A novel monoclinic phase of impurity-doped CaGa₂S₄ as a phosphor with high emission intensity

In the solid-state synthesis of impurity-doped CaGa₂S₄, calcium tetra­thio­digallate(III), a novel phosphor material (denominated as the X-phase), with monoclinic symmetry in the space group P2₁/a, has been discovered. Its emission intensity is higher than that of the known ortho­rhom­bic polymorph of CaGa₂S₄ crystallizing in the space group Fddd. The asymmetric unit of the monoclinic phase consists of two Ca, four Ga and eight S sites. Each of the Ca and Ga atoms is surrounded by seven and four sulfide ions, respectively, thereby sharing each of the sulfur sites with the nearest neighbours. In contrast, the corresponding sites in the ortho­rhom­bic phase are surrounded by eight and four S atoms, respectively. The photoluminescence peaks from Mn²⁺ and Ce³⁺ in the doped X-phase, both of which are supposed to replace Ca²⁺ ions, have been observed to shift towards the high energy side in comparison with those in the ortho­rhom­bic phase. This suggests that the crystal field around the Mn²⁺ and Ce³⁺ ions in the X-phase is weaker than that in the ortho­rhom­bic phase.

Key indicators

• Single-crystal X-ray study
• T = 270 K
• Mean [sigma](Ga-S) = 0.001 Å
• R factor = 0.038
• wR factor = 0.050
• Data-to-parameter ratio = 49.1

checkCIF/PLATON results

No syntax errors found



Alert level B
PLAT974_ALERT_2_B Large Calcd. Negative Residual Density on    Ga2      -1.93 eA-3
PLAT974_ALERT_2_B Large Calcd. Negative Residual Density on    Ga4      -1.76 eA-3
PLAT974_ALERT_2_B Large Calcd. Negative Residual Density on    Ga1      -1.73 eA-3
PLAT974_ALERT_2_B Large Calcd. Negative Residual Density on    Ga3      -1.64 eA-3

Alert level C
DIFMN02_ALERT_2_C  The minimum difference density is < -0.1*ZMAX*0.75
            _refine_diff_density_min given =     -3.100
            Test value =     -2.325
DIFMN03_ALERT_1_C  The minimum difference density is < -0.1*ZMAX*0.75
            The relevant atom site should be identified.
DIFMX01_ALERT_2_C  The maximum difference density is > 0.1*ZMAX*0.75
            _refine_diff_density_max given =      2.640
            Test value =      2.325
DIFMX02_ALERT_1_C  The maximum difference density is > 0.1*ZMAX*0.75
            The relevant atom site should be identified.
PLAT045_ALERT_1_C Calculated and Reported Z Differ by ............       0.50 Ratio
PLAT097_ALERT_2_C Large Reported Max.  (Positive) Residual Density       2.64 eA-3
PLAT098_ALERT_2_C Large Reported Min.  (Negative) Residual Density      -3.10 eA-3
PLAT250_ALERT_2_C Large U3/U1 Ratio for Average U(i,j) Tensor ....        2.1
PLAT910_ALERT_3_C Missing # of FCF Reflections Below Th(Min) .....          4
PLAT911_ALERT_3_C Missing # FCF Refl Between THmin & STh/L=  0.600         13
PLAT912_ALERT_4_C Missing # of FCF Reflections Above STh/L=  0.600          9
PLAT918_ALERT_3_C Reflection(s) # with I(obs) much smaller I(calc)          1
PLAT924_ALERT_1_C The Reported and Calculated Rho(min) Differ by .       1.17 eA-3
PLAT925_ALERT_1_C The Reported and Calculated Rho(max) Differ by .       1.76 eA-3

Alert level G
PLAT004_ALERT_5_G Info: Polymeric Structure Found with Dimension .          1
PLAT005_ALERT_5_G No _iucr_refine_instructions_details in CIF ....          ?
PLAT128_ALERT_4_G Alternate Setting of Space-group P21/c   .......      P21/a
PLAT232_ALERT_2_G Hirshfeld Test Diff (M-X)  Ga4    --  S5      ..        5.8 su
PLAT790_ALERT_4_G Centre of Gravity not Within Unit Cell: Resd.  #          2
              Ca
PLAT808_ALERT_5_G No Parseable SHELXL Style Weighting Scheme Found          !
PLAT929_ALERT_5_G No Weight Pars,Obs and Calc R1,wR2,S not checked          !

   0 ALERT level A = Most likely a serious problem - resolve or explain
   4 ALERT level B = A potentially serious problem, consider carefully
  14 ALERT level C = Check. Ensure it is not caused by an omission or oversight
   7 ALERT level G = General information/check it is not something unexpected

   5 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
  10 ALERT type 2 Indicator that the structure model may be wrong or deficient
   3 ALERT type 3 Indicator that the structure quality may be low
   3 ALERT type 4 Improvement, methodology, query or suggestion
   4 ALERT type 5 Informative message, check

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S1. Comment

The alkaline earth thiodigallates MGa₂S₄ (M = Ca, Sr, Ba) have been studied as candidates for phosphor host materials because of their various emissions when doped with a rare earth element (Peters & Baglio, 1972; Georgobiani et al., 1995; Bessière et al., 2004; Takizawa & Hidaka, 2008). Especially, CaGa₂S₄ doped with Ce³⁺ and Eu²⁺ shows strong blue and green emissions. This compound normally belongs to the orthorhombic system, crystallizing in space group Fddd (Eisenmann et al., 1983). However, in the synthesis of CaGa₂S₄ using solid state reactions, a novel phosphor (we call it the X-phase) has unexpectedly appeared. In this paper, the crystal structure of the X-phase investigated by powder and single-crystal X-ray diffraction (XRD) measurements is reported.

Powder XRD patterns of the X-phase are shown in Fig. 1. This phase happened to be generated when doped with one of the impurities such as Mn, Ge, Sn, La, Ce, Nd, Sm, Dy, intentionally incorporated as an activator of fluorescence or phosphorescence. Thus it is expected that the X-phase is strongly related with the dopant. However, detailed conditions how to prepare the X-phase from a directed preparation route have not been clarified yet. From the analysis of the single-crystal XRD data, the chemical formula of the compound in the X-phase was shown to be CaGa₂S₄. The simulation of the powder XRD pattern corresponds well to the experimental pattern as shown in Fig. 1. Hence we can conclude that the X-phase is a newly found polymorph of CaGa₂S₄.

The unit cell of the X-phase is shown in Figs. 2 and 3; the asymmetric unit consists of two Ca sites, four Ga sites and seven S sites. Figs. 4 and 5 show the environment of the cation sites in the unit cell. In the X-phase, each Ca site is surrounded by seven sulfur atoms forming a distorted enneahedron. Each of the involved sulfur atoms is shared by the adjacent one or two Ca sites and by two Ga sites. The Ca—S distances range from 2.8261 (10) to 3.0823 (13) Å. Each Ga site is tetrahedrally surrounded by sulfur atoms which are also shared by adjacent two Ca sites and two Ga sites. The Ga—S distances and the S—Ga—S angles range from 2.2254 (11) to 2.3116 (11) Å and from 93.54 (3) to 124.12 (3) °, respectively. In the orthorhombic phase, each of the three Ca sites and the two Ga sites is in an eightfold and fourfold coordination environment, respectively, by sulfur atoms. Each of the sulfur atoms of these sites is shared by adjacent two Ca sites and two Ga sites. The Ca—S distances in this polymorph range from 2.970 to 3.130 Å. The Ga—S distances and the S—Ga—S angles range from 2.240 to 2.318 Å and from 96.6 to 125°. It should be noted that the coordination number of the Ca sites in the X-phase is reduced by one compared to that of the orthorhombic phase, while the Ga sites are tetrahedrally surrounded in both phases. Nevertheless, the framework built up from the GaS₄ tetrahedra and their connection modes (corner and edge-sharing) is quite different in the two phases.

The intensities of photoluminescence from Mn²⁺ and Ce³⁺ in the X-phase were about four and eight times higher than those in the orthorhombic phase. These emission peaks shifted toward the high energy side in comparison with those in the orthorhombic phase. Mn²⁺ and Ce³⁺ ions are known to be very sensitive with respect to the crystal field (Peters & Baglio, 1972; Provenzano & White, 1991; Barthou et al., 1994; Wang et al., 2003). Thus the observed shifts of the emission peaks are assumed to be caused by a weakened crystal field originating from the decrease in the coordination number of the Ca sites in the X-phase.

Related literature

For the crystal structure of the orthorhombic form of CaGa₂S₄, see: Eisenmann et al. (1983). For the emission properties of CaGa₂S₄, see: Peters & Baglio (1972); Georgobiani et al. (1995); Bessière et al. (2004); Takizawa & Hidaka (2008). For synthetic details, see: Boitier et al. (2009); Obonai et al. (2009). For the Mn²⁺ emission properties in various compounds, see: Barthou et al. (1994); Provenzano & White (1991); Wang et al. (2003). For crystallographic background, see: Carruthers & Watkin (1979).

S2. Experimental

A mixture of CaS (4 N) and Ga₂S₃ (6 N) was used as a starting material added with a small amount of a rare earth element (REE) or a transition metal (TM) as an activator. It was weighed to 0.5 g in total according to the formula Ca_1-xM_xGa₂S₄ (M = REE or TM) (Boitier et al., 2009; Obonai et al., 2009). The mixture was carefully stirred to be homogenized under Ar atmosphere, and then sealed in a silica glass capsule under vacuum of 10 ^-4 Pa, where the inner surface of the capsule was coated with a carbon film to prevent the reaction between the starting materials and the container. It was sintered at 1411 K for 1 h. The X-phase samples were sometimes and unexpectedly synthesized and the detailed condition how and when the X-phase emerges has not been clarified yet.

S3. Refinement

Freeing of the site occupation factors for the metal and the sulfur atoms revealed no noticeable incorporation of the dopant metals or of vacancies at the S positions. The highest difference peak of 2.64 e Å^-3 is located 1.40 Å from the Ga4 atom; the deepest hole (-3.11 e Å^-3) is 1.39 Å from the Ga4 atom.

Computing details

Data collection: CrystalClear (Rigaku/MSC and Rigaku, 2006); cell refinement: CrystalClear (Rigaku/MSC and Rigaku, 2006); data reduction: CrystalStructure (Rigaku/MSC and Rigaku, 2006); program(s) used to solve structure: SIR92 (Altomare et al., 1994); program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003); molecular graphics: VESTA 3 (Momma & Izumi, 2011); software used to prepare material for publication: CrystalStructure (Rigaku/MSC and Rigaku, 2006).

Figures

	Fig. 1. Experimental and siumlated X-ray powder diffraction patterns of the X-phase of CaGa2S4 together with the known orthorhombic form for comparison.
	Fig. 2. The unit cell of the X-phase of CaGa2S4 viewed along [100].
	Fig. 3. The unit cell of the X-phase of CaGa2S4 viewed along [001].
	Fig. 4. The environment of the cation sites in the X-phase: Ca sites.
	Fig. 5. The environment of the cation sites in the X-phase: Ga sites.

calcium tetrathiodigallate(III)

Crystal data

CaGa2S4	F(000) = 1168.00
Mr = 307.76	Dx = 3.237 Mg m^−3
Monoclinic, P21/a	Mo Kα radiation, λ = 0.71075 Å
Hall symbol: -P 2yab	Cell parameters from 3521 reflections
a = 6.841 (3) Å	θ = 3.2–27.5°
b = 27.069 (9) Å	µ = 10.52 mm^−1
c = 7.231 (3) Å	T = 270 K
β = 109.413 (5)°	Block, colorless
V = 1262.9 (8) Å^3	0.10 × 0.10 × 0.05 mm
Z = 8

Data collection

Rigaku Saturn724+ diffractometer	2869 independent reflections
Graphite monochromator	256 reflections with F^2 > 2σ(F^2)
Detector resolution: 7.31 pixels mm^-1	Rint = 0.047
ω scans	θmax = 27.5°
Absorption correction: multi-scan (REQABS; Jacobson, 1998)	h = −8→6
Tmin = 0.417, Tmax = 0.591	k = −35→26
8869 measured reflections	l = −9→9

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.038	Secondary atom site location: difference Fourier map
wR(F^2) = 0.050	Chebychev polynomial with 3 parameters (Carruthers & Watkin, 1979) 6334.0000 8721.6900 0.0000
S = 1.21	(Δ/σ)max < 0.001
2869 reflections	Δρmax = 2.64 e Å^−3
127 parameters	Δρmin = −3.10 e Å^−3

Special details

Geometry. ENTER SPECIAL DETAILS OF THE MOLECULAR GEOMETRY

Refinement. Refinement was performed using reflections with F² > 2.0 σ(F²). The weighted R-factor (wR) and goodness of fit (S) are based on F². R-factor (gt) are based on F. The threshold expression of F² > 2.0 σ(F²) is used only for calculating R-factor (gt).

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

	x	y	z	Uiso*/Ueq
Ga1	0.41763 (6)	0.234320 (10)	0.54983 (6)	0.01027 (10)
Ga2	0.63163 (6)	0.150170 (10)	0.29040 (6)	0.01047 (10)
Ga3	−0.05236 (6)	0.052250 (10)	0.27118 (6)	0.01054 (10)
Ga4	0.23350 (6)	0.064220 (10)	0.01510 (6)	0.01095 (10)
Ca1	−0.44242 (12)	0.07086 (3)	−0.32662 (11)	0.0133 (2)
Ca2	0.09658 (12)	0.19323 (3)	0.04330 (11)	0.0145 (2)
S1	−0.08531 (14)	0.09720 (3)	−0.01062 (13)	0.0114 (2)
S2	−0.13487 (14)	0.09906 (4)	0.49207 (13)	0.0125 (2)
S3	0.24485 (13)	0.25319 (4)	0.75754 (13)	0.0128 (2)
S4	0.37219 (14)	0.15701 (3)	0.42780 (13)	0.0115 (2)
S5	0.28330 (14)	0.02921 (3)	0.31401 (13)	0.0112 (2)
S6	0.30654 (14)	0.27904 (3)	0.26168 (13)	0.0114 (2)
S7	−0.26440 (15)	−0.01372 (4)	0.21648 (14)	0.0157 (2)
S8	0.42875 (14)	0.13001 (3)	−0.02150 (13)	0.0118 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ga1	0.0099 (2)	0.0137 (2)	0.0084 (2)	0.00054 (16)	0.00453 (16)	−0.00112 (16)
Ga2	0.0109 (2)	0.0120 (2)	0.0094 (2)	0.00015 (16)	0.00450 (16)	−0.00010 (16)
Ga3	0.0111 (2)	0.0126 (2)	0.0100 (2)	0.00015 (16)	0.00645 (16)	−0.00067 (16)
Ga4	0.0114 (2)	0.0141 (2)	0.0091 (2)	−0.00123 (17)	0.00581 (16)	−0.00087 (16)
Ca1	0.0127 (4)	0.0164 (4)	0.0114 (3)	−0.0016 (3)	0.0049 (3)	0.0007 (3)
Ca2	0.0146 (4)	0.0145 (4)	0.0140 (4)	−0.0003 (3)	0.0044 (3)	−0.0005 (3)
S1	0.0106 (4)	0.0161 (4)	0.0078 (4)	0.0007 (3)	0.0037 (3)	0.0016 (3)
S2	0.0153 (4)	0.0151 (5)	0.0084 (4)	0.0037 (3)	0.0056 (3)	−0.0004 (3)
S3	0.0074 (4)	0.0234 (5)	0.0088 (4)	0.0017 (3)	0.0043 (3)	−0.0004 (3)
S4	0.0134 (4)	0.0118 (4)	0.0114 (4)	−0.0002 (3)	0.0069 (3)	−0.0008 (3)
S5	0.0118 (4)	0.0151 (4)	0.0070 (4)	0.0024 (3)	0.0035 (3)	0.0015 (3)
S6	0.0135 (5)	0.0130 (4)	0.0094 (4)	0.0015 (3)	0.0062 (3)	0.0006 (3)
S7	0.0197 (5)	0.0167 (5)	0.0168 (5)	−0.0072 (3)	0.0142 (4)	−0.0073 (3)
S8	0.0124 (4)	0.0145 (4)	0.0093 (4)	−0.0029 (3)	0.0049 (3)	−0.0019 (3)

Geometric parameters (Å, º)

Ga1—S3	2.2569 (11)	Ga4—S8	2.2936 (9)
Ga1—S3^i	2.2685 (8)	Ca1—S1	2.8261 (10)
Ga1—S4	2.2522 (8)	Ca1—S2^iv	2.9260 (14)
Ga1—S6	2.3090 (9)	Ca1—S4^v	2.9500 (11)
Ga2—S2^ii	2.2458 (9)	Ca1—S5^v	2.8814 (10)
Ga2—S4	2.3116 (11)	Ca1—S5^iii	2.9095 (11)
Ga2—S6^i	2.3048 (9)	Ca1—S7^vi	2.8480 (14)
Ga2—S8	2.2868 (8)	Ca1—S8^vii	3.0823 (13)
Ga3—S1	2.3190 (10)	Ca2—S1	2.8522 (11)
Ga3—S2	2.2526 (11)	Ca2—S3^iv	3.0538 (13)
Ga3—S5	2.2989 (10)	Ca2—S3^viii	2.9762 (10)
Ga3—S7	2.2513 (10)	Ca2—S4	2.9599 (10)
Ga4—S1	2.3062 (10)	Ca2—S6	2.9059 (11)
Ga4—S5	2.2795 (10)	Ca2—S6^ix	3.0127 (14)
Ga4—S7^iii	2.2254 (11)	Ca2—S8	3.0033 (13)
S5···S7^x	3.4654 (14)	S7···S5^x	3.4654 (14)
S3—Ga1—S3^i	98.37 (3)	S3^iv—Ca2—S6^ix	130.31 (3)
S3—Ga1—S4	115.87 (4)	S3^iv—Ca2—S8	76.03 (3)
S3—Ga1—S6	113.19 (3)	S3^viii—Ca2—S4	158.30 (4)
S3^i—Ga1—S4	112.04 (3)	S3^viii—Ca2—S6	97.31 (3)
S3^i—Ga1—S6	118.40 (3)	S3^viii—Ca2—S6^ix	73.81 (3)
S4—Ga1—S6	99.93 (3)	S3^viii—Ca2—S8	130.42 (3)
S2^ii—Ga2—S4	104.61 (3)	S4—Ca2—S6	73.08 (2)
S2^ii—Ga2—S6^i	106.99 (3)	S4—Ca2—S6^ix	85.13 (3)
S2^ii—Ga2—S8	124.12 (3)	S4—Ca2—S8	71.28 (3)
S4—Ga2—S6^i	117.90 (3)	S6—Ca2—S6^ix	78.97 (3)
S4—Ga2—S8	98.16 (3)	S6—Ca2—S8	106.10 (3)
S6^i—Ga2—S8	105.82 (3)	S6^ix—Ca2—S8	152.63 (3)
S1—Ga3—S2	110.72 (3)	Ga3—S1—Ga4	85.00 (3)
S1—Ga3—S5	93.54 (3)	Ga3—S1—Ca1	112.55 (3)
S1—Ga3—S7	113.14 (3)	Ga3—S1—Ca2	116.58 (3)
S2—Ga3—S5	122.11 (3)	Ga4—S1—Ca1	120.51 (4)
S2—Ga3—S7	105.79 (4)	Ga4—S1—Ca2	89.07 (3)
S5—Ga3—S7	111.40 (3)	Ca1—S1—Ca2	124.13 (3)
S1—Ga4—S5	94.40 (3)	Ga2^vii—S2—Ga3	100.25 (3)
S1—Ga4—S7^iii	120.06 (3)	Ga2^vii—S2—Ca1^xi	89.39 (3)
S1—Ga4—S8	105.16 (3)	Ga3—S2—Ca1^xi	123.91 (4)
S5—Ga4—S7^iii	115.87 (3)	Ga1—S3—Ga1^ix	102.30 (3)
S5—Ga4—S8	121.53 (3)	Ga1—S3—Ca2^xi	134.04 (4)
S7^iii—Ga4—S8	100.69 (4)	Ga1—S3—Ca2^xii	95.21 (3)
S1—Ca1—S2^iv	74.89 (3)	Ga1^ix—S3—Ca2^xi	92.90 (3)
S1—Ca1—S4^v	111.74 (3)	Ga1^ix—S3—Ca2^xii	141.19 (4)
S1—Ca1—S5^v	163.07 (4)	Ca2^xi—S3—Ca2^xii	99.38 (3)
S1—Ca1—S5^iii	89.75 (3)	Ga1—S4—Ga2	102.54 (3)
S1—Ca1—S7^vi	114.26 (3)	Ga1—S4—Ca1^xiii	121.53 (3)
S1—Ca1—S8^vii	70.50 (3)	Ga1—S4—Ca2	91.27 (3)
S2^iv—Ca1—S4^v	75.72 (3)	Ga2—S4—Ca1^xiii	87.56 (3)
S2^iv—Ca1—S5^v	92.74 (3)	Ga2—S4—Ca2	87.89 (3)
S2^iv—Ca1—S5^iii	86.54 (3)	Ca1^xiii—S4—Ca2	147.08 (3)
S2^iv—Ca1—S7^vi	160.92 (4)	Ga3—S5—Ga4	86.08 (3)
S2^iv—Ca1—S8^vii	127.19 (3)	Ga3—S5—Ca1^xiii	109.71 (4)
S4^v—Ca1—S5^v	75.27 (2)	Ga3—S5—Ca1^iii	127.11 (3)
S4^v—Ca1—S5^iii	146.76 (4)	Ga4—S5—Ca1^xiii	122.66 (3)
S4^v—Ca1—S7^vi	113.32 (3)	Ga4—S5—Ca1^iii	110.69 (4)
S4^v—Ca1—S8^vii	81.50 (3)	Ca1^xiii—S5—Ca1^iii	102.20 (3)
S5^v—Ca1—S5^iii	77.80 (3)	Ga1—S6—Ga2^ix	112.31 (4)
S5^v—Ca1—S7^vi	74.43 (3)	Ga1—S6—Ca2	91.50 (3)
S5^v—Ca1—S8^vii	126.39 (3)	Ga1—S6—Ca2^i	121.80 (3)
S5^iii—Ca1—S7^vi	77.09 (3)	Ga2^ix—S6—Ca2	122.40 (3)
S5^iii—Ca1—S8^vii	130.86 (3)	Ga2^ix—S6—Ca2^i	106.99 (3)
S7^vi—Ca1—S8^vii	71.73 (3)	Ca2—S6—Ca2^i	101.95 (3)
S1—Ca2—S3^iv	128.30 (3)	Ga3—S7—Ga4^iii	113.74 (5)
S1—Ca2—S3^viii	97.70 (3)	Ga3—S7—Ca1^vi	148.67 (5)
S1—Ca2—S4	86.52 (3)	Ga4^iii—S7—Ca1^vi	97.39 (4)
S1—Ca2—S6	156.52 (4)	Ga2—S8—Ga4	104.91 (4)
S1—Ca2—S6^ix	88.01 (3)	Ga2—S8—Ca1^ii	127.28 (3)
S1—Ca2—S8	77.16 (3)	Ga2—S8—Ca2	87.30 (3)
S3^iv—Ca2—S3^viii	69.21 (3)	Ga4—S8—Ca1^ii	89.73 (3)
S3^iv—Ca2—S4	124.09 (3)	Ga4—S8—Ca2	85.67 (3)
S3^iv—Ca2—S6	74.18 (3)	Ca1^ii—S8—Ca2	144.97 (3)
S3—Ga1—S3^i—Ga1^i	−153.70 (4)	S5^v—Ca1—S2^iv—Ga3^iv	−38.96 (4)
S3—Ga1—S3^i—Ca2^xii	−17.36 (4)	S2^iv—Ca1—S5^iii—Ga3^iii	33.05 (5)
S3^i—Ga1—S3—Ga1^ix	163.03 (4)	S2^iv—Ca1—S5^iii—Ga4^iii	134.24 (3)
S3^i—Ga1—S3—Ca2^xi	−90.54 (5)	S5^iii—Ca1—S2^iv—Ga3^iv	38.63 (4)
S3^i—Ga1—S3—Ca2^xii	17.88 (4)	S2^iv—Ca1—S7^vi—Ga3^vi	−17.88 (16)
S3—Ga1—S4—Ga2	−167.10 (3)	S7^vi—Ca1—S2^iv—Ga3^iv	7.90 (13)
S3—Ga1—S4—Ca2	104.78 (3)	S2^iv—Ca1—S8^vii—Ga2^vii	−64.03 (6)
S3—Ga1—S4—Ca1^xiii	−72.20 (5)	S2^iv—Ca1—S8^vii—Ga4^vii	−172.68 (3)
S4—Ga1—S3—Ga1^ix	−77.44 (4)	S2^iv—Ca1—S8^vii—Ca2^vii	105.26 (6)
S4—Ga1—S3—Ca2^xi	28.99 (5)	S8^vii—Ca1—S2^iv—Ga3^iv	179.61 (3)
S4—Ga1—S3—Ca2^xii	137.40 (3)	S4^v—Ca1—S5^v—Ga3^v	−62.52 (4)
S3—Ga1—S6—Ca2	−106.34 (3)	S4^v—Ca1—S5^v—Ga4^v	35.72 (5)
S3—Ga1—S6—Ga2^ix	19.83 (5)	S5^v—Ca1—S4^v—Ga1^v	170.74 (5)
S3—Ga1—S6—Ca2^i	148.59 (4)	S5^v—Ca1—S4^v—Ga2^v	−86.03 (3)
S6—Ga1—S3—Ga1^ix	37.16 (5)	S5^v—Ca1—S4^v—Ca2^v	−3.70 (8)
S6—Ga1—S3—Ca2^xi	143.58 (4)	S4^v—Ca1—S5^iii—Ga3^iii	90.16 (7)
S6—Ga1—S3—Ca2^xii	−108.00 (3)	S4^v—Ca1—S5^iii—Ga4^iii	−168.64 (6)
S3^i—Ga1—S4—Ga2	−55.34 (4)	S5^iii—Ca1—S4^v—Ga1^v	−152.37 (6)
S3^i—Ga1—S4—Ca2	−143.46 (3)	S5^iii—Ca1—S4^v—Ga2^v	−49.14 (7)
S3^i—Ga1—S4—Ca1^xiii	39.56 (6)	S5^iii—Ca1—S4^v—Ca2^v	33.19 (13)
S4—Ga1—S3^i—Ga1^i	83.93 (5)	S4^v—Ca1—S7^vi—Ga3^vi	97.24 (8)
S4—Ga1—S3^i—Ca2^xii	−139.73 (3)	S7^vi—Ca1—S4^v—Ga1^v	105.29 (5)
S3^i—Ga1—S6—Ca2	139.35 (4)	S7^vi—Ca1—S4^v—Ga2^v	−151.48 (3)
S3^i—Ga1—S6—Ga2^ix	−94.47 (5)	S7^vi—Ca1—S4^v—Ca2^v	−69.15 (9)
S3^i—Ga1—S6—Ca2^i	34.28 (5)	S4^v—Ca1—S8^vii—Ga2^vii	−128.79 (4)
S6—Ga1—S3^i—Ga1^i	−31.56 (5)	S4^v—Ca1—S8^vii—Ga4^vii	122.55 (3)
S6—Ga1—S3^i—Ca2^xii	104.78 (4)	S4^v—Ca1—S8^vii—Ca2^vii	40.50 (7)
S4—Ga1—S6—Ca2	17.50 (4)	S8^vii—Ca1—S4^v—Ga1^v	39.47 (5)
S4—Ga1—S6—Ga2^ix	143.67 (4)	S8^vii—Ca1—S4^v—Ga2^v	142.70 (3)
S4—Ga1—S6—Ca2^i	−87.57 (4)	S8^vii—Ca1—S4^v—Ca2^v	−134.97 (8)
S6—Ga1—S4—Ga2	70.95 (3)	S5^v—Ca1—S5^iii—Ga3^iii	126.60 (5)
S6—Ga1—S4—Ca2	−17.17 (4)	S5^v—Ca1—S5^iii—Ga4^iii	−132.21 (4)
S6—Ga1—S4—Ca1^xiii	165.85 (4)	S5^iii—Ca1—S5^v—Ga3^v	137.15 (4)
S2^ii—Ga2—S4—Ga1	107.72 (3)	S5^iii—Ca1—S5^v—Ga4^v	−124.60 (5)
S2^ii—Ga2—S4—Ca2	−161.45 (3)	S5^v—Ca1—S7^vi—Ga3^vi	31.29 (8)
S2^ii—Ga2—S4—Ca1^xiii	−14.07 (3)	S7^vi—Ca1—S5^v—Ga3^v	57.35 (4)
S4—Ga2—S2^ii—Ga3^ii	138.58 (3)	S7^vi—Ca1—S5^v—Ga4^v	155.60 (5)
S2^ii—Ga2—S6^i—Ga1^i	−68.55 (5)	S5^v—Ca1—S8^vii—Ga2^vii	166.65 (4)
S2^ii—Ga2—S6^i—Ca2^i	−175.65 (4)	S5^v—Ca1—S8^vii—Ga4^vii	58.00 (4)
S6^i—Ga2—S2^ii—Ga3^ii	−95.60 (4)	S5^v—Ca1—S8^vii—Ca2^vii	−24.06 (9)
S2^ii—Ga2—S8—Ga4	61.50 (6)	S8^vii—Ca1—S5^v—Ga3^v	4.92 (6)
S2^ii—Ga2—S8—Ca2	146.29 (4)	S8^vii—Ca1—S5^v—Ga4^v	103.16 (5)
S2^ii—Ga2—S8—Ca1^ii	−39.84 (7)	S5^iii—Ca1—S7^vi—Ga3^vi	−49.43 (8)
S8—Ga2—S2^ii—Ga3^ii	27.86 (6)	S7^vi—Ca1—S5^iii—Ga3^iii	−156.82 (5)
S4—Ga2—S6^i—Ga1^i	48.85 (4)	S7^vi—Ca1—S5^iii—Ga4^iii	−55.63 (3)
S4—Ga2—S6^i—Ca2^i	−58.25 (5)	S5^iii—Ca1—S8^vii—Ga2^vii	59.76 (6)
S6^i—Ga2—S4—Ga1	−10.94 (4)	S5^iii—Ca1—S8^vii—Ga4^vii	−48.89 (4)
S6^i—Ga2—S4—Ca2	79.88 (3)	S5^iii—Ca1—S8^vii—Ca2^vii	−130.95 (6)
S6^i—Ga2—S4—Ca1^xiii	−132.73 (3)	S8^vii—Ca1—S5^iii—Ga3^iii	−105.41 (6)
S4—Ga2—S8—Ga4	−52.39 (4)	S8^vii—Ca1—S5^iii—Ga4^iii	−4.21 (6)
S4—Ga2—S8—Ca2	32.40 (3)	S7^vi—Ca1—S8^vii—Ga2^vii	113.12 (4)
S4—Ga2—S8—Ca1^ii	−153.73 (4)	S7^vi—Ca1—S8^vii—Ga4^vii	4.47 (2)
S8—Ga2—S4—Ga1	−123.75 (3)	S7^vi—Ca1—S8^vii—Ca2^vii	−77.59 (6)
S8—Ga2—S4—Ca2	−32.92 (3)	S8^vii—Ca1—S7^vi—Ga3^vi	169.08 (8)
S8—Ga2—S4—Ca1^xiii	114.47 (2)	S1—Ca2—S3^iv—Ga1^iv	−40.82 (6)
S6^i—Ga2—S8—Ga4	−174.53 (3)	S3^iv—Ca2—S1—Ga3	155.55 (4)
S6^i—Ga2—S8—Ca2	−89.74 (3)	S3^iv—Ca2—S1—Ga4	71.61 (4)
S6^i—Ga2—S8—Ca1^ii	84.13 (5)	S3^iv—Ca2—S1—Ca1	−55.44 (7)
S8—Ga2—S6^i—Ga1^i	157.33 (3)	S1—Ca2—S3^viii—Ga1^viii	−114.19 (4)
S8—Ga2—S6^i—Ca2^i	50.23 (5)	S1—Ca2—S3^viii—Ca2^ix	109.55 (4)
S1—Ga3—S2—Ga2^vii	30.00 (4)	S3^viii—Ca2—S1—Ga3	−134.92 (4)
S1—Ga3—S2—Ca1^xi	126.23 (4)	S3^viii—Ca2—S1—Ga4	141.13 (3)
S2—Ga3—S1—Ga4	133.76 (3)	S3^viii—Ca2—S1—Ca1	14.08 (6)
S2—Ga3—S1—Ca1	−105.20 (4)	S1—Ca2—S4—Ga1	−154.26 (4)
S2—Ga3—S1—Ca2	47.31 (5)	S1—Ca2—S4—Ga2	103.24 (3)
S1—Ga3—S5—Ga4	−7.49 (3)	S1—Ca2—S4—Ca1^xiii	21.00 (9)
S1—Ga3—S5—Ca1^xiii	115.89 (3)	S4—Ca2—S1—Ga3	23.68 (4)
S1—Ga3—S5—Ca1^iii	−120.58 (4)	S4—Ca2—S1—Ga4	−60.26 (3)
S5—Ga3—S1—Ga4	7.41 (3)	S4—Ca2—S1—Ca1	172.69 (5)
S5—Ga3—S1—Ca1	128.44 (4)	S1—Ca2—S6—Ga1	17.08 (11)
S5—Ga3—S1—Ca2	−79.04 (4)	S1—Ca2—S6—Ga2^ix	−100.72 (10)
S1—Ga3—S7—Ga4^iii	54.29 (5)	S1—Ca2—S6—Ca2^i	140.07 (9)
S1—Ga3—S7—Ca1^vi	−132.51 (7)	S6—Ca2—S1—Ga3	−5.63 (13)
S7—Ga3—S1—Ga4	−107.68 (3)	S6—Ca2—S1—Ga4	−89.57 (10)
S7—Ga3—S1—Ca1	13.35 (5)	S6—Ca2—S1—Ca1	143.38 (8)
S7—Ga3—S1—Ca2	165.87 (4)	S1—Ca2—S6^ix—Ga1^ix	136.61 (3)
S2—Ga3—S5—Ga4	−124.70 (4)	S1—Ca2—S6^ix—Ca2^ix	−124.02 (3)
S2—Ga3—S5—Ca1^xiii	−1.32 (5)	S6^ix—Ca2—S1—Ga3	−61.56 (4)
S2—Ga3—S5—Ca1^iii	122.21 (5)	S6^ix—Ca2—S1—Ga4	−145.50 (3)
S5—Ga3—S2—Ga2^vii	138.38 (3)	S6^ix—Ca2—S1—Ca1	87.45 (5)
S5—Ga3—S2—Ca1^xi	−125.39 (4)	S1—Ca2—S8—Ga2	−116.60 (3)
S2—Ga3—S7—Ga4^iii	175.67 (3)	S1—Ca2—S8—Ga4	−11.41 (2)
S2—Ga3—S7—Ca1^vi	−11.14 (9)	S1—Ca2—S8—Ca1^ii	71.92 (6)
S7—Ga3—S2—Ga2^vii	−92.93 (4)	S8—Ca2—S1—Ga3	95.26 (4)
S7—Ga3—S2—Ca1^xi	3.30 (5)	S8—Ca2—S1—Ga4	11.32 (2)
S5—Ga3—S7—Ga4^iii	−49.58 (5)	S8—Ca2—S1—Ca1	−115.73 (5)
S5—Ga3—S7—Ca1^vi	123.62 (8)	S3^iv—Ca2—S3^viii—Ga1^viii	13.97 (3)
S7—Ga3—S5—Ga4	109.08 (3)	S3^iv—Ca2—S3^viii—Ca2^ix	−122.30 (3)
S7—Ga3—S5—Ca1^xiii	−127.55 (4)	S3^viii—Ca2—S3^iv—Ga1^iv	−124.07 (5)
S7—Ga3—S5—Ca1^iii	−4.01 (6)	S3^iv—Ca2—S4—Ga1	70.62 (5)
S1—Ga4—S5—Ga3	7.54 (3)	S3^iv—Ca2—S4—Ga2	−31.88 (4)
S1—Ga4—S5—Ca1^xiii	−103.42 (4)	S3^iv—Ca2—S4—Ca1^xiii	−114.12 (8)
S1—Ga4—S5—Ca1^iii	135.89 (3)	S4—Ca2—S3^iv—Ga1^iv	75.36 (6)
S5—Ga4—S1—Ga3	−7.48 (3)	S3^iv—Ca2—S6—Ga1	−147.66 (3)
S5—Ga4—S1—Ca1	−120.76 (4)	S3^iv—Ca2—S6—Ga2^ix	94.54 (4)
S5—Ga4—S1—Ca2	109.31 (3)	S3^iv—Ca2—S6—Ca2^i	−24.67 (3)
S1—Ga4—S7^iii—Ga3^iii	−55.77 (5)	S6—Ca2—S3^iv—Ga1^iv	131.51 (4)
S7^iii—Ga4—S1—Ga3	115.90 (4)	S3^iv—Ca2—S6^ix—Ga1^ix	−81.77 (5)
S7^iii—Ga4—S1—Ca1	2.62 (6)	S3^iv—Ca2—S6^ix—Ca2^ix	17.60 (5)
S7^iii—Ga4—S1—Ca2	−127.31 (4)	S6^ix—Ca2—S3^iv—Ga1^iv	−168.56 (4)
S1—Ga4—S8—Ga2	100.35 (4)	S3^iv—Ca2—S8—Ga2	108.02 (3)
S1—Ga4—S8—Ca2	14.31 (3)	S3^iv—Ca2—S8—Ga4	−146.80 (3)
S1—Ga4—S8—Ca1^ii	−130.93 (3)	S3^iv—Ca2—S8—Ca1^ii	−63.47 (6)
S8—Ga4—S1—Ga3	−131.83 (3)	S8—Ca2—S3^iv—Ga1^iv	19.95 (4)
S8—Ga4—S1—Ca1	114.88 (4)	S3^viii—Ca2—S4—Ga1	−52.14 (11)
S8—Ga4—S1—Ca2	−15.04 (3)	S3^viii—Ca2—S4—Ga2	−154.64 (10)
S5—Ga4—S7^iii—Ga3^iii	56.51 (5)	S3^viii—Ca2—S4—Ca1^xiii	123.12 (10)
S7^iii—Ga4—S5—Ga3	−119.03 (3)	S4—Ca2—S3^viii—Ga1^viii	145.80 (9)
S7^iii—Ga4—S5—Ca1^xiii	130.02 (4)	S4—Ca2—S3^viii—Ca2^ix	9.54 (12)
S7^iii—Ga4—S5—Ca1^iii	9.33 (5)	S3^viii—Ca2—S6—Ga1	146.44 (3)
S5—Ga4—S8—Ga2	−4.69 (5)	S3^viii—Ca2—S6—Ga2^ix	28.64 (5)
S5—Ga4—S8—Ca2	−90.73 (4)	S3^viii—Ca2—S6—Ca2^i	−90.57 (3)
S5—Ga4—S8—Ca1^ii	124.03 (3)	S6—Ca2—S3^viii—Ga1^viii	83.93 (4)
S8—Ga4—S5—Ga3	118.33 (3)	S6—Ca2—S3^viii—Ca2^ix	−52.34 (4)
S8—Ga4—S5—Ca1^xiii	7.37 (6)	S3^viii—Ca2—S6^ix—Ga1^ix	−124.78 (4)
S8—Ga4—S5—Ca1^iii	−113.32 (4)	S3^viii—Ca2—S6^ix—Ca2^ix	−25.41 (3)
S7^iii—Ga4—S8—Ga2	−134.25 (3)	S6^ix—Ca2—S3^viii—Ga1^viii	160.16 (3)
S7^iii—Ga4—S8—Ca2	139.71 (3)	S6^ix—Ca2—S3^viii—Ca2^ix	23.89 (3)
S7^iii—Ga4—S8—Ca1^ii	−5.53 (3)	S3^viii—Ca2—S8—Ga2	154.19 (4)
S8—Ga4—S7^iii—Ga3^iii	−170.40 (3)	S3^viii—Ca2—S8—Ga4	−100.62 (4)
S1—Ca1—S2^iv—Ga3^iv	129.31 (4)	S3^viii—Ca2—S8—Ca1^ii	−17.29 (9)
S2^iv—Ca1—S1—Ga3	−148.00 (4)	S8—Ca2—S3^viii—Ga1^viii	−34.53 (5)
S2^iv—Ca1—S1—Ga4	−50.23 (4)	S8—Ca2—S3^viii—Ca2^ix	−170.80 (4)
S2^iv—Ca1—S1—Ca2	61.91 (5)	S4—Ca2—S6—Ga1	−13.63 (3)
S1—Ca1—S4^v—Ga1^v	−25.51 (7)	S4—Ca2—S6—Ga2^ix	−131.43 (5)
S1—Ca1—S4^v—Ga2^v	77.72 (4)	S4—Ca2—S6—Ca2^i	109.36 (3)
S1—Ca1—S4^v—Ca2^v	160.05 (7)	S6—Ca2—S4—Ga1	13.98 (3)
S4^v—Ca1—S1—Ga3	144.50 (4)	S6—Ca2—S4—Ga2	−88.53 (3)
S4^v—Ca1—S1—Ga4	−117.73 (4)	S6—Ca2—S4—Ca1^xiii	−170.76 (8)
S4^v—Ca1—S1—Ca2	−5.59 (7)	S4—Ca2—S6^ix—Ga1^ix	49.94 (4)
S1—Ca1—S5^v—Ga3^v	−179.34 (12)	S4—Ca2—S6^ix—Ca2^ix	149.31 (3)
S1—Ca1—S5^v—Ga4^v	−81.09 (14)	S6^ix—Ca2—S4—Ga1	−65.96 (3)
S5^v—Ca1—S1—Ga3	−103.81 (14)	S6^ix—Ca2—S4—Ga2	−168.46 (3)
S5^v—Ca1—S1—Ga4	−6.04 (16)	S6^ix—Ca2—S4—Ca1^xiii	109.30 (8)
S5^v—Ca1—S1—Ca2	106.10 (13)	S4—Ca2—S8—Ga2	−25.94 (2)
S1—Ca1—S5^iii—Ga3^iii	−41.83 (5)	S4—Ca2—S8—Ga4	79.25 (3)
S1—Ca1—S5^iii—Ga4^iii	59.36 (4)	S4—Ca2—S8—Ca1^ii	162.58 (6)
S5^iii—Ca1—S1—Ga3	−61.51 (4)	S8—Ca2—S4—Ga1	128.13 (3)
S5^iii—Ca1—S1—Ga4	36.26 (5)	S8—Ca2—S4—Ga2	25.63 (2)
S5^iii—Ca1—S1—Ca2	148.40 (5)	S8—Ca2—S4—Ca1^xiii	−56.61 (8)
S1—Ca1—S7^vi—Ga3^vi	−133.22 (7)	S6—Ca2—S6^ix—Ga1^ix	−23.74 (4)
S7^vi—Ca1—S1—Ga3	14.18 (5)	S6—Ca2—S6^ix—Ca2^ix	75.63 (3)
S7^vi—Ca1—S1—Ga4	111.95 (5)	S6^ix—Ca2—S6—Ga1	74.59 (3)
S7^vi—Ca1—S1—Ca2	−135.91 (5)	S6^ix—Ca2—S6—Ga2^ix	−43.21 (4)
S1—Ca1—S8^vii—Ga2^vii	−12.04 (4)	S6^ix—Ca2—S6—Ca2^i	−162.43 (3)
S1—Ca1—S8^vii—Ga4^vii	−120.69 (3)	S6—Ca2—S8—Ga2	39.37 (3)
S1—Ca1—S8^vii—Ca2^vii	157.25 (6)	S6—Ca2—S8—Ga4	144.56 (3)
S8^vii—Ca1—S1—Ga3	72.56 (4)	S6—Ca2—S8—Ca1^ii	−132.12 (6)
S8^vii—Ca1—S1—Ga4	170.33 (4)	S8—Ca2—S6—Ga1	−77.71 (4)
S8^vii—Ca1—S1—Ca2	−77.53 (5)	S8—Ca2—S6—Ga2^ix	164.48 (4)
S2^iv—Ca1—S4^v—Ga1^v	−92.49 (5)	S8—Ca2—S6—Ca2^i	45.27 (3)
S2^iv—Ca1—S4^v—Ga2^v	10.73 (2)	S6^ix—Ca2—S8—Ga2	−57.78 (7)
S2^iv—Ca1—S4^v—Ca2^v	93.07 (8)	S6^ix—Ca2—S8—Ga4	47.41 (7)
S4^v—Ca1—S2^iv—Ga3^iv	−113.01 (4)	S6^ix—Ca2—S8—Ca1^ii	130.74 (7)
S2^iv—Ca1—S5^v—Ga3^v	−136.98 (3)	S8—Ca2—S6^ix—Ga1^ix	80.03 (8)
S2^iv—Ca1—S5^v—Ga4^v	−38.74 (5)	S8—Ca2—S6^ix—Ca2^ix	179.40 (6)

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