Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270103025277/iz1035sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270103025277/iz1035Isup2.hkl |
In order to obtain the maximum number of superstructure reflections, we chose a high angle, θmax, of measured reflections. Therefore, and because of the general weakness of the superstructure reflections, we unavoidably obtained many reflections below the 2σ(I) threshold, making the refinement a little clumsy. Moreover, the pseudo-symmetries imposed by the substructure result in strong correlations of several parameters. Additional correlations are possibly introduced via absorption correction errors (see above). As a result of the correlations, the convergence of the refinement is bad. The use of damping parameters was necessary in the last cycles of refinement. A final cycle with no damping was added. Because of the presence of a pseudo-centre of symmetry, the absolute structure could not be determined. The Flack parameter is 0.1, with a standard uncertainty of 0.5. Simple twinning models based on primitive monoclinic lattices neither resulted in a better convergence of the refinement nor removed the pseudo-centre of symmetry. However, if the transformation of potassium nitrate from the trigonal ferroelectric high-temperature γ-phase to the room-temperature α-phase is led by symmetry then, in? the α-phase, a C-centred cell lacking a centre of symmetry is desired. Therefore, the pseudo-symmetries may be true features of the α-phase structure.
Data collection: COLLECT (Nonius 1999); cell refinement: COLLECT; data reduction: DENZO (Otwinowski & Minor, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).
KNO3 | F(000) = 800 |
Mr = 101.11 | Dx = 2.101 Mg m−3 |
Orthorhombic, Cmc21 | Mo Kα radiation, λ = 0.71070 Å |
Hall symbol: C 2c -2 | Cell parameters from 2170 reflections |
a = 10.825 (6) Å | θ = 1.0°–40.3°° |
b = 18.351 (10) Å | µ = 1.46 mm−1 |
c = 6.435 (3) Å | T = 293 K |
V = 1278.3 (12) Å3 | Irregular, approximately isometric, colourless |
Z = 16 | 0.33 × 0.25 × 0.17 mm |
Nonius KappaCCD diffractometer | 3857 independent reflections |
Radiation source: fine-focus sealed tube | 1069 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.000 |
area detector scans | θmax = 40.2°, θmin = 2.2° |
Absorption correction: analytical face-indexing analytical, see text | h = −19→19 |
Tmin = 0.65, Tmax = 0.78 | k = −33→33 |
3857 measured reflections | l = −11→11 |
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0308P)2 + 2.4843P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.037 | (Δ/σ)max = 0.036 |
wR(F2) = 0.160 | Δρmax = 0.46 e Å−3 |
S = 1.04 | Δρmin = −0.35 e Å−3 |
3857 reflections | Extinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
101 parameters | Extinction coefficient: 0.0097 (7) |
1 restraint | Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881 |
Primary atom site location: structure-invariant direct methods | Absolute structure parameter: 0.1 (5) |
KNO3 | V = 1278.3 (12) Å3 |
Mr = 101.11 | Z = 16 |
Orthorhombic, Cmc21 | Mo Kα radiation |
a = 10.825 (6) Å | µ = 1.46 mm−1 |
b = 18.351 (10) Å | T = 293 K |
c = 6.435 (3) Å | 0.33 × 0.25 × 0.17 mm |
Nonius KappaCCD diffractometer | 3857 independent reflections |
Absorption correction: analytical face-indexing analytical, see text | 1069 reflections with I > 2σ(I) |
Tmin = 0.65, Tmax = 0.78 | Rint = 0.000 |
3857 measured reflections |
R[F2 > 2σ(F2)] = 0.037 | 1 restraint |
wR(F2) = 0.160 | Δρmax = 0.46 e Å−3 |
S = 1.04 | Δρmin = −0.35 e Å−3 |
3857 reflections | Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881 |
101 parameters | Absolute structure parameter: 0.1 (5) |
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. |
x | y | z | Uiso*/Ueq | ||
K1 | 0.0000 | 0.41703 (12) | 0.2604 (3) | 0.0310 (6) | |
K2 | 0.5000 | 0.41679 (12) | 0.2614 (3) | 0.0305 (6) | |
K3 | 0.24980 (14) | 0.16670 (8) | 0.25104 (8) | 0.0303 (4) | |
N1 | 0.0000 | 0.2483 (6) | 0.4215 (19) | 0.026 (2) | |
N2 | 0.5000 | 0.2469 (6) | 0.4208 (19) | 0.031 (2) | |
N3 | 0.2497 (6) | 0.4979 (4) | 0.0911 (18) | 0.0271 (18) | |
O1 | 0.0000 | 0.1807 (4) | 0.414 (2) | 0.043 (3) | |
O2 | 0.5000 | 0.1788 (4) | 0.4138 (19) | 0.038 (2) | |
O3 | 0.0999 (4) | 0.2830 (3) | 0.4206 (15) | 0.0401 (15) | |
O4 | 0.3987 (4) | 0.2809 (3) | 0.4248 (15) | 0.0434 (18) | |
O5 | 0.1506 (4) | 0.5313 (3) | 0.0984 (15) | 0.0405 (18) | |
O6 | 0.3479 (4) | 0.5321 (3) | 0.0896 (16) | 0.044 (2) | |
O7 | 0.2478 (5) | 0.4296 (3) | 0.0937 (18) | 0.043 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
K1 | 0.0274 (12) | 0.0276 (13) | 0.0381 (15) | 0.000 | 0.000 | −0.0011 (14) |
K2 | 0.0286 (12) | 0.0278 (13) | 0.0352 (15) | 0.000 | 0.000 | −0.0009 (14) |
K3 | 0.0262 (8) | 0.0280 (8) | 0.0366 (12) | 0.0000 (7) | 0.0004 (7) | 0.0008 (12) |
N1 | 0.021 (4) | 0.030 (4) | 0.028 (6) | 0.000 | 0.000 | 0.000 (5) |
N2 | 0.038 (5) | 0.036 (5) | 0.019 (6) | 0.000 | 0.000 | −0.002 (5) |
N3 | 0.026 (3) | 0.031 (3) | 0.024 (5) | 0.007 (3) | −0.003 (3) | −0.001 (4) |
O1 | 0.038 (5) | 0.031 (4) | 0.059 (7) | 0.000 | 0.000 | 0.001 (5) |
O2 | 0.045 (5) | 0.025 (4) | 0.044 (6) | 0.000 | 0.000 | 0.002 (5) |
O3 | 0.031 (3) | 0.047 (3) | 0.042 (4) | −0.007 (3) | −0.004 (3) | −0.005 (4) |
O4 | 0.026 (3) | 0.045 (3) | 0.059 (5) | 0.009 (3) | 0.003 (3) | −0.010 (4) |
O5 | 0.029 (3) | 0.036 (3) | 0.057 (5) | 0.002 (3) | −0.004 (3) | −0.001 (4) |
O6 | 0.028 (3) | 0.037 (3) | 0.066 (6) | −0.007 (3) | 0.006 (3) | 0.002 (4) |
O7 | 0.045 (4) | 0.032 (3) | 0.052 (6) | −0.003 (3) | 0.000 (3) | −0.011 (4) |
K1—O2i | 2.840 (11) | K3—O4i | 2.814 (8) |
K1—O5ii | 2.854 (7) | K3—O7vii | 2.826 (10) |
K1—O5 | 2.854 (7) | K3—O3i | 2.832 (8) |
K1—O3ii | 2.878 (7) | K3—O4 | 2.870 (6) |
K1—O3 | 2.878 (7) | K3—O5viii | 2.881 (6) |
K1—O5iii | 2.879 (8) | K3—O6viii | 2.881 (7) |
K1—O5iv | 2.879 (8) | K3—O3 | 2.894 (6) |
K1—O7 | 2.898 (7) | K3—O1 | 2.911 (5) |
K1—O7ii | 2.898 (7) | K3—O2 | 2.912 (5) |
K2—O6v | 2.837 (8) | N1—O1 | 1.241 (12) |
K2—O6iii | 2.837 (8) | N1—O3 | 1.255 (6) |
K2—O1i | 2.864 (11) | N1—O3ii | 1.255 (6) |
K2—O6vi | 2.900 (7) | N2—O2 | 1.250 (12) |
K2—O6 | 2.900 (7) | N2—O4vi | 1.262 (6) |
K2—O4 | 2.921 (7) | N2—O4 | 1.262 (6) |
K2—O4vi | 2.921 (7) | N3—O6 | 1.235 (8) |
K2—O7vi | 2.945 (7) | N3—O5 | 1.237 (8) |
K2—O7 | 2.945 (7) | N3—O7 | 1.253 (9) |
O2i—K1—O5ii | 99.7 (3) | O1i—K2—O7vi | 76.3 (2) |
O2i—K1—O5 | 99.7 (3) | O6vi—K2—O7vi | 43.59 (16) |
O5ii—K1—O5 | 69.7 (2) | O6—K2—O7vi | 109.1 (2) |
O2i—K1—O3ii | 75.66 (18) | O4—K2—O7vi | 123.25 (14) |
O5ii—K1—O3ii | 122.98 (16) | O4vi—K2—O7vi | 81.52 (15) |
O5—K1—O3ii | 166.82 (11) | O6v—K2—O7 | 141.6 (3) |
O2i—K1—O3 | 75.66 (18) | O6iii—K2—O7 | 73.05 (18) |
O5ii—K1—O3 | 166.82 (11) | O1i—K2—O7 | 76.3 (2) |
O5—K1—O3 | 122.98 (16) | O6vi—K2—O7 | 109.1 (2) |
O3ii—K1—O3 | 44.14 (19) | O6—K2—O7 | 43.59 (16) |
O2i—K1—O5iii | 142.86 (12) | O4—K2—O7 | 81.52 (15) |
O5ii—K1—O5iii | 110.96 (16) | O4vi—K2—O7 | 123.25 (14) |
O5—K1—O5iii | 73.17 (12) | O7vi—K2—O7 | 135.9 (4) |
O3ii—K1—O5iii | 102.9 (3) | O4i—K3—O7vii | 143.24 (16) |
O3—K1—O5iii | 78.3 (2) | O4i—K3—O3i | 69.9 (2) |
O2i—K1—O5iv | 142.86 (12) | O7vii—K3—O3i | 141.67 (16) |
O5ii—K1—O5iv | 73.17 (12) | O4i—K3—O4 | 111.22 (15) |
O5—K1—O5iv | 110.96 (16) | O7vii—K3—O4 | 98.5 (3) |
O3ii—K1—O5iv | 78.3 (2) | O3i—K3—O4 | 74.44 (17) |
O3—K1—O5iv | 102.9 (3) | O4i—K3—O5viii | 104.7 (3) |
O5iii—K1—O5iv | 69.0 (3) | O7vii—K3—O5viii | 73.93 (17) |
O2i—K1—O7 | 76.0 (2) | O3i—K3—O5viii | 79.1 (2) |
O5ii—K1—O7 | 109.6 (3) | O4—K3—O5viii | 123.52 (15) |
O5—K1—O7 | 43.72 (16) | O4i—K3—O6viii | 79.3 (2) |
O3ii—K1—O7 | 123.27 (14) | O7vii—K3—O6viii | 75.43 (17) |
O3—K1—O7 | 81.56 (16) | O3i—K3—O6viii | 102.7 (3) |
O5iii—K1—O7 | 74.28 (19) | O4—K3—O6viii | 166.55 (12) |
O5iv—K1—O7 | 141.0 (3) | O5viii—K3—O6viii | 43.54 (13) |
O2i—K1—O7ii | 76.0 (2) | O4i—K3—O3 | 73.07 (17) |
O5ii—K1—O7ii | 43.72 (16) | O7vii—K3—O3 | 99.9 (3) |
O5—K1—O7ii | 109.6 (3) | O3i—K3—O3 | 111.39 (15) |
O3ii—K1—O7ii | 81.56 (16) | O4—K3—O3 | 68.28 (15) |
O3—K1—O7ii | 123.27 (14) | O5viii—K3—O3 | 166.94 (12) |
O5iii—K1—O7ii | 141.0 (3) | O6viii—K3—O3 | 124.20 (15) |
O5iv—K1—O7ii | 74.28 (19) | O4i—K3—O1 | 73.0 (2) |
O7—K1—O7ii | 135.5 (5) | O7vii—K3—O1 | 77.5 (3) |
O6v—K2—O6iii | 70.9 (3) | O3i—K3—O1 | 140.8 (3) |
O6v—K2—O1i | 141.98 (13) | O4—K3—O1 | 108.5 (3) |
O6iii—K2—O1i | 141.98 (13) | O5viii—K3—O1 | 123.12 (16) |
O6v—K2—O6vi | 73.34 (11) | O6viii—K3—O1 | 82.21 (18) |
O6iii—K2—O6vi | 111.83 (16) | O3—K3—O1 | 43.81 (17) |
O1i—K2—O6vi | 99.1 (3) | O4i—K3—O2 | 140.7 (3) |
O6v—K2—O6 | 111.83 (16) | O7vii—K3—O2 | 76.0 (3) |
O6iii—K2—O6 | 73.34 (11) | O3i—K3—O2 | 73.2 (2) |
O1i—K2—O6 | 99.1 (3) | O4—K3—O2 | 44.11 (16) |
O6vi—K2—O6 | 69.2 (2) | O5viii—K3—O2 | 80.81 (17) |
O6v—K2—O4 | 103.4 (3) | O6viii—K3—O2 | 122.45 (15) |
O6iii—K2—O4 | 78.3 (2) | O3—K3—O2 | 109.3 (2) |
O1i—K2—O4 | 75.38 (19) | O1—K3—O2 | 136.7 (4) |
O6vi—K2—O4 | 166.79 (11) | O1—N1—O3 | 120.4 (5) |
O6—K2—O4 | 123.20 (16) | O1—N1—O3ii | 120.4 (5) |
O6v—K2—O4vi | 78.3 (2) | O3—N1—O3ii | 119.2 (10) |
O6iii—K2—O4vi | 103.4 (3) | O2—N2—O4vi | 119.8 (5) |
O1i—K2—O4vi | 75.38 (19) | O2—N2—O4 | 119.8 (5) |
O6vi—K2—O4vi | 123.19 (16) | O4vi—N2—O4 | 120.4 (10) |
O6—K2—O4vi | 166.79 (11) | O6—N3—O5 | 119.8 (7) |
O4—K2—O4vi | 44.09 (19) | O6—N3—O7 | 121.5 (6) |
O6v—K2—O7vi | 73.05 (18) | O5—N3—O7 | 118.6 (6) |
O6iii—K2—O7vi | 141.6 (3) |
Symmetry codes: (i) −x+1/2, −y+1/2, z−1/2; (ii) −x, y, z; (iii) x, −y+1, z+1/2; (iv) −x, −y+1, z+1/2; (v) −x+1, −y+1, z+1/2; (vi) −x+1, y, z; (vii) −x+1/2, −y+1/2, z+1/2; (viii) −x+1/2, y−1/2, z. |
Experimental details
Crystal data | |
Chemical formula | KNO3 |
Mr | 101.11 |
Crystal system, space group | Orthorhombic, Cmc21 |
Temperature (K) | 293 |
a, b, c (Å) | 10.825 (6), 18.351 (10), 6.435 (3) |
V (Å3) | 1278.3 (12) |
Z | 16 |
Radiation type | Mo Kα |
µ (mm−1) | 1.46 |
Crystal size (mm) | 0.33 × 0.25 × 0.17 |
Data collection | |
Diffractometer | Nonius KappaCCD diffractometer |
Absorption correction | Analytical face-indexing analytical, see text |
Tmin, Tmax | 0.65, 0.78 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 3857, 3857, 1069 |
Rint | 0.000 |
(sin θ/λ)max (Å−1) | 0.909 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.037, 0.160, 1.04 |
No. of reflections | 3857 |
No. of parameters | 101 |
No. of restraints | 1 |
Δρmax, Δρmin (e Å−3) | 0.46, −0.35 |
Absolute structure | Flack H D (1983), Acta Cryst. A39, 876-881 |
Absolute structure parameter | 0.1 (5) |
Computer programs: COLLECT (Nonius 1999), COLLECT, DENZO (Otwinowski & Minor, 1997), SHELXS97 (Sheldrick, 1990), SHELXL97 (Sheldrick, 1997).
N1—O1 | 1.241 (12) | N2—O4 | 1.262 (6) |
N1—O3 | 1.255 (6) | N3—O6 | 1.235 (8) |
N1—O3i | 1.255 (6) | N3—O5 | 1.237 (8) |
N2—O2 | 1.250 (12) | N3—O7 | 1.253 (9) |
N2—O4ii | 1.262 (6) | ||
O1—N1—O3 | 120.4 (5) | O4ii—N2—O4 | 120.4 (10) |
O1—N1—O3i | 120.4 (5) | O6—N3—O5 | 119.8 (7) |
O3—N1—O3i | 119.2 (10) | O6—N3—O7 | 121.5 (6) |
O2—N2—O4ii | 119.8 (5) | O5—N3—O7 | 118.6 (6) |
O2—N2—O4 | 119.8 (5) |
Symmetry codes: (i) −x, y, z; (ii) −x+1, y, z. |
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Potassium nitrate is known to be both a mineral (niter) and an inexpansive chemical compound. On heating, it shows two phase transitions at atmosheric pressure. The first transition is from the α-phase to the β-phase and the second is from the β-phase to the melt. These transitions are widely used to calibrate differential thermal analysis (DTA) devices (Barshad, 1952; Greis et al., 1985). The crystal structure of the α-phase was determined by Edwards (1931), and it was redetermined by Nimmo & Lucas (1973) and Holden & Dickinson (1975) using neutrons and X-rays, respectively. All these authors found an aragonite-type structure with space group Pmnc.
For many years, we have used potassium nitrate to calibrate a DTA apparatus and to teach graduate students phase transitions observed by DTA and X-ray powder diffraction. Then, in addition, we advantageously used the same compound to teach structure determination as well. To study the structure, we employed a Weissenbrg camera and an Enraf–Nonius CAD-4 diffractometer. The Weissenberg photographs never showed a sign of a superstructure and, therefore, the known space group, Pmnc, was confirmed. However, the situation was completely different when we used a Nonius KappaCCD diffractometer. In the latter case, space group Cmc21 was determined, with doubled crystallographic a0 and b0 axes. All corresponding reflections with odd h or k indices have weak intensities, thus showing a 2x2x1 superstructure. Based on the criterion I>2σ(I), 1060 reflections are classified as significant, of which 1012 belong to the sublattice and 48 to the superlattice, including 17 Friedel pairs. The intensity of the strongest superlattice reflection is less than 2% of that of the strongest sublattice reflection.
The space group of the superstructure (Cmc21) is a subgroup of that given in the literature (Pmcn) for α-KNO3. As can be seen from the International Tables for Crystallography (1983, Vol·A), both space groups are connected via the minimal supergroup (maximal subgroup) Pmc21 (Cmc21 < Pmc21 < Pmcn). According to the work? of Lima-de-Faria et al. (1990), the superstructure of α-KNO3 and the formerly described aragonite-type structure of this compound are homeotypic. Regarding the geometric properties, the superstructure differs little from the aragonite-type structure. However, the superstructure has a lowered symmetry and hence a higher number of crystallographically independent atoms in the asymmetric unit. While the true aragonite-type structure has one unique K atom and one unique N atom, each of them sitting on a mirror plane, the superstructure contains three unique atoms of both elements. Each of these elements occupies two unique sites on a mirror plane and one at a general position, as depicted in Fig. 1.
There are seven unique O atoms in the superstructure of α-KNO3. All seven are bonded to N atoms, forming nitrate ions, of which three are unique (see Table 1 for selected bond lengths and angles). In each nitrate ion, the N atom deviates by 2 s.u. or less from the plane through the O atoms. Each of the three unique potassium ions is surrounded by nine O atoms from six nitrate ions, thereby building an irregular coordination polyhedron.
A face-indexing analytical absorption correction was applied, based on a data crystal bound by ten faces, viz. (0–11), (01–1), (010), (0–10), (110), (−1–10), (0–1-1), (−111), (−110) and (1–10), with face-to-center distances of 0.11, 0.06, 0.16, 0.17, 0.13, 0.11, 0.12, 0.15, 0.10 and 0.17 mm, respectively. Neither looking orthorhombic nor resembling a sphere, the shape of the crystal is a little strange, which makes absorption correction extremely difficult.