A-site order in rhombohedral perovskite-like oxides La_2−xSr_xCoTiO₆ (0.6 ≤ x ≤ 1.0)

The evolution of the room-temperature structure of the oxide series La_2−xSr_xCoTiO₆ (0.6 ≤ x ≤ 1.0) was studied as a function of the Sr content using different diffraction techniques and applying the symmetry-adapted modes formalism (AMPLIMODES). The title compounds adopt perovskite-like structures of rhombohedral symmetry with an octahedral tilting scheme (a⁻a⁻a⁻) with either space group or R32. The latter symmetry is observed in those cases (for x ≃ 0.6) where additional rock-salt-like ordering of La and Sr is produced in the perovskite A sites. Two composition-driven phase transitions are observed in the whole series La_2−xSr_xCoTiO₆ (0.0 ≤ x ≤ 1.0). Using the concept of internal pressure, the effect of doping with Sr on the structure can be properly discussed. Both phase transitions seem to be of first order since they can be associated with discontinuities either in the entropy or in the structure. The first transition (P2₁/n → Pnma) occurs as the B cations become totally disordered. Along the whole compositional range the modes responsible for the out-of-phase tilting of BO₆ octahedra remain active, but those associated with the in-phase octahedral tilting vanish for x ≥ 0.6, this being associated with the second transition (Pnma → ). Finally, for x = 1.0 the three pseudo-cubic cell parameters become very similar, pointing to a transition to a cubic structure which could be obtained by applying pressure or raising the temperature.

S1. Comment

Symmetry-adapted Rietveld refinement is a powerfull tool to understand the physical mechanism which stabilize a certain structured derived from a high simmetry parent structure within displazative-type phase transitions.

S2. Experimental

Samples of compositions La2-xSrxCoTiO6 (0.6 =< x =< 1.0) were prepared by a modified Peccini method by solving stoichiometric amounts of high purity Co(CH3COO)2.4H2O (Aldrich, 99.99%), La2O3 (Aldrich, 99.9%)and SrCO3 (Aldrich 99.9%) in ca 20 ml of concentrated hot nitric acid (Panreac 66%) and ca 50 ml of distillate water was added. Under heating and vigorous stirring, citric acid was added in a molar ratio citric acid to metal ions of 3:1. Then, titanium was added as anatase (Aldrich, purity 99.9%) to obtain a homogeneous suspension, since TiO2 is not soluble. When the solution was concentrated to half of its initial volume, 3 ml of diethyleneglycol was added to promote polymerization. When a solid resin is formed it is allowed to cool down to room temperature and then milled in an agate mortar; the obtained powder was burn at 1073 K to remove organic matter. After milling and homogenization the resulted powder was heated at 1773 K for 48 h and cooled down (at a rate of 2 K/min) to room temperature to obtain well crystallized materials.

S3. Refinement

The powder diffraction pattern was indexed in a rhomboedral S·G. R-3c with a unit cell ((2^{1/2)ac, 2*(3}(1/2))ac where ac is the lattice parameter of the parent cubic perovskite.

Computing details

For all compounds, program(s) used to refine structure: FULLPROF.

Figures

Fig. 1. Schematic representation of the unique Irrep mode in the R-3c configuration: BO6 octahedra in blue, La and Sr have been omitted for clarity and oxygen atoms in red in the octahedra corners.

Fig. 2. HREM image of La1.4Sr0.6CoTiO6 along [110]p. Optical FFT of the image (a). A simulated image is shown in the inset (?t = 5 nm and ?f = −30 nm).

Fig. 3. HREM image of La1.4Sr0.6CoTiO6 along [1–21]p. Optical FFT of the image (a). A simulated image is seen at the inset (?t = 5 nm and ?f = −30 nm)..

Fig. 4. Convergent Beam Electron Diffraction pattern along [001] for La1.4Sr0.6CoTiO6, showing a p3m1 symmetry

Fig. 5. HREM image of La1.0Sr1.0CoTiO6 along [110]p ([010]R). (a) optical FFT of the image. A simulated image is seen at the inset (?t = 5 nm and ?f = −30 nm).

Fig. 6. HREM image of La1.0Sr1.0CoTiO6 along [1–21]p ([1–10]R). Optical FFT of the image is presented in (a). A simulated image is seen at the inset (?t = 5 nm and ?f = −30 nm).

Fig. 7. Evolution of the normalized pseudo-cubic cell parameters and reduced volume along the La2-xSrxCoTiO6 (0 ? x ? 1.0) series. Lines are guides for the eye.

Fig. 8 Evolution of the modes amplitudes with the Sr-content for La2-xSrxCoTiO6 (0.0 ? x ? 1.0); the degree of B-ion order for x < 0.3 is also plotted. Lines are guides for the eyes.

(LSCT60_SXRD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.7O3Sr0.3Ti0.5	? _exptl_crystal_density_diffrn 6.360(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 598.6
Mr = 224.94	Synchrotron radiation, λ = 0.621000 Å
Trigonal, R3c	µ = 7.37 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.50899 (6) Å	Particle morphology: plate-like SEM
c = 13.36485 (15) Å	black
V = 351.27 (1) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

Home-made heavy-duty Theta-2theta goniometer diffractometer	Scan method: step
Radiation source: Synchrotron	Absorption correction: for a cylinder mounted on the φ axis Cromer and Liberman algorithm
Si 111 monochromator
Specimen mounting: Borosilicate 0.3 mm capillary	2θmin = 6.044°, 2θmax = 46.984°, 2θstep = 0.010°
Data collection mode: transmission

Refinement

Refinement on Inet	4095 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.070	24 parameters
Rwp = 0.093	0 restraints
Rexp = 0.058	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.042	(Δ/σ)max = 0.01
χ^2 = 6.299	Background function: Set of experimental background points

Special details

Experimental. Synchrotron source

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.00562*	0.50000
Ti1	0.00000	0.00000	0.00000	0.00562*	0.50000
La1	0.00000	0.00000	0.25000	0.0080 (2)*	0.69951
Sr1	0.00000	0.00000	0.25000	0.0080 (2)*	0.29947
O1	0.12242 (12)	0.33333	0.08333	0.01017 (18)*

Geometric parameters (Å, º)

La1—O1	2.7478 (1)	La1—O1^ix	2.9982 (3)
La1—O1^i	2.7478 (3)	La1—O1^x	2.9982 (3)
La1—O1^ii	2.7478 (4)	La1—O1^xi	2.5107 (3)
La1—O1^iii	2.7478 (4)	Co1—O1	1.9567 (1)
La1—O1^iv	2.7478 (1)	Co1—O1^i	1.9567 (4)
La1—O1^v	2.7478 (3)	Co1—O1^ii	1.9567 (5)
La1—O1^vi	2.5107 (7)	Co1—O1^xii	1.9567 (1)
La1—O1^vii	2.9982 (7)	Co1—O1^xiii	1.9567 (4)
La1—O1^viii	2.5108 (3)	Co1—O1^xiv	1.9567 (5)
O1—Co1—O1^i	90.807 (19)	O1^i—Co1—O1^xiv	89.19 (2)
O1—Co1—O1^ii	90.81 (3)	O1^ii—Co1—O1^xii	89.19 (2)
O1—Co1—O1^xii	180.000 (8)	O1^ii—Co1—O1^xiii	89.19 (2)
O1—Co1—O1^xiii	89.19 (2)	O1^ii—Co1—O1^xiv	180.00 (5)
O1—Co1—O1^xiv	89.19 (2)	O1^xii—Co1—O1^xiii	90.807 (19)
O1^i—Co1—O1^ii	90.81 (4)	O1^xii—Co1—O1^xiv	90.81 (3)
O1^i—Co1—O1^xii	89.19 (2)	O1^xiii—Co1—O1^xiv	90.81 (4)
O1^i—Co1—O1^xiii	180.00 (4)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT70_SXRD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.65O3Sr0.35Ti0.5	? _exptl_crystal_density_diffrn 6.391(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 598.0
Mr = 222.37	Cu Kα1 radiation, λ = 1.540560 Å
Trigonal, R3c	T = 295 K
Hall symbol: -R 3 2"c	Particle morphology: plate-like SEM
a = 5.49515 (11) Å	black
c = 13.3529 (3) Å	flat_sheet, 20 × 20 mm
V = 349.19 (1) Å^3	Specimen preparation: Cooled at 2 K min^−1
Z = 6

Data collection

Bruker D8 Advance diffractometer	Data collection mode: reflexion
Radiation source: sealed X-ray tube	Scan method: step
Ge (111) monochromator	2θmin = 19.880°, 2θmax = 99.882°, 2θstep = 0.020°
Specimen mounting: Aluminium Sample holder

Refinement

Refinement on Inet	3583 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.028	25 parameters
Rwp = 0.037	0 restraints
Rexp = 0.024	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.032	(Δ/σ)max = 0.01
χ^2 = 5.660	Background function: Set of experimental background points

Special details

Experimental. Conventional X-Ray source

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.0099 (12)*	0.50000
Ti1	0.00000	0.00000	0.00000	0.0099 (12)*	0.50000
La1	0.00000	0.00000	0.25000	0.0095 (3)*	0.69333
Sr1	0.00000	0.00000	0.25000	0.0095 (3)*	0.30667
O1	0.12612 (14)	0.33333	0.08333	0.0105 (2)*

Geometric parameters (Å, º)

La1—O1	2.7421 (1)	La1—O1^ix	2.9704 (4)
La1—O1^i	2.7421 (4)	La1—O1^x	2.9704 (4)
La1—O1^ii	2.7421 (4)	La1—O1^xi	2.5248 (4)
La1—O1^iii	2.7421 (4)	Co1—O1	1.9504 (1)
La1—O1^iv	2.7421 (1)	Co1—O1^i	1.9504 (5)
La1—O1^v	2.7421 (4)	Co1—O1^ii	1.9504 (6)
La1—O1^vi	2.5248 (8)	Co1—O1^xii	1.9504 (1)
La1—O1^vii	2.9704 (8)	Co1—O1^xiii	1.9504 (5)
La1—O1^viii	2.5248 (4)	Co1—O1^xiv	1.9504 (6)
O1—Co1—O1^i	90.68 (2)	O1^i—Co1—O1^xiv	89.32 (2)
O1—Co1—O1^ii	90.68 (3)	O1^ii—Co1—O1^xii	89.32 (3)
O1—Co1—O1^xii	180.000 (9)	O1^ii—Co1—O1^xiii	89.32 (2)
O1—Co1—O1^xiii	89.32 (3)	O1^ii—Co1—O1^xiv	180.00 (5)
O1—Co1—O1^xiv	89.32 (3)	O1^xii—Co1—O1^xiii	90.68 (2)
O1^i—Co1—O1^ii	90.68 (5)	O1^xii—Co1—O1^xiv	90.68 (3)
O1^i—Co1—O1^xii	89.32 (3)	O1^xiii—Co1—O1^xiv	90.68 (5)
O1^i—Co1—O1^xiii	180.00 (5)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT80_SXRD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.6O3Sr0.4Ti0.5	? _exptl_crystal_density_diffrn 6.316(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 588.1
Mr = 219.81	Synchrotron radiation, λ = 1.594000 Å
Trigonal, R3c	µ = 8.56 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.48545 (5) Å	Particle morphology: plate-like SEM
c = 13.34921 (14) Å	black
V = 347.87 (1) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

Home-made heavy-duty Theta-2theta goniometer diffractometer	Scan method: step
Radiation source: Synchrotron	Absorption correction: for a cylinder mounted on the φ axis Cromer and Liberman algorithm
Si 111 monochromator
Specimen mounting: Borosilicate 0.3 mm capillary	2θmin = 0.233°, 2θmax = 160.183°, 2θstep = 0.050°
Data collection mode: transmission

Refinement

Refinement on Inet	3894 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.057	24 parameters
Rwp = 0.075	0 restraints
Rexp = 0.053	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.035	(Δ/σ)max = 0.01
χ^2 = 3.864	Background function: Set of experimental background points

Special details

Experimental. Synchrotron source

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.0057 (9)*	0.50000
Ti1	0.00000	0.00000	0.00000	0.0057 (9)*	0.50000
La1	0.00000	0.00000	0.25000	0.0092 (2)*	0.61034
Sr1	0.00000	0.00000	0.25000	0.0092 (2)*	0.38804
O1	0.13016 (10)	0.33333	0.08333	0.01079 (16)*

Geometric parameters (Å, º)

La1—O1	2.7382 (1)	La1—O1^ix	2.9430 (3)
La1—O1^i	2.7382 (3)	La1—O1^x	2.9430 (3)
La1—O1^ii	2.7382 (3)	La1—O1^xi	2.5425 (3)
La1—O1^iii	2.7382 (3)	Co1—O1	1.9455 (1)
La1—O1^iv	2.7382 (1)	Co1—O1^i	1.9455 (4)
La1—O1^v	2.7382 (3)	Co1—O1^ii	1.9455 (4)
La1—O1^vi	2.5425 (5)	Co1—O1^xii	1.9455 (1)
La1—O1^vii	2.9430 (5)	Co1—O1^xiii	1.9455 (4)
La1—O1^viii	2.5425 (3)	Co1—O1^xiv	1.9455 (4)
O1—Co1—O1^i	90.551 (17)	O1^i—Co1—O1^xiv	89.449 (16)
O1—Co1—O1^ii	90.55 (2)	O1^ii—Co1—O1^xii	89.449 (19)
O1—Co1—O1^xii	180.000 (6)	O1^ii—Co1—O1^xiii	89.449 (16)
O1—Co1—O1^xiii	89.45 (2)	O1^ii—Co1—O1^xiv	180.00 (4)
O1—Co1—O1^xiv	89.449 (19)	O1^xii—Co1—O1^xiii	90.551 (17)
O1^i—Co1—O1^ii	90.55 (4)	O1^xii—Co1—O1^xiv	90.55 (2)
O1^i—Co1—O1^xii	89.45 (2)	O1^xiii—Co1—O1^xiv	90.55 (4)
O1^i—Co1—O1^xiii	180.00 (3)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT90_XRD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.55O3Sr0.45Ti0.5	? _exptl_crystal_density_diffrn 6.253(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 583.5
Mr = 217.24	Cu Kα1 radiation, λ = 1.540560 Å
Trigonal, R3c	T = 295 K
Hall symbol: -R 3 2"c	Particle morphology: plate-like SEM
a = 5.47672 (5) Å	black
c = 13.34634 (14) Å	flat_sheet, 20 × 20 mm
V = 346.68 (1) Å^3	Specimen preparation: Cooled at 2 K min^−1
Z = 6

Data collection

Bruker D8 Advance diffractometer	Data collection mode: reflexion
Radiation source: sealed X-ray tube	Scan method: step
Ge (111) monochromator	2θmin = 20.066°, 2θmax = 99.939°, 2θstep = 0.020°
Specimen mounting: Aluminium Sample holder

Refinement

Refinement on Inet	4047 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.029	22 parameters
Rwp = 0.039	0 restraints
Rexp = 0.025	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.062	(Δ/σ)max = 0.01
χ^2 = 5.831	Background function: Set of experimental background points

Special details

Experimental. Conventional X-Ray source

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.01527*	0.50000
Ti1	0.00000	0.00000	0.00000	0.01527*	0.50000
La1	0.00000	0.00000	0.25000	0.00863*	0.566 (16)
Sr1	0.00000	0.00000	0.25000	0.00863*	0.434 (16)
O1	0.13421 (12)	0.33333	0.08333	0.00916*

Geometric parameters (Å, º)

La1—O1	2.7348 (1)	La1—O1^ix	2.9160 (3)
La1—O1^i	2.7348 (3)	La1—O1^x	2.9161 (3)
La1—O1^ii	2.7348 (4)	La1—O1^xi	2.5607 (3)
La1—O1^iii	2.7348 (4)	Co1—O1	1.9411 (1)
La1—O1^iv	2.7348 (1)	Co1—O1^i	1.9411 (4)
La1—O1^v	2.7348 (3)	Co1—O1^ii	1.9411 (5)
La1—O1^vi	2.5607 (7)	Co1—O1^xii	1.9411 (1)
La1—O1^vii	2.9161 (7)	Co1—O1^xiii	1.9411 (4)
La1—O1^viii	2.5607 (3)	Co1—O1^xiv	1.9411 (5)
O1—Co1—O1^i	90.44 (2)	O1^i—Co1—O1^xiv	89.56 (2)
O1—Co1—O1^ii	90.44 (3)	O1^ii—Co1—O1^xii	89.56 (2)
O1—Co1—O1^xii	180.000 (6)	O1^ii—Co1—O1^xiii	89.56 (2)
O1—Co1—O1^xiii	89.56 (2)	O1^ii—Co1—O1^xiv	180.00 (5)
O1—Co1—O1^xiv	89.56 (2)	O1^xii—Co1—O1^xiii	90.44 (2)
O1^i—Co1—O1^ii	90.44 (4)	O1^xii—Co1—O1^xiv	90.44 (3)
O1^i—Co1—O1^xii	89.56 (2)	O1^xiii—Co1—O1^xiv	90.44 (4)
O1^i—Co1—O1^xiii	180.00 (4)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT100_SXRD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.5O3Sr0.5Ti0.5	? _exptl_crystal_density_diffrn 6.219(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 580.0
Mr = 214.68	Synchrotron radiation, λ = 0.621000 Å
Trigonal, R3c	µ = 8.86 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.4713 (2) Å	Particle morphology: plate-like SEM
c = 13.3472 (8) Å	black
V = 346.02 (3) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

Home-made heavy-duty Theta-2theta goniometer diffractometer	Scan method: step
Radiation source: Synchrotron	Absorption correction: for a cylinder mounted on the φ axis Cromer and Liberman algorithm
Si 111 monochromator
Specimen mounting: Borosilicate 0.3 mm capillary	2θmin = 8.038°, 2θmax = 46.978°, 2θstep = 0.010°
Data collection mode: transmission

Refinement

Refinement on Inet	3895 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.056	26 parameters
Rwp = 0.076	0 restraints
Rexp = 0.049	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.067	(Δ/σ)max = 0.01
χ^2 = 5.833	Background function: Set of experimental background points

Special details

Experimental. Synchrotron source

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.0184 (9)*	0.50000
Ti1	0.00000	0.00000	0.00000	0.0184 (9)*	0.50000
La1	0.00000	0.00000	0.25000	0.0070 (3)*	0.53504
Sr1	0.00000	0.00000	0.25000	0.0070 (3)*	0.46496
O1	0.13685 (16)	0.33333	0.08333	0.0090 (2)*

Geometric parameters (Å, º)

La1—O1	2.7331 (1)	La1—O1^ix	2.8988 (5)
La1—O1^i	2.7331 (4)	La1—O1^x	2.8988 (4)
La1—O1^ii	2.7331 (5)	La1—O1^xi	2.5725 (4)
La1—O1^iii	2.7331 (5)	Co1—O1	1.9386 (1)
La1—O1^iv	2.7331 (1)	Co1—O1^i	1.9386 (6)
La1—O1^v	2.7331 (4)	Co1—O1^ii	1.9386 (7)
La1—O1^vi	2.5725 (9)	Co1—O1^xii	1.9386 (1)
La1—O1^vii	2.8988 (9)	Co1—O1^xiii	1.9386 (6)
La1—O1^viii	2.5725 (4)	Co1—O1^xiv	1.9386 (7)
O1—Co1—O1^i	90.36 (3)	O1^i—Co1—O1^xiv	89.64 (3)
O1—Co1—O1^ii	90.36 (4)	O1^ii—Co1—O1^xii	89.64 (3)
O1—Co1—O1^xii	180.000 (10)	O1^ii—Co1—O1^xiii	89.64 (3)
O1—Co1—O1^xiii	89.64 (3)	O1^ii—Co1—O1^xiv	180.00 (6)
O1—Co1—O1^xiv	89.64 (3)	O1^xii—Co1—O1^xiii	90.36 (3)
O1^i—Co1—O1^ii	90.36 (6)	O1^xii—Co1—O1^xiv	90.36 (4)
O1^i—Co1—O1^xii	89.64 (3)	O1^xiii—Co1—O1^xiv	90.36 (6)
O1^i—Co1—O1^xiii	180.00 (5)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT60_NPD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.7O3Sr0.3Ti0.5	? _exptl_crystal_density_diffrn 6.360(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 100.9
Mr = 224.94	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
Trigonal, R3c	µ = 0.000 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.50899 (6) Å	Particle morphology: plate-like SEM
c = 13.36485 (15) Å	black
V = 351.27 (1) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

High-resolution two-axis diffractometer	Data collection mode: transmission
Radiation source: nuclear reactor, D2B beamline ILL	Scan method: step
Ge monochromator	2θmin = 0.313°, 2θmax = 160.224°, 2θstep = 0.050°
Specimen mounting: 'vanadium can'

Refinement

Refinement on Inet	4095 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.042	24 parameters
Rwp = 0.055	0 restraints
Rexp = 0.027	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.023	(Δ/σ)max = 0.01
χ^2 = 16.441	Background function: Set of experimental background points

Special details

Experimental. Neutron reactor

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.00562*	0.50000
Ti1	0.00000	0.00000	0.00000	0.00562*	0.50000
La1	0.00000	0.00000	0.25000	0.0080 (2)*	0.69951
Sr1	0.00000	0.00000	0.25000	0.0080 (2)*	0.29947
O1	0.12242 (12)	0.33333	0.08333	0.01017 (18)*

Geometric parameters (Å, º)

La1—O1	2.7478 (1)	La1—O1^ix	2.9982 (3)
La1—O1^i	2.7478 (3)	La1—O1^x	2.9982 (3)
La1—O1^ii	2.7478 (4)	La1—O1^xi	2.5107 (3)
La1—O1^iii	2.7478 (4)	Co1—O1	1.9567 (1)
La1—O1^iv	2.7478 (1)	Co1—O1^i	1.9567 (4)
La1—O1^v	2.7478 (3)	Co1—O1^ii	1.9567 (5)
La1—O1^vi	2.5107 (7)	Co1—O1^xii	1.9567 (1)
La1—O1^vii	2.9982 (7)	Co1—O1^xiii	1.9567 (4)
La1—O1^viii	2.5108 (3)	Co1—O1^xiv	1.9567 (5)
O1—Co1—O1^i	90.807 (19)	O1^i—Co1—O1^xiv	89.19 (2)
O1—Co1—O1^ii	90.81 (3)	O1^ii—Co1—O1^xii	89.19 (2)
O1—Co1—O1^xii	180.000 (8)	O1^ii—Co1—O1^xiii	89.19 (2)
O1—Co1—O1^xiii	89.19 (2)	O1^ii—Co1—O1^xiv	180.00 (5)
O1—Co1—O1^xiv	89.19 (2)	O1^xii—Co1—O1^xiii	90.807 (19)
O1^i—Co1—O1^ii	90.81 (4)	O1^xii—Co1—O1^xiv	90.81 (3)
O1^i—Co1—O1^xii	89.19 (2)	O1^xiii—Co1—O1^xiv	90.81 (4)
O1^i—Co1—O1^xiii	180.00 (4)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT70_NPD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.65O3Sr0.35Ti0.5	? _exptl_crystal_density_diffrn 6.391(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 100.9
Mr = 222.37	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
Trigonal, R3c	µ = 0.000 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.49515 (11) Å	Particle morphology: plate-like SEM
c = 13.3529 (3) Å	black
V = 349.19 (1) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

High-resolution two-axis diffractometer	Data collection mode: transmission
Radiation source: nuclear reactor, D2B beamline ILL	Scan method: step
Ge monochromator	2θmin = 0.332°, 2θmax = 160.243°, 2θstep = 0.050°
Specimen mounting: 'vanadium can'

Refinement

Refinement on Inet	4095 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.035	25 parameters
Rwp = 0.044	0 restraints
Rexp = 0.030	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.022	(Δ/σ)max = 0.01
χ^2 = 4.885	Background function: Set of experimental background points

Special details

Experimental. Neutron reactor

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.0099 (12)*	0.50000
Ti1	0.00000	0.00000	0.00000	0.0099 (12)*	0.50000
La1	0.00000	0.00000	0.25000	0.0095 (3)*	0.69333
Sr1	0.00000	0.00000	0.25000	0.0095 (3)*	0.30667
O1	0.12612 (14)	0.33333	0.08333	0.0105 (2)*

Geometric parameters (Å, º)

La1—O1	2.7421 (1)	La1—O1^ix	2.9704 (4)
La1—O1^i	2.7421 (4)	La1—O1^x	2.9704 (4)
La1—O1^ii	2.7421 (4)	La1—O1^xi	2.5248 (4)
La1—O1^iii	2.7421 (4)	Co1—O1	1.9504 (1)
La1—O1^iv	2.7421 (1)	Co1—O1^i	1.9504 (5)
La1—O1^v	2.7421 (4)	Co1—O1^ii	1.9504 (6)
La1—O1^vi	2.5248 (8)	Co1—O1^xii	1.9504 (1)
La1—O1^vii	2.9704 (8)	Co1—O1^xiii	1.9504 (5)
La1—O1^viii	2.5248 (4)	Co1—O1^xiv	1.9504 (6)
O1—Co1—O1^i	90.68 (2)	O1^i—Co1—O1^xiv	89.32 (2)
O1—Co1—O1^ii	90.68 (3)	O1^ii—Co1—O1^xii	89.32 (3)
O1—Co1—O1^xii	180.000 (9)	O1^ii—Co1—O1^xiii	89.32 (2)
O1—Co1—O1^xiii	89.32 (3)	O1^ii—Co1—O1^xiv	180.00 (5)
O1—Co1—O1^xiv	89.32 (3)	O1^xii—Co1—O1^xiii	90.68 (2)
O1^i—Co1—O1^ii	90.68 (5)	O1^xii—Co1—O1^xiv	90.68 (3)
O1^i—Co1—O1^xii	89.32 (3)	O1^xiii—Co1—O1^xiv	90.68 (5)
O1^i—Co1—O1^xiii	180.00 (5)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT80_NPD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.6O3Sr0.4Ti0.5	? _exptl_crystal_density_diffrn 6.316(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 100.9
Mr = 219.81	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
Trigonal, R3c	µ = 0.000 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.48545 (5) Å	Particle morphology: plate-like SEM
c = 13.34921 (14) Å	black
V = 347.87 (1) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

High-resolution two-axis diffractometer	Data collection mode: transmission
Radiation source: nuclear reactor, D2B beamline ILL	Scan method: step
Ge monochromator	2θmin = 0.233°, 2θmax = 160.183°, 2θstep = 0.050°
Specimen mounting: 'vanadium can'

Refinement

Refinement on Inet	4095 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.039	24 parameters
Rwp = 0.051	0 restraints
Rexp = 0.028	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.020	(Δ/σ)max = 0.01
χ^2 = 11.616	Background function: Set of experimental background points

Special details

Experimental. Neutron reactor

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.0057 (9)*	0.50000
Ti1	0.00000	0.00000	0.00000	0.0057 (9)*	0.50000
La1	0.00000	0.00000	0.25000	0.0092 (2)*	0.61034
Sr1	0.00000	0.00000	0.25000	0.0092 (2)*	0.38804
O1	0.13016 (10)	0.33333	0.08333	0.01079 (16)*

Geometric parameters (Å, º)

La1—O1	2.7382 (1)	La1—O1^ix	2.9430 (3)
La1—O1^i	2.7382 (3)	La1—O1^x	2.9430 (3)
La1—O1^ii	2.7382 (3)	La1—O1^xi	2.5425 (3)
La1—O1^iii	2.7382 (3)	Co1—O1	1.9455 (1)
La1—O1^iv	2.7382 (1)	Co1—O1^i	1.9455 (4)
La1—O1^v	2.7382 (3)	Co1—O1^ii	1.9455 (4)
La1—O1^vi	2.5425 (5)	Co1—O1^xii	1.9455 (1)
La1—O1^vii	2.9430 (5)	Co1—O1^xiii	1.9455 (4)
La1—O1^viii	2.5425 (3)	Co1—O1^xiv	1.9455 (4)
O1—Co1—O1^i	90.551 (17)	O1^i—Co1—O1^xiv	89.449 (16)
O1—Co1—O1^ii	90.55 (2)	O1^ii—Co1—O1^xii	89.449 (19)
O1—Co1—O1^xii	180.000 (6)	O1^ii—Co1—O1^xiii	89.449 (16)
O1—Co1—O1^xiii	89.45 (2)	O1^ii—Co1—O1^xiv	180.00 (4)
O1—Co1—O1^xiv	89.449 (19)	O1^xii—Co1—O1^xiii	90.551 (17)
O1^i—Co1—O1^ii	90.55 (4)	O1^xii—Co1—O1^xiv	90.55 (2)
O1^i—Co1—O1^xii	89.45 (2)	O1^xiii—Co1—O1^xiv	90.55 (4)
O1^i—Co1—O1^xiii	180.00 (3)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT90_NPD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.55O3Sr0.45Ti0.5	? _exptl_crystal_density_diffrn 6.253(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 100.9
Mr = 217.24	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
Trigonal, R3c	µ = 0.000 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.47672 (5) Å	Particle morphology: plate-like SEM
c = 13.34634 (14) Å	black
V = 346.68 (1) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

High-resolution two-axis diffractometer	Data collection mode: transmission
Radiation source: nuclear reactor, D2B beamline ILL	Scan method: step
Ge monochromator	2θmin = 0.222°, 2θmax = 160.172°, 2θstep = 0.050°
Specimen mounting: 'vanadium can'

Refinement

Refinement on Inet	4095 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.040	22 parameters
Rwp = 0.052	0 restraints
Rexp = 0.028	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.020	(Δ/σ)max = 0.01
χ^2 = 12.561	Background function: Set of experimental background points

Special details

Experimental. Neutron reactor

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.01527*	0.50000
Ti1	0.00000	0.00000	0.00000	0.01527*	0.50000
La1	0.00000	0.00000	0.25000	0.00863*	0.566 (16)
Sr1	0.00000	0.00000	0.25000	0.00863*	0.434 (16)
O1	0.13421 (12)	0.33333	0.08333	0.00916*

Geometric parameters (Å, º)

La1—O1	2.7348 (1)	La1—O1^ix	2.9160 (3)
La1—O1^i	2.7348 (3)	La1—O1^x	2.9161 (3)
La1—O1^ii	2.7348 (4)	La1—O1^xi	2.5607 (3)
La1—O1^iii	2.7348 (4)	Co1—O1	1.9411 (1)
La1—O1^iv	2.7348 (1)	Co1—O1^i	1.9411 (4)
La1—O1^v	2.7348 (3)	Co1—O1^ii	1.9411 (5)
La1—O1^vi	2.5607 (7)	Co1—O1^xii	1.9411 (1)
La1—O1^vii	2.9161 (7)	Co1—O1^xiii	1.9411 (4)
La1—O1^viii	2.5607 (3)	Co1—O1^xiv	1.9411 (5)
O1—Co1—O1^i	90.44 (2)	O1^i—Co1—O1^xiv	89.56 (2)
O1—Co1—O1^ii	90.44 (3)	O1^ii—Co1—O1^xii	89.56 (2)
O1—Co1—O1^xii	180.000 (6)	O1^ii—Co1—O1^xiii	89.56 (2)
O1—Co1—O1^xiii	89.56 (2)	O1^ii—Co1—O1^xiv	180.00 (5)
O1—Co1—O1^xiv	89.56 (2)	O1^xii—Co1—O1^xiii	90.44 (2)
O1^i—Co1—O1^ii	90.44 (4)	O1^xii—Co1—O1^xiv	90.44 (3)
O1^i—Co1—O1^xii	89.56 (2)	O1^xiii—Co1—O1^xiv	90.44 (4)
O1^i—Co1—O1^xiii	180.00 (4)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.

(LSCT100_NPD) Lanthanum Strontium Cobalt(II) Titanium(IV) oxide

Crystal data

Co0.5La0.5O3Sr0.5Ti0.5	? _exptl_crystal_density_diffrn 6.219(1) _exptl_crystal_density_meas ? _exptl_crystal_density_method 'not measured' _exptl_crystal_F_000 100.9
Mr = 214.68	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
Trigonal, R3c	µ = 0.000 mm^−1
Hall symbol: -R 3 2"c	T = 295 K
a = 5.4713 (2) Å	Particle morphology: plate-like SEM
c = 13.3472 (8) Å	black
V = 346.02 (3) Å^3	cylinder, 15 × 20 mm
Z = 6

Data collection

High-resolution two-axis diffractometer	Data collection mode: transmission
Radiation source: nuclear reactor, D2B beamline ILL	Scan method: step
Ge monochromator	2θmin = 0.291°, 2θmax = 160.202°, 2θstep = 0.050°
Specimen mounting: 'vanadium can'

Refinement

Refinement on Inet	4095 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.039	26 parameters
Rwp = 0.049	0 restraints
Rexp = 0.033	Weighting scheme based on measured s.u.'s 1/[Yi + σ(Yi)]
RBragg = 0.015	(Δ/σ)max = 0.01
χ^2 = 4.619	Background function: Set of experimental background points

Special details

Experimental. Neutron reactor

Refinement. Symmetry-adapted Rietveld refinement by simulteneuos fitting of SXRD and NPD data.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co1	0.00000	0.00000	0.00000	0.0184 (9)*	0.50000
Ti1	0.00000	0.00000	0.00000	0.0184 (9)*	0.50000
La1	0.00000	0.00000	0.25000	0.0070 (3)*	0.53504
Sr1	0.00000	0.00000	0.25000	0.0070 (3)*	0.46496
O1	0.13685 (16)	0.33333	0.08333	0.0090 (2)*

Geometric parameters (Å, º)

La1—O1	2.7331 (1)	La1—O1^ix	2.8988 (5)
La1—O1^i	2.7331 (4)	La1—O1^x	2.8988 (4)
La1—O1^ii	2.7331 (5)	La1—O1^xi	2.5725 (4)
La1—O1^iii	2.7331 (5)	Co1—O1	1.9386 (1)
La1—O1^iv	2.7331 (1)	Co1—O1^i	1.9386 (6)
La1—O1^v	2.7331 (4)	Co1—O1^ii	1.9386 (7)
La1—O1^vi	2.5725 (9)	Co1—O1^xii	1.9386 (1)
La1—O1^vii	2.8988 (9)	Co1—O1^xiii	1.9386 (6)
La1—O1^viii	2.5725 (4)	Co1—O1^xiv	1.9386 (7)
O1—Co1—O1^i	90.36 (3)	O1^i—Co1—O1^xiv	89.64 (3)
O1—Co1—O1^ii	90.36 (4)	O1^ii—Co1—O1^xii	89.64 (3)
O1—Co1—O1^xii	180.000 (10)	O1^ii—Co1—O1^xiii	89.64 (3)
O1—Co1—O1^xiii	89.64 (3)	O1^ii—Co1—O1^xiv	180.00 (6)
O1—Co1—O1^xiv	89.64 (3)	O1^xii—Co1—O1^xiii	90.36 (3)
O1^i—Co1—O1^ii	90.36 (6)	O1^xii—Co1—O1^xiv	90.36 (4)
O1^i—Co1—O1^xii	89.64 (3)	O1^xiii—Co1—O1^xiv	90.36 (6)
O1^i—Co1—O1^xiii	180.00 (5)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) y−1/3, −x+y−2/3, −z+1/3; (ix) y−1/3, −x+y+1/3, −z+1/3; (x) x−y−1/3, x−2/3, −z+1/3; (xi) x−y+2/3, x+1/3, −z+1/3; (xii) −x, −y, −z; (xiii) y, −x+y, −z; (xiv) x−y, x, −z.