Rietveld refinement of langbeinite-type K₂YHf(PO₄)₃

Potassium yttrium hafnium tris­(orthophosphate) belongs to the langbeinite-family and is built up from [MO₆] octa­hedra [in which the positions of the two independent M sites are mutually occupied by Y and Hf in a 0.605 (10):0.395 (10) ratio] and [PO₄] tetra­hedra connected via vertices into a three-dimensional framework. This framework is penetrated by large closed cavities in which the two independent K atoms are located; one of the K atoms is nine-coordinated and the other is 12-coordinated by surrounding O atoms. The K, Y and Hf atoms lie on threefold rotation axes, whereas the P and O atoms are located in general positions.

Related literature

For the structure of the mineral langbeinite, see: K₂Mg₂(SO₄)₃ (Zemann & Zemann, 1957). For powder diffraction investigations and Rietveld refinements of phosphate-based langbeinites, see: K₂MZr(PO₄)₃, M = Y, Gd (Wulff et al., 1992); K₂FeZr(PO₄)₃ (Orlova et al., 2003); K₂LnZr(PO₄)₃, Ln = Ce—Lu (Trubach et al., 2004). Hafnium-containing phosphate langbeinites are reported for K₂BiHf(PO₄)₃ (Losilla et al., 1998) and K_1.93Mn_0.53Hf_1.47(PO₄)₃ (Ogorodnyk et al., 2007a). For the synthesis of zirconium- or hafnium-containing langbeinite-related phosphates from fluoride precursors using flux techniques, see: Ogorodnyk et al. (2007a,b). Parameters needed to calculate bond-valence sums were taken from Brown & Altermatt (1985) and Brese & O'Keeffe (1991), respectively. For ionic radii, see: Shannon (1976). For crystallographic background, see: Boultif & Louër (2004).

Experimental

Crystal data

• K₂YHf(PO₄)₃

• M_r = 630.51

• Cubic, P 2₁ 3

• a = 10.30748 (9) Å

• V = 1095.11 (2) ų

• Z = 4

• Cu Kα radiation

• T = 293 K

• Specimen shape: flat sheet

• 15 × 15 × 1 mm

• Specimen prepared at 101.3 kPa

• Specimen prepared at 293 K

• Particle morphology: isometric, colourless

Data collection

• Shimadzu XRD-6000 diffractometer

• Specimen mounting: glass container

• Specimen mounted in reflection mode

• Scan method: step

• 2θ_min = 5.0, 2θ_max = 105.0°

• Increment in 2θ = 0.02°

Refinement

• R_p = 5.375

• R_wp = 7.075

• R_exp = 2.809

• R_B = 4.248

• S = 2.51

• Wavelength of incident radiation: 1.540530 Å

• Profile function: Thompson–Cox–Hastings pseudo-Voigt with axial divergence asymmetry (Thompson et al., 1987)

• 528 reflections

• 48 parameters

Table 1
Selected geometric parameters (Å, °). M = Hf, Y

K1—O1^i	2.981 (16)
K1—O2^ii	3.345 (14)
K1—O4^ii	3.413 (16)
K2—O3^ii	2.907 (14)
K2—O2^iii	2.912 (14)
K2—O4^ii	3.207 (17)
K2—O4^iii	3.336 (17)
M1—O1	2.148 (14)
M1—O2^iv	2.085 (15)
M2—O3^i	2.211 (14)
M2—O4	2.113 (17)
P1—O1	1.518 (16)
P1—O2	1.621 (17)
P1—O3	1.470 (16)
P1—O4	1.497 (19)

O1—P1—O2	100.5 (9)
O1—P1—O3	113.0 (9)
O1—P1—O4	106.9 (9)
O2—P1—O3	121.4 (8)
O2—P1—O4	107.7 (9)
O3—P1—O4	106.5 (9)
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) .

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

Supporting information

S1. Comment

Among a great variety of langbeinite-type based phosphate (mineral langbeinite K₂Mg₂(SO₄)₃, Zemann & Zemann, 1957), only several compounds containing hafnium were reported: K₂BiHf(PO₄)₃ (Losilla et al., 1998) and K_1.93Mn_0.53Hf_1.47(PO₄)₃ (Ogorodnyk et al., 2007a). At the same time a great number of zirconium-containing phosphates with langbeinite framework were synthesized and structurally characterized: K₂MZr(PO₄)₃, M = Y, Gd (Wulff et al., 1992); K₂FeZr(PO₄)₃ (Orlova et al., 2003); K₂LnZr(PO₄)₃, Ln = Ce—Lu (Trubach et al., 2004b); Cs_1+xLn_xZr_2-x(PO₄)₃, Ln = Sm—Lu (Ogorodnyk et al., 2007b). This can be connected with the similarity of chemical behavior of zirconium and hafnium on the one hand and the rareness (or, possibly, the high prices) of hafnium raw materials in comparison with zirconium ones on the other hand.

Due to similar chemical properties of Zr and Hf and the close values of their ionic radii (for coordination number 6 they are 0.72 and 0.71 Å for Zr and Hf, respectively; Shannon, 1976) the cell parameters of K₂YHf(PO₄)₃ are slightly smaller than of K₂YZr(PO₄)₃ (a= 10.3346 (1) Å; Wulff et al., 1992).

K, Y and Hf atoms lie on the 3-fold rotation axes in 4a positions (Fig. 1). P and O atoms are located in 12b positions. Both Y and Hf atoms occupy two hexacoordinated positions competitively. M1 position is preferably occupied by Hf while M2 is by Y. The structure contains [MO₆] octahedra and [PO₄] tetrahedra which are connected via vertices. Two nearest [MO₆] octahedra are joined to each other by three bridging orthophosphate tetrahedra forming {M₂P₃O₁₈} groups. These groups form three-dimensional framework penetrated with large closed cavities. Two independent potassium atoms are located in each cavity. K1 atom is nine-coordinated, while K2 is twelve-coordinated.

Bond valence sums (BVS) were calculated using parameters for Hf, Y, P from Brese & O'Keeffe (1991) and for K from Brown & Altermatt (1985). The calculation were performed for formula sum K₂YHf(PO₄)₃ taking into account occupancies of the octahedrally coordinatedd M positions. The sum of BVS of positively charged atoms is equal to 24.16 while the chemical charge of the remaining O atoms is equal to -24.

Related literature

For the structure of the mineral langbeinite, see: K₂Mg₂(SO₄)₃ (Zemann & Zemann, 1957). For powder diffraction investigations and Rietveld refinements of phosphate-based langbeinites, see: K₂MZr(PO₄)₃, M = Y, Gd (Wulff et al., 1992); K₂FeZr(PO₄)₃ (Orlova et al., 2003); K₂LnZr(PO₄)₃, Ln = Ce—Lu (Trubach et al., 2004). Hafnium-containing phosphate langbeinites are reported for K₂BiHf(PO₄)₃ (Losilla et al., 1998) and K_1.93Mn_0.53Hf_1.47(PO₄)₃ (Ogorodnyk et al., 2007a). For the synthesis of zirconium- or hafnium-containing langbeinite-related phosphates from fluoride precursors using flux techniques, see: Ogorodnyk et al. (2007a,b). Parameters needed to calculate bond-valence sums were taken from Brown & Altermatt (1985) and Brese & O'Keeffe (1991), respectively. For ionic radii, see: Shannon (1976). For crystallographic background, see: Boultif & Louër (2004).

S2. Experimental

Well-shaped tetrahedral crystals of K₂YHf(PO₄)₃ were grown using a flux technique. A mixture of 4.52 g KPO₃ and 3.4 g K₄P₂O₇ (initial K/P molar ratio was set equal to 1.35) was melted in a platinum crucible at 1273 K. The melt was kept at this temperature for 1 h and after that the temperature was decreased to 1173 K. Dispersed in an agate mortar, a mixture of 1.36 g HfF₄ and 0,78 g YF₃ was added to the phosphate flux under stirring. The crystallization of the melts was performed from 1173 to 893 K at a rate of 30 K/h. The synthesized crystalline sample was separated from remaining glass by leaching with hot water. The dimensions of the crystals were found to be in a range 0.01–0.05 mm. The sample was ground in an agate mortar before performing powder XRD data collection. The recorded powder pattern indicated a single phase material.

The element ratio was determined using ICP-AES analyses (Shimadzu ICPE-9000 spectrometer). The sample for measurements was prepared by dissolution of calculated amount of K₂YHf(PO₄)₃ in sulfuric acid (98%) with final dilution by bidistilled water. Element ratio was found to be: 2.02:0.97:0.98:3.04 for K:Y:Hf:P which fits well with the theoretical values.

S3. Refinement

The cubic cell was found by Dicvol 2004 (Boultif & Louër, 2004). The Hf-containing langbeinite-related compound with general composition K_1.93Mn_0.53Hf_1.47(PO₄)₃ (ICSD-418669, Ogorodnyk et al., 2007a) was selected as a starting model for Rietveld refinement. At first profile matching refinement was performed. Then background and scaling factors were added to the refined parameters. The background was approximated using a 6-coefficient polynomial function. Modified pseudo-Voigt function (Thompson et al., 1987) was used for the profile refinement. On the next stage atomic positions were refined. Due to previous investigations of langbeinite-related phosphates and close ionic radii of Y and Hf common positions M1 and M2 occupied by both these elements were suggested. Their coordinates, anisotropic displacement parameters (ADP) and occupancies were constrained. After the refinement of the metal occupancies in M1 and M2 positions and refinement of isotropic displacement parameters, we tried to refine ADPs of the heavy atoms (Y, Hf and K). The isotropic displacement parameters of the four O atoms were constrained to be equal before the final cycles of the refinement. The experimental, calculated and difference pattern of the Rietveld refinement is shown in Fig. 2.

Computing details

Data collection: PCXRD (Shimadzu, 2006); cell refinement: FULLPROF (Rodriguez-Carvajal, 2006); data reduction: FULLPROF (Rodriguez-Carvajal, 2006); program(s) used to solve structure: coordinates taken from an isotypic structure; 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. A view of the asymmetric unit of K2YHf(PO4)3. Displacement ellipsoids are drawn at the 50% probability level.
	Fig. 2. Rietveld refinement of K2YHf(PO4)3. Experimental (dots), calculated (red curve) and difference (blue curve) data for 2θ range 8-72°.

Potassium yttrium hafnium tris(orthophosphate)

Crystal data

K2HfY(PO4)3	Cu Kα radiation, λ = 1.540530 Å
Mr = 630.51	T = 293 K
Cubic, P213	Particle morphology: isometric
a = 10.30748 (9) Å	colourless
V = 1095.11 (2) Å^3	flat_sheet, 15 × 15 mm
Z = 4	Specimen preparation: Prepared at 293 K and 101.3 kPa
Dx = 3.824 Mg m^−3

Data collection

Shimadzu XRD-6000 diffractometer	Data collection mode: reflection
Radiation source: X-ray tube, X-ray	Scan method: step
Graphite monochromator	2θmin = 5.023°, 2θmax = 105.023°, 2θstep = 0.02°
Specimen mounting: glass container

Refinement

Rp = 5.375	Profile function: Thompson–Cox–Hastings pseudo-Voigt Axial divergence asymmetry (Thompson et al., 1987)
Rwp = 7.075	48 parameters
Rexp = 2.809	0 restraints
RBragg = 4.248	14 constraints
R(F) = 3.14	Standard least squares refinement
χ^2 = 6.300	(Δ/σ)max = 0.001
5001 data points	Background function: FullProf Background 6-coeficient polynomial function
Excluded region(s): undef

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	0.6984 (4)	0.6984 (4)	0.6984 (4)	0.12 (9)
K2	0.9307 (5)	0.9307 (5)	0.9307 (5)	0.07 (9)
Y1	0.14694 (11)	0.14694 (11)	0.14694 (11)	0.06 (9)	0.395 (10)
Y2	0.41559 (18)	0.41559 (18)	0.41559 (18)	0.05 (9)	0.605 (10)
Hf1	0.14694 (11)	0.14694 (11)	0.14694 (11)	0.06 (9)	0.605 (10)
Hf2	0.41559 (18)	0.41559 (18)	0.41559 (18)	0.05 (9)	0.395 (10)
P1	0.4609 (5)	0.2311 (8)	0.1292 (8)	0.06 (9)
O1	0.3207 (14)	0.2448 (13)	0.0864 (15)	0.07 (9)
O2	0.5337 (12)	0.3118 (13)	0.0155 (16)	0.07 (9)
O3	0.4970 (13)	0.0965 (13)	0.1595 (13)	0.07 (9)
O4	0.4750 (14)	0.3063 (15)	0.2526 (17)	0.07 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.12 (9)	0.12 (9)	0.12 (9)	−0.031 (4)	−0.031 (4)	−0.031 (4)
K2	0.07 (9)	0.07 (9)	0.07 (9)	−0.019 (3)	−0.019 (3)	−0.019 (3)
Y1	0.06 (9)	0.06 (9)	0.06 (9)	0.0018 (9)	0.0018 (9)	0.0018 (9)
Y2	0.05 (9)	0.05 (9)	0.05 (9)	0.0034 (9)	0.0034 (9)	0.0034 (9)
Hf1	0.06 (9)	0.06 (9)	0.06 (9)	0.0018 (9)	0.0018 (9)	0.0018 (9)
Hf2	0.05 (9)	0.05 (9)	0.05 (9)	0.0034 (9)	0.0034 (9)	0.0034 (9)

Geometric parameters (Å, º)

K1—O1^i	2.981 (16)	Hf1—O1^xiii	2.148 (14)
K1—O2^ii	3.345 (14)	Hf1—O2^xiv	2.085 (15)
K1—O4^ii	3.413 (16)	Hf2—O3^i	2.211 (14)
K1—O1^iii	2.981 (16)	Hf2—O4	2.113 (17)
K1—O2^iv	3.345 (14)	Hf2—O4^xi	2.113 (17)
K1—O4^iv	3.413 (16)	Hf2—O3^iii	2.211 (14)
K1—O1^v	2.981 (16)	Hf2—O4^xiii	2.113 (17)
K1—O2^vi	3.345 (14)	Hf2—O3^v	2.211 (14)
K1—O4^vi	3.413 (16)	Y1—O1	2.148 (14)
K2—O3^ii	2.907 (14)	Y1—O2^x	2.085 (15)
K2—O2^vii	2.912 (14)	Y1—O2^xii	2.085 (15)
K2—O4^ii	3.207 (17)	Y1—O1^xiii	2.148 (14)
K2—O4^vii	3.336 (17)	Y1—O2^xiv	2.085 (15)
K2—O3^iv	2.907 (14)	Y1—O1^xi	2.148 (14)
K2—O2^viii	2.912 (14)	Y2—O3^i	2.211 (14)
K2—O4^iv	3.207 (17)	Y2—O4	2.113 (17)
K2—O4^viii	3.336 (17)	Y2—O3^v	2.211 (14)
K2—O3^vi	2.907 (14)	Y2—O4^xi	2.113 (17)
K2—O2^ix	2.912 (14)	Y2—O3^iii	2.211 (14)
K2—O4^vi	3.207 (17)	Y2—O4^xiii	2.113 (17)
K2—O4^ix	3.336 (17)	P1—O1	1.518 (16)
Hf1—O1	2.148 (14)	P1—O2	1.621 (17)
Hf1—O2^x	2.085 (15)	P1—O3	1.470 (16)
Hf1—O1^xi	2.148 (14)	P1—O4	1.497 (19)
Hf1—O2^xii	2.085 (15)
O1—Hf1—O2^x	97.9 (5)	O2^x—Y1—O2^xii	80.1 (5)
O1—Hf1—O1^xi	89.3 (5)	O1^xiii—Y1—O2^x	172.6 (5)
O1—Hf1—O2^xii	172.6 (5)	O2^x—Y1—O2^xiv	80.1 (5)
O1—Hf1—O1^xiii	89.3 (5)	O1^xi—Y1—O2^xii	97.9 (5)
O1—Hf1—O2^xiv	92.5 (5)	O1^xi—Y1—O1^xiii	89.3 (5)
O1^xi—Hf1—O2^x	92.5 (5)	O1^xi—Y1—O2^xiv	172.6 (5)
O2^x—Hf1—O2^xii	80.1 (5)	O1^xiii—Y1—O2^xii	92.5 (5)
O1^xiii—Hf1—O2^x	172.6 (5)	O2^xii—Y1—O2^xiv	80.1 (5)
O2^x—Hf1—O2^xiv	80.1 (5)	O1^xiii—Y1—O2^xiv	97.9 (5)
O1^xi—Hf1—O2^xii	97.9 (5)	O3^i—Y2—O4	93.1 (6)
O1^xi—Hf1—O1^xiii	89.3 (5)	O4—Y2—O4^xi	87.8 (6)
O1^xi—Hf1—O2^xiv	172.6 (5)	O3^iii—Y2—O4	171.5 (6)
O1^xiii—Hf1—O2^xii	92.5 (5)	O4—Y2—O4^xiii	87.8 (6)
O2^xii—Hf1—O2^xiv	80.1 (5)	O3^v—Y2—O4	83.9 (5)
O1^xiii—Hf1—O2^xiv	97.9 (5)	O3^i—Y2—O4^xi	83.9 (5)
O3^i—Hf2—O4	93.1 (6)	O3^i—Y2—O3^iii	95.4 (5)
O4—Hf2—O4^xi	87.8 (6)	O3^i—Y2—O4^xiii	171.5 (6)
O3^iii—Hf2—O4	171.5 (6)	O3^i—Y2—O3^v	95.4 (5)
O4—Hf2—O4^xiii	87.8 (6)	O3^iii—Y2—O4^xi	93.1 (6)
O3^v—Hf2—O4	83.9 (5)	O4^xi—Y2—O4^xiii	87.8 (6)
O3^i—Hf2—O4^xi	83.9 (5)	O3^v—Y2—O4^xi	171.5 (6)
O3^i—Hf2—O3^iii	95.4 (5)	O3^iii—Y2—O4^xiii	83.9 (5)
O3^i—Hf2—O4^xiii	171.5 (6)	O3^iii—Y2—O3^v	95.4 (5)
O3^i—Hf2—O3^v	95.4 (5)	O3^v—Y2—O4^xiii	93.1 (6)
O3^iii—Hf2—O4^xi	93.1 (6)	O1—P1—O2	100.5 (9)
O4^xi—Hf2—O4^xiii	87.8 (6)	O1—P1—O3	113.0 (9)
O3^v—Hf2—O4^xi	171.5 (6)	O1—P1—O4	106.9 (9)
O3^iii—Hf2—O4^xiii	83.9 (5)	O2—P1—O3	121.4 (8)
O3^iii—Hf2—O3^v	95.4 (5)	O2—P1—O4	107.7 (9)
O3^v—Hf2—O4^xiii	93.1 (6)	O3—P1—O4	106.5 (9)
O1—Y1—O2^x	97.9 (5)	Hf1—O1—P1	131.7 (9)
O1—Y1—O1^xi	89.3 (5)	Y1—O1—P1	131.7 (9)
O1—Y1—O2^xii	172.6 (5)	Hf1^xv—O2—P1	160.8 (9)
O1—Y1—O1^xiii	89.3 (5)	Hf2^xvi—O3—P1	145.6 (9)
O1—Y1—O2^xiv	92.5 (5)	Hf2—O4—P1	157.5 (10)
O1^xi—Y1—O2^x	92.5 (5)	Y2—O4—P1	157.5 (10)

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.