Half a century ago the synthesis of acentric hexagonal Bi_19/3IS₉ by chemical transport reaction has been reported and a structure proposal based on a sub-cell relationship was given, showing a Fibonacci relation between their lattice parameters with a_sub = a/√13 [1] [2] . Later the crystal structure of this compound has been described by others [3] , followed by syntheses of the isotypicbismuth sulfide bromide and chloride, respectively [4] [5] . Eventually, Mariolacos [6] determined the crystal structure of the bromide sulfosalt. The formula was given as Bi(Bi₂S₃)₉Br₃ despite the fact that the assumed unit cell actually contains fewer atoms. However, the structure determinations by Miehe & Kupcic [3] and Mariolacos [6] appear to be less reliable. Although the author of this contribution had previously pointed out parallels to other compounds with a superstructure of multiplicity 13, this reasonable approach has not been pursued further [1] . For instance, benstonite, Ca₇Ba₆(CO₃)₁₃ [7] , reveals ordering of the differently size dcations on sites of the calcite structure that leads to a superstructure with a geometrical relations similar to the unit cell and sub-cell of the bismuth sulfide iodide. Further examples for such geometrical relations are found in clockmannite, CuSe, senaite, Pb(Ti, Fe, Mn, Mg)₂₄O₃₈ [8] and davidite, (La, Ca, Ce) (Y, U) (Ti, Fe³⁺)₂₀O₃₈. The superstructure of CuSe with a 13-fold larger a translation period compared to the covel line (CuS) lattice parameter has been explained as the result of different mesh widths of Kagomé nets and tetrahedral sites of the prototypic CuS sheet structure [9] . Alternatively, this superstructure has been interpreted by Taylor & Underwood [10] invoking additional twinning. Davidite shows the full basket of Fibonacci relations between sub-cell, cell and super-cell [11] . The true cell consists of a rhombohedral sequence of layers, formed by 12 sub-cells of hexagonal-closed packed oxygen atoms supplemented by one heavy atom at the cell origin to yield 12 + 1 → 13 ones. The super-cell is the result of twinning in the (520) plane. In contrast to this, davidite crystals without twinning show the true cell size.

Recently, a novel superstructure was observed for the photocatalyst Bi₁₉S₂₇Br₃ on HRTEM images with lattice spacing of 3.73 Å, corresponding to the interlayer spacing of the (310) plane [12] .

In the meantime extended work has been undertaken to clear up the boundary lines of the bismuth sulfide halo genide pseudo-binary systems [13] [14] . According to that the stability field of bismuth sulfide iodide extends above 200˚C. Crystals can be maintained stable at room temperature for years.

The reason to revisit new/old crystal-chemical detail of the title compound is based on its suggested applicability in thin film solar cells or dye-cells due to its potentially interesting electronic properties.

In the following chapters first the result of the determination of the “averaged” structure with the original unit cell size will be discussed. From this, shortcomings of earlier interpretation attempts will become obvious, leading to strong evidence of a Fibonacci super-cell with a still fractional chemical cell content, and eventually to the formula Bi_5−x(Bi₂S₃)₃₉I₁₂S. Finally, possible ambient temperature synthesis routes and solar cell application of the compound will be highlighted.

Members of the Fibonacci numbers sequence like 1, 2, 3, 5, …, 13, … which occurred in the morphology of crystals and during the structure determination, inspired the naming Fibonacci superstructure.

As described long time ago [1] , highly reflecting crystal needles of the title compound are formed, if Bi₂S₃ powder is transported with iodine vapor in a partially evacuated vitreous silica ampoule from a temperature of 700˚C to the equilibrium temperature of about 550˚C, determined through T(ΔG = 0) = ΔH/ΔS of the underlying gas reaction involving BiI_g. The hexagonal crystals develop the {100} and {110} prisms as well as less pronounced {210} and {310} faces that allow looking inside their atomic structure (morphologic aspect). The hexagonal crystals with lattice parameters of a = 15.629(3) Å, c = 4.015(1) Å (see Table 1) (Cu-Kα₁ Guinier data) belong to the polar space group P6₃ (No. 173), because the centrosymmetric space group P6₃/m, also possible due to systematically absent reflections found, could be excluded by virtue of the pyroelectric response observing qualitatively spontaneous polarization under a static temperature change. The unit cell content of two Bi_19/3IS₉ formula units agreed with the chemical analysis and the observed density of D_obs = 6.74(4) Mg・m⁻³, obviously confirming some not fully occupied metal positions; the calculated density was D_x = 6.76 Mg・m⁻³. A super-cell could not be verified at that time.

From strong hk0 reflections, 310 and 250 respectively, which correspond to morphologically observed faces, one constructed a sub-cell with grid points that indicate the heavy atom positions projected on (001) (see Figure 1). In this way the x and y coordinates of two six-fold Bi positions have been found as multiples of 1/13. We notice that the sum of h² + k² + h・k for h = 3, k = 1 gives the Fibonacci number 13. In addition, the equal intensity distribution on records with l = 0, 1, 2 is indicative for z coordinates of the heavy atoms near 1/4 or 3/4 respective-

ly. With the assumed positions for Bi (1) as 1/13, 4/13, 1/4 and Bi (2) as 2/13, 8/13, 3/4a least squares refinement and a subsequent difference Fourier synthesis confirmed the positions of all atoms. The sub-cell concept as a tool for solving crystal structures was used in the determination of the crystal structure of Pb₆[Ge₆O₁₈]・2H₂O, too [15] . Integrated intensities from Weissenberg multiple film records, taken with Cu-Kα radiation, have been thoroughly corrected according to a procedure published previously [16] . After merging symmetrically equivalent reflections at least 582 independent ones remained with Fo > 4σ (Fo). An absorption correction for cylindrical samples [17] was made for the used prismatic crystal needle of only 12.5 μm effective diameter giving μR = 0.909. Corrected secondary extinction corresponds to a fitted mosaic domain radius of 0.452 μm [18] . The structure refinement was performed with the PCSHELXL software package [19] using atomic form amplitudes for Bi³⁺, S²⁻ and I¹⁻ from International Tables IV. The absolute configuration is revealed within significant sign of twinning (Flack parameterx = 0.01(10)). Final reliability factors of w R2 = 0.076 and R1 = 0.036 (goodness of fit S = 1.28) were obtained with the residual electron density of Δρ_max = 1.99e/ų, Δρ_min= −2.06 e/ų and Δρ_rms= 0.45e/ų. Atom parameters and anisotropic displacement coefficients of the “averaged” structure are summarized in the Table 2 and Table 3. Table 4 gives bond lengths and calculated bond valence sums. The bond valence sums = Σs_i was calculated according to Brow & Shannon [20] using s_i = (d_i(Me − S)/d₀)^−N with d₀ = 2.459(7) Å, N = 5.3(7) [21] .

The crystals are stable under ambient conditions, especially stable against humidity, and contain less toxic elements as prerequisites for any application. Therefore, ambient temperature synthesis routes such as co-precipi- tation from solution are under investigation, in case the compound is considered as alternative, environmentally benign solar energy harvesting material in thin film solar cells or dye-sensitized ones [23] . The suggested energy gap of E_g = 1.6 eV is lying between the indirectly allowed band gap of photo-conducting and ferroelectric BiSI, reported as E_g = 1.57 eV [24] [25] [26] , and E_g = 1.69 eV of Bi₂S₃ [27] . For comparison, methyl ammonium lead iodide (MAPbI₃) has a gap of E_g = 1.55 eV. Today, this toxic organic-inorganic perovskite, first synthesized by Weber [28] , and since 2009 applied in “dye” solar cells, reaches today a solar efficiency of about 20% [29] and emits light as OILED, when reversely used under voltage [30] - [32] .

The title compound belongs to the family of n-type semiconductors. The high refractivity index, roughly estimated as n ≈ 2.8 by applying the Moss relation (n⁴E_g = 95 eV) [33] , results in small effective masses and enhanced born charges, favoring effective carrier transport properties. The carrier life time as a dominant factor for an effective solar cell will be affected by iodine and bismuth vacancies suggesting deep charge-state transition levels within the complex band gap. As in the case of MAPbI₃ [34] , some energetically favorable dimers of Bi and I may be formed along [001]. When the polar axis of the nano-sized needles can be aligned normal to the back electrode, charge separation of sunlight induced carriers should be supported. So the compound may offer a basket of physically interesting properties.

Simple techniques have been proposed to grow perfectly oriented crystalline layers. For example, copper alloyed with some Au, thermally vapor deposited on a freshly cleaved mica sheet with its Kagomé surface, is ideally adapted to act as substrate for epitaxial deposition of (001) layers or nano-rod carpets of the hexagonal bismuth sulfide iodide. The lattice parameter of cubic Cu_0.848Au_0.152 is 3.6837 Å giving a distance of d₍₁₁₁₎ = 2.6048 Å; the a parameter of the bismuth sulfide iodidevery well complies with a multiple of this distance: a = 6・d₍₁₁₁₎(alloy). More important, the ratio of the sub-cell length (a_sub = 4.335 Å) to d₍₁₁₁₎(alloy) yields exactly 5/3 and promises success. Another synthesis route may be found insono-chemical preparation from a gel in alcoholic solution, because acoustic cavitation produces intense local heating and enhanced reactivity. This method has recently been applied in the synthesis of chemically similar compounds such as SbS I [35] .

Dealing now with solar cell construction made from bismuth sulfide iodide. When the copper bearing alloy is annealed in iodine vapor before epitaxial deposition of bismuth sulfide iodide, then a smart hole conducting layer may be created between photoconductor and back electrode due to the formation of (111) oriented sphalerite-type CuI with its favorable band gap of about 3.1 eV, dielectric constant of ε = 6.5, and small effective hole mass of m_h* = 0.38 [36] - [38] . The Cu-I distance of 2.62 Å would agree very well with d₍₁₁₁₎ of an alloy of composition Cu_0.805Au_0.795 allowing still for subsequent perfectly epitaxial growth of the bismuth sulfide iodide film onto CuI. The remaining gold at the mica surface once copper is transformed into iodide will accumulate to nano- clusters due to its high surface mobility. As an optical meta-material these clusters do not lessen the transparency, but even increase the conductivity effectively cooperating with CuI as back electrode, transporting light-in- duced hole carriers away.

On the other hand one does not need a metallic back electrode at all but uses directly CuI because of its sufficiently high hole conductivity. So CuI can be prepared by evaporating pure copper onto freshly cleaved muscovite mica in vacuum and then transformed into CuI by vapor from a weak solution of iodine.

Because muscovite mica is a less disposable natural material, supporting the deposition of highly oriented CuI transparent films for research purposes, it may in future be replaces by transparent and less costly substrates. Mercapto-silane surface activated fused silica has been reported to strongly bind thin gold films deposited by e- beam or thermal evaporation [39] . The deposition of a copper bearing alloy discussed before may bind the better at the activated silica surface. Evading vacuum technology, a solution processed deposition route was recommended for substrates like fused silica, using acetonitrile solved CuI in combination with a stabilizer like tetramethyleethylenediamine (TMED) [40] .

If both surfaces of the silica substrate being CuI coated, then the centerpiece of a completely inorganic twin solar cell is realized. Figure 6 shows the layer structure of such semi-transparent solar cell based on hexagonal bismuth sulfide iodide, but as a twin cell device with enhanced solar efficiency and low environmental footprint. This construction is even advisable for toxic perovskite solar cells and may considerably enhance the efficiency over that of a recently realized perovskite-silicon solar tandem cell [41] .

New evidence was collected for the existence of hexagonal bismuth sulfide iodide in a superstructure, characterized by the idealized formula Bi_5−x(Bi₂S₃)₃₉I₁₂S, Z = 2, space group P6₃, enlarged lattice parameter of a’ = √13・a = 56.351(9) Å in comparison to the still used “averaged” structure, and c’ = c = 4.018(1) Å. The superstructure concept guarantees more structural stability due to compensation of the basal plane dipole momentum of the Bi lone electron pairs.

Appropriate methods such as atomic force microscopy (AFM), high-resolution transmission electron microscopy (HRTEM) or diffraction experiments with synchrotron radiation will help to further clarify structural details. Possible variation of the chemical composition should be investigated, too.

Because the pyroelectric effect is able to enhance charge separation of light induced excitons in semiconductors, the pyroelectric title compound with its suitable energy gap is a candidate for photovoltaic respectively photocatalytic applications and should be further examined for details of such properties, especially light-in- duced changes of the dipole momentum and the existence of a ferroelectric phase transition. The influence of empty channels down [001] and anyway of the unit cell inflation on the band structure and energy gap is of partial interest.

Finally, fast progress in the construction of a completely inorganic and environmental benign thin film twin solar cell device is desirable, using c-axis oriented nano-rod bismuth sulfide iodide films as light harvesting layers, epitaxially grown onto (111) oriented CuI hole conducting layers, which were in turn deposited on both sides of a transparent substrate.

The author wishes to thank Prof. Dr. R. B. Heimann for critical reading of the manuscript.