Reinvestigation of polyhalite, K₂Ca₂Mg(SO₄)₄·2H₂O

The crystal structure of the mineral polyhalite, or dipotassium dicalcium magnesium tetra­kis­[sulfate­(VI)] dihydrate, was reinvestigated by means of single-crystal X-ray diffraction data. The structural model previously reported was confirmed, although a higher precision of the refinement has been achieved. The structure consists of K^[11] and Ca^[8] polyhedra and [MgO₄(H₂O)₂] octa­hedra sharing edges and faces; SO₄ tetra­hedra share edges with the polyhedra.

Key indicators

• Single-crystal X-ray study
• T = 298 K
• Mean [sigma](Wave) = 0.000 Å
• H-atom completeness 1%
• R factor = 0.048
• wR factor = 0.143
• Data-to-parameter ratio = 12.3

checkCIF/PLATON results

No syntax errors found



Alert level G
FORMU01_ALERT_2_G  There is a discrepancy between the atom counts in the
            _chemical_formula_sum and the formula from the _atom_site* data.
            Atom count from _chemical_formula_sum:H4 Ca2 K2 Mg1 O18 S4
            Atom count from the _atom_site data:  Ca2 K2 Mg1 O18 S4
CELLZ01_ALERT_1_G Difference between formula and atom_site contents detected.
CELLZ01_ALERT_1_G WARNING: H atoms missing from atom site list. Is this intentional?
           From the CIF: _cell_formula_units_Z    1
           From the CIF: _chemical_formula_sum  Ca2 H4 K2 Mg1 O18 S4
           TEST: Compare cell contents of formula and atom_site data

           atom    Z*formula  cif sites diff
           Ca         2.00      2.00    0.00
           H          4.00      0.00    4.00
           K          2.00      2.00    0.00
           Mg         1.00      1.00    0.00
           O         18.00     18.00    0.00
           S          4.00      4.00    0.00

   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   0 ALERT level C = Check and explain
   3 ALERT level G = General alerts; check

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

---

Computing details

Data collection: CrysAlis CCD (Oxford Diffraction, 2002); cell refinement: CrysAlis CCD; data reduction: CrysAlis RED (Oxford Diffraction, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: Xtal–DRAW (Downs & Hall-Wallace, 2003) and ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXL97.

Dipotassium Dicalcium Magnesium Tetrakis[sulfate(VI)] Dihydrate

Crystal data

K2Ca2Mg(SO4)4·2H2O	Z = 1
Mr = 602.92	F(000) = 302
Triclinic, P1	Dx = 2.763 Mg m^−3
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 6.975 (3) Å	Cell parameters from 1206 reflections
b = 6.984 (3) Å	θ = 10.2–26.4°
c = 8.899 (3) Å	µ = 2.09 mm^−1
α = 104.01 (3)°	T = 298 K
β = 101.19 (3)°	Prism, colourless
γ = 114.10 (6)°	0.35 × 0.33 × 0.32 mm
V = 362.3 (4) Å^3

Data collection

Oxford Diffraction Xcalibur-3 diffractometer	1525 independent reflections
Radiation source: fine-focus sealed tube	1305 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.025
ω scans	θmax = 31.3°, θmin = 4.2°
Absorption correction: multi-scan (DENZO-SMN; Otwinowski & Minor, 1997)	h = −9→6
Tmin = 0.493, Tmax = 0.510	k = −7→10
2629 measured reflections	l = −10→12

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)] = 0.048	H-atom parameters not defined
wR(F^2) = 0.143	w = 1/[σ^2(Fo^2) + (0.0856P)^2 + 1.9844P] where P = (Fo^2 + 2Fc^2)/3
S = 0.97	(Δ/σ)max < 0.001
1525 reflections	Δρmax = 1.19 e Å^−3
124 parameters	Δρmin = −0.68 e Å^−3
0 restraints

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
S1	0.31293 (17)	0.56434 (16)	0.14152 (12)	0.0125 (3)
S2	−0.05661 (18)	0.18567 (16)	0.35769 (12)	0.0131 (3)
Mg	0.0000	0.0000	0.0000	0.0153 (5)
Ca	0.12539 (14)	0.36459 (14)	−0.25711 (10)	0.0146 (3)
K	0.52448 (17)	0.78828 (17)	0.57178 (12)	0.0229 (3)
O1	−0.0370 (5)	0.0082 (5)	0.2369 (4)	0.0174 (7)
O2	0.1284 (6)	0.3354 (5)	0.0387 (4)	0.0220 (7)
O3	0.4986 (5)	0.5540 (5)	0.2415 (4)	0.0202 (7)
O4	−0.2344 (5)	0.3100 (5)	0.7517 (4)	0.0189 (7)
O5	0.3782 (6)	0.6721 (5)	0.0222 (4)	0.0216 (7)
O6	−0.1728 (5)	0.2786 (5)	0.2687 (4)	0.0188 (7)
O7	−0.1778 (6)	0.0844 (5)	0.4601 (4)	0.0211 (7)
O8	0.1677 (5)	0.3610 (5)	0.4680 (4)	0.0223 (7)
O9	0.3107 (5)	0.0432 (5)	0.0829 (4)	0.0152 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
S1	0.0121 (6)	0.0127 (5)	0.0125 (5)	0.0065 (4)	0.0044 (4)	0.0028 (4)
S2	0.0144 (6)	0.0125 (5)	0.0124 (4)	0.0073 (4)	0.0045 (4)	0.0030 (4)
Mg	0.0140 (10)	0.0152 (10)	0.0138 (9)	0.0065 (8)	0.0030 (8)	0.0028 (7)
Ca	0.0132 (5)	0.0144 (5)	0.0162 (4)	0.0067 (4)	0.0049 (3)	0.0052 (3)
K	0.0199 (6)	0.0244 (6)	0.0227 (5)	0.0100 (5)	0.0070 (4)	0.0067 (4)
O1	0.0246 (17)	0.0158 (15)	0.0138 (13)	0.0126 (13)	0.0066 (12)	0.0031 (11)
O2	0.0187 (17)	0.0153 (15)	0.0239 (16)	0.0065 (14)	0.0019 (13)	0.0007 (12)
O3	0.0186 (17)	0.0232 (16)	0.0172 (15)	0.0114 (14)	0.0033 (13)	0.0038 (12)
O4	0.0172 (16)	0.0203 (16)	0.0156 (14)	0.0086 (13)	0.0057 (12)	0.0010 (12)
O5	0.0253 (18)	0.0211 (16)	0.0200 (15)	0.0115 (15)	0.0094 (13)	0.0077 (13)
O6	0.0213 (17)	0.0190 (15)	0.0186 (14)	0.0129 (14)	0.0045 (13)	0.0065 (12)
O7	0.0229 (18)	0.0223 (16)	0.0219 (15)	0.0107 (14)	0.0118 (14)	0.0108 (13)
O8	0.0168 (17)	0.0198 (16)	0.0191 (15)	0.0052 (14)	0.0003 (13)	−0.0002 (12)
O9	0.0132 (15)	0.0135 (15)	0.0244 (15)	0.0083 (13)	0.0103 (13)	0.0090 (12)

Geometric parameters (Å, º)

S1—O3	1.461 (3)	Ca—S2^vi	3.141 (2)
S1—O4^i	1.471 (3)	Ca—K^vi	3.990 (3)
S1—O5	1.482 (3)	K—O8	2.768 (4)
S1—O2	1.484 (4)	K—O8^iii	2.787 (4)
S1—Ca	3.249 (2)	K—O7^ix	2.804 (4)
S1—K	3.508 (2)	K—O9^iii	2.815 (4)
S2—O6	1.461 (3)	K—O7^i	2.886 (4)
S2—O8	1.472 (4)	K—O4^i	2.916 (4)
S2—O7	1.473 (3)	K—O3	2.928 (3)
S2—O1	1.504 (3)	K—O6^i	2.998 (4)
S2—Ca^ii	3.141 (2)	K—O4^ix	3.129 (4)
S2—K^i	3.507 (2)	K—O1^iii	3.164 (4)
S2—K^iii	3.563 (2)	K—O3^iii	3.196 (4)
Mg—O9^iv	2.017 (3)	K—S2^i	3.507 (2)
Mg—O9	2.017 (3)	O1—Ca^iv	2.479 (3)
Mg—O2	2.045 (3)	O1—K^iii	3.164 (4)
Mg—O2^iv	2.045 (3)	O3—Ca^viii	2.413 (4)
Mg—O1^iv	2.164 (3)	O3—K^iii	3.196 (4)
Mg—O1	2.164 (3)	O4—S1^i	1.471 (3)
Mg—Ca	3.7765 (17)	O4—Ca^ii	2.399 (3)
Mg—Ca^iv	3.7765 (17)	O4—K^i	2.916 (4)
Mg—K^v	4.009 (3)	O4—K^x	3.129 (4)
Mg—K^iii	4.009 (3)	O6—Ca^vii	2.407 (3)
Ca—O4^vi	2.399 (3)	O6—K^i	2.998 (4)
Ca—O6^vii	2.407 (3)	O7—Ca^ii	2.609 (4)
Ca—O3^viii	2.413 (4)	O7—K^x	2.804 (4)
Ca—O1^iv	2.479 (3)	O7—K^i	2.886 (4)
Ca—O8^vi	2.516 (4)	O8—Ca^ii	2.516 (4)
Ca—O5	2.554 (4)	O8—K^iii	2.787 (4)
Ca—O7^vi	2.609 (4)	O9—K^iii	2.815 (4)
Ca—O2	2.686 (4)
O3—S1—O4^i	109.71 (18)	O7^i—K—O3	107.94 (10)
O3—S1—O5	111.3 (2)	O4^i—K—O3	48.44 (9)
O4^i—S1—O5	109.75 (19)	O8—K—O6^i	62.04 (10)
O3—S1—O2	111.0 (2)	O8^iii—K—O6^i	139.56 (10)
O4^i—S1—O2	110.41 (19)	O7^ix—K—O6^i	144.82 (10)
O5—S1—O2	104.6 (2)	O9^iii—K—O6^i	65.64 (10)
O6—S2—O8	111.4 (2)	O7^i—K—O6^i	48.48 (9)
O6—S2—O7	111.0 (2)	O4^i—K—O6^i	95.12 (10)
O8—S2—O7	107.1 (2)	O3—K—O6^i	130.99 (10)
O6—S2—O1	109.36 (18)	O8—K—O4^ix	153.33 (10)
O8—S2—O1	109.03 (19)	O8^iii—K—O4^ix	110.59 (11)
O7—S2—O1	108.91 (19)	O7^ix—K—O4^ix	57.78 (10)
O9^iv—Mg—O9	180.0 (2)	O9^iii—K—O4^ix	62.28 (9)
O9^iv—Mg—O2	90.04 (14)	O7^i—K—O4^ix	74.23 (11)
O9—Mg—O2	89.96 (14)	O4^i—K—O4^ix	106.94 (9)
O9^iv—Mg—O2^iv	89.96 (14)	O3—K—O4^ix	125.63 (10)
O9—Mg—O2^iv	90.04 (14)	O6^i—K—O4^ix	92.18 (10)
O2—Mg—O2^iv	180.00 (8)	O8—K—O1^iii	132.35 (11)
O9^iv—Mg—O1^iv	90.24 (13)	O8^iii—K—O1^iii	47.53 (9)
O9—Mg—O1^iv	89.76 (13)	O7^ix—K—O1^iii	63.64 (10)
O2—Mg—O1^iv	80.97 (13)	O9^iii—K—O1^iii	59.10 (9)
O2^iv—Mg—O1^iv	99.03 (13)	O7^i—K—O1^iii	140.33 (10)
O9^iv—Mg—O1	89.76 (13)	O4^i—K—O1^iii	139.29 (9)
O9—Mg—O1	90.24 (13)	O3—K—O1^iii	100.55 (10)
O2—Mg—O1	99.03 (13)	O6^i—K—O1^iii	124.55 (9)
O2^iv—Mg—O1	80.97 (13)	O4^ix—K—O1^iii	66.78 (10)
O1^iv—Mg—O1	180.0 (3)	O8—K—O3^iii	57.04 (10)
O4^vi—Ca—O6^vii	83.00 (13)	O8^iii—K—O3^iii	69.66 (10)
O4^vi—Ca—O3^viii	174.75 (10)	O7^ix—K—O3^iii	140.08 (10)
O6^vii—Ca—O3^viii	94.95 (13)	O9^iii—K—O3^iii	61.17 (9)
O4^vi—Ca—O1^iv	90.45 (13)	O7^i—K—O3^iii	117.51 (10)
O6^vii—Ca—O1^iv	173.31 (11)	O4^i—K—O3^iii	127.44 (11)
O3^viii—Ca—O1^iv	91.47 (13)	O3—K—O3^iii	104.25 (9)
O4^vi—Ca—O8^vi	112.64 (12)	O6^i—K—O3^iii	69.91 (9)
O6^vii—Ca—O8^vi	74.40 (11)	O4^ix—K—O3^iii	123.14 (9)
O3^viii—Ca—O8^vi	71.24 (11)	O1^iii—K—O3^iii	80.03 (10)
O1^iv—Ca—O8^vi	109.59 (11)	S2—O1—Mg	127.23 (18)
O4^vi—Ca—O5	101.30 (12)	S2—O1—Ca^iv	122.93 (17)
O6^vii—Ca—O5	70.77 (11)	Mg—O1—Ca^iv	108.66 (12)
O3^viii—Ca—O5	73.45 (12)	S2—O1—K^iii	92.51 (15)
O1^iv—Ca—O5	109.45 (12)	Mg—O1—K^iii	95.77 (12)
O8^vi—Ca—O5	127.08 (12)	Ca^iv—O1—K^iii	92.57 (12)
O4^vi—Ca—O7^vi	70.09 (11)	S1—O2—Mg	145.4 (2)
O6^vii—Ca—O7^vi	102.05 (12)	S1—O2—Ca	98.19 (17)
O3^viii—Ca—O7^vi	115.12 (11)	Mg—O2—Ca	105.10 (13)
O1^iv—Ca—O7^vi	76.80 (12)	S1—O3—Ca^viii	138.7 (2)
O8^vi—Ca—O7^vi	55.02 (11)	S1—O3—K	100.78 (15)
O5—Ca—O7^vi	169.78 (11)	Ca^viii—O3—K	105.95 (12)
O4^vi—Ca—O2	76.04 (11)	S1—O3—K^iii	127.72 (19)
O6^vii—Ca—O2	113.02 (11)	Ca^viii—O3—K^iii	89.58 (11)
O3^viii—Ca—O2	100.46 (11)	K—O3—K^iii	75.75 (9)
O1^iv—Ca—O2	63.77 (10)	S1^i—O4—Ca^ii	134.43 (19)
O8^vi—Ca—O2	169.77 (11)	S1^i—O4—K^i	101.03 (16)
O5—Ca—O2	53.15 (11)	Ca^ii—O4—K^i	110.68 (12)
O7^vi—Ca—O2	127.00 (11)	S1^i—O4—K^x	125.78 (17)
O8—K—O8^iii	94.64 (11)	Ca^ii—O4—K^x	95.02 (12)
O8—K—O7^ix	142.43 (11)	K^i—O4—K^x	73.06 (9)
O8^iii—K—O7^ix	73.59 (11)	S1—O5—Ca	104.04 (17)
O8—K—O9^iii	108.26 (11)	S2—O6—Ca^vii	140.1 (2)
O8^iii—K—O9^iii	95.22 (10)	S2—O6—K^i	97.74 (16)
O7^ix—K—O9^iii	108.27 (11)	Ca^vii—O6—K^i	94.55 (11)
O8—K—O7^i	82.76 (11)	S2—O7—Ca^ii	96.67 (17)
O8^iii—K—O7^i	168.11 (10)	S2—O7—K^x	163.9 (2)
O7^ix—K—O7^i	101.46 (10)	Ca^ii—O7—K^x	98.62 (12)
O9^iii—K—O7^i	96.61 (10)	S2—O7—K^i	102.25 (17)
O8—K—O4^i	71.25 (11)	Ca^ii—O7—K^i	105.67 (11)
O8^iii—K—O4^i	108.62 (10)	K^x—O7—K^i	78.54 (10)
O7^ix—K—O4^i	78.88 (11)	S2—O8—Ca^ii	100.65 (17)
O9^iii—K—O4^i	156.15 (9)	S2—O8—K	151.1 (2)
O7^i—K—O4^i	59.54 (9)	Ca^ii—O8—K	97.98 (11)
O8—K—O3	74.07 (11)	S2—O8—K^iii	109.64 (16)
O8^iii—K—O3	60.27 (10)	Ca^ii—O8—K^iii	107.37 (13)
O7^ix—K—O3	69.10 (11)	K—O8—K^iii	85.36 (11)
O9^iii—K—O3	155.38 (10)	Mg—O9—K^iii	111.05 (12)

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