Structure of the quaternary alloy Zn0.6Mn0.4In2S4 from synchrotron powder diffraction and electron transmission microscopy

Ávila-Godoy, R.; Mora, A.J.; Acosta-Najarro, D.R.; Delgado, G.E.; López-Rivera, S.A.; Fitch, A.N.; Mora, A.E.; Steeds, J.W.

doi:10.1107/S0021889805032656

research papers

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 39| Part 1| February 2006| Pages 1-5

https://doi.org/10.1107/S0021889805032656

Structure of the quaternary alloy Zn_0.6Mn_0.4In₂S₄ from synchrotron powder diffraction and electron transmission microscopy

Rosario Ávila-Godoy,^a Asiloé J. Mora,^b ^* Dwight R. Acosta-Najarro,^c Gerzon E. Delgado,^b Santos A. López-Rivera,^a Andrew N. Fitch,^d Andrés E. Mora ^a,^e and John W. Steeds ^e

^aDepartamento de Física, Universidad de Los Andes, Mérida, Venezuela, ^bDepartamento de Química, Universidad de Los Andes, Mérida, Venezuela, ^cInstituto de Física, Universidad Nacional Autónoma de México, México DF, México, ^dEuropean Synchrotron Radiation Facility, Grenoble CEDEX, France, and ^ePhysics Department, University of Bristol, Bristol BS8 1TL, UK
^*Correspondence e-mail: asiloe@ula.ve

(Received 10 June 2005; accepted 11 October 2005)

The aim of the present work was to determine the structure of the quaternary alloy Zn_0.6Mn_0.4In₂S₄ and to locate the Mn²⁺. This was accomplished by means of powder synchrotron X-ray diffraction, high-resolution microscopy and convergent-beam electron diffraction (CBED). The powder X-ray diffraction pattern was indexed in a rhombohedral cell, with cell constants a = 3.875 (2), c = 37.208 (4) Å, and possible space groups R $[\bar{3}]$ m or R3m. Rietveld refinements using different cationic arrangements in these space groups were performed. A model in space group R3m, in which the tetrahedral and octahedral sites were occupied by different proportions of Zn, Mn and In atoms, gave the best result. The Rietveld refinement of this model led to figures of merit R_wp = 9.8%, R_p = 9.1% and χ² = 11.1. Selected-area electron diffraction patterns and high-resolution transmission electron micrographs along [001] reveal the rhombohedral configuration. CBED patterns perpendicular to [001], showing the distinctive 3m symmetry, confirmed space group R3m and the breaking of the centrosymmetry of the parent compound, ZnIn₂S₄.

Keywords: semiconductor alloys; powder diffraction; transmission electron microscopy ; convergent beam electron diffraction.

1. Introduction

The quaternary alloy Zn_0.6Mn_0.4In₂S₄ is a member of the family of defect semiconductors which originates from the ternary systems ZnIn₂S₄ and MnIn₂S₄. These end groups have different crystal structures that show some degree of disorder. There are three structural reports for MnIn₂S₄. Two of them show a partially inverse spinel structure belonging to the space group Fd $[\bar{3}]$ m, with the lattice parameter a being close to 10.719 Å (Wakaki et al., 1983 ; Lutz & Jun, 1989 ). In the third report, MnIn₂S₄ is a cubic F $[\bar{4}]$ 3m structure with a = 10.720 Å (Lutz & Jun, 1989). The other member, ZnIn₂S₄, shows a wurtzite-like structure and is considered to be the prototype of layered semiconductors. It has been thoroughly investigated owing to the outstanding anisotropy in its properties, the presence of polytypes and the possibility of intercalating diverse types of species between its layers (Atwood et al., 1984 ). The range of inter-solubility is not well known; however, the phase diagram of the binary system ZnS–MnS, reported by Sombuthawee et al. (1978 ), has been used to establish that the ternary system ZnIn₂S₄–MnIn₂S₄ should show similar structural characteristics. Therefore, the transition from wurtzite to zinc blende observed in the binary system at 40–50% of MnZn should also be observed in the ternary system for a similar composition. The optical absorption and photoluminescence spectra, interpreted using crystal field analysis (Pineda et al., 1998 ), show that the Mn atoms occupy tetrahedral positions in R $[\bar{3}]$ m symmetry. On the other hand, the magnetic properties, reported by Sagredo et al. (1993 ), show that the Mn²⁺ ions could be placed at random in tetrahedral and octahedral sites in a non-centrosymmetric R3m structure. The analysis of the mid-IR spectra (Fontal et al., 1996 ), in the 800–400 cm⁻¹ region, suggest that the Mn²⁺ ions replace the Zn²⁺ ions in the tetrahedral sites, close to the S…S interlayer of the R $[\bar{3}]$ m structure of the parent compound, ZnIn₂S₄ (Berand & Range, 1994 ). Tatsi et al. (2002 ) studied the compositions Zn_0.6Mn_0.4In₂S₄ and Zn_0.7Mn_0.3In₂S₄ under hydrostatic pressures and ambient conditions, and suggest that the crystal structures of these compounds are R $[\bar{3}]$ m. It is evident that contradictory results point towards two different crystal structures: centrosymmetric R $[\bar{3}]$ m and non-centrosymmetric R3m. The difference between the structures is based only on the cation distribution and its degree of disorder in the different crystal sites. The elucidation of the structure to this degree of precision requires the best diffraction data from a highly crystalline material. However, this could be difficult to achieve considering that it is known that ZnIn₂S₄ exists as different polytypes depending on the method of growth, which generate a large number of crystalline defects that limit the precise knowledge of the distribution of the atoms in the unit cell. On the other hand, when the solid solution Zn_0.6Mn_0.4In₂S₄ forms, the material departs from the stoichiometry of the parent compound ZnIn₂S₄; therefore, it is likely that some cation sites lose the 3m point symmetry owing to the need to place different proportions of Zn, In and Mn in these sites. This might induce a change in the crystal symmetry from R $[\bar{3}]$ m to R3m. Finally, it is necessary to inquire about the likelihood of placing the magnetic ions Mn²⁺ in tetrahedral sites or octahedral sites in the unit cell of Zn_0.6Mn_0.4In₂S₄.

2. Experimental

2.1. Synthesis

Stoichiometric amounts of ZnS, MnS and In₂S₃ were pulverized to small grain size, mixed and compacted into cylindrical pellets at a pressure of 1300 MPa. These pellets were then placed into quartz capsules under vacuum and heated to 1373 K for 48 h. Yellow sheet-like crystals were grown by the chemical-transport technique using iodine as transporting agent, and heating the sample at 1773 K, above the melting point of ZnIn₂S₄ (Giriat, 1985 ). The chemical composition of the alloy, confirmed from energy dispersive X-ray spectra (EDX) at 20.48 kV in a Jeol 5600 Electron Microscope, gave the atomic ratios Zn:Mn:In:S 0.59:0.39:2.0:4.0, which matched the nominal composition within 0.01. The error in standardless analysis was around 5%.

2.2. X-ray diffraction

For the X-ray analysis, a small quantity of the alloy was ground in an agate mortar and pestle, avoiding any excess of pressure, to prevent the degradation of the crystalline quality of the material. The resulting powder was mounted on a flat zero-background silicon [511] crystal holder, covered with a thin layer of petroleum jelly. Diffraction data were collected on a Siemens D5005 diffractometer, set up in θ/θ reflection mode, equipped with a diffracted-beam graphite monochromator and an X-ray tube (Cu Kα radiation: λ = 1.54059 Å, 30 kV, 15 mA). A fixed aperture and divergence slit of 1 mm, a 0.1 mm monochromator slit, and a 0.6 mm detector slit were used. Patterns were recorded between 5 and 100° 2θ, with increments of 0.02°, counting at each step for 35 s.

For the Rietveld analysis, improved diffraction data were collected on the high-resolution powder diffractometer of beamline ID31 at the European Synchrotron Radiation Facility (ESRF), in Grenoble, France, using a wavelength of 0.499229 (5) Å taken from an undulator source (Fitch, 1996 , 2004 ). For these experiments, specimens were prepared in borosilicate capillaries, 0.5 mm in diameter, sealed at one end and spun at 100 r.p.m on the axis of the diffractometer to improve randomization of the individual crystallite orientations.

2.3. Electron microscopy

The morphological study and chemical composition analysis of the samples were carried out in a Jeol-5600 Scanning Electron Microscope (SEM) equipped with a Noran X-ray detector. The electron diffraction patterns were obtained in a Jeol CX-100 electron microscope, while the high-resolution electron images and the convergent-beam diffraction patterns were recorded in a Jeol-EX4000 and in a Philips EM-430 electron microscope, respectively. In the latter a double-tilt holder was required. All the micrographs were digitized in a CCD camera. For the different transmission microscopy studies, crystals with exactly defined thickness were used. The crystallographic study was carried out using the CRISP program (Hovmöller, 1992 ).

3. Results

3.1. X-ray structure analysis

Preliminary experiments using a laboratory diffractometer using Bragg–Brentano reflection symmetry clearly showed that this material is greatly affected by preferred orientation, particularly with reflection 009. Therefore, it was necessary to perform diffraction experiments on the parallel-beam diffractometer of beamline ID31 at the ESRF, which allows the collection of diffraction data in capillary-transmission mode.

The pattern was indexed using the auto-indexing program DICVOL91 (Boultif & Louër, 1991 ) with figures of merit M₍₂₀₎ = 44.0 (de Wolff, 1968 ) and F₍₃₀₎ = 37.7 (Smith & Snyder, 1979 ). Cell parameters are a = 3.875 (2) and c = 37.208 (4) Å.

Evaluation of the systematic absences shows that the condition of reflection is −h + k + l = 00l = 3n. This condition establishes that the possible space groups are R3m (No. 160) and R $[\bar{3}]$ m (No. 166). As starting models, those of Berand & Range (1994), for space group R $[\bar{3}]$ m, and Lappe et al. (1962 ), for R3m, were used.

Different cationic arrangements were assessed using the Rietveld (1967 ) method. The models were introduced into the program GSAS (Larson & von Dreele, 2001 ) using as starting cell parameters those obtained from the refinement of the laboratory diffraction data. The background was modelled using the automatic linear extrapolation of 15 points throughout the whole pattern. The peak shapes were modeled using a pseudo-Voigt peak shape function that included the axial divergence asymmetry correction (van Laar & Yelon, 1984 ; Finger et al., 1994 ). Two isotropic temperature factors were refined, one for the Zn, Mn and In ions, and the other for the S atoms. Preferred orientation was corrected using the March–Dollase model (Dollase, 1986 ). However, this problem, particularly deleterious in these types of lamellar materials, is still present, as depicted in the exceptionally intense 009 reflection. Table 1 shows the results for the different structural models tested.

Table 1
Allowed cationic distributions for the quaternary alloy Zn_0.6Mn_0.4In₂S₄

Models constructed from Berand & Range (1994) (R $[\bar{3}]$ m) and Lappe et al. (1962) (R3m). Occ. = occupancy; Tet = tetrahedral; Oct = octahedral.

Model	Atom	Site	x	y	z		Occ.	R_wp (%)	R_p (%)	χ²
R $[\bar{3}]$ m
I	Zn	6c	0	0	0.77	Tet	0.3
	Mn						0.2
	In						0.5
	In	3a	0	0	0	Oct	1.0	28.5	25.3	92.8

R3m
I	Zn	3a	0	0	0.40	Tet	0.6
	Mn						0.4
	In	3a	0	0	0.17	Oct	1.0
	In	3a	0	0	0.93	Tet	1.0	16.7	14.3	32.0

II	Zn	3a	0	0	0.40	Tet	0.6
	In						0.4
	Mn	3a	0	0	0.17	Oct	0.4
	In						0.6
	In	3a	0	0	0.93	Tet	1.0	11.3	10.1	14.5

III	Zn	3a	0	0	0.40	Tet	0.6
	In						0.4
	Mn	3a	0	0	0.17	Oct	0.2
	In						0.8
	Mn	3a	0	0	0.93	Tet	0.2
	In						0.8	16.5	14.0	31.1

IV	Zn	3a	0	0	0.40	Tet	0.4
	Mn						0.2
	In						0.4
	Zn	3a	0	0	0.17	Oct	0.2
	Mn						0.2
	In						0.6
	In	3a	0	0	0.93	Tet	1.0	9.8	9.1	11.1

V	Zn	3a	0	0	0.40	Tet	0.3
	Mn						0.2
	In						0.5
	Zn	3a	0	0	0.17	Oct	0.3
	Mn						0.2
	In						0.5
	In	3a	0	0	0.93	Tet	1.0	10.9	9.9	13.6

VI	Zn	3a	0	0	0.40	Tet	0.6
	Mn						0.2
	In						0.2
	In	3a	0	0	0.17	Oct	1.0
	Mn	3a	0	0	0.93	Tet	0.2
	In						0.8	14.9	12.4	25.3

VII	Zn	3a	0	0	0.40	Tet	0.4
	Mn						0.2
	In						0.4
	In	3a	0	0	0.17	Oct	0.6
	Zn	3a	0	0	0.93	Tet	0.2
	Mn						0.2
	In						1.0	14.0	12.0	22.3

3.1.1. Centrosymmetric model in the R $[\bar{\bf 3}]$ m space group

Berand & Range (1994) and López-Rivera et al. (2001 ) described the structure of the ternary compound ZnIn₂S₄ in the space group R $[\bar{3}]$ m in terms of a close packing of S atoms, with Zn atoms and half of the In atoms distributed at random in tetrahedral sites, while the other half of the In atoms were placed in octahedral sites. This distribution of ions produces a disordered layered structure. For the Zn_0.6Mn_0.4In₂S₄ alloy, the Mn atoms substitute Zn atoms in the structure of ZnIn₂S₄, preserving the centrosymmetry of the parent structure. As Table 2 shows, the fit of this model to the experimental diffraction data was poor, giving high figures of merit R_wp = 28.5% and R_p = 25.3%, for 26 variables. In particular, the reflection 006 has zero calculated intensity and therefore does not fit at all.

Table 2
Final atomic positions and isotropic temperature factors for the quaternary alloy Zn_0.6Mn_0.4In₂S₄, space group R3m, Z = 3, a = 3875 (2), c = 37208 (4) Å

Atom	Occupancy	x	y	z	U_iso (Å²)
Mn(1)	0.2				0.01311
Zn(1)	0.4	0	0	0.392584	0.01311
In(1)	0.4				0.01311
Mn(2)	0.2				0.01311
Zn(2)	0.2	0	0	0.161237	0.01311
In(2)	0.6				0.01311
In(3)	1.0	0	0	0.929657	0.01311
S(1)	1.0	0	0	0.036750	0.01119
S(2)	1.0	0	0	0.288360	0.01119
S(3)	1.0	0	0	0.458145	0.01119
S(4)	1.0	0	0	0.863597	0.01119

3.1.2. Non-centrosymmetric models in the R3m space group

In the model of Lappe et al. (1962), all the atoms occupy Wyckoff positions 3a, with the Zn atoms and half of the In atoms placed in separate tetrahedral positions. In this case, different distributions of cations in the tetrahedral and octahedral sites are feasible, which are summarized in Table 1. The cationic distribution in the different models is such that the local 3m symmetry is preserved. The best fit to the experimental data corresponded to model IV, in which the Mn ions occupy tetrahedral and octahedral positions adjacent in the cell, shared with the Zn and In atoms in Zn:Mn:In ratios of 0.4:0.2:0.4 and 0.2:0.2:0.6, respectively. The final Rietveld plot is shown in Fig. 1. There is significant improvement in the fit to the experimental profile, and in particular with the 006 reflection. Table 2 shows the final atomic positions and isotropic temperature factors for the Zn_0.6Mn_0.4In₂S₄ alloy.

Figure 1
Final observed (points), calculated (lines), and difference profiles for the Rietveld refinement of the quaternary alloy Zn_0.6Mn_0.4In₂S₄ from high-resolution powder diffraction data. (a) Data from 5 to 20° 2θ. (b) Data from 20 to 45° 2θ.

3.2. Selected-area electron diffraction (SAED)

The reciprocal lattice along the [001] direction for the alloy Zn_0.6Mn_0.4In₂S₄ was studied using SAED patterns. Fig. 2 shows the pattern recorded on an image plate. The structural analysis, following standard electron diffraction procedures, reveals a rhombohedral unit with a = 3.06 Å.

Figure 2
SAED of Zn_0.6Mn_0.4In₂S₄ along the [001] direction.

3.3. High-resolution electron microscopy (HRTEM)

A digitalized high-resolution image of the alloy Zn_0.6Mn_0.4In₂S₄ along the [001] direction is shown in Fig. 3. Contrast changes due to thickness variations along vertical and horizontal directions are observed. The zone selected at the right of the image was processed with the program CRISP (Hovmöller, 1992) to obtain crystallographic phases imposing the p6 symmetry on the projection. The cell parameter a was found, giving a value of 21.5 Å, a multiple of 3.06 Å, with good discrepancy values of R_symmetry = 15.3% and φ_residual = 0.1.

Figure 3
HRTEM of the alloy Zn_0.6Mn_0.4In₂S₄.

3.4. Convergent-beam electron diffraction (CBED)

In the CBED patterns, the contrast details arising from the dynamical diffraction effects and the geometrical configurations derived from structural arrays in our samples, in direct and diffracted beams, allow the detection, identification and differentiation of space groups R $[\bar{3}]$ m and R3m by checking the symmetry of the diffraction pattern obtained perpendicular to the [001] direction, as shown in Table 3 (Buxton et al., 1976 ). Fig. 4 shows a micrograph for the alloy Zn_0.6Mn_0.4In₂S₄ collected at an acceleration potential of 150 kV, using a large convergence angle along [001], with its simulated image placed at its right. The pattern contains both zero-order Laue zone (ZOLZ) and high-order Laue zone (HOLZ) information, and Kikuchi lines. At the zero level, the pattern shows rotational symmetry of order 3, as shown by the triangle in the centre of the micrograph. Three mirror planes intercepting at angles of 120° are also depicted. In Table 3, the symmetries of the micrographs with rhombohedral cells perpendicular to [001] are given. All this information clearly points towards a micrograph with point symmetry 3m. Therefore, it can be concluded unambiguously that the structure of the quaternary alloy is non-centrosymmetric R3m.

Table 3
Zone-axis symmetry for the [001] direction for the point groups $[\bar{3}]$ m and 3m from Buxton et al. (1976)

Point group	[001]
$[\bar{3}]$ m	6mm_R
3m	3m

Figure 4
CBED patterns of the alloy Zn_0.6Mn_0.4In₂S₄ at 150 kV.

4. Conclusions

The quaternary alloy Zn_0.6Mn_0.4In₂S₄ shows a rhombohedral layered crystal structure, in space group R3m (160). The sequence of layers is:

$[{\rm S In_{tet}S(Zn_{0.2}Mn_{0.2}In_{0.6})_{oct}S(Zn_{0.4}Mn_{0.2}In_{0.4})_{tet}S \ldots SIn_{tet} }.]$

A diagram of the layers in the structure along the c axis is shown in Fig. 5. The 3m symmetry of a CBED micrograph with zone-axis [001] confirmed the space-group symmetry R3m. The Zn, Mn and In atoms occupy both tetrahedral and octahedral sites in the structure in a disordered way, but in such proportions that the local $[\bar{3}]$ m symmetry of the parent compound, ZnIn₂S₄, is broken.

Figure 5
A view showing the unit cell of the Zn_0.6Mn_0.4In₂S₄ structure (model IV) in the R3m space group.

Supporting information

Crystal structure: contains datablocks Z_publ, I. DOI: https://doi.org/10.1107/S0021889805032656/zm5036sup1.cif

Rietveld powder data: contains datablock I. DOI: https://doi.org/10.1107/S0021889805032656/zm5036Isup2.rtv

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S0021889805032656/zm5036Isup3.hkl

Computing details top

Program(s) used to refine structure: GSAS.

(I) top

Crystal data top

In_2.00Mn_0.40S₄Zn_0.60	c = 37.20846 (11) Å
M_r = 419.09	V = 483.91 (1) Å³
Trigonal, R3m	Z = 3
a = 3.875218 (8) Å

Data collection top

2θ_min = 1.002°, 2θ_max = 53.052°, 2θ_step = 0.002°

Refinement top

Least-squares matrix: full	Profile function: CW Profile function number 3 with 19 terms Pseudovoigt profile coefficients as parameterized in P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83. Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994). J. Appl. Cryst.,27,892-900. #1(GU) = 0.000 #2(GV) = 0.000 #3(GW) = 0.000 #4(GP) = 0.000 #5(LX) = 0.245 #6(LY) = 10.010 #7(S/L) = 0.0005 #8(H/L) = 0.0005 #9(trns) = 0.00 #10(shft)= 0.0000 #11(stec)= 0.00 #12(ptec)= 0.00 #13(sfec)= 0.00 #14(L11) = 0.081 #15(L22) = 0.010 #16(L33) = 0.000 #17(L12) = 0.098 #18(L13) = 0.008 #19(L23) = -0.004 Peak tails are ignored where the intensity is below 0.0100 times the peak Aniso. broadening axis 0.0 0.0 1.0
R_p = 0.091	36 parameters
R_wp = 0.098	0 restraints
R_exp = 0.030	(Δ/σ)_max = 2.79
R(F²) = 0.11431	Background function: GSAS Background function number 7 with 15 terms. Linear interpolation 1: 367.197 2: 259.848 3: 425.772 4: 414.925 5: 453.275 6: 355.583 7: 421.634 8: 367.229 9: 329.349 10: 302.797 11: 316.815 12: 267.840 13: 237.159 14: 223.553 15: 190.082
26026 data points	Preferred orientation correction: March-Dollase AXIS 1 Ratio= 1.05095 h= 0.000 k= 0.000 l= 1.000 Prefered orientation correction range: Min= 0.86147, Max= 1.07741

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Mn1	0.0	0.0	0.395962 (30	0.01312 (8)*	0.2
Zn1	0.0	0.0	0.395962 (30	0.01312 (8)*	0.4
In1	0.0	0.0	0.395962 (30	0.01312 (8)*	0.4
Mn2	0.0	0.0	0.16463 (7)	0.01312 (8)*	0.2
Zn2	0.0	0.0	0.16463 (7)	0.01312 (8)*	0.2
In2	0.0	0.0	0.16463 (7)	0.01312 (8)*	0.6
In3	0.0	0.0	0.93304	0.01312 (8)*
S1	0.0	0.0	0.04013 (10)	0.01120 (17)*
S2	0.0	0.0	0.29173 (11)	0.01120 (17)*
S3	0.0	0.0	0.46154 (12)	0.01120 (17)*
S4	0.0	0.0	0.86700 (12)	0.01120 (17)*

Geometric parameters (Å, º) top

Mn1—S1ⁱ	2.3889 (15)	S1—Mn1^iv	2.3889 (15)
Mn1—S1ⁱⁱ	2.3889 (15)	S1—Mn1^v	2.3889 (15)
Mn1—S1ⁱⁱⁱ	2.3889 (15)	S1—Mn1^vi	2.3889 (15)
Mn1—S3	2.440 (5)	S1—Zn1^iv	2.3889 (15)
Zn1—S1ⁱ	2.3889 (15)	S1—Zn1^v	2.3889 (15)
Zn1—S1ⁱⁱ	2.3889 (15)	S1—Zn1^vi	2.3889 (15)
Zn1—S1ⁱⁱⁱ	2.3889 (15)	S1—In1^iv	2.3889 (15)
Zn1—S3	2.440 (5)	S1—In1^v	2.3889 (15)
In1—S1ⁱ	2.3889 (15)	S1—In1^vi	2.3889 (15)
In1—S1ⁱⁱ	2.3889 (15)	S2—In3^vii	2.4281 (16)
In1—S1ⁱⁱⁱ	2.3889 (15)	S2—In3^viii	2.4281 (16)
In1—S3	2.440 (5)	S2—In3^ix	2.4281 (16)
Mn2—S3^iv	2.616 (3)	S3—Mn1	2.440 (5)
Mn2—S3^v	2.616 (3)	S3—Zn1	2.440 (5)
Mn2—S3^vi	2.616 (3)	S3—In1	2.440 (5)
Mn2—S4^vii	2.602 (3)	S3—Mn2ⁱ	2.616 (3)
Mn2—S4^viii	2.602 (3)	S3—Mn2ⁱⁱ	2.616 (3)
Mn2—S4^ix	2.602 (3)	S3—Mn2ⁱⁱⁱ	2.616 (3)
Zn2—S3^iv	2.616 (3)	S3—Zn2ⁱ	2.616 (3)
Zn2—S3^v	2.616 (3)	S3—Zn2ⁱⁱ	2.616 (3)
Zn2—S3^vi	2.616 (3)	S3—Zn2ⁱⁱⁱ	2.616 (3)
Zn2—S4^vii	2.602 (3)	S3—In2ⁱ	2.616 (3)
Zn2—S4^viii	2.602 (3)	S3—In2ⁱⁱ	2.616 (3)
Zn2—S4^ix	2.602 (3)	S3—In2ⁱⁱⁱ	2.616 (3)
In2—S3^iv	2.616 (3)	S4—Mn2^x	2.602 (3)
In2—S3^v	2.616 (3)	S4—Mn2^xi	2.602 (3)
In2—S3^vi	2.616 (3)	S4—Mn2^xii	2.602 (3)
In2—S4^vii	2.602 (3)	S4—Zn2^x	2.602 (3)
In2—S4^viii	2.602 (3)	S4—Zn2^xi	2.602 (3)
In2—S4^ix	2.602 (3)	S4—Zn2^xii	2.602 (3)
In3—S2^x	2.4281 (16)	S4—In2^x	2.602 (3)
In3—S2^xi	2.4281 (16)	S4—In2^xi	2.602 (3)
In3—S2^xii	2.4281 (16)	S4—In2^xii	2.602 (3)
In3—S4	2.457 (5)	S4—In3	2.457 (5)

S1ⁱ—Mn1—S1ⁱⁱ	108.41 (10)	Zn1^iv—S1—Zn1^v	108.41 (10)
S1ⁱ—Mn1—S1ⁱⁱⁱ	108.41 (10)	Zn1^iv—S1—Zn1^vi	108.41 (10)
S1ⁱ—Mn1—S3	110.52 (10)	Zn1^iv—S1—In1^iv	0.0
S1ⁱⁱ—Mn1—S1ⁱⁱⁱ	108.41 (10)	Zn1^iv—S1—In1^v	108.41 (10)
S1ⁱⁱ—Mn1—S3	110.52 (10)	Zn1^iv—S1—In1^vi	108.41 (10)
S1ⁱⁱⁱ—Mn1—S3	110.52 (10)	Zn1^v—S1—Zn1^vi	108.41 (10)
S1ⁱ—Zn1—S1ⁱⁱ	108.41 (10)	Zn1^v—S1—In1^iv	108.41 (10)
S1ⁱ—Zn1—S1ⁱⁱⁱ	108.41 (10)	Zn1^v—S1—In1^v	0.0
S1ⁱ—Zn1—S3	110.52 (10)	Zn1^v—S1—In1^vi	108.41 (10)
S1ⁱⁱ—Zn1—S1ⁱⁱⁱ	108.41 (10)	Zn1^vi—S1—In1^iv	108.41 (10)
S1ⁱⁱ—Zn1—S3	110.52 (10)	Zn1^vi—S1—In1^v	108.41 (10)
S1ⁱⁱⁱ—Zn1—S3	110.52 (10)	Zn1^vi—S1—In1^vi	0.0
S1ⁱ—In1—S1ⁱⁱ	108.41 (10)	In1^iv—S1—In1^v	108.41 (10)
S1ⁱ—In1—S1ⁱⁱⁱ	108.41 (10)	In1^iv—S1—In1^vi	108.41 (10)
S1ⁱ—In1—S3	110.52 (10)	In1^v—S1—In1^vi	108.41 (10)
S1ⁱⁱ—In1—S1ⁱⁱⁱ	108.41 (10)	In3^vii—S2—In3^viii	105.88 (10)
S1ⁱⁱ—In1—S3	110.52 (10)	In3^vii—S2—In3^ix	105.88 (10)
S1ⁱⁱⁱ—In1—S3	110.52 (10)	In3^viii—S2—In3^ix	105.88 (10)
S3^iv—Zn2—S3^v	95.59 (14)	Mn1—S3—Zn1	0.0
S3^iv—Zn2—S3^vi	95.59 (14)	Mn1—S3—In1	0.0
S3^iv—Zn2—S4^vii	84.07 (3)	Mn1—S3—Zn2ⁱ	121.20 (10)
S3^iv—Zn2—S4^viii	84.07 (3)	Mn1—S3—Zn2ⁱⁱ	121.20 (10)
S3^iv—Zn2—S4^ix	179.4925 (17)	Mn1—S3—Zn2ⁱⁱⁱ	121.20 (10)
S3^v—Zn2—S3^vi	95.59 (14)	Mn1—S3—In2ⁱ	121.20 (10)
S3^v—Zn2—S4^vii	84.07 (3)	Mn1—S3—In2ⁱⁱ	121.20 (10)
S3^v—Zn2—S4^viii	179.4929 (17)	Mn1—S3—In2ⁱⁱⁱ	121.20 (10)
S3^v—Zn2—S4^ix	84.07 (3)	Zn1—S3—In1	0.0
S3^vi—Zn2—S4^vii	179.4933 (17)	Zn1—S3—Zn2ⁱ	121.20 (10)
S3^vi—Zn2—S4^viii	84.07 (3)	Zn1—S3—Zn2ⁱⁱ	121.20 (10)
S3^vi—Zn2—S4^ix	84.07 (3)	Zn1—S3—Zn2ⁱⁱⁱ	121.20 (10)
S4^vii—Zn2—S4^viii	96.26 (13)	Zn1—S3—In2ⁱ	121.20 (10)
S4^vii—Zn2—S4^ix	96.26 (13)	Zn1—S3—In2ⁱⁱ	121.20 (10)
S4^viii—Zn2—S4^ix	96.26 (13)	Zn1—S3—In2ⁱⁱⁱ	121.20 (10)
S3^iv—In2—S3^v	95.59 (14)	In1—S3—Zn2ⁱ	121.20 (10)
S3^iv—In2—S3^vi	95.59 (14)	In1—S3—Zn2ⁱⁱ	121.20 (10)
S3^iv—In2—S4^vii	84.07 (3)	In1—S3—Zn2ⁱⁱⁱ	121.20 (10)
S3^iv—In2—S4^viii	84.07 (3)	In1—S3—In2ⁱ	121.20 (10)
S3^iv—In2—S4^ix	179.4925 (17)	In1—S3—In2ⁱⁱ	121.20 (10)
S3^v—In2—S3^vi	95.59 (14)	In1—S3—In2ⁱⁱⁱ	121.20 (10)
S3^v—In2—S4^vii	84.07 (3)	Zn2ⁱ—S3—Zn2ⁱⁱ	95.59 (14)
S3^v—In2—S4^viii	179.4929 (17)	Zn2ⁱ—S3—Zn2ⁱⁱⁱ	95.59 (14)
S3^v—In2—S4^ix	84.07 (3)	Zn2ⁱ—S3—In2ⁱ	0.0
S3^vi—In2—S4^vii	179.4933 (17)	Zn2ⁱ—S3—In2ⁱⁱ	95.59 (14)
S3^vi—In2—S4^viii	84.07 (3)	Zn2ⁱ—S3—In2ⁱⁱⁱ	95.59 (14)
S3^vi—In2—S4^ix	84.07 (3)	Zn2ⁱⁱ—S3—Zn2ⁱⁱⁱ	95.59 (14)
S4^vii—In2—S4^viii	96.26 (13)	Zn2ⁱⁱ—S3—In2ⁱ	95.59 (14)
S4^vii—In2—S4^ix	96.26 (13)	Zn2ⁱⁱ—S3—In2ⁱⁱ	0.0
S4^viii—In2—S4^ix	96.26 (13)	Zn2ⁱⁱ—S3—In2ⁱⁱⁱ	95.59 (14)
S2^x—In3—S2^xi	105.88 (10)	Zn2ⁱⁱⁱ—S3—In2ⁱ	95.59 (14)
S2^x—In3—S2^xii	105.88 (10)	Zn2ⁱⁱⁱ—S3—In2ⁱⁱ	95.59 (14)
S2^x—In3—S4	112.86 (9)	Zn2ⁱⁱⁱ—S3—In2ⁱⁱⁱ	0.0
S2^xi—In3—S2^xii	105.88 (10)	In2ⁱ—S3—In2ⁱⁱ	95.59 (14)
S2^xi—In3—S4	112.86 (9)	In2ⁱ—S3—In2ⁱⁱⁱ	95.59 (14)
S2^xii—In3—S4	112.86 (9)	In2ⁱⁱ—S3—In2ⁱⁱⁱ	95.59 (14)
Mn1^iv—S1—Mn1^v	108.41 (10)	Zn2^x—S4—Zn2^xi	96.26 (13)
Mn1^iv—S1—Mn1^vi	108.41 (10)	Zn2^x—S4—Zn2^xii	96.26 (13)
Mn1^iv—S1—Zn1^iv	0.0	Zn2^x—S4—In2^x	0.0
Mn1^iv—S1—Zn1^v	108.41 (10)	Zn2^x—S4—In2^xi	96.26 (13)
Mn1^iv—S1—Zn1^vi	108.41 (10)	Zn2^x—S4—In2^xii	96.26 (13)
Mn1^iv—S1—In1^iv	0.0	Zn2^x—S4—In3	120.70 (10)
Mn1^iv—S1—In1^v	108.41 (10)	Zn2^xi—S4—Zn2^xii	96.26 (13)
Mn1^iv—S1—In1^vi	108.41 (10)	Zn2^xi—S4—In2^x	96.26 (13)
Mn1^v—S1—Mn1^vi	108.41 (10)	Zn2^xi—S4—In2^xi	0.0
Mn1^v—S1—Zn1^iv	108.41 (10)	Zn2^xi—S4—In2^xii	96.26 (13)
Mn1^v—S1—Zn1^v	0.0	Zn2^xi—S4—In3	120.70 (10)
Mn1^v—S1—Zn1^vi	108.41 (10)	Zn2^xii—S4—In2^x	96.26 (13)
Mn1^v—S1—In1^iv	108.41 (10)	Zn2^xii—S4—In2^xi	96.26 (13)
Mn1^v—S1—In1^v	0.0	Zn2^xii—S4—In2^xii	0.0
Mn1^v—S1—In1^vi	108.41 (10)	Zn2^xii—S4—In3	120.70 (10)
Mn1^vi—S1—Zn1^iv	108.41 (10)	In2^x—S4—In2^xi	96.26 (13)
Mn1^vi—S1—Zn1^v	108.41 (10)	In2^x—S4—In2^xii	96.26 (13)
Mn1^vi—S1—Zn1^vi	0.0	In2^x—S4—In3	120.70 (10)
Mn1^vi—S1—In1^iv	108.41 (10)	In2^xi—S4—In2^xii	96.26 (13)
Mn1^vi—S1—In1^v	108.41 (10)	In2^xi—S4—In3	120.70 (10)
Mn1^vi—S1—In1^vi	0.0	In2^xii—S4—In3	120.70 (10)

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

Acknowledgements

We thank the ESRF for providing synchrotron radiation beam time, FONACIT-Venezuela and CDCHT-ULA.

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Volume 39| Part 1| February 2006| Pages 1-5

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