minerals Article Twinning of Tetrahedrite—OD Approach Emil Makovicky Department of Geoscience and Natural Resources Management, University of Copenhagen, Østervoldgade 10, 1350 København, Denmark; [email protected]; Tel.: +45-35322432 Abstract: The common twinning of tetrahedrite and tennantite can be described as an order–disorder (OD) phenomenon. The unit OD layer is a one-tetrahedron-thick (111) layer composed of six-member rings of tetrahedra, with gaps between them filled with Sb(As) coordination pyramids and triangular- coordinated (Cu, Ag). The stacking sequence of six-member rings is ABCABC, which can also be expressed as a sequence of three consecutive tetrahedron configurations, named α, β, and γ. When the orientation of component tetrahedra is uniform, the α, β, γ, α sequence builds the familiar cage structure of tetrahedrite. However, when the tetrahedra of the β layer are rotated by 180◦ against those in the underlying α configurations and/or when a rotated α configuration follows after the β configuration (instead of γ), twinning is generated. If repeated, this could generate the ABAB sequence which would modify the structure considerably. If the rest of the structure grows as a regular cubic tetrahedrite structure, the single occurrence of the described defect sequences creates a twin. Keywords: tetrahedrite; tennantite; twinning; order–disorder approach; tetrahedral framework 1. Introduction Tetrahedrite is an old, long-known mineral species. It was known already to old miners as fahlerz, weissgiltigerz, grey ore, or panabase, under names mostly related to its Citation: Makovicky, E. Twinning of macroscopic appearance in hand specimens. Its present name “tetrahedrite” was given by Tetrahedrite—OD Approach. Haidinger [1] because of the common tetrahedral form shown by its crystals. The name Minerals 2021, 11, 170. https:// “tennantite” was given to its As-based analogue, first described by W. and R. Phillips [2,3] doi.org/10.3390/min11020170 from Cornwall. Early reports of the occurrence of Fe and Zn in tetrahedrite were the starting point of the long research path which, among other results, led to the chemical Academic Editor: Giovanni Ferraris formula Cu (Fe,Zn) (Sb,As) S for the most common tetrahedrite—tennantite solid so- Received: 19 January 2021 12 2 4 13 lution. The voluminous literature concerned with the chemistry of natural and synthetic Accepted: 3 February 2021 Published: 7 February 2021 tetrahedrite and tennantite and with selected synonyms (e.g., binnite and coppite) has re- cently been summarized and referenced by Biagioni et al. [4]. The principal complication 3+ 2+ Publisher’s Note: MDPI stays neutral of the chemistry of this solid solution, the interplay of Fe and Fe in tetrahedrite and ten- with regard to jurisdictional claims in natite, has been studied by several authors (e.g., Makovicky et al. [5,6]; Andreasen et al. [7]; published maps and institutional affil- Nasonova et al. [8]). It does not alter the crystal structure principles of these minerals. iations. The crystal structure of tetrahedrite (Figure1) was refined by Wuensch [ 9] using a sample from Horhausen, Westerwald (Germany). That of tennantite was refined by Wuensch et al. [10] starting with older data of Pauling and Neuman [11], and for the tennantite-(Cu) by [12]. Structures of silver varieties were refined by, e.g., Peterson and Miller [13], Johnson and Burnham [14], Rozhdestvenskaya et al. [15], and Welch et al. [16]. Copyright: © 2021 by the author. Karanovi´cet al. [17] reported the crystal structure of mercurian tetrahedrite from Serbia, Licensee MDPI, Basel, Switzerland. This article is an open access article confirming the results of Kalbskopf [18]. Other crystal structure investigations on mercurian distributed under the terms and tetrahedrite were reported by Kaplunnik et al. [19], Foit and Hughes [20], as well as conditions of the Creative Commons Biagioni et al. [21], and on hakite by Škácha et al. [22]. The crystal structure of synthetic Mn- Attribution (CC BY) license (https:// tetrahedrite was described by Chetty et al. [23], whereas Barbier et al. [24] determined the creativecommons.org/licenses/by/ crystal structure of a Ni-containing synthetic tetrahedrite. This count can be continued by 4.0/). Minerals 2021, 11, 170. https://doi.org/10.3390/min11020170 https://www.mdpi.com/journal/minerals Minerals 2021, 11, x 2 of 10 Minerals 2021, 11, 170 2 of 10 by recent studies of tetrahedrite by materials scientists. What is remarkable for the tetra- hedrite–tennantiterecent studies of tetrahedrite structure type, by materials is the stability scientists. of What structure is remarkable motif (Figure for the 1) tetrahedrite– under all thesetennantite element structure substitutions. type, is the stability of structure motif (Figure1) under all these element substitutions. Figure 1. Crystal structure of tetrahedrite–tennantite. MeS4 coordination tetrahedra (light blue) and Figure 1. Crystal structure of tetrahedrite–tennantite. MeS4 coordination tetrahedra (light blue) majority of the (Cu,Ag)S3 coordination triangles (yellow) are shown in polyhedral representation, and majority of the (Cu,Ag)S3 coordination triangles (yellow) are shown in polyhedral representa- the Sb(As)S3 coordination pyramids as cation-anion bonds. Note filling of truncated-tetrahedron tion, the Sb(As)S3 coordination pyramids as cation-anion bonds. Note filling of truncated-tetrahe- cavities in the tetrahedral framework by “spinners” composed of triangular co-ordinations. Inset: dron cavities in the tetrahedral framework by “spinners” composed of triangular co-ordinations. “spinner” of (Cu,Ag)S coordination triangles with (Sb,As)S coordination pyramids surrounding Inset: “spinner” of (Cu,Ag)S3 3 coordination triangles with (Sb,As)S3 3 coordination pyramids sur- roundingspinner cavity.spinner cavity. 2. Twinning of Tetrahedrite 2. Twinning of Tetrahedrite The well-known twinning of tetrahedrite–tennantite (Figure2) has been repeatedly The well-known twinning of tetrahedrite–tennantite (Figure 2) has been repeatedly described by (a selection of) those twin elements which constitute the difference between described by (a selection of) those twin elements which constitute the difference between the holohedral cubic point-group symmetry 4/m −3 2/m and the point group symmetry of the holohedral cubic point-group symmetry 4/m −3 2/m and the point group symmetry of tetrahedrite, which is −43m, as demonstrated by its morphology (Figure2). In the present tetrahedrite,study, we attempt which is to − describe43m, as demonstrated the structural by aspect its morphology of this twinning (Figure by 2). means In the of present defects study,which we can attempt occur during to describe the growth the structural of tetrahedrite aspect crystals.of this twinning We concentrate by means on theof defects growth whichscheme can of occur this structure, during the selecting growth the of tetrahed layer-by-layerrite crystals. mechanism, We concentrate the most probable on the growth growth schemelayers beingof this one-tetrahedron-thick structure, selecting (111) the inlayer-by-layer the cubic structure, mechanism, which alsothe most are the probable principal growthcrystal layers form ofbeing these one-tetrahedron-thick minerals. Although the (111) tetrahedrite in the cubic structure structure, often which is “derived” also are fromthe principalthe sphalerite crystal structure, form of these presence minerals. of large Alth cavitiesough the separated tetrahedrite from structure one another often by is single- “de- rived”polyhedron-thick from the sphalerite walls leads structure, to a much presence more of complicatedlarge cavities configuration separated from of one (111) another growth bylayers single-polyhedron-thick than found in sphalerite walls (Figureleads to3 a). much Variation more in complicated stacking of configuration these layers ought of (111) to growthbe the reasonlayers than for twinning. found in Insphalerite the present (Figure model, 3). Variation we present in a stacking potentially of these free stacking layers oughtvariation to be of the layers reason but for within twinning. well-defined In the present layer-match model, rules, we present i.e., we presumea potentially that free they stackingbehave variation as order-disorder of layers (OD) but within layers aswell-defined defined by layer-match Dornberger-Schiff rules, i.e., [25], weDuroviˇc[ˇ presume26 ], thatand they Ferraris behave et al. as [27 order-disorder], among others. (OD) layers as defined by Dornberger-Schiff [25], ĎuroviThereč [26], is and a limited Ferraris number et al. [27], of types among of such others. layers in any OD structure (only one layer typeThere in our is case),a limited with number own layer-group of types of symmetry such layers and in 2D any architecture. OD structure Their (only relationships one layer typein any in our layer case), pair with (of two own identical layer-group layers) sy ismmetry in the OD and structure 2D architecture. always describedTheir relation- by the shipssame in set any of layer symmetry pair (of operations. two identical However, layers) thisis in doesthe OD not structure guarantee always fixed described relationships, by theand same periodicity, set of symmetry for triple operations. layers and higherHowever,n-tuples, this does as it not does guarantee in the majority fixed relation- of crystal ships,structures. and periodicity, This results for in triple a disordered layers and layer higher stacking n-tuples, while maintainingas it does in thethe