Sodium carbonate revisited

We present the structure of anhydrous sodium carbonate at room temperature (phase γ) and 110 K (phase δ) based on single-crystal X-ray diffraction data. The incommensurate phase γ was determined almost 30 years ago in the harmonic approximation using one modulation wave and first-order satellites. In our work we use satellites up to fifth order and additional harmonic waves to model the anharmonic features of the structure. The commensurate phase δ is presented for the first time. Using the superspace approach, both phases are compared in order to find common trends in the whole range of the sodium carbonate phases. We present arguments supporting the hypothesis that the driving force of the phase transitions may originate in the unsaturated bonding potential of one of the Na ions.

Computing details

For both compounds, data collection: (CCD, Kuma Diffraction, 1998); cell refinement: (RED v.168, Oxford Diffraction, 2001); data reduction: (RED v.168, Oxford Diffraction, 2001); program(s) used to solve structure: (Jana2000, Petricek and Dusek, 2000); program(s) used to refine structure: (Jana2000, Petricek and Dusek, 2000); molecular graphics: (Diamond 2.1c, Brandenburg, 1999) (Pictur, Dusek, 1994); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

(I) sodium carbonate

Crystal data

Na2CO3	F(000) = 208
Mr = 106	Dx = 2.574 Mg m^−3
Monoclinic, C2/m(αlpha0γamma)0s†	Melting point: 851 C K
q = 0.16667a* + 0.33333c*	Mo Kα radiation, λ = 0.71069 Å
a = 8.898 (7) Å	Cell parameters from 1280 reflections
b = 5.237 (5) Å	θ = 10–43°
c = 5.996 (5) Å	µ = 0.50 mm^−1
β = 101.87 (8)°	T = 110K K
V = 273.4 (8) Å^3	Potato, white
Z = 4	0.5mm × 0.45mm × 0.4mm mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2−x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2+x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2−x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2+x₄.

Data collection

Xcalibur diffractometer	No. of measured, independent and observed reflections: 61103, 12347, 5695 [I > 3σ(I)]; 2163, 2163, 1090 (Main); 3894, 3894, 1901 (Sat1); 4347, 4347, 1869 (Sat2); 1942, 1942, 837 (Sat3)
Radiation source: X-ray tube	Rint = 0.067, 0.056 (Main), 0.066 (Sat1), 0.116 (Sat2), 0.156 (Sat3)
Graphite monochromator	θmax = 45.7°, θmin = 4.1°
Detector resolution: 8 pixels mm^-1	h = −18→18
ο–scans	k = −10→10
Wave-vector determination: commensurate structure	l = −12→11

Refinement

Refinement on F	205 parameters
R[F^2 > 2σ(F^2)] = 0.045	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
wR(F^2) = 0.066	(Δ/σ)max = 0.003
S = 1.31	Δρmax = 0.69 e Å^−3
5695 reflections	Δρmin = −0.64 e Å^−3

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

	x	y	z	Uiso*/Ueq
Na1	0	0	0	0.00886 (10)
Na2	0	0	0.5	0.00855 (10)
Na3	0.17125 (4)	0.5	0.74784 (6)	0.01267 (8)
C	0.16454 (7)	0.5	0.24887 (10)	0.00695 (12)
O1	0.10175 (5)	0.29345 (6)	0.28667 (7)	0.01312 (9)
O2	0.28941 (6)	0.5	0.17472 (9)	0.01135 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.00927 (18)	0.00910 (12)	0.00885 (17)	0	0.00338 (15)	0
Na2	0.01018 (18)	0.00779 (11)	0.00831 (17)	0	0.00332 (15)	0
Na3	0.01204 (15)	0.01238 (10)	0.01448 (16)	0	0.00482 (13)	0
C	0.0071 (2)	0.00690 (14)	0.0072 (2)	0	0.00232 (19)	0
O1	0.01620 (17)	0.00969 (10)	0.01463 (16)	−0.00452 (10)	0.00584 (14)	0.00021 (10)
O2	0.00874 (19)	0.01506 (15)	0.0115 (2)	0	0.00509 (17)	0

(II) sodium carbonate

Crystal data

Na2CO3	F(000) = 208
Mr = 106	Dx = 2.536 Mg m^−3
Monoclinic, C2/m(αlpha0γamma)0s†	Melting point: 851 C K
q = 0.18200a* + 0.32200c*	Mo Kα radiation, λ = 0.71073 Å
a = 8.9195 Å	Cell parameters from 1610 reflections
b = 5.2454 Å	θ = 10–43°
c = 6.05 Å	µ = 0.49 mm^−1
β = 101.354°	T = 295K K
V = 277.52 Å^3	Potato, white
Z = 4	0.5mm × 0.45mm × 0.4mm mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2−x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2+x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2−x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2+x₄.

Data collection

Xcalibur diffractometer	No. of measured, independent and observed reflections: 77868, 14118, 4178 [I > 3σ(I)]; 1155, 1155, 814 (Main); 2070, 2070, 1244 (Sat1); 2298, 2298, 1033 (Sat2); 2044, 2044, 595 (Sat3); 2284, 2284, 330 (Sat4); 2022, 2022, 113 (Sat5); 2245, 2245, 49 (Sat6)
Radiation source: X-ray tube	Rint = 0.064, 0.046 (Main), 0.055 (Sat1), 0.106 (Sat2), 0.274 (Sat3), 0.727 (Sat4), 1.211 (Sat5), 1.396 (Sat6)
Graphite monochromator	θmax = 45.7°, θmin = 4.0°
Detector resolution: 8 pixels mm^-1	h = −18→18
ο–scans	k = −10→10
Wave-vector determination: Refined with cell parameters	l = −12→12

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
R[F^2 > 2σ(F^2)] = 0.045, wR(F^2) = 0.057, S = 1.50; R[F^2 > 2σ(F^2)] = 0.0354, R(F^2) = 0.0618 (); R[F^2 > 2σ(F^2)] = 0.0340, R(F^2) = 0.0419 (); R[F^2 > 2σ(F^2)] = 0.0527, R(F^2) = 0.0592 (); R[F^2 > 2σ(F^2)] = 0.0795, R(F^2) = 0.1049 (); R[F^2 > 2σ(F^2)] = 0.1110, R(F^2) = 0.1592 (); R[F^2 > 2σ(F^2)] = 0.2223, R(F^2) = 0.4069 (); R[F^2 > 2σ(F^2)] = 0.7863, R(F^2) = 0.8210 ()	(Δ/σ)max = 0.0002
4129 reflections	Δρmax = 0.54 e Å^−3
180 parameters	Δρmin = −0.60 e Å^−3

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

	x	y	z	Uiso*/Ueq
Na1	0	0	0	0.01731 (11)
Na2	0	0	0.5	0.01673 (11)
Na3	0.17055 (4)	0.5	0.74801 (6)	0.02554 (10)
C	0.16446 (7)	0.5	0.24914 (10)	0.01155 (13)
O1	0.10159 (5)	0.29384 (7)	0.28535 (7)	0.02607 (12)
O2	0.28987 (6)	0.5	0.17757 (11)	0.02274 (14)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.01757 (18)	0.01860 (15)	0.01713 (19)	0	0.00672 (16)	0
Na2	0.01919 (19)	0.01561 (15)	0.01686 (19)	0	0.00714 (17)	0
Na3	0.02174 (16)	0.02568 (14)	0.0307 (2)	0	0.00888 (16)	0
C	0.0111 (2)	0.01219 (17)	0.0119 (2)	0	0.0037 (2)	0
O1	0.0318 (2)	0.01881 (14)	0.0299 (2)	−0.00956 (13)	0.01172 (18)	0.00055 (13)
O2	0.0148 (2)	0.0324 (3)	0.0237 (3)	0	0.0104 (2)	0