Crystal structures of the silver iodide sulfates Ag3ISO4 and Ag4I2SO4

Matsushima, Y.; Uchida, K.; Kawanago, R.; Yamamoto, M.; Yamane, H.

doi:10.1107/S2056989025008898

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Volume 81| Part 11| November 2025| Pages 1080-1085

https://doi.org/10.1107/S2056989025008898

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Crystal structures of the silver iodide sulfates Ag₃ISO₄ and Ag₄I₂SO₄

Yuta Matsushima,^a ^* Kento Uchida,^a ‡ Ryota Kawanago,^a Mizuki Yamamoto ^a and Hisanori Yamane ^b

^aApplied Chemistry, Chemical Engineering, and Biochemical Engineering, Yamagata, University, 4-3-16 Jonan, Yonezawa-shi, Yamagata, 992-8510, Japan, and ^bInstitute of Multidisciplinary Research for Advanced Materials, Tohoku, University, 2-1-1 Katahira, Aoba-ku, Sendai, 980- 8577, Japan
^*Correspondence e-mail: [email protected]

Edited by M. Weil, Vienna University of Technology, Austria (Received 1 September 2025; accepted 13 October 2025; online 31 October 2025)

The crystal structures of two phases in the AgI–Ag₂SO₄ system, Ag₃ISO₄ (AgI:Ag₂SO₄ = 1:1; systematic name: trisilver iodide sulfate), and Ag₄I₂SO₄ (AgI:Ag₂SO₄ = 2:1; systematic name: tetrasilver diiodide sulfate), were determined by single-crystal X-ray diffraction. The crystal structure model of Ag₃ISO₄ contains triangularly arranged Ag atoms in zigzag ladder chains extending parallel to the a axis. The Ag zigzag ladder chains alternate with rows of SO₄ groups, while iodine atoms are accommodated within the concavities of the zigzag ladders. The crystal structure of Ag₄I₂SO₄ was refined using a split-atom model for two of the four Ag sites. The disordered Ag sites are situated between the layers containing SO₄ groups parallel to the ac plane, whereas the Ag sites within the SO₄ layers are fully occupied and exhibit no disorder. The positional disorder of some of the Ag sites is considered to be associated with the moderate ionic conductivity of Ag₄I₂SO₄, approximately 10⁻³ S cm⁻¹ at room temperature. This is the first report describing the crystal structures of compounds containing Ag⁺, SO₄^2– and I⁻.

Keywords: silver iodide sulfate; ionic conductivity; Ag⁺ Ag⁺ interaction; crystal structure.

CCDC references: 2494919; 2494918

1. Chemical context

α-Silver iodide (α-AgI) has been known as an Ag⁺ superionic conductor. The superionic conductive phase of AgI arises above the phase transition temperature of 420 K, and the ionic conductivity reaches a few S cm⁻¹ (Tubandt & Lorenz, 1914 ; Boyce & Huberman, 1979 ). α-AgI undergoes a phase transition to the β phase when the temperature is decreased, and the superionic conductivity is lost on the phase transition. The superionic conductivity of Ag⁺ at room temperature (RT) has been reported in ternary phases of AgI and alkali halides such as Ag₄RbI₅ (Owens & Argue, 1970 , 1967 ; Geller, 1967 ; Bradley & Greene, 1967a ,b ), Ag₄KI₅ (Owens & Argue, 1967; Bradley & Greene, 1966 , 1967a,b), and Ag₃KI₄ (Takahashi et al., 1970 ), and AgI and silver oxyacid salts in the glass states such as 0.8AgI–0.2(Ag₂O–B₂O₃) (Chiodelli et al., 1983 ), 0.58AgI–0.19Ag₂O–0.23WO₃ (Kuwano, 1990 ), 0.85AgI–0.15Ag₄P₂O₇ (Minami et al., 1977 , 1980 ) and 0.75AgI–0.25Ag₂MoO₄ (Minami & Tanaka, 1980a ,b ), and in the crystalline state such as Ag₁₉I₁₅P₂O₇, Ag₇I₄PO₄ (Takahashi et al., 1972a ) and Ag₂₆I₁₈(WO₄)₄ (Chan & Geller, 1977 ). We have recently reported two crystalline compounds Ag₁₇(CO₃)₃I₁₁ (Watanabe et al., 2021 ) and Ag₁₀(CO₃)₃I₄ (Suzuki et al., 2021 ) in the AgI–Ag₂CO₃ system and found that the former, Ag₁₇(CO₃)₃I₁₁, is a superionic conductor with a conductivity of about 0.1 S/cm at RT.

According to the phase diagram of the AgI–Ag₂SO₄ system proposed by Takahashi et al. (1972b ), there is no stable crystalline phase with a specific composition. They reported an ionic conductivity of 5.0×10⁻² S cm⁻¹ in the glass phase with composition (1 − x) AgI–x(Ag₂SO₄) at x = 0.18–0.25. We synthesized new crystalline compounds at x = 0.5 (Ag₃ISO₄) and 0.33 (Ag₄I₂SO₄). Polycrystalline bulk samples of Ag₃ISO₄ and Ag₄I₂SO₄ prepared at 443 and 417 K had ionic conductivities of 9.5×10⁻⁶ and 9.2×10⁻⁴ S cm⁻¹ at RT, respectively. These values are higher or comparable with those of Ag₁₃(AsO₄)₃I₄ (6.4×10⁻⁶ S cm⁻¹ at 303 K; Pitzschke et al., 2009a ) and Ag₁₀(CO₃)₃I₄ (4.4×10⁻⁶ S cm⁻¹ at RT; Suzuki et al., 2021). The ionic conductivities of Ag₃ISO₄ and Ag₄I₂SO₄ are not necessarily high compared to the Ag⁺ superionic conductors, but these compounds are important as precursors of superionic conductors in the (1 − x) AgI–x(Ag₂SO₄) system.

2. Structural commentary

Ag₃ISO₄ and Ag₄I₂SO₄ crystallize with orthorhombic symmetry in the space groups Pnma and Pna2₁, respectively. Figs. 1 and 2 show perspective views of the crystal structures of Ag₃ISO₄ and Ag₄I₂SO₄, and selected interatomic distances are collated in Tables 1 and 2.

Table 1
Selected bond lengths (Å) for Ag₃ISO₄

Ag1—O1ⁱ	2.384 (3)	Ag2—O1ⁱ	2.436 (3)
Ag1—O3	2.413 (3)	Ag2—O2	2.467 (4)
Ag1—O2	2.473 (3)	Ag2—I1^vi	2.8066 (7)
Ag1—I1ⁱⁱ	2.7838 (5)	Ag2—I1	3.1714 (7)
Ag1—Ag2ⁱⁱ	2.9973 (6)	S1—O1^vii	1.474 (3)
Ag1—Ag1ⁱⁱⁱ	3.0604 (8)	S1—O1	1.474 (3)
Ag1—Ag2^iv	3.2744 (6)	S1—O3	1.475 (4)
Ag2—O1^v	2.436 (3)	S1—O2^viii	1.488 (4)
Symmetry codes: (i) $[-x+{\script{1\over 2}}, y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (ii) $[-x+{\script{1\over 2}}, -y+1, z-{\script{1\over 2}}]$ ; (iii) $[x, -y+{\script{3\over 2}}, z]$ ; (iv) ; (v) $[-x+{\script{1\over 2}}, -y, z+{\script{1\over 2}}]$ ; (vi) $[x+{\script{1\over 2}}, y, -z+{\script{3\over 2}}]$ ; (vii) $[x, -y+{\script{1\over 2}}, z]$ ; (viii) $[x-{\script{1\over 2}}, y, -z+{\script{1\over 2}}]$ .

Table 2
Selected bond lengths (Å) for Ag₄I₂SO₄

Ag1A—O3	2.462 (5)	Ag3A—I1^v	2.838 (3)
Ag1A—O1ⁱ	2.468 (7)	Ag3A—Ag4	3.184 (2)
Ag1A—I2	2.863 (2)	Ag3B—O2	2.375 (18)
Ag1A—I2ⁱⁱ	3.038 (2)	Ag3B—I2	2.608 (17)
Ag1A—I1ⁱⁱⁱ	3.039 (5)	Ag3B—I1	2.686 (15)
Ag1A—Ag3B	3.256 (18)	Ag3C—O2	2.385 (19)
Ag1B—O3	2.412 (8)	Ag3C—I1^v	2.620 (17)
Ag1B—O4ⁱⁱ	2.541 (10)	Ag3C—I1	2.694 (16)
Ag1B—Ag3B	2.805 (19)	Ag3C—I2	3.263 (17)
Ag1B—I2	2.889 (7)	Ag3C—Ag4	3.290 (16)
Ag1B—I2ⁱⁱ	3.039 (7)	Ag4—O3^v	2.421 (6)
Ag1B—Ag3A	3.194 (10)	Ag4—O3^vi	2.469 (7)
Ag2—O1	2.347 (6)	Ag4—I1^v	3.0237 (13)
Ag2—O4^iv	2.386 (7)	Ag4—I2	3.0879 (13)
Ag2—O2ⁱ	2.423 (5)	Ag4—I1^iv	3.1247 (12)
Ag2—I2	2.8799 (9)	Ag4—I2^vii	3.1741 (13)
Ag2—Ag3C^iv	3.283 (18)	S1—O1^viii	1.466 (6)
Ag3A—O2	2.522 (6)	S1—O2^viii	1.468 (5)
Ag3A—I2	2.798 (3)	S1—O4	1.469 (7)
Ag3A—I1	2.8113 (19)	S1—O3	1.505 (5)
Symmetry codes: (i) $[-x, -y+1, z-{\script{1\over 2}}]$ ; (ii) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z]$ ; (iii) ; (iv) $[-x+{\script{1\over 2}}, y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ ; (v) $[x+{\script{1\over 2}}, -y+{\script{1\over 2}}, z]$ ; (vi) $[-x+{\script{1\over 2}}, y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (vii) $[-x+1, -y+1, z+{\script{1\over 2}}]$ ; (viii) $[-x+{\script{1\over 2}}, y-{\script{1\over 2}}, z-{\script{1\over 2}}]$ .

Figure 1
Perspective view of the crystal structure of Ag₃ISO₄. The probability of the anisotropic displacement ellipsoids is 50%. The asterisk denotes atoms located within the asymmetric unit.

Figure 2
Perspective view of the crystal structure of Ag₄I₂SO₄. The probability of the anisotropic displacement ellipsoids is 50%.. The asterisk denotes atoms located within the asymmetric unit.

Ag₃ISO₄ contains two Ag sites, one I site, one S site, and three O sites in the asymmetric unit; Ag₄I₂SO₄ contains four Ag sites, two I sites, one S site, and four O sites. Among the four Ag sites in Ag₄I₂SO₄, Ag1 and Ag3 are split into two and three sites, respectively, with occupancies of 0.74 (1) and 0.26 (1) for Ag1A and Ag1B, and 0.803 (4), 0.098 (4), and 0.099 (4) for Ag3A, Ag3B, and Ag3C. S atoms in both compounds form tetrahedral SO₄ groups, and their S—O distances are 1.474 (3) Å for two O1, 1.488 (4) Å for O2, and 1.475 (4) Å for O3 in Ag₃ISO₄ and 1.466 (6) Å for O1, 1.468 (5) Å for O2, 1.505 (5) Å for O3, and 1.469 (7) Å for O4 in Ag₄I₂SO₄. These values are comparable to the bond lengths between S and O in the SO₄ groups found in inorganic crystals, including minerals and compounds such as barite, BaSO₄ (1.464–1.483 Å; Sawada & Takeuchi, 1990 ), Ag₂SO₄ (1.473 Å; Mehrotra et al., 1978 ), Na₂SO₄ (1.479 Å; Hawthorne & Ferguson, 1975 ), and gypsum, CaSO₄·2H₂O (1.457–1.461 Å; Cole & Lancucki, 1974 ).

In Ag₃ISO₄, Ag1 and O1 occupy the Wykoff position 8d with site symmetry 1. Ag2, S, O2, O3, and I reside at the 4c position with site symmetry m perpendicular to the b axis. In Ag₄I₂SO₄, all the atoms lie on a general position 4a.

The silver atoms in Ag₃ISO₄ and Ag₄I₂SO₄ are surrounded by oxygen and iodine atoms, and the coordination environments are different between the two structures. All silver atoms in Ag₃ISO₄ are coordinated by three O atoms and one I atom. On the other hand, in Ag₄I₂SO₄, Ag1 (split into Ag1A and Ag1B) is surrounded by three O atoms belonging to two SO₄ groups and nearly coplanar by four I atoms; Ag2 is surrounded by three O atoms of three different SO₄ groups and three I atoms; Ag3 (split into Ag3A, Ag3B, and Ag3C) is coordinated by two O atoms and three I atoms; Ag4 is coordinated in form of a distorted octahedron with four I atoms at the equatorial and two O atoms at the axial positions. Table 3 compares the shortest and average distances of Ag—O and Ag—I in Ag₃ISO₄ and Ag₄I₂SO₄ with several silver compounds. Here, the averages were calculated for Ag—O distances shorter than ∼2.8 Å and for Ag—I shorter than ∼3.7 Å. These boundaries are based on the ionic radii of Ag⁺, O^2–, and I⁻ (Shannon, 1976 ). In averaging, a weight was taken into account, and the weight corresponds to the number of bonds present in the unit cell, which is calculated by multiplying the site multiplicity and the occupancy. The shortest Ag—O distances range from 1.886 Å in Ag₁₆I₁₂P₂O₇ to 2.405 Å in Ag₂SO₄. The shortest Ag—I distances in Ag₃ISO₄ and Ag₄I₂SO₄ are between the shortest Ag—I distance of 2.312 Å in Ag₂₆I₁₈(WO₄)₄ and 2.841 Å in Ag₃I(NO₃)₂. The average values of Ag—O and Ag—I distances in the title compounds are comparable to those observed for the other silver compounds listed in Table 3; the average Ag—I distance in Ag₃ISO₄, 2.791 Å, is slightly shorter than those in the other compounds, such as 2.814 Å in γ-AgI and 2.835 Å in Ag₁₆I₁₂P₂O₇.

Table 3
Comparison of interatomic distances (Å) between Ag atoms and anions in several silver compounds

Compound	Shortest Ag—O	Average Ag—O	Shortest Ag—I	Average Ag—I	Reference
Ag₃ISO₄	2.384	2.431	2.784	2.791	This work
Ag₄I₂SO₄	2.346	2.564	2.607	3.034	This work
Ag₂SO₄	2.405	2.511	–	–	Mehrotra et al. (1978)
Ag₂CO₃	2.245	2.421	–	–	Norby et al. (2002)
Ag₁₀(CO₃)₃I₄ⁱ	2.252	2.437	2.714	3.004	Suzuki et al. (2021)
γ-AgI	–	–	2.814	2.814	Hull & Keen (1999 )
Ag₁₃(AsO₄)₃I₄	2.293	2.375	2.708	3.071	Pitzschke et al. (2009a)
Ag₂₆I₁₈(WO₄)₄	2.195	2.478	2.312	2.916	Chan & Geller (1977)
Ag₄IPO₄ⁱⁱ	2.278	2.368	2.706	3.034	Oleneva et al. (2008)
Ag₁₆I₁₂P₂O₇	1.886	2.340	2.680	2.835	Garrett et al. (1982)
Ag₅IP₂O₇	2.274	2.466	2.765	2.948	Adams & Preusser (1999)
Ag₃I(NO₃)₂	2.250	2.594	2.841	2.942	Birnstock & Britton (1970)
Ag₈(CrO₄)₃I₂ⁱⁱⁱ	2.384	2.446	2.809	3.053	Pitzschke et al. (2009b)
Ag₉I₃(IO₃)₂(SeO₄)₂	2.306	2.508	2.719	2.886	Pitzschke et al. (2008b)
Ag₃ITeO₄	2.238	2.455	2.775	2.928	Pitzschke et al. (2008a)
Ag₄I₂SeO₄	2.322	2.508	2.822	3.069	Pitzschke et al. (2008a)
Ag₈I₄V₂O₇	2.182	2.364	1.927	3.128	Adams (1996)
Ag₉(GeO₄)₂I	2.106	2.222	3.364	3.431	Pitzschke et al. (2009c)
Measurement temperatures: (i) 90 K, (ii) 173 K, (iii) 273 K.

The shortest Ag—Ag distance of 2.9973 (6) Å is observed in Ag₃ISO₄ between Ag1 and Ag2 generated by the symmetry operation −x + $[{1\over 2}]$ , −y + 1, z − $[{1\over 2}]$ . The second shortest Ag—Ag distance is 3.0604 (8) Å between the adjacent Ag1 sites. Ag₄I₂SO₄ shows the shortest Ag—Ag distance between Ag1B and Ag3B of 2.805 (19) Å. These values are comparable to 2.873 Å in Ag₂CO₃ (Norby et al., 2002 ), 2.880 Å in Ag₈(CrO₄)₃I₂ (Pitzschke et al., 2009b ), and 2.942 Å in Ag₃I(NO₃)₂ (Birnstock & Britton, 1970 ). These rather short Ag—Ag distances are considered to be due to the argentophilic interaction between Ag⁺ ions in the d¹⁰ configuration, which often leads to characteristic arrangements of Ag in several inorganic crystals (Schmidbaur & Schier, 2015 ; Jansen, 1987 ). The arrangements of the silver atoms in the crystal structure of Ag₃ISO₄ and Ag₄I₂SO₄, excluding the other atoms, are illustrated in Figs. 3 and 4, respectively. In Ag₃ISO₄, the silver atoms form triangles, which are connected to each other by sharing the Ag1—Ag1 edges and the Ag2 corners, comprising zigzag ladder chains extending parallel to the a axis (Fig. 3). Fig. S1 (electronic supplementary information) shows the projected views of the crystal structure of Ag₃ISO₄ along the a axis (a) and b axis (b). It shows that the rows of SO₄ and the zigzag ladders of Ag are arranged alternately (a), and the iodine atoms are held in the concavities of the zigzag ladder chains (b). In Ag₄I₂SO₄, the Ag atoms form Ag₄ clusters, the arrangement of which in the crystal structure is shown in Fig. 4. The shortest and the second shortest I⋯I distances in Ag₄I₂SO₄ are 4.2135 (10) nd 4.3301 (8) Å. By connecting I1 and I2, helical chains of iodine atoms along the c axis are recognized in Ag₄I₂SO₄ (Fig. S2). The Ag₄ clusters and the SO₄ groups in Ag₄I₂SO₄ fill the space between the helical chains of I atoms.

Figure 3
Arrangement of Ag atoms in Ag₃ISO₄. The linkers connect the Ag atoms within 3.3 Å for ease of visibility.

Figure 4
Arrangement of Ag atoms in Ag₄I₂SO₄ (sliced view in the range x = 0.5–1.0). The linkers connect the Ag atoms within 3.3 Å for ease of visibility.

3. Database survey

The Inorganic Crystal Structure Database (ICSD; Zagorac et al., 2019 ) contains the crystal structure data for quaternary solid-state inorganic compounds comprising silver and iodide ions and oxyacid groups, such as Ag₃I(NO₃)₂ (Birnstock & Britton, 1970), Ag₁₆I₁₂P₂O₇ (Garrett et al., 1982 ), Ag₅IP₂O₇ (Adams & Preusser, 1999 ), Ag₄IPO₄ (Oleneva et al., 2008 ), Ag₈(CrO₄)₃I₂ (Pitzschke et al., 2009b), Ag₉(GeO₄)₂I (Pitzschke et al., 2009c ), Ag₈I₄V₂O₇ (Adams, 1996 ), Ag₁₃(AsO₄)₃I₄ (Pitzschke et al., 2009a), Ag₄I₂SeO₄ (Pitzschke et al., 2008a ), Ag₃ITeO₄ (Pitzschke et al., 2008a), Ag₉I₃(IO₃)₂(SeO₄)₂ (Pitzschke et al., 2008b ) and Ag₂₆I₁₈(WO₄)₄ (Chan & Geller, 1977). We have recently reported the crystal structures of two silver carbonate iodides with compositions of Ag₁₇(CO₃)₃I₁₁ (Watanabe et al., 2021) and Ag₁₀(CO₃)₃I₄ (Suzuki et al., 2021).

There are no data in the ICSD of a phase containing Ag⁺, I⁻, and SO₄^2–. Compounds containing I⁻ and SO₄^2– in the crystal structure included in ICSD are (Pt(NH₃)₄)₂I₂(HSO₄)₃OH·H₂O (Clark et al., 1982 ), (Pt(NH₃)₄)(PtI₂(NH₃)₄)(HSO₄)₄·2H₂O (Tanaka et al., 1986 ) and H(I(SO₄)₂) (Jansen & Müller, 1998 ).

4. Synthesis and crystallization

The starting material AgI was precipitated at 323 K in aqueous solutions of AgNO₃ (99.8%, Kanto Chemical, Japan) and KI (99.5%, Kanto Chemical, Japan); Ag₂SO₄ was precipitated at RT in an aqueous solution of AgNO₃ and 5-times diluted sulfuric acid (Kanto Chemical, Japan). The resulting AgI and Ag₂SO₄ powders were thoroughly mixed in an agate mortar at a molar ratio of 1:1 using a small amount of water as a mixing medium. The mixed powder was placed in a glass tube with one end open, heated in air at 433 K for 1 h, and cooled slowly to 408 K at a rate of 0.5 K/h. These conditions were determined after thermogravimetric-differential thermal analysis (TG-DTA) under constant flow of synthetic dry air (Fig. S3). Fig. S3 shows the TG-DTA curves of a mixture of AgI and Ag₂SO₄ powders in a 1:1 ratio. A sharp endothermic effect was observed at 431 K, corresponding to the melting point of this composition. The TG curve showed no substantial mass loss, indicating thermal stability in air up to 520 K. Upon cooling to RT, translucent pale brown lumps were obtained. Like other silver compounds, the silver iodide sulfates are moderately photosensitive, so the samples were treated in the dark under red light through the color filter from an LED lamp. Each fragment of the two types of crystals found in the lumps was fixed on glass fibers with an epoxy resin and mounted on a goniometer. The XRD data were collected at RT in the dark.

Powder samples of Ag₃ISO₄ and Ag₄I₂SO₄ were prepared from AgI and Ag₂SO₄ to verify the validity of the crystal structure models determined by single crystal XRD, and the powder data were analyzed using the Rietveld method. Ag₂SO₄ was prepared from an aqueous solution of AgNO₃ and sulfuric acid for the synthesis of Ag₃ISO₄, and from aqueous solutions of AgNO₃ and Na₂SO₄ for the synthesis of Ag₄I₂SO₄. AgI and Ag₂SO₄ were then mixed in molar ratios of 1:1 and 1:2, and heated in air at 414 K for 1 h to obtain Ag₃ISO₄, and at 411 K for 3 h to obtain Ag₄I₂SO₄. For Ag₄I₂SO₄, in order to reduce unreacted AgI and the by-product Ag₃ISO₄ phase, the heated mixture was slowly cooled to 373 K in the heater, followed by the repeated heat treatment after thorough grinding.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 4.

Table 4
Experimental details

	Ag₃ISO₄	Ag₄I₂SO₄
Crystal data
Chemical formula	Ag₃ISO₄	Ag₄I₂SO₄
M_r	546.57	781.34
Crystal system, space group	Orthorhombic, Pnma	Orthorhombic, Pna2₁
Temperature (K)	300	301
a, b, c (Å)	8.9418 (6), 6.9182 (5), 10.2660 (7)	9.2072 (3), 13.1007 (4), 6.9528 (2)
V (Å³)	635.07 (8)	838.65 (4)
Z	4	4
Radiation type	Mo Kα	Mo Kα
μ (mm⁻¹)	14.28	16.77
Crystal size (mm)	0.05 × 0.04 × 0.04	0.10 × 0.03 × 0.01

Data collection
Diffractometer	Bruker APEXII CCD	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )	Multi-scan (SADABS; Krause et al., 2015)
T_min, T_max	0.615, 0.746	0.53, 0.75
No. of measured, independent and observed [I > 2σ(I)] reflections	16851, 790, 770	6220, 1806, 1768
R_int	0.039	0.035
(sin θ/λ)_max (Å⁻¹)	0.650	0.649

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.020, 0.047, 1.15	0.022, 0.051, 1.08
No. of reflections	790	1806
No. of parameters	49	115
No. of restraints	0	2
Δρ_max, Δρ_min (e Å⁻³)	1.18, −0.87	0.93, −0.79
Absolute structure	–	Refined as an inversion twin
Absolute structure parameter	–	0.35 (4)
Computer programs: APEX3 and SAINT (Bruker, 2017 ), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ), VESTA (Momma & Izumi, 2011 ) and publCIF (Westrip, 2010 ).

In the refined model of Ag₃ISO₄, the highest difference electron density peak of 1.18 e Å⁻³ is at a position 0.8646 (5) Å distant from I1. Two difference peaks of 1.10 and 1.03 e Å⁻³ remained at positions 0.7562 (5) and 0.7659 (4) Å distant from Ag1, and two peaks of 0.94 and 0.90 e Å⁻³ at positions 0.7782 (6) and 0.9591 (6) Å distant from Ag2. Difference peaks lower than 0.8 e Å⁻³ were detected near I1 (0.76 e Å⁻³), O3 (0.60 e Å⁻³), and Ag2 (0.55 e Å⁻³).

The crystal structure of Ag₄I₂SO₄ was refined using a split-atom model for the Ag1 and Ag3 sites. For Ag1, 74.2% of the silver atoms occupy the Ag1A site, while the remaining 25.8% are distributed over the Ag1B site, located 0.595 (13) Å distant from Ag1A. For the Ag3 site, 80.3% of the silver atoms reside on the Ag3A site, with approximately 10% each distributed on the Ag3B and Ag3C sites, located 0.508 (17) and 0.49 (3) Å distant from Ag3A, respectively. Figure S4 presents a projection of the crystal structure of Ag₄I₂SO₄ along the a axis. The disordered Ag1 and Ag3 sites are located between SO₄ layers parallel to the ac plane, whereas the Ag2 and Ag4 sites within the SO₄ layers are fully occupied. As described in section 1, Ag₄I₂SO₄ exhibits a moderate ionic conductivity of 9.2×10⁻⁴ S cm⁻¹ at RT, and the positional disorder of the Ag sites is considered to be associated with this conductivity. Furthermore, the disorder observed at the Ag1 and Ag3 sites suggests site-dependent contributions to Ag⁺ conduction. Specifically, Ag⁺ diffusion occurs preferentially within the interlayer spaces between the SO₄ layers via the Ag1 and Ag3 sites, whereas silver atoms at the Ag2 and Ag4 sites provide a minor contribution to Ag⁺ conduction. In the refined model of Ag₄I₂SO₄, the highest difference electron density peak of 0.93 e Å⁻³ is near the Ag3 site, with distances between 0.800 (3) Å from Ag3A and 1.16 (2) Å from Ag3C. The second and fourth highest difference peaks (0.79 and 0.57 e Å⁻³) are at positions 0.8720 (7) and 0.7644 (7) Å distant from I1. The third-highest difference peak of 0.64 e Å⁻³ is found at (0.2880, 0.2611, 0.7269), corresponding to an interstitial position surrounded by two Ag atoms (Ag2 and Ag3), three I atoms, and O1. The distances are 1.86 (3) Å from Ag3C, 2.7660 (9) Å from Ag2, 2.6543 (7) and 2.6599 (7) Å from I1, 2.7182 (7) Å from I2, and 2.235 (7) Å from O1.

The structure models refined on basis of single crystal XRD data were verified by powder X-ray data using a Rietveld analysis (PDXL; Rigaku, 2018 ). The powder XRD data were collected using a Rigaku MiniFlex 600 powder X-ray diffractometer with Cu Kα radiation (λ = 1.54183 Å) equipped with a 1D detector (Rigaku D/teX Ultra 250). The refinements were carried out with the atomic coordinates (x, y, z) and the atomic displacement parameters (B) fixed to those determined by the single crystal XRD study, and converged with R_wp/R_p/S = 5.31%/3.53%/3.98 for Ag₃ISO₄ and 3.06%/2.40%/1.33 for Ag₄I₂SO₄ (Figure S5). The lattice parameters refined by the Rietveld analysis are a = 8.9437 (2), b = 6.9241 (2), and c = 10.2516 (2) Å for Ag₃ISO₄, and a = 9.2026 (4), b = 13.1072 (5), and c = 6.9545 (3) Å for Ag₄I₂SO₄. These values are in good agreement with those obtained by the single crystal XRD analysis (Table 4).

Supporting information

CCDC references: 2494919; 2494918

Crystal structure: contains datablocks global, Ag3ISO4, Ag4I2SO4. DOI: https://doi.org/10.1107/S2056989025008898/wm5769sup1.cif

Structure factors: contains datablock Ag3ISO4. DOI: https://doi.org/10.1107/S2056989025008898/wm5769Ag3ISO4sup2.hkl

Structure factors: contains datablock Ag4I2SO4. DOI: https://doi.org/10.1107/S2056989025008898/wm5769Ag4I2SO4sup3.hkl

Rietveld powder data: contains datablock Ag3ISO4. DOI: https://doi.org/10.1107/S2056989025008898/wm5769Ag3ISO4sup4.rtv

Rietveld powder data: contains datablock Ag4I2SO4. DOI: https://doi.org/10.1107/S2056989025008898/wm5769Ag4I2SO4sup5.rtv

checkCIF report

Computing details top

Trisilver iodide sulfate (Ag3ISO4) top

Crystal data top

Ag₃ISO₄	D_x = 5.717 Mg m⁻³
M_r = 546.57	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pnma	Cell parameters from 9985 reflections
a = 8.9418 (6) Å	θ = 3.0–27.5°
b = 6.9182 (5) Å	µ = 14.28 mm⁻¹
c = 10.2660 (7) Å	T = 300 K
V = 635.07 (8) Å³	Block, translucent colourless-brown
Z = 4	0.05 × 0.04 × 0.04 mm
F(000) = 968

Data collection top

Bruker APEXII CCD diffractometer	790 independent reflections
Radiation source: micro focus sealed tube	770 reflections with I > 2σ(I)
Detector resolution: 7.3910 pixels mm^-1	R_int = 0.039
φ and ω scans	θ_max = 27.5°, θ_min = 3.0°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −11→11
T_min = 0.615, T_max = 0.746	k = −8→8
16851 measured reflections	l = −13→13

Refinement top

Refinement on F²	49 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.020	w = 1/[σ²(F_o²) + (0.0157P)² + 3.707P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.047	(Δ/σ)_max = 0.001
S = 1.15	Δρ_max = 1.18 e Å⁻³
790 reflections	Δρ_min = −0.87 e Å⁻³

Special details top

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 (Å²) top

	x	y	z	U_iso*/U_eq
Ag1	0.32585 (4)	0.52882 (5)	0.31134 (4)	0.03257 (12)
Ag2	0.36026 (6)	0.250000	0.61963 (5)	0.02763 (13)
S1	0.13364 (15)	0.250000	0.10724 (13)	0.0164 (3)
O1	0.1902 (3)	0.0758 (4)	0.0410 (3)	0.0241 (6)
O2	0.4673 (4)	0.250000	0.3981 (4)	0.0228 (9)
O3	0.1830 (5)	0.250000	0.2443 (4)	0.0261 (9)
I1	0.00623 (4)	0.250000	0.63835 (4)	0.02701 (12)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ag1	0.0456 (2)	0.0224 (2)	0.0297 (2)	−0.00483 (15)	−0.00981 (15)	0.00358 (13)
Ag2	0.0364 (3)	0.0214 (2)	0.0251 (2)	0.000000	0.00360 (19)	0.000000
S1	0.0173 (6)	0.0124 (6)	0.0196 (6)	0.000000	−0.0023 (5)	0.000000
O1	0.0279 (15)	0.0149 (14)	0.0296 (16)	0.0039 (12)	0.0007 (12)	−0.0033 (12)
O2	0.0167 (19)	0.022 (2)	0.029 (2)	0.000000	0.0022 (17)	0.000000
O3	0.032 (2)	0.025 (2)	0.021 (2)	0.000000	−0.0065 (18)	0.000000
I1	0.0207 (2)	0.0343 (2)	0.0260 (2)	0.000000	−0.00100 (15)	0.000000

Geometric parameters (Å, º) top

Ag1—O1ⁱ	2.384 (3)	Ag2—O1ⁱ	2.436 (3)
Ag1—O3	2.413 (3)	Ag2—O2	2.467 (4)
Ag1—O2	2.473 (3)	Ag2—I1^vi	2.8066 (7)
Ag1—I1ⁱⁱ	2.7838 (5)	Ag2—I1	3.1714 (7)
Ag1—Ag2ⁱⁱ	2.9973 (6)	S1—O1^vii	1.474 (3)
Ag1—Ag1ⁱⁱⁱ	3.0604 (8)	S1—O1	1.474 (3)
Ag1—Ag2^iv	3.2744 (6)	S1—O3	1.475 (4)
Ag2—O1^v	2.436 (3)	S1—O2^viii	1.488 (4)

O1ⁱ—Ag1—O3	111.03 (13)	Ag1^x—Ag2—I1	53.562 (13)
O1ⁱ—Ag1—O2	77.35 (12)	O1^v—Ag2—Ag1^iv	131.52 (7)
O3—Ag1—O2	75.51 (11)	O1ⁱ—Ag2—Ag1^iv	78.36 (7)
O1ⁱ—Ag1—I1ⁱⁱ	126.05 (7)	O2—Ag2—Ag1^iv	82.36 (9)
O3—Ag1—I1ⁱⁱ	122.87 (11)	I1^vi—Ag2—Ag1^iv	53.825 (13)
O2—Ag1—I1ⁱⁱ	112.50 (9)	Ag1^ix—Ag2—Ag1^iv	95.464 (13)
O1ⁱ—Ag1—Ag2ⁱⁱ	123.11 (7)	Ag1^x—Ag2—Ag1^iv	124.916 (17)
O3—Ag1—Ag2ⁱⁱ	85.82 (8)	I1—Ag2—Ag1^iv	147.406 (12)
O2—Ag1—Ag2ⁱⁱ	156.75 (9)	O1^v—Ag2—Ag1^xi	78.36 (7)
I1ⁱⁱ—Ag1—Ag2ⁱⁱ	66.419 (15)	O1ⁱ—Ag2—Ag1^xi	131.52 (7)
O1ⁱ—Ag1—Ag1ⁱⁱⁱ	82.17 (7)	O2—Ag2—Ag1^xi	82.36 (9)
O3—Ag1—Ag1ⁱⁱⁱ	143.06 (8)	I1^vi—Ag2—Ag1^xi	53.825 (13)
O2—Ag1—Ag1ⁱⁱⁱ	141.27 (8)	Ag1^ix—Ag2—Ag1^xi	124.916 (17)
I1ⁱⁱ—Ag1—Ag1ⁱⁱⁱ	56.657 (9)	Ag1^x—Ag2—Ag1^xi	95.464 (13)
Ag2ⁱⁱ—Ag1—Ag1ⁱⁱⁱ	59.302 (9)	I1—Ag2—Ag1^xi	147.406 (12)
O1ⁱ—Ag1—Ag2^iv	76.94 (7)	Ag1^iv—Ag2—Ag1^xi	55.720 (16)
O3—Ag1—Ag2^iv	152.71 (9)	O1^vii—S1—O1	109.7 (3)
O2—Ag1—Ag2^iv	81.26 (8)	O1^vii—S1—O3	109.73 (16)
I1ⁱⁱ—Ag1—Ag2^iv	54.469 (13)	O1—S1—O3	109.73 (16)
Ag2ⁱⁱ—Ag1—Ag2^iv	112.299 (13)	O1^vii—S1—O2^viii	109.04 (16)
Ag1ⁱⁱⁱ—Ag1—Ag2^iv	62.141 (8)	O1—S1—O2^viii	109.04 (16)
O1^v—Ag2—O1ⁱ	135.36 (14)	O3—S1—O2^viii	109.5 (3)
O1^v—Ag2—O2	76.49 (8)	S1—O1—Ag1^xii	123.18 (18)
O1ⁱ—Ag2—O2	76.49 (8)	S1—O1—Ag2^xiii	122.67 (17)
O1^v—Ag2—I1^vi	112.31 (7)	Ag1^xii—O1—Ag2^xiii	100.99 (11)
O1ⁱ—Ag2—I1^vi	112.31 (7)	S1^xiv—O2—Ag2	114.9 (2)
O2—Ag2—I1^vi	129.46 (10)	S1^xiv—O2—Ag1^vii	119.86 (13)
O1^v—Ag2—Ag1^ix	125.95 (7)	Ag2—O2—Ag1^vii	97.68 (11)
O1ⁱ—Ag2—Ag1^ix	69.06 (7)	S1^xiv—O2—Ag1	119.86 (13)
O2—Ag2—Ag1^ix	145.14 (4)	Ag2—O2—Ag1	97.68 (11)
I1^vi—Ag2—Ag1^ix	71.152 (15)	Ag1^vii—O2—Ag1	102.54 (15)
O1^v—Ag2—Ag1^x	69.06 (7)	S1—O3—Ag1^vii	115.50 (15)
O1ⁱ—Ag2—Ag1^x	125.95 (7)	S1—O3—Ag1	115.50 (15)
O2—Ag2—Ag1^x	145.14 (4)	Ag1^vii—O3—Ag1	106.12 (16)
I1^vi—Ag2—Ag1^x	71.152 (15)	Ag1^ix—I1—Ag1^x	66.688 (19)
Ag1^ix—Ag2—Ag1^x	61.397 (17)	Ag1^ix—I1—Ag2^xv	71.707 (15)
O1^v—Ag2—I1	80.51 (7)	Ag1^x—I1—Ag2^xv	71.707 (15)
O1ⁱ—Ag2—I1	80.51 (7)	Ag1^ix—I1—Ag2	60.018 (13)
O2—Ag2—I1	116.30 (10)	Ag1^x—I1—Ag2	60.018 (13)
I1^vi—Ag2—I1	114.243 (18)	Ag2^xv—I1—Ag2	121.190 (18)
Ag1^ix—Ag2—I1	53.563 (13)

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

Tetrasilver diiodide sulfate (Ag4I2SO4) top

Crystal data top

Ag₄I₂SO₄	D_x = 6.188 Mg m⁻³
M_r = 781.34	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pna2₁	Cell parameters from 6005 reflections
a = 9.2072 (3) Å	θ = 2.7–27.5°
b = 13.1007 (4) Å	µ = 16.77 mm⁻¹
c = 6.9528 (2) Å	T = 301 K
V = 838.65 (4) Å³	Platelet, translucent light colourless-brown
Z = 4	0.10 × 0.03 × 0.01 mm
F(000) = 1368

Data collection top

Bruker APEXII CCD diffractometer	1806 independent reflections
Radiation source: micro focus sealed tube	1768 reflections with I > 2σ(I)
Detector resolution: 7.3910 pixels mm^-1	R_int = 0.035
φ and ω scans	θ_max = 27.5°, θ_min = 2.7°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −11→11
T_min = 0.53, T_max = 0.75	k = −14→17
6220 measured reflections	l = −8→9

Refinement top

Refinement on F²	w = 1/[σ²(F_o²) + (0.017P)² + 1.4488P] where P = (F_o² + 2F_c²)/3
Least-squares matrix: full	(Δ/σ)_max < 0.001
R[F² > 2σ(F²)] = 0.022	Δρ_max = 0.93 e Å⁻³
wR(F²) = 0.051	Δρ_min = −0.79 e Å⁻³
S = 1.08	Extinction correction: SHELXL-2017/1 (Sheldrick 2015b)
1806 reflections	Extinction coefficient: 0.00063 (15)
115 parameters	Absolute structure: Refined as an inversion twin
2 restraints	Absolute structure parameter: 0.35 (4)

Special details top

Refinement. Refined as a 2-component inversion twin.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ag1A	0.0380 (2)	0.24220 (17)	0.0000 (8)	0.0529 (8)	0.742 (10)
Ag1B	0.0376 (7)	0.2412 (6)	0.0855 (16)	0.0529 (8)	0.258 (10)
Ag2	0.11553 (8)	0.58050 (6)	0.06521 (13)	0.04291 (19)
Ag3A	0.2608 (2)	0.31320 (14)	0.4098 (4)	0.0525 (4)	0.803 (4)
Ag3B	0.2122 (16)	0.3217 (11)	0.379 (3)	0.0525 (4)	0.098 (4)
Ag3C	0.2674 (19)	0.3129 (13)	0.480 (3)	0.0525 (4)	0.099 (4)
Ag4	0.48770 (11)	0.48881 (8)	0.31016 (16)	0.0547 (3)
S1	0.31461 (18)	0.07193 (12)	0.0636 (3)	0.0208 (3)
O1	0.1337 (7)	0.6252 (5)	0.3912 (9)	0.0317 (14)
O2	0.1397 (6)	0.4646 (4)	0.5663 (12)	0.0350 (13)
O3	0.1513 (5)	0.0756 (4)	0.0660 (10)	0.0263 (11)
O4	0.3705 (7)	0.1259 (5)	0.2334 (10)	0.0337 (15)
I1	0.04299 (6)	0.19055 (4)	0.57387 (12)	0.03413 (16)
I2	0.26710 (6)	0.38893 (4)	0.03359 (10)	0.03490 (16)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ag1A	0.0359 (4)	0.0306 (4)	0.092 (2)	0.0056 (3)	−0.0114 (10)	0.0028 (11)
Ag1B	0.0359 (4)	0.0306 (4)	0.092 (2)	0.0056 (3)	−0.0114 (10)	0.0028 (11)
Ag2	0.0453 (4)	0.0525 (4)	0.0309 (4)	0.0006 (3)	−0.0006 (3)	−0.0021 (4)
Ag3A	0.0425 (8)	0.0608 (7)	0.0541 (11)	−0.0027 (6)	0.0023 (10)	0.0136 (8)
Ag3B	0.0425 (8)	0.0608 (7)	0.0541 (11)	−0.0027 (6)	0.0023 (10)	0.0136 (8)
Ag3C	0.0425 (8)	0.0608 (7)	0.0541 (11)	−0.0027 (6)	0.0023 (10)	0.0136 (8)
Ag4	0.0615 (5)	0.0574 (5)	0.0452 (5)	0.0062 (4)	0.0188 (4)	−0.0102 (4)
S1	0.0196 (8)	0.0210 (7)	0.0218 (8)	−0.0008 (6)	0.0004 (7)	−0.0001 (9)
O1	0.036 (3)	0.036 (4)	0.023 (3)	0.005 (3)	−0.006 (2)	0.001 (3)
O2	0.029 (3)	0.025 (2)	0.051 (4)	−0.004 (2)	0.004 (3)	0.003 (4)
O3	0.019 (2)	0.030 (2)	0.030 (3)	0.0000 (19)	0.004 (3)	0.008 (3)
O4	0.036 (3)	0.036 (4)	0.029 (3)	−0.001 (3)	−0.005 (3)	−0.005 (3)
I1	0.0326 (3)	0.0300 (3)	0.0397 (3)	−0.00035 (19)	0.0040 (3)	0.0033 (3)
I2	0.0268 (3)	0.0339 (3)	0.0440 (4)	0.00010 (18)	0.0011 (3)	0.0008 (3)

Geometric parameters (Å, º) top

Ag1A—Ag1B	0.595 (7)	Ag3A—I1^v	2.838 (3)
Ag1A—O3	2.462 (5)	Ag3A—Ag4	3.184 (2)
Ag1A—O1ⁱ	2.468 (7)	Ag3B—Ag3C	0.88 (3)
Ag1A—I2	2.863 (2)	Ag3B—O2	2.375 (18)
Ag1A—I2ⁱⁱ	3.038 (2)	Ag3B—I2	2.608 (17)
Ag1A—I1ⁱⁱⁱ	3.039 (5)	Ag3B—I1	2.686 (15)
Ag1A—Ag3B	3.256 (18)	Ag3C—O2	2.385 (19)
Ag1B—O3	2.412 (8)	Ag3C—I1^v	2.620 (17)
Ag1B—O4ⁱⁱ	2.541 (10)	Ag3C—I1	2.694 (16)
Ag1B—Ag3B	2.805 (19)	Ag3C—I2	3.263 (17)
Ag1B—I2	2.889 (7)	Ag3C—Ag4	3.290 (16)
Ag1B—I2ⁱⁱ	3.039 (7)	Ag4—O3^v	2.421 (6)
Ag1B—Ag3A	3.194 (10)	Ag4—O3^vi	2.469 (7)
Ag2—O1	2.347 (6)	Ag4—I1^v	3.0237 (13)
Ag2—O4^iv	2.386 (7)	Ag4—I2	3.0879 (13)
Ag2—O2ⁱ	2.423 (5)	Ag4—I1^iv	3.1247 (12)
Ag2—I2	2.8799 (9)	Ag4—I2^vii	3.1741 (13)
Ag2—Ag3C^iv	3.283 (18)	S1—O1^viii	1.466 (6)
Ag3A—Ag3B	0.508 (14)	S1—O2^viii	1.468 (5)
Ag3A—O2	2.522 (6)	S1—O4	1.469 (7)
Ag3A—I2	2.798 (3)	S1—O3	1.505 (5)
Ag3A—I1	2.8113 (19)

Ag1B—Ag1A—O3	78.3 (9)	I2—Ag4—I1^iv	88.37 (3)
Ag1B—Ag1A—O1ⁱ	108.5 (9)	O3^v—Ag4—I2^vii	94.40 (13)
O3—Ag1A—O1ⁱ	162.3 (2)	O3^vi—Ag4—I2^vii	77.50 (12)
Ag1B—Ag1A—I2	86.5 (9)	I1^v—Ag4—I2^vii	88.60 (3)
O3—Ag1A—I2	105.54 (14)	I2—Ag4—I2^vii	170.55 (4)
O1ⁱ—Ag1A—I2	91.39 (17)	I1^iv—Ag4—I2^vii	83.97 (3)
Ag1B—Ag1A—I2ⁱⁱ	84.5 (9)	O3^v—Ag4—Ag3A	107.99 (13)
O3—Ag1A—I2ⁱⁱ	80.34 (13)	O3^vi—Ag4—Ag3A	80.56 (12)
O1ⁱ—Ag1A—I2ⁱⁱ	84.01 (16)	I1^v—Ag4—Ag3A	54.34 (5)
I2—Ag1A—I2ⁱⁱ	168.03 (17)	I2—Ag4—Ag3A	52.97 (5)
Ag1B—Ag1A—I1ⁱⁱⁱ	165.8 (9)	I1^iv—Ag4—Ag3A	131.78 (6)
O3—Ag1A—I1ⁱⁱⁱ	88.7 (2)	I2^vii—Ag4—Ag3A	136.45 (6)
O1ⁱ—Ag1A—I1ⁱⁱⁱ	82.4 (2)	O3^v—Ag4—Ag3C	113.0 (3)
I2—Ag1A—I1ⁱⁱⁱ	102.59 (13)	O3^vi—Ag4—Ag3C	75.2 (3)
I2ⁱⁱ—Ag1A—I1ⁱⁱⁱ	87.79 (10)	I1^v—Ag4—Ag3C	48.8 (3)
Ag1B—Ag1A—Ag3B	37.0 (9)	I2—Ag4—Ag3C	61.4 (3)
O3—Ag1A—Ag3B	85.6 (3)	I1^iv—Ag4—Ag3C	136.5 (3)
O1ⁱ—Ag1A—Ag3B	109.8 (3)	I2^vii—Ag4—Ag3C	128.0 (3)
I2—Ag1A—Ag3B	49.9 (3)	Ag3A—Ag4—Ag3C	8.6 (3)
I2ⁱⁱ—Ag1A—Ag3B	121.5 (3)	O1^viii—S1—O2^viii	111.9 (4)
I1ⁱⁱⁱ—Ag1A—Ag3B	148.5 (3)	O1^viii—S1—O4	108.3 (3)
Ag1A—Ag1B—O3	87.8 (9)	O2^viii—S1—O4	110.5 (4)
Ag1A—Ag1B—O4ⁱⁱ	113.2 (9)	O1^viii—S1—O3	108.6 (4)
O3—Ag1B—O4ⁱⁱ	154.4 (5)	O2^viii—S1—O3	108.5 (3)
Ag1A—Ag1B—Ag3B	135.6 (10)	O4—S1—O3	109.0 (4)
O3—Ag1B—Ag3B	97.5 (4)	S1^vi—O1—Ag2	134.0 (4)
O4ⁱⁱ—Ag1B—Ag3B	78.2 (4)	S1^vi—O1—Ag1A^x	107.0 (4)
Ag1A—Ag1B—I2	81.6 (9)	Ag2—O1—Ag1A^x	115.2 (3)
O3—Ag1B—I2	106.1 (3)	S1^vi—O2—Ag3B	131.9 (5)
O4ⁱⁱ—Ag1B—I2	92.0 (3)	S1^vi—O2—Ag3C	130.8 (5)
Ag3B—Ag1B—I2	54.5 (3)	Ag3B—O2—Ag3C	21.2 (6)
Ag1A—Ag1B—I2ⁱⁱ	84.3 (9)	S1^vi—O2—Ag2^x	120.8 (3)
O3—Ag1B—I2ⁱⁱ	81.1 (2)	Ag3B—O2—Ag2^x	94.5 (4)
O4ⁱⁱ—Ag1B—I2ⁱⁱ	86.4 (2)	Ag3C—O2—Ag2^x	105.9 (5)
Ag3B—Ag1B—I2ⁱⁱ	140.1 (5)	S1^vi—O2—Ag3A	128.4 (4)
I2—Ag1B—I2ⁱⁱ	163.8 (4)	Ag3B—O2—Ag3A	11.4 (4)
Ag1A—Ag1B—Ag3A	134.0 (10)	Ag3C—O2—Ag3A	11.1 (4)
O3—Ag1B—Ag3A	91.5 (3)	Ag2^x—O2—Ag3A	103.6 (2)
O4ⁱⁱ—Ag1B—Ag3A	84.3 (3)	S1—O3—Ag1B	117.6 (3)
Ag3B—Ag1B—Ag3A	6.3 (3)	S1—O3—Ag4ⁱⁱ	128.2 (4)
I2—Ag1B—Ag3A	54.51 (14)	Ag1B—O3—Ag4ⁱⁱ	90.2 (3)
I2ⁱⁱ—Ag1B—Ag3A	141.0 (4)	S1—O3—Ag1A	116.7 (3)
O1—Ag2—O4^iv	150.21 (19)	Ag1B—O3—Ag1A	13.97 (18)
O1—Ag2—O2ⁱ	97.3 (3)	Ag4ⁱⁱ—O3—Ag1A	100.2 (2)
O4^iv—Ag2—O2ⁱ	96.7 (3)	S1—O3—Ag4^viii	119.7 (4)
O1—Ag2—I2	104.87 (16)	Ag1B—O3—Ag4^viii	103.3 (3)
O4^iv—Ag2—I2	96.73 (16)	Ag4ⁱⁱ—O3—Ag4^viii	91.27 (16)
O2ⁱ—Ag2—I2	104.94 (13)	Ag1A—O3—Ag4^viii	93.1 (2)
O1—Ag2—Ag3C^iv	85.3 (4)	S1—O4—Ag2^ix	132.5 (4)
O4^iv—Ag2—Ag3C^iv	65.0 (3)	S1—O4—Ag1B^v	102.5 (4)
O2ⁱ—Ag2—Ag3C^iv	123.0 (3)	Ag2^ix—O4—Ag1B^v	122.0 (4)
I2—Ag2—Ag3C^iv	129.4 (3)	Ag3Cⁱⁱ—I1—Ag3B	116.6 (6)
Ag3B—Ag3A—O2	68 (2)	Ag3Cⁱⁱ—I1—Ag3C	133.9 (5)
Ag3B—Ag3A—I2	63 (2)	Ag3B—I1—Ag3C	18.7 (5)
O2—Ag3A—I2	97.68 (19)	Ag3Cⁱⁱ—I1—Ag3A	126.9 (4)
Ag3B—Ag3A—I1	70.6 (18)	Ag3B—I1—Ag3A	10.3 (3)
O2—Ag3A—I1	87.66 (14)	Ag3C—I1—Ag3A	10.0 (4)
I2—Ag3A—I1	126.63 (9)	Ag3Cⁱⁱ—I1—Ag3Aⁱⁱ	9.3 (4)
Ag3B—Ag3A—I1^v	168.1 (17)	Ag3B—I1—Ag3Aⁱⁱ	109.8 (3)
O2—Ag3A—I1^v	104.18 (17)	Ag3C—I1—Ag3Aⁱⁱ	128.0 (4)
I2—Ag3A—I1^v	111.27 (7)	Ag3A—I1—Ag3Aⁱⁱ	119.99 (8)
I1—Ag3A—I1^v	118.69 (9)	Ag3Cⁱⁱ—I1—Ag4ⁱⁱ	70.9 (4)
Ag3B—Ag3A—Ag4	109.1 (17)	Ag3B—I1—Ag4ⁱⁱ	106.8 (4)
O2—Ag3A—Ag4	79.38 (13)	Ag3C—I1—Ag4ⁱⁱ	116.4 (4)
I2—Ag3A—Ag4	61.75 (5)	Ag3A—I1—Ag4ⁱⁱ	108.56 (5)
I1—Ag3A—Ag4	165.76 (9)	Ag3Aⁱⁱ—I1—Ag4ⁱⁱ	65.71 (4)
I1^v—Ag3A—Ag4	59.95 (5)	Ag3Cⁱⁱ—I1—Ag1A^xi	103.4 (4)
Ag3B—Ag3A—Ag1B	37 (2)	Ag3B—I1—Ag1A^xi	111.0 (4)
O2—Ag3A—Ag1B	104.6 (2)	Ag3C—I1—Ag1A^xi	96.5 (4)
I2—Ag3A—Ag1B	57.19 (18)	Ag3A—I1—Ag1A^xi	106.20 (7)
I1—Ag3A—Ag1B	70.03 (18)	Ag3Aⁱⁱ—I1—Ag1A^xi	112.45 (6)
I1^v—Ag3A—Ag1B	150.21 (16)	Ag4ⁱⁱ—I1—Ag1A^xi	139.61 (5)
Ag4—Ag3A—Ag1B	118.82 (19)	Ag3Cⁱⁱ—I1—Ag4^ix	91.6 (4)
Ag3A—Ag3B—Ag3C	29 (2)	Ag3B—I1—Ag4^ix	149.2 (3)
Ag3A—Ag3B—O2	101 (2)	Ag3C—I1—Ag4^ix	134.4 (4)
Ag3C—Ag3B—O2	80.0 (16)	Ag3A—I1—Ag4^ix	139.57 (5)
Ag3A—Ag3B—I2	107 (2)	Ag3Aⁱⁱ—I1—Ag4^ix	96.54 (5)
Ag3C—Ag3B—I2	132.3 (15)	Ag4ⁱⁱ—I1—Ag4^ix	69.285 (12)
O2—Ag3B—I2	107.1 (6)	Ag1A^xi—I1—Ag4^ix	71.00 (5)
Ag3A—Ag3B—I1	99.1 (19)	Ag3B—I2—Ag3A	10.0 (3)
Ag3C—Ag3B—I1	81.2 (14)	Ag3B—I2—Ag1A	72.9 (4)
O2—Ag3B—I1	93.7 (6)	Ag3A—I2—Ag1A	79.80 (12)
I2—Ag3B—I1	142.4 (7)	Ag3B—I2—Ag2	97.5 (3)
Ag3A—Ag3B—Ag1B	137 (2)	Ag3A—I2—Ag2	103.15 (5)
Ag3C—Ag3B—Ag1B	150.2 (19)	Ag1A—I2—Ag2	103.55 (5)
O2—Ag3B—Ag1B	122.3 (6)	Ag3B—I2—Ag1B	61.1 (4)
I2—Ag3B—Ag1B	64.4 (4)	Ag3A—I2—Ag1B	68.3 (2)
I1—Ag3B—Ag1B	78.1 (4)	Ag1A—I2—Ag1B	11.86 (15)
Ag3A—Ag3B—Ag1A	135 (2)	Ag2—I2—Ag1B	102.70 (14)
Ag3C—Ag3B—Ag1A	153.4 (19)	Ag3B—I2—Ag1A^v	92.2 (3)
O2—Ag3B—Ag1A	123.9 (6)	Ag3A—I2—Ag1A^v	83.59 (11)
I2—Ag3B—Ag1A	57.2 (4)	Ag1A—I2—Ag1A^v	102.64 (3)
I1—Ag3B—Ag1A	85.3 (4)	Ag2—I2—Ag1A^v	153.71 (5)
Ag1B—Ag3B—Ag1A	7.34 (19)	Ag1B—I2—Ag1A^v	103.38 (17)
Ag3B—Ag3C—O2	78.8 (15)	Ag3B—I2—Ag1B^v	82.0 (4)
Ag3B—Ag3C—I1^v	139.8 (16)	Ag3A—I2—Ag1B^v	73.0 (2)
O2—Ag3C—I1^v	115.5 (7)	Ag1A—I2—Ag1B^v	103.69 (16)
Ag3B—Ag3C—I1	80.1 (14)	Ag2—I2—Ag1B^v	151.25 (14)
O2—Ag3C—I1	93.3 (6)	Ag1B—I2—Ag1B^v	102.05 (7)
I1^v—Ag3C—I1	132.3 (7)	Ag1A^v—I2—Ag1B^v	11.23 (14)
Ag3B—Ag3C—I2	36.3 (13)	Ag3B—I2—Ag4	72.4 (3)
O2—Ag3C—I2	89.1 (5)	Ag3A—I2—Ag4	65.28 (5)
I1^v—Ag3C—I2	104.0 (5)	Ag1A—I2—Ag4	145.07 (11)
I1—Ag3C—I2	114.2 (6)	Ag2—I2—Ag4	84.37 (3)
Ag3B—Ag3C—Ag2^ix	117.2 (18)	Ag1B—I2—Ag4	133.4 (2)
O2—Ag3C—Ag2^ix	152.8 (7)	Ag1A^v—I2—Ag4	75.37 (8)
I1^v—Ag3C—Ag2^ix	67.8 (4)	Ag1B^v—I2—Ag4	67.96 (17)
I1—Ag3C—Ag2^ix	69.9 (4)	Ag3B—I2—Ag4^xii	139.4 (3)
I2—Ag3C—Ag2^ix	117.0 (5)	Ag3A—I2—Ag4^xii	130.63 (5)
Ag3B—Ag3C—Ag4	88.6 (15)	Ag1A—I2—Ag4^xii	145.36 (11)
O2—Ag3C—Ag4	79.1 (5)	Ag2—I2—Ag4^xii	86.69 (3)
I1^v—Ag3C—Ag4	60.3 (3)	Ag1B—I2—Ag4^xii	156.9 (2)
I1—Ag3C—Ag4	167.4 (7)	Ag1A^v—I2—Ag4^xii	70.35 (7)
I2—Ag3C—Ag4	56.2 (3)	Ag1B^v—I2—Ag4^xii	76.02 (16)
Ag2^ix—Ag3C—Ag4	120.8 (5)	Ag4—I2—Ag4^xii	67.860 (11)
O3^v—Ag4—O3^vi	171.17 (7)	Ag3B—I2—Ag3C	11.5 (5)
O3^v—Ag4—I1^v	92.83 (15)	Ag3A—I2—Ag3C	3.2 (3)
O3^vi—Ag4—I1^v	90.48 (13)	Ag1A—I2—Ag3C	82.7 (3)
O3^v—Ag4—I2	79.91 (14)	Ag2—I2—Ag3C	101.2 (3)
O3^vi—Ag4—I2	107.64 (13)	Ag1B—I2—Ag3C	71.2 (4)
I1^v—Ag4—I2	99.15 (3)	Ag1A^v—I2—Ag3C	84.3 (3)
O3^v—Ag4—I1^iv	89.01 (14)	Ag1B^v—I2—Ag3C	73.4 (4)
O3^vi—Ag4—I1^iv	86.69 (13)	Ag4—I2—Ag3C	62.3 (3)
I1^v—Ag4—I1^iv	172.46 (4)	Ag4^xii—I2—Ag3C	128.3 (3)

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

Comparison of interatomic distances (Å) between Ag atoms and anions in several silver compounds top

Compound	Shortest Ag—O	Average Ag—O	Shortest Ag—I	Average Ag—I	Reference
Ag₃ISO₄	2.384	2.431	2.784	2.791	This work
Ag₄I₂SO₄	2.346	2.564	2.607	3.034	This work
Ag₂SO₄	2.405	2.511	–	–	Mehrotra et al. (1978)
Ag₂CO₃	2.245	2.421	–	–	Norby et al. (2002)
Ag₁₀(CO₃)₃I₄ⁱ	2.252	2.437	2.714	3.004	Suzuki et al. (2021)
γ-AgI	–	–	2.814	2.814	Hull & Keen (1999)
Ag₁₃(AsO₄)₃I₄	2.293	2.375	2.708	3.071	Pitzschke et al. (2009a)
Ag₂₆I₁₈(WO₄)₄	2.195	2.478	2.312	2.916	Chan & Geller (1977)
Ag₄IPO₄ⁱⁱ	2.278	2.368	2.706	3.034	Oleneva et al. (2008)
Ag₁₆I₁₂P₂O₇	1.886	2.340	2.680	2.835	Garrett et al. (1982)
Ag₅IP₂O₇	2.274	2.466	2.765	2.948	Adams & Preusser (1999)
Ag₃I(NO₃)₂	2.250	2.594	2.841	2.942	Birnstock & Britton (1970)
Ag₈(CrO₄)₃I₂ⁱⁱⁱ	2.384	2.446	2.809	3.053	Pitzschke et al. (2009b)
Ag₉I₃(IO₃)₂(SeO₄)₂	2.306	2.508	2.719	2.886	Pitzschke et al. (2008b)
Ag₃ITeO₄	2.238	2.455	2.775	2.928	Pitzschke et al. (2008a)
Ag₄I₂SeO₄	2.322	2.508	2.822	3.069	Pitzschke et al. (2008a)
Ag₈I₄V₂O₇	2.182	2.364	1.927	3.128	Adams (1996)
Ag₉(GeO₄)₂I	2.106	2.222	3.364	3.431	Pitzschke et al. (2009c)

Measurement temperatures: (i) 90 K, (ii) 173 K, (iii) 273 K.

Footnotes

‡Deceased 15 February 2024

Funding information

This work was performed under the Cooperative Research Program of Network Joint Research Center for Materials and Devices and financially supported by Grants-in-Aid for Scientific Research (KAKENHI) 25 K08784.

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