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ISSN: 2056-9890

Ca4As3 – a new binary calcium arsenide

aTechnische Universität München, Department of Chemistry, Lichtenbergstr. 4, 85747 Garching, Germany
*Correspondence e-mail: viktor.hlukhyy@lrz.tum.de

Edited by P. Roussel, ENSCL, France (Received 17 November 2015; accepted 23 November 2015; online 28 November 2015)

The crystal structure of the binary compound tetra­calcium triarsenide, Ca4As3, was investigated by single-crystal X-ray diffraction. Ca4As3 crystallizes in the Ba4P3 structure type and is thus a homologue of isotypic Sr4As3. The unit cell contains 32 Ca2+ cations, 16 As3− isolated anions and four centrosymmetric [As2]4– dumbbells. The As atoms in each of the dumbbells are connected by a single bond, thus this calcium arsenide is a Zintl phase.

1. Chemical context

Six binary compounds have been reported so far in the binary phase diagram Ca–As: CaAs3 (Brice et al., 1976[Brice, J. F., Courtois, A., Protas, J. & Aubry, J. (1976). J. Solid State Chem. 17, 393-397.]), Ca2As3 (Deller & Eisenmann, 1976[Deller, K. & Eisenmann, B. (1976). Z. Naturforsch. Teil B, 31, 1023-1027.]), CaAs (Iandelli & Franceschi, 1973[Iandelli, A. & Franceschi, E. (1973). J. Less-Common Met. 30, 211-216.]), Ca16As11 (Leon-Escamilla et al., 1997[Leon-Escamilla, E. A., Hurng, W. M., Peterson, E. S. & Corbett, J. D. (1997). Inorg. Chem. 36, 703-710.]), Ca5As3 (Hütz & Nagorsen, 1975[Hütz, A. & Nagorsen, G. (1975). Z. Metallkd. 66, 314.]) and Ca2As (Hütz & Nagorsen, 1974[Hütz, A. & Nagorsen, G. (1974). Z. Metallkd. 65, 618-623.]). In the binary phase system, the following trend is observed: with increasing As-content the number of covalent As—As bonds increases. Ca2As and Ca5As3 are reported as inter­metallic phases. In the Ca-richest compound Ca2As, the Ca atoms in the first coordination sphere of As adopt a monocapped square-anti­prismatic geometry (CN = 9), while the Ca atoms are situated inside cubocta­hedra (eight Ca and four As atoms) or 13-vertex polyhedra (eight Ca and five As atoms). In Ca5As3, nine Ca atoms form deformed monocapped square anti­prisms around As while the coordination polyhedra of Ca atoms are formed by bicapped-hexa­gonal anti­prismatic (eight Ca and six As atoms) and 15-vertex polyhedra (ten Ca and five As atoms). No covalent bonds are found in either compound. The other four Ca–As compounds are Zintl phases containing polyanionic As-substructures. The polyarsenic substructure varies with the atomic percentage of Ca. Compounds with 50–59.3 at.% of Ca (CaAs, Ca16As11 and the title compound Ca4As3) all contain [As2]4– dumbbells as a structure motif. Ca2As3 contains two types of As chains: [As4]6– and [As8]10–. The structure of the CaAs3 compound with the highest As content contains a two-dimensional [As3]2– network as a polyarsenic substructure besides the three bonded [As]0 and two bonded [As]1– atoms in a ratio of 1:2.

2. Structural commentary

The unit cell of the title compounds is shown in Fig. 1[link]. The phase Ca4As3 (Z = 8) with 57 at.% Ca fulfils the 8-N rule according to a salt-like compound: the charge of 32 Ca2+ cations are counterbalanced by 16 isolated As3– anions and four [As2]4– dumbbells (two As2—As2 dumbbells and two As5—As5 dumbbells) per unit cell. The dumbbells formed by the As2 anions, with an inter­atomic distance of of 2.507 (2) Å, lie in the ab plane. The second type of dumbbells of the As5 anions, with d(As5—As5) of 2.527 (2) Å, lie along the c-axis direction, thus the two dumbbells are oriented perpendicular with respect to each other. Both As—As distances are in the range of covalent single bonds observed in elemental As and other binary Ca–As compounds (2.44–2.57 Å). Each As atom of the dumbbells is coordinated by eight Ca cations. Six Ca cations form a distorted trigonal prism while two Ca cations cap two of the rectangular faces of the prism; the third rectangular prism face is capped by the covalently bonded As atom (Fig. 2b,d[link]). The two trigonal prisms around As2 or As5 share their tetra­gonal faces, each with the As dumbbell in the center of the eight-vertex polyhedron of Ca atoms. Two of the As3– anions (As1 and As3) that are not bonded to further As atoms are coordinated by Ca atoms in form of distorted trigonal prisms (Fig. 2a,c[link]). For As1, two faces of the prism are capped while for As3, three faces are capped with Ca atoms. The trigonal–prismatic coordination polyhedra of As1 and As3 are connected by sharing edges. In contrast to the other As atoms, As4 possesses a different coordination sphere having also the highest coordination number (CN = 10) of Ca atoms, forming a polyhedron with 14 faces (Fig. 2e[link]). The coordination sphere can be described as an icosa­hedron with two removed adjacent vertices.

[Figure 1]
Figure 1
Crystal structure of Ca4As3 shown along the a axis. The Ca atoms are shown in gray and the As atoms in magenta as anisotropic displacement ellipsoids with a 90% probability level. The As—As dumbbell bonds are shown in magenta.
[Figure 2]
Figure 2
The coordination polyhedra of As atoms. The Ca atoms are shown in gray and the As atoms in magenta as anisotropic displacement ellipsoids with a 90% probability level. The As—As dumbbell bonds are emphasized in magenta.

The coordination around the Ca cations is formed by six or seven As atoms and eight to ten Ca atoms (Fig. 3[link]). Distorted octa­hedra are formed by six As atoms around Ca1, Ca4, Ca5 and Ca6. For Ca4 and Ca5, one edge is formed by an As5 dumbbell. The faces of the octa­hedra are capped by Ca atoms. In most cases d(Ca—Ca) is longer than 3.5 Å; however, a rather short distance of 3.289 (2) Å is observed between Ca4 and Ca5. Those two Ca atoms are coordinated by the As5 dumbbells (Fig. 3[link]d,e). The distorted As octa­hedra around Ca4 and Ca5 share a common face (As1–As1–As4) in the ab plane. Ca2 and Ca3 are surrounded by seven As atoms (Fig. 3[link]b,c). In both cases, the coordination polyhedron resembles a distorted penta­gonal bipyramid. For Ca2, one edge of the penta­gon is an As2 dumbbell. Each of the trigonal faces is capped by Ca atoms.

[Figure 3]
Figure 3
The coordination polyhedra of Ca atoms. The Ca atoms are shown in gray and the As atoms in magenta as anisotropic displacement ellipsoids with a 90% probability level. The As—As dumbbells are emphasized in magenta.

3. Comparison with isostructural compounds

Comparison of Ca4As3 with the isostructural Sr4As3 (Somer et al., 1995[Somer, M., Carrillo-Cabrera, W., Peters, K., Peters, K. & von Schnering, H. G. (1995). Z. Kristallogr. 210, 142.]) and Ba4P3 (Hadenfeldt et al., 1993[Hadenfeldt, C., Terschüren, H. U., Hönle, W., Schröder, L. & von Schnering, H. G. (1993). Z. Anorg. Allg. Chem. 619, 843-848.]) show that the lattice parameters increase in accordance with the cation size. The distances in the As–As dumbbells for Sr4As3 are 2.52 and 2.55 Å, which is slightly longer than observed in dumbbells of Ca4As3 [2.507 (2) Å and 2.527 (2) Å, respectively]. The lattice parameters for Ba4P3 are further increased due to the larger Ba atoms. However, the distances in the dumbbells [d(P—P) of 2.25 and 2.32 Å] are shorter than in the As compounds due to the smaller covalent radius of P.

4. Synthesis and crystallization

Single crystals of the title compound were obtained from experiments aiming at an alloy with the nominal composition of 12Ca:10Fe:10As:4Rh:8Si. A mixture of Ca (2.35 mmol), Fe (1.96 mmol), As (1.96 mmol) and pre-prepared `Rh:2Si' precursor (0.78 mmol) was placed in an alumina crucible which was sealed in a tantalum ampoule under an argon atmosphere. The ampoule was heated in a resistances furnace to 1373 K and held for 24 h. Afterwards, the temperature was reduced to 1248 K at a rate of 0.1 K min−1 and held there for a week. Single crystals of the title compound could be isolated from the product. Energy-dispersive X-ray analysis (EDX) of the crystals showed an atomic ratio of Ca/As close to 4:3 in all analysed crystals. No impurity elements heavier than sodium were observed. The binary Ca4As3 phase was subsequently synthesized from the pure elements.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1[link]. All atoms were refined with anisotropic displacement parameters. The remaining maximum and minimum electron densities are located 1.29 Å from As2 and 0.03 Å from As5, respectively.

Table 1
Experimental details

Crystal data
Chemical formula Ca4As3
Mr 385.08
Crystal system, space group Orthorhombic, Pbam
Temperature (K) 150
a, b, c (Å) 11.5137 (5), 12.0584 (6), 10.3426 (4)
V3) 1435.93 (11)
Z 8
Radiation type Mo Kα
μ (mm−1) 16.61
Crystal size (mm) 0.08 × 0.04 × 0.01
 
Data collection
Diffractometer Oxford Diffraction Xcalibur 3
Absorption correction Multi-scan (CrysAlis RED; Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis CCD and CrysAlis RED. Oxford Diffraction Ltd, Yarnton, England.])
Tmin, Tmax 0.683, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections 26414, 2659, 1273
Rint 0.143
(sin θ/λ)max−1) 0.764
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.034, 0.054, 0.68
No. of reflections 2659
No. of parameters 74
Δρmax, Δρmin (e Å−3) 1.95, −1.56
Computer programs: CrysAlis CCD and CrysAlis RED (Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis CCD and CrysAlis RED. Oxford Diffraction Ltd, Yarnton, England.]), SHELXS97 and SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]) and DIAMOND (Brandenburg, 2012[Brandenburg, K. (2012). DIAMOND. Crystal Impact GbR, Bonn, Germany.]).

Supporting information


Computing details top

Data collection: CrysAlis CCD (Oxford Diffraction, 2009); cell refinement: CrysAlis RED (Oxford Diffraction, 2009); data reduction: CrysAlis RED (Oxford Diffraction, 2009); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2012).

Tetracalcium triarsenide top
Crystal data top
Ca4As3F(000) = 1432
Mr = 385.08Dx = 3.563 Mg m3
Orthorhombic, PbamMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2 2abCell parameters from 2659 reflections
a = 11.5137 (5) Åθ = 3.4–32.9°
b = 12.0584 (6) ŵ = 16.61 mm1
c = 10.3426 (4) ÅT = 150 K
V = 1435.93 (11) Å3Needle, metallic dark grey
Z = 80.08 × 0.04 × 0.01 mm
Data collection top
Oxford Diffraction Xcalibur 3
diffractometer
2659 independent reflections
Radiation source: Enhance (Mo) X-ray Source1273 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.143
Detector resolution: 16.0238 pixels mm-1θmax = 32.9°, θmin = 3.4°
ω and π scansh = 1717
Absorption correction: multi-scan
(CrysAlis RED; Oxford Diffraction, 2009)
k = 1818
Tmin = 0.683, Tmax = 1.000l = 1414
26414 measured reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.034Secondary atom site location: difference Fourier map
wR(F2) = 0.054 w = 1/[σ2(Fo2) + (0.0138P)2]
where P = (Fo2 + 2Fc2)/3
S = 0.68(Δ/σ)max < 0.001
2659 reflectionsΔρmax = 1.95 e Å3
74 parametersΔρmin = 1.56 e Å3
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.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
As10.33718 (5)0.17628 (5)0.23336 (5)0.00964 (12)
As20.03879 (7)0.09712 (7)0.50000.01132 (19)
As30.13520 (7)0.38636 (7)0.50000.01069 (19)
As40.14021 (7)0.35690 (7)0.00000.01187 (19)
As50.00000.00000.12216 (8)0.00906 (18)
Ca10.09403 (10)0.23535 (9)0.27341 (10)0.0113 (2)
Ca20.32326 (10)0.43298 (9)0.32339 (10)0.0122 (2)
Ca30.37493 (14)0.13596 (14)0.50000.0134 (4)
Ca40.22573 (13)0.07676 (14)0.00000.0110 (4)
Ca50.39968 (14)0.29309 (13)0.00000.0103 (4)
Ca60.00000.50000.18518 (16)0.0129 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
As10.0085 (3)0.0117 (3)0.0087 (3)0.0010 (2)0.0005 (3)0.0004 (2)
As20.0109 (4)0.0121 (5)0.0110 (5)0.0005 (3)0.0000.000
As30.0099 (4)0.0122 (4)0.0101 (4)0.0019 (3)0.0000.000
As40.0096 (4)0.0118 (4)0.0141 (4)0.0002 (3)0.0000.000
As50.0079 (4)0.0106 (4)0.0087 (4)0.0008 (3)0.0000.000
Ca10.0089 (5)0.0118 (6)0.0132 (6)0.0003 (5)0.0002 (5)0.0002 (5)
Ca20.0119 (6)0.0135 (6)0.0112 (6)0.0002 (5)0.0023 (5)0.0009 (5)
Ca30.0148 (9)0.0154 (9)0.0099 (8)0.0018 (7)0.0000.000
Ca40.0091 (8)0.0142 (9)0.0098 (8)0.0018 (7)0.0000.000
Ca50.0119 (8)0.0096 (8)0.0096 (8)0.0016 (7)0.0000.000
Ca60.0081 (8)0.0103 (8)0.0202 (9)0.0003 (7)0.0000.000
Geometric parameters (Å, º) top
As1—Ca32.8338 (6)Ca2—As5i3.0209 (12)
As1—Ca6i2.8777 (6)Ca2—As2i3.1027 (13)
As1—Ca52.8857 (10)Ca2—As2viii3.1268 (13)
As1—Ca12.9182 (13)Ca2—As1xv3.5897 (13)
As1—Ca42.9853 (11)Ca2—Ca2iv3.653 (2)
As1—Ca1i3.1707 (13)Ca2—Ca1i3.7559 (16)
As1—Ca23.2364 (13)Ca2—Ca1xv3.8037 (16)
As1—Ca2ii3.5898 (13)Ca2—Ca4x3.8093 (14)
As2—As2iii2.5068 (17)Ca2—Ca3viii3.8123 (18)
As2—Ca12.9453 (12)Ca3—As1iv2.8338 (6)
As2—Ca1iv2.9453 (12)Ca3—As3i3.0088 (18)
As2—Ca2v3.1026 (13)Ca3—As3vii3.0119 (18)
As2—Ca2vi3.1026 (13)Ca3—Ca1xvi3.7768 (17)
As2—Ca2ii3.1267 (13)Ca3—Ca1i3.7768 (17)
As2—Ca2vii3.1267 (13)Ca3—Ca2ii3.8123 (18)
As3—Ca22.8880 (13)Ca3—Ca2vii3.8123 (18)
As3—Ca2iv2.8880 (13)Ca3—Ca6i3.9196 (16)
As3—Ca1iv3.0054 (12)Ca3—Ca6vii3.9196 (16)
As3—Ca13.0054 (12)Ca3—Ca2iv4.0643 (19)
As3—Ca3v3.0088 (18)Ca4—As1xi2.9853 (11)
As3—Ca3viii3.0119 (18)Ca4—As5xii3.0344 (14)
As4—Ca63.0417 (12)Ca4—As4xiii3.0677 (19)
As4—Ca6ix3.0417 (12)Ca4—Ca53.289 (2)
As4—Ca4x3.0678 (19)Ca4—Ca5xiii3.713 (2)
As4—Ca53.0850 (18)Ca4—Ca1xi3.7353 (15)
As4—Ca1xi3.2291 (12)Ca4—Ca6i3.8075 (16)
As4—Ca13.2291 (12)Ca4—Ca6xiii3.8075 (16)
As4—Ca5v3.3076 (18)Ca5—As1xi2.8857 (10)
As4—Ca43.5186 (19)Ca5—As5i3.0258 (14)
As5—As5xii2.5268 (16)Ca5—As5x3.0258 (14)
As5—Ca2ii3.0209 (12)Ca5—As4i3.3076 (18)
As5—Ca2v3.0209 (12)Ca5—Ca1i3.6223 (15)
As5—Ca5xiii3.0258 (14)Ca5—Ca1xvii3.6223 (15)
As5—Ca5v3.0258 (14)Ca5—Ca4x3.713 (2)
As5—Ca4xii3.0344 (14)Ca5—Ca2xi3.8480 (13)
As5—Ca43.0344 (14)Ca6—As1xv2.8777 (6)
As5—Ca13.4166 (12)Ca6—As1v2.8777 (6)
As5—Ca1xiv3.4166 (12)Ca6—As4ix3.0417 (12)
Ca1—As1v3.1707 (13)Ca6—Ca1xviii3.4913 (12)
Ca1—Ca63.4913 (12)Ca6—Ca4v3.8075 (16)
Ca1—Ca23.5933 (16)Ca6—Ca4x3.8075 (16)
Ca1—Ca5v3.6223 (15)Ca6—Ca6ix3.831 (3)
Ca1—Ca43.7353 (15)Ca6—Ca3viii3.9196 (16)
Ca1—Ca2v3.7559 (16)Ca6—Ca3v3.9196 (16)
Ca1—Ca3v3.7768 (17)
Ca3—As1—Ca6i86.67 (5)As1—Ca3—As3i99.68 (3)
Ca3—As1—Ca5149.25 (5)As1iv—Ca3—As3vii99.53 (4)
Ca6i—As1—Ca593.05 (4)As1—Ca3—As3vii99.53 (4)
Ca3—As1—Ca192.92 (4)As3i—Ca3—As3vii87.09 (5)
Ca6i—As1—Ca1146.08 (3)As1iv—Ca3—Ca1xvi55.12 (3)
Ca5—As1—Ca1103.82 (4)As1—Ca3—Ca1xvi129.48 (5)
Ca3—As1—Ca4141.60 (5)As3i—Ca3—Ca1xvi51.06 (3)
Ca6i—As1—Ca480.97 (4)As3vii—Ca3—Ca1xvi115.88 (4)
Ca5—As1—Ca468.11 (4)As1iv—Ca3—Ca1i129.48 (5)
Ca1—As1—Ca478.49 (4)As1—Ca3—Ca1i55.12 (3)
Ca3—As1—Ca1i77.73 (4)As3i—Ca3—Ca1i51.06 (3)
Ca6i—As1—Ca1i70.32 (3)As3vii—Ca3—Ca1i115.88 (4)
Ca5—As1—Ca1i73.30 (4)Ca1xvi—Ca3—Ca1i76.70 (4)
Ca1—As1—Ca1i142.58 (3)As1iv—Ca3—Ca2ii118.99 (5)
Ca4—As1—Ca1i129.91 (4)As1—Ca3—Ca2ii63.39 (3)
Ca3—As1—Ca283.78 (4)As3i—Ca3—Ca2ii122.60 (5)
Ca6i—As1—Ca2142.05 (3)As3vii—Ca3—Ca2ii48.34 (3)
Ca5—As1—Ca277.65 (4)Ca1xvi—Ca3—Ca2ii163.92 (5)
Ca1—As1—Ca271.23 (3)Ca1i—Ca3—Ca2ii111.49 (3)
Ca4—As1—Ca2126.57 (4)As1iv—Ca3—Ca2vii63.39 (3)
Ca1i—As1—Ca271.77 (3)As1—Ca3—Ca2vii118.99 (5)
Ca3—As1—Ca2ii71.72 (4)As3i—Ca3—Ca2vii122.60 (5)
Ca6i—As1—Ca2ii77.08 (2)As3vii—Ca3—Ca2vii48.34 (3)
Ca5—As1—Ca2ii138.09 (4)Ca1xvi—Ca3—Ca2vii111.49 (3)
Ca1—As1—Ca2ii70.67 (3)Ca1i—Ca3—Ca2vii163.92 (5)
Ca4—As1—Ca2ii70.12 (3)Ca2ii—Ca3—Ca2vii57.26 (4)
Ca1i—As1—Ca2ii136.12 (3)As1iv—Ca3—Ca6i159.48 (6)
Ca2—As1—Ca2ii132.97 (3)As1—Ca3—Ca6i47.13 (2)
As2iii—As2—Ca1127.28 (3)As3i—Ca3—Ca6i66.21 (3)
As2iii—As2—Ca1iv127.28 (3)As3vii—Ca3—Ca6i66.19 (3)
Ca1—As2—Ca1iv105.44 (5)Ca1xvi—Ca3—Ca6i116.23 (4)
As2iii—As2—Ca2v66.78 (3)Ca1i—Ca3—Ca6i53.91 (2)
Ca1—As2—Ca2v76.73 (3)Ca2ii—Ca3—Ca6i63.47 (2)
Ca1iv—As2—Ca2v135.02 (4)Ca2vii—Ca3—Ca6i110.45 (4)
As2iii—As2—Ca2vi66.78 (3)As1iv—Ca3—Ca6vii47.13 (2)
Ca1—As2—Ca2vi135.02 (4)As1—Ca3—Ca6vii159.48 (6)
Ca1iv—As2—Ca2vi76.73 (3)As3i—Ca3—Ca6vii66.21 (3)
Ca2v—As2—Ca2vi72.13 (4)As3vii—Ca3—Ca6vii66.19 (3)
As2iii—As2—Ca2ii65.77 (4)Ca1xvi—Ca3—Ca6vii53.91 (2)
Ca1—As2—Ca2ii77.51 (3)Ca1i—Ca3—Ca6vii116.23 (4)
Ca1iv—As2—Ca2ii135.51 (4)Ca2ii—Ca3—Ca6vii110.45 (4)
Ca2v—As2—Ca2ii89.33 (4)Ca2vii—Ca3—Ca6vii63.47 (2)
Ca2vi—As2—Ca2ii132.54 (3)Ca6i—Ca3—Ca6vii112.34 (5)
As2iii—As2—Ca2vii65.77 (4)As1iv—Ca3—Ca2iv52.34 (3)
Ca1—As2—Ca2vii135.51 (4)As1—Ca3—Ca2iv105.29 (5)
Ca1iv—As2—Ca2vii77.51 (3)As3i—Ca3—Ca2iv102.98 (4)
Ca2v—As2—Ca2vii132.54 (3)As3vii—Ca3—Ca2iv151.04 (3)
Ca2vi—As2—Ca2vii89.33 (4)Ca1xvi—Ca3—Ca2iv57.10 (3)
Ca2ii—As2—Ca2vii71.49 (4)Ca1i—Ca3—Ca2iv90.83 (4)
Ca2—As3—Ca2iv78.47 (5)Ca2ii—Ca3—Ca2iv133.91 (5)
Ca2—As3—Ca1iv136.83 (4)Ca2vii—Ca3—Ca2iv105.24 (3)
Ca2iv—As3—Ca1iv75.11 (3)Ca6i—Ca3—Ca2iv142.72 (4)
Ca2—As3—Ca175.11 (3)Ca6vii—Ca3—Ca2iv92.81 (2)
Ca2iv—As3—Ca1136.83 (4)As1iv—Ca3—Ca2105.29 (5)
Ca1iv—As3—Ca1102.48 (5)As1—Ca3—Ca252.34 (3)
Ca2—As3—Ca3v139.83 (3)As3i—Ca3—Ca2102.98 (4)
Ca2iv—As3—Ca3v139.83 (3)As3vii—Ca3—Ca2151.03 (3)
Ca1iv—As3—Ca3v77.80 (3)Ca1xvi—Ca3—Ca290.83 (4)
Ca1—As3—Ca3v77.80 (3)Ca1i—Ca3—Ca257.10 (3)
Ca2—As3—Ca3viii80.48 (4)Ca2ii—Ca3—Ca2105.24 (3)
Ca2iv—As3—Ca3viii80.48 (4)Ca2vii—Ca3—Ca2133.91 (5)
Ca1iv—As3—Ca3viii126.82 (3)Ca6i—Ca3—Ca292.81 (2)
Ca1—As3—Ca3viii126.82 (3)Ca6vii—Ca3—Ca2142.72 (4)
Ca3v—As3—Ca3viii92.91 (5)Ca2iv—Ca3—Ca253.41 (4)
Ca6—As4—Ca6ix78.05 (5)As1—Ca4—As1xi107.90 (5)
Ca6—As4—Ca4x77.10 (3)As1—Ca4—As5xii145.83 (4)
Ca6ix—As4—Ca4x77.10 (3)As1xi—Ca4—As5xii98.87 (2)
Ca6—As4—Ca5130.95 (3)As1—Ca4—As598.87 (2)
Ca6ix—As4—Ca5130.95 (3)As1xi—Ca4—As5145.83 (4)
Ca4x—As4—Ca574.23 (4)As5xii—Ca4—As549.21 (4)
Ca6—As4—Ca1xi136.18 (4)As1—Ca4—As4xiii97.54 (4)
Ca6ix—As4—Ca1xi67.59 (3)As1xi—Ca4—As4xiii97.54 (4)
Ca4x—As4—Ca1xi118.37 (2)As5xii—Ca4—As4xiii99.63 (5)
Ca5—As4—Ca1xi92.65 (3)As5—Ca4—As4xiii99.63 (5)
Ca6—As4—Ca167.59 (3)As1—Ca4—Ca554.51 (3)
Ca6ix—As4—Ca1136.18 (4)As1xi—Ca4—Ca554.51 (3)
Ca4x—As4—Ca1118.37 (2)As5xii—Ca4—Ca5139.78 (5)
Ca5—As4—Ca192.65 (3)As5—Ca4—Ca5139.78 (5)
Ca1xi—As4—Ca1122.26 (5)As4xiii—Ca4—Ca5112.28 (6)
Ca6—As4—Ca5v82.29 (3)As1—Ca4—As474.59 (4)
Ca6ix—As4—Ca5v82.29 (3)As1xi—Ca4—As474.60 (4)
Ca4x—As4—Ca5v153.36 (5)As5xii—Ca4—As493.05 (4)
Ca5—As4—Ca5v132.41 (3)As5—Ca4—As493.05 (4)
Ca1xi—As4—Ca5v67.29 (3)As4xiii—Ca4—As4166.04 (5)
Ca1—As4—Ca5v67.29 (3)Ca5—Ca4—As453.77 (4)
Ca6—As4—Ca4133.88 (3)As1—Ca4—Ca5xiii122.51 (3)
Ca6ix—As4—Ca4133.88 (3)As1xi—Ca4—Ca5xiii122.51 (3)
Ca4x—As4—Ca4133.54 (3)As5xii—Ca4—Ca5xiii52.11 (3)
Ca5—As4—Ca459.31 (4)As5—Ca4—Ca5xiii52.11 (3)
Ca1xi—As4—Ca467.07 (3)As4xiii—Ca4—Ca5xiii53.09 (4)
Ca1—As4—Ca467.07 (3)Ca5—Ca4—Ca5xiii165.37 (6)
Ca5v—As4—Ca473.10 (4)As4—Ca4—Ca5xiii140.86 (5)
As5xii—As5—Ca2ii133.55 (2)As1—Ca4—Ca149.96 (3)
As5xii—As5—Ca2v133.55 (2)As1xi—Ca4—Ca1125.50 (6)
Ca2ii—As5—Ca2v92.90 (5)As5xii—Ca4—Ca197.10 (4)
As5xii—As5—Ca5xiii65.320 (18)As5—Ca4—Ca159.55 (3)
Ca2ii—As5—Ca5xiii79.04 (3)As4xiii—Ca4—Ca1130.29 (3)
Ca2v—As5—Ca5xiii139.94 (3)Ca5—Ca4—Ca180.86 (4)
As5xii—As5—Ca5v65.320 (18)As4—Ca4—Ca152.76 (3)
Ca2ii—As5—Ca5v139.94 (3)Ca5xiii—Ca4—Ca1108.29 (4)
Ca2v—As5—Ca5v79.04 (3)As1—Ca4—Ca1xi125.50 (6)
Ca5xiii—As5—Ca5v130.64 (4)As1xi—Ca4—Ca1xi49.96 (3)
As5xii—As5—Ca4xii65.395 (18)As5xii—Ca4—Ca1xi59.55 (3)
Ca2ii—As5—Ca4xii141.46 (4)As5—Ca4—Ca1xi97.10 (4)
Ca2v—As5—Ca4xii77.97 (3)As4xiii—Ca4—Ca1xi130.29 (3)
Ca5xiii—As5—Ca4xii84.35 (4)Ca5—Ca4—Ca1xi80.86 (4)
Ca5v—As5—Ca4xii75.56 (4)As4—Ca4—Ca1xi52.76 (3)
As5xii—As5—Ca465.395 (18)Ca5xiii—Ca4—Ca1xi108.29 (4)
Ca2ii—As5—Ca477.97 (3)Ca1—Ca4—Ca1xi98.41 (5)
Ca2v—As5—Ca4141.46 (4)As1—Ca4—Ca6i48.28 (3)
Ca5xiii—As5—Ca475.57 (4)As1xi—Ca4—Ca6i98.51 (4)
Ca5v—As5—Ca484.35 (4)As5xii—Ca4—Ca6i147.74 (6)
Ca4xii—As5—Ca4130.79 (4)As5—Ca4—Ca6i115.26 (3)
As5xii—As5—Ca1117.25 (2)As4xiii—Ca4—Ca6i51.14 (3)
Ca2ii—As5—Ca172.14 (3)Ca5—Ca4—Ca6i71.80 (4)
Ca2v—As5—Ca171.08 (3)As4—Ca4—Ca6i117.74 (4)
Ca5xiii—As5—Ca1139.04 (4)Ca5xiii—Ca4—Ca6i95.66 (4)
Ca5v—As5—Ca168.11 (3)Ca1—Ca4—Ca6i94.61 (3)
Ca4xii—As5—Ca1135.68 (4)Ca1xi—Ca4—Ca6i147.35 (5)
Ca4—As5—Ca170.48 (3)As1—Ca4—Ca6xiii98.51 (4)
As5xii—As5—Ca1xiv117.25 (2)As1xi—Ca4—Ca6xiii48.28 (3)
Ca2ii—As5—Ca1xiv71.08 (3)As5xii—Ca4—Ca6xiii115.26 (3)
Ca2v—As5—Ca1xiv72.14 (3)As5—Ca4—Ca6xiii147.74 (6)
Ca5xiii—As5—Ca1xiv68.11 (3)As4xiii—Ca4—Ca6xiii51.14 (3)
Ca5v—As5—Ca1xiv139.04 (4)Ca5—Ca4—Ca6xiii71.80 (4)
Ca4xii—As5—Ca1xiv70.48 (3)As4—Ca4—Ca6xiii117.74 (4)
Ca4—As5—Ca1xiv135.68 (4)Ca5xiii—Ca4—Ca6xiii95.66 (4)
Ca1—As5—Ca1xiv125.50 (4)Ca1—Ca4—Ca6xiii147.35 (5)
As1—Ca1—As2100.48 (4)Ca1xi—Ca4—Ca6xiii94.61 (3)
As1—Ca1—As396.16 (4)Ca6i—Ca4—Ca6xiii60.40 (5)
As2—Ca1—As375.91 (3)As1—Ca5—As1xi113.52 (6)
As1—Ca1—As1v163.39 (4)As1—Ca5—As5i98.54 (2)
As2—Ca1—As1v95.32 (4)As1xi—Ca5—As5i147.88 (4)
As3—Ca1—As1v92.60 (3)As1—Ca5—As5x147.88 (4)
As1—Ca1—As480.13 (3)As1xi—Ca5—As5x98.54 (2)
As2—Ca1—As4171.57 (4)As5i—Ca5—As5x49.36 (4)
As3—Ca1—As4112.45 (4)As1—Ca5—As483.12 (4)
As1v—Ca1—As483.49 (3)As1xi—Ca5—As483.12 (4)
As1—Ca1—As592.08 (3)As5i—Ca5—As499.44 (4)
As2—Ca1—As579.97 (3)As5x—Ca5—As499.44 (4)
As3—Ca1—As5155.54 (4)As1—Ca5—Ca457.38 (3)
As1v—Ca1—As585.63 (3)As1xi—Ca5—Ca457.38 (3)
As4—Ca1—As591.62 (3)As5i—Ca5—Ca4152.44 (3)
As1—Ca1—Ca6118.91 (4)As5x—Ca5—Ca4152.44 (3)
As2—Ca1—Ca6131.17 (4)As4—Ca5—Ca466.93 (5)
As3—Ca1—Ca672.48 (4)As1—Ca5—As4i86.67 (4)
As1v—Ca1—Ca650.906 (19)As1xi—Ca5—As4i86.67 (4)
As4—Ca1—Ca653.65 (3)As5i—Ca5—As4i97.54 (4)
As5—Ca1—Ca6122.77 (4)As5x—Ca5—As4i97.54 (4)
As1—Ca1—Ca258.51 (3)As4—Ca5—As4i161.30 (6)
As2—Ca1—Ca2114.80 (4)Ca4—Ca5—As4i94.37 (5)
As3—Ca1—Ca250.96 (3)As1—Ca5—Ca1i56.97 (2)
As1v—Ca1—Ca2118.75 (4)As1xi—Ca5—Ca1i139.54 (6)
As4—Ca1—Ca272.78 (3)As5i—Ca5—Ca1i61.07 (3)
As5—Ca1—Ca2148.16 (4)As5x—Ca5—Ca1i99.68 (4)
Ca6—Ca1—Ca270.07 (3)As4—Ca5—Ca1i128.45 (3)
As1—Ca1—Ca5v117.30 (4)Ca4—Ca5—Ca1i107.53 (4)
As2—Ca1—Ca5v115.73 (4)As4i—Ca5—Ca1i55.32 (3)
As3—Ca1—Ca5v139.77 (5)As1—Ca5—Ca1xvii139.54 (6)
As1v—Ca1—Ca5v49.73 (3)As1xi—Ca5—Ca1xvii56.97 (2)
As4—Ca1—Ca5v57.39 (3)As5i—Ca5—Ca1xvii99.68 (4)
As5—Ca1—Ca5v50.81 (3)As5x—Ca5—Ca1xvii61.07 (3)
Ca6—Ca1—Ca5v72.00 (4)As4—Ca5—Ca1xvii128.45 (3)
Ca2—Ca1—Ca5v128.96 (4)Ca4—Ca5—Ca1xvii107.53 (4)
As1—Ca1—Ca451.55 (3)As4i—Ca5—Ca1xvii55.32 (3)
As2—Ca1—Ca4113.60 (4)Ca1i—Ca5—Ca1xvii102.64 (5)
As3—Ca1—Ca4146.77 (4)As1—Ca5—Ca4x110.65 (4)
As1v—Ca1—Ca4116.86 (4)As1xi—Ca5—Ca4x110.65 (4)
As4—Ca1—Ca460.17 (3)As5i—Ca5—Ca4x52.32 (3)
As5—Ca1—Ca449.97 (3)As5x—Ca5—Ca4x52.32 (3)
Ca6—Ca1—Ca4113.33 (4)As4—Ca5—Ca4x52.67 (4)
Ca2—Ca1—Ca498.64 (4)Ca4—Ca5—Ca4x119.60 (5)
Ca5v—Ca1—Ca467.13 (3)As4i—Ca5—Ca4x146.03 (6)
As1—Ca1—Ca2v133.15 (4)Ca1i—Ca5—Ca4x109.11 (4)
As2—Ca1—Ca2v53.52 (3)Ca1xvii—Ca5—Ca4x109.11 (4)
As3—Ca1—Ca2v110.55 (4)As1—Ca5—Ca255.25 (2)
As1v—Ca1—Ca2v54.93 (3)As1xi—Ca5—Ca2152.12 (6)
As4—Ca1—Ca2v120.16 (4)As5i—Ca5—Ca250.42 (2)
As5—Ca1—Ca2v49.54 (2)As5x—Ca5—Ca295.09 (4)
Ca6—Ca1—Ca2v105.82 (3)As4—Ca5—Ca270.68 (3)
Ca2—Ca1—Ca2v161.49 (4)Ca4—Ca5—Ca2102.03 (3)
Ca5v—Ca1—Ca2v62.84 (3)As4i—Ca5—Ca2115.54 (3)
Ca4—Ca1—Ca2v99.47 (4)Ca1i—Ca5—Ca260.28 (3)
As1—Ca1—Ca3v146.01 (4)Ca1xvii—Ca5—Ca2149.46 (5)
As2—Ca1—Ca3v66.08 (3)Ca4x—Ca5—Ca260.47 (3)
As3—Ca1—Ca3v51.14 (3)As1—Ca5—Ca2xi152.12 (6)
As1v—Ca1—Ca3v47.15 (2)As1xi—Ca5—Ca2xi55.25 (2)
As4—Ca1—Ca3v117.83 (4)As5i—Ca5—Ca2xi95.09 (4)
As5—Ca1—Ca3v114.44 (4)As5x—Ca5—Ca2xi50.42 (2)
Ca6—Ca1—Ca3v65.13 (3)As4—Ca5—Ca2xi70.68 (3)
Ca2—Ca1—Ca3v97.40 (4)Ca4—Ca5—Ca2xi102.03 (3)
Ca5v—Ca1—Ca3v96.35 (4)As4i—Ca5—Ca2xi115.54 (3)
Ca4—Ca1—Ca3v162.04 (5)Ca1i—Ca5—Ca2xi149.46 (5)
Ca2v—Ca1—Ca3v65.31 (4)Ca1xvii—Ca5—Ca2xi60.28 (3)
As3—Ca2—As5i173.15 (5)Ca4x—Ca5—Ca2xi60.47 (3)
As3—Ca2—As2i101.80 (3)Ca2—Ca5—Ca2xi120.73 (5)
As5i—Ca2—As2i84.15 (3)As1xv—Ca6—As1v160.05 (7)
As3—Ca2—As2viii97.73 (3)As1xv—Ca6—As4ix92.05 (2)
As5i—Ca2—As2viii83.74 (3)As1v—Ca6—As4ix100.50 (3)
As2i—Ca2—As2viii47.46 (3)As1xv—Ca6—As4100.51 (3)
As3—Ca2—As191.89 (4)As1v—Ca6—As492.05 (2)
As5i—Ca2—As191.39 (3)As4ix—Ca6—As4101.95 (5)
As2i—Ca2—As191.02 (3)As1xv—Ca6—Ca1115.33 (3)
As2viii—Ca2—As1138.45 (4)As1v—Ca6—Ca158.77 (2)
As3—Ca2—As1xv86.41 (3)As4ix—Ca6—Ca1147.96 (4)
As5i—Ca2—As1xv87.09 (3)As4—Ca6—Ca158.76 (2)
As2i—Ca2—As1xv131.29 (4)As1xv—Ca6—Ca1xviii58.77 (2)
As2viii—Ca2—As1xv84.01 (3)As1v—Ca6—Ca1xviii115.33 (3)
As1—Ca2—As1xv137.10 (4)As4ix—Ca6—Ca1xviii58.76 (2)
As3—Ca2—Ca153.93 (3)As4—Ca6—Ca1xviii147.97 (4)
As5i—Ca2—Ca1124.96 (4)Ca1—Ca6—Ca1xviii149.70 (6)
As2i—Ca2—Ca1126.48 (4)As1xv—Ca6—Ca4v143.80 (4)
As2viii—Ca2—Ca1151.28 (4)As1v—Ca6—Ca4v50.75 (2)
As1—Ca2—Ca150.26 (3)As4ix—Ca6—Ca4v51.76 (3)
As1xv—Ca2—Ca197.28 (3)As4—Ca6—Ca4v89.17 (4)
As3—Ca2—Ca2iv50.77 (2)Ca1—Ca6—Ca4v99.58 (3)
As5i—Ca2—Ca2iv133.55 (2)Ca1xviii—Ca6—Ca4v95.54 (3)
As2i—Ca2—Ca2iv53.93 (2)As1xv—Ca6—Ca4x50.75 (2)
As2viii—Ca2—Ca2iv54.26 (2)As1v—Ca6—Ca4x143.80 (4)
As1—Ca2—Ca2iv106.72 (2)As4ix—Ca6—Ca4x89.17 (4)
As1xv—Ca2—Ca2iv105.034 (19)As4—Ca6—Ca4x51.76 (3)
Ca1—Ca2—Ca2iv98.27 (2)Ca1—Ca6—Ca4x95.54 (3)
As3—Ca2—Ca1i127.17 (4)Ca1xviii—Ca6—Ca4x99.58 (3)
As5i—Ca2—Ca1i59.38 (3)Ca4v—Ca6—Ca4x119.60 (5)
As2i—Ca2—Ca1i49.75 (3)As1xv—Ca6—Ca6ix99.97 (3)
As2viii—Ca2—Ca1i90.05 (4)As1v—Ca6—Ca6ix99.97 (3)
As1—Ca2—Ca1i53.30 (3)As4ix—Ca6—Ca6ix50.97 (2)
As1xv—Ca2—Ca1i146.42 (4)As4—Ca6—Ca6ix50.97 (2)
Ca1—Ca2—Ca1i103.38 (3)Ca1—Ca6—Ca6ix105.15 (3)
Ca2iv—Ca2—Ca1i97.91 (2)Ca1xviii—Ca6—Ca6ix105.15 (3)
As3—Ca2—Ca1xv117.40 (4)Ca4v—Ca6—Ca6ix59.80 (2)
As5i—Ca2—Ca1xv58.75 (3)Ca4x—Ca6—Ca6ix59.80 (2)
As2i—Ca2—Ca1xv89.54 (4)As1xv—Ca6—Ca3viii46.20 (3)
As2viii—Ca2—Ca1xv49.11 (3)As1v—Ca6—Ca3viii113.85 (5)
As1—Ca2—Ca1xv149.92 (4)As4ix—Ca6—Ca3viii118.74 (3)
As1xv—Ca2—Ca1xv46.38 (2)As4—Ca6—Ca3viii124.43 (3)
Ca1—Ca2—Ca1xv143.14 (4)Ca1—Ca6—Ca3viii92.94 (4)
Ca2iv—Ca2—Ca1xv97.81 (2)Ca1xviii—Ca6—Ca3viii60.95 (3)
Ca1i—Ca2—Ca1xv106.95 (4)Ca4v—Ca6—Ca3viii145.51 (4)
As3—Ca2—Ca4x122.20 (4)Ca4x—Ca6—Ca3viii90.66 (3)
As5i—Ca2—Ca4x51.17 (3)Ca6ix—Ca6—Ca3viii146.17 (2)
As2i—Ca2—Ca4x133.52 (4)As1xv—Ca6—Ca3v113.85 (5)
As2viii—Ca2—Ca4x107.46 (4)As1v—Ca6—Ca3v46.20 (3)
As1—Ca2—Ca4x100.95 (4)As4ix—Ca6—Ca3v124.43 (3)
As1xv—Ca2—Ca4x47.48 (3)As4—Ca6—Ca3v118.74 (3)
Ca1—Ca2—Ca4x93.83 (4)Ca1—Ca6—Ca3v60.95 (3)
Ca2iv—Ca2—Ca4x151.41 (3)Ca1xviii—Ca6—Ca3v92.94 (4)
Ca1i—Ca2—Ca4x104.36 (4)Ca4v—Ca6—Ca3v90.66 (3)
Ca1xv—Ca2—Ca4x58.77 (3)Ca4x—Ca6—Ca3v145.51 (4)
As3—Ca2—Ca3viii51.18 (3)Ca6ix—Ca6—Ca3v146.17 (2)
As5i—Ca2—Ca3viii124.16 (4)Ca3viii—Ca6—Ca3v67.66 (5)
As2i—Ca2—Ca3viii105.77 (4)As1xv—Ca6—Ca259.33 (2)
As2viii—Ca2—Ca3viii67.53 (3)As1v—Ca6—Ca2112.86 (3)
As1—Ca2—Ca3viii141.40 (4)As4ix—Ca6—Ca2145.04 (3)
As1xv—Ca2—Ca3viii44.89 (2)As4—Ca6—Ca267.851 (19)
Ca1—Ca2—Ca3viii93.16 (4)Ca1—Ca6—Ca256.14 (3)
Ca2iv—Ca2—Ca3viii61.37 (2)Ca1xviii—Ca6—Ca2111.93 (3)
Ca1i—Ca2—Ca3viii155.47 (4)Ca4v—Ca6—Ca2152.53 (3)
Ca1xv—Ca2—Ca3viii66.39 (3)Ca4x—Ca6—Ca257.74 (2)
Ca4x—Ca2—Ca3viii92.29 (3)Ca6ix—Ca6—Ca2110.57 (3)
As1iv—Ca3—As1153.39 (7)Ca3viii—Ca6—Ca256.98 (3)
As1iv—Ca3—As3i99.68 (3)Ca3v—Ca6—Ca287.77 (4)
Symmetry codes: (i) x+1/2, y+1/2, z; (ii) x+1/2, y1/2, z; (iii) x, y, z+1; (iv) x, y, z+1; (v) x1/2, y+1/2, z; (vi) x1/2, y+1/2, z+1; (vii) x+1/2, y1/2, z+1; (viii) x+1/2, y+1/2, z+1; (ix) x, y+1, z; (x) x+1/2, y+1/2, z; (xi) x, y, z; (xii) x, y, z; (xiii) x+1/2, y1/2, z; (xiv) x, y, z; (xv) x+1/2, y+1/2, z; (xvi) x+1/2, y+1/2, z+1; (xvii) x+1/2, y+1/2, z; (xviii) x, y+1, z.
 

Acknowledgements

This research was supported financially by the Deutsche Forschungsgemeinschaft within the priority program SPP 1458 and the Technische Universität München within the funding program Open Access Publishing.

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