Incommensurate density modulation in a Na-rich plagioclase feldspar: Z-contrast imaging and single-crystal X-ray diffraction study

Plagioclase feldspars are the most abundant mineral in the Earth's crust. Intermediate plagioclase feldspars commonly display incommensurately modulated or aperiodic structures. Z-contrast images show both Ca–Na ordering and density modulation. The local structure of lamellae domains has I1-like symmetry. The neighboring lamellae domains are in an inversion twinning relationship. With a state-of-the-art X-ray diffraction unit, second-order satellite reflections (f-reflections) are observed for the first time in andesine (An₄₅), a Na-rich e-plagioclase. The f-reflections indicate a structure with a density modulation which is close to a Ca-rich e-plagioclase. The similarity between this e-andesine structure and previously solved e-labradorite structure is confirmed. Refinement of the structure shows density modulation of ∼ 7 mol % in compositional variation of the anorthite (An) component. The results from Z-contrast imaging and low-temperature single X-ray diffraction (XRD) provide a structure consistent with density modulation. The discovery of f-reflections in Na-rich e-plagioclase extends the composition range of e1 structure with density modulation to as low as at least An₄₅, which is the lower end of the composition range of Bøggild intergrowth. The new result supports the loop-shaped solvus for Bøggild intergrowth, below which is a homogenous stable area for e1 structure in the phase diagram. The phase transition between e2 structure without density modulation and e1 structure with density modulation should happen at low temperature. There is a change in modulation period accompanying the phase transition, as well as higher occupancy of Al in the T₁o site. The andesine with density modulation also indicates extremely slow cooling of its host rock.

Computing details

(I)

Crystal data

Ca0.49Na0.51Si2.56Al1.44O8	V = 1336.52 (7) Å^3
Mr = 270.1	Z = 8
Triclinic, X1(αβγ)0†	F(000) = 1071
q = 0.091630a* + 0.025810b* + -0.284580c*	Dx = 2.685 Mg m^−3
a = 8.1661 (3) Å	Mo Kα radiation, λ = 0.71073 Å
b = 12.8545 (2) Å	µ = 1.24 mm^−1
c = 14.2350 (4) Å	T = 100 K
α = 93.5777 (8)°	Block, colorless
β = 116.3090 (7)°	0.08 × 0.06 × 0.05 mm
γ = 89.593 (3)°

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

Data collection

Bruker CCD diffractometer	Rint = 0.081
Radiation source: X-ray tube	θmax = 29.6°, θmin = 2.1°
Graphite monochromator	h = −11→11
146201 measured reflections	k = −17→17
9366 independent reflections	l = −20→20
7205 reflections with I > 3σ(I)

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.029	250 constraints
wR(F^2) = 0.111	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0016I^2)
S = 1.84	(Δ/σ)max = 0.049
9366 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
642 parameters	Extinction coefficient: 3500 (700)

Special details

Refinement. Ristrictions

restric T1o* -1 restric T1m* -1 restric T2o* -1 restric T2m* -1 restric M1* 11 restric M* -4

Equations

equation : o[M1Na]=1-o[M2Ca]-o[M1Ca] equation : o[T1oAl]=1-o[T1oSi] equation : o[T1mAl]=1-o[T1mSi] equation : o[T2oAl]=1-o[T2oSi] equation : o[T2mAl]=1-o[T2mSi]

Fixed Commands

fixed ind o[T*] fixed ind osin1[T*] fixed ind ocos1[T*] fixed ind osin2[T*] fixed ind ocos2[T*]

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
M1na	0.26775 (13)	−0.01365 (17)	0.07936 (18)	0.0202 (4)	0.510 (4)
M1ca	0.26775 (13)	−0.01365 (17)	0.07936 (18)	0.0202 (4)	0.154 (6)
M2ca	0.26963 (19)	0.02545 (17)	0.05004 (14)	0.0233 (5)	0.336 (7)
T1osi	0.49368 (3)	0.335066 (19)	−0.10656 (2)	0.00664 (9)	0.3575
T1msi	0.50306 (3)	0.318113 (18)	0.116245 (18)	0.00665 (9)	0.7438
T2osi	0.68597 (3)	0.109332 (18)	0.15800 (2)	0.00649 (10)	0.7467
T2msi	0.18102 (3)	0.379800 (18)	0.178557 (18)	0.00642 (10)	0.712
T1oal	0.49368 (3)	0.335066 (19)	−0.10656 (2)	0.00664 (9)	0.6425
T1mal	0.50306 (3)	0.318113 (18)	0.116245 (18)	0.00665 (9)	0.2562
T2oal	0.68597 (3)	0.109332 (18)	0.15800 (2)	0.00649 (10)	0.2533
T2mal	0.18102 (3)	0.379800 (18)	0.178557 (18)	0.00642 (10)	0.288
Oa1	0.49699 (10)	0.37113 (5)	0.01169 (5)	0.0142 (2)
Oa2	0.58167 (9)	−0.00654 (5)	0.13895 (5)	0.0095 (2)
Obo	0.81207 (9)	0.10585 (5)	0.09456 (6)	0.0130 (2)
Obm	0.31727 (10)	0.35300 (6)	0.12377 (6)	0.0176 (3)
Oco	0.48737 (10)	0.20658 (5)	−0.13874 (5)	0.0129 (2)
Ocm	0.51582 (9)	0.18991 (5)	0.10842 (5)	0.0136 (2)
Odo	0.29948 (9)	0.39226 (5)	0.30739 (5)	0.0120 (2)
Odm	0.68923 (10)	0.36738 (5)	0.21617 (5)	0.0141 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
M1na	0.0067 (3)	0.0328 (6)	0.0158 (6)	−0.0014 (3)	0.0025 (3)	−0.0160 (4)
M1ca	0.0067 (3)	0.0328 (6)	0.0158 (6)	−0.0014 (3)	0.0025 (3)	−0.0160 (4)
M2ca	0.0125 (5)	0.0331 (12)	0.0168 (7)	0.0053 (5)	0.0014 (4)	−0.0106 (7)
T1osi	0.00689 (13)	0.00851 (13)	0.00426 (13)	−0.00095 (9)	0.00212 (10)	0.00110 (9)
T1msi	0.00713 (13)	0.00836 (12)	0.00405 (13)	0.00284 (8)	0.00214 (9)	0.00042 (8)
T2osi	0.00643 (13)	0.00551 (12)	0.00658 (13)	0.00046 (9)	0.00208 (10)	0.00001 (9)
T2msi	0.00649 (13)	0.00629 (12)	0.00591 (14)	0.00097 (8)	0.00214 (10)	0.00120 (9)
T1oal	0.00689 (13)	0.00851 (13)	0.00426 (13)	−0.00095 (9)	0.00212 (10)	0.00110 (9)
T1mal	0.00713 (13)	0.00836 (12)	0.00405 (13)	0.00284 (8)	0.00214 (9)	0.00042 (8)
T2oal	0.00643 (13)	0.00551 (12)	0.00658 (13)	0.00046 (9)	0.00208 (10)	0.00001 (9)
T2mal	0.00649 (13)	0.00629 (12)	0.00591 (14)	0.00097 (8)	0.00214 (10)	0.00120 (9)
Oa1	0.0205 (3)	0.0166 (3)	0.0078 (3)	0.0023 (2)	0.0081 (3)	0.0030 (2)
Oa2	0.0104 (3)	0.0089 (3)	0.0086 (3)	0.0007 (2)	0.0035 (2)	0.0019 (2)
Obo	0.0127 (3)	0.0123 (3)	0.0160 (3)	−0.0010 (2)	0.0082 (3)	−0.0001 (2)
Obm	0.0143 (3)	0.0178 (3)	0.0243 (4)	0.0010 (3)	0.0121 (3)	−0.0021 (3)
Oco	0.0124 (3)	0.0149 (3)	0.0109 (3)	−0.0011 (2)	0.0046 (2)	0.0013 (2)
Ocm	0.0125 (3)	0.0144 (3)	0.0103 (3)	0.0044 (2)	0.0022 (2)	−0.0022 (2)
Odo	0.0127 (3)	0.0119 (3)	0.0073 (3)	−0.0001 (2)	0.0005 (2)	0.0017 (2)
Odm	0.0124 (3)	0.0128 (3)	0.0102 (3)	0.0013 (2)	−0.0009 (3)	−0.0012 (2)

Bond lengths (Å)

	Average	Minimum	Maximum
M1na—M1na^i	3.963 (4)	3.923 (4)	4.041 (4)
M1na—M1ca	0	0	0
M1na—M1ca^i	3.963 (4)	3.923 (4)	4.041 (4)
M1na—M2ca	0.682 (9)	0.204 (10)	1.069 (10)
M1na—M2ca^i	3.940 (4)	3.876 (5)	4.002 (5)
M1na—T1osi^ii	3.166 (5)	3.089 (6)	3.291 (6)
M1na—T1osi^iii	3.255 (6)	3.147 (7)	3.324 (7)
M1na—T1msi^ii	3.294 (6)	3.115 (7)	3.628 (7)
M1na—T2osi	3.463 (4)	3.192 (5)	3.670 (5)
M1na—T2msi^iv	3.363 (4)	3.151 (5)	3.660 (5)
M1na—T1oal^ii	3.166 (5)	3.089 (6)	3.291 (6)
M1na—T1oal^iii	3.255 (6)	3.147 (7)	3.324 (7)
M1na—T1mal^ii	3.294 (6)	3.115 (7)	3.628 (7)
M1na—T1mal^iii	3.783 (6)	3.417 (7)	4.074 (7)
M1na—T2oal	3.463 (4)	3.192 (5)	3.670 (5)
M1na—T2mal^iv	3.363 (4)	3.151 (5)	3.660 (5)
M1na—Oa1^ii	2.454 (5)	2.291 (6)	2.709 (6)
M1na—Oa2	2.345 (3)	2.302 (4)	2.405 (4)
M1na—Odo^v	2.419 (7)	2.403 (8)	2.465 (8)
M1ca—M1ca^i	3.963 (4)	3.923 (4)	4.041 (4)
M1ca—M2ca	0.682 (9)	0.204 (10)	1.069 (10)
M1ca—M2ca^i	3.940 (4)	3.876 (5)	4.002 (5)
M1ca—T1osi^ii	3.166 (5)	3.089 (6)	3.291 (6)
M1ca—T1osi^iii	3.255 (6)	3.147 (7)	3.324 (7)
M1ca—T1msi^ii	3.294 (6)	3.115 (7)	3.628 (7)
M1ca—T2osi	3.463 (4)	3.192 (5)	3.670 (5)
M1ca—T2msi^iv	3.363 (4)	3.151 (5)	3.660 (5)
M1ca—T1oal^ii	3.166 (5)	3.089 (6)	3.291 (6)
M1ca—T1oal^iii	3.255 (6)	3.147 (7)	3.324 (7)
M1ca—T1mal^ii	3.294 (6)	3.115 (7)	3.628 (7)
M1ca—T1mal^iii	3.783 (6)	3.417 (7)	4.074 (7)
M1ca—T2oal	3.463 (4)	3.192 (5)	3.670 (5)
M1ca—T2mal^iv	3.363 (4)	3.151 (5)	3.660 (5)
M1ca—T2mal^v	3.615 (7)	3.562 (8)	3.705 (8)
M1ca—Oa1^ii	2.454 (5)	2.291 (6)	2.709 (6)
M1ca—Oa2	2.345 (3)	2.302 (4)	2.405 (4)
M1ca—Odo^v	2.419 (7)	2.403 (8)	2.465 (8)
M2ca—M2ca^i	4.028 (5)	3.945 (6)	4.197 (6)
M2ca—T1osi^ii	3.316 (4)	3.268 (5)	3.365 (5)
M2ca—T1osi^iii	3.129 (4)	3.047 (6)	3.198 (6)
M2ca—T1msi^iii	3.235 (4)	3.160 (5)	3.320 (5)
M2ca—T2osi	3.212 (3)	3.142 (5)	3.344 (5)
M2ca—T1oal^ii	3.316 (4)	3.268 (5)	3.365 (5)
M2ca—T1oal^iii	3.129 (4)	3.047 (6)	3.198 (6)
M2ca—T1mal^iii	3.235 (4)	3.160 (5)	3.320 (5)
M2ca—T2oal	3.212 (3)	3.142 (5)	3.344 (5)
M2ca—T2oal^vi	3.498 (5)	3.440 (6)	3.560 (6)
M2ca—T2mal^iv	3.613 (4)	3.436 (5)	3.766 (5)
M2ca—Oa1^iii	2.387 (4)	2.314 (5)	2.457 (5)
M2ca—Oa2	2.342 (3)	2.278 (5)	2.446 (5)
M2ca—Obo^vi	2.431 (4)	2.390 (6)	2.486 (6)
T1osi—T1oal	0	0	0
T1osi—Oa1	1.7070 (17)	1.6437 (17)	1.7514 (17)
T1osi—Obo^vii	1.6981 (17)	1.6410 (17)	1.7381 (17)
T1osi—Oco	1.6812 (15)	1.6156 (15)	1.7270 (15)
T1osi—Odo^viii	1.7122 (13)	1.6483 (14)	1.7593 (14)
T1msi—T1mal	0	0	0
T1msi—Oa1	1.6586 (17)	1.6149 (17)	1.7241 (17)
T1msi—Obm	1.6307 (19)	1.601 (2)	1.690 (2)
T1msi—Ocm	1.6525 (15)	1.6107 (15)	1.7170 (15)
T1msi—Odm	1.6503 (13)	1.6131 (13)	1.7048 (13)
T2osi—T2oal	0	0	0
T2osi—Oa2	1.6681 (14)	1.6416 (14)	1.7126 (14)
T2osi—Obo	1.6459 (19)	1.616 (2)	1.693 (2)
T2osi—Ocm	1.6476 (15)	1.6166 (15)	1.6883 (15)
T2osi—Odm^ix	1.6296 (13)	1.6024 (13)	1.6693 (13)
T2msi—T2mal	0	0	0
T2msi—Oa2^x	1.6710 (13)	1.6379 (14)	1.7246 (14)
T2msi—Obm	1.644 (2)	1.605 (2)	1.705 (2)
T2msi—Oco^iii	1.6430 (15)	1.5998 (16)	1.7085 (16)
T2msi—Odo	1.6486 (13)	1.6147 (13)	1.7096 (13)
T1oal—T2mal^iii	3.0203 (7)	2.9880 (8)	3.0472 (8)
T1oal—Oa1	1.7070 (17)	1.6437 (17)	1.7514 (17)
T1oal—Obo^vii	1.6981 (17)	1.6410 (17)	1.7381 (17)
T1oal—Oco	1.6812 (15)	1.6156 (15)	1.7270 (15)
T1oal—Odo^viii	1.7122 (13)	1.6483 (14)	1.7593 (14)
T1mal—T2oal	3.0240 (7)	2.9907 (7)	3.0465 (7)
T1mal—Oa1	1.6586 (17)	1.6149 (17)	1.7241 (17)
T1mal—Obm	1.6307 (19)	1.601 (2)	1.690 (2)
T1mal—Ocm	1.6525 (15)	1.6107 (15)	1.7170 (15)
T1mal—Odm	1.6503 (13)	1.6131 (13)	1.7048 (13)
T2oal—T2mal^iv	2.9863 (7)	2.9719 (7)	3.0005 (7)
T2oal—Oa2	1.6681 (14)	1.6416 (14)	1.7126 (14)
T2oal—Obo	1.6459 (19)	1.616 (2)	1.693 (2)
T2oal—Ocm	1.6476 (15)	1.6166 (15)	1.6883 (15)
T2oal—Odm^ix	1.6296 (13)	1.6024 (13)	1.6693 (13)
T2mal—Oa2^x	1.6710 (13)	1.6379 (14)	1.7246 (14)
T2mal—Obm	1.644 (2)	1.605 (2)	1.705 (2)
T2mal—Oco^iii	1.6430 (15)	1.5998 (16)	1.7085 (16)
T2mal—Odo	1.6486 (13)	1.6147 (13)	1.7096 (13)

Symmetry codes: (i) −x₁, −x₂, −x₃, −x₄; (ii) x₁−1/2, x₂−1/2, x₃, x₄+1/2; (iii) −x₁+1/2, −x₂+1/2, −x₃, −x₄+1/2; (iv) x₁+1/2, x₂−1/2, x₃, x₄+1/2; (v) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄; (vi) −x₁+1, −x₂, −x₃, −x₄; (vii) −x₁+3/2, −x₂+1/2, −x₃, −x₄+1/2; (viii) x₁, x₂, x₃−1/2, x₄+1/2; (ix) −x₁+3/2, −x₂+1/2, −x₃+1/2, −x₄; (x) x₁−1/2, x₂+1/2, x₃, x₄+1/2.