Building Units and Intergrowths: Toward the Design of an Extended

Finally, it is noteworthy that BUs with n = 3n′ + 2 are structurally polar from the point of view of their Bi3+ repartition. In the here-observed ma...
0 downloads 0 Views 8MB Size
Download PDF
Chem. Mater. 2009, 21, 4019–4029 4019 DOI:10.1021/cm901466e

Building Units and Intergrowths: Toward the Design of an Extended Family of Acentric Bi-Based Materials with Second Harmonic Generacy Marielle Huve,† Marie Colmont,† Julien Lejay,‡ Patrick Aschehoug,‡ and Olivier Mentre*,† †

UCCS, Equipe de Chimie du Solide, UMR CNRS 8181, ENSC Lille - UST Lille, BP 90108, 59652 Villeneuve d’Ascq Cedex, France., and ‡LCMCP - UMR 7574 ENSCP, 11 rue Curie, F-75231 Paris Cedex 05, France Received May 29, 2009. Revised Manuscript Received July 16, 2009

The concerted use of transmission electron microscopy and X-ray diffraction has been exploited to point out the existence of versatile 2D building units (BUs) able to organize in 3D regular intergrowths, on the basis of an extended series of new Bi oxophosphate materials. Here, the socalled BUs consist of ribbon-like polycations formed of the linkage of n O(Bi,M)4 tetrahedra along their width. Previous results about the relationships between short (n = 1 to 6) BUs and their specific HREM contrasts have been extended to longer BUs identified in this work (n = 8 to 12) in the inhomogeneous sample with the bulk-formula Bi6Li2Zn2P4O22. Seven new intergrowths between them (new materials), with PO4 interfacial species, have been fully rationalized, enabling the predictive design of future new materials. Finally, it is noteworthy that BUs with n = 3n0 + 2 are structurally polar from the point of view of their Bi3+ repartition. In the here-observed materials, it yields acentric intergrowths between BUs with a large deviation from centrosymmetry in term of electronic density repartition. The acentric space group was checked by preliminary secondharmonic generation (SHG). The mega-series corresponding to the intergrowths between the same ribbons has been rationalized as a function of n. One third of them should preferentially be acentric materials due to the most stable ferro-arrangement between the polar BUs. Introduction During the last decades, a special effort has been centered on the predictive approach for creating new inorganic structures. This is an important challenge of today’s solid state chemistry, as mentioned in the last report on the third workshop on solid state chemistry:1 “... Most research efforts in current solid-state chemistry are concerned with the Design and prediction of new structures and materials...”. Such difficult “predicting aspect” is possible for example by using the assembly of building units (BUs).2 The main difficulty arises from the identification of BUs able to arrange into versatile structural types with strong similarities. For instance, hexagonal perovskite compounds are generally described by the close packing of anionic layers that can be considered as 2D BUs able to stack according hexagonal or cubic packing. Then, all intermediates between the three-dimensional 3C-LaMnO3 type and the mono-dimensional 2H-BaNiO3 type can be envisaged3 while the use of *To whom correspondence should be addressed. E-mail: olivier.mentre@ ensc-lille.fr. Tel: +33 (0)3 20337721. Fax: +33 (0)320436814.

(1) Kanatzidis, M. G., Poeppelmeier, K. R., Eds. Prog. Solid State Chem. 2007, 36, 1-133. (2) (a) Mrotzek, A.; Kanatzidis, M. G. J. Solid State Chem. 2002, 167, 299. (b) O'Keeffe, M.; Eddaoudi, M.; Li, H.; Reineke, T.; Yaghi, O. M. J. Solid State Chem. 2000, 152, 3. (c) Krivovichev, S. V.; Armbruster, T.; Depmeier, W. J. Solid State Chem. 2004, 177, 1321. (3) (a) Naray-Szabo, S. Naturwissenschaften 1943, 31, 466. (b) Lander, J. J. Acta Crystallogr. 1951, 4, 148. (c) Darriet, J.; Subramanian, M. A. J. Mater. Chem. 1995, 5, 543. r 2009 American Chemical Society

particular layers such as [BaOX] (X = F, Cl)4 can rationally create particular stacking sequences. Of course, the filling of octahedral interstices achieved the creation process. This approach is all the more efficient in the field of 2D-layered compounds, in which modulable blocks superimpose in the solid. For example, among the number of examples, we can report the stacking of [Bi2O2]2+ layers and [An-1MnO3n+1]2- perovskite like blocks in the Aurivilius series,5 the rationalization of the stacking of rocksalt-type fragments in the Am[M1+lSe2+l]2m[M2l+nSe2+3l+n] series,6 but also the Magneli phases,7 Dionjacobson series,8 and so on. Here it is worth mentioning the more recent design of new layered compounds through the assembly of [A2F2]2+ donor fluorite blocks and various acceptor blocks including antifluorite and rock-salt like blocks.9 However, in the field of oxide this prospecting aspect is often limited by the possibility of competing corner/ edges/face-sharing that may cause unpredicted edifices. (4) Ehora, G.; Renard, C.; Daviero-Minaud, S.; Mentre, O. Chem. Mater. 2007, 19, 2180. (5) Aurivillius, B. Ark. Kemi 1949, 1, 463. (6) Mrotzek, A.; Kanatzidis, M. G. Acc. Chem. Res. 2003, 36, 111. (7) Magneli, A. Acta Crystallogr. 1953, 6, 495. (8) (a) Dion, M.; Ganne, M.; Tournoux, M. Mater. Res. Bull. 1981, 16, 1429. (b) Dion, M.; Ganne, M.; Tournoux, M.; Ravez, J. Rev. Chim. Miner. 1984, 21, 92. (c) Jacobson, A. J.; Johnson, J. W.; Lewandowski, J. T. Inorg. Chem. 1985, 24, 3727. (9) (a) Kabbour, H.; Cario, L.; Danot, M.; Meerschaut, A. Inorg. Chem. 2006, 45, 917. (b) Kabbour, H.; Cario, L. Inorg. Chem. 2006, 45, 27.

Published on Web 08/12/2009

pubs.acs.org/cm

4020

Chem. Mater., Vol. 21, No. 17, 2009

We have shown in the past decade the utility of the antistructure concept,10 that is, arrangement of anion centered polyhedra, for the description of most of the compounds of the Bi2O3-MO-X2O5 phase diagrams (M = Cu, Zn, Mn, Mg, ..., X = P, As, V).11 In these series of disordered materials O(Bi,M)4 tetrahedra share edges to form polycationic ribbons able to self-assemble in various intergrowths while being isolated by XO4 spacers. Then, the possibility to predict/formulate new compounds from the assembly of the polycations appears particularly well adapted to these series, but the next step forward would consist of the possibility to modulate the size of BUs ribbons to diversify the structural archetypes. In previous works we have shown the possibility to stabilize n = 1 to 6 tetrahedra wide ribbons.11b,c Considering recent results about similar infinite planes surrounded by PO4 groups including recent oxy-fluorophosphates,12 the preparation and evidence of new n-sized ribbons and intergrowth turned out to be a challenge to overcome. In that field, the importance of high resolution electron microscopy (HREM) for investigation of local defects, intergrowth, and so forth13 has been known for a long time. Furthermore, we already pointed out that this technique is particularly well suited to the identification of new structural types in the concerned Bi-M-X-O system from the analysis of a single crystallite, eventually in an inhomogeneous mixture.11b,d This work describes the evidence of new structural intergrowths of (new) BUs. In a first part, the state of the art is established, on the basis of structural particularities of this family of compounds. The second part deals with the elaboration of several new structural models from high resolution images of several domains of a unique Li-containing sample. The crystal structure corresponding to the major phase (n=11 wide ribbons) has been possibly refined from single crystal data, in good agreement with the prior deduced model. It is noteworthy that it crystallizes in the acentric Im space group due to individual polar BUs and their ferro arrangement. As a matter of fact, we will establish (10) (a) O’Keefe, M.; Hyde, B. G. Struct. Bonding (Berlin) 1985, 61, 79. (b) Keller, H. L. Z. Anorg. Allg. Chem. 1982, 491, 191. (11) (a) Abraham, F.; Cousin, O.; Mentre, O.; Ketatni, E. M. J. Solid State Chem. 2002, 167, 168. (b) Huve, M.; Colmont, M.; Mentre, O. Inorg. Chem. 2006, 45(17), 6604. (c) Colmont, M.; Huve, M.; Mentre, O. Inorg. Chem. 2006, 45, 6612. (d) Huve, M.; Colmont, M.; Mentre, O. Chem. Mater. 2004, 16(13), 2628. (e) Colmont, M.; Huve, M.; Ketatni, E. M.; Mentre, O. Solid State Sci. 2008, 10, 533. (f) Colmont, M.; Huve, M.; Ketatni, E. M.; Abraham, F.; Mentre, O. J. Solid State Chem. 2003, 176, 221. (g) Ketatni, E. M.; Huve, M.; Abraham, F.; Mentre, O. J. Solid State Chem. 2003, 172, 327. (h) Colmont, M.; Huve, M.; Abraham, F.; Mentre, O. J. Solid State Chem. 2004, 177, 4149. (12) Steinfink, H.; Lynch, V. J. Solid State Chem. 2004, 177, 1412. (b) Colmont, M.; Huve, M.; Ketatni, E. M.; Mentre, O. Solid State Sci. 2008, 10, 533. (c) Arumugam, N.; Lynch, V.; Steinfink, H. J. Solid State Chem. 2007, 180, 2690. (d) Arumugam, N.; Lynch, V.; Steinfink, H. J. Solid State Chem. 2007, 180, 1504. (13) (a) Martin, C.; Maignan, A.; Huve, M.; Hervieu, M.; Michel, C.; Raveau, B. Physica C 1991, 179, 1. (b) Huve, M.; Michel, C.; Maignan, A.; Hervieu, M.; Martin, C.; Raveau, B. Physica C 1993, 205, 219. (c) Hervieu, M. J. Electron Microsc. Tech. 1989, 11, 202. (d) Van Tendeloo, G.; Amelinckx, S. J. Electron Microsc. Tech. 1988, 8, 285. (e) Erwerft, M.; Van Tendeloo, G. J. Electron Microsc. Tech. 1991, 17, 70. (f) Van Tendeloo, G.; Krekels, T.; Amelinckx, S.; Babu, T. G.; Greaves, C.; Hervieu, M.; Michel C.; Raveau, B. Micros. Res. Tech. 1995, 30, 102.

Huv e et al.

that every BU with ntetrahedra = 3n0 + 2 should be acentric and yield preferentially acentric materials by intergrowth. Experimental Section Synthesis. After the evidence and of versatile BiM2+2XO6 (M = Mg, Ca, Pb, Cu, Co, Zn, ...)14 structural type that corresponds to the n = 2 term, we explored related phase diagrams, containing alkali, such as Li+. The Bi6Li2Zn2P4O22 (= Bi42Li14Zn14P28O154) powder sample has been prepared by heating a stoichiometric mixture of Bi2O3, ZnO, Li2CO3, and (NH4)2HPO4. Several heating-grinding steps from 200 to 800 C are applied for 72 h, and the final powder is quenched at room temperature. Single crystals of Bi57.28Zn7.976Li8.208(PO4)28O56 were obtained by melting the powder at 900 C with subsequent slow cooling to room temperature. The corresponding powder was prepared at 800 C and shows a nearly single phase. Characterization. X-ray powder diffraction data were collected at room temperature using a D8 Bruker diffractometer. Selected area electron diffraction (SAED) patterns as well as high resolution images were obtained on a JEOL 4000EX transmission electron microscope. EDS analysis was performed on a Philips CM30 transmission electron microscope. Materials were crushed and dispersed on a holey carbon film deposited on a Cu grid. All the ED patterns and images presented in this paper were obtained from the same powder sample (Bi6Li2Zn2P4O22). Single crystal X-ray diffraction data were collected using a BRUKER X8 diffractometer equipped with a fine-focus Motarget X-ray tube (λ = 0.71073 A˚). The intensity data have been extracted from the collected frames using the program Saint Plus 6.02.15a The lattice parameters were refined from the complete data set. An absorption correction based on an empirical absorption correction was performed for Bi57.28Zn7.976Li8.208(PO4)28O56 using SADABS.15b The structural refinements have been performed with the JANA software.15c Second Harmonic Generation (SHG). To determine the second harmonic generation (SHG) efficiency, pertinent powders were compared to standards, using the Kurtz method.16 This technique is based on the measurement of the second harmonic intensity generated by a pulsed YAG:Nd3+ laser (1064 nm with 10 Hz frequency, 8 ns pulse duration, and 5 mm diameter) on a thin powder layer. The powders were grinded and sieved to adjust the particle size between 80 and 125 μm. The YAG:Nd3+ laser beam crosses a powder-layer of 1.6 mm thickness. This distance and the incident beam diameter are largely bigger than the particle size. So, we ensure that a large number of particles with random orientation were stroked for an accurate statistical average. The incident beam is cutoff with several filters, and SHG is collected by using a Pacific photomultiplier (PMT), visualized, and time-averaged on a Tektronix oscilloscope. (14) (a) Ketatni, E. M.; Abraham, F.; Mentre, O. Solid State Sci. 1999, 1, 449. (b) Abraham, F.; Ketatni, M.; Mairesse, G.; Mernari, B. Eur. J. Solid State Chem. 1994, 31, 313. (c) Mizrahi, A.; Wignacourt and, J. P.; Steinfink, H. J. Solid State Chem. 1997, 133, 516. (d) Mentre, O.; Ketatni, E. M.; Colmont, M.; Huve, M.; Abraham, F.; Petricek, V.; Amer, J. Chem. Soc. 2006, 128, 10857. (15) (a) SAINTþ, Version 5.00; Bruker Analytical X-ray Systems: Madison, WI, (x2) 2001. (b) SADABS, Version 2.03; Bruker Analytical X-ray Systems: Madison, WI, (x2) 2001 (Bruker/Siemens Area detector absorption and other corrections). (c) Petricek, V.; Dusek, M.; Palatinus, L. JANA2000; Institute of Physics: Praha, Czech Republic, 2005. (16) Kurtz, S. K.; Perry, T. T. J. Appl. Phys. 1968, 39, 3798.

Article

Chem. Mater., Vol. 21, No. 17, 2009

Figure 1. Projection along b of the crystal structures of (a) the (3)(3)/ t(2)t(2) (e.g., Bi3Cd3.72Co1.28O5(PO4)3, ref 11f) and (b) the (6)/(4) (e.g., Bi5.625Cu2.062(PO4)3O6, ref 11c) intergrowths. Some of the “structural rules” developed in the text, e.g., (n)t nomenclature, overlap of ribbons along the a-axis (gray band), requested space for existence of the tunnels (7.5 A˚) versus ribbon-ribbon stacking (3.5 A˚), and detail of the number of surrounding entities Ex + PO4...) are visually given.

State of the Art Extended Series of Ribbon-Based Materials. Up to now, several oxide bismuth phosphates have been evidenced and characterized. The high cationic disorder existing in some of them leads to their description using the antiphase approach.10 This alternative description based on the assembly of MOx frameworks has been developed for a long time and appears strongly efficient in several cases, including disordered materials and/or particular cations with complex surrounding oxygen polyhedra (Pb2+, Bi3+, ...). In the number of Bi oxo-salts evidenced so far, it systematically points out a rigid framework formed of Bi-M-O polycationic ribbons by edge sharing O(Bi,M)4 tetrahedra. These ribbons are isolated by PO4 groups and interstitial cationic 1D channels (hereafter, t for tunnels). Empirical structural rules well adapted to this family of inorganic materials have been deduced from the observation of the so-called parent compounds, and their validities have been checked in further investigation.11 In addition, these rules are at the basis of the potential easy design of new compounds since they deal with the prediction and chemical formulation of possible arrangements of ribbons, tunnels, and surrounding phosphates. Structural Particularities. They are listed above and detailed on Figure 1: (i) The sizes of the ribbons vary from the single chain (n tetrahedra along the width = 1) to n = 2, 3, 4, 5, 6, then

4021

leading to a continuous series of polycations. Theoretically, the ribbon size is unlimited. Up to now, structural types with ribbons of variable width (n = 1, 2, 3, 4, 5, 6 and n = ¥ O(Bi,M)4 tetrahedra wide) have been characterized. At this point, the question of the stability of long-sized ribbons against either their slicing in shorter ones in the materials or the creation of infinite layers remains unanswered. (ii) The number of surrounding PO4 groups is mathematically defined as a function of n. (iii) The intergrowth of different sized ribbons is one of the keys of the richness of this structural series. (iv) Because of their similar inter- and intraribbon organization, most of these materials crystallize in an (pseudo)orthorhombic unit cell with two common parameters. The first one (conventionally, the a axis), ∼11.5 A˚, corresponds to the ribbons/PO4 ordered periodicity perpendicular to the infinite dimension of the ribbons. The second, ∼5.5 A˚ (conventionally, the b axis) is inherent to the structure of ribbons and corresponds to the height of two edge-shared O(Bi,M)4 tetrahedra along the infinite axis. Finally, the c axis is variable and depends on the size and sequence of ribbons in each particular material. (v) For n e 3, the tunnels “t” are located in between two edges of ribbons separated by in-plane distances of about 7.5 A˚. Four columns of the surrounding PO4 form their 1D cavities. The occupancy of tunnels is disordered, and at least can we empirically announce that along one b-period (∼5.5 A˚) t should contain a maximum of two M2+ cations to respect plausible M-M distances. (vi) The cores C of ribbons are solely occupied by Bi3+ while their edges (E) can be suited by M2+ or mixed Bi3+/ M2+. These mixed Bi3+/M2+ positions are generally responsible for a disorder in the inter-ribbon space, namely, the competition between several orientations of the PO4 groups depending on their local Bi/M environment. Formulation of Compounds. As first evidenced in ref 11b, 11c, two cases have to be distinguished depending on the size n of adjacent tetrahera along the involved building ribbons. For n e 3,11d the polycation is purely bidimensional and can be formulated [(M/Bi)4Bi2n-2O2n]x+ where M/Bi stands for the mixed edges of and Bi for their cores. In the (a,c) plane, each polycation is surrounded by 2n + 2 PO4 groups while the final formulation depends on the imbrications of the ribbons, for example, the distance between them along c involving or not the presence of tunnels. Note the exception for n = 1 surrounded by six PO4 groups, only found so far in the BiMPO5 well ordered compounds. For n > 3,11b,c the cohesion with surrounding PO4 groups is effected by 3-D excrescences (Ex) decorating the ribbon of every three O(Bi/M)4 tetrahedra. Ex are formed by additional BiO groups growing perpendicular to the width of the ribbons. Then, the additional oxygen atom is penta-coordinated (four Bi from the ribbons + the extra Bi). In between two parallel ribbons; the Ex

4022

Chem. Mater., Vol. 21, No. 17, 2009

systematically point toward each other. This particular configuration should be stabilized by the creation of a complex lattice of interactions between positive Bi centers and negative lonepairs, as shown on Figure 2 for an ideal structure. It was checked, from the observation of prior compounds, that for n > 3, the number of surrounding [Ex+PO4] is also 2n+2. Here, the systematic overlapping along c of the ribbons at x = 0 and x = 1/2 leads to 2(n - 1) neighboring [Ex+PO4] per ribbon. It is shown on the Figure 1b for intergrowth between n = 4 and n = 5 ribbons but has been verified for all the compounds determined until now, including new intergrowths at the basis of the present work. If one distinguishes between surrounding Ex and PO4, it yields NPO4 = 2[(n - 1) (int[(n - 1)/3])]+4 and NEx = 2 int[(n - 1)/3] where int[x] stand for the integer part of x. Finally, it corresponds to a normalized number of PO4 per ribbon of 2[(n - 1) - (int[(n - 1)/3])]. As shown in the Table 1, the corresponding formula for large ribbons is [(M/Bi)E4BiC2n-2BiEx2int[(n-1)/3]]O2n+2int[(n-1)/3]]x+ where E, C, and Ex stand for edges, cores, and excrescences, respectively. Polarity of the BUs. Taking into account the systematic location of the first Ex at the vertices of the third or fourth bismuth position along the ribbon (i.e., second or third tetrahedra) and a regular dispostion of them every three tetrahedra, as soon as n 6¼ 3n0 + 2 the BUs can be assorted with a polar character, see the example of ribbons with n = 8 in Table 1. Furthermore, it yields strong deviation from the centrosymmetry in term of electronic repartition since Bi3+ atoms are involved. These structural rules are important for a rational design of new materials. Indeed, it can lead to a series of predicted acentric compounds as detailed in the devoted section. Related materials with infinite [Bi2O2]2+ planes have been recently isolated in two polymorphs of the Bi6+xM1-xP2O16-y oxyfluorides.12b The crystal structure of the so-called form I is essentially similar to those of Bi4V2O10.66, in which the 3D-excressences are replaced for octahedral vanadium and the PO4 for tetrahedral V5+.17 HREM Analysis From Image Code to Structure Determination. Many original structural types have first been deduced from high-resolution TEM analysis.11d Indeed the intergrowths of the ribbon-like BUs surrounded by PO4 are responsible for close Bi/M/P/O compositions of different structural types and subsequent polyphased samples. The scale of observation of TEM enables an individual examination of a single crystallite or even domains. Here, the corresponding HREM contrasts can be interpreted in terms of the ribbon-like BU arrangements, using an image code previously deduced from well-known parent compounds. It yields an easy formulation based on the (17) Joubert, O.; Jouanneaux, A.; Ganne, M. Mater. Res. Bull. 1994, 29, 175.

Huv e et al.

Figure 2. Interaction between two ribbons along the a-axis. The biexcrescences (Ex, Ex0 ), bicore of the ribbons (Bi), and lone pairs (LP) of each Bi3+ form an array of positive and negative charges. The distances between the species are reported at the top of the figure.

rules given above and the possible preparation of the corresponding single phase. The HR experimental contrast for a defocus of -10 nm and a thickness of 3.2 nm, corresponding to the ribbons for ntetrahedra > 3, that is, with OBi excrescences, observed up to now11b,c for these materials is summarized in the Figure 3. For each contrast the corresponding chain is superimposed for an easy comparison. n = 4 labeled (4), 5 (5), 6 (6) sized-ribbons respectively take place in the dark region between respectively white oval (Figure 3a), white oval with one terminal chevron (Figure 3b), and white oval surrounded by two terminal chevrons (Figure 3c). They are respectively surrounding by 8, 10, and 12 isolated PO4 tetrahedra. These images have been used to build (by slicing and pasting) the new contrasts corresponding to greater n sizes. Each of the following observation follows from the same initial multiphased preparation. Before the HREM study an electron diffraction investigation was first carried out. Evidence of Original Phases by Electron Diffraction. The Bi6Li2Zn2P4O22 powder sample has been checked by electron diffraction. The majority of crystals exhibit an I-centered orthorhombic unit cell with aI ∼ 11.5 A˚, bI ∼ 5.5 A˚, and cI ∼ 58 A˚ (Figure 4a). As already highlighted, a and b are common to the concerned inorganic family while the c value is reminiscent of a dominating original phase. After deduction of the accurate formula Bi57.28Zn7.976Li8.208(PO4)28O56 from single crystal XRD data and preparation of the powdered sample, the lattice parameters refined from XRD powder data are a = 11.5826(3), b = 5.4736(2), c = 58.9041(19) A˚, and β = 90.55(1). The indexed powder pattern given in the Supporting Information, Figure S1, shows a nearly pure sample. However, a number of different c axis values, for example, c ∼ 48 A˚, Figure 4 b, or local defects have also been pointed out, leading to new intergrowths. On Figure 4b,c, the streaks are probably due to the presence of these defects that will be analyzed carefully below. Intergrowths of New n = 11 BUs. For the major phase, the reconstruction of the reciprocal space is compatible

Article

Chem. Mater., Vol. 21, No. 17, 2009

4023

Table 1. Nomenclature Detailed for Each Evidenced Polycation: View along the b-Axis, Former Nomenclature, Current Nomenclature, and Formula

with an I space group. The observed HREM contrast is built on columns of a new motif. This latter can be described by three white ovals with one single terminal chevron (Figure 5a). Two neighboring columns along c are translated by a/2 in good agreement with the body centered lattice. By itself the (a,c) projection does not evidence any possible inversion center, reminiscent of an acentric symmetry. It is possible to reconstruct the motif on the basis of the known contrasts (n tetrahedra = 4, 5) of Figure 3. Indeed the new BU, noted 11 (n = 11), results from the sum of three contrasts (Figure 5b). The first and last correspond to n = 4 (see Figure 3a) and n = 5 (see Figure 3b) BUs, respectively, while the central part can be deduced from n = 4 by removal of the edges as schematized on Figure 5b. It consists in the creation of a pseudo n = 2 contrast. The total motif is consistent with n = 11 motifs decorated by three excrescences Ex outward from the ribbon and surrounded by 18 PO4 tetrahedra. It is in correct agreement with our previous deductions: N PO4 = 2[(n - 1) - (int[(n - 1)/3])] + 4, where n is the number of adjacent O(Bi,M)4 tetrahedra. The ribbon takes place in the dark region between two of these motifs along a. The decoding of the full unit cell yields the (11)ttt/(11)ttt sequence according to the nomenclature defined in ref 11, Figure 5c. It denotes that, along the c axis, the existence of acentric (n = 11) ribbon is followed by three tunnels alternating at x = 0 and at x = 1/2. The c parameter results approximately from the alignment of 20 tetrahedra interspacing (taking into account the overlap of two ribbons at their edges). It corresponds well to ∼20  2.9 A˚ = 58 A˚. Taking into account the established structural rules, a global formulation can be deduced from this (a, c) projected structure. It leads to (11)2t6(PO4)28 with (11) = Bi20(Bi,Zn)4Bi6O28, t = (Zn, Li)x