Rietveld refinement of the langbeinite-type mixed-metal phosphate K₂Ni_0.5Zr_1.5(PO₄)₃

Dipotassium [nickel(II) zirconium(IV)] tris­(orthophosphate) was prepared from a self-flux in the system K₂O–P₂O₅–NiO–K₂ZrF₆. The title compound belongs to the langbeinite family and is built up from two [MO₆] octa­hedra [M = Ni:Zr with mixed occupancy in ratios of 0.21 (4):0.79 (4) and 0.29 (4):0.71 (4), respectively] and [PO₄] tetra­hedra inter­linked via vertices into a ³_∞[M₂(PO₄)₃] framework. Two independent K⁺ cations are located in large cavities of the framework, with coordination numbers to O²⁻ anions of nine and twelve. The K, Ni, and Zr sites are located on threefold rotation axes.

Key indicators

• Powder X-ray study
• T = 293 K
• Mean [sigma](P-O) = 0.016 Å
• Disorder in main residue
• R factor = 0.000
• wR factor = 0.000
• Data-to-parameter ratio = 0.0

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT041_ALERT_1_C Calc. and Reported SumFormula    Strings  Differ     Please Check
PLAT799_ALERT_4_C Numeric Label on Displacement Par. Record ......          ?

Alert level G
PLAT004_ALERT_5_G Polymeric Structure Found with Dimension .......          3 Info
PLAT042_ALERT_1_G Calc. and Reported MoietyFormula Strings  Differ     Please Check
PLAT045_ALERT_1_G Calculated and Reported Z Differ by ............       0.50 Ratio
PLAT152_ALERT_1_G The Supplied and Calc. Volume s.u. Differ by ...          2 Units
PLAT301_ALERT_3_G Main Residue  Disorder ............ Percentage =         16 Note
PLAT791_ALERT_4_G The Model has Chirality at P1      .............          S Verify
PLAT811_ALERT_5_G No ADDSYM Analysis: Too Many Excluded Atoms ....          ! Info
PLAT860_ALERT_3_G Number of Least-Squares Restraints .............          2 Note
PLAT982_ALERT_1_G The  K-f'=     0.365 Deviates from the  IT-value      0.387
PLAT982_ALERT_1_G The Ni-f'=    -2.956 Deviates from the  IT-value     -3.003
PLAT982_ALERT_1_G The  O-f'=     0.047 Deviates from the  IT-value      0.049
PLAT982_ALERT_1_G The  P-f'=     0.283 Deviates from the  IT-value      0.296
PLAT982_ALERT_1_G The Zr-f'=    -0.314 Deviates from the  IT-value     -0.186

   0 ALERT level A = Most likely a serious problem - resolve or explain
   0 ALERT level B = A potentially serious problem, consider carefully
   2 ALERT level C = Check. Ensure it is not caused by an omission or oversight
  13 ALERT level G = General information/check it is not something unexpected

   9 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   0 ALERT type 2 Indicator that the structure model may be wrong or deficient
   2 ALERT type 3 Indicator that the structure quality may be low
   2 ALERT type 4 Improvement, methodology, query or suggestion
   2 ALERT type 5 Informative message, check

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S1. Comment

Phosphates of the langbeinite structure type are considered as favorable for environmentally safe crystalline forms of radioactive waste solidification (Orlova et al., 2003). Langbeinite-type frameworks ³_∞[M₂(PO₄)₃] can be composed of various polyvalent metal pairs, for example, K₂Ni_0.5Ti_1.5(PO₄)₃ (Ogorodnyk et al., 2007b), K_1.96Mn_0.57Zr_1.43(PO₄)₃ and K_1.93Mn_0.53Hf_1.47(PO₄)₃ (Ogorodnyk et al., 2007b), K₂FeZr(PO₄)₃ (Orlova et al., 2003), K₂REZr(PO₄)₃, RE = Y, Gd (Wulff et al., 1992). Herein the powder X-ray refinement of a phosphate, structurally isotypic with the mineral langbenite, K₂Mg₂(SO₄)₃ (Zemann & Zemann, 1957), K₂Ni_0.5Zr_1.5(PO₄)₃, (I), is presented (Fig. 1).

The K, Ni, and Zr sites lie on threefold rotation axes in positions 4 a with the sequence {(Zr,Ni)1—(Zr,Ni)2—K1—K2} where (Zr,Ni)1 and (Zr,Ni)2 are metal sites with a mixed occupancy (Fig. 2). P and O atoms are located in 12 b positions.

The structure of (I) contains two independent [(Zr,Ni)O₆] octahedra and one [PO₄] tetrahedron which are linked together via common vertices, forming a three-dimensional framework (Fig. 3). The (Zr,Ni)–O bond lengths are 2.070 (14) Å, 2.098 (14) Å and 2.036 (12) Å, 2.041 (16) Å for [(Zr,Ni)1O₆] and [(Zr,Ni)2O₆], respectively. It should be noted that the occupancy of the metal sites by Ni²⁺ is slightly different (0.21 (4) for the M1 site and 0.29 (4) for the M2 site) whereas in case of K₂Ni_0.5Ti_1.5(PO₄)₃ (Ogorodnyk et al., 2007b) Ni²⁺ ions are almost equally distributed (occupancy of 0.25 for both positions), with ((Ti,Ni)—O bonds ranging from 1.938 (5) to 1.962 (5) Å. The three-dimensional framework ³_∞[(Zr,Ni)₂(PO₄)₃] has large closed cavities where the two independent K⁺ cations are located. K1 is coordinated by nine O atoms, while K2 is surrounded by twelve O atoms (Fig. 4), with K—O bond lengths ranging from 2.956 (16) to 3.332 (15) Å (Table 1).

Related literature

For the structure of the mineral langbeinite, see: Zemann & Zemann (1957). For langbeinite-related phosphates based on different pairs of polyvalent metals, see: Wulff et al. (1992) for K₂REZr(PO₄)₃ (RE = Y, Gd); Orlova et al. (2003) for K₂FeZr(PO₄)₃; Ogorodnyk et al. (2007a) for K_1.96Mn_0.57Zr_1.43(PO₄)₃ and K_1.93Mn_0.53Hf_1.47(PO₄)₃; Ogorodnyk et al. (2007b) for K₂Ni_0.5Ti_1.5(PO₄)₃. For the profile function used in the Rietveld refinement, see: Thompson et al. (1987).

S2. Experimental

A well-ground mixture of 11.8 g KPO₃ and 1.12 g NiO was placed in a platinum crucible and then was heated up to 1273 K. The temperature was kept constant during one hour and after that it was decreased to 1173 K. 4.25 g of K₂ZrF₆ were added to the flux under stirring with a platinum stirrer (initial K:P, Zr:P and Zr:Ni ratio equal to 1.3, 0.15, and 1.0, respectively). The crystallization of the melt was performed in the temperature range from 1173 to 913 K at an rate of 25 K/h. Finally, the crucible was cooled down to room temperature. The obtained material of (I) was recovered by washing with hot deionized water. The small crystals of (I) had the form of regular tetrahedra and were of light-yellow colour. The atomic ratio of the elements in (I) was found to be 4:1:3:6 for K/Ni/Zr/P, respectively: The sample was dissolved in 80% sulfuric acid under heating. The amount of the elements was then determined by atomic emission spectroscopy with inductive coupled plasma, AES-ICP, Spectroflame Modula ICP "Spectro".

S3. Refinement

The powder pattern of (I) was indexed in the cubic system using DICVOL-2004 (Boultif & Louër, 2004). The pattern indexing showed that the sample was a single phase. Atomic coordinates of K_1.96Mn_0.57Zr_1.43(PO₄)₃ (Ogorodnyk et al., 2007a) were used during Rietveld refinement as a starting model. For profile refinement a pseudo-Voigt function with axial divergence asymmetry (Thompson et al., 1987) was used. First, the scaling factor, background, cell parameters etc. were refined during profile matching. Atomic coordinates were then refined during the next step. Atomic coordinates and displacement parameters of corresponding Zr and Ni sites were constrained to be the same. Isotropic displacement parameters of all atoms were appended to the refinement. The occupancies of K, Ni and Zr were refined taking into account that the occupancies of the hexacoordinated metal site should be equal to unity which was done using occupancy constraints. As the occupancy of the K sites was found to be 1, the occupancy factors of K1 and K2 were fixed at 1. The displacement factors of the O atoms were spread over a large range which is meaningless in this case due to the quality of the powder diffraction data. Thus U_iso values for all O atoms were constrained to be equal. As a result, the values of U_iso and their e.s.d.'s have close values. At the final refinement cycles two geometric restraints were applied to the lengths of P—O bonds because their values were unsatisfactory for the model (without restraints, one was ≈ 1.44 Å while another was close to 1.57 Å). Experimental, calculated and difference patterns are shown in Fig. 1.

Computing details

Data collection: PCXRD (Shimadzu, 2006); cell refinement: DICVOL-2004 (Boultif & Louër, 2004); data reduction: FULLPROF (Rodriguez-Carvajal, 2006); program(s) used to solve structure: FULLPROF (Rodriguez-Carvajal, 2006); program(s) used to refine structure: FULLPROF (Rodriguez-Carvajal, 2006); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: PLATON (Spek, 2009) and enCIFer (Allen et al., 2004).

Figures

	Fig. 1. Results of the Rietveld refinement of K2Ni0.5Zr1.5(PO4)3. Experimental (dots), calculated (red curve) and difference (blue curve) data.
	Fig. 2. A view of the asymmetric unit of K2Ni0.5Zr1.5(PO4)3. Displacement ellipsoid are drawn at the 50% probability level.
	Fig. 3. A projection of the structure of (I) along [111]. PO4 tetrahedra are pink, (Zr,Ni)1O6 octahedra are turquoise, (Zr,Ni)2O6 octahedra are green, K^+ cations are shown as yellow spheres.
	Fig. 4. The O environment of K1^+ and K2^+ cations for (I). Displacement ellipsoid are drawn at the 50% probability level.

Dipotassium [nickel(II) zirconium(IV)] tris(orthophosphate)

Crystal data

K2Ni0.5Zr1.5(PO4)3	Dx = 3.355 Mg m^−3
Mr = 529.29	Cu Kα radiation, λ = 1.540598 Å
Cubic, P213	T = 293 K
Hall symbol: P 2ac 2ab 3	Particle morphology: isometric
a = 10.15724 (13) Å	yellow
V = 1047.92 (2) Å^3	flat sheet, 25 × 25 mm
Z = 4	Specimen preparation: Prepared at 293 K and 101.3 kPa

Data collection

Shimadzu LabX XRD-6000 diffractometer	Data collection mode: reflection
Radiation source: X-ray tube, X-ray	Scan method: step
Graphite monochromator	2θmin = 10.910°, 2θmax = 104.911°, 2θstep = 0.020°
Specimen mounting: glass container

Refinement

Rp = 0.100	107 parameters
Rwp = 0.134	2 restraints
Rexp = 0.034	9 constraints
RBragg = 0.041	Standard least squares refinement
R(F) = 0.035	(Δ/σ)max = 0.001
4701 data points	Background function: Linear Interpolation between a set background points with refinable heights
Profile function: Thompson-Cox-Hastings pseudo-Voigt * Axial divergence asymmetry	Preferred orientation correction: March-Dollase Numeric Multiaxial Function

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All su's are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.7043 (6)	0.7043 (6)	0.7043 (6)	0.054 (5)*
K2	0.9317 (7)	0.9317 (7)	0.9317 (7)	0.052 (4)*
Zr1	0.1448 (2)	0.1448 (2)	0.1448 (2)	0.007 (2)*	0.79 (4)
Zr2	0.4146 (3)	0.4146 (3)	0.4146 (3)	0.004 (2)*	0.71 (4)
Ni1	0.1448 (2)	0.1448 (2)	0.1448 (2)	0.007 (2)*	0.21 (4)
Ni2	0.4146 (3)	0.4146 (3)	0.4146 (3)	0.004 (2)*	0.29 (4)
P1	0.4581 (6)	0.2296 (8)	0.1286 (7)	0.004 (2)*
O1	0.3180 (14)	0.2335 (14)	0.0844 (15)	0.003 (2)*
O2	0.5417 (12)	0.2950 (14)	0.0238 (14)	0.003 (2)*
O3	0.5025 (12)	0.0869 (16)	0.1471 (13)	0.003 (2)*
O4	0.4729 (14)	0.3039 (12)	0.2580 (10)	0.003 (2)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

Geometric parameters (Å, º)

K1—O1^i	2.956 (16)	Zr1—O1^xiii	2.070 (14)
K1—O2^ii	3.165 (14)	Zr1—O2^xiv	2.098 (14)
K1—O4^ii	3.325 (14)	Zr2—O4	2.036 (12)
K1—O1^iii	2.956 (16)	Zr2—O3^i	2.041 (16)
K1—O2^iv	3.165 (14)	Zr2—O4^xi	2.036 (12)
K1—O4^iv	3.325 (14)	Zr2—O3^iii	2.041 (16)
K1—O1^v	2.956 (16)	Zr2—O4^xiii	2.036 (12)
K1—O2^vi	3.165 (14)	Zr2—O3^v	2.041 (16)
K1—O4^vi	3.325 (14)	Ni1—O2^xii	2.098 (14)
K2—O3^ii	2.973 (15)	Ni1—O1^xiii	2.070 (14)
K2—O2^vii	3.026 (16)	Ni1—O2^xiv	2.098 (14)
K2—O4^ii	3.127 (15)	Ni1—O1^xi	2.070 (14)
K2—O4^vii	3.332 (15)	Ni1—O1	2.070 (14)
K2—O3^iv	2.973 (15)	Ni1—O2^x	2.098 (14)
K2—O2^viii	3.026 (16)	Ni2—O4	2.036 (12)
K2—O4^iv	3.127 (15)	Ni2—O3^v	2.041 (16)
K2—O4^viii	3.332 (15)	Ni2—O3^i	2.041 (16)
K2—O3^vi	2.973 (15)	Ni2—O4^xi	2.036 (12)
K2—O2^ix	3.026 (16)	Ni2—O3^iii	2.041 (16)
K2—O4^vi	3.127 (15)	Ni2—O4^xiii	2.036 (12)
K2—O4^ix	3.332 (15)	P1—O3	1.530 (18)
Zr1—O1	2.070 (14)	P1—O4	1.523 (13)
Zr1—O2^x	2.098 (14)	P1—O2	1.515 (15)
Zr1—O1^xi	2.070 (14)	P1—O1	1.493 (16)
Zr1—O2^xii	2.098 (14)
O1—Zr1—O2^x	93.2 (5)	O1—Ni1—O2^x	93.2 (5)
O1—Zr1—O1^xi	90.6 (6)	O1—Ni1—O1^xi	90.6 (6)
O1—Zr1—O2^xii	175.9 (5)	O1—Ni1—O2^xii	175.9 (5)
O1—Zr1—O1^xiii	90.6 (6)	O1—Ni1—O1^xiii	90.6 (6)
O1—Zr1—O2^xiv	87.7 (6)	O1—Ni1—O2^xiv	87.7 (6)
O1^xi—Zr1—O2^x	87.7 (6)	O1^xi—Ni1—O2^x	87.7 (6)
O2^x—Zr1—O2^xii	88.6 (5)	O2^x—Ni1—O2^xii	88.6 (5)
O1^xiii—Zr1—O2^x	175.9 (5)	O1^xiii—Ni1—O2^x	175.9 (5)
O2^x—Zr1—O2^xiv	88.6 (5)	O2^x—Ni1—O2^xiv	88.6 (5)
O1^xi—Zr1—O2^xii	93.2 (5)	O4^xi—Ni2—O4^xiii	87.5 (5)
O1^xi—Zr1—O1^xiii	90.6 (6)	O3^v—Ni2—O4^xi	170.8 (5)
O1^xi—Zr1—O2^xiv	175.9 (5)	O3^iii—Ni2—O4^xiii	84.5 (5)
O1^xiii—Zr1—O2^xii	87.7 (6)	O3^iii—Ni2—O3^v	92.1 (5)
O2^xii—Zr1—O2^xiv	88.6 (5)	O3^v—Ni2—O4^xiii	96.5 (5)
O1^xiii—Zr1—O2^xiv	93.2 (5)	O3^i—Ni2—O3^iii	92.1 (5)
O3^i—Zr2—O4	96.5 (5)	O3^i—Ni2—O4	96.5 (5)
O4—Zr2—O4^xi	87.5 (5)	O4—Ni2—O4^xi	87.5 (5)
O3^iii—Zr2—O4	170.8 (5)	O3^iii—Ni2—O4	170.8 (5)
O4—Zr2—O4^xiii	87.5 (5)	O4—Ni2—O4^xiii	87.5 (5)
O3^v—Zr2—O4	84.5 (5)	O3^v—Ni2—O4	84.5 (5)
O3^i—Zr2—O4^xi	84.5 (5)	O3^i—Ni2—O4^xi	84.5 (5)
O3^i—Zr2—O3^iii	92.1 (5)	O3^iii—Ni2—O4^xi	96.5 (5)
O3^i—Zr2—O4^xiii	170.8 (5)	O3^i—Ni2—O4^xiii	170.8 (5)
O3^i—Zr2—O3^v	92.1 (5)	O3^i—Ni2—O3^v	92.1 (5)
O3^iii—Zr2—O4^xi	96.5 (5)	O3—P1—O4	109.5 (8)
O4^xi—Zr2—O4^xiii	87.5 (5)	O1—P1—O2	108.1 (9)
O3^v—Zr2—O4^xi	170.8 (5)	O1—P1—O3	110.1 (9)
O3^iii—Zr2—O4^xiii	84.5 (5)	O1—P1—O4	109.9 (9)
O3^iii—Zr2—O3^v	92.1 (5)	O2—P1—O3	109.7 (8)
O3^v—Zr2—O4^xiii	96.5 (5)	O2—P1—O4	109.5 (9)
O1^xi—Ni1—O2^xii	93.2 (5)	Zr1—O1—P1	135.2 (10)
O1^xi—Ni1—O1^xiii	90.6 (6)	Ni1—O1—P1	135.2 (10)
O1^xi—Ni1—O2^xiv	175.9 (5)	Zr1^xv—O2—P1	168.8 (10)
O1^xiii—Ni1—O2^xii	87.7 (6)	Zr2^xvi—O3—P1	153.7 (9)
O2^xii—Ni1—O2^xiv	88.6 (5)	Zr2—O4—P1	156.8 (9)
O1^xiii—Ni1—O2^xiv	93.2 (5)	Ni2—O4—P1	156.8 (9)

Symmetry codes: (i) −x+1, y+1/2, −z+1/2; (ii) −x+3/2, −y+1, z+1/2; (iii) −z+1/2, −x+1, y+1/2; (iv) −y+1, z+1/2, −x+3/2; (v) y+1/2, −z+1/2, −x+1; (vi) z+1/2, −x+3/2, −y+1; (vii) −z+1, x+1/2, −y+3/2; (viii) −y+3/2, −z+1, x+1/2; (ix) x+1/2, −y+3/2, −z+1; (x) x−1/2, −y+1/2, −z; (xi) z, x, y; (xii) −z, x−1/2, −y+1/2; (xiii) y, z, x; (xiv) −y+1/2, −z, x−1/2; (xv) x+1/2, −y+1/2, −z; (xvi) −x+1, y−1/2, −z+1/2.