Re-investigation and correct symmetry of Ca₃CoAl₄O₁₀

A re-investigation of the crystal structure of tricalcium cobalt(II) tetra­aluminate, Ca₃CoAl₄O₁₀, using single-crystal X-ray diffraction data, revealed ortho­rhom­bic (Pbcm) symmetry. The present contribution corrects the results of a previous X-ray powder diffraction study [Vazquez et al. (2002). J. Solid State Chem. 166, 191–196] where this phase has been described in an unnecessarily low space-group symmetry (Pbc2₁). The compound belongs to the group of tetra­hedral framework structures. The distribution of the aluminium and cobalt ions among the centres of the four different tetra­hedra within the asymmetric unit has been studied in detail. Charge compensation is achieved by the incorporation of two symmetrically independent calcium ions located in voids of the tetra­hedral framework. Ca₃CoAl₄O₁₀ is isotypic with Ca₃MgAl₄O₁₀.

1. Chemical context

In a recent paper on the phase relationships in the system CaO–MgO–Al₂O₃, we reported the existence and the crystal structure of Ca₃MgAl₄O₁₀ (Kahlenberg et al., 2018), a phase of inter­est for slags occurring in secondary refining processes in metallurgy or refractories, for example. In the course of this study it became obvious that the compound is closely related to the corresponding Zn and Co analogues that have already been reported in the literature (Barbanyagre et al., 1997; Vazquez et al., 2002). In fact Vazquez et al. (2002) used the coordinates from the Zn compound as a starting model for their Rietveld refinement of Ca₃CoAl₄O₁₀. The major difference from our investigation on Ca₃MgAl₄O₁₀ results from the fact that the previous study attributed Ca₃CoAl₄O₁₀ to the acentric space group Pbc2₁, while Ca₃MgAl₄O₁₀ crystallizes in the centrosymmetric space group Pbcm. However, for the former compound the description in an acentric space group has to be scrutinized. A detailed analysis of the atomic coordinates using the program PSEUDO (Kroumova et al., 2001) indicated that the published model fulfills the symmetry requirements of Pbcm. Notably, Vazquez et al. (2002) reported problems during their structure analysis of Ca₃CoAl₄O₁₀, including unstable refinements and unrealistically short cation–oxygen distances. Both observations are typical features when a structure is refined in an unnecessarily low space-group symmetry (Baur & Tillmanns, 1986). Therefore, it was deemed appropriate to re-investigate the crystal structure of Ca₃CoAl₄O₁₀ using single-crystal X-ray diffraction data obtained from melt-grown crystals.

2. Structural commentary

The crystal structure of Ca₃CoAl₄O₁₀ can be described as a three-dimensional network with four symmetrically different corner-sharing [(Al,Co)O₄] tetra­hedra around the central atoms T1–T4 (Fig. 1). The basic building units of the structure are chains of tetra­hedra running parallel to [001]. Using the crystal chemical classification developed by Liebau (1985), these linear elements can be described as mixed-branched vierer single chains (Fig. 2). Condensation of adjacent chains along [010] results in the formation of stepped layers parallel to (100) (Fig. 3). Within these layers, channels can be identified which host the additional calcium ions.

Figure 1 Projection of the crystal structure of Ca3CoAl4O10 in a view parallel to [100]. Displacement ellipsoids are shown at the 90% probability level. Colour codings for the atoms and polyhedra are as follows: blue: oxygen; red: aluminium/cobalt; Ca1: pink; Ca2: green; cobalt-containing tetra­hedra ([T1O4] and [T2O4]): lilac; pure aluminium tetra­hedra ([T3O4] and [T4O4]): grey.

Figure 2 A single mixed-branched vierer single chain (running parallel to [001]) representing the backbone of the framework in Ca3CoAl4O10. Displacement ellipsoids as in Fig. 1.

Figure 3 Projection of the crystal structure of Ca3CoAl4O10 in a view parallel to [001]. Displacement ellipsoids as in Fig. 1.

Site-occupancy refinements indicated that cobalt incorporation is limited to two of the four T sites within the asymmetric unit (T1 and T2). T3 and T4 are virtually cobalt free. The spread of the individual T—O bond lengths and the O—T—O angles follow expected crystallochemical trends. For the average T—O values, two groups can be distinguished: T1, T2: 1.808 Å and T3, T4: 1.758 Å. These values reflect the larger ionic radius of Co²⁺ for fourfold coordination [r(Co^2+,[4]): 0.58 Å] when compared to the corresponding value for Al³⁺ [r(Al^3+,[4]): 0.39 Å] (Shannon, 1976), and can be used as an indication that T1 and T2 have higher Co contents. This observation compares well with the site-population refinements. Quadratic elongations as defined by Robinson et al. (1971), which can be used as numerical descriptors for the distortions, take the following values for the individual [(Al,Co)O₄]-groups: T1: 1.015, T2: 1.006, T3: 1.016, T4: 1.001.

Among the extra-framework cations, two crystallographically independent calcium sites (Ca1, Ca2) can be distinguished. They are coordinated by six and eight nearest oxygen neighbours. Their coordination polyhedra can be described as distorted octa­hedra and square anti­prisms, respectively. Each two [Ca1O₆] octa­hedra and a single [Ca2O₈] square anti­prism form a polyhedral unit by sharing edges.

A detailed analysis of the topological features of the tetra­hedral network including coordination sequences and extended point symbols has been already presented for isotypic Ca₃MgAl₄O₁₀ (Kahlenberg et al., 2018) and will not be duplicated here. However, it is inter­esting to note that the framework consists of three (T3), four (T4) and five (T1, T2)-connected tetra­hedra. Notably, the net contains an O^[3]-type bridging oxygen (O3), simultaneously linking three tetra­hedra (one [T2O₄]- and two [T1O₄]-units). In oxo-silicates that are based on [SiO₄] units, for example, only terminal (O^[1]) and simple bridging (O^[2]) oxygen atoms have been observed so far. In the present structure, the oxygen atoms O1 and O2, O4, O5, O6, O7 belong to these two groups. Notably, O3 is solely involved in O—T bonds with the two tetra­hedra showing an Al/Co substitution.

3. Database survey

As mentioned above, the title compound is isotypic with Ca₃MgAl₄O₁₀. For the calculation of several qu­anti­tative descriptors for the characterization of the degree of similarity between the crystal structures of Ca₃CoAl₄O₁₀ and Ca₃MgAl₄O₁₀, the program COMPSTRU (de la Flor et al., 2016) was employed. For the given two structures, the degree of lattice distortion S, i.e. the spontaneous strain obtained from the eigenvalues of the finite Lagrangian strain tensor calculated in a Cartesian reference system, has a value of S = 0.0010. The structure of Ca₃CoAl₄O₁₀ was transformed to the most similar configuration of Ca₃MgAl₄O₁₀. The calculations revealed the following atomic displacements (in Å) between the corresponding atoms in Ca₃CoAl₄O₁₀ and Ca₃MgAl₄O₁₀: Ca1: 0.036; Ca2: 0.028; T1: 0.044; T2: 0.010; T3: 0.027; T4: 0.031; O1: 0.026; O2: 0.030; O3: 0.019; O4: 0.024; O5: 0.000; O6: 0.031; O7: 0.040, i.e. the maximum displacement is lower than 0.05 Å. The measure of similarity (Δ) as defined by Bergerhoff et al. (1999) has a value of 0.007. Notably, for both structures the divalent cations Co²⁺ and Mg²⁺ are enriched in the tetra­hedral positions T1 and T2.

The distribution of the cobalt and aluminium ions on the different T sites is another difference between the new centrosymmetric model in Pbcm (this work) and the previous acentric model in Pbc2₁ (Vazquez et al., 2002). Actually, in the latter case five different tetra­hedral positions have to be distinguished. The authors considered four of them to be exclusively occupied with Al while the remaining fifth position was attributed to be a pure cobalt site. This distribution, however, was derived from the crystal-structure refinement of the zinc analog (Barbanyagre et al., 1997) and not determined by site-occupancy refinements.

Furthermore, the new model in Pbcm results in considerably less distorted tetra­hedra. Although soft constraints on the Al—O and Co—O bond lengths had been applied, individual T—O distances and O—T—O angles in the Pbc2₁ structure model showed a pronounced variation between 1.68 and 2.05 Å and 92.9 and 124.6°, respectively. The corresponding values in the present model are in the ranges from 1.719 (4) to 1.847 (2) Å and from 98.95 (16) to 120.38 (18)°, respectively. Finally, the displacement parameters in Pbcm are all well behaved, while the overall isotropic temperature factor for the oxygen atoms reported in the study of Vazquez et al. (2002) takes a physically unrealistic value of U_iso = 0.001 (2) Ų.

4. Synthesis and crystallization

Single crystals of Ca₃CoAl₄O₁₀ were obtained during a series of synthesis experiments in the system CaO–CoO–Al₂O₃. 1.35 g of the educts consisting of CaCO₃, CoO and Al₂O₃ in the molar ratio 14:6:5 were homogenized in an agate mortar, transferred into a platinum crucible and covered with a lid. The container was fired in a resistance-heated furnace from 590 to 1623 K with a ramp of 100 K h⁻¹. The target temperature was held for 1 h. Subsequently, the sample was cooled down to 1273 K at a rate of 7.5 K h⁻¹ and, finally, the temperature was reduced to 473 K at a rate of 100 K h⁻¹. After removal of the crucible, the solidified melt cake was immediately crushed in an agate mortar and transferred to a glass slide under a polarizing binocular. A first inspection revealed the presence of two crystalline phases: larger colourless optically isotropic crystals of Ca₃Al₂O₆ (up to 500 µm in size) and considerably smaller, intensively blue birefringent crystals of Ca₃CoAl₄O₁₀. A platy fragment of the latter compound showing sharp extinction under crossed polarizers was selected for further structural studies and mounted on the tip of a glass fibre using fingernail hardener as glue.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Starting parameters for the atomic coordinates were taken from the crystal structure of Ca₃Al₄MgO₁₀ (Kahlenberg et al., 2018). Initially, mixed cobalt–aluminium populations were considered for all four T sites. However, the resulting values of the site occupancies for T3 and T4 indicated pure Al populations (within two standard uncertainties each). In the final cycles a restraint was introduced, fixing the total amount of cobalt distributed among the remaining T1 and T2 sites to four atoms per unit cell.

Table 1
Experimental details

Crystal data
Chemical formula	Al4Ca3CoO10
Mr	447.09
Crystal system, space group	Orthorhombic, Pbcm
Temperature (K)	293
a, b, c (Å)	5.1324 (6), 16.7550 (19), 10.6822 (12)
V (Å^3)	918.60 (18)
Z	4
Radiation type	Mo Kα
μ (mm^−1)	3.97
Crystal size (mm)	0.12 × 0.09 × 0.06
Data collection
Diffractometer	Rigaku Oxford Diffraction Xcalibur, Ruby, Gemini ultra
Absorption correction	Analytical (CrysAlis PRO; Rigaku OD, 2015). Analytical numeric absorption correction using a multifaceted crystal model based on expressions published by Clark & Reid (1995).
Tmin, Tmax	0.759, 0.898
No. of measured, independent and observed [I > 2σ(I)] reflections	5719, 973, 791
Rint	0.065
(sin θ/λ)max (Å^−1)	0.621
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.030, 0.061, 1.07
No. of reflections	973
No. of parameters	96
No. of restraints	1
Δρmax, Δρmin (e Å^−3)	0.6, −0.64
Computer programs: CrysAlis PRO (Rigaku OD, 2015), SHELXL2017/1 (Sheldrick, 2015), VESTA3 (Momma & Izumi, 2011), publCIF (Westrip, 2010) and WinGX (Farrugia, 2012).

Supporting information

Computing details

Data collection: CrysAlis PRO (Rigaku OD, 2015); cell refinement: CrysAlis PRO (Rigaku OD, 2015); data reduction: CrysAlis PRO (Rigaku OD, 2015); program(s) used to solve structure: coordinates from isotypic structure; program(s) used to refine structure: SHELXL2017/1 (Sheldrick, 2015); molecular graphics: VESTA3 (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010) and WinGX (Farrugia, 2012).

Tricalcium cobalt(II) tetraaluminate

Crystal data

Ca3CoAl4O10	F(000) = 876
Mr = 447.09	Dx = 3.233 Mg m^−3
Orthorhombic, Pbcm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2c 2b	Cell parameters from 939 reflections
a = 5.1324 (6) Å	θ = 5.0–28.4°
b = 16.7550 (19) Å	µ = 3.97 mm^−1
c = 10.6822 (12) Å	T = 293 K
V = 918.60 (18) Å^3	Fragment, colourless
Z = 4	0.12 × 0.09 × 0.06 mm

Data collection

Rigaku Oxford Diffraction Xcalibur, Ruby, Gemini ultra diffractometer	973 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	791 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.065
Detector resolution: 10.3575 pixels mm^-1	θmax = 26.2°, θmin = 3.8°
ω scans	h = −5→6
Absorption correction: analytical (CrysAlisPro; Rigaku OD, 2015). Analytical numeric absorption correction using a multifaceted crystal model based on expressions published by Clark & Reid (1995).	k = −20→15
Tmin = 0.759, Tmax = 0.898	l = −12→10
5719 measured reflections

Refinement

Refinement on F^2	1 restraint
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0197P)^2 + 0.4838P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.030	(Δ/σ)max < 0.001
wR(F^2) = 0.061	Δρmax = 0.6 e Å^−3
S = 1.07	Δρmin = −0.64 e Å^−3
973 reflections	Extinction correction: SHELXL-2017/1 (Sheldrick 2015), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
96 parameters	Extinction coefficient: 0.0014 (4)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.63528 (15)	−0.07769 (4)	0.59968 (7)	0.0076 (2)	0.6196 (19)
Co1	0.63528 (15)	−0.07769 (4)	0.59968 (7)	0.0076 (2)	0.3804 (19)
Al2	0.1321 (2)	−0.02939 (7)	0.75	0.0068 (4)	0.761 (4)
Co2	0.1321 (2)	−0.02939 (7)	0.75	0.0068 (4)	0.239 (4)
Al3	0.2463 (3)	0.16550 (9)	0.75	0.0043 (3)
Al4	0.3045 (3)	0.25	0.5	0.0062 (4)
Ca1	0.80287 (14)	0.10873 (4)	0.57559 (7)	0.0093 (2)
Ca2	0.7833 (2)	0.20768 (6)	0.25	0.0131 (3)
O1	0.5811 (6)	0.1666 (2)	0.75	0.0085 (8)
O2	0.0758 (7)	0.0742 (2)	0.75	0.0102 (8)
O3	0.4655 (8)	−0.0615 (2)	0.75	0.0192 (10)
O4	0.1005 (5)	0.21476 (14)	0.6201 (2)	0.0084 (6)
O5	0.5	0	0.5	0.0174 (9)
O6	0.4916 (5)	−0.17398 (15)	0.5570 (2)	0.0130 (6)
O7	−0.0172 (5)	−0.07854 (19)	0.8828 (2)	0.0249 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Al1	0.0068 (4)	0.0079 (5)	0.0082 (4)	−0.0011 (3)	−0.0006 (3)	−0.0001 (3)
Co1	0.0068 (4)	0.0079 (5)	0.0082 (4)	−0.0011 (3)	−0.0006 (3)	−0.0001 (3)
Al2	0.0072 (7)	0.0052 (7)	0.0080 (7)	0.0001 (5)	0	0
Co2	0.0072 (7)	0.0052 (7)	0.0080 (7)	0.0001 (5)	0	0
Al3	0.0042 (8)	0.0054 (8)	0.0034 (7)	−0.0015 (6)	0	0
Al4	0.0072 (8)	0.0058 (8)	0.0056 (8)	0	0	0.0003 (6)
Ca1	0.0080 (4)	0.0119 (4)	0.0080 (4)	−0.0004 (3)	−0.0010 (3)	−0.0005 (3)
Ca2	0.0116 (6)	0.0077 (6)	0.0200 (6)	−0.0011 (5)	0	0
O1	0.0035 (19)	0.013 (2)	0.0085 (17)	0.0022 (15)	0	0
O2	0.009 (2)	0.010 (2)	0.0120 (18)	0.0015 (15)	0	0
O3	0.021 (2)	0.026 (3)	0.011 (2)	0.0087 (19)	0	0
O4	0.0083 (13)	0.0085 (15)	0.0083 (12)	−0.0018 (10)	−0.0007 (11)	0.0021 (10)
O5	0.017 (2)	0.017 (2)	0.018 (2)	−0.0078 (17)	0.0023 (18)	0.0007 (17)
O6	0.0126 (15)	0.0155 (16)	0.0109 (13)	0.0068 (12)	−0.0013 (11)	−0.0033 (11)
O7	0.0163 (16)	0.043 (2)	0.0152 (14)	−0.0090 (14)	−0.0037 (13)	0.0088 (14)

Geometric parameters (Å, º)

T1—O7^i	1.794 (3)	T4—O4^v	1.758 (2)
T1—O5	1.8194 (7)	Ca1—O6^iv	2.342 (3)
T1—O6	1.831 (3)	Ca1—O1	2.389 (2)
T1—O3	1.847 (2)	Ca1—O7^vi	2.389 (3)
T2—O2	1.759 (4)	Ca1—O4^vii	2.391 (3)
T2—O3	1.794 (4)	Ca1—O2^vii	2.402 (2)
T2—O7	1.810 (3)	Ca1—O5	2.5273 (8)
T2—O7^ii	1.810 (3)	Ca2—O1^v	2.348 (4)
T3—O1	1.719 (4)	Ca2—O4^viii	2.503 (3)
T3—O2	1.762 (4)	Ca2—O4^ix	2.503 (3)
T3—O4^ii	1.780 (3)	Ca2—O6^vi	2.561 (3)
T3—O4	1.780 (3)	Ca2—O6^iv	2.561 (3)
T4—O6^iii	1.758 (3)	Ca2—O3^iv	2.762 (4)
T4—O6^iv	1.758 (3)	Ca2—O7^iv	2.852 (3)
T4—O4	1.758 (2)	Ca2—O7^vi	2.852 (3)
O7^i—T1—O5	116.51 (11)	O2^vii—Ca1—O5	115.65 (9)
O7^i—T1—O6	114.80 (13)	O1^v—Ca2—O4^viii	79.73 (9)
O5—T1—O6	109.33 (9)	O1^v—Ca2—O4^ix	79.73 (9)
O7^i—T1—O3	112.30 (14)	O4^viii—Ca2—O4^ix	67.34 (11)
O5—T1—O3	102.92 (12)	O1^v—Ca2—O6^vi	87.38 (8)
O6—T1—O3	98.95 (16)	O4^viii—Ca2—O6^vi	156.79 (9)
O2—T2—O3	116.90 (19)	O4^ix—Ca2—O6^vi	91.52 (8)
O2—T2—O7	112.29 (13)	O1^v—Ca2—O6^iv	87.38 (8)
O3—T2—O7	105.50 (13)	O4^viii—Ca2—O6^iv	91.52 (8)
O2—T2—O7^ii	112.29 (13)	O4^ix—Ca2—O6^iv	156.79 (9)
O3—T2—O7^ii	105.50 (13)	O6^vi—Ca2—O6^iv	107.20 (12)
O7—T2—O7^ii	103.2 (2)	O1^v—Ca2—O3^iv	126.24 (12)
O1—T3—O2	120.38 (18)	O4^viii—Ca2—O3^iv	139.56 (7)
O1—T3—O4^ii	114.55 (12)	O4^ix—Ca2—O3^iv	139.56 (7)
O2—T3—O4^ii	101.18 (12)	O6^vi—Ca2—O3^iv	63.24 (7)
O1—T3—O4	114.55 (12)	O6^iv—Ca2—O3^iv	63.24 (7)
O2—T3—O4	101.18 (12)	O1^v—Ca2—O7^iv	150.06 (6)
O4^ii—T3—O4	102.48 (17)	O4^viii—Ca2—O7^iv	113.33 (9)
O6^iii—T4—O6^iv	106.90 (19)	O4^ix—Ca2—O7^iv	81.05 (8)
O6^iii—T4—O4	110.19 (11)	O6^vi—Ca2—O7^iv	70.38 (8)
O6^iv—T4—O4	111.36 (12)	O6^iv—Ca2—O7^iv	117.70 (9)
O6^iii—T4—O4^v	111.36 (12)	O3^iv—Ca2—O7^iv	61.43 (9)
O6^iv—T4—O4^v	110.19 (11)	O1^v—Ca2—O7^vi	150.06 (6)
O4—T4—O4^v	106.90 (18)	O4^viii—Ca2—O7^vi	81.05 (8)
O6^iv—Ca1—O1	88.56 (9)	O4^ix—Ca2—O7^vi	113.33 (9)
O6^iv—Ca1—O7^vi	82.78 (10)	O6^vi—Ca2—O7^vi	117.70 (9)
O1—Ca1—O7^vi	167.86 (11)	O6^iv—Ca2—O7^vi	70.38 (8)
O6^iv—Ca1—O4^vii	100.70 (9)	O3^iv—Ca2—O7^vi	61.43 (9)
O1—Ca1—O4^vii	81.24 (10)	O7^iv—Ca2—O7^vi	59.64 (11)
O7^vi—Ca1—O4^vii	91.99 (9)	T2—O2—T3	140.8 (2)
O6^iv—Ca1—O2^vii	163.33 (10)	T2—O3—T1^ii	119.61 (11)
O1—Ca1—O2^vii	76.74 (10)	T2—O3—T1	119.61 (11)
O7^vi—Ca1—O2^vii	110.44 (10)	T1^ii—O3—T1	120.8 (2)
O4^vii—Ca1—O2^vii	69.64 (11)	T4—O4—T3	118.32 (15)
O6^iv—Ca1—O5	75.31 (7)	T1—O5—T1^iv	180.00 (4)
O1—Ca1—O5	104.40 (9)	T4^iv—O6—T1	119.00 (15)
O7^vi—Ca1—O5	81.67 (7)	T1^x—O7—T2	119.94 (16)
O4^vii—Ca1—O5	172.84 (7)

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