Rietveld refinement of the langbeinite-type phosphate K₂Ni_0.5Hf_1.5(PO₄)₃

Polycrystalline potassium nickel(II) hafnium(IV) tris­(orthophosphate), a langbeinite-type phosphate, was synthesized by a solid-state method. The three-dimensional framework of the title compound is built up from two types of [MO₆] octa­hedra [the M sites are occupied by Hf:Ni in ratios of 0.754 (8):0.246 (8) and 0.746 (8):0.254 (8), respectively] and [PO₄] tetra­hedra are connected via O vertices. The K⁺ cations are located in two positions within large cavities of the framework, having coordination numbers of 9 and 12. The Hf, Ni and K sites lie on threefold rotation axes, while the P and O atoms are situated in general positions.

1. Chemical context

Langbeinite-related complex oxides have a variety of inter­esting properties, for example, ferroelectricity or ferroelasticity (Norberg, 2002). In particular, complex phosphates of this type have attracted attention for their high thermal and chemical stability, and many different combinations for structural substitutions are possible (Wulff et al., 1992; Slobodyanik et al., 2012). These characteristics made it possible to propose the family of langbeinite-type phosphates as successful hosts for the immobilization of radioactive waste (Orlova et al., 2011). Moreover, in the last decade rare-earth (RE)-containing langbeinite-type phosphates have been studied intensively owing to their outstanding luminescent properties and applications in LEDs (Liang & Wang, 2011; Liu et al., 2016; Sadhasivam et al., 2017; Terebilenko et al., 2020). Accordingly, further studies of iso- and heterovalent substitution within the cationic sites of the langbeinite structure are important. Structural data for langbeinite-type Hf-containing phosphates are scarce and include only K_1.93Mn_0.53Hf_1.47(PO₄)₃ (Ogorodnyk et al., 2007a) and K₂YHf(PO₄)₃ (Ogorodnyk et al., 2009).

In this report, we describe the powder X-ray refinement using the Rietveld method for the multimetal phosphate K₂Ni_0.5Hf_1.5(PO₄)₃ (I), structurally isotypic with the mineral langbeinite, K₂Mg₂(SO₄)₃ (Zemann & Zemann, 1957).

2. Structural commentary

As shown in Fig. 1, in the structure of (I) the K, Ni and Hf sites are localized on threefold rotation axes (Wyckoff position 4 a), while the P and all O atoms occupy general sites (12 b). Two metallic sites (Hf,Ni)1 and (Hf,Ni)2 show mixed occupancy with a Hf:Ni ratio of about 0.75:0.25 (nickel proportion 0.246 (8) for the M1 site and 0.254 (8) for the M2 site). A similar M^II:M^IV ratio was also observed for isostructural phosphates of general composition M^IM^II_0.5M^IV_1.5(PO₄)₃, viz. K₂Ni_0.5Ti_1.5(PO₄)₃ (Ogorodnyk et al., 2007b), Rb₂Ni_0.5Ti_1.5(PO₄)₃ (Strutynska et al., 2015), K₂Co_0.5Ti_1.5(PO₄)₃ and K₂Mn_0.5Ti_1.5(PO₄)₃ (Ogorodnyk et al., 2006), K₂Ni_0.5Zr_1.5(PO₄)₃ (Zatovsky, 2014), K_1.96Mn_0.57Zr_1.43(PO₄)₃ and K_1.93Mn_0.53Hf_1.47(PO₄)₃ (Ogorodnyk et al., 2007a).

Figure 1 A view of the asymmetric unit of K2Ni0.5Hf1.5(PO4)3, with displacement spheres drawn at the 50% probability level.

The (Hf,Ni)—O distances in (I) are 1.989 (15) and 2.121 (14) Å for the [(Hf,Ni)1O₆] octa­hedron, and 2.131 (17) and 2.172 (16) Å for the [(Hf,Ni)2O₆] octa­hedron. The two independent [(Hf,Ni)O₆] octa­hedra are linked by three [PO₄] tetra­hedra to form an [M₂P₃O₁₈] building unit (Fig. 2). These building units are arranged along three directions (threefold rotation axes) and linked together via oxygen vertices, forming a three-dimensional framework structure. Pairs of K⁺ cations (two independent sites) are localized in large cavities of the resulting framework. The potassium cations are found in 9- and 12-coordination by O atoms with K—O distances ranging from 2.854 (17) Å to 3.372 (18) Å (Table 1, Fig. 3), leading to distorted polyhedra. The [PO₄] tetra­hedron shows considerable distortion (Table 1).

Table 1
Selected geometric parameters (Å, °)

K1—O1^i	2.854 (17)	K2—O4^iii	3.372 (18)
K1—O4^ii	3.082 (17)	P1—O1	1.503 (15)
K1—O2^ii	3.103 (15)	P1—O2	1.533 (17)
K2—O3^ii	2.944 (16)	P1—O3	1.48 (2)
K2—O2^iii	2.987 (18)	P1—O4	1.506 (18)
K2—O4^ii	3.041 (18)
O1—P1—O2	110.2 (10)	O2—P1—O3	112.6 (10)
O1—P1—O3	107.4 (10)	O2—P1—O4	106.0 (10)
O1—P1—O4	120.1 (10)	O3—P1—O4	100.3 (11)
Symmetry codes: (i) ; (ii) ; (iii) .

Figure 2 [M2P3O18] building unit (highlighted in red frames) for (I). K^+ cations are shown as blue spheres of arbitrary radius.

Figure 3 Coordination polyhedra [K1O9] and [K2O12] for (I). Displacement spheres are drawn at the 50% probability level. [Symmetry codes: (i) −x + 1, y + , −z + ; (ii) −x + , −y + 1, z + ; (iii) −z + , −x + 1, y + ; (iv) −y + 1, z + , −x + ; (v) y + , −z + , −x + 1; (vi) z + , −x + , −y + 1; (vii) −z + 1, x + , −y + ; (viii) −y + , −z + 1, x + ; (ix) x + , −y + , −z + 1].

For (I), the calculation of BVS (bond-valence sums) was performed using the parameters for Hf from Brese & O'Keeffe (1991), for Ni from Brown (private communication, 2001) and for K, P from Brown & Altermatt (1985). The corresponding occupation of the M sites by Hf and Ni atoms was taken into account. The sum of BVS of the cations is +23.67 valence units (v.u.), which is close to the −24 v.u. required for the O atoms.

3. Synthesis and crystallization

Compound (I) was synthesized using a solid-state reaction method. A well-ground starting mixture of 3.157 g HfO₂, 0.374 g NiO, 2.361 g KPO₃ and 1.150 g NH₄H₂PO₄ (molar ratio K:Ni:Hf:P = 4:1:3:6) was transferred to a ceramic crucible and pre-heated at 553 K for 2 h. The powder was re-ground, heated at 823 K for 3 h and then milled for 0.5 h in an agate mortar. The resulting fine powder was pressed into a pill and finally calcined at 1273 K for 100 h. The sample was ground before performing powder XRD data collection. Scanning electron microscopy (SEM, Magellan 400, recorded at 10 kV) showed that the obtained sample is an aggregate of small crystallites with a size less than 1 µm (Fig. 4).

Figure 4 SEM image for (I) (Insert: image at higher magnification).

4. Refinement

The experimental, calculated and difference pattern are shown in Fig. 5. Crystal data, data collection and structure refinement details are summarized in Table 2. Structure refinement was performed using K₂YHf(PO₄)₃ (Ogorodnyk et al., 2009) as a starting model. A modified pseudo-Voigt function (Thompson et al., 1987) was used for the profile refinement. The similar shape of the transition-metal octa­hedra indicated that both M positions are occupied by Ni and Hf simultaneously. For the refinement of their occupancies their coordinates and U_iso values were constrained together, and the sum of occupancies constrained to unity for both sites.

Table 2
Experimental details

Crystal data
Chemical formula	K2Ni0.5Hf1.5(PO4)3
Mr	660.19
Crystal system, space group	Cubic, P213
Temperature (K)	293
a (Å)	10.12201 (5)
V (Å^3)	1037.05 (1)
Z	4
Radiation type	Cu Kα1, λ = 1.540598 Å
Specimen shape, size (mm)	Flat sheet, 15 × 15
Data collection
Diffractometer	Haoyuan Instrument Co. Ltd DX-2700B
Specimen mounting	Glass container
Data collection mode	Reflection
Scan method	Step
2θ values (°)	2θmin = 10.008 2θmax = 105.008 2θstep = 0.020
Refinement
R factors and goodness of fit	Rp = 6.111, Rwp = 7.831, Rexp = 4.020, RBragg = 4.709, R(F) = 3.21, χ^2 = 4.410
No. of parameters	107
No. of restraints	3
Computer programs: data-collection and reduction software supplied by instrument manufacturer (https://www.haoyuanyiqi.com/en/xsxysy/s_23_30.html), FULLPROF (Rodriguez-Carvajal, 2020), DIAMOND (Brandenburg, 2006), PLATON (Spek, 2020), WinGX (Farrugia, 2012) and enCIFer (Allen et al., 2004).

Figure 5 Rietveld refinement of K2Ni0.5Hf1.5(PO4)3. Experimental (dots), calculated (red curve) and difference (blue curve) data for 2θ range 10–108°.

Supporting information

Computing details

Data collection: Software supplied by instrument manufacturer (https://www.haoyuanyiqi.com/en/xsxysy/s_23_30.html); cell refinement: FULLPROF (Rodriguez-Carvajal, 2020); data reduction: Software supplied by instrument manufacturer (https://www.haoyuanyiqi.com/en/xsxysy/s_23_30.html); program(s) used to solve structure: isomorphic replacement; program(s) used to refine structure: FULLPROF (Rodriguez-Carvajal, 2020); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: PLATON (Spek, 2020), WinGX (Farrugia, 2012) and enCIFer (Allen et al., 2004).

(I)

Crystal data

K2Ni0.5Hf1.5(PO4)3	Dx = 4.228 Mg m^−3
Mr = 660.19	Cu Kα radiation, λ = 1.540598 Å
Cubic, P213	T = 293 K
Hall symbol: P 2ac 2ab 3	Particle morphology: tetrahedra
a = 10.12201 (5) Å	yellow
V = 1037.05 (1) Å^3	flat_sheet, 15 × 15 mm
Z = 4	Specimen preparation: Prepared at 293 K and 101.3 kPa

Data collection

Haoyuan Instrument Co. Ltd DX-2700B diffractometer	Data collection mode: reflection
Radiation source: X-ray tube, X-ray	Scan method: step
Graphite monochromator	2θmin = 10.008°, 2θmax = 105.008°, 2θstep = 0.020°
Specimen mounting: glass container

Refinement

Rp = 6.111	107 parameters
Rwp = 7.831	3 restraints
Rexp = 4.020	3 constraints
RBragg = 4.709	Standard least squares refinement
R(F) = 3.21	(Δ/σ)max = 0.001
4751 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: Modified March's Function

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.7042 (5)	0.7042 (5)	0.7042 (5)	0.028 (4)*
K2	0.9319 (8)	0.9319 (8)	0.9319 (8)	0.044 (4)*
Ni1	0.14423 (16)	0.14423 (16)	0.14423 (16)	0.0022 (12)*	0.246 (8)
Ni2	0.4147 (2)	0.4147 (2)	0.4147 (2)	0.0019 (12)*	0.254 (8)
Hf1	0.14423 (16)	0.14423 (16)	0.14423 (16)	0.0022 (12)*	0.754 (8)
Hf2	0.4147 (2)	0.4147 (2)	0.4147 (2)	0.0019 (12)*	0.746 (8)
P1	0.4624 (6)	0.2349 (10)	0.1229 (9)	0.004 (2)*
O1	0.3218 (13)	0.2314 (17)	0.0752 (16)	0.011 (6)*
O2	0.5508 (14)	0.3023 (16)	0.0201 (15)	0.008 (4)*
O3	0.5028 (13)	0.0973 (17)	0.1500 (18)	0.008 (6)*
O4	0.4953 (16)	0.2985 (17)	0.2533 (14)	0.009 (6)*

Atomic displacement parameters (Ų)

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

Geometric parameters (Å, º)

K1—O1^i	2.854 (17)	Hf1—O1	2.121 (14)
K1—O4^ii	3.082 (17)	Hf1—O2^x	1.989 (15)
K1—O2^ii	3.103 (15)	Hf1—O1^xi	2.121 (14)
K1—O1^iii	2.854 (17)	Hf1—O2^xii	1.989 (15)
K1—O4^iv	3.082 (17)	Hf2—O4	2.172 (16)
K1—O2^iv	3.103 (15)	Hf2—O3^i	2.131 (17)
K1—O1^v	2.854 (17)	Hf2—O4^xi	2.172 (16)
K1—O4^vi	3.082 (17)	Hf2—O3^iii	2.131 (17)
K1—O2^vi	3.103 (15)	Ni1—O1	2.121 (14)
K2—O3^ii	2.944 (16)	Ni1—O2^x	1.989 (15)
K2—O2^vii	2.987 (18)	Ni1—O1^xi	2.121 (14)
K2—O4^ii	3.041 (18)	Ni1—O2^xii	1.989 (15)
K2—O4^vii	3.372 (18)	Ni2—O4	2.172 (16)
K2—O3^iv	2.944 (16)	Ni2—O3^i	2.131 (17)
K2—O2^viii	2.987 (18)	Ni2—O4^xi	2.172 (16)
K2—O4^iv	3.041 (18)	Ni2—O3^iii	2.131 (17)
K2—O4^viii	3.372 (18)	P1—O1	1.503 (15)
K2—O3^vi	2.944 (16)	P1—O2	1.533 (17)
K2—O2^ix	2.987 (18)	P1—O3	1.48 (2)
K2—O4^vi	3.041 (18)	P1—O4	1.506 (18)
K2—O4^ix	3.372 (18)
O1—Hf1—O2^x	90.8 (6)	O1^xi—Ni1—O2^x	87.8 (6)
O1—Hf1—O1^xi	93.7 (6)	O2^x—Ni1—O2^xii	87.7 (6)
O1—Hf1—O2^xii	175.2 (6)	O1^xi—Ni1—O2^xii	90.8 (6)
O1^xi—Hf1—O2^x	87.8 (6)	O3^i—Ni2—O4	95.2 (6)
O2^x—Hf1—O2^xii	87.7 (6)	O4—Ni2—O4^xi	94.5 (6)
O1^xi—Hf1—O2^xii	90.8 (6)	O3^iii—Ni2—O4	168.5 (6)
O3^i—Hf2—O4	95.2 (6)	O3^i—Ni2—O4^xi	78.6 (6)
O4—Hf2—O4^xi	94.5 (6)	O3^i—Ni2—O3^iii	92.7 (6)
O3^iii—Hf2—O4	168.5 (6)	O3^iii—Ni2—O4^xi	95.2 (6)
O3^i—Hf2—O4^xi	78.6 (6)	O1—P1—O2	110.2 (10)
O3^i—Hf2—O3^iii	92.7 (6)	O1—P1—O3	107.4 (10)
O3^iii—Hf2—O4^xi	95.2 (6)	O1—P1—O4	120.1 (10)
O1—Ni1—O2^x	90.8 (6)	O2—P1—O3	112.6 (10)
O1—Ni1—O1^xi	93.7 (6)	O2—P1—O4	106.0 (10)
O1—Ni1—O2^xii	175.2 (6)	O3—P1—O4	100.3 (11)

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.