn2—O21	79.19 (13)
O23—Na1—O11^vi	72.5 (2)	O33^viii—Mn2—O13	83.36 (17)
O23^i—Na1—O33^ii	143.2 (2)	O23^ix—Mn2—O13	102.85 (16)
O23^i—Na1—O33^iii	76.2 (2)	O32^vii—Mn2—O13	162.72 (16)
O23^i—Na1—O14^iv	134.9 (2)	O21—Mn2—O13	85.26 (15)
O23^i—Na1—O14^v	104.2 (2)	O33^viii—Mn2—O11^iv	155.56 (16)
O23^i—Na1—O21	99.0 (2)	O23^ix—Mn2—O11^iv	83.45 (16)
O23^i—Na1—O21^i	48.4 (2)	O32^vii—Mn2—O11^iv	98.33 (14)
O23^i—Na1—O13^vi	117.2 (2)	O21—Mn2—O11^iv	94.96 (16)
O23^i—Na1—O11^vi	72.5 (2)	O13—Mn2—O11^iv	75.42 (15)
O33^ii—Na1—O33^iii	117.6 (2)	O43^x—Mn3—O42^xi	99.06 (15)
O33^ii—Na1—O14^iv	74.3 (2)	O43^x—Mn3—O31^ii	95.48 (14)
O33^ii—Na1—O14^v	112.2 (2)	O42^xi—Mn3—O31^ii	153.49 (14)
O33^ii—Na1—O21	77.7 (2)	O43^x—Mn3—O41^viii	160.10 (15)
O33^ii—Na1—O21^i	160.4 (2)	O42^xi—Mn3—O41^viii	90.61 (14)
O33^ii—Na1—O13^vi	59.1 (2)	O31^ii—Mn3—O41^viii	82.83 (13)
O33^ii—Na1—O11^vi	77.6 (2)	O43^x—Mn3—O22	117.32 (14)
O33^iii—Na1—O14^iv	112.2 (2)	O42^xi—Mn3—O22	75.24 (13)
O33^iii—Na1—O14^v	74.3 (2)	O31^ii—Mn3—O22	78.41 (14)
O33^iii—Na1—O21	160.4 (2)	O41^viii—Mn3—O22	81.89 (13)
O33^iii—Na1—O21^i	77.7 (2)	O43^x—Mn3—O43	77.55 (15)
O33^iii—Na1—O13^vi	59.1 (2)	O42^xi—Mn3—O43	119.17 (13)
O33^iii—Na1—O11^vi	77.6 (2)	O31^ii—Mn3—O43	85.53 (13)
O14^iv—Na1—O14^v	44.5 (2)	O41^viii—Mn3—O43	82.55 (13)
O14^iv—Na1—O21	57.8 (2)	O22—Mn3—O43	158.86 (13)
O14^iv—Na1—O21^i	88.7 (2)	O11—P1—O13	115.8 (3)
O14^iv—Na1—O13^vi	103.4 (2)	O11—P1—O14	106.7 (2)
O14^iv—Na1—O11^vi	151.6 (2)	O13—P1—O14	111.31 (19)
O14^v—Na1—O21	88.7 (2)	O11—P1—O14^i	106.7 (2)
O14^v—Na1—O21^i	57.8 (2)	O13—P1—O14^i	111.31 (19)
O14^v—Na1—O13^vi	103.4 (2)	O14—P1—O14^i	104.2 (3)
O14^v—Na1—O11^vi	151.6 (2)	P1—O14—P2	137.1 (3)
O21—Na1—O21^i	84.9 (2)	O23—P2—O22	115.8 (2)
O21—Na1—O13^vi	136.7 (2)	O23—P2—O21	111.4 (2)
O21—Na1—O11^vi	119.6 (2)	O22—P2—O21	115.0 (2)
O21^i—Na1—O13^vi	136.7 (2)	O23—P2—O14	105.9 (2)
O21^i—Na1—O11^vi	119.6 (2)	O22—P2—O14	100.8 (2)
O13^vi—Na1—O11^vi	57.4 (2)	O21—P2—O14	106.48 (19)
O32^vii—Mn1—O22^iv	96.72 (14)	O33—P3—O31	113.4 (2)
O32^vii—Mn1—O31^ii	157.17 (15)	O33—P3—O32	112.7 (2)
O22^iv—Mn1—O31^ii	94.87 (14)	O31—P3—O32	111.5 (2)
O32^vii—Mn1—O41^viii	94.35 (14)	O33—P3—O34	110.9 (2)
O22^iv—Mn1—O41^viii	157.51 (14)	O31—P3—O34	103.5 (2)
O31^ii—Mn1—O41^viii	81.97 (13)	O32—P3—O34	104.0 (2)
O32^vii—Mn1—O42	115.81 (14)	P4—O34—P3	153.0 (3)
O22^iv—Mn1—O42	77.21 (14)	O41—P4—O43	112.4 (2)
O31^ii—Mn1—O42	85.93 (14)	O41—P4—O42	113.2 (2)
O41^viii—Mn1—O42	80.35 (14)	O43—P4—O42	111.7 (2)
O32^vii—Mn1—O21	77.18 (13)	O41—P4—O34	106.9 (2)
O22^iv—Mn1—O21	111.60 (14)	O43—P4—O34	110.3 (2)
O31^ii—Mn1—O21	80.27 (13)	O42—P4—O34	101.6 (2)

Symmetry codes: (i) x, −y+1/2, z; (ii) −x+1, −y+1, −z+1; (iii) −x+1, y−1/2, −z+1; (iv) x+1, y, z; (v) x+1, −y+1/2, z; (vi) x+1, y, z+1; (vii) −x+1, −y+1, −z; (viii) −x, −y+1, −z; (ix) x, y, z−1; (x) −x, −y+1, −z+1; (xi) x−1, y, z.

(II) Potassium hexacadmium bis(diphosphate) triphosphate

Crystal data

Cd6KO24P7	F(000) = 1208
Mr = 1314.29	Dx = 4.542 Mg m^−3
Monoclinic, P21/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yb	Cell parameters from 19 reflections
a = 5.479 (1) Å	θ = 4.3–11.4°
b = 27.112 (6) Å	µ = 7.45 mm^−1
c = 6.769 (1) Å	T = 293 K
β = 107.11 (2)°	Chunk, colourless
V = 961.0 (3) Å^3	0.1 × 0.1 × 0.1 mm
Z = 2

Data collection

Syntex P4 four-circle diffractometer	2575 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.061
Graphite monochromator	θmax = 30.0°, θmin = 3.0°
θ/2θ scans	h = −7→1
Absorption correction: ψ scan (XEMP; Siemens, 1991)	k = −1→38
Tmin = 0.422, Tmax = 0.475	l = −9→9
3802 measured reflections	3 standard reflections every 97 reflections
2866 independent reflections	intensity decay: none

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.040	w = 1/[σ^2(Fo^2) + (0.1P)^2] where P = (Fo^2 + 2F^c)/3
wR(F^2) = 0.124	(Δ/σ)max = 0.001
S = 1.01	Δρmax = 0.03 e Å^−3
2866 reflections	Δρmin = −0.02 e Å^−3
179 parameters	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0312 (14)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles: correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Cd1	0.21476 (7)	0.401065 (14)	0.07936 (5)	0.01012 (15)
Cd2	−0.10831 (7)	0.316993 (14)	−0.29375 (6)	0.01007 (15)
Cd3	−0.18227 (7)	0.456654 (15)	0.31341 (5)	0.01075 (15)
K1	0.2879 (4)	0.2500	0.3631 (3)	0.0266 (4)
P1	−0.5288 (3)	0.2500	−0.1049 (3)	0.0079 (3)
O11	−0.8080 (10)	0.2500	−0.2252 (8)	0.0098 (10)
O13	−0.3447 (10)	0.2500	−0.2337 (8)	0.0109 (10)
O14	−0.4861 (7)	0.29599 (15)	0.0434 (6)	0.0126 (7)
P2	−0.2451 (2)	0.33017 (5)	0.17738 (19)	0.0079 (3)
O21	−0.0561 (7)	0.33212 (16)	0.0509 (6)	0.0117 (7)
O22	−0.3768 (8)	0.37833 (15)	0.1914 (6)	0.0122 (7)
O23	−0.1360 (9)	0.30321 (16)	0.3791 (6)	0.0162 (8)
P3	0.6729 (2)	0.60837 (5)	0.39189 (19)	0.0083 (3)
O31	0.8494 (7)	0.59582 (16)	0.6056 (6)	0.0121 (8)
O32	0.8272 (8)	0.62120 (16)	0.2444 (6)	0.0136 (8)
O33	0.4811 (9)	0.64668 (19)	0.3980 (7)	0.0241 (10)
O34	0.5386 (9)	0.55736 (18)	0.3061 (7)	0.0213 (9)
P4	0.2908 (2)	0.52490 (5)	0.20808 (19)	0.0080 (3)
O41	0.1374 (7)	0.54910 (15)	0.0079 (6)	0.0105 (7)
O42	0.4073 (7)	0.47592 (15)	0.1744 (6)	0.0120 (7)
O43	0.1384 (8)	0.52033 (17)	0.3621 (6)	0.0138 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cd1	0.0104 (2)	0.0082 (2)	0.0111 (2)	−0.00023 (13)	0.00208 (14)	−0.00173 (12)
Cd2	0.0113 (2)	0.0075 (2)	0.0108 (2)	−0.00068 (13)	0.00228 (14)	−0.00017 (12)
Cd3	0.0105 (2)	0.0103 (2)	0.0105 (2)	0.00100 (13)	0.00159 (15)	−0.00161 (13)
K1	0.0191 (9)	0.0385 (13)	0.0216 (9)	0.000	0.0051 (7)	0.000
P1	0.0083 (7)	0.0047 (8)	0.0097 (7)	0.000	0.0014 (6)	0.000
O11	0.006 (2)	0.008 (2)	0.012 (2)	0.000	−0.0036 (18)	0.000
O13	0.016 (2)	0.005 (2)	0.015 (2)	0.000	0.010 (2)	0.000
O14	0.0119 (16)	0.0060 (17)	0.0192 (17)	−0.0026 (14)	0.0035 (14)	−0.0054 (14)
P2	0.0100 (5)	0.0038 (6)	0.0092 (5)	0.0000 (4)	0.0018 (4)	−0.0004 (4)
O21	0.0129 (17)	0.0133 (19)	0.0101 (15)	−0.0027 (15)	0.0052 (13)	−0.0016 (14)
O22	0.0131 (17)	0.0036 (17)	0.0196 (17)	0.0016 (14)	0.0041 (14)	−0.0027 (13)
O23	0.026 (2)	0.0100 (19)	0.0130 (16)	0.0062 (17)	0.0063 (15)	0.0019 (15)
P3	0.0084 (5)	0.0067 (6)	0.0088 (5)	−0.0002 (4)	0.0007 (4)	0.0009 (4)
O31	0.0121 (17)	0.016 (2)	0.0067 (14)	0.0021 (14)	0.0000 (13)	0.0004 (13)
O32	0.0181 (18)	0.0091 (19)	0.0137 (16)	−0.0063 (15)	0.0048 (15)	−0.0028 (14)
O33	0.023 (2)	0.026 (3)	0.022 (2)	0.018 (2)	0.0061 (17)	0.0075 (19)
O34	0.019 (2)	0.014 (2)	0.026 (2)	−0.0095 (17)	−0.0012 (17)	−0.0010 (17)
P4	0.0090 (5)	0.0057 (6)	0.0081 (5)	−0.0004 (5)	0.0007 (4)	0.0002 (4)
O41	0.0110 (16)	0.0098 (18)	0.0097 (15)	0.0031 (14)	0.0013 (13)	0.0017 (13)
O42	0.0105 (16)	0.0044 (17)	0.0194 (17)	0.0025 (14)	0.0019 (14)	−0.0005 (14)
O43	0.0143 (17)	0.016 (2)	0.0124 (16)	−0.0025 (15)	0.0061 (14)	−0.0032 (15)

Geometric parameters (Å, º)

Cd1—O32^i	2.219 (4)	K1—O14^x	3.058 (4)
Cd1—O22^ii	2.228 (4)	K1—O14^ii	3.058 (4)
Cd1—O31^iii	2.263 (4)	K1—O21^viii	3.261 (4)
Cd1—O41^iv	2.286 (4)	K1—O21	3.261 (4)
Cd1—O42	2.291 (4)	K1—O33^iii	3.296 (6)
Cd1—O21	2.359 (4)	K1—O33^xi	3.296 (6)
Cd2—O33^iv	2.189 (5)	P1—O11	1.507 (5)
Cd2—O23^v	2.207 (4)	P1—O13	1.515 (5)
Cd2—O32^i	2.234 (4)	P1—O14	1.575 (4)
Cd2—O21	2.302 (4)	P1—O14^viii	1.575 (4)
Cd2—O13	2.335 (3)	P2—O23	1.508 (4)
Cd2—O11^ii	2.403 (3)	P2—O22	1.508 (4)
Cd3—O43^vi	2.228 (4)	P2—O21	1.526 (4)
Cd3—O42^vii	2.229 (4)	P3—O33	1.487 (5)
Cd3—O31^iii	2.250 (4)	P3—O31	1.523 (4)
Cd3—O41^iv	2.265 (4)	P3—O32	1.526 (4)
Cd3—O22	2.410 (4)	P3—O34	1.594 (5)
Cd3—O43	2.416 (4)	O34—P4	1.590 (4)
K1—O23^viii	2.763 (5)	P4—O41	1.517 (4)
K1—O23	2.763 (5)	P4—O42	1.519 (4)
K1—O13^ix	2.875 (6)	P4—O43	1.520 (4)
K1—O11^ix	2.983 (6)
O32^i—Cd1—O22^ii	93.59 (15)	O11^ix—K1—O14^ii	151.68 (10)
O32^i—Cd1—O31^iii	160.28 (15)	O14^x—K1—O14^ii	48.13 (15)
O22^ii—Cd1—O31^iii	96.23 (14)	O23^viii—K1—O21^viii	48.44 (11)
O32^i—Cd1—O41^iv	94.09 (15)	O23—K1—O21^viii	92.85 (13)
O22^ii—Cd1—O41^iv	159.76 (15)	O13^ix—K1—O21^viii	136.47 (8)
O31^iii—Cd1—O41^iv	82.43 (14)	O11^ix—K1—O21^viii	112.23 (10)
O32^i—Cd1—O42	115.07 (15)	O14^x—K1—O21^viii	62.61 (10)
O22^ii—Cd1—O42	79.40 (14)	O14^ii—K1—O21^viii	95.56 (11)
O31^iii—Cd1—O42	83.61 (15)	O23^viii—K1—O21	92.85 (13)
O41^iv—Cd1—O42	80.38 (14)	O23—K1—O21	48.44 (11)
O32^i—Cd1—O21	79.86 (14)	O13^ix—K1—O21	136.47 (8)
O22^ii—Cd1—O21	110.69 (15)	O11^ix—K1—O21	112.23 (10)
O31^iii—Cd1—O21	80.68 (14)	O14^x—K1—O21	95.56 (11)
O41^iv—Cd1—O21	89.10 (15)	O14^ii—K1—O21	62.61 (10)
O42—Cd1—O21	162.12 (14)	O21^viii—K1—O21	86.13 (15)
O33^iv—Cd2—O23^v	88.32 (17)	O23^viii—K1—O33^iii	129.10 (14)
O33^iv—Cd2—O32^i	104.34 (18)	O23—K1—O33^iii	75.11 (13)
O23^v—Cd2—O32^i	96.77 (16)	O13^ix—K1—O33^iii	58.24 (8)
O33^iv—Cd2—O21	94.15 (16)	O11^ix—K1—O33^iii	71.91 (10)
O23^v—Cd2—O21	176.90 (15)	O14^x—K1—O33^iii	121.12 (13)
O32^i—Cd2—O21	80.80 (14)	O14^ii—K1—O33^iii	79.84 (12)
O33^iv—Cd2—O13	83.88 (18)	O21^viii—K1—O33^iii	164.54 (12)
O23^v—Cd2—O13	99.51 (17)	O21—K1—O33^iii	78.64 (11)
O32^i—Cd2—O13	161.98 (17)	O23^viii—K1—O33^xi	75.11 (13)
O21—Cd2—O13	82.65 (16)	O23—K1—O33^xi	129.10 (14)
O33^iv—Cd2—O11^ii	157.44 (17)	O13^ix—K1—O33^xi	58.24 (8)
O23^v—Cd2—O11^ii	84.64 (17)	O11^ix—K1—O33^xi	71.91 (10)
O32^i—Cd2—O11^ii	97.77 (15)	O14^x—K1—O33^xi	79.84 (12)
O21—Cd2—O11^ii	93.74 (16)	O14^ii—K1—O33^xi	121.12 (13)
O13—Cd2—O11^ii	76.22 (15)	O21^viii—K1—O33^xi	78.64 (11)
O43^vi—Cd3—O42^vii	98.81 (15)	O21—K1—O33^xi	164.54 (12)
O43^vi—Cd3—O31^iii	95.30 (15)	O33^iii—K1—O33^xi	116.43 (17)
O42^vii—Cd3—O31^iii	153.59 (15)	O11—P1—O13	115.5 (3)
O43^vi—Cd3—O41^iv	162.87 (16)	O11—P1—O14	106.3 (2)
O42^vii—Cd3—O41^iv	89.53 (14)	O13—P1—O14	111.57 (19)
O31^iii—Cd3—O41^iv	83.18 (14)	O11—P1—O14^viii	106.3 (2)
O43^vi—Cd3—O22	119.55 (15)	O13—P1—O14^viii	111.57 (19)
O42^vii—Cd3—O22	76.84 (14)	O14—P1—O14^viii	104.7 (3)
O31^iii—Cd3—O22	76.79 (14)	P1—O14—P2	137.8 (3)
O41^iv—Cd3—O22	76.84 (14)	O23—P2—O22	115.6 (2)
O43^vi—Cd3—O43	78.60 (15)	O23—P2—O21	111.8 (2)
O42^vii—Cd3—O43	119.53 (15)	O22—P2—O21	114.9 (2)
O31^iii—Cd3—O43	85.05 (16)	O23—P2—O14	105.4 (2)
O41^iv—Cd3—O43	84.26 (14)	O22—P2—O14	101.6 (2)
O22—Cd3—O43	155.08 (14)	O21—P2—O14	106.0 (2)
O23^viii—K1—O23	63.0 (2)	O33—P3—O31	112.7 (3)
O23^viii—K1—O13^ix	108.95 (14)	O33—P3—O32	113.0 (3)
O23—K1—O13^ix	108.95 (14)	O31—P3—O32	110.7 (2)
O23^viii—K1—O11^ix	65.33 (12)	O33—P3—O34	111.2 (3)
O23—K1—O11^ix	65.33 (12)	O31—P3—O34	104.4 (2)
O13^ix—K1—O11^ix	51.69 (15)	O32—P3—O34	104.1 (2)
O23^viii—K1—O14^x	109.57 (13)	P4—O34—P3	151.4 (4)
O23—K1—O14^x	139.53 (13)	O41—P4—O42	113.0 (2)
O13^ix—K1—O14^x	110.82 (13)	O41—P4—O43	112.1 (2)
O11^ix—K1—O14^x	151.68 (10)	O42—P4—O43	111.8 (2)
O23^viii—K1—O14^ii	139.53 (13)	O41—P4—O34	108.3 (2)
O23—K1—O14^ii	109.57 (12)	O42—P4—O34	101.6 (3)
O13^ix—K1—O14^ii	110.82 (13)	O43—P4—O34	109.5 (2)

Symmetry codes: (i) −x+1, −y+1, −z; (ii) x+1, y, z; (iii) −x+1, −y+1, −z+1; (iv) −x, −y+1, −z; (v) x, y, z−1; (vi) −x, −y+1, −z+1; (vii) x−1, y, z; (viii) x, −y+1/2, z; (ix) x+1, y, z+1; (x) x+1, −y+1/2, z; (xi) −x+1, y−1/2, −z+1.