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Acta Crystallogr Sect E Struct Rep Online. 2009 August 1; 65(Pt 8): i63–i64.
Published online 2009 July 18. doi:  10.1107/S1600536809027573
PMCID: PMC2977454

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 [triangle]). For powder diffraction investigations and Rietveld refinements of phosphate-based langbeinites, see: K2 MZr(PO4)3, M = Y, Gd (Wulff et al., 1992 [triangle]); K2FeZr(PO4)3 (Orlova et al., 2003 [triangle]); K2 LnZr(PO4)3, Ln = Ce—Lu (Trubach et al., 2004 [triangle]). Hafnium-containing phosphate langbeinites are reported for K2BiHf(PO4)3 (Losilla et al., 1998 [triangle]) and K1.93Mn0.53Hf1.47(PO4)3 (Ogorodnyk et al., 2007a [triangle]). For the synthesis of zirconium- or hafnium-containing langbeinite-related phosphates from fluoride precursors using flux techniques, see: Ogorodnyk et al. (2007a [triangle],b [triangle]). Parameters needed to calculate bond-valence sums were taken from Brown & Altermatt (1985 [triangle]) and Brese & O’Keeffe (1991 [triangle]), respectively. For ionic radii, see: Shannon (1976 [triangle]). For crystallographic background, see: Boultif & Louër (2004 [triangle]).


Crystal data

  • K2YHf(PO4)3
  • M r = 630.51
  • Cubic, An external file that holds a picture, illustration, etc.
Object name is e-65-00i63-efi1.jpg
  • a = 10.30748 (9) Å
  • V = 1095.11 (2) Å3
  • 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
  • min = 5.0, 2θmax = 105.0°
  • Increment in 2θ = 0.02°


  • 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 [triangle])
  • 528 reflections
  • 48 parameters

Data collection: PCXRD (Shimadzu, 2006 [triangle]); cell refinement: FULLPROF (Rodriguez-Carvajal, 2006 [triangle]); 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 [triangle]); software used to prepare material for publication: PLATON (Spek, 2009 [triangle]) and enCIFer (Allen et al., 2004 [triangle]).

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

Supplementary Material

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536809027573/wm2244sup1.cif

Rietveld powder data: contains datablocks I. DOI: 10.1107/S1600536809027573/wm2244Isup2.rtv

Additional supplementary materials: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information


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 K1.93Mn0.53Hf1.47(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); Cs1+xLnxZr2-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.


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.


The cubic cell was found by Dicvol 2004 (Boultif & Louër, 2004). The Hf-containing langbeinite-related compound with general composition K1.93Mn0.53Hf1.47(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.


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°.

Crystal data

K2HfY(PO4)3Cu Kα radiation, λ = 1.540530 Å
Mr = 630.51T = 293 K
Cubic, P213Particle morphology: isometric
a = 10.30748 (9) Åcolourless
V = 1095.11 (2) Å3flat_sheet, 15 × 15 mm
Z = 4Specimen preparation: Prepared at 293 K and 101.3 kPa
Dx = 3.824 Mg m3

Data collection

Shimadzu XRD-6000 diffractometerData collection mode: reflection
Radiation source: X-ray tube, X-rayScan method: step
graphitemin = 5.02°, 2θmax = 105.02°, 2θstep = 0.02°
Specimen mounting: glass container


Rp = 5.375Profile function: Thompson–Cox–Hastings pseudo-Voigt Axial divergence asymmetry (Thompson et al., 1987)
Rwp = 7.07548 parameters
Rexp = 2.8090 restraints
RBragg = 4.24814 constraints
R(F) = 3.14 Standard least squares refinement
χ2 = 6.300(Δ/σ)max = 0.001
5001 data pointsBackground 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 (Å2)

xyzUiso*/UeqOcc. (<1)
K10.6984 (4)0.6984 (4)0.6984 (4)0.12 (9)
K20.9307 (5)0.9307 (5)0.9307 (5)0.07 (9)
Y10.14694 (11)0.14694 (11)0.14694 (11)0.06 (9)0.395 (10)
Y20.41559 (18)0.41559 (18)0.41559 (18)0.05 (9)0.605 (10)
Hf10.14694 (11)0.14694 (11)0.14694 (11)0.06 (9)0.605 (10)
Hf20.41559 (18)0.41559 (18)0.41559 (18)0.05 (9)0.395 (10)
P10.4609 (5)0.2311 (8)0.1292 (8)0.06 (9)
O10.3207 (14)0.2448 (13)0.0864 (15)0.07 (9)
O20.5337 (12)0.3118 (13)0.0155 (16)0.07 (9)
O30.4970 (13)0.0965 (13)0.1595 (13)0.07 (9)
O40.4750 (14)0.3063 (15)0.2526 (17)0.07 (9)

Atomic displacement parameters (Å2)

K10.12 (9)0.12 (9)0.12 (9)−0.031 (4)−0.031 (4)−0.031 (4)
K20.07 (9)0.07 (9)0.07 (9)−0.019 (3)−0.019 (3)−0.019 (3)
Y10.06 (9)0.06 (9)0.06 (9)0.0018 (9)0.0018 (9)0.0018 (9)
Y20.05 (9)0.05 (9)0.05 (9)0.0034 (9)0.0034 (9)0.0034 (9)
Hf10.06 (9)0.06 (9)0.06 (9)0.0018 (9)0.0018 (9)0.0018 (9)
Hf20.05 (9)0.05 (9)0.05 (9)0.0034 (9)0.0034 (9)0.0034 (9)

Geometric parameters (Å, °)

K1—O1i2.981 (16)Hf1—O1xiii2.148 (14)
K1—O2ii3.345 (14)Hf1—O2xiv2.085 (15)
K1—O4ii3.413 (16)Hf2—O3i2.211 (14)
K1—O1iii2.981 (16)Hf2—O42.113 (17)
K1—O2iv3.345 (14)Hf2—O4xi2.113 (17)
K1—O4iv3.413 (16)Hf2—O3iii2.211 (14)
K1—O1v2.981 (16)Hf2—O4xiii2.113 (17)
K1—O2vi3.345 (14)Hf2—O3v2.211 (14)
K1—O4vi3.413 (16)Y1—O12.148 (14)
K2—O3ii2.907 (14)Y1—O2x2.085 (15)
K2—O2vii2.912 (14)Y1—O2xii2.085 (15)
K2—O4ii3.207 (17)Y1—O1xiii2.148 (14)
K2—O4vii3.336 (17)Y1—O2xiv2.085 (15)
K2—O3iv2.907 (14)Y1—O1xi2.148 (14)
K2—O2viii2.912 (14)Y2—O3i2.211 (14)
K2—O4iv3.207 (17)Y2—O42.113 (17)
K2—O4viii3.336 (17)Y2—O3v2.211 (14)
K2—O3vi2.907 (14)Y2—O4xi2.113 (17)
K2—O2ix2.912 (14)Y2—O3iii2.211 (14)
K2—O4vi3.207 (17)Y2—O4xiii2.113 (17)
K2—O4ix3.336 (17)P1—O11.518 (16)
Hf1—O12.148 (14)P1—O21.621 (17)
Hf1—O2x2.085 (15)P1—O31.470 (16)
Hf1—O1xi2.148 (14)P1—O41.497 (19)
Hf1—O2xii2.085 (15)
O1—Hf1—O2x97.9 (5)O2x—Y1—O2xii80.1 (5)
O1—Hf1—O1xi89.3 (5)O1xiii—Y1—O2x172.6 (5)
O1—Hf1—O2xii172.6 (5)O2x—Y1—O2xiv80.1 (5)
O1—Hf1—O1xiii89.3 (5)O1xi—Y1—O2xii97.9 (5)
O1—Hf1—O2xiv92.5 (5)O1xi—Y1—O1xiii89.3 (5)
O1xi—Hf1—O2x92.5 (5)O1xi—Y1—O2xiv172.6 (5)
O2x—Hf1—O2xii80.1 (5)O1xiii—Y1—O2xii92.5 (5)
O1xiii—Hf1—O2x172.6 (5)O2xii—Y1—O2xiv80.1 (5)
O2x—Hf1—O2xiv80.1 (5)O1xiii—Y1—O2xiv97.9 (5)
O1xi—Hf1—O2xii97.9 (5)O3i—Y2—O493.1 (6)
O1xi—Hf1—O1xiii89.3 (5)O4—Y2—O4xi87.8 (6)
O1xi—Hf1—O2xiv172.6 (5)O3iii—Y2—O4171.5 (6)
O1xiii—Hf1—O2xii92.5 (5)O4—Y2—O4xiii87.8 (6)
O2xii—Hf1—O2xiv80.1 (5)O3v—Y2—O483.9 (5)
O1xiii—Hf1—O2xiv97.9 (5)O3i—Y2—O4xi83.9 (5)
O3i—Hf2—O493.1 (6)O3i—Y2—O3iii95.4 (5)
O4—Hf2—O4xi87.8 (6)O3i—Y2—O4xiii171.5 (6)
O3iii—Hf2—O4171.5 (6)O3i—Y2—O3v95.4 (5)
O4—Hf2—O4xiii87.8 (6)O3iii—Y2—O4xi93.1 (6)
O3v—Hf2—O483.9 (5)O4xi—Y2—O4xiii87.8 (6)
O3i—Hf2—O4xi83.9 (5)O3v—Y2—O4xi171.5 (6)
O3i—Hf2—O3iii95.4 (5)O3iii—Y2—O4xiii83.9 (5)
O3i—Hf2—O4xiii171.5 (6)O3iii—Y2—O3v95.4 (5)
O3i—Hf2—O3v95.4 (5)O3v—Y2—O4xiii93.1 (6)
O3iii—Hf2—O4xi93.1 (6)O1—P1—O2100.5 (9)
O4xi—Hf2—O4xiii87.8 (6)O1—P1—O3113.0 (9)
O3v—Hf2—O4xi171.5 (6)O1—P1—O4106.9 (9)
O3iii—Hf2—O4xiii83.9 (5)O2—P1—O3121.4 (8)
O3iii—Hf2—O3v95.4 (5)O2—P1—O4107.7 (9)
O3v—Hf2—O4xiii93.1 (6)O3—P1—O4106.5 (9)
O1—Y1—O2x97.9 (5)Hf1—O1—P1131.7 (9)
O1—Y1—O1xi89.3 (5)Y1—O1—P1131.7 (9)
O1—Y1—O2xii172.6 (5)Hf1xv—O2—P1160.8 (9)
O1—Y1—O1xiii89.3 (5)Hf2xvi—O3—P1145.6 (9)
O1—Y1—O2xiv92.5 (5)Hf2—O4—P1157.5 (10)
O1xi—Y1—O2x92.5 (5)Y2—O4—P1157.5 (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.


Supplementary data and figures for this paper are available from the IUCr electronic archives (Reference: WM2244).


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