Modulated corrugations in the crystal structure of the superconductor CaAlSi

Sparta, K.M.; Müller, R.; Merz, M.; Roth, G.; Adelmann, P.; Wolf, T.

doi:10.1107/S0108768106025900

Modulated corrugations in the crystal structure of the superconductor CaAlSi

K. M. Sparta, R. Müller, M. Merz, G. Roth, P. Adelmann and T. Wolf

We report the crystal structure analyses of CaAlSi from single-crystal and powder X-ray diffraction and the existence of two commensurately modulated phases, a sixfold and a fivefold modulated structure. This polymorphism seems to be correlated to the thermal history of the sample. We describe both modulated structures using a three-dimensional and a (3 + 1)-dimensional formalism.

Keywords: superconductors; CaAlSi; single-crystal X-ray diffraction; powder X-ray diffraction; commensurately modulated structures.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768106025900/ck5016sup1.cif Contains datablocks global, 6-fold_superstructure_298K, 5-fold_superstructure_298K
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768106025900/ck50166-foldsup2.hkl Contains datablock 6-fold_superstructure_(298K)
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768106025900/ck50165-foldsup3.hkl Contains datablock 5-fold_superstructure_(298K)

Computing details top

For both compounds, data collection: X-AREA (Stoe, 2002); cell refinement: FullProf Suite (Rodriguez-Carvajal); data reduction: X-RED (Stoe, 1996); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ATOMS Version 5.1; software used to prepare material for publication: WinGX 1.64.05 (Farrugia, 1999).

Figures top

(6-fold_superstructure_298K) top

Crystal data top

AlSiCa	D_x = 2.383 Mg m⁻³ D_m = 2.383 Mg m⁻³ D_m measured by not measured
M_r = 95.15	Melting point: 0 K
Hexagonal, P6m2	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P -6 2	Cell parameters from 23 reflections
a = 4.17720 (4) Å	θ = 10.1–47.2°
c = 26.3246 (4) Å	µ = 2.76 mm⁻¹
V = 397.80 (1) Å³	T = 298 K
Z = 6	Cuboid, metallic dark grey
F(000) = 282	0.18 × 0.16 × 0.15 × 0 (radius) mm

Data collection top

STOE IPDS 2 diffractometer	233 reflections with I > 2σ(I)
rotation method scans	R_int = 0.049
Absorption correction: empirical (using intensity measurements) X-SHAPE (Stoe & Cie, 1996)	θ_max = 27.1°, θ_min = 1.6°
T_min = 0.557, T_max = 0.660	h = −5→5
3136 measured reflections	k = −5→5
429 independent reflections	l = −33→33

Refinement top

Refinement on F²	0 constraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.013P)²] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.03	(Δ/σ)_max < 0.001
wR(F²) = 0.082	Δρ_max = 0.25 e Å⁻³
S = 1.96	Δρ_min = −0.29 e Å⁻³
429 reflections	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
31 parameters	Absolute structure parameter: 0.1 (3)
0 restraints

Crystal data top

AlSiCa	Z = 6
M_r = 95.15	Mo Kα radiation
Hexagonal, P6m2	µ = 2.76 mm⁻¹
a = 4.17720 (4) Å	T = 298 K
c = 26.3246 (4) Å	0.18 × 0.16 × 0.15 × 0 (radius) mm
V = 397.80 (1) Å³

Data collection top

STOE IPDS 2 diffractometer	429 independent reflections
Absorption correction: empirical (using intensity measurements) X-SHAPE (Stoe & Cie, 1996)	233 reflections with I > 2σ(I)
T_min = 0.557, T_max = 0.660	R_int = 0.049
3136 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.03	0 restraints
wR(F²) = 0.082	Δρ_max = 0.25 e Å⁻³
S = 1.96	Δρ_min = −0.29 e Å⁻³
429 reflections	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
31 parameters	Absolute structure parameter: 0.1 (3)

Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ca1	0	0	0.08205 (12)	0.0160 (6)
Ca2	0	0	0.24927 (15)	0.0151 (6)
Ca3	0	0	0.41729 (14)	0.0172 (7)
SI1	0.3333	0.6667	0	0.038 (2)	0.5
SI2	0.6667	0.3333	0	0.0147 (14)	0.5
SI3	0.3333	0.6667	0.1605 (2)	0.0217 (12)	0.5
SI4	0.6667	0.3333	0.17111 (19)	0.0145 (12)	0.5
SI5	0.3333	0.6667	0.32802 (15)	0.0128 (10)	0.5
SI6	0.6667	0.3333	0.3412 (2)	0.0219 (11)	0.5
SI7	0.3333	0.6667	0.5	0.0084 (11)	0.5
SI8	0.6667	0.3333	0.5	0.039 (3)	0.5
AL1	0.3333	0.6667	0	0.038 (2)	0.5
AL2	0.6667	0.3333	0	0.0147 (14)	0.5
AL3	0.3333	0.6667	0.1605 (2)	0.0217 (12)	0.5
AL4	0.6667	0.3333	0.17111 (19)	0.0145 (12)	0.5
AL5	0.3333	0.6667	0.32802 (15)	0.0128 (10)	0.5
AL6	0.6667	0.3333	0.3412 (2)	0.0219 (11)	0.5
AL7	0.3333	0.6667	0.5	0.0084 (11)	0.5
AL8	0.6667	0.3333	0.5	0.039 (3)	0.5

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ca1	0.0189 (9)	0.0189 (9)	0.0104 (11)	0.0094 (5)	0	0
Ca2	0.0158 (8)	0.0158 (8)	0.0139 (10)	0.0079 (4)	0	0
Ca3	0.0156 (9)	0.0156 (9)	0.0202 (14)	0.0078 (5)	0	0
SI1	0.0141 (19)	0.0141 (19)	0.086 (7)	0.0071 (10)	0	0
SI2	0.0130 (18)	0.0130 (18)	0.018 (3)	0.0065 (9)	0	0
SI3	0.0168 (14)	0.0168 (14)	0.032 (3)	0.0084 (7)	0	0
SI4	0.0073 (12)	0.0073 (12)	0.029 (3)	0.0036 (6)	0	0
SI5	0.0115 (13)	0.0115 (13)	0.015 (2)	0.0057 (7)	0	0
SI6	0.0127 (12)	0.0127 (12)	0.040 (3)	0.0063 (6)	0	0
SI7	0.0048 (15)	0.0048 (15)	0.015 (3)	0.0024 (7)	0	0
SI8	0.0088 (18)	0.0088 (18)	0.101 (8)	0.0044 (9)	0	0
AL1	0.0141 (19)	0.0141 (19)	0.086 (7)	0.0071 (10)	0	0
AL2	0.0130 (18)	0.0130 (18)	0.018 (3)	0.0065 (9)	0	0
AL3	0.0168 (14)	0.0168 (14)	0.032 (3)	0.0084 (7)	0	0
AL4	0.0073 (12)	0.0073 (12)	0.029 (3)	0.0036 (6)	0	0
AL5	0.0115 (13)	0.0115 (13)	0.015 (2)	0.0057 (7)	0	0
AL6	0.0127 (12)	0.0127 (12)	0.040 (3)	0.0063 (6)	0	0
AL7	0.0048 (15)	0.0048 (15)	0.015 (3)	0.0024 (7)	0	0
AL8	0.0088 (18)	0.0088 (18)	0.101 (8)	0.0044 (9)	0	0

Bond lengths (Å) top

Ca1—SI3	3.175 (4)	Ca3—Ca3ⁱⁱⁱ	4.1772
Ca1—AL3ⁱ	3.175 (4)	Ca3—Ca3^viii	4.355 (7)
Ca1—SI3ⁱ	3.175 (4)	SI1—AL2^v	2.4117
Ca1—AL3ⁱⁱ	3.175 (4)	SI1—AL2ⁱⁱⁱ	2.4117
Ca1—SI3ⁱⁱ	3.175 (4)	SI1—SI2^v	2.4117
Ca1—AL2ⁱⁱ	3.238 (2)	SI1—SI2ⁱⁱⁱ	2.4117
Ca1—AL1ⁱⁱ	3.238 (2)	SI1—SI2	2.4117
Ca1—SI2ⁱⁱ	3.238 (2)	SI1—Ca1^iv	3.238 (2)
Ca1—SI1ⁱⁱ	3.238 (2)	SI1—Ca1^v	3.238 (2)
Ca1—AL2ⁱⁱⁱ	3.238 (2)	SI1—Ca1^vii	3.238 (2)
Ca1—AL1ⁱ	3.238 (2)	SI1—Ca1^ix	3.238 (2)
Ca1—SI2ⁱⁱⁱ	3.238 (2)	SI1—Ca1^x	3.238 (2)
Ca1—SI1ⁱ	3.238 (2)	SI1—SI3	4.224 (5)
Ca1—SI2	3.238 (2)	SI2—AL1^vi	2.4117
Ca1—SI1	3.238 (2)	SI2—AL1ⁱ	2.4117
Ca1—SI4	3.363 (5)	SI2—SI1^vi	2.4117
Ca1—AL4ⁱⁱⁱ	3.363 (5)	SI2—SI1ⁱ	2.4117
Ca1—SI4ⁱⁱⁱ	3.363 (5)	SI2—Ca1^iv	3.238 (2)
Ca1—AL4ⁱⁱ	3.363 (5)	SI2—Ca1^vi	3.238 (2)
Ca1—SI4ⁱⁱ	3.363 (5)	SI2—Ca1^vii	3.238 (2)
Ca1—Ca1ⁱⁱ	4.1772	SI2—Ca1^xi	3.238 (2)
Ca1—Ca1^iv	4.1772	SI2—Ca1^x	3.238 (2)
Ca1—Ca1^v	4.1772	SI2—SI4	4.504 (5)
Ca1—Ca1ⁱⁱⁱ	4.1772	SI3—AL4^v	2.4279 (7)
Ca1—Ca1ⁱ	4.1772	SI3—SI4^v	2.4279 (7)
Ca1—Ca1^vi	4.1772	SI3—AL4ⁱⁱⁱ	2.4279 (6)
Ca1—Ca1^vii	4.320 (7)	SI3—SI4ⁱⁱⁱ	2.4279 (6)
Ca1—Ca2	4.402 (5)	SI3—SI4	2.4279 (7)
Ca2—AL4ⁱⁱ	3.170 (4)	SI3—Ca1^v	3.175 (4)
Ca2—SI4ⁱⁱ	3.170 (4)	SI3—Ca1^iv	3.175 (4)
Ca2—AL4ⁱⁱⁱ	3.170 (4)	SI3—Ca2^iv	3.359 (5)
Ca2—SI4ⁱⁱⁱ	3.170 (4)	SI3—Ca2^v	3.359 (5)
Ca2—SI4	3.170 (4)	SI3—SI5	4.411 (5)
Ca2—SI5	3.180 (4)	SI4—AL3ⁱ	2.4279 (6)
Ca2—AL5ⁱ	3.180 (4)	SI4—SI3ⁱ	2.4279 (6)
Ca2—SI5ⁱ	3.180 (4)	SI4—AL3^vi	2.4279 (7)
Ca2—AL5ⁱⁱ	3.180 (4)	SI4—SI3^vi	2.4279 (7)
Ca2—SI5ⁱⁱ	3.180 (4)	SI4—Ca2^iv	3.170 (4)
Ca2—AL3ⁱⁱ	3.359 (5)	SI4—Ca2^vi	3.170 (4)
Ca2—SI3ⁱⁱ	3.359 (5)	SI4—Ca1^vi	3.363 (5)
Ca2—AL3ⁱ	3.359 (5)	SI4—Ca1^iv	3.363 (5)
Ca2—SI3ⁱ	3.359 (5)	SI4—SI6	4.479 (8)
Ca2—SI3	3.359 (5)	SI5—AL6^v	2.4367 (9)
Ca2—SI6	3.417 (5)	SI5—SI6^v	2.4367 (9)
Ca2—AL6ⁱⁱⁱ	3.417 (5)	SI5—AL6ⁱⁱⁱ	2.4367 (9)
Ca2—SI6ⁱⁱⁱ	3.417 (5)	SI5—SI6ⁱⁱⁱ	2.4367 (9)
Ca2—AL6ⁱⁱ	3.417 (5)	SI5—SI6	2.4367 (9)
Ca2—SI6ⁱⁱ	3.417 (5)	SI5—Ca2^v	3.180 (4)
Ca2—Ca2^iv	4.1772	SI5—Ca2^iv	3.180 (4)
Ca2—Ca2ⁱⁱ	4.1772	SI5—Ca3^iv	3.367 (4)
Ca2—Ca2ⁱ	4.1772	SI5—Ca3^v	3.367 (4)
Ca2—Ca2ⁱⁱⁱ	4.1772	SI5—SI7	4.527 (4)
Ca2—Ca2^vi	4.1772	SI6—AL5ⁱ	2.4367 (9)
Ca2—Ca2^v	4.1772	SI6—SI5ⁱ	2.4367 (9)
Ca2—Ca3	4.423 (5)	SI6—AL5^vi	2.4367 (9)
Ca3—AL6ⁱⁱ	3.134 (5)	SI6—SI5^vi	2.4367 (9)
Ca3—SI6ⁱⁱ	3.134 (5)	SI6—Ca3^iv	3.134 (5)
Ca3—AL6ⁱⁱⁱ	3.134 (5)	SI6—Ca3^vi	3.134 (5)
Ca3—SI6ⁱⁱⁱ	3.134 (5)	SI6—Ca2^vi	3.417 (5)
Ca3—SI6	3.134 (5)	SI6—Ca2^iv	3.417 (5)
Ca3—SI8	3.249 (2)	SI6—SI8	4.179 (6)
Ca3—SI7	3.249 (2)	SI7—AL8^v	2.4117
Ca3—AL8ⁱⁱⁱ	3.249 (2)	SI7—AL8ⁱⁱⁱ	2.4117
Ca3—AL7ⁱ	3.249 (2)	SI7—SI8^v	2.4117
Ca3—SI8ⁱⁱⁱ	3.249 (2)	SI7—SI8ⁱⁱⁱ	2.4117
Ca3—SI7ⁱ	3.249 (2)	SI7—SI8	2.4117
Ca3—AL8ⁱⁱ	3.249 (2)	SI7—Ca3^xii	3.249 (2)
Ca3—AL7ⁱⁱ	3.249 (2)	SI7—Ca3^xiii	3.249 (2)
Ca3—SI8ⁱⁱ	3.249 (2)	SI7—Ca3^v	3.249 (2)
Ca3—SI7ⁱⁱ	3.249 (2)	SI7—Ca3^viii	3.249 (2)
Ca3—AL5ⁱⁱ	3.367 (4)	SI7—Ca3^iv	3.249 (2)
Ca3—SI5ⁱⁱ	3.367 (4)	SI8—AL7^vi	2.4117
Ca3—AL5ⁱ	3.367 (4)	SI8—AL7ⁱ	2.4117
Ca3—SI5ⁱ	3.367 (4)	SI8—SI7^vi	2.4117
Ca3—SI5	3.367 (4)	SI8—SI7ⁱ	2.4117
Ca3—Ca3^iv	4.1772	SI8—Ca3^xii	3.249 (2)
Ca3—Ca3ⁱⁱ	4.1772	SI8—Ca3^xiv	3.249 (2)
Ca3—Ca3ⁱ	4.1772	SI8—Ca3^vi	3.249 (2)
Ca3—Ca3^vi	4.1772	SI8—Ca3^viii	3.249 (2)
Ca3—Ca3^v	4.1772	SI8—Ca3^iv	3.249 (2)

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

(5-fold_superstructure_298K) top

Crystal data top

AlSiCa	D_x = 2.383 Mg m⁻³ D_m = 2.383 Mg m⁻³ D_m measured by not measured
M_r = 95.15	Melting point: 0 K
Hexagonal, P6m2	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P -6 2	Cell parameters from 23 reflections
a = 4.17720 (4) Å	θ = 10.1–47.2°
c = 21.9372 (3) Å	µ = 2.76 mm⁻¹
V = 331.50 (1) Å³	T = 298 K
Z = 5	Cuboid, metallic dark grey
F(000) = 235	0.21 × 0.20 × 0.18 × 0 (radius) mm

Data collection top

STOE IPDS 2 diffractometer	340 reflections with I > 2σ(I)
rotation method scans	R_int = 0.058
Absorption correction: empirical (using intensity measurements) X-SHAPE (Stoe & Cie, 1996)	θ_max = 29.2°, θ_min = 1.9°
T_min = 0.531, T_max = 0.607	h = −5→5
4754 measured reflections	k = −5→5
422 independent reflections	l = −30→30

Refinement top

Refinement on F²	0 constraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.023P)²] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.035	(Δ/σ)_max < 0.001
wR(F²) = 0.086	Δρ_max = 0.46 e Å⁻³
S = 1.99	Δρ_min = −0.41 e Å⁻³
422 reflections	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
26 parameters	Absolute structure parameter: 0.5 (4)
0 restraints

Crystal data top

AlSiCa	Z = 5
M_r = 95.15	Mo Kα radiation
Hexagonal, P6m2	µ = 2.76 mm⁻¹
a = 4.17720 (4) Å	T = 298 K
c = 21.9372 (3) Å	0.21 × 0.20 × 0.18 × 0 (radius) mm
V = 331.50 (1) Å³

Data collection top

STOE IPDS 2 diffractometer	422 independent reflections
Absorption correction: empirical (using intensity measurements) X-SHAPE (Stoe & Cie, 1996)	340 reflections with I > 2σ(I)
T_min = 0.531, T_max = 0.607	R_int = 0.058
4754 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.035	0 restraints
wR(F²) = 0.086	Δρ_max = 0.46 e Å⁻³
S = 1.99	Δρ_min = −0.41 e Å⁻³
422 reflections	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
26 parameters	Absolute structure parameter: 0.5 (4)

Special details top

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ca1	0	0	0	0.0202 (6)
Ca2	0	0	0.19941 (8)	0.0160 (4)
Ca3	0	0	0.40126 (5)	0.0165 (5)
Si1	0.3333	0.6667	0.08767 (12)	0.0210 (5)	0.5
Si2	0.6667	0.3333	0.10556 (8)	0.0120 (6)	0.5
Si3	0.3333	0.6667	0.29191 (9)	0.0122 (5)	0.5
Si4	0.6667	0.3333	0.30909 (12)	0.0241 (7)	0.5
Si5	0.3333	0.6667	0.5	0.0136 (6)	0.5
Si6	0.6667	0.3333	0.5	0.0472 (14)	0.5
Al1	0.3333	0.6667	0.08767 (12)	0.0210 (5)	0.5
Al2	0.6667	0.3333	0.10556 (8)	0.0120 (6)	0.5
Al3	0.3333	0.6667	0.29191 (9)	0.0122 (5)	0.5
Al4	0.6667	0.3333	0.30909 (12)	0.0241 (7)	0.5
Al5	0.3333	0.6667	0.5	0.0136 (6)	0.5
Al6	0.6667	0.3333	0.5	0.0472 (14)	0.5

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ca1	0.0203 (10)	0.0203 (10)	0.0202 (10)	0.0101 (5)	0	0
Ca2	0.0155 (5)	0.0155 (5)	0.0169 (5)	0.0078 (3)	0	0
Ca3	0.0189 (7)	0.0189 (7)	0.0116 (6)	0.0095 (3)	0	0
Si1	0.0137 (8)	0.0137 (8)	0.0356 (9)	0.0068 (4)	0	0
Si2	0.0097 (8)	0.0097 (8)	0.0167 (7)	0.0048 (4)	0	0
Si3	0.0088 (7)	0.0088 (7)	0.0189 (7)	0.0044 (3)	0	0
Si4	0.0150 (10)	0.0150 (10)	0.0422 (10)	0.0075 (5)	0	0
Si5	0.0088 (9)	0.0088 (9)	0.0231 (12)	0.0044 (4)	0	0
Si6	0.0137 (14)	0.0137 (14)	0.114 (4)	0.0068 (7)	0	0
Al1	0.0137 (8)	0.0137 (8)	0.0356 (9)	0.0068 (4)	0	0
Al2	0.0097 (8)	0.0097 (8)	0.0167 (7)	0.0048 (4)	0	0
Al3	0.0088 (7)	0.0088 (7)	0.0189 (7)	0.0044 (3)	0	0
Al4	0.0150 (10)	0.0150 (10)	0.0422 (10)	0.0075 (5)	0	0
Al5	0.0088 (9)	0.0088 (9)	0.0231 (12)	0.0044 (4)	0	0
Al6	0.0137 (14)	0.0137 (14)	0.114 (4)	0.0068 (7)	0	0

Bond lengths (Å) top

Ca1—Si1	3.0846 (17)	Ca3—Al5^v	3.2416 (8)
Ca1—Al1ⁱ	3.0846 (17)	Ca3—Si6^v	3.2416 (8)
Ca1—Si1ⁱ	3.0846 (17)	Ca3—Si5^v	3.2416 (8)
Ca1—Al1ⁱⁱ	3.0846 (17)	Ca3—Al3^v	3.4016 (15)
Ca1—Al1ⁱⁱⁱ	3.0846 (17)	Ca3—Si3^v	3.4016 (15)
Ca1—Si1ⁱⁱ	3.0846 (17)	Ca3—Al3ⁱⁱⁱ	3.4016 (15)
Ca1—Si1ⁱⁱⁱ	3.0846 (17)	Ca3—Si3ⁱⁱⁱ	3.4016 (15)
Ca1—Al1^iv	3.0846 (17)	Ca3—Si3	3.4016 (15)
Ca1—Al1^v	3.0846 (17)	Ca3—Ca3^viii	4.1772
Ca1—Si1^iv	3.0846 (17)	Ca3—Ca3^v	4.1772
Ca1—Si1^v	3.0846 (17)	Ca3—Ca3ⁱⁱⁱ	4.1772
Ca1—Si2	3.3435 (12)	Ca3—Ca3^ix	4.1772
Ca1—Al2ⁱ	3.3435 (12)	Ca3—Ca3^x	4.1772
Ca1—Si2ⁱ	3.3435 (12)	Ca3—Ca3^vii	4.1772
Ca1—Al2^vi	3.3435 (12)	Ca3—Ca3^xi	4.332 (2)
Ca1—Al2^vii	3.3435 (12)	Si1—Al2^x	2.4434 (4)
Ca1—Si2^vi	3.3435 (12)	Si1—Si2^x	2.4434 (4)
Ca1—Si2^vii	3.3435 (12)	Si1—Al2^vii	2.4434 (4)
Ca1—Al2^iv	3.3435 (12)	Si1—Si2^vii	2.4434 (4)
Ca1—Si2^v	3.3435 (12)	Si1—Si2	2.4434 (4)
Ca1—Si2^iv	3.3435 (12)	Si1—Ca1^x	3.0846 (17)
Ca1—Al2^v	3.3435 (12)	Si1—Ca1^viii	3.0846 (17)
Ca1—Ca1^viii	4.1772	Si1—Ca2^viii	3.439 (3)
Ca1—Ca1^v	4.1772	Si1—Ca2^x	3.439 (3)
Ca1—Ca1ⁱⁱⁱ	4.1772	Si2—Al1ⁱⁱⁱ	2.4434 (4)
Ca1—Ca1^ix	4.1772	Si2—Si1ⁱⁱⁱ	2.4434 (4)
Ca1—Ca1^vii	4.1772	Si2—Al1^ix	2.4434 (4)
Ca1—Ca1^x	4.1772	Si2—Si1^ix	2.4434 (4)
Ca1—Ca2^iv	4.3746 (18)	Si2—Ca2^viii	3.1710 (14)
Ca1—Ca2	4.3746 (18)	Si2—Ca2^ix	3.1710 (14)
Ca2—Si3	3.1518 (15)	Si2—Ca1^ix	3.3435 (12)
Ca2—Al3ⁱⁱⁱ	3.1518 (15)	Si2—Ca1^viii	3.3435 (12)
Ca2—Si3ⁱⁱⁱ	3.1518 (15)	Si3—Al4^x	2.4410 (3)
Ca2—Al3^v	3.1518 (15)	Si3—Si4^x	2.4410 (3)
Ca2—Si3^v	3.1518 (15)	Si3—Al4^vii	2.4410 (3)
Ca2—Al2^v	3.1710 (14)	Si3—Si4^vii	2.4410 (3)
Ca2—Si2^v	3.1710 (14)	Si3—Si4	2.4410 (3)
Ca2—Al2^vii	3.1710 (14)	Si3—Ca2^x	3.1518 (15)
Ca2—Si2^vii	3.1710 (14)	Si3—Ca2^viii	3.1518 (15)
Ca2—Si2	3.1710 (14)	Si3—Ca3^viii	3.4016 (15)
Ca2—Si4	3.407 (2)	Si3—Ca3^x	3.4016 (15)
Ca2—Al4^vii	3.407 (2)	Si4—Al3ⁱⁱⁱ	2.4410 (3)
Ca2—Si4^vii	3.407 (2)	Si4—Si3ⁱⁱⁱ	2.4410 (3)
Ca2—Al4^v	3.407 (2)	Si4—Al3^ix	2.4410 (3)
Ca2—Si4^v	3.407 (2)	Si4—Si3^ix	2.4410 (3)
Ca2—Si1^v	3.439 (3)	Si4—Ca3^viii	3.1472 (18)
Ca2—Al1^v	3.439 (3)	Si4—Ca3^ix	3.1472 (18)
Ca2—Al1ⁱⁱⁱ	3.439 (3)	Si4—Ca2^ix	3.407 (2)
Ca2—Si1ⁱⁱⁱ	3.439 (3)	Si4—Ca2^viii	3.407 (2)
Ca2—Si1	3.439 (3)	Si5—Al6^x	2.4117
Ca2—Ca2^v	4.1772	Si5—Al6^vii	2.4117
Ca2—Ca2^viii	4.1772	Si5—Si6^x	2.4117
Ca2—Ca2^x	4.1772	Si5—Si6^vii	2.4117
Ca2—Ca2^vii	4.1772	Si5—Si6	2.4117
Ca2—Ca2ⁱⁱⁱ	4.1772	Si5—Ca3^xii	3.2416 (8)
Ca2—Ca2^ix	4.1772	Si5—Ca3^xiii	3.2416 (8)
Ca2—Ca3	4.4280 (18)	Si5—Ca3^x	3.2416 (8)
Ca3—Al4^v	3.1472 (18)	Si5—Ca3^xi	3.2416 (8)
Ca3—Si4^v	3.1472 (18)	Si5—Ca3^viii	3.2416 (8)
Ca3—Al4^vii	3.1472 (18)	Si6—Al5^ix	2.4117
Ca3—Si4^vii	3.1472 (18)	Si6—Al5ⁱⁱⁱ	2.4117
Ca3—Si4	3.1472 (18)	Si6—Si5^ix	2.4117
Ca3—Si6	3.2416 (8)	Si6—Si5ⁱⁱⁱ	2.4117
Ca3—Si5	3.2416 (8)	Si6—Ca3^xii	3.2416 (8)
Ca3—Al6^vii	3.2416 (8)	Si6—Ca3^xiv	3.2416 (8)
Ca3—Al5ⁱⁱⁱ	3.2416 (8)	Si6—Ca3^ix	3.2416 (8)
Ca3—Si6^vii	3.2416 (8)	Si6—Ca3^xi	3.2416 (8)
Ca3—Si5ⁱⁱⁱ	3.2416 (8)	Si6—Ca3^viii	3.2416 (8)
Ca3—Al6^v	3.2416 (8)

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

Experimental details

	(6-fold_superstructure_298K)	(5-fold_superstructure_298K)
Crystal data
Chemical formula	AlSiCa	AlSiCa
M_r	95.15	95.15
Crystal system, space group	Hexagonal, P6m2	Hexagonal, P6m2
Temperature (K)	298	298
a, c (Å)	4.17720 (4), 26.3246 (4)	4.17720 (4), 21.9372 (3)
V (Å³)	397.80 (1)	331.50 (1)
Z	6	5
Radiation type	Mo Kα	Mo Kα
µ (mm⁻¹)	2.76	2.76
Crystal size (mm)	0.18 × 0.16 × 0.15 × 0 (radius)	0.21 × 0.20 × 0.18 × 0 (radius)

Data collection
Diffractometer	STOE IPDS 2 diffractometer	STOE IPDS 2 diffractometer
Absorption correction	Empirical (using intensity measurements) X-SHAPE (Stoe & Cie, 1996)	Empirical (using intensity measurements) X-SHAPE (Stoe & Cie, 1996)
T_min, T_max	0.557, 0.660	0.531, 0.607
No. of measured, independent and observed [I > 2σ(I)] reflections	3136, 429, 233	4754, 422, 340
R_int	0.049	0.058
(sin θ/λ)_max (Å⁻¹)	0.641	0.686

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.03, 0.082, 1.96	0.035, 0.086, 1.99
No. of reflections	429	422
No. of parameters	31	26
Δρ_max, Δρ_min (e Å⁻³)	0.25, −0.29	0.46, −0.41
Absolute structure	Flack H D (1983), Acta Cryst. A39, 876-881	Flack H D (1983), Acta Cryst. A39, 876-881
Absolute structure parameter	0.1 (3)	0.5 (4)

Computer programs: X-AREA (Stoe, 2002), FullProf Suite (Rodriguez-Carvajal), X-RED (Stoe, 1996), SHELXL97 (Sheldrick, 1997), ATOMS Version 5.1, WinGX 1.64.05 (Farrugia, 1999).

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