Modular Crystal Chemistry of Thallium Sulfosalts

Abstract

Complex sulfides of thallium with As, Sb, or Bi and with other cations (‘thallium sulfosalts’) are a large group of crystal structures with extreme variability. Incorporation of the large Tl⁺ cation in them is solved in several different ways: housing of Tl in columns of capped trigonal coordination prisms, which form separate walls in the structure (in different combinations with Pb and/or Sb), regular alternation of large Tl with small cations (As), presence of structural arrays of Tl coordination polyhedra paralleled by arrays of As coordination pyramids with a frequency ratio 1:2, omission derivatives with cavities for Tl accommodation and formation of layer structures with thallium concentrated into separate (inter)layers of different types. The first principle leads to a large family of sartorite homologues and rare lillianite homologues, as well as to the chabournéite group. The second one to the hutchinsonite family, omission derivatives form the routhierite and galkhaite groups, and the 1:2 periodicity ratio principle results in several outstanding structures from different groups. Layer structures consist of two-component and three-component layer combinations. Close cation-cation interactions are present but rare.

1. Introduction

The complex sulfides of thallium with formally trivalent As, Sb, or Bi associated with other cations are structurally perhaps the most complicated group of sulfosalts. The principal factor is the size of the univalent thallium ion, which is larger than lead and larger than bismuth, and is comparable in size to monovalent alkali ions—especially potassium, rubidium and cesium, and to the larger divalent cations, especially barium. Sulfosalts of the latter elements mostly belong to the realm of synthetics because they (and partly thallium itself) are consumed by late magmatic, pegmatitic and metamorphic processes, participating in or directly forming silicates. Monovalent thallium has one substantial difference against these cations—its lone electron pair character, similar to Pb²⁺ and Bi³⁺. The relative weakness of this character, however, is apparent when examining the coordination polyhedron of thallium in different sulfosalts.

The large ion radius of Tl precludes its simple incorporation into PbS-like arrays and causes problems even in more tolerant SnS-like arrays. These two arrays determine the structures of many common Tl-free sulfosalts of especially Pb, Sb, Bi, As, Cu and Ag. The size of Tl⁺ also complicates or prevents formation of the incommensurate interfaces, which are known from these sulfosalts. In a number of cases with higher contents of Tl in the complex sulfide, its structural characteristics remind more of complex silicates of Ba or K than that of the ‘common’ sulfosalts like aikinite, boulangerite or emplectite. This bears additional complication, however, because instead of arrays of silicate coordination tetrahedra, polymerization in these sulfosalts joins MS₃ or/and MS₅ coordination pyramids which have the cation in an exposed position, and this has a lone electron pair. Different ways in which the large coordination polyhedra of thallium are accommodated in the structure, and the kind of structure which results from this accommodation, will be the principal classification criteria we shall use.

The majority of thallium sulfosalts are sulfo-arsenites, with or without Pb, a product of special and fairly rarely occurring ore solution geochemistry with its cocktail of Tl, As, Pb, Hg and Sb, which certainly is problematic for the communities underneath the weathering outcrop [1]. The opposite happens at the famous locality of Lengenbach (Wallis, Switzerland), where this cocktail upkeeps the local tourist aficionado business. The recent discovery of tsygankoite and vorontsovite is an example that the spectrum of locality types is diversifying and new types and sites of thallium-bearing assemblages are being constantly discovered.

This review profits from a number of analyses and structure determinations which were made by many devoted crystallographers and mineralogists, some of whom are specialists in the Tl containing minerals and compounds. Their individual contributions can best be appreciated when scanning the long list of references and the list of minerals/phases treated, which is given in

Table 1. Minerals and synthetic phases dealt with in the review.

Lorándite	TlAsS2	galkhaite	(Cs,Tl)(Hg,Cu,Zn)6As4S12
weissbergite	TlSbS2	vorontsovite	Hg5CuTlAs4S12
synth.	TlSbSe2	ferrovorontsovite	Fe5CuTlAs2S12
synth.	TlPbSbS3	Kutinaite	(K,Tl)0.25Cu14Ag6.75
Hutchinsonite	TlPbAs5S9	Synth.	Tl3SbS3
bernardite	TlAs5S8	Parapierrotite	TlSb5S8
imhofite	Tl5.6As15S25.3	synth.	KSb5S8
edenharterite	TlPbAs3S6	synth.	(Tl0.6K0.4)Sb5S8
jentschite	TlPbAs2SbS6	protochabournéite	Tl2PbSb8.5As1.5S17
Heptasartorite	Tl7Pb22As55S108	chabournéite	~Tl2PbSb6As4S17
enneasartorite	Tl6Pb32As70S140	dalnegroite	Tl4Pb2As12Sb8S34
hendekasartorite	Tl2Pb48As82S172	Tsygankoite	Mn8Tl8Hg2Sb21Pb2TlS48
twinnite	Pb8Tl1As8Sb13S40	rouxelite	Cu2HgPb22Sb28S64(O,S)2
guettardite	PbSb1.1As0.8S4	Simonite	TlHgAs3S6
philrothite	TlAs3S5	Synth.	TlBiS2
dufrénoysite	Pb2As2S5	Synth.	Tl3AsS3
veenite	Pb16Sb9As7S40	christite	HgTlAsS3
rathite	Pb9.5TlAg2As18.5SbS40	Synth.	Tl3Ag3Sb2S6
pierrotite	Tl2(Sb,As)10S16	synth.	Tl3Ag3As2S6
baumauerite	Pb12As16S36	Erniggliite	Tl2SnAs2S6
Argentobaum-hauerite	Ag1.5Pb22As33.5S72	synth.	TlMnAs2S5
écrinsite	AgTl3Pb4As11Sb9S36	raberite	Tl5Ag4As6SbS15
boscardinite	AgTl3Pb4Sb14As6S36	spaltiite	Cu2Tl2As2S5
Sicherite	TlAg2(As,Sb)3S6	wallisite	PbTl(Cu0.65Ag0.35)As2S5
Andreadinite	CuHgAg7Pb7Sb24S48	hatchite	PbTlAgAs2S5
synth.	TlSb3S5	richardsollyite	TlPbAsS3
synth.	Tl4Bi2S5	vrbaite	Tl4Hg3As8Sb2S20
Gillulyite	Tl2(As,Sb)8S13	rebulite	Tl5Sb5As8S22
Routhierite	CuHg2TlAs2S6	jankovićite	Tl5Sb10As3S22
stalderite	CuZn2TlAs2S6	gabrielite	Tl2AgCu2As3S7
arsiccioite	AgHg2TlAs2S6
ferrostalderite	CuFe2TlAs2S6
ralphcannonite	AgZn2TlAs2S6
tetrahedrite	Cu10(Fe,Zn)2Sb4S13
tennantite	Cu10(Fe,Zn)2As4S13
synth.	Cu10Hg2Sb4S13

. Thallium sulfosalt mineralogy and crystal chemistry was a topic of the overviews by Nowacki et al. [2], Zemann [3], Gržetić & Balić-Žunić [4], as well as of the more detailed analyses of pairs and groups of Tl sulfosalts produced by the cooperation of the current author with Drs. T. Balić-Žunić and P. Berlepsch. Mineral syntheses in the realm of Tl sulfosalts were performed especially by Sobott [5,6,7,8], Gržetić and Moh [9] and other members of the ‘Heidelberg circle’; in lesser volume, also by Balić-Žunić et al. [10] and others. The current review combines the observations obtained from the reanalysis of all published sulfosalt structures with the ideas presented in the above reviews and structure papers.

Except for several very recent structures, the structures analyzed in this contribution were published and collected in the Inorganic Crystal Structure Data file. They were obtained from the data collected by means of single-crystal x-ray diffraction and refined with a good reliability factor.

2. Basic Notions and Categories

The crystal structures of sulfosalts rich in As, Sb and/or Bi, in combination with Pb, Sn²⁺, eventually smaller amounts of Tl⁺, Ag and Cu often obey one of the two configurations which became known as the PbS and the SnS archetypes [11,12,13,14]. In the well-known PbS archetype, all cations have octahedral coordination, their coordination octahedra are edge sharing and form the F-centered galena-like (sub)structure. In real structures the motif can be somewhat distorted when different cations are combined in one structure, or when some cations have a moderate lone electron pair (LEP) activity. In the structure which obeys a generalized SnS archetype (Figure 1), the structure is divided into double layers (if the archetype is present as a thick slab, into double-ribbons) which contain cations with short strong bonds, binding the two atomic planes of such a pair together, and weak cation-anion interactions situated between layer pairs. The interspaces host lone electron pairs of cations with strong LEP-activity; these block closer cation-anion interactions and require steric accommodation, usually in form of trigonal prismatic volumes to which the tight cation coordination itself represents a capping ‘square’ pyramid. Thus, a monocapped trigonal coordination prism (CN = 7) is a typical coordination of cations with a pronounced lone electron pair activity in sulfosalts. The details of coordinations and polymerization of adjacent cation polyhedra, differ—that is why we talk about a generalized SnS archetype.

Three-dimensional (3D) development of an archetype structure is rare. Usually, they are developed in form of layers, slabs or rods; the latter two may be interconnected in the form of ‘rod-layers’. These complex elements are then recombined into a structure by means of the operations of ‘unit-cell twinning’: mirror (reflection) twinning, glide-reflection twinning, cyclic twinning, bridging of a pseudotetragonal/pseudohexagonal interface, etc. [14]. A special case are omission derivatives, in which either a cluster of coordination polyhedra was omitted and replaced by a completely new atomic choice and configuration, or just a single cation or anion is missing.

Cations with lone electron pairs (i.e., those that are not engaged in bonding) often congregate in the crystal structure, forming an envelope of a common structural volume into which they extend their lone electron pairs. These configurations (the common LEP volume and the cations forming its ‘skin’) are called lone electron pair micelles, which are typical for the structures based on the SnS archetype. Cases when structure consists of atom groups which orient their LEPs outwards, into surrounding structural space, contain ‘inverted lone electron pair micelles’ [15].

Further useful definitions are as follows:

Isotypes are crystal structures with cations and anions of comparable crystal chemical characteristics, closely comparable coordinates in the structure, closely comparable coordination polyhedra, comparable ratios of, and angles between, crystal axes and identical local point-group symmetries (these are ‘isopointal’), as well as with the same overall space group of symmetry. Homeotypes have one or more of the isotype-defining principles relaxed—e.g., they obey a lower space group of symmetry, have differently distorted coordination polyhedra, contain (partial) atom vacancies, etc.

Accretional homologous series is a series of structures in which the type(s) of building blocks (rods, layers) and the principles that define their mutual relationships remain preserved but the size of these blocks varies incrementally by varying the number of constituting coordination polyhedra in them. The plesiotype series is constituted by members which contain the same type of fundamental blocks (slabs, etc., homologously expanded or not) and display the same general rules of recombination of these blocks. However, different members of the series contain different additional blocks/elements, or details of the building blocks, or of their interconnection, differ from member to member in non-homologous ways. Merotypic series combines two types of blocks (etc.); one type is constant (including its homologous expansion derivatives), whereas the representatives of the alternating set can represent different structure types. More details about the modular nomenclature are in [14,15,16,17].

3. Classification Principles

The sulfide crystal radius of univalent thallium by Shannon [18] is about 1.45 Å for CN = 6, and 1.69 Å for CN = 8. Trivalent thallium has r = 0.90 Å (CN = 4) and 0.96 Å (CN = 6), resulting in a quite different crystal chemistry. Shannon’s value for divalent Pb is 1.27 Å (CN = 6), however, the presence of lone electron pairs makes the definition complicated (two radii: for the strong-bond side and for the LEP side, respectively) [19], or completely irrelevant, as for As and Sb. Crystal radii for tetrahedral Ag, Cu⁺ and Hg in sulfides [18] are 0.92 Å, 0.635 Å and 0.84 Å, respectively, however, the (2 + 4) coordinations of Hg and Ag have two sets of very different distances. The crystal radius for the anions, compatible with the given cation radii, is 1.70 Å for S and 1.84 Å for Se. Comparing Shannon’s Tl–S value for CN8 (3.39 Å) and that for CN6 (3.15 Å) with the Pb–S values (CN6; 2.95 Å) shows that accommodation of Tl in the structures has problems different from those connected with the incorporation of Pb, Sn²⁺ and other cations. Tl is a large ‘soft cation’, which sometimes displays one-sidedness because of its LEP.

The spectrum of thallium sulfosalts is very varied; structure types depend on the Tl: cation ratio, types of associated cations, presence or absence of Sb and more. The sulfosalts of thallium can be divided into groups according to the way thallium is structurally accommodated. A large group of structures consists of large slabs, rods or blocks of the two above mentioned archetypal structures, or their combination, joined by structure-building operators, which are based on Tl–Pb(Sb) interplay in columns of bi- and tri-capped trigonal coordination pyramids. Alternation of large Tl with much smaller polyhedra of especially As or Sb in selected structure rows produces another important group of structures. Several structures (often from different groups) are created when pure sequences of Tl polyhedra are paralleled by sequences of As/Sb coordination pyramids, which are then present with doubled frequency (in 1:2 ratio).

Finally, an important cluster of structures are those composed of two (less frequently three) compositionally different component layers in regular alternation, i.e., ‘layer structures’, in which the layers share the boundary anions. The component layers are of rather variable architecture, dictated by the cations present and their percentages. The thallium-free layers/portions of the layer structures can then be compared/classified using the degree of lone-electron pair activity and distribution of spaces filled by lone electron pairs (LEP) of As and Sb in them, types of aggregates formed by AsS₃ groups, presence or absence of channels hosting other cations, etc. The other criterion is the architecture of thallium containing layers. The most important difference in the space and wall architecture is the difference between the Tl-layers in which thallium is distributed in the layer volume and those, in which it lines the walls of the layer-like interspace; combined cases occur as well.

Below, individual phases/minerals are assembled in groups according to their structural properties, and their characteristic and/or interesting details are described. Sometimes, the structure follows more than one principle, complicating this approach somewhat. This part will be followed by general conclusions, and a critical look at the selected aspects of their crystal chemistry and classification.

4. The ‘Classical’ Sulfosalt Archetypes: SnS Archetype

4.1. Lorándite and Weissbergite

Lorándite, TlAsS₂, is the most widespread sulfosalt of thallium because its crystallization conditions [20] coincide with those of the usual, low-temperature hydrothermal deposits of orpiment and realgar. The crystal structure was determined by Zemann & Zemann [21], refined by Fleet [22] and further refined by Balić-Žunić et al. [10]. Although the structure is broadly related to those following the SnS archetype, its arrangement of coordination polyhedra of As and Tl displays specific features of its own.

Using the data of [10], lorándite is monoclinic, space group P2₁/a, a 12.296 Å, b 11.313 Å, c 6.114 Å, β 104.21°. The AsS₃ pyramids with short bonds (2.20–2.33 Å; Balić-Žunić et al. [10]) are interconnected via common sulfur atoms into spiral [010] chains. The periodicity of spirals determines the b parameter (11.313 Å); there are four pyramids in the b period. Each spiral builds a four-sided rod, with As atoms on its edges and with all lone electron pairs oriented outwards, out of the body of the rod (Figure 2). One of the longer As–S interactions (3.191–3.323 Å), opposed to the short ones, completes the edge of the rod, whereas the other two long interactions (3.953 Å and longer), which extend to sulfurs of two adjacent rods, bridge the inter-rod space.

Tl atoms are positioned approximately above rod edges, always opposing an As atom (Figure 2). Cation spacing along each edge of the As rod is significant: one Tl polyhedron for two As coordination pyramids. Thus the formation of the As rod with its ‘spiral staircase’ of AsS₃ pyramids in the observed orientation is not only a way to satisfy the As bonding requirements but also means of contradiction-free packing of As pyramids and large Tl polyhedra.

Tl is slightly above the edge and surface of the As rod, with the opposing bond pairs 3.013 + 3.470 Å (Tl1) and 2.905 + 3.344 Å (Tl2) completing the rod edges. Further bonds of the CN = 7 thallium interconnect the rods: 3.226 Å and 3.645 Å in the ±[100]* direction and 3.063 Å and 3.185 Å in the c direction. Average Tl–S bond length is 3.30 Å in both cases.

Full CN = 5 coordination polyhedra of As are trapezoidal to irregular, because the large Tl polyhedra determine the geometry of the structure. Combination of the orientation of strong As–S bonds and weak interactions in the (100) plane of lorándite with the action of 2₁ operator parallel to the b direction rotates the AsS–configurations on the opposite sides of the plane at 90° against one another (Figure 2), with important consequences for the interlayer space.

The remarkable relation between the SnS archetype and the crystal structure of lorándite is best seen in the projection parallel to [012]_lorándite (Figure 3): the SnS-like mutual shift of tightly-bonded (100) double layers in lorándite corresponds very well to that in SnS, however, its orientation changes by 90° from one interspace to another. The coordination pyramids of cations in the tightly bonded double-layers each have a trigonal coordination prism in the interspace, in which the lone electron pair of the cation is accommodated. Whereas in SnS and in the majority of derivative structures all such prisms have their zone axes parallel, in lorándite their orientation changes by 90° from one interspace to the next one.

The structural data on weissbergite, TlSbS₂, by Rey et al. [23] indicate space group P-1, a 6.123 Å, b 6.293 Å, c 11.838 Å, α 101.34°, β 98.39°,γ 103.21°, unit cell volume 426.61 ų. The crystal structure is of a general SnS archetype, with a shift of tightly-bonded Tl–Sb (010) double-layers yielding a typical SnS-like arrangement in projection along [20-1]. Orientation of long M–S distances and of the trigonal prismatic spaces for the lone electron pairs of especially Sb is uniform throughout (Figure 4). In the (010) atomic layers, Sb forms coordination pyramids with trapezoidal bases, paired together via short Sb–S bonds to two common sulfurs, i.e., via the shortest S–S edge. Tl forms irregular, larger pyramids completed by two long distances in the interlayer space.

Sb1–Sb2 pairs on one side of the double layer decorate unit cell corners (Figure 5), whereas the pair on the opposing surface is central to the cell and inverted in respect to the opposite side. The pyramidal vertex is at Sb–S equal to 2.405 Å for Sb1, the opposing distances in the base are 2.448–3.690 Å and 2.602–2.961 Å. For Sb2, the same sequence is 2.433 Å, 2.456–3.702 Å, and 2.710–2.812 Å. This might indicate certain amount of cation flipping in respect to one of the bond pairs, especially in the case of Sb2, across the weakly bonded (001) interspace. The long interlayer Sb–S distances are 4.018 Å and 3.839 Å; their bifurcation is rare.

Thallium coordinations start at fairly low Tl–S distances, 3.071 Å and 3.181 Å for Tl1 and 3.046–3.059 Å for Tl2. The intralayer distances reach 3.374 Å at maximum. The (010) interspaces are the basis of cleavage observed.

The crystal structure of the selenosalt TlSbSe₂ [24] is also based on SnS archetype. The high-temperature modification (above 380 °C), has statistical disorder of Tl and Sb over one cation position of the space group Amam, with unit cell defined by a 4.514 Å, b 11.979 Å and c 4.198 Å (measured on a quenched sample). Slow cooling produces a partial ordering, whereas the ordered low temperature phase (Figure 6) has space group P2₁, a 9.137 Å, b 4.097 Å, c 12.765 Å, β 111.75°, unit cell volume 443.8 ų [24]. The two Sb positions are similar: the square coordination pyramid of Sb1 has the Sb–S vertex bond 2.576 Å, base bonds: 2.762 Å opposed by 3.025 Å, another one 2.780 Å versus 3.047 Å, and the under-base distances equal to 3.919 and 3.940 Å. For Sb2, the same sequence is 2.580 Å, opposing pairs 2.788–3.000 Å, 2.812–3.000 Å, under base of the pyramid 3.820 and 3.855 Å. Antimony pyramids are connected via pyramidal edges, forming [010] double chains, which then give (100) layers via the under-base interactions.

Thallium coordination polyhedra (CN = 7) form [010] chains, amalgamated into planar (100) blocks of four Tl chains by edge sharing; blocks are separated by a stagger one octahedron wide. Tl–Se distances start at 3.222 Å for Tl1 and 3.012 Å for Tl2; they stay mostly below 3.33 Å and reach up to 3.633 Å.

The crystal structure of the low-temperature modification of TlPbSbS₃ was refined from powder data by Balić-Žunić and Bente [25], with space group P2₁/c, a 4.171 Å, b 4.286 Å, c 12.157 Å, β 105.489°. Cation sites showed a disordered distribution of Tl, Pb and Sb. This modification resulted from one month annealing (at 300 °C) of high-temperature modification synthetized at about 530 °C.

Solid solution between TlAsS₂ and TlSbS₂ was investigated by [10]. Electron microprobe and powder diffraction data show miscibility gaps between 54 and 85 mol% TlAsS₂ and, for preparations made at 250 °C, most likely also between 24 and 34 mol% TlAsS₂. The intermediate compositions then might form a separate mixed-cation phase.

4.2. The Hutchinsonite Plesiotypic Series

Structures of this series are based on regular alternation of Tl with As along the infinite direction of SnS-like double-rods. The type mineral of the series is hutchinsonite, TlPbAs₅S₉. Its crystal structure was determined by Takéuchi et al. [26] and refined by Matsushita & Takéuchi [27]. This arsenic-rich structure (

Table 2. Members of the hutchinsonite plesiotype family.

Mineral	a (Å)	b (Å)	c (Å)	α (deg)	β (deg)	γ (deg)	Space Group	Reference
Hutchinsonite	10.786	35.389	8.141				Pbca	[26,27]
Bernardite	15.647	8.038	10.750		91.27		P21/c	[28]
Imhofite (*subcell)	8.755	24.425	5.739 True cell 11.478		108.28		P21/n*	[30,31]
Edenharterite	47.453	15.476	5.847				Fdd2	[33]
Jentschite	8.096	23.917	5.888		108.063		P21/n	[32]

) is composed of two kinds of (010) slabs in regular alternation. The ‘B’ slab structure conforms to a general SnS archetype, with the fragments of SnS-like tightly-bonded slabs two cation-centred polyhedra wide on one side and three polyhedra broad from the opposite side (Figure 7). The former surface is populated by As, whereas the three polyhedra wide surface has Pb in the central columns and alternating As and Tl in the lateral columns [27]. The latter As site is shared with the polyhedral chains in the complex ‘A’ slab (Figure 8). Individual strongly-bonded rods in the ‘B’ slab are related by (local) glide planes (Figure 9).

The ‘A’ slab consists of AsS₃ coordination pyramids connected via common S atoms in the corners, forming a very complicated layer. They form two irregular loops: the As3–As5–As4–As3–As5–As4–six-member ring, and the As3–As4–As5–As4–As5–As3–As4–As5–As4–As5–ten-member loop. The 6-member rings are connected with one another via the S7 atom of the As4 pyramid to the As5 position. The As5–S7 bond, 2.255 Å long, is the only bond bridging the LEP-occupied gap in the SnS-like slab, in agreement with the weak and adjustable character of these gaps.

The closest plesiotype of hutchinsonite is bernardite, TlAs₅S₈, described by Pašava et al. [28], composed again of the two above mentioned kinds of slabs (Figure 10). The ‘B’ slabs (in the parlance used for hutchinsonite) are two cation polyhedra broad; one column is occupied by pure As polyhedra, whereas the other is occupied by alternating Tl1 and As3 sites; the latter polyhedron has adapted its shape to the intervening large Tl polyhedron by having an open trapezoidal base of the AsS₅ configuration. The two sides of the ‘B-type’ tightly-bonded slab are related by symmetry centers. The complex ‘A’ layer contains two different small loops of corner-interconnected AsS₃ pyramids: a fourfold ring As1–As4–As1–As4, and a sixfold ring As3–As2–As5–As3–As2–As5 whereas the large loop is converted into an infinite zig-zagging space, with boundaries defined as the sequence As1–As4*–As3–As2–As5–As3*–As4–As1 again, etc. (Figure 11). The chain is not flat, it has ‘recessed’ pyramids (asterisk), and it repeats along the opposite edge of the zig-zag space but in opposite sense (the As1 pyramids face one another). Inversion centers in the ‘A’ layer are reflected in the numbering of As atoms in this layer (Figure 11).

Both slab types are centrosymmetric and the space group is P2₁/c, unlike that of hutchinsonite, which is Pbca. The a parameter of bernardite is 15.647 Å, the corresponding b parameter of hutchinsonite is 35.389 Å. The thallium atom has CN = 10, with the shortest Tl–S bonds equal to 3.051 and 3.088 Å, approximately opposed by the longest bonds, 3.746 and 3.908 Å.

The next plesiotype, imhofite [29], posed compositional and crystallographic problems since its description. Divjaković and Nowacki [30] determined the substructure of imhofite (Table 2), with the majority of Tl, As, and some S sites partly occupied to various degrees, and with the resulting near-balanced formula Tl_5.6As₁₅S_25.3. The substructure was determined in the space group P2₁/n, the b parameter equal to 24.425 Å. Balić-Žunić & Makovicky [31] interpreted the true structure of imhofite as an OD structure, in which selected (100) layers can assume with equal probability two positions, c_subcell apart. A random stacking of these layers creates the observed structure, which is a superposition structure. As determined, the partly occupied atom positions in this structure describe both stacking alternatives.

The partial structure of ‘B’ slabs is SnS-like, with a column of alternating As and Tl polyhedra on each side of a tightly-bonded [101] rod. This rod is fully occupied by As which has alternating strong and weak bond orientations. This three-column assemblage (Figure 12) is completed on the opposite surface of the rod by two, in principle half-occupied As columns which flank the [101] rod (every second polyhedron is Tl).

The ‘A’ slabs partly intermesh with the rods of the ‘B’ slabs. The space left between marginal S atoms of two adjacent B slabs is just ½ of the S–S edge of an AsS₃ pyramid but, with indentations into the B slabs, the configurations of the A slab are 1½ edge lengths broad. The polyhedra forming the A layer are positioned on two (010) planes, just ½ polyhedron width apart. They form [001] ribbons (configurationally double-bands, Figure 13) with internal symmetry p2₁/m (m is perpendicular to the ribbon length) and both edges populated by alternation of As₂S₅ groups, composed of S-sharing of As4S₃ and As5S₃ pyramids, and TlS₅ configurations. In the band stack, a double-band is related to the preceding one by a glide-reflection connected with a shift of ½ of the c period to the right or to the left, with equal probability, resulting in the (ideally) fully disordered band stacking (Figure 14).

The structure-derived chemical formula of imhofite, given by [30] is Tl_5.6As₁₅S_25.3. The order-disorder model with full occupancies gives Tl₆As₁₆S₂₆, i.e., not a fully balanced formula. Structure determination suggests that the positions in the B slabs are fully occupied.

The pyramidal pair As4–As5 appears unperturbed but the alternating Tl2 is vacated in nearly one third of instances in favour of appearance of more spherically coordinated Tl2a. The latter in not compatible with the marginal As2 polyhedron of the B slab and this site becomes partly vacated. As stated by [31], site occupancy problems in the original superposition structure determined by [30] preclude finalization of the formula versus structure discrepancies. Imhofite differs from the two previous plesiotypes, hutchinsonite and bernardite, by a content of thallium in the ‘A’ interlayer which separates the slabs of SnS-archetype.

When we deal with the end-members of a plesiotypic (especially merotypic) group of structures, one layer type can be completely absent, so that they contain only one type of layers. This is the case of the homeotypic pair edenharterite (TlPbAs₃S₆)–jentschite (TlPbAs₂SbS₆) from Lengenbach, Binntal (Switzerland) [32,33,34].

These structures are homeotypes on the polyhedral and chain level but very different on the modular level. Both structures consist of slabs based on the SnS archetype, which are very similar to the slabs observed in hutchinsonite. Both Tl and Pb are seven-coordinated; Pb forms distorted trigonal prisms which are capped on one prism face; distortion is more pronounced for Tl. Trigonal coordination pyramids of As and Sb are interconnected to form As₆S₁₂, respectively, As₄Sb₂S₁₂ chains As3–As2–As1 = As1–As2–As3 (respectively –Sb1 = Sb1–) with As₂S₂ or Sb₂S₂ rings (indicated here by ‘=’) in their central portions (Figure 15). These rings straddle the slab boundary whereas the ‘wings’ of chains partake in the square coordination pyramids AsS₅ in the two-polyhedron face of a tightly-bonded rod in the SnS-like slab (Figure 16). The intra-ring metalloid distances are: As1–As1 equal to 3.228 Å, Sb1–Sb1 to 3.440 Å; these are somewhat compressed against the sums of van der Waals radii [35]. The different modular arrangement of jentschite (Figure 17) is caused by the occupancy of boundary rings by (in nature only majoritarian) Sb, whereas in synthetic TlPbAs₃S₆ these positions are occupied by pure As, and in natural edenharterite they contain only minor Sb (total compositions up to As_2.81Sb_0.19). Total compositions of natural jentschite were given as As_2.19Sb_0.81 to As_2.82Sb_0.18, although a possible inheritance of the motif from the majoritarian As:Sb ratio was not discussed by [32].

The two ‘chain wings’ defined above are in cis-position in edenharterite (Figure 18) and in trans-position in jenschite (Figure 19), a fact unrecognizable in a view along [001]. The Tl–Tl distances across the slab boundary are 4.342 Å in edenharterite and 3.920 Å alternating with 4.987 Å in jentschite. Relation of chains to slabs is shown in Figure 19. The quantitative data come from [34]. The resulting modular configurations are the antiparallel arrangement of SnS-like slabs in jentschite, and a diverging orientation of adjacent SnS-like slabs in edenharterite where they meet via As1S₃ pyramids which share the S1–S1 edge (Figure 20). The divergence angle is 41.4°.

4.3. Sartorite Homologous Series

Crystal structures of this homologous series consist of slices of the SnS-like structure, cut and glide-plane twinned along the (301)_SnS and (30-1)_SnS planes. The SnS archetypal configuration [12] has been adopted, because of higher lone electron pair activity of component cations—As, Sb, Pb and Tl in different proportions. Ag coordination is adapting to the situation dictated by these cations. The crystal chemical formula is Me⁺_xMe²⁺_4N−8−2xMe³⁺_8+xS_4N+4 for the 8.4 Å repeating unit of one tightly-bonded (100)_SnS double-ribbon stretched diagonally across the above defined slice.

The interior of a slice, i.e., the positions in the double ribbons, is composed primarily of trapezoidally distorted tetragonal coordination pyramids of As and/or Sb, with lone electron pairs pointing into the interspaces of the SnS-like slice (Figure 21). Complete coordination of such a cation, including the space for its lone electron pair, is a monocapped prism; this is adopted also by the cations occasionally substituting for As/Sb, such as Pb, Ag and possibly even Tl. Patterns of short strong bonds mostly result in crankshaft chains, which are diagonal across the (100)_SnS double-layer. Crankshaft chains on the two surfaces of the double-layer can be (anti)parallel or perpendicular to one another.

The last, marginal coordination polyhedron in each (100)_SnS plane populated by coordination pyramids is differently coordinated. Its ligands include those from surrounding double-ribbons, some of them from the adjacent (301)_SnS slab. It always is a sub-regular tricapped trigonal coordination prism, a large-cation site suitable for Pb and/or Tl. The prominent zig-zag walls of such prisms are a characteristic feature of the sartorite homologues. If, for valence reasons, these large cations are to be mixed with trivalent Sb (or As) in the same column, the large cations dictate the configuration of the Pb/Tl column and the trivalent ones occupy either a base or one face of the prism.

Because of the sub-regular capped trigonal coordination prisms which form continuous partitions in their structures, the sartorite homologous series has much greater affinity to thallium, including at least two ideally pure–Tl–As(Sb) members. Tl participation in the interior of slabs is much less definite, especially because of the refinement problems in discerning Tl (Z = 81) from Pb (Z = 82).

For the homologue order N = 3, the misfit between the periodicity of the arsenic-based array of pyramids and the dimension of the column of Pb coordination prisms is solved by creating a complicated sequence of As₄S₅ chains, As₂S₂ groups and AsS₂ coordinations in each (100)_SnS face of the double-ribbon; these are variously interconnected via the diameter of the double ribbon. In the ‘chelating space’ of a special ‘amalgamated’ W-shaped chain which occurs on each surface, one of the sulfur atoms that define the columns of the Pb coordination prisms is omitted. The frequency of this W-shaped chain and of the omitted S position results in an anion-omission series with the order M signifying the multiple of the 4.2 Å subcells (i.e., a superstructure period) in which the omission occurs once per Pb column (=7, 9, 11, and 13) [36,37,38] (

Table 3. Members of the sartorite homologous series quoted in this contribution.

Mineral Homologue Order	a (Å)	b (Å)	c (Å)	α (deg)	β (deg)	γ (deg)	Space Group	Reference
Heptasartorite 3;3	29.269	7.877	20.128		102.065		P21/c	[38]
Enneasartorite 3;3	37.612	7.878	20.071		101.930		P21/c	[38]
Hendekasartorite 3;3	31.806	7.889	28.556		99.034		P21/c	[37]
Twinnite 3;3	7.997	19.517	8.634		91.061		P21/n	[39,40]
Guettardite 3;3	8.527	7.971	20.102		101.814		P21/c	[40]
Philrothite 4;4	8.013	24.829	11.762		132.84		P21/c	[41]
Dufrénoysite 4;4	7.90	25.740	8.37		90.35		P21	[42]
Rathite 4;4	8.496	7.969	25.122		100.704		P21/c	[44]
Pierrotite 3;3	38.746	8.816	7.989				Pna21	[47,48]
Baumhauerite 3;4	7.884	8.345	22.811	90.069	97.255	90.082	P1	[51]
Argentobaumhauerite 3;4	7.905	8.468	44.410	84.614	86.469	89.810	P-1	[51]
Écrinsite 3;4	8.080	8.533	22.613	90.23	97.17	90.83	P1	[52]
Boscardinite 3;4	8.093	8.761	22.497	90.868	97.247	90.793	P1	[53,54]

). Whereas the ideal formula of the N = 3 sartorite homologue is PbAs₂S₄, with the possible substitution Tl + As ↔ 2Pb, the anion vacancy (Figure 22) requires additional compensation, which can happen either by 2Tl⁺ per superstructure period substituting for 2Pb²⁺, or by 2Pb²⁺ per superstructure period substituting for 2 As³⁺. For example, for heptasartorite (M = 7), the first mechanism, if complete, yields the composition Pb₅Tl₂As₁₄S₂₇, whereas the second one gives Pb₉As₁₂S₂₇. For each M, the two compensation mechanisms compete, with the former one representing almost 90% for heptasartorite, and less than 40% for hendekasarorite [37]. For these calculations we assume that the simple Tl + As ↔ 2Pb substitution becomes active only when the omission has been compensated for.

There is no separate thallium-destined cation site in these structures. Mixed Pb–Tl sites were evaluated primarily by comparing their polyhedron volume with that of pure Pb and Tl coordination prisms in closely related structures. Four prismatic sites in heptasartorite account for about 63% of the total Tl content indicated by chemical analysis (maximum calculated content is 58% Tl for Pb4 site), the rest must be spread over the remaining three prismatic sites and one mixed ‘Pb,As’ site in the W-shaped chain. Two prismatic sites in enneasartorite, with about 44% Tl in each, and one site with about 26% Tl are accompanied by the remaining polyhedra of lead (two are mixed Pb–As sites) with much lower calculated thallium contents [37].

The N = 3 sartorite homologues with mixed As–Sb contents do not have such misfit problems (the As–Sb array has larger dimensions, better suited to match the Pb array). Correspondingly, twinnite Pb_0.8Tl_0.1As_0.8Sb_1.3S₄ has only 1.96 wt. % Tl and guettardite, Pb_1.02Sb_1.11As_0.81S₄.₀₆ [39] and Pb_0.95–0.96Sb_0.96–1.02As_1.03–1.06S₄ [40] is Tl-free. However, the structurally not analyzed guettardite from Jas Roux, associated with écrinsite, pierrotite, and chabournéite has the electron microprobe composition Tl_0.31Pb_7.58Sb_7.46As_8.71S_31.95.

The Tl-substituted N = 4 end-member, philrothite TlAs₃S₅, is monoclinic, space group P2₁/c, has a 8.013 Å, b 24.829 Å, c 11.762 Å, β 132.84° [41]. Tricapped prismatic Tl sites form [010] columns (Figure 23). However, philrothite contains some Pb and Ag as substituents, giving the formula Tl_0.789Pb_0.198Ag_0.142As_2.662Sb_0.159S_5.044. Crystal quality limited the structure refinement to R = 0.098. The capped trigonal Tl(Pb) coordination prisms have mean bond distances 3.22 Å and 3.32 Å, respectively, with the shortest distances 3.13–3.14 Å (5 distances) and one distance of 3.08 Å and one 3.15 Å (the longest distance equal to 3.59 Å) for the two prisms which follow one another in each column of Tl prisms. This was interpreted as a more ionic and a more lone-electron-pair character of Tl–S interactions, respectively.

The 2Pb ↔ (As,Sb) + (Tl,Ag) substitution line for the N = 4 homologues contains Pb–As based dufrénoysite [42], Pb–(As,Sb) based veenite [43], and the Ag–Tl substituted phase, rathite (Figure 21; Table 3). The published crystal structure refinement for rathite by Berlepsch et al. [44] was performed on the compositions Pb_9.15–9.98Tl_1.37–0.89Ag_1.89–2.03As_{17.94–19.09}Sb_0.83–1.27S₄₀ (the extreme values are from different samples). Literature data collected by [44] show between 0.27 and 0.9 Tl apfu. Laroussi et al. [45] quote only the value of 0.36 apfu Tl for rathite, confirming the range of substitutions given.

In the structure determination by [44], 0.47 silver occurs in a split position with 0.53 As in the As-based slabs. Silver was not identified by [46], however. Authors suggest that this should be the only or strongly preferred Ag position. A Tl-enriched site could not be selected from the two Pb prism sites which alternate in each Pb column, which do not appear to show important differences between the prism dimensions: 3.022–3.497 Å for Pb1 and 2.973–3.472 Å for Pb2.

The N = 4 line also contains the end-member, pierrotite Tl₂(Sb,As)₁₀S₁₆ [47,48], with the structural formula corrected against the original one.

Alternating zig-zag rows of this structure (Figure 24) have differently distorted capped trigonal coordination prisms of Tl; these were called a Tl1-row and a Tl2-row by the authors. The stoichiometry of this sulfosalt does not produce pure Tl columns in the Pb-free N = 4 homologues. Therefore, in their respective columns, the Tl coordination prisms alternate with antimony pyramids, Tl1 with a side-ways oriented Sb2 polyhedron and Tl2 with a predominantly top-oriented but sideways flipping Sb4 polyhedron (Figure 25).

Tl1 has Tl–S distances to the prism vertices between 3.349 and 3.391 Å, with one corner at 3.527 Å, and caps at 3.178, 3.254, and 3.430 Å. Tl2 has a more distorted coordination prism, with distances 3.181 to 3.522 Å, and caps at 3.176, 3.368, and 3.408 Å. Sb2 has a regular set of three short bonds, 2.512–2.543 Å whereas Sb4 has a pair, 2.453 Å and 2.475 Å, accompanied by oppositely oriented 2.687 Å and 2.825 Å. This is indication of a disordered two-point Sb position. The differences between thallium ‘walls’ in pierrotite are connected with their environment: the Tl1 site has Sb-richer environment, and only one of its ligand columns is also connected to arsenic polyhedra; the ligands of the Tl2 site all connect with mixed, As–Sb rows of cations.

The composite diagonal chains on the two faces of the double-ribbon are parallel and overlapping, leaving secondary lone-electron-pair interspaces. The only violating atom is Sb2, which reaches into the interspace. If we accept the longer interactions of the apparently flipping Sb5 position, a complex chain Sb2–Sb1–Sb6–As2–Sb5–As4 = Sb3 results (As4 = Sb3 represents an annular connection), with an additional As3 loop connecting As2 and Sb5, and a Sb4 loop connecting Sb5 and Sb3. This chain spans both faces of the double-ribbon. In spite of similar chemistry (TlSb₅S₈) and similarly built zig-zag Tl–Sb partitions of two kinds, the structure of parapierrotite [49,50] is different from the Tl–As structure. It is based on the PbS archetype and not on the SnS archetype; this will be discussed in detail further below.

The N = 3;4, i.e., N_chem = 3.5 homologues with the 3;4;3;4… slab sequence contain low-thallium phases, baumhauerite with ideal composition Pb₁₂As₁₆S₃₆ (no Tl in the material from [51]) and argentobaumhauerite, from Binntal, Switzerland [51]. The latter had microprobe composition Cu_0.06Ag_1.20Tl_0.18Pb_21.46As_32.28Sb_0.56S_72.26 (i.e., 0.40 wt. % Tl) whereas the associated Binntal baumhauerite gave formula Cu_0.01Ag_0.06Tl_0.09Pb_12.23As_16.28Sb_0.18S_35.82 (0.39 wt. % Tl). Evaluation in terms of the possible complete Tl + (As,Sb) ↔ 2Pb substitution, gives the substitution percentage as 1.5 and 1.4%, respectively.

The situation is different for the Ag–Tl substitution percentages of 30 percent and higher. Such N = 3;4 homologues are the As-dominant écrinsite, ideal formula AgTl₃Pb₄As₁₁Sb₉S₃₆ [52] and the Sb-dominant, idealized AgTl₃Pb₄Sb₁₄As₆S₃₆ to AgTl₂Pb₆Sb₁₅As₄S₃₆ boscardinite [53,54]. The Tl substitution percentage in écrinsite [52] varies between 31% and almost 55%, i.e., from 7.52 to 14.57 wt. % Tl. That in boscardinite [53,54] varies between approximately 37% and 50%. Both minerals are acentric, space group P1, with very similar crystal lattices. The main difference is an increment of 0.23 Å on the b parameter and 0.63° on the α value, so that the unit cell volume of boscardinite is 1582.0 ų, whereas that of écrinsite is 1546.7 ų.

The N = 3 slab of écrinsite (Figure 26) includes a column of fairly regular tricapped trigonal coordination prisms of Tl1 in alternation with (Tl_0.82Pb_0.18)2 prisms along [010]. The N = 4 slab includes a column of less regular capped prisms of Pb4 in alternation with a split site of (Pb_0.64Sb_0.36)3. The two shortest bonds of Pb3 are 2.75–2.77 Å, the corresponding Sb–S bonds are too long (or averaged) except for one, 2.477 Å long. Separation of large cation polyhedra into two different, alternating columns is a remarkable adjustment to different atom radii of the largest cations.

Polymerization of (As,Sb)S₃ pyramids, or of the more complete (As,Sb)S₅ versions in which the intermediate cation-anion bonds are also considered, leads in the N = 3 double-ribbon of écrinsite to annular As4–Sb1 groups and isolated Sb2 and As3 polyhedra in the ribbon surface (Figure 26). Across the ribbon, however, they coalesce into a zig-zag chain Sb1–As4/Sb2/Sb2/As4–Sb1 which switches the surface involved three times (switch indicated by ‘/’) and forms three two-cation annuli.

The crankshaft chains in the N = 4 slab of écrinsite (Figure 26) are As5–As6–As8–(Sb7 + As7) + (As10 + Ag10)/side–chainSb9/(As10 + Ag10) + (Sb7 + As7)/side–chain Sb9/As8–As6–As5, i.e., a combination of mixed sites, surface switches and two-atom and three-atom annuli. Secondary lone-electron spaces between chains and groups are well developed in both slab types. The pure-thallium Tl1 position is not influenced by any short bond in adjacent polyhedra, the mixed (Tl,Pb)2 site is partly constrained by the short bonds of adjacent Sb2 pyramid. In type boscardinite, the analogous chain has an occupancy scheme as follows: (Sb_0.78As_0.22)5–Sb6–(Sb_0.53As_0.47)8–Sb7(a flipping bonding scheme)–(Sb_0.71Ag_0.29)10–(Sb_0.81Pb_0.19)9, in agreement with its Sb-rich character and lower substitution percentage. In contrast, in argentobaumhauerite from Lengenbach, which has only traces of Tl and very low Sb contents (see above), such chains are interrupted by an Ag site after five As atoms, or flip to the opposite face of the double ribbon only once, at the fifth As atom [51]. Thus far, a completely Tl-substituted N = 3.5 homologue has not been found.

4.4. Sicherite

Sicherite, TlAg₂(As,Sb)₃S₆, was described from the Lengenbach material by Graeser et al. [55]. The mineral is orthorhombic, space group Pmnb (another orientation of the frequent group Pnma (#62)), with a 12.418 Å, b 15.427 Å and c 5.6895 Å. The crystal structure (Figure 27) is a layered structure with As–Sb based layers alternating with Tl–Ag-hosting, slightly corrugated layers. The As–Sb based layers obey the principles of the SnS archetype, with the orientation of the SnS-like tightly bonded ribbons parallel to (01 ± 1) of the sicherite cell; however, these are only one (Sb,As) polyhedron broad. The ribbon fragments are infinite along [100]. There are two mixed (As,Sb) ‘B’ positions, forming triplets of BS3 pyramids via common S positions; the short B–S distances vary between 2.289 Å and 2.438 Å, each short distance is countered by a long one, between 3.251 Å and 3.695 Å, forming trapezoidal BS5 pyramid plus a distance below base. The pyramidal motif can be interpreted as unit-cell twinned by reflection on (100) at (As,Sb)1 (Figure 28).

Thallium is eight-coordinated, in a somewhat one-sided coordination: three shorter bonds 3.174–3.184 Å oppose the longer ones (3.235–3.897 Å); the average is 3.333 Å. Tl–Tl distances are very long and the Tl–Ag distances are 3.631 Å and 3.846 Å (next only 4.126 Å). Silver has a kinked linear coordination to sulfur (2.504 and 2.511 Å) completed by one 2.885 Å sidewise Ag–S bond. Sb1 has the lone electron pair oriented towards Tl, the Sb2–Tl distance is 3.608 Å. Sb2 has its lone electron pair oriented away from Tl and the distance is 4.200 Å. Penetration of Sb and Ag into the coordination sphere of Tl is modest at best.

5. PbS Archetype

5.1. Lillianite Homologous Series

Homologues of lillianite, Pb₃Bi₂S₆, are sulfosalts with structures composed of (311)_PbS slabs with internal structure close to that of the PbS archetype, which are unit-cell twinned (i.e., with segments periodically reflected into one another) on the (311)_PbS planes [11]. Cations are octahedrally (or near-octahedrally) coordinated except for the cation on the composition plane of slabs, which is coordinated by a trigonal prism of ligands, with two out of three prism faces capped by an additional ligand. Individual homologues differ by homologue order N which is identical with the number N of coordination octahedra along a chain of octahedra, which runs diagonally across a slab, parallel to [011]_PbS. The adjacent slabs each can have its N value, i.e., N1 and N2. The chemical composition of lillianite homologues is given as M²⁺_N−1−2x M³⁺_2+xM⁺S_N−2. The most frequent cations which compose lillianite homologues are Pb, Bi and/or Sb, Ag, in some cases accompanied by Mn, Fe, As, lesser Cu, Cd, Sn and other cations. The latest detailed account dealing with the lillianite homologous series has been written by Makovicky & Topa [56].

Natural thallium-based homologues are not known, although traces of Tl were found in andreadiniite, CuHgAg₇Pb₇Sb₂₄S₄₈, a fourfold superstructure of the andorite type (Biagioni et al. [57]) which contains 0.15 Tl per the above formula unit. The authors ascribe Tl tentatively to (one of) prismatic Pb positions. However, the N = 3;3 member of this homologous series, TlSb₃S₅, was synthetized and described by Gostojic et al. [58]. It was recognized and described as a lillianite homologue by [59]. In spite of the lone electron pair character of Sb, the PbS-like slab has a rather regular PbS-like structure when projected along the 8.95 Å c axis. In the characteristic (100)_PbS plane, the coordination pyramids of three distinct Sb atoms have trapezoidal cross-sections, and the short Sb–S bonds in their bases join into diagonally-oriented Sb₃S₇ crank-shaft chains separated by interspaces containing long interactions. In adjacent (100)_PbS planes, the chains are parallel-shifted.

The resulting two-tier (2 × 4.48 Å) structure of TlSb₃S₅ is monoclinic, space group P2₁/c, a 7.225 Å, b 15.547 Å, c 8.946 Å, β 113.55° (Figure 29). The coordination prism of thallium has bonds to prism corners from 3.042 Å to 3.443 Å and one of them to 3.531 Å, whereas the two caps have Tl–S distances of 3.334 Å and 3.558 Å. This can be compared to the simplified corresponding Pb–S distances in the bicapped coordination prism of lead in quatrandorite [60], 4 × 3.166 Å and 2 × 2.756 Å, with the two caps at 3.072 Å. This difference is an indication of problems which should occur with Tl inserted instead of Pb in the majority of homologues. The antimonian N = 3;3 thallium member of the lillianite homologous series stands in contradiction to the arsenian sartorite homologue N = 3;3, philrothite [41]. This difference can be ascribed to the difference in the ratio of effective crystal radius of Tl to that of Sb and to As, respectively.

5.2. Tl₄Bi₂S₅

The crystal structure of this synthetic sulfosalt is a rare case of a bismuth—thallium sulfosalt; it was structurally analyzed by [61]. It is orthorhombic, in space group Pnam, a 16.760 Å, b 17.396 Å, c 4.09 Å, Z = 4. In a PbS-like structure, there are multiple sulfur vacancies that are surrounded by an octahedron of cations. Among these, there are two CN = 5 atoms and four (in stoichiometry actually two) CN = 4 atoms; the latter display a kinked linear coordination plus two side-bonds. The CN = 6 cations with a complete ligand sphere are interpreted as Bi (bonding distances from 2.64 to 3.05 Å), whereas the atoms surrounding the vacancy are Tl (bonds from 2.88 to 3.28 Å, average 3.06 Å). The octahedron of cations with ‘incomplete ligand sphere’ shares faces with several tetrahedra formed by such ‘defect‘ cations, resulting in complex diagonal and mutually intersecting planes occupied by Tl. They enclose rod-like islands of Bi–S octahedral structure (Figure 30). The Tl–Tl distances are rather large, 3.767–3.869 Å.

5.3. Gillulyite, Tl₂(As,Sb)₈S₁₃

The crystal structure of gillulyite was determined by Foit et al. [62]. The unit cell they established is monoclinic, P2/n, a 9.584 Å, b 5.679 Å, c 21.501 Å, β 100.07°. They recognized, however, that it was only a substructure with a halved b parameter and with several half-occupied and almost overlapping cation and sulfur positions. Their attempt to derive the true structure of gillulyite from this data resulted in a model with As–As and S–S bonds. Makovicky & Balić-Žunić [63] reinterpreted these substructure data in terms of structural order-disorder phenomena, removing the need for the above covalent bonds.

The crystal structure of gillulyite can be described in terms of two alternating layer types (Figure 31). The structure of the A layers shares certain important features with imhofite; however, the B layers can be described as an extremely distorted PbS-like motif which is periodically twinned by insertion of another (As,Sb) polyhedron, and is filled with lone electron pairs and weak interactions [63]. In projection on (100) of gillulyite, the A layer of gillulyite has surfaces like those in imhofite, and they again form part of its order-disorder mechanism: the surface is formed by paired As4 and As5 coordination pyramids interconnected via S7, which alternate with 4 + 1 coordinated Tl1 (which is also cross-bonded to S7 on the opposing side of the layer) (Figure 32). These configurations are shifted by half-a-polyhedron in the [100] direction across the thickness of the A layer by the action of a two-fold screw axis. However, they are separated by 2 to 3 polyhedra of As across the B layer. The A and B layers in gillulyite are different from, and run perpendicular to those in imhofite. The As4 and As5 polyhedra, combined with arsenic polyhedra in the B layer of gillulyite, form complex zig-zag (As,Sb)₄S₇ [100] chains of AsS₃ pyramids.

The sequence of Tl1 polyhedra and As4&As5 pairs on the surface of the A layer (Figure 32) is another example of the 1:2 polyhedral frequency ratio. These polyhedra form a primitive mesh or a chess-board pattern (two-dimensional symmetry p2₁/m or c2/m, respectively). Across an A layer, the B layers can either obey the [010] 2₁ axis or symmetry centers, resulting in two different layer sequences. In a similar way, the A layers can obey alternative choices from symmetry elements that are in the B layer. Together with further complications which are due to the ordering of Tl and As,Sb pyramids in the A layer, [63] derived six possible symmetries and unit cells, from P-1 to P2₁22₁, although most of them are monoclinic. Only a find of a better ordered specimen will decide which one occurs in nature.

6. Sphalerite Archetype

Cage Structures

Five isotype sulfosalts of Tl, routhierite (ideally CuHg₂TlAs₂S₆ [64,65,66]), stalderite (ideally CuZn₂TlAs₂S₆ [67]), arsiccioite (ideally AgHg₂TlAs₂S₆ [68]), ralphcannonite (ideally AgZn₂TlAs₂S₆ [69]), and ferrostalderite (ideally CuFe₂TlAs₂S₆ [70]), can be best characterized as cage structures, which are topologically related to the tetrahedrite–tennantite group [71,72]. They are based on a cubic packing of coordination tetrahedra of cations (Cu,Hg,Zn,Feand Ag) from which the same set of tetrahedra as in tetrahedrite–tennantite [15] has been vacated. Another set of tetrahedra was substituted by (As,Sb)₃ pyramids. Similarity of these two groups of sulfosalts can be appreciated, e.g., by comparing the unit cell of routhierite (a 9.978 Å, c 11.376 Å [66]), stalderite (a 9.865 Å, c 10.938 Å), arsiccioite (a 10.139 Å, c 11.344 Å), ralphcannonite (a 9.861 Å, c 11.125 Å) and ferrostalderite (a 9.879 Å, c 10.849 Å) with that of Fe-rich tennantite (a 10.216 Å [71]) and synthetic Cu₁₀Hg₂Sb₄S₁₃ (a 10.515 Å, [72]). The space group of routhierite/stalderite/arsiccioite/ferrostalderite/ralphcannonite is tetragonal I-42m; that of tetrahedrite–tennantite is cubic I-43m.

Unlike the tetrahedra in cubic tetrahedrite–tennantite (Figure 33), the tetrahedral array is differenciated into two alternating layers of tetrahedra: one is an (Hg,Zn) level of larger tetrahedra (Me–S averaged to 2.563 Å in routhierite of [66], 2.405 Å in stalderite, and 2.570 Å in arsiccioite (in which this site was interpreted as an (Ag,Hg) site)). The other is a (Cu,Ag) level of smaller tetrahedra (2.355 Å in the quoted routhierite, 2.357 Å in stalderite, and 2.473 Å in arsiccioite (a mixed (Hg,Ag,Cu,Zn) site; [68]). In ferrostalderite, this ratio is reduced to a minimum value (2.385 Å/2.332 Å), whereas in ralphcannonite it maintains its level (2.468 Å/2.358 Å). The latter levels contain all (As,Sb)S₃ coordination pyramids (As–S equal to 2.322 Å for As_0.68Sb_0.30 in the just mentioned routhierite structure, and to 2.304 Å in arsiccioite for As_0.77Sb_0.23). The nearly clean arsenic site in ralphcannonite has the As–S bond of 2.257 Å, and the pure As site in ferrostalderite it has 2.272 Å. The differences in bond distances and the resulting tetrahedron size are compensated for in the [001] direction rather than in the dimensions of the (001) planes. Details of site population in this group of minerals were discussed by Biagioni et al. [68].

The latter situation is in agreement with the population and orientation of cavities: They contain two Tl atoms each (Figure 34), with the linear Tl–Tl distance of 3.279 Å in stalderite and ferrostalderite, 3.284 Å in ralphcannonite, and 3.33–3.47 Å in the routhierite samples, always elongate in the [001] direction. Bonding distances from Tl to the S atoms along the continuation of the [001] direction are 2 × 2.96 Å in stalderite and 2 × 3.00 in Å routhierite. These short Tl–S distances indicate that the lone electron pairs of Tl are oriented towards the opposing Tl atom, away from the S atoms ‘above’ and ‘below’ the pair, in agreement with [68]. The remaining Tl–S distances (perpendicular to the Tl–Tl pair) are 3.50 Å and 3.44 Å for the above two compounds. In arsiccioite, the Tl position is split into 36% occupied Tl1 site and 64% occupied Tl2 site. The above mentioned pair of bonds is 2.895 Å and 3.044 Å for Tl1 and Tl2, respectively. Remarkably, the majoritarian Tl2 site is about 0.26 Å off the ‘Tl1–Tl1 axis’ at (0,0), resulting in the Tl–As distance of only 3.347 Å (compare below) and two pairs of ‘equatorial’ Tl–S distances, 3.308 Å and 3.672 Å, instead of four equal 3.488 Å Tl–S distances for Tl1. The Tl–Tl bonds in this split situation vary between 3.25 Å for Tl2–Tl2 and 3.51 Å for Tl1–Tl1; the mixed one results in 3.38 Å.

The Tl–Tl pair is chelated by four (As,Sb)S₃ pyramids in a tetrahedral arrangement, the Tl–As distance is 3.48 Å in stalderite, 3.567 Å in routhierite (Figure 34), whereas it is visibly reduced for Tl2 in arsiccioite (3.347 Å). This makes it difficult to decide whether the lone electron pairs of (As,Sb) are engaged with the electron shell of Tl, although this is strongly suggested by the Tl behavior in arsiccioite. Based on the inward-oriented (As,Sb) atoms, in these minerals the cage is an elongated tetrahedron (Figure 35) as already noted by Borisov et al. [73] in their Figure 7; whereas with all eight (in- and outward oriented) (As,Sb) atoms included, it is a distorted cube (Figure 36).

For a time, a similar cubic structure of galkhaite (Cs,Tl)(Hg,Cu,Zn)₆As₄S₁₂ [74] was considered an example of a Tl-hosting structure with a cage, which itself was generated by the presence of the large cation, i.e., thallium. Later investigations corrected this assumption–the principal large, rattling cation in the cavity is cesium, whereas Tl occurs in lesser amounts [74]. The charge balance is achieved by heavy substitution of tetrahedral Cu⁺ by Hg²⁺; the resulting unit cell parameter a is 10.365 Å. The (Cs,Tl) cation is 12-coordinated, with the cation–S distance 3.863 Å.

Two galkhaite-like minerals are currently under description and publication [75]. Vorontsovite, with ideal formula (Hg₅Cu)_Σ6TlAs₄S₁₂ and ferrovorontsovite, (Fe₅Cu)_Σ6TlAs₄S₁₂ are end-members of a solid-solution series. Mercury and/or Fe²⁺ with minor amounts of Zn are the tetrahedrally coordinated cations forming the framework of the structure, together with MeS₃ coordination pyramids of As (with minor Sb). It is a well-known tetrahedrite-like scheme with a large truncated-tetrahedron (Laves polyhedron) cage. Thallium assumes the central position in this cage, with a considerable U_eq parameter, indicating a ‘rattling’ cation, smaller than cesium in galkhaite; these minerals contain only 0.09 Cs apfu at maximum.

The cubic unit cell parameter a of the Hg-based vorontsovite is 10.296 Å, that of Fe-based ferrovorontsovite is 10.239 Å, and that of original galkhaite, idealized Hg₅CuCsAs₄S₁₂, is 10.443 Å; the unit-cell volumes of the first two phases are 1091.3 ų and 1073.4 ų. The space group is I-43m. The tetrahedral ‘Hg’–S distance is 2.443 Å, reduced to 2.408 Å in the ‘Fe’–S case; the As–S distance is typical for As: 2.282–2.288 Å. The twelve Tl–S distances, an expression of the cage radius, are 3.893 Å, increased in the Fe case to 3.902 Å. A comparison with Tl–S distances in the routhierite group of structures on the one hand confirms the degree of Tl rattling in the vorontsovite cage. On the other hand, it suggests a reason for the existence of more ‘compact’ routhierite-like arrangements.

One more remarkable cage structure with thallium is that of natural kutinaite, (K,Tl)_0.25Cu₁₄Ag₆As_6.75, from Krkonoše, Czech Republic [76]. This is an alloy full of metal-metal bonds; however, As still plays a role of anion in it. Unlike synthetic ‘kutinaite’ Cu₁₄Ag₆As₇ [77,78] which is cubic, Pm-3m and full of partly occupied atom sites without cavities, natural kutinaite turned out to be tetragonal (a 11.789 Å, c 11.766 Å), space group P4/mmm. In this structure, clusters of 8 edge-sharing tetrahedra of copper alternate in a three-dimensional chess-board pattern with octahedral clusters of six silver atoms, surrounded by triangularly coordinated copper atoms, situated in eight faces of a cuboctahedron. Partly occupied (K,Tl) sites are in large cavities, coordinated by 18 Ag and As ligands.

7. Tl-Rich Structures

The structure of Tl₃SbS₃ [79] is quite different from the arsenic analogue, Tl₃AsS₃. The structure is rhombohedral, space group R3mH, unit cell a 9.519 Å, c 7.36 Å, γ 120°, cell volume 577.55 ų (Figure 37). Thallium has five Tl–S bonds (two opposing bonds 3.076 Å, the longest bond 3.367 Å, and six short Tl–Tl distances: always a triplet of 3.665 Å; the rest are at 3.843 Å distances. There is a fundamental problem: the ‘SbS₃’ trigonal pyramids are very flat, with Sb–S distances of only 2.133 Å, too short even for arsenic. This might have been a mirror-twinned structure where the presumed ‘SbS₃’ groups are a weighted average of two mirror-related true SbS₃ pyramids, which face the opposite way.

8. Structures Based on a Combination of Two Archetypes

8.1. Chabournéite Homeotypes and Parapierrotite

Pierrotite [48], described in detail above, is a structure in which the SnS-like slabs are in their geometry transitional between the SnS archetype as seen in rathite, and the PbS archetype, so that the double-ribbons are ‘slanting sideways’ when compared with ideal PbS. Parapierrotite, TlSb₅S₈ [49,50], with the structure still closer to an ideal PbS geometry, is monoclinic, with space group Pn, a 8.098 Å, b 19.415 Å, c 9.059 Å, β 91.96°. Unit cell data for the natural parapierrotite from Vorontsovskoye, Tl_1.01Sb_4.75As_0.28S_7.95 [50], are nearly identical with the ones given here.

The superficial similarity between pierrotite (Figure 24) and parapierrotite transpires from the projection along [001] of parapierrotite (Figure 38). In parapierrotite, mixed Tl–Sb columns of zig-zagging tricapped trigonal coordination prisms separate slabs of PbS-like structure composed of Sb coordination polyhedra, though with the caps of one Tl–Sb coordination prism inserted into each (100)_PbS plane. The Tl1 prism is more regular (Tl–S distances between 3.235 Å and 3.695 Å; average 3.389 Å), however, Tl2, with distances 3.126 Å to 3.712 Å (average 3.311 Å), is closer to a bicapped coordination prism as present in lillianite homologues (Figure 38). Modestly pronounced and fairly narrow lone electron pair micelles in the slab are closed by bonded Sb on both ends; cation sequences of these marginal sites are split in such a way that some Sb atoms have the coordination pyramid vertex pointing one way, and the alternating ones the opposite way, i.e., not all pointing one way like in the atomic plane of the SnS archetype. The Sb coordinations which alternate with Tl in the two types of the [001] Tl–Sb columns differ. In the Tl1 column, Sb3 has three short bonds oriented equally so that the SbS3 pyramid points down in the [001] Tl–Sb channel (with one longer additional bond to S12; Figure 39), whereas in the Tl2 column, Sb9 is side-attached by the way of S9–S11 to the wall of the Tl2 channel (Figure 40). Lack of inversion makes especially the Tl1 channel polar.

By their orientation, the (100)_PbS planes of the PbS-like slab approximate (120) of the parapierrotite lattice. According to [80], the PbS-like slab is cut parallel to (211)_PbS. The slabs are composed of steeply oriented, complex and tightly bonded chains of interconnected polyhedra of Sb1, 2, 4, 5, 7 and 8, arranged into inclined ‘sheets’ of Sb atoms with three short strong Sb–S bonds, to which Sb1, 10, and to a degree also Sb6 with two short and two intermediate bonds, are added. The latter polyhedra indicate a partial occupation of two competing orientations of the actual 3-fold Sb coordination. The Sb3 and Sb9 atoms from the Tl–Sb columns are attached to this framework via shared sulfur atoms. These ‘sheets’ are separated by lone electron pair interspaces with Sb–S distances between 3.40 and 3.80 Å. Via Sb3 and Sb9 in the columns, they also connect with adjacent slabs into a 3D network. The often published projection of the parapierrotite structure along [−101] as was done in [49] illustrates this modular aspect of the structure.

However, the structure of parapierrotite is amenable to one more interpretation. Its (010) layers of PbS-like structure can be interpreted as being composed of lozenge-shaped rods of PbS archetype, three octahedra wide and four cation-anion (100)_PbS planes thick (Figure 41). These rods are inserted into one another by a width of one octahedron (a volume of two half-octahedra), in a way in which many Pb- and some Sn-sulfosalts have been interpreted [13]. This creates a zig-zagging rod-layer surface, alternating one square-shaped Q (primitive pseudotetragonal) interval occupied by Tl with one orthohexagonal H subcell formed by S atoms. More than ½ of the H width matches with the Q interval; the rest participates as a wall in an empty triangular channel, which is traceable in the corner portion of the interspace (Figure 41). Thus, parapierrotite is a rod-layer structure with small, heavily overlapping rods, with adjacent rods interconnected by two atomic (100)_PbS planes. In Pb sulfosalts, the Q intervals are usually formed by several Pb polyhedra; here, by one Tl polyhedron.

Berlepsch et al. [81] determined and refined the crystal structures of KSb₅S₈ and (Tl_0.6K_0.4)Sb₅S₈ (Figure 42) and found them to be isotypes of TlSb₅S₈. The mixed Tl–K sulfosalt has the unit cell parameters a 8.115 Å, b 19.425 Å, c 9.048 Å, β 91.97°, i.e., a slight expansion of unit cell volume from 1400.5 ų to 1425.46 ų, pure K-sulfosalt has 1437.23 ų. The bonds of all atoms have the same bond-length schemes as in TlSb₅S₈, the most interesting alternation of (Tl,K) and Sb in the trigonal-prismatic columns of the structure is fully present (Figure 43), and the sphericities of the large cation site in these phases are very similar. The sphericity of the M1 site (0.970) is significantly higher than that of the M2 site (0.93–0.88 according to the choice of S ligands), in agreement with the above.

Protochabournéite, approximately Tl₂Pb(Sb_9-to-8As_1-to-2)_Σ10S₁₇, was described by Orlandi et al. [82]. The space group is P-1, a 8.150 Å, b 8.716 Å, c 21.579 Å, α 85.18°, β 96.94°, γ 88.60°, the unit cell volume 1515.4 ų. This mineral is homeotypic with chabournéite, which has doubled a and c parameters. Substructure of chabournéite was described by Nagl [83], full structure by Biagioni et al. [84]. Dalnegroite [85] also has doubled a and c parameters. Thus, protochabourneite (Figure 44) is the simplest representative of the chabournéite homeotype family [82] whereas the two other structures are superstructures on its motif. That explains the doubts arising from centrosymmetricity tests: they all have pronounced centrosymmetric substructures, although the true structure is acentric.

The fact that the structure consists of two alternating, substantially different types of slabs was quite a surprise: [12] (a) slabs of PbS archetype cut according to (211)_PbS and alternatively two- and three octahedra wide, (b) slabs of SnS archetype, three pyramids (including one pyramidal cap of the Tl polyhedron) wide. They are separated by a zig-zag wall of alternating columns of Tl- and Pb–Sb coordination prisms. As it is usual for the sartorite homologous series, exclusively composed of SnS-like slabs, the Tl site has been included in calculating the N = 3 homologue order of the SnS layer.

The PbS-like slabs resemble those in parapierrotite, though differ in detail. The (100)_PbS planes in parapierrotite contained (in projection, Figure 38) two coordination octahedra of Sb and a (Pb,Sb) column. In protochabournéite, they have a width of three Sb coordination octahedra (Sb position in the central column of them is heavily split), alternating with ribbons of only two octahedra plus a (Pb,Sb) column. The rod-layer interpretation of this layer differs from that in parapierrotite (which was described above): the PbS layer in protochabournéite consists of lozenge-shaped rods, three octahedra wide and three atomic planes thick, which do not overlap but share a two-octahedra broad stripe of the (100)_PbS surface (as traceable in Figure 44). A similar interpretation in [82] does not include the (Pb,Sb) columns, which in our interpretation stand for the pseudotetragonal Q surface intervals of rod-layers (compare with [13]).

In the Tl column of the protochabournéite structure (Figure 44), Tl1 (a pure Tl site; average of 9 bonds equal to 3.417 Å) alternates with (Tl_0.70Pb_0.30)2, with an average bond length of 3.355 Å. In the Pb-based column, which is orientated towards the PbS-like slab, Pb1 has a bond average of 3.160 Å, when considered as a bicapped coordination prism. Two of the mixed (Sb,As) sites are in the SnS-like portions of the structure, one more mixed site with only 10% As is the central split site in the PbS-like slab.

The configuration of diagonal tightly-bonded Sb–S chains in the SnS-like portions is strongly influenced by the presence of Sb: the six-member chains contain three eyelets, either formed by two Sb atoms or by one Sb and one As atom. These are joined to one another by short bonds to two common S atoms. Orlandi et al. [82] defined a 19 (or even 21)-member strongly-bonded [210]_PbS (Sb,As)–S chain in the PbS-like slabs. In [10-1] projection, the PbS-like slabs show similar separation of atomic planes into tightly-bonded double-ribbons and LEP interspaces as is observed in parapierrotite (above).

The structural differences between homeotypes are caused by differences in composition. In the potential ‘chabournéite composition field’ [82], protochabournéite, with the composition of the structurally investigated sample Tl_1.70Pb_1.60(Sb_8.80As_0.90)_Σ9.70S₁₇, is the Sb-rich phase, with the Sb/(Sb + As) ratio centered on 0.8–0.9 and the Pb/(Pb + 2Tl) ratio centered on 0.24–0.30. At least preliminarily, chabournéite is defined as Sb/(Sb + As) = 0.50 to 0.60 [84], however, the ‘Pb-character’ of it lies between Pb-free (approximately (Tl_2.5Sb_2.5)(Sb₄As₅)S₁₇) and Pb-rich, with Pb/(Pb + 2Tl) up to 0.23, and with the Sb/(Sb + As) ratio reaching almost 0.6, typified as Tl₂PbSb(Sb₅As₄)S₁₇. It is not clear whether the structurally fully investigated specimen Ag_0.04Tl_2.15Pb_0.64Sb_5.12As_5.05S_17.32, with the Sb ratio of 0.503 and Pb-ratio of 0.13 [84] structurally represents the entire chabournéite field. It lies rather centrally in the field, designated as chabournéite by [82]; this field is based on a combination of chemical and structural data. This structure is triclinic, with space group P1, a 8.520 Å, b 42.461 Å, c 16.293 Å, α 83.351°, β 90.958°, γ 84.275°, unit cell volume 5823 ų. These values correspond to those given by [83], who determined only a substructure of chabournéite (used, e.g., by [12]), though only partly to those given by Johan et al. [86]. Further increasing the uncertainties, Bonaccorsi et al. [87] originally referred to a protochabournéite sample with space group P-1, a 8.150 Å, b 8.716 Å, c 21.579 Å, α 85.12°, β 96.94°, γ 88.60°, V 1515 ų as ‘chabournéite from Apuan Alps’, which then becomes quoted in the literature [85].

In chabournéite (Figure 45), Tl atoms reside in tricapped trigonal prisms, which line the SnS-like structure slabs. There are 16 pure Tl sites, with average bond distances between 3.339 Å and 3.410 Å, and bond extremes between 3.166 and 3.667 Å. The alternating component of zig-zag walls are columns of distorted bi- to tricapped coordination prisms housing Pb and Sb, which were refined in different combinations: (Pb,Tl) sites, (Pb,Sb) and (Sb,Pb) sites, pure Sb sites and split (Pb,Sb) and (Sb,Sb) sites. Among the Me³⁺ sites forming the two types of slabs, 18 pure Sb sites, 18 pure As sites and 36 mixed (As,Sb) sites (2/3 As dominant) were found.

In the SnS-like slabs (Figure 46), the same tightly-bonded chain (Sb,As)₆S₁₀, and groups are found as in protochabournéite. As/(As + Sb) ratios in the two different, though substructurally identical, portions of the 43 Å cell differ only slightly; they approximate 0.51 and 0.52 for the SnS-like portions and a more pronounced difference of 0.54 versus 0.62 in the two PbS-related portions. This means that arsenic is relatively concentrated in the PbS-like portions, in their central parts, which exhibit a distinct split in cation positions. Tightly-bonded groups in these portions are (Sb,As)₃S₆, (Sb,As)₅S₉ and (Sb,As)₇S₁₂. The Sb-containing sites in the Pb–Sb columns determine the final As/Sb ratio.

Nestola et al. [88] described an As-dominant member of the chabournéite homeotypic series, which they named dalnegroite, with ideal composition Tl₄Pb₂(As₁₂Sb₈)_Σ20S₃₄. Bindi et al. [85] described its crystal structure in the space group P1, a 16.218 Å, b 42.546 Å, c 8.558 Å, α 95.70°, β 90.18°, γ 96.38°, cell volume 5838.9 ų. 980 structure parameters were refined from 22,226 good reflections. The size of the refined set can already be appreciated from, e.g., presence of 136 independent sulfur positions; overloading is visible on structural details. Unit cell parameters are close to those of chabournéite (above), the largest difference is in the β values.

The approximately 7.8 Å thick SnS-like layer of dalnegroite alternates with the 13.6 Å thick PbS-like layer. The structure contains 16 independent Tl positions, 18 mixed Pb–Sb sites which appear as more distant from the trigonal prismatic model than those in chabournéite, two Pb sites, 32 Sb and 48 As sites. Tl–S distances start at a rare 2.71 Å value, however, a bulk of them are distinctly over 3 Å, up to 3.86 Å. The (Pb,Sb)–S distances start from 2.43 Å, though preferably from about 2.76 Å. The As–S distances appear to suffer most from the overloaded refinement. The authors stress a high number of apparently pure cation sites, when compared with the heavily mixed positions in chabournéite. They suggest that there is an important difference between these two structures: In chabournéite, there are distinct cation-anion levels (001)* (asterisk signifies a level perpendicular to c) and the orientation of the As₂Sb₄S₁₀ chain, which runs diagonally across the SnS-like double-ribbon, can be approximated as [u −vw], whereas in dalnegroite, the near-identical chain runs in the [u +vw] direction (in the chabournéite-like designation of axes). This is possible because the zig-zagging wall of Tl- and Pb(Sb) prisms in these structures exhibits a series of approximate mirror planes perpendicular to [001] (in chabournéite-like orientation of axes) and the initial Sb–As eyelet of the chain always attaches by straddling symmetrically such a mirror plane (Figure 46), and then continuing ‘up-’ or ‘downwards’ across the double-ribbon. This OD phenomenon should also act as a twinning mechanism in chabournéite.

The story of chabournéite and homeotypes reminds of similar cases from among sartorite homologues: on the one hand, the 44.4 Å structure of argentobaumhauerite is developed as an Ag-containing composition-and-superstructure variant of the 22.8 Å structure of Ag-free baumhauerite [51]. On the other hand, the heptasartorite–hyršlite–guettardite–twinnite homeotypic series of N = 3 sartorite homologues (in press) is created by a progressively increasing Sb/(As+Sb) ratio.

8.2. Tsygankoite

Tsygankoite [89] is monoclinic, with space group C2/m, with a = 21.362 Å, b = 3.8579 Å, c = 27.135 Å, β = 106.944°, V = 2139.19 ų, Z = 1. The ideal chemical formula of tsygankoite is Mn₈Tl₈Hg₂(Sb₂₁Pb₂Tl)_Σ24S₄₈, whereas the empirical formula (based on 90 atoms in formula unit) is: Mn_8.06Tl_8.97Pb_1.98Hg_1.90Fe_0.03Cu_0.02Ag_0.01Sb_17.85As_3.18S_48.00Se_0.01. Pb and Tl play an important role in the substitution for (Sb + As)³⁺ and are necessary for the stabilization of the structure. The crystal structure of tsygankoite (Figure 47) contains 11 independent cation sites (four of which are mixed sites) and 12 distinct sulfur sites. It consists of an alternation of two thick layer-like arrays; both are typical for sulfosalt structures.

The PbS-like array contains an Hg site with a typical pair of short opposing bonds (Hg–S × 2.321 Å and 4 × 3.290 Å), a Tl site, the octahedrally coordinated Mn1 site (Mn–S from 2.573 Å and 2.728 Å) and two pure Sb sites, labeled Sb1 and Sb2. The alternating array, with a general bond scheme, represented by the SnS archetype (an array with a more pronounced steric role of lone electron pairs) contains four distinct Sb sites, all of which statistically mix with either heavier cations (refined as Pb or Tl component) or with arsenic. Embedded in this array is a thallium site (refined as “Tl3”), and a Mn²⁺ site (Mn–S 2.536–2.636 Å), this being apical to the second array. Interesting is the close spatial relationship of large Tl⁺ and small Mn²⁺ polyhedra in the former array and along its contact with the latter array. The thallium polyhedra have trigonal prismatic Tl–S distances between 3.120 and 3.240 Å, and between 3.129 and 3.470 Å for Tl2 and Tl3, respectively, with capping distances 3.096 and 3.363 Å, and 3.075 Å, in the same order. This suggests pure thallium sites.

The PbS-like portions represent a sequence of interconnected rods, each of them four (100)_PbS planes thick, and ideally, three polyhedra broad though heavily overlapped (for the definition of rod-based sulfosalt structures, consult [13]). The contact/overlap portions of two adjacent rods are formed by the coordination octahedron of Hg, surrounded by two Mn octahedra and two bicapped trigonal coordination prisms of Tl; paired columns of Sb coordination pyramids form the cores of rods, with a lone electron space in between the pyramidal pairs (Figure 47).

The layer based on the SnS-archetype represents a step-like cut-out of an SnS-like, antimony-based sulfide slab, limited by the overall (410)_SnS planes (Figure 47). It consists of a set of double-ribbons, separated by planar LEP micelles. In subsurface portions of this layer, one site is occupied by thallium (Tl3), whereas the step tips are formed by an octahedron of Mn2. Sb3 and Sb6 contain approximately 0.40 (Pb,Tl), these being a mixture of Pb and, presumably, Tl. The more marginal sites Sb4 and Sb5 contain 0.23 As and 0.32 As, respectively. The distribution of bonds in the central portions of this layer is dictated by their lengthening due to the partial substitutions of Sb by (Pb,Tl). The complicated match of the two-layer arrays proceeds via Mn octahedra, followed by a space for lone electron pairs of Sb from the PbS-like layer, of Tl from the SnS-like layer and a trigonal coordination prism of Tl (Tl2).

Biagioni et al. [90] found 0.6–1.7 wt. % Tl in rouxelite from Monte Arsiccio (Tuscany), in gross correlation Pb ↔ Tl + Sb. For this substitution, similarities in selected structural configurations of rouxelite to those in tsygankoite [60] may be important.

9. Chain Structures

Simonite, TlHgAs₃S₆, is monoclinic, P2₁/n, a 5.948 Å, b 11.404 Å, c 15.979 Å, β 90° [91]. In the crystal structure (Figure 48), the AsS₃ coordination pyramids form infinite six-member AsS₂ chains parallel to [101] of simonite. However, they are composed of moderately offset [102] chain fragments. The meeting of the As1 and As2 pyramids in a chain leads to an offset of the layer, creating a new alignment of these chains, which, additionally, offsets the interlayer space. In all projections, the chains are separated by interspaces hosting Tl and Hg so that simonite is a chain structure. The interspaces are divided into Hg–Tl–Tl–Hg segments, although less pronounced than in the tubular structures.

The As1–As3 pyramids all have one short As–S distance in the principal direction of their chain, sending their lone electron pair diagonally into the interspace with large cations. Although Tl is centrally accommodated in the interlayer space, its bonds reach deep into the complex structure formed by the As–S chain. Individual bonds vary in length, between Tl–S1 equal to 3.200 Å to Tl–S4 equal to 3.840 Å, although their distribution appears to be especially determined by the presence of the above offsets. Mercury has a linear, slightly kinked coordination: 2.398 Å opposed by 2.412 Å, with an additional distance of 2.726 Å, which causes the kink. Perpendicular to these are two long distances: 3.726 Å opposed by 3.056 Å. The 2.726 Å bond has no opposing bond to sulfur, with only a modest distance to As1, equal to 3.822 Å. No short Hg–Tl distance was observed; the Hg–Hg distance is 3.960 Å.

The short As–S bonds vary between 2.181 Å and 2.340 Å (both extremes are for As2) and all As atoms have a rich spectrum of long distances. ‘Regular’ long distances are 3.672 Å to 3.800 Å (both As3), however, As1 has an As–S1 distance of 3.138 Å, opposing a distance of 2.321 Å. This configuration is exceptional in such a structure. It appears to be a forced distance brought about by the combination of adjacent short As2–S4, As2–S1, As1–S4 bonds, and possibly also by Hg1–S1 bonds.

10. Layer Structures with Thallium-Rich Layers

10.1. Simple Two-Component Structures: TlBiS₂

The unit cell of this layered structure [92] represents a narrow column, a 4.1041Å and c 21.872 Å, γ 120°, V 319.05ų, space group R- -3mH. It is a typical, simple layer structure in which the two types of layers share common sulfur atoms (Figure 49). The octahedral Tl layer has Tl–S distances equal to 3.162 Å, and the octahedral Bi layer has the measured distances equal to 2.832 Å. The bond length differences are solved by reducing the thickness of the Bi layer and augmenting the ‘height’ of Tl octahedra.

10.2. The Tl₃AsS₃ Type of a Two-Component Structure; Christite

Tl₃AsS₃ is an orthorhombic structure, with space group Pbca [93]. Unit cell dimensions are a 5.695 Å, b 12.205 Å, c 21.6340 Å, V 1503.72 ų. In spite of a simple chemical formula, the crystal structure is a fairly complicated layer structure, with two configurationally distinct layer types. The first recognizable layer type are (a) thicker (001) layers (z = ¼ and ¾) with surfaces hosting the As atoms and one of their short As–S bonds (all pointing one way, +b or −b, though alternating in adjacent (a) layers). These layers accommodate two internal planes populated by the sulfurs of the inward pointing short As–S bonds, and the Tl1 and Tl3 sites (Tl1–Tl3 3.619 Å); the (b) layers (z = 0 and ½) share As with the previous layer type, and concentrate the LEPs of arsenic, as well as Tl2 in a diagonal [100] zig-zag arrangement (Tl2–Tl2 3.612 Å) running through the center of the (b) layer. The (a) layers have an internal a glide plane; the (b) layers an inversion center (Figure 50). The isolated AsS₃ pyramids are regular (bonds 2.257, 2.226, and 2.249 Å, countered in the same order by long distances 4.260 Å, plus a deviating distance of 4.012 Å, 3.470 and 4.333 Å). The shortest Tl–S distances observed are 2.895 and 2.961 Å. The (b) layer contains the shortest observed Tl–As distances, 3.493 and 3.684 Å.

The (a) layers contain four-sided [100] ‘channels’ of spirally arranged Tl1 and Tl3 positions. Anions do not partake in the ‘channel/chimney’. The lone electrons of thallium concentrate into the channel volumes and the quoted short Tl–S distances tie the channel ‘corners’ to the surrounding sulfurs of the AsS₃ groups. The latter groups form a sort of a ‘box’ enclosing the thallium channel. The two-atom Tl2 ‘staircase’ is in a similar situation although the LEPs of As are oriented towards Tl2.

Christite, HgTlAsS₃, is monoclinic, with space group P2₁/n, a 6.113 Å, b 16.188 Å, c 6.111 Å, β 96.71°; these are the values obtained on a synthetic product by [94]. The crystal structure of christite (Figure 51) consists of three atomic levels thick (100)_PbS slabs containing aligned isolated AsS₃ coordination pyramids and Hg atoms. The Tl interlayer separating them, about 3.77 Å thick, shares the S sheets with the former slabs; Tl atoms are tightly placed just under its boundaries. In fact, they can be interpreted as slightly extruded cation sites in the surfaces of the PbS-like layer. Orientation of the AsS₃ pyramids follows the PbS-like scheme nicely (Figure 51) and makes the PbS-like slab polar in the [001] direction. This orientation also makes the lone electron pairs of As oriented diagonally outward from the PbS-like slab. The two Tl levels in the thallium interlayer can be interpreted as mutually sheared by ¼[100]_PbS.

The Hg coordination is an irregular tetrahedron with distances 2.460 Å, 2.472 Å, 2.647 Å and 2.661 Å. Hg–Hg distance is 4.567 Å and more. The As–Hg distances are 3.796 Å and 3.846 Å. Tl–S varies from 3.109 Å (and 3.111 Å) to 3.398 Å for the distances to the nearby slab, and 3.509 Å and 3.520 Å for those across the interspace. The closest Tl–Tl contact is 3.389 Å, the Tl–Hg contacts are 4.114 and 4.119 Å, then only 4.893 Å. As–Tl distances are 3.499 Å and 3.881 Å, outlining a ‘lozenge’ in the Tl layer.

10.3. Thallium-Silver Sulfosalts: Two-Component Structures

The structurally simple representatives of this category are the synthetic sulfosalts Tl₃Ag₃Sb₂S₆ and Tl₃Ag₃As₂S₆ [95]. These compounds, intermediate between Ag₃(As,Sb)S₃ and Tl₃(As,Sb)S₃, were synthetized from binary sulfides at 200 °C. They are isostructural, space group P2₁/c with a 11.685 Å, b 11.860 Å, c 12.129 Å, β 123.36° for Tl₃Ag₃Sb₂S₆, and a 11.442 Å, b 11.753 Å, c 11.988 Å, β 123.52° for Tl₃Ag₃As₂S₆. The difference in unit cell volumes, 1404.1 ų versus 1344.0 ų, is due to the Sb/As exchange in this case.

The structures consist of two kinds of slabs parallel to (100), which share the boundary sulfur atoms (Figure 52) and contain isolated SbS₃ pyramids. The A slab is a double layer with two levels of Tl atoms (Tl1–Tl3), interspersed by inclined SbS₃ pyramids and ‘standing’ AgS₃ coordination triangles of Ag3 (Figure 53). Tl1S₈ is a coordination antiprism, Tl2S₆ is transitional between a trigonal prism and an octahedron and Tl3S₅Ag is a distorted prism as well, with one Ag atom as a ligand of thallium. Thallium exhibits bond-length variation with the coordination number: average Tl1–S bond length (given for Sb compound/As compound) is 3.393 Å/3.356 Å, Tl2–S is 3.236 Å/3.238 Å, and average Tl3–S is 3.165 Å/3.155 Å. The Tl3–Ag3 contact is very short, 2.959 Å/2.922 Å in the above order (Figure 54). The A slab is divided by a planar (100) net of S atoms into two inversion-related half-slabs.

The B slab is much thinner, with the corrugated sulfur boundaries enclosing a system of AgS₄ tetrahedra and Sb(As) coordination pyramids (Figure 55). The Sb2S₃ coordination pyramids form disjoint [010] rows, in which two additional S1 atoms complete the Sb coordination to a SbS5 pyramid with a broad trapezoidal basis. The (3 + 1) coordination tetrahedra of silver form [010] chains by alternatively sharing vertices (Ag1 with Ag2) and common edges (Ag1–Ag1 equal to 3.370 Å and Ag2–Ag2 to 3.545 Å).

In the A slab, the median S4 and S5 atoms form a distorted 3.4.3.3.4 net (each node is surrounded by 3 triangular and 2 square fields; plane group symmetry p4gm further reduced to pgg). Thallium atoms form a net of distended pentagons, separated by rectangle-and-triangle [001] strips. This is also reflected in the configuration of S net situated in the sulfur layer between the A and B slabs. The Sb1S3 pyramids are in the pentagonal spaces and alternate along [010] with the above mentioned Tl3S₄Ag3 ‘sunken’-pyramidal coordination.

Lone electron pairs of Sb1 and Tl3 seem to avoid one another, although placed in one cavity. Tl3 with the Tl–Ag bond, appears concentrated into (010) zones alternating with zones lined by Tl1 and Tl2 positions. The As compound is fully isotypic with the Sb compound (Figure 55), with distances slightly reduced as the consequence of smaller AsS₃ polyhedra.

10.4. Two-Component Structures with Octahedral Elements

Tl₂MnAs₂S₅ is a synthetic sulfosalt prepared and investigated by Gostojić et al. [96]. Symmetry is orthorhombic, space group Cmca, a 15.340 Å, b 7.608 Å, and c 16.651 Å. The crystal structure consists of complex (001) layers based on a set of parallel MnS₄ columns which contain edge-sharing irregular MnS₆ octahedra and are framed by paired AsS₃ pyramids (Figure 56). Interlayers are filled by elongated Tl2S₆ coordination octahedra which share ligands with the main layers. Tl1 is a part of the complex (001) layer, however, interconnecting the Mn octahedral rods in this layer (Figure 57).

In Tl₂MnAs₂S₅, Tl1 and Tl2 are six-coordinated, although far from regular polyhedra. Unlike Tl1, the (001) layers of Tl2 polyhedra contain only Tl. Trigonal As pyramids are paired via a common S atom; along the [100] direction a pyramidal pair matches two Tl2 polyhedra. The basal As–S distances of distorted AsS₅ pyramids are: 2.290 Å opposed by 3.410 Å, and 2.257 Å opposed by 3.877 Å. The vertex distance 2.220 Å lacks a distant opposing distance within a 4 Å range. The complete AsS₅ pyramids are variously oriented, not in a simple stacking sequence.

Erniggliite, a sulfosalt of Tl⁺ and Sn⁴⁺, Tl₂SnAs₂S₆ [97] is trigonal, with space group P-3, a 6.675 Å, c 7.152 Å. It is composed of two types of (001) layers: (a) the compact layers of inwards oriented isolated As³⁺S₃ coordination pyramids combined with SnS₆ octahedra, which are separated by planar sheets of S from pure (b) Tl layers, with Tl atoms situated fairly close to layer boundaries (Figure 58).

The AsS₃ coordination is completed into a trapezoidally distorted octahedral one, with opposing pairs of bonds/distances: 2.243–3.778 Å, 2.242–3.779 Å, and 2.243–3.775 Å.

The 2.243 Å bond is also opposed by the As–Tl distance of 3.259 Å. The coordination octahedron of tin has six Sn–S distances equal to 2.559 Å. Thallium has [6 + 3] coordination, consisting of triples of 3.268 Å and 3.748 Å bonds to the nearby As–Sn layer, and a triple of 3.373 Å bonds to the opposite As–Sn layer. The average of bond lengths for Tl is 3.463 Å. The boundary sulfur layer has a configuration of 6.3.6.3; the hexagons accommodate Tl atoms situated above them. The triangular S configuration serving as a base of AsS₃ pyramids is opposed in the related S sheet of the Sn–As layer (Figure 59) by a hexagonal configuration, because the Tl atom above it is connected by the short 3.259 Å interaction with the As atom at the tip of the former AsS₃ pyramid. The closest Tl–Tl distances are 4.205 Å.

10.5. Layer Structures with Lone-Electron-Pair Channels

10.5.1. Raberite Tl₅Ag₄As₆SbS₁₅

In respect to the distribution of thallium, the crystal structure of raberite [98] is a typical layered structure. Thallium-lined (010) layers with some silver in the walls alternate with layers of As–Sb polyhedra and lone-electron pairs, which contain Ag not only in boundary walls but also in a central plane of S atoms (Figure 60). The triclinic structure, with space group P-1, has unit cell parameters a 8.920 Å, b 9.429 Å, c 20.062 Å, α 79.66°, β 88.84°, and γ 62.72°, Z = 2. The structure contains 5 crystallographically distinct Tl sites, six distinct As ˃ Sb sites, one Sb ˃ As site and four different silver positions. Mixed sites have compositions from As_0.73Sb_0.27 to As_0.98Sb_0.02, and Sb_0.63As_0.37, and the (As,Sb)–S distances vary accordingly.

The trigonal AsS₃ coordination pyramids are connected into a long seven-member [001] chain As7–As3–As4–As1–Sb2–As6–As5 in which the LEPs of the italicized polyhedra face sideways (outwards), whereas the rest (the inner portion of the chain) has lone electron pairs oriented into the central common volume (‘an LEP tube’, Figure 61). Thallium and sulfur form a common Tl–S net; for Tl alone or S alone, the net is 4².3³. It is interrupted at the region of As6–Ag4. Thallium is nine-coordinated; all Tl atoms have asymmetric coordination, with a bundle of three long Tl–S distances opposing an approximate half-sphere of shorter bonds. All Tl coordination polyhedra are nested in pentagonally configured ‘bases’. Distribution of different Tl polyhedra along the c direction is seen in Figure 62. The extreme of Tl–S distances is found for the Tl3 site, from 3.048 Å to 3.918 Å. Tl is embedded in the walls of the Tl layer, the Tl–S distances across this layer are 3.219–3.306 Å. Silver Ag1–Ag3 occupies coordination triangles whereas Ag4 appears to have a kinked linear coordination. Silver-silver distances in [001] chains of silver atoms are 3.049 Å (Ag3–Ag4), 3.060 Å (Ag2–Ag2), and 3.375–3.743 Å for the rest of Ag–Ag contacts.

A detailed look at the (001) projection and along the [001] rods and channels reveals that the structure contains also another system of channel-dividers, those primarily occupied by silver (Figure 61). Silver is joined by Tl where these dividers cross the Tl-based layer. Prominent are the [001] channels filled by silver, running uninterrupted through the structure (Figure 63). They parallel the [001] tubular rods (LEP channels) which host lone electron pairs of the majority of As atoms. In these rods, created by As₆Sb chains paired via inversion, the lone electron pairs of all atoms are oriented into the same tubular inner space (Figure 61), except for those of As6.

Thus, raberite is an LEP-tubular structure, perhaps the best defined one among the Tl sulfosalts, among which LEP-rod structures with lone electron pairs oriented ‘outwards’, towards the rest of the structure, are the usual norm. These differences in configuration represent the difference between a lone-electron-pair micelle and inverted lone electron pair micelle [15].

10.5.2. Spaltiite

Spaltiite, Cu₂Tl₂As₂S₅, is monoclinic, with space group P2₁/c. Unit cell parameters of spaltiite derived from single crystal diffractometer data are a 15.846 Å, b 10.024 Å, c 6.343 Å, β 99.037(8)° [99]. The crystal structure of spaltiite contains two independent Tl sites, two As sites and two distinct copper sites. There are five different sulfur positions.

Spaltiite is a distinctly layered structure, with alternation of polar As–Cu layers, and of two somewhat different types of thallium layers: one type with Tl lining the walls, the other with Tl situated deeper in the layer volume (Figure 64). The As–Cu layer is of periodically varying thickness—it is composed of strips, parallel to [001], which have one surface arsenic-rich, whereas the other surface contains Cu and As combined. The strips are interconnected into a (100) layer by tetrahedrally coordinated copper Cu2. The strips are actually channels that host trigonal prismatic configurations; these accommodate trigonal pyramidal As1, opposed by flat pyramidal, nearly triangularly coordinated Cu1 in the opposite prism base; it slightly approaches the As1 site and it is situated at only 2.65 Å from the opposing As. The lateral walls of the channels accommodate inclined three-fold coordinations of As2, with lone electron pairs oriented into the channel volume. Bonds of As2 are oriented towards the Cu1-covered surface of the (100) layer. These remarkable rods/channels, have anions only on outward surfaces, whereas all As and Cu coordinations are oriented inwards. They form LEP tubes filled by lone electron pairs and by Cu–As interactions, the latter acting across the flattened diameter of the channel (Figure 65).

Thallium is eight-coordinated; Tl1 has two short Tl–S distances (3.134 and 3.181 Å), three intermediate distances (3.295–3.315 Å) and three distances longer than 3.37 Å, whereas Tl2 has one very short distance (3.018 Å), two longer ones (3.234–3.303 Å), and a spectrum of five moderately long distances (3.411 Å to 3.535 Å). The volume of the CN = 8 sphere circumscribed to the polyhedron is close to 158 ų in both cases. The closest sulfur atoms, S1, are in the median-plane portions of the Cu–As layers. Position of Tl atoms in relation to the elements of the As–Cu layer is seen in Figure 66.

The arsenic site As1 has a symmetrical AsS₃ coordination, with distances 2.208–2.338 Å and a very limited angular variation (95.6–93.6°); the rest of the distances are 3.739, 3.846 and 3.992 Å. Remarkable is its 2.65 Å bonding connection to Cu1, directed exactly in the direction of the presumed lone electron pair of As. Coordination of the sideways placed As2 is regular as well. As2–S distances are 2.256–2.267 Å, and the pyramidal coordination is flatter (99.8–101.8°). The long As2–S distances are 3.475, 3.693, and 3.986 Å. The As–As distances are far beyond any interaction range.

The two copper sites have very different coordinations. Cu1 is a regular trigonal planar coordination (2.269–2.352 Å), however, it is drawn from the plane by interaction with As1, mentioned above. Therefore, the central angles are 110.5–118.9°, instead of 120°. The tetrahedral coordination of Cu2 is fairly regular, 2.330–2.394 Å, with the two bonds to the S1 site distinctly shorter than the rest. The central angles vary between 99.0 and 119.1 degrees. Tetrahedral Cu2 copper avoids any cation-cation interactions (Figure 65 and Figure 67). The (100) layers are facing one another, alternatively: either both of them with the Cu1 occupied surfaces, or both of them with the copper-free surfaces. This results in two types of thallium embedding. On the copper-free surface, thallium is very close to the plane of surface sulfurs (S21–S23), whereas on the surface populated by triangular coordinations of Cu1, Tl is deeper in its interlayer. The [010] view gives a false impression of the three-plane thick solid sulfide layers with double-layers of Tl. The close-to-embedded Tl has eight Tl–S distances, approaching a 4 + 1 coordination pyramid with three additional Tl–S distances under its trapezoidal base. Both Tl coordination polyhedra reach deep into the Cu–As layer, with a pyramidal-vertex [100]* bond to the sulfur atom, which is situated in the median-plane portions of the layer.

Therefore, spaltiite is a distinctly layered structure, with polar As–Cu layers composed of a series of LEP channels with remarkable Cu–As interactions (Figure 68). Inner organization of channels appears to be governed by the 2.65 Å Cu1–As1 contacts. They are polar in the [001] directions and the layers are also polar in the [100] orientation. Adjacent (100) layers are inversion-related on both the contacts of As1–As1 layer surfaces and on the contact of Cu1–Cu1 surfaces of two adjacent layers. The latter contacts are most responsible for the monoclinic angle β. The adjacent As–Cu layers are displaced by ½ [010]. Zig-zagging pairs of Tl atoms alternatively approach one layer and the opposite layer. Thallium and the sulfur atoms on the channel surfaces combine into an infinite, warped 3⁶ cation–anion sheet. The excellent cleavage of the mineral takes place in the weakly bonded thallium layers.

The cation–pnictogen interaction observed in the present structure for Cu1–As1, equal to 2.65 Å, is an unusual feature of this structure (Figure 65). The distance is at the upper range of distances observed in copper arsenides, which are 2.41–2.60 Å in low domeykite (Iglesias and Nowacki [100]) and 2.28–2.58 Å in natural kutinaite [76]. If it was a strong single bond in a tetrahedral configuration, it should be shorter. Instead, we have interpreted it as a rare case of interaction of the original lone electron pair of As with a typical metal atom. The latter is drawn in in order to shorten the As–Cu distance to an appropriate length.

The Tl–Cu distances are 3.57 Å and 3.74 Å, respectively. The As1–As1 distances are 3.34 Å and 3.52 Å. The bond length distribution of both Tl atoms suggests a weak but distinct lone electron pair activity.

10.5.3. Other Layer & Channel Structures: Wallisite and Hatchite

Wallisite, PbTl(Cu_0.65Ag_0.35)As₂S₅, is triclinic, with space group P-1, a 9.071 Å, b 7.787 Å, c 8.039 Å, α 65.828°, β 65.047°, and γ 74.220° (Boiocchi & Callegari [101], refining the structure of Takeuchi et al. [102]). Hatchite, ideally PbTlAgAs₂S₅, is isostructural with wallisite. It is triclinic, P-1, unit cell dimensions are a 9.37 Å, b 7.84 Å, c 8.06 Å, α 66.42°, β 63.33°, γ 84.97°; another choice of triclinic cell [103]. These structures contain eight-coordinated Pb and Tl (each in its own structure site), two distinct 3-coordinated As sites (which can also be interpreted as trapezoidal-pyramidal five-fold coordination) and (3 + 1)-coordinated (Cu,Ag) and Ag, respectively. Figure 69 and Figure 70 show the structure of hatchite and the latter unit cell choice.

The crystal structure contains wavy planar (010) interspaces, with no strong As–S bonds crossing them. They separate complex layers, which contain both the paired AsS₃ coordination pyramids and the coordination polyhedra of Tl and Pb (Figure 69). The (010) interspaces are themselves lined by the cations—Pb, Tl, (Cu,Ag) and As2 (all of them in the walls). These interspaces are bridged by the bonds of these elements to sulfur and filled by lone electron pairs of As2. In the complex (010) layers, narrow [100] channels can be discerned, which are formed by As₂S₅ groups in alternation with Tl polyhedra. They are separated by zig-zag sequences of Tl and Pb coordination polyhedra in alternation (Figure 69). Projection of one (010) layer (Figure 70) shows how the slightly diagonally disposed As₂S₅ groups envelope the channel, exchanged further below and above along [100] by interactions of Tl and Ag, then come As groups again, etc. The Tl–Tl interaction suggested in Figure 70 (cyan-coloured bar) is weak—the thallium atoms are 3.982 Å apart.

The As–S formed channels accommodate the lone electron pairs of As1 in their interior whereas those of As2 project powerfully outwards, into (010) interspaces (Figure 69). Tl interspersed with As1 along [100] is not excessively displaced towards the channel.

In projections perpendicular to [100], we observe slabs of structure about 1½ square As-pyramidal bases broad, with boundary formed by S plus As, and their center populated with scattered S, As and all Pb. Tl plus Ag are in the faces of these slabs: they form the lining of the (100) walls. The As coordination pyramids have two orientations, with their trapezoidal bases nearly parallel and nearly perpendicular to the slab face. The substructure appears slightly slanting across the slab; however, this detail dissolves when examining the individual As₂S₅ pairs. Thus, there are at least two planes of weakness in the structure.

Thallium in wallisite has CN = 8, the shortest distances are 3.018 and 3.103 Å, whereas the longer distances are 3.784 Å and 3.638 Å. Pb has smaller coordination polyhedra, with seven bonds from 2.771 Å to 3.300 Å, a very distorted monocapped trigonal coordination prism. As1 forms a coordination pyramid with three short bonds (2.233–2.318 Å) and a very open trapezoidal base (distances 3.472 Å and 3.443 Å) plus under-base distances 3.694 Å and 3.911 Å. The As2 pyramid has similar short distances: 2.246–2.313 Å. The (Cu,Ag)—S distances vary between 2.349 Å and 2.414 Å. Next, the Cu–S distance is non-bonding 3.614 Å. The Cu–Tl distance is long as well: 4.401 Å. In hatchite, Tl–S distances vary from 3.119 Å to 3.650 Å, the Ag–S distances define an asymmetric tetrahedron, with Ag–S equal to 2.481 Å, 2.520 Å, 2.539 Å and 2. 934Å. The AsS₃ pyramid is regular: for As2, the As–S distances are 2.251 Å, 2.270 Å and 2.302 Å. For As1, they are 2.227 Å, 2.235 Å and 2.353 Å. The shortest As–Tl contacts are 3.480 Å and 4.139 Å for As1, and 3.820 Å and 4.296 Å for As2.

10.6. Complicated Layer Types

10.6.1. Richardsollyite—Accordion-Folded Layers

Richardsollyite, with ideal composition TlPbAsS₃, is monoclinic, with space group P2₁/c, a 8.925 Å, b 8.4154 Å, c 8.5754 Å, β 108.665° [104]. The structure is composed of two alternating (100) layers housing different large cations: (a) a wavy Tl-containing layer; and (b) an interesting Pb-accommodating layer, which can be described as consisting of two systems of parallel Pb-housing channels, the two systems being perpendicular to one another (Figure 71 and Figure 72). The AsS₃ groups, which line the Tl-containing layer and outline the channels of the Pb-containing layer, are isolated from one another. The short As–S bonds are opposed by two long As–S bonds and one As–Tl distance: 2.274 Å versus 3.706 Å, 2.255 Å versus 3.599 Å and 2.246 Å versus Tl–As equal to 3.397 Å.

The Tl-layer is fully filled up with Tl coordination polyhedra (CN = 8); the closest Tl–Tl distances are 5.130 Å and 3.787 Å (the latter distance between Tl paired in the direction of [001] channels in the Tl layer).

Tl–S distances vary from 3.111 Å to 3.837 Å; however, five of them are below 3.5 Å. The 3.433 Å long Tl–S distance reaches deep into the Pb-containing layer. Tl–As distances are moderate: 3.630 Å and 3.397 Å; each As atom displays both these distances (Figure 72). Additionally, the Pb layer is fully occupied by Pb coordination polyhedra (CN = 8); Pb–Pb distances are 4.354 Å and 3.743 Å (these in [010] channels). No close Pb–Tl and Pb–As distances were observed. Pb–S distances vary between 2.906 and 3.451 Å. The As–As distance for two rows with lone electron pairs orientated indirectly against one another is 5.440 Å.

10.6.2. Vrbaite—A Chess-Board Scheme

Vrbaite Tl₄Hg₃As₈Sb₂S₂₀ is a cation-rich sulfosalt, crystalizing in orthorhombic space group Aba2, with a 11.287 Å, b 23.389 Å, and c 13.399 Å [105]. The structure contains two different Tl sites, two Hg sites, four As sites and one Sb site. Thallium 1 is six-coordinated, with extremely one sided coordination (short bonds 3.086 Å and 3.152 Å opposed by very long distances) whereas Tl2 is nine-coordinated, as a base-capped tetragonal prism, with bond lengths from 3.149 Å to 3.812 Å, somewhat one-sided in diagonal direction. Hg1 forms coordination tetrahedra with bonds 2.571 Å × 2, 2.581 Å × 2, whereas Hg2 is linear-coordinated at 2.367 Å and 2.400 Å, with an additional interaction of 2.866 Å (Figure 73). Tl1–Tl2 distance is 3.750 Å, whereas the shortest Hg2–Hg2 distance is merely 3.142 Å.

In [100] projection, the structure is a chess-board pattern of complex As(Sb)–S chains alternating with ‘channels’ occupied by Hg or occupied in broadened fashion by Tl (Figure 74). Hg and Tl are disposed on distinct (001) levels; there are two ‘channels’ of each cation on its level per one [010] distance. The [100] chains on the two levels differ from one another. On the Tl level, the periodically interrupted chain consists of the [S1–As1–S7–As2 = S2 + S4] configuration, which ends with two independent ligands attached side by side to the same cation. As2 in the pyramidal base faces As2 in the base of the opposing pyramid. On the Tl level, the [100] three–(or six) –member chain is uninterrupted, composed of a repeating complex motif: [S5–Sb1 = S10 and S6 (side by side), then As3 attached to S10, and As4 to S6, these As atoms then joined by S3; the chain continues by S5 which is attached to As4]. Lone electron pairs of As3 and As4 are oriented inwards, into the channel, those of Sb1 outwards.

The [001] projections of the Tl and Hg levels, alone or in overlap, reveal that the complicated As(Sb) chains are created by the fit of a polymerized aggregate of As(Sb)S₃ and As(Sb)S₅ pyramids to the periodicity of thallium, which is defined as a chain of square prisms of Tl2 and, attached to them, Tl1 (Figure 75). The short bonds of As1, plus a vertex of As2 (via common S7) and long bonds in its base, form a diatomic group which matches the Tl2–Tl2 period along [100] (Figure 75). This is copied by the As3 & As4 group with a common pyramid vertex S3 on the Hg level, which alternates with a single Sb1 polyhedron, from which one short (2.522 Å) and one opposing long distance (3.442 Å) in the pyramid base is involved.

Thus, the sequences: 2 (As) pyramids-2 pyramids-2 etc., and 2 (As) pyramids-1 (Sb) pyramid-2 pyramids-1 pyramid, etc., match the 1 Tl polyhedron, 1 Tl polyhedron, 1 Tl polyhedron, etc., i.e., the sequence of Tl polyhedra along the [100] direction of the structure of vrbaite. This represents a distant analogy to the situation in selected barium inosilicates [106], with two tetrahedra per one Ba polyhedron.

However, in the present case, additional adjustment arises from long under-base interactions between the As1–As1 and As2–As2 pyramids in disjoined chains (3.819 Å and 3.435 Å, respectively, Figure 75), and between As3–As4 pyramids in the continuous chains (3.572–3.684 Å, the pyramids pairwise face one another with their trapezoidal bases).

The long As–S interactions within the bases of the latter pyramids are less extended: merely 3.212–3.361 Å. The structure of vrbaite (Figure 76), with its combination of different polyhedron sizes and shapes, lone electron pairs and inter-polyhedron fits, serves as the best illustration why chain and rod-like arrangement of pyramids in the thallium sulfosalts is complex.

10.7. Three-Component Layer Structures

10.7.1. The Rebulite—Jankovićite Pair

The crystal structure of rebulite, ideal composition Tl₅Sb₅As₈S_22, was described by Balić-Žunić et al. [107], whereas that of jankovićite, Tl₅Sb₁₀As₃S₂₂, was described by Libowitzky et al. [108]. Both were described from the material originating in the Tl–As–Sb Allchar deposit, Macedonia. Various aspects of both structures were analyzed in detail by Makovicky & Balić-Žunić [109]. Rebulite (Figure 77) is monoclinic, with space group P2₁/c, a 17.44 Å, b 7.36 Å, c 32.05 Å, β 105.03°. Jankovićite is triclinic, with space group P-1, a 7.393 Å, b 8.711 Å, c 17.58 Å, α 103.81°, β 91.81°, and γ 109.51°. Interestingly, jankovićite diplays perfect (100) cleavage, which is absent in rebulite.

Both crystal structures are layer structures [109]. Similar to the Tl₃Ag₃Sb₂S₆ and Tl₃Ag₃As₂S₆ synthetics [95], they contain one polyhedron thick layers (at x = ½ in Figure 77, denoted as B below in order to preserve notation continuity), and two-polyhedra thick layers with a median sheet of S atoms, at x = 0, denoted as the C type). However, these layers are separated on their contact by the one-polyhedron thick layer A which (ideally) contains a central mirror-reflection plane, indexed as (100) in rebulite, and (001) in jankovićite.

One polyhedron thick layer A (Figure 78) combines coordination cubes of Tl with 3-to-5 coordinated Sb/As atoms. These are As1 and 2 plus Sb1 and 2 in rebulite, which are equivalent to Sb2 and 4 in jankovićite. These layers have composition TlSb(As,Sb)S₅, when sharing of S with adjacent B and C layers is taken into account. One polyhedron thick B layers (Figure 79), which simulate the (210) layers of the SnS archetype, have two adjacent A layers. Their overall configuration approximates monocapped trigonal coordination prisms which ‘lie’ in the plane of the layer and have cations in their volume (Tl) or prism walls (Sb,As). With S shared, the formula is TlAs₂(As,Sb)S₄. The thicker C-type layers (Figure 80) display analogous organization, and composition Tl₂Sb₂(As,Sb)S₈. Two A layers, one B and one C layer result in 22 S atoms and 18 cations in the formula. The sulfur-populated surfaces of these layers have configurations 4².3³, though only one out of two ‘squares’ overlies the coordination cube of Tl. This configuration corresponds to the (210) cut of SnS archetype [109]. The SnS-like (or TlSbS₂-like) configuration of the B and C layers is prominent especially in the (010) projection of the crystal structure of jankovićite (Figures below); in general features, this configuration reminds of the structure of kirkiite-jordanite homologues.

The A layer of rebulite contains Tl1 and Tl2 coordination cubes with Tl–S distances 3.248–3.594 Å and 3.186–3.498 Å, respectively (averages 3.362 Å and 3.345 Å, respectively). The square coordination pyramids of As1, As2 and Sb1, Sb2 are oriented with their pyramidal vertices sideways and with their bases perpendicular to the layer. Short As–S distances are 2.307–2.356 Å; the Sb–S distances 2.493–2.565 Å are associated with distances which apparently manifest short-bond flipping for both Sb polyhedra, i.e., 2.679–2.792 Å.

In perpendicular projection, the differences between the A layer of rebulite (Figure 78) and jankovicite (Figure 81) are intriguing. In jankovicite, [110] Tl2–Sb2–Tl2–Sb2–chains (interconnected by Sb4 which corresponds to As1 and As2 in rebulite) are uninterruptedly continuing, and a (010) band, which is one Tl2–Sb2 interval broad and stacked along [110], can be ‘cut out’ of the structure for unit cell twinning considerations. In rebulite, this chain is mimicked by a Tl2–Sb1, or by a Tl1–Sb2 fragment running along [021] and [0-21], respectively, always across two repeating bands (which are (001) in rebulite), i.e., Tl–Sb–Tl–Sb. The structure is then unit-cell twinned on the (010) c-glide reflection plane. The easy-to-recognize unit cell twinning scheme continues through the B and C layers (Figure 82 and Figure 83), in the a direction in rebulite and c direction in jankovicite. The obvious derivative of it is a hypothetical structure, in which the unit-cell twinning on a glide plane would occur after each (and not after every second, as observed) (010) band, which has been defined above. The formula would be Tl₃(As,Sb)₁₁S₁₈, to be compared with Tl₅(As,Sb)₁₃S₂₂ of rebulite. Thus, in rebulite (Figure 84) pseudocubic coordination of thallium in the A layers is complicated by the unit-cell twinning of this layer.

In jankovićite (Figure 85), thallium Tl5 in the thin B layer is centrally positioned and eight-coordinated, with the average bond length 3.346 Å (extremes 3.142 Å and 3.650 Å). Tl3 and Tl4 in the C slab are below the surfaces of the double-layer (a sort of ‘lining the walls’). Tl3 is seven-coordinated, average Tl–S bond length 3.270 Å, with bonds spanning a range from a sideways oriented 3.055 Å bond to 3.484 Å. Tl4 is eight-coordinated, with Tl–S bond average 3.337 Å, and with extremes: three short bonds, 3.121–3.212 Å, and the longest bond, 3.897 Å.

Considering only the short (As,Sb)–S distances, up to 2.4 Å for As and 2.9 Å for Sb (making 4 ligands for some of the Sb polyhedra), the As and Sb coordination polyhedra are connected into a three-dimensional framework in rebulite, though only into corrugated double-layers in jankovićite [107,108]. Ten-, nine-, and eight-member rings of pyramids in jankovićite correspond to 10-member rings and 12-member and eight-member spirals in rebulite.

10.7.2. Gabrielite

A detailed account of the crystal structure of gabrielite, found by Graeser in form of pseudohexagonal crystals, was given by Balić-Žunić et al. [110]. Gabrielite, with ideal formula Tl₂AgCu₂As₃S₇, is triclinic, space group P-1, a 12.138 Å, b 12.196 Å, c 15.944 Å, α 78.537°, β 84.715°, γ 60.47°, unit cell volume 2012.7 ų.

The crystal structure of gabrielite is composed of three types of (001) slabs alternating in a complex sequence (Figure 86). They share well defined sulfur sheets on their boundaries, which for the thickest slab also occur in its interior. The thickest slabs contain aggregates of As(Sb) coordination polyhedra with some Tl in interspaces. The other prominent slab type is a slab in which thallium alone fills the space between sulfur sheets. On all boundaries, these two slab types are separated by another slab, consisting of triangularly and tetrahedrally coordinated, mostly mixed copper-silver sites (Figure 86). Thus, gabrielite is the most complicated structure of the layer type.

The sulfur sheets between (and in) the (slightly idealized) layers are (1) 3⁴.6 mesh of slightly staggered hexagons with mutual boundaries composed of triangles; plane group symmetry p6, and (2) an ornamental sheet composed of triangles, squares and pentagons, with plane group symmetry p31m, and with mesh composed of six 3.4.5² nodes combined with three 3.4².5 nodes per cell. Thus, all sulfurs have triangular, square and pentagonal sulfur configurations surrounding them. Type (1) and its enantiomorph occur in the As(Sb) layer, whereas the Tl layer is sandwiched between two Type (2) sheets. The Cu–Ag layer is in a complicated situation, sandwiched between Type (1), and Type (2) sheet on its opposing surface.

The arsenic (antimony)-rich layer contains chair-like (As,Sb)₄S₈ configurations, which in the (001) projection look like fragments of Sb₂S₄ rods composed of square coordination pyramids sharing a common edge (Figure 87 and Figure 88). In their disposition, they mimic a (0001) slice of a cyclically twinned P6 sulfosalt structure; compare with [111]. From the three symmetrically non-equivalent groups, those based on As4–As5 and As6–As7 are similar, the third variant based on As8–As9 is differently configured. The strong As–S bonds vary in a relatively narrow range: between 2.222 Å and 2.357 Å. Arsenic atoms extend long-range interactions to one or two S atoms in adjacent groups. These interactions populate a range from 3.232 Å to 3.372 Å. The pseudo-hexagonal cavity in this rather loose array is occupied by Tl6 with a coordination of trigonal antiprism (bond range 3.101–3.814 Å), and the ‘trigonal prismatic’ cavities are occupied by Tl5 (bond range 3.206–3.473 Å) (Figure 88).

The thallium layer contains four differently coordinated thallium sites, Tl1–Tl4 (Figure 89 and Figure 90). Only Tl1 is close to the layer wall, the remaining sites are clearly in the volume of the interspace between the Type 2 layers (Figure 86). The sandwich mimics the C2/m symmetry. Tl1 (CN = 9 with distances evenly increasing from 3.097 Å to 3.682 Å) occurs as two joined polyhedra; Tl2 and Tl3 are eight-coordinated (3.104 Å to 3.592 Å, and 3.171 Å to 3.979 Å, respectively), they occur in strips parallel to [100]; whereas Tl4 with CN = 7, and distances from 3.130 Å to 3.431 Å, followed by 3.835 Å, occurs in strips parallel to [010]. As mentioned above, Tl5, and Tl6 occur in interspaces of the As–Sb layer. The surface of the Tl layer (Figure 90) shows the relationship between the Type 2 grid of S atoms and the disposition of Tl species nicely. The pentagon-shaped mesh is decorated by a combination of Tl1, Tl3 and Tl4 polyhedra, whereas the triple of coordination squares is decorated by Tl2, another Tl2 and the opposite side of the Tl4 polyhedron.

The cations of the third layer type, the Cu–Ag layer (Figure 91), are divided into three tetrahedral and six trigonal-planar sites. Ag dominates in the tetrahedral Me8 and Me9 sites, is in minority on the Me7 site and only in minor amounts in the trigonal planar sites, being absent, or nearly so, from the Cu3 and (Cu,Ag)4 and 5 sites. The cation ordering in this layer is rather complex; Figure 90 reveals its reasons: the Cu,Ag atoms reside (or nearly reside) over the midpoints of shared edges of two and two adjacent thallium polyhedra from the thallium layer. The arsenic atoms As1, As2 and As3 are embedded in the triangles of the Type 2 sulfur sheet, with As oriented into the Cu–Ag layer, in 2/3 of cases pointing directly towards Tl5 and Tl6. These As sites (isolated AsS₃ groups) share common S atoms with, and in this way fix, the attachment of (Cu,Ag) polyhedra to the Type 2 layer. As1 (average As–S bond is 2.245 Å) is pure As, whereas bond distances of As2 andAs3 suggest about 5% Sb in each.

A specific feature of gabrielite are short cation—cation (Tl–Cu, Tl–Tl, and Tl–As) contacts. Tl–Cu distances of 3.03 to 3.08 Å occur for Tl1, Tl3, and Tl4, between the Tl-packed and the Cu–Ag layers. The exceptionally short Tl–Tl contact, 3.09 Å, for Tl6–Tl6, and the shortest Tl6–As1 contact of 3.11 Å occurs in the column of trigonal coordination antiprisms situated in the As(Sb)-rich layer. The lone electron pair of As1 points toward the Tl6 position and the As1–Tl6–Tl6–As1 group is almost linear.

11. Crystal—Chemical Generalizations

11.1. Types of Layer Configurations

The thallium-free layers in Tl sulfosalts with layer structures can be classified as (a) the LEP-filled (or LEP-concentrating) layers, with the non-bonding side of As(Sb) atoms oriented into the layer (as in raberite and rebulite, for example), (b) LEP-repelling layers (these are rare, e.g., in richardsollyite), and several cases where LEP face outwards in an oblique fashion (placed primarily outside the layer), and the AsS₃ groups enclose the layer interior in a special ‘box-like’ way (e.g., in Tl₃AsS₃, Tl₂MnAs₂S₅, and christite), (c) layers which contain LEP channels, with the lone electron pairs of As oriented into a small common linear volume (e.g., spaltiite, raberite) or (d) layers with the opposite arrangement, i.e., rods of As–S aggregates with LEPs oriented into the surrounding structure (e.g., lorándite, simonite). Intermediate categories between (c) and (d), with both LEP orientations occurring along the chain length, are frequent. Some of these structures also contain cation channels (e.g., for Ag); these can be one system (e.g., raberite), two parallel systems (e.g., vrbaite) or two intersecting systems (richardsolleyite). Thus far, hydrated structures, known for sodium or other, mostly synthetic sulfosalts, have not been described for thallium, possibly because of its large ion size connected with weak hydration.

The previously mentioned types of architecture of the thallium-rich layers (or of corresponding structure portions of a non-layer structure) appear to be about equally frequent in the realm of Tl sulfosalts. The members of the hutchinsonite plesioseries typically have Tl embedded in a wall of LEP interspace, whereas the homologues and homeotypes of sartorite contain Tl substituting for Pb in the columns, well within the volume of the capped prismatic [6 + 3] coordination. In some of these structures (e.g., écrinsite), this set is differentiated into Tl-rich positions and Tl-poor positions. Such differentiation is pronounced especially for the homeotypic chabournéite family [82,83,84,85,86,87,88]. When stoichiometry requires, the prism columns host Tl–Sb sequencies. The layer-wall lining by Tl is typical for Tl-hosting layers in hatchite-wallisite, raberite, spaltiite and erniggliite, whereas the synthetic Tl₃AsS₃, Tl₂MnAs₂S₅, sicherite, richardsollyite and partly vrbaite have Tl which occupies the volume of its layer. Wall-lining means that nearly one half of the Tl coordination sphere reaches rather deep into the volume of the ‘Tl-free’ layer and the wall has a correspondingly ‘open’ structure. Tl chains were observed only in simonite.

11.2. Cation–Cation Interactions

The examined spectrum of sulfosalts contains several, although infrequent, instances of short cation-cation interactions. The problem is, whether for evaluation of bonding interactions between cations one should use crystal radii from covalent/ionic structures, or radii from alloys, or even (poorly known) van der Waals radii. In the cases in which the LEPs probably engage in newly formed bonding—does that mean a complete rearrangement of electron distribution and bonding distances?

Tl–Tl pairs: Shannon’s crystal radii suggest tentatively that for CN8 thallium, Tl–Tl distances below 3.4 Å are of special interest with respect to a possible cation-cation interaction. Further indications of such bonding can be extracted from the situations observed in structures of alkali or Ba thallides: the two-electron Tl–Tl bonds in the tetrahedral Tl skeleton of NaTl are 3.24 Å long, and Tl–Tl tetrahedral distances in the hexagonal BaTl₂ are equal to 3.10 Å (three bonds) and 3.45 Å (one bond). Tl clusters, which range in size from Tl₄ tetrahedra to Tl₁₁ groups, display bonding Tl–Tl distances from 3.06 Å to 3.26 Å long; however, forced distances are at 3.47 Å [112]. Thus, these criteria suggest a presence of Tl–Tl interactions or even Tl–Tl bonds in the cases when similar short distances occur in the sulfosalts. The same conclusion follows from metal radii [35]. Among Tl sulfosalts, the most straightforward candidate is the Tl–Tl pair in routhierite and stalderite (Tl–Tl 3.33–3.67 Å and 3.279 Å, respectively). Further cases are arsiccioite with 3.25–3.51 Å, christite (3.389 Å), and the exceptional 3.09 Å value in gabrielite, between two Tl6 atoms with the bond perpendicular to the As(Sb) rich layer. The much more frequent Tl–Tl distances of 3.62–3.78 Å, and more, suggest that absence of substantial interactions between Tl neighbours is the predominant feature of Tl sulfosalts.

A short T–Ag distance, 2.922 and 2.959 Å, is observed in synthetics [95], instead of the usual distances (e.g., 3.631 and more in sicherite). Similar are the Tl–Cu distances of 3.03–3.08 Å in gabrielite. These distances correspond to metal radii [35].

The Hg–Tl association which is present in several thallium sulfosalts (christite, simonite, vrbaite, vorontsovite and tsygankoite) calls for closer investigation. Is the interesting sulfide, Hg₃Tl₂S₄ [113], a prototype of structural relations between Tl and Hg? This compound is monoclinic, a 11.493 Å, b 6.6953 Å, c 12.937 Å, β 114.98°, space group C2/c (Figure 92).

In this compound, mercury (Hg2) shows 3.382 Å Hg–Hg interactions which are completed to Hg (010) triangles by two Hg1–Hg2 distances of 3.678 Å and, on the opposite side, by two distances 3.824 Å, attached to the next triangle. Tl forms 3.442 Å Tl–Tl pairs, subparallel to the Hg2–Hg2 joins and each Tl forms a 3.526 Å pair with one Hg2, one pair oriented ‘up’, the opposite ‘down’, resulting in rectangular zig-zagged [010] chains of preferred cation-cation contacts. The Tl–S distances vary between 2.940 Å and 3.817 Å, and the Tl–Hg join points from Tl to the Hg atom exactly in the direction of thallium’s LEP, as indicated by distribution of short and long Tl–S bonds (Figure 92).

The situation is different in simonite [91]. The shortest Tl–Tl distances are 6.313 Å, Hg–Hg distances are 3.960 Å, and the shortest Hg–Tl distance is equal to 4.426 Å, followed by 4.816 Å, i.e., no serious interactions. In vrbaite [105] the Tl–Tl distances are 3.750 Å, and the Hg–Hg distance is only 3.142 Å. The latter, however, is still considerably longer than the covalently bonded Hg–Hg distance of 2.595 Å in Hg₂Cl₂ [114]. The Tl–Hg distances, however, are long: 4.819 and 4.834 Å. In the cage structure of routhierie, the (predominantly) Hg tetrahedral site never comes close to Tl positioned in the cage: 4.971 Å for Hg ‘below’ Tl dumb-bell and 5.652 Å ‘sideways’. In tsygankoite [75], the Tl–Hg distance is 4.378 Å, whereas the Hg–Hg and Tl–Tl distances are 3.858 Å, which is the periodicity of the monoclinic structure along [010]. Disappointingly, the interesting ‘modest’ Hg–Tl interplay from the Hg–Tl sulfide does not repeat in the examined sulfosalts. Vrbaite is the only known Tl sulfosalt in which the inter-cation distance suggests a degree of direct Hg–Hg interaction.

Tl–As is equal to 3.347–3.567 Å in arsiccioite, and 3.11 Å in gabrielite; in these cases the LEP of As is obviously engaged in bonding. Further interesting Tl–As distances are 3.259 Å in erniggliite, 3.480 Å in hatchite, 3.499 Å in christite and 3.397 Å in richardsolleyite.

The As–As distance in spaltiite is 3.34 Å and 3.52 Å. These distances can be compared with As–As distances in the As₄S₁₂ clusters, which are present in the natural sinnerite, Cu₆As₄S₉ [115]. These are 3.36–3.62 Å and 3.48–3.71 Å, respectively, indicating for spaltiite an equally tight arrangement with LEPs pointing into a common space as in sinnerite.

Copper interacting with LEP of As at the distance of 2.64 Å in spaltiite is in agreement with the As–Cu bond lengths in natural kutinaite [76] (which is arsenide of Cu–Ag with minor Tl) which lie between 2.280 and 2.578 Å, though mostly above the 2.46 Å threshold. The short Ag–As distance of 3.049–3.060 Å, observed in raberite, agrees with the set of As–Ag bond lengths in natural kutinaite [76], which span 2.926–3.091 Å.

11.3. Types of Component Layers and Configurations

Unfortunately, there are a limited number of examples in each category of component-layer type at present. This is true also for the first such category—the silver—copper based layers. Karanović’s synthetics [95], as well as gabrielite and raberite contain the Ag–Cu populated layers, whereas hatchite (wallisite) does not contain enough Ag/Cu to form a distinct layer. Gabrielite [110] and Karanović’s synthetics house the same basic coordination polyhedra: coordination tetrahedra and triangles of Ag and trigonal coordination pyramids of As. The Ag (Cu) layer in the [95] phases has layer symmetry Pbcm with [010] rows of partly edge-sharing Ag tetrahedra, which alternate with isolated AsS₃ pyramids (Figure 54). Mutual shifts and sequences of AsS₃ pyramids in gabrielite are different, so that the net of Ag tetrahedra and triangles, plus the Cu site, must be differently organized, typically forming cation triplets (Figure 87). Raberite for which the LEP channels for As(Sb) are typical, contains Ag-filled channels parallel to the LEP ones, mostly formed by a sequence of nearly perpendicular-oriented AgS₃ coordination triangles. These channels have further Ag attached where their surface is open to the Tl-occupied layers (Figure 61 and Figure 63).

The Tl-rich layers in [95] synthetic phases (Figure 53) contain thallium positioned above selected S atoms from the adjacent silver-rich layers; only Tl3 connected to Ag3 is substantially shifted away from such a position. The closest Tl–Tl contacts are 4.194Å. In spaltiite, Tl positions (which line the layer walls) correlate with S in the layers as well (Figure 66); the shortest Tl–Tl contacts are 3.808–4.237 Å. In raberite, in which Tl also lines the layer walls, this contact is 3.973 Å, in spite of the complicated and crowded accommodation of Tl in the layer (Figure 63). The Tl-crowded thallium layer in gabrielite [110] contains several coordination types of Tl in close contact (Figure 90); however, the Tl–Tl distances are much less ‘crowded’: the shortest Tl1–Tl3 contact is 3.821 Å, Tl1–Tl1 is 3.921 Å, while the rest is 4.132–4.174 Å, and more. The exceptional Tl–Tl pair of 3.09 Å is not situated in these layers. Simonite has only long Tl–Tl contacts, Tl₂MnAs₂S₅ has a bit closer coordination, with Tl1–Tl2 equal to 3.684 Å, followed by vrbaite with 3.750 Å. The layer structure of erniggliite has Tl atoms 4.205 Å apart, richardsollyite 3.787 Å apart, whereas in rebulite-jankovicite, with their admirable architecture of Tl-hosting layers (Figure 84 and Figure 85), and in sicherite, they are more than 5 Å from one another. Finally, the shortest Tl–Tl distances in lorándite are 4.045 Å.

The structure of Tl₃AsS₃ (Figure 50) with its two-point and four-point contacts of Tl atoms, is still in the realm of weak interactions: the Tl–Tl distances are 3.612 Å, 3.619, 3.691, 3.804, and 4.021 Å. As mentioned above, this review shows that candidates for Tl–Tl bonding are unexpectedly rare among layered sulfosalts, in spite of the visual impression to the contrary.

The ‘Sb–As sulfide layers’: gabrielite is the structure with the best developed and voluminous ‘(As,Sb)-sulfide’ layer (Figure 87). Its distinct pseudohexagonal character, insertion of trigonally coordinated Tl5 and Tl6, and presence of ‘inverted lone electron pair micelles’ with substantial free space for LEPs, parallels those in the cyclically twinned sulfosalts [111]. With some allowances in bonding details, it is close to the (0001) projection of the crystal structure of Bi₄Cl₂S₅, which according to [111] is “the zeroth homologue of a hypothetical zinkenite series”.

No other As–Sb sulfide layers achieve this volume and ‘purity’ of semimetal character. Prominent among them are the long As–Sb chains in raberite, which are rolled up into LEP channels (Figure 60), the intimately folded layers in richardsollyite (Figure 71) which host Pb atoms in two sets of intersecting channels (Figure 71 and Figure 72), and the chess-board—like scheme of vrbaite (Figure 74).

11.4. Matching Rules for Cation Polyhedra

In several thallium sulfosalts, the complicated As(Sb) sequences are created by the fit of a polymerized aggregate of As(Sb)S₃ and As(Sb)S₅ pyramids, respectively, (varying from pairs to chains) to the periodicity of thallium polyhedra. For example, in vrbaite (Figure 75), thallium Tl2 forms square prisms with attached Tl1. The short bonds of the As1–As2 group, plus the long bonds in the base of the As2 pyramid form a configuration which matches a single Tl2–Tl2 period along [100]. This is also copied by the As3 & As4 group in this structure. In the case of lorándite (Figure 2), two As coordination pyramids (parts of the rectangular-spiral chain) match with one Tl polyhedron outside the spiral. In imhofite (Figure 13) and in gillulyite (Figure 32), the dimensional equivalence between a pair of As pyramids (As4 and As5) and the dimension of the intervening Tl polyhedron is the basis of their OD character.

This represents a distant analogy to the situation present in selected barium inosilicates [106], with two Si tetrahedra per every Ba polyhedron, a fit different from the familiar polyhedron matches present in the wollastonite and pyroxene families. However, in the present cases, additional adjustment possibility arises from the presence of long under-base interactions between the As pyramids in the cases of disjoined chains/sequences. The 2-pyramids: 1 Tl polyhedron principle is an important rule in the architecture of thallium sulfosalts, very different from the Pb:Sb match and stronger than the Pb:As match in many sulfosalts. However, it is not absolute, for example, in Tl₂MnAs₂S₅ 2 As pyramids match 2 Tl polyhedra along the [100] direction. In raberite, the 2:1 match in the regular chain intervals becomes 2½:1 in intervals with disturbed chain regularity. In jankovicite, the 2:1 match and the 1½:1 match coexist in different [010] strings of the structure.

11.5. Differences between As and Sb Sulfosalts

When related to the bond characteristics of thallium, the difference between arsenic and antimony in their lone electron pair activity, LEP eccentricity and the length of covalent cation-anion bonds is important for the configuration of thallium sulfosalts. Thus, Tl₃AsS₃ and Tl₃SbS₃ have quite different structures. Although the rebulite-jankovićite, edenharterite—jentschite and pierrotite-parapierrotite pairs have a number of similar local configurations, they differ in (an) important structural detail(s), resulting in different crystal structures for the two members of each pair. Addition of the ‘opposite semimetal‘ to the principal one (mostly addition of Sb to the As sulfosalt) sometimes brings about a new structure type, e.g., gillulyite, or a superstructure (as witnessed by the still insufficiently understood situation in the chabourneite group) and it probably is the reason of existence for the rebulite-jankovićite pair and for raberite. Isostructural cases with pure ‘opposing’ compositions like Tl₃Ag₃Sb₂S₆ and Tl₃Ag₃As₂S₆ [95] are rare, although it should be noted that for a great number of structures only one of the As and Sb composition end-members (or only one near-endmember composition) has been found or synthesized.

11.6. Aggregation of (As,Sb)S Pyramids into Frameworks

In the Tl sulfosalts with structures built according to the principles of the PbS and SnS archetype, aggregation of BS₃ or BS₅ pyramids (according to the description one prefers) into pairs, groups, chains or 3D aggregates of them, is widespread. Chain lengths, configurations and details are a function of the homologous order N, of the ’metal’/’semimetal’ cation ratios, of the types of cations present and even of the anion/cation omissions in some positions of the structure. A detailed description of these complicated edifices is the usual part of original structure descriptions, together with comparisons between Tl-containing and Tl-free species.

Lesser attention has been given to these phenomena in the layer structures. In these, two configurations largely prevail: isolated (As,Sb)S₃ pyramids and infinite chains. Isolated pyramids are observed in Tl₃AsS₃, christite, Karanović’s synthetics, erniggliite, and richardsollyite. Isolated pyramids occur as a minoritorian configuration type also in spaltiite and gabrielite. Paired pyramids, As₂S₅, are developed in Tl₂MnAs₂S₅ and wallisite–hatchite. Gabrielite contains chair-like (As,Sb)₄S₈ groups and isolated AsS₃ pyramids.

The chain repertory is varied. Spaltiite contains two-fold infinite chains As₂S₄ accompanied by isolated pyramids, simonite has infinite chains with a six-fold repetition period, vrbaite contains infinite sixfold (or rather 2 × 3-fold) As₆S₁₀ chains which combine Sb and As, associated with As₂S₅ pairs. Finally, raberite contains a complex seven-fold chain.

The octahedral Bi layer in TlBiS₂ appears to be the only example of such layer_. Layers in rebulite and jankovićite present SnS-like slabs with short (As,Sb)–S bonds, which interconnect them over planes of unit cell pseudotwinning into complex 2D–3D edifices, described at the Section 10.7.1.

12. Conclusions

Incorporation of the large Tl⁺ cation in sulfosalt structures, which can proceed in several different ways, is the determining factor of their formation and architecture. In the case of sartorite homologues (and rare lillianite homologues) the resulting structures are part of a larger homologous series, which also contain a number of Tl-free members. In other cases, especially in a spectrum of layer structures, the thallium-containing structures form a separate group, without thallium-free analogues. The exceptions from this rule are some related structures with alkali and calcium-group cations, nearly absent in nature. Direct cation-cation interactions are present but very rare. Spectrum of cations involved in thallium sulfosalts is determined by the geochemistry of their deposits.