Electron density distribution and Madelung potential in α-spodumene, LiAl(SiO₃)₂, from two-wavelength high-resolution X-ray diffraction data

The electron density distribution in α-spodumene, LiAl(SiO₃)₂, was derived from high-resolution X-ray diffraction experiments. The results obtained from both Mo Kα- and Ag Kα-wavelength data sets are reported. The features of the Si—O and Al—O bonds are related to the geometrical parameters of the Si—O—Al and Si—O—Si bridges on the one hand and to the O...Li⁺ interaction on the other. Kappa refinements against the two data sets yielded almost the same net charges for the Si (+1.8 e) and O (−1.0 e) atoms in spodumene. However, the Al net charge obtained from the Ag Kα data (+1.9 e) is larger than the net charge derived from the Mo Kα data (+1.5 e). This difference correlates with a more contracted Al valence shell revealed by the shorter X-ray wavelength (κ = 1.4 for the Ag Kα data set). The derived net charges were used to calculate the Madelung potential at the spodumene atomic sites. The electrostatic energy for the chemical formula LiAl(SiO₃)₂ was −8.60 e² Å⁻¹ (−123.84 eV) from the net charges derived from the Ag Kα data and −6.97 e² Å⁻¹ (−100.37 eV) from the net charges derived from the Mo Kα data.

Computing details

For both compounds, data collection: CAD-4 (Enraf-Nonius, 1989); cell refinement: CAD-4 (Enraf-Nonius, 1989); data reduction: DREADD (Blessing, 1987, 1989); program(s) used to refine structure: MOLLY (Hansen & Coppens, 1978).

(I)

Crystal data

LiAl(SiO3)2	F(000) = 368.0
Mr = 186.09	Dx = 3.18 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.7107 Å
a = 9.462 (1) Å	Cell parameters from 25 reflections
b = 8.392 (1) Å	θ = 16.4–30.5°
c = 5.221 (1) Å	µ = 1.05 mm^−1
β = 110.18 (1)°	T = 293 K
V = 389.12 (8) Å^3	Parallelepiped, colourless
Z = 4	0.36 × 0.18 × 0.06 mm

Data collection

Enraf-Nonius CAD4 diffractometer	Rint = 0.021
ω/2θ scans	θmax = 60.1°, θmin = 3.3°
Absorption correction: integration empirical (using intensity measurements) integration (ABSORB, G. de Titta, 1985) and empirical (using intensity measurements) (DREADD, R. Blessing, 1995)	h = −22→22
Tmin = 0.68, Tmax = 0.95	k = −18→20
12984 measured reflections	l = −12→11
2945 independent reflections	3 standard reflections every 120 min
2366 reflections with I > 3σ(I)	intensity decay: none

Refinement

Refinement on F	w = 1/[σ^2(F^2) + (0.0130F^2)^2]
R[F^2 > 2σ(F^2)] = 0.014	(Δ/σ)max < 0.001
wR(F^2) = 0.015	Δρmax = 0.3 e Å^−3
S = 0.97	Δρmin = −0.1 e Å^−3
2366 reflections	Extinction correction: Becker-Coppens type 1 Lorentzian isotropic
138 parameters	Extinction coefficient: 5.0x10^2

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

	x	y	z	Uiso*/Ueq
Si	0.29410 (1)	0.09347 (1)	0.25592 (1)	0.00377 (2)
Al	0.00000	0.90667 (1)	0.25000	0.00409 (2)
O1	0.10971 (2)	0.08232 (2)	0.14056 (4)	0.00479 (4)
O2	0.36470 (2)	0.26713 (2)	0.30048 (4)	0.00758 (5)
O3	0.35663 (2)	0.98674 (3)	0.05827 (4)	0.00749 (5)
Li	0.00000	0.27467 (13)	0.25000	0.01464 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Si	0.00360 (2)	0.00432 (2)	0.00332 (2)	−0.00061 (2)	0.00109 (2)	−0.00019 (2)
Al	0.00407 (3)	0.00419 (3)	0.00393 (3)	0.00000	0.00126 (3)	0.00000
O1	0.00368 (4)	0.00563 (5)	0.00463 (5)	−0.00036 (4)	0.00090 (4)	0.00013 (4)
O2	0.00799 (6)	0.00560 (5)	0.00983 (6)	−0.00293 (4)	0.00393 (5)	−0.00098 (5)
O3	0.00572 (5)	0.01129 (6)	0.00508 (5)	0.00067 (5)	0.00139 (4)	−0.00337 (5)
Li	0.0146 (4)	0.0139 (4)	0.0159 (4)	0.00000	0.0058 (3)	0.00000

Geometric parameters (Å, º)

Si—O2	1.5866 (2)	Al—O1^iv	1.9451 (2)
Si—O3^i	1.6242 (2)	Al—O1^v	1.9965 (2)
Si—O3^ii	1.6280 (2)	Li—O1	2.1021 (8)
Si—O1	1.6404 (2)	Li—O3^vi	2.2524 (9)
Al—O2^iii	1.8200 (2)	Li—O2^vii	2.2797 (3)
O2—Si—O3^i	111.87 (1)	O1—Li—O3^xii	116.70 (1)
O2—Si—O3^ii	104.11 (1)	O1—Li—O3^vi	139.84 (1)
O2—Si—O1	116.55 (1)	O2^xi—Li—O1	75.92 (2)
O3^i—Si—O3^ii	107.32 (1)	O2^vii—Li—O1	90.40 (3)
O3^i—Si—O1	108.04 (1)	O3^xii—Li—O2^vii	68.03 (1)
O3^ii—Si—O1	108.50 (1)	O3^xii—Li—O2^xi	128.13 (4)
O2^iii—Al—O2^viii	99.90 (1)	Si—O1—Al^iv	119.85 (1)
O2^iii—Al—O1^ix	88.43 (1)	Si—O1—Al^i	121.95 (1)
O2^iii—Al—O1^v	167.85 (1)	Si—O2—Al^xiii	148.37 (1)
O1^v—Al—O1^ix	84.82 (1)	Si^v—O3—Si^xiv	138.91 (1)
O2^iii—Al—O1^ii	91.52 (1)	Al^iv—O1—Al^i	101.12 (1)
O2^iii—Al—O1^iv	91.98 (1)	Si—O1—Li	114.76 (2)
O1^ii—Al—O1^ix	78.88 (1)	Si—O2—Li^vii	93.91 (3)
O1^ii—Al—O1^v	97.05 (1)	Si^v—O3—Li^xv	116.68 (1)
O1^iv—Al—O1^ii	174.55 (1)	Si^xiv—O3—Li^xv	93.78 (2)
O1—Li—O1^x	79.67 (4)	Al^iv—O1—Li	96.51 (1)
O2^vii—Li—O2^xi	162.29 (5)	Al^i—O1—Li	97.76 (2)
O3^vi—Li—O3^xii	75.59 (3)	Al^xiii—O2—Li^vii	94.29 (2)

Symmetry codes: (i) x, y−1, z; (ii) x, −y+1, z+1/2; (iii) x−1/2, y+1/2, z; (iv) −x, −y+1, −z; (v) x, y+1, z; (vi) x−1/2, y−1/2, z; (vii) −x+1/2, −y+1/2, −z+1; (viii) −x+1/2, y+1/2, −z+1/2; (ix) −x, y+1, −z+1/2; (x) −x, y, −z+1/2; (xi) x−1/2, −y+1/2, z−1/2; (xii) −x+1/2, y−1/2, −z+1/2; (xiii) x+1/2, y−1/2, z; (xiv) x, −y+1, z−1/2; (xv) x+1/2, y+1/2, z.

(II)

Crystal data

LiAl(SiO3)2	F(000) = 368.0
Mr = 186.09	Dx = 3.18 Mg m^−3
Monoclinic, C2/c	Ag Kα radiation, λ = 0.5608 Å
a = 9.456 (1) Å	Cell parameters from 25 reflections
b = 8.386 (1) Å	θ = 9.4–23.6°
c = 5.216 (1) Å	µ = 0.54 mm^−1
β = 110.13 (1)°	T = 293 K
V = 388.36 (9) Å^3	Parallelepiped, colourless
Z = 4	0.36 × 0.18 × 0.06 mm

Data collection

Enraf-Nonius CAD4 diffractometer	Rint = 0.021
ω/2θ scans	θmax = 45.0°, θmin = 2.6°
Absorption correction: integration empirical (using intensity measurements) integration (ABSORB, G. de Titta, 1985) and empirical (using intensity measurements) (DREADD, R. Blessing, 1995)	h = −23→23
Tmin = 0.82, Tmax = 0.97	k = −21→21
15850 measured reflections	l = −13→13
3241 independent reflections	4 standard reflections every 120 min
2261 reflections with I > 3σ(I)	intensity decay: none

Refinement

Refinement on F	w = 1/[σ^2(F^2) + (0.0160F^2)^2]
R[F^2 > 2σ(F^2)] = 0.016	(Δ/σ)max < 0.001
wR(F^2) = 0.015	Δρmax = 0.2 e Å^−3
S = 0.84	Δρmin = −0.1 e Å^−3
2261 reflections	Extinction correction: Becker-Coppens type 1 Lorentzian isotropic
138 parameters	Extinction coefficient: 4.9.10^2

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

	x	y	z	Uiso*/Ueq
Si	0.29410 (1)	0.09345 (1)	0.25593 (2)	0.00397 (3)
Al	0.00000	0.90669 (2)	0.25000	0.00424 (4)
O1	0.10975 (2)	0.08237 (2)	0.14061 (4)	0.00495 (5)
O2	0.36470 (3)	0.26708 (3)	0.30050 (5)	0.00771 (6)
O3	0.35663 (2)	0.98668 (3)	0.05824 (4)	0.00766 (6)
Li	0.00000	0.27494 (14)	0.25000	0.01474 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Si	0.00386 (3)	0.00447 (3)	0.00355 (3)	−0.00062 (2)	0.00125 (2)	−0.00020 (2)
Al	0.00420 (4)	0.00427 (4)	0.00418 (4)	0.00000	0.00134 (3)	0.00000
O1	0.00389 (5)	0.00587 (6)	0.00469 (6)	−0.00033 (5)	0.00096 (4)	0.00020 (5)
O2	0.00817 (7)	0.00569 (6)	0.00991 (7)	−0.00291 (5)	0.00392 (6)	−0.00084 (6)
O3	0.00590 (6)	0.01141 (8)	0.00529 (6)	0.00068 (6)	0.00145 (5)	−0.00339 (6)
Li	0.0154 (5)	0.0137 (5)	0.0151 (5)	0.00000	0.0051 (4)	0.00000

Geometric parameters (Å, º)

Si—O2	1.5852 (2)	Al—O1^iv	1.9447 (2)
Si—O3^i	1.6230 (2)	Al—O1^v	1.9951 (2)
Si—O3^ii	1.6268 (2)	Li—O1	2.1019 (9)
Si—O1	1.6393 (2)	Li—O3^vi	2.2491 (9)
Al—O2^iii	1.8190 (2)	Li—O2^vii	2.2791 (3)
O2—Si—O3^i	111.89 (1)	O1—Li—O3^xii	116.68 (1)
O2—Si—O3^ii	104.07 (1)	O1—Li—O3^vi	139.84 (1)
O2—Si—O1	116.54 (1)	O2^xi—Li—O1	75.92 (2)
O3^i—Si—O3^ii	107.32 (1)	O2^vii—Li—O1	90.32 (3)
O3^i—Si—O1	108.02 (1)	O3^xii—Li—O2^vii	68.00 (1)
O3^ii—Si—O1	108.55 (1)	O3^xii—Li—O2^xi	128.22 (4)
O2^iii—Al—O2^viii	99.87 (2)	Si—O1—Al^iv	119.90 (1)
O2^iii—Al—O1^ix	88.45 (1)	Si—O1—Al^i	121.93 (1)
O2^iii—Al—O1^v	167.87 (2)	Si—O2—Al^xiii	148.39 (2)
O1^v—Al—O1^ix	84.80 (1)	Si^v—O3—Si^xiv	138.89 (2)
O2^iii—Al—O1^ii	91.55 (1)	Al^iv—O1—Al^i	101.07 (1)
O2^iii—Al—O1^iv	91.94 (1)	Si—O1—Li	114.76 (2)
O1^ii—Al—O1^ix	78.93 (1)	Si—O2—Li^vii	93.89 (3)
O1^ii—Al—O1^v	97.02 (1)	Si^v—O3—Li^xv	116.65 (1)
O1^iv—Al—O1^ii	174.59 (1)	Si^xiv—O3—Li^xv	93.86 (2)
O1—Li—O1^x	79.60 (4)	Al^iv—O1—Li	96.48 (1)
O2^vii—Li—O2^xi	162.21 (6)	Al^i—O1—Li	97.81 (2)
O3^vi—Li—O3^xii	75.72 (3)	Al^xiii—O2—Li^vii	94.28 (2)

Symmetry codes: (i) x, y−1, z; (ii) x, −y+1, z+1/2; (iii) x−1/2, y+1/2, z; (iv) −x, −y+1, −z; (v) x, y+1, z; (vi) x−1/2, y−1/2, z; (vii) −x+1/2, −y+1/2, −z+1; (viii) −x+1/2, y+1/2, −z+1/2; (ix) −x, y+1, −z+1/2; (x) −x, y, −z+1/2; (xi) x−1/2, −y+1/2, z−1/2; (xii) −x+1/2, y−1/2, −z+1/2; (xiii) x+1/2, y−1/2, z; (xiv) x, −y+1, z−1/2; (xv) x+1/2, y+1/2, z.