Victor A Drits

Bruno Lanson
email: bruno.lanson@obs.ujf-grenoble.fr

Anne-Claire Gaillot

Drits

Gaillot Lanson

Birnessite polytype systematics and identification by powder X-ray diffraction Revision 1

The polytypes of birnessite with a periodic stacking along the c* axis of one-, two-, and three-layers are derived in terms of an anion close-packing formalism. Birnessite layers may be stacked so as to build two types of interlayers: P-type in which basal O atoms from adjacent layers coincide in projection along the c* axis, thus forming interlayer prisms; and, O-type in which these O atoms form interlayer octahedra. The polytypes can be categorized into three groups that depend on the type of interlayers: polytypes consisting of homogeneous interlayers of O-or P-type, and polytypes in which both interlayer types alternate. Ideal birnessite layers can be described by a hexagonal unit-cell (a h = b h ≈ 2.85 Å and γ = 120°) or by an orthogonal C-centered cell (a = √3 b, b h ≈ 2.85 Å and γ = 90°); and, hexagonal birnessite polytypes (1H, 2H 1 , 2H 2 , 3R 1 , 3R 2 , 3H 1 , and 3H 2 ) have orthogonal analogues (1O, 2O 1 , 2O 2 , 1M 1 , 1M 2 , 3O 1 , and 3O 2 ). X-ray diffraction (XRD) patterns from different polytypes having the same layer symmetry and the same number of layers per unit cell exhibit hkl reflections at identical 2θ positions. XRD patterns corresponding to such polytypes differ only by their hkl intensity distributions, thus leading to possible ambiguities in polytype identification. In addition, the characteristics of the birnessite XRD patterns depends not only on the layer stacking but also on the presence of vacant layer sites, and on the type, location and local environment of interlayer cations. Several structure models are described for birnessite consisting of orthogonal vacancyfree or of hexagonal vacancy-bearing layers. These models differ by their stacking modes and by their interlayer structures, which contain mono-, di-, or tri-valent cations. Calculated XRD patterns for these models show that the hkl intensity distributions are determined by the polytype, with limited influence of the interlayer structure. Actual structures of Identification of birnessite polytypes 1 Drits, Lanson, Gaillot phyllomanganates can thus be approximated by idealized models for polytype identification purpose. General rules for this identification are formulated. Finally, the occurrence of the different polytypes among natural and synthetic birnessite described in the literature is considered with special attention given to poorly understood structural and crystal-chemical features.

Identification of birnessite polytypes

INTRODUCTION

Birnessite is a hydrous layered manganese oxide (phyllomanganate). Its layers consist of edge-sharing MnO 6 octahedra and these layers are separated from each other by hydrated interlayer cations. These cations compensate for a layer charge deficit arising either from the presence of vacant layer sites or from the coexistence of heterovalent Mn cations in the octahedral layer. Birnessite interlayers incorporate a single sheet of interlayer H 2 O molecules, and exhibit a minimum periodicity along the c* axis of ~7 Å (Giovanoli et al. 1970a(Giovanoli et al. , 1970b;;[START_REF] Burns | The mineralogy and crystal chemistry of deep-sea manganese nodules, a polymetallic resource of the twenty-first century[END_REF][START_REF] Chukhrov | Birnessite characterization[END_REF][START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF]. In the following the term "birnessite" will be used to describe all natural and synthetic materials with such a layer structure, whatever the origin of the layer charge, and the actual configuration and chemical composition of the interlayers.

Over the last few decades, birnessite has attracted a wide interest for several reasons. First, it is ubiquitous in geological environments in spite of the low abundance of Mn. It is for example a major component of Mn nodules, which cover huge areas of the ocean floor and the bottom of some lakes. It is also present in soils, sediments, and Mn-rich ore deposits (Burns andBurns 1977, 1978;[START_REF] Chukhrov | Birnessite characterization[END_REF][START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF]Golden et al. 1986;[START_REF] Cornell | Transformation of hausmannite into birnessite in alkaline media[END_REF]Manceau et al. 2000c). It was recently shown that bacteria play a major role in the formation of birnessite in most of these environments (Tebo and He 1999;Tebo et al. 2004;and references therein). Second, this mineral plays an essential role in different ion-exchange and redox processes because of its unique surface charge, and adsorption and redox properties [START_REF] Manceau | X-ray absorption spectroscopic study of the sorption of Cr(III) at the oxide-water interface[END_REF]Manceau et al. 1992aManceau et al. , 1992b;;[START_REF] Paterson | The influence of structure on Ba and K uptake by a synthetic phyllomangante[END_REF]Stone et al. 1994;Tu et al. 1994;Le Goff et al. 1996;[START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]. In particular, birnessite plays a pivotal role in the fate of heavy metals and other pollutants in contaminated water systems and soils [START_REF] Chao | The significance of secondary iron and manganese oxides in geochemical exploration[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF][START_REF] Manceau | Application of polarized EXAFS to fine-grained layered minerals[END_REF]Manceau et al. , 2000aManceau et al. , 2000b)). Despite its low concentration, birnessite controls the distribution of some trace elements such as radionuclides, Pt-group elements, and rare earth elements [START_REF] Manceau | Application of polarized EXAFS to fine-grained layered minerals[END_REF]). In addition, birnessite has also attracted special attention because of its potential use as materials for batteries and other industrial applications [START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF].

Third, birnessite can be synthesized under a variety of physico-chemical conditions and from 0 to 1000°C. Synthetic birnessite is used to mimic naturally occurring redox and adsorption processes, being considered as analogous to natural varieties. Birnessite can be synthesized by the oxidation of Mn 2+ in a highly alkaline medium (Giovanoli et al. 1970a(Giovanoli et al. , 1970b;;[START_REF] Cornell | Transformation of hausmannite into birnessite in alkaline media[END_REF][START_REF] Kim | Factors controlling the stability of O3and P2-type layered MnO 2 structures and spinel transition tendency in Li secondary batteries[END_REF], leading, for example, to the topotactic transformation of Mn(OH) 2 when subjected to the action of different oxidizers. Other methods using MnO 4 -as starting reagent [START_REF] Herbstein | The thermal decompoition of Potassium Permanganate and related substances. Part I. Chemical aspects[END_REF][START_REF] Ching | Sol-Gel synthesis of birnessite from KMnO 4 and simple sugars[END_REF]Ching et al. , 1997aChing et al. , 1997b;;Chen et al. 1996aChen et al. , 1996b;;Ching and Suib 1997;[START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF]) include mild hydrothermal syntheses (Feng et al. 1995;Chen et al. 1996aChen et al. , 1996b)), sol-gel processes [START_REF] Bach | Sol-gel synthesis of manganese oxides[END_REF][START_REF] Bach | Electrochemical sodium insertion into the sol-gel birnessite manganese dioxide[END_REF][START_REF] Goff | Structural and electrochemical properties of layered manganese dioxides in relation to their synthesis: Classical and sol-gel routes[END_REF][START_REF] Ching | Sol-Gel synthesis of birnessite from KMnO 4 and simple sugars[END_REF]Ching et al. , 1997a;;[START_REF] Cho | Improvement of Structural Stability of LiMn 2 O 4 Cathode Material on 55°C Cycling by Sol-Gel Coating of LiCoO 2[END_REF], interactions of KMnO 4 with hydrochloric acid, and ion-exchange of the hydrogen form of birnessite to the Na-or K-forms (Tsuji et al. 1992;[START_REF] Leroux | The 2D rancieite-type manganic acid and its alkali-exchanged derivatives: Part I -Chemical characterization and thermal behavior[END_REF], and thermal decomposition of KMnO 4 at high temperature [START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF].

These different methods lead to the crystallization of birnessite having different layer stackings and different interlayer structures, which depend on the chemical nature of interlayer cations, their amounts, distribution, and coordination geometry. In addition birnessite is, as a rule, fine-grained and contains stacking faults and/or consists of interstratified layer types corresponding to different birnessite polytypes (Drits et al. 1997a[START_REF] Drits | Structure of heavy-metal sorbed birnessite: Part 2. Results from electron diffraction[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]Manceau et al. 2000c[START_REF] Manceau | Structure of heavy metal sorbed birnessite. Part III: Results from powder and polarized extended X-ray absorption fine structure spectroscopy[END_REF]Lanson et al. 2002aLanson et al. , 2002b)). As a result, strikingly different X-ray diffraction patterns are obtained from birnessite crystallized under different physico-chemical conditions. As a consequence, there has been a lot of confusion, even in the recent literature, as to the structure of these layer manganates (e.g., Chen et al. 1996b;[START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF][START_REF] Yang | Syntheses and characterization of well-crystallized birnessite[END_REF]. One difficulty in the interpretation of the birnessite XRD patterns is that until recently even unit-cell parameters reported in the literature were not determined unambiguously. Therefore, determination of birnessite structure was sometimes limited to a general description of the XRD patterns without any indexing or accurate determination of the unit-cell parameters (Feng et al. 1997a(Feng et al. , 1997b;;[START_REF] Aronson | Synthesis, characterization, and electrochemical properties of magnesium birnessite and zinc chalcophanite prepared by a low-temperature route[END_REF][START_REF] Ma | Syntheses of birnessites using alcohols as reducing reagents: Effects of synthesis parameters on the formation of birnessites[END_REF][START_REF] Yang | Syntheses and characterization of well-crystallized birnessite[END_REF]. In some cases indexing of hkl reflections was carried out without proper justification (e.g., [START_REF] Goff | Structural and electrochemical properties of layered manganese dioxides in relation to their synthesis: Classical and sol-gel routes[END_REF], 1996;[START_REF] Ching | Sol-Gel synthesis of birnessite from KMnO 4 and simple sugars[END_REF][START_REF] Aronson | Synthesis, characterization, and electrochemical properties of magnesium birnessite and zinc chalcophanite prepared by a low-temperature route[END_REF]). Significant progress was achieved recently in the structural characterization of birnessite [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF][START_REF] Kuma | Crystal structures of synthetic 7 Å and 10 Å manganates substituted by mono-and divalent cations[END_REF]Drits et al. 1997a[START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Drits | Structure of heavy-metal sorbed birnessite: Part 2. Results from electron diffraction[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]Manceau et al. , 2000c[START_REF] Manceau | Structure of heavy metal sorbed birnessite. Part III: Results from powder and polarized extended X-ray absorption fine structure spectroscopy[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b) ) and specifically in the determination of their unit-cell parameters (Chen et al. 1996a(Chen et al. , 1996b;;[START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b)). However, no systematic description of reliable criteria for the identification of birnessite polytypes is available, to our knowledge, in existing literature.

As for layer silicates (Bailey 1988) the optimal way to establish such criteria is to deduce theoretically all birnessite polytypes taking into account the main crystal chemical features of their layers and interlayers, to calculate the corresponding XRD patterns and to formulate diffraction criteria for their identification. This paper is devoted to such a systematic approach and describes how birnessite polytypes having the same unit-cell parameters can be identified.

BIRNESSITE POLYTYPE DIVERSITY

Polytype diversity in terms of close-packing formalism

The two-dimensional periodicity of birnessite layers can be described either by a O layer from adjacent layers define interlayer prisms. This type of interlayer will be referred to as a P-type interlayer and denoted with an equal sign (=). If they are located in A or B sites, O layer from adjacent layers define interlayer octahedra. These interlayers are referred to as Otype and denoted with a dash sign (-) to distinguish them from the P-type interlayers. Using the above notions, a one-layer polytype having O-type interlayer (Fig. 1a) can be represented as:

AbC -AbC… 1H

Systematic consideration of possible two-layer polytypes leads to two independent hexagonal polytypes having homogeneous interlayers (Figs. 1b-c):

AbC = CbA = AbC… 2H 1 AbC -AcB -AbC… 2H 2
With this notation the first digit indicates the number of layers per unit-cell, the letter corresponds to the layer symmetry (H, R, and M standing for hexagonal, rhombohedral, and monoclinic, respectively), and the final numerical subscript determines the polytype. In 2H 1 and 2H 2 polytypes adjacent layers are rotated with respect to each other by 180° around the axis parallel to the c axis and passing either through Mn atoms of adjacent layers (2H 1 ) or through the "lower" O layer (A sites -2H 2 ). In 1H and 2H 1 the Mn layer octahedral sites overlap in projection on the ab plane, whereas these sites are distributed more homogeneously in 2H 2 .

Analysis of three-layer polytypes leads to two independent modifications with rhombohedral symmetry (3R). These two polytypes differ from each other by their interlayer structures (Figs. 2a-b):

AbC = CaB = BcA = AbC … 3R 1 AbC -BcA -CaB -AbC … 3R 2
Two additional three-layer polytypes having O-type interlayers and hexagonal symmetry may also be derived :

AbC -AcB -AcB -AbC … 3H 1 AbC -AcB -CaB -AbC … 3H 2
In terms of the C-centered orthogonal unit cell successive layers in 3R 1 and 3R 2 polytypes are shifted by -a/3 and +a/3, respectively. As in 2H 2 polytype successive layers in 3H 1 and 3H 2 polytypes are not related by the same interlayer displacement. In addition, layers from different layer pairs are related to each other by different elements of symmetry in 3H 1 and 3H 2 polytypes. For example, layers in the first layer pair of the 3H 1 polytype are related by a 180° rotation along the c axis passing through A sites, whereas they are superimposed in the second pair (Fig. 2c). In the latter layer pairs, Mn octahedral sites overlap in projection on the ab plane, whereas in 3R 1 , 3R 2 and 3H 2 polytypes, layer Mn cations are distributed homogeneously among all possible sites (Figs. 2a,b,d).

Heterogeneity arising from the coexistence of O-and P-type interlayers in a given birnessite polytype is likely not energetically favorable. Polytypes with alternating O-and Ptype interlayers were thus excluded from the current study. However, transformation from one polytype to the other likely often occurs through layer translations. Such displacements occur, for example, as a result of cation exchange or during hydration-dehydration processes.

Therefore, among birnessite polytypes some unusual modifications can be formed from onelayer polytype by shifting the layers. For example, a two-layer structure AbC -BcA = AbC with both interlayer types can be obtained if successive layers are shifted alternately by +a/3 and -a/3 along the a axis of the C-centered unit cell.

The above idealized birnessite polytypes are similar to those of oxides with general formula A x MO 2 [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF]). These authors deduced four polytypes, T1, P2, P3, and O3, which correspond to 1H 1 , 2H 2 , 3R 1 , and 3R 2 modifications in the present nomenclature.

Birnessite polytypes are also similar to those of natural and synthetic layer double hydroxides [START_REF] Drits | Electron diffraction and high-resolution electron microscopy of mineral structures[END_REF][START_REF] Bookin | Polytype diversity of the hydrotalcite-like minerals. I. Possible polytypes and their diffraction features[END_REF] and to those of other natural and synthetic layered compounds [START_REF] Bailey | Structures of layer silicates[END_REF].

x/2 4 3 2

3 x 2 x 1 ) SO , (CO )(OH) R (R + + -

Layer symmetry and polytype diversity

Structural characterization of birnessite shows layers with either hexagonal or pseudohexagonal symmetry. Birnessite has an hexagonal layer symmetry when octahedral vacancies represent the major source of layer charge deficit (Giovanoli et al. 1970b;[START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]2002b;Gaillot et al. 2003;2005). By contrast, birnessite has an orthogonal layer symmetry when the main source of negative charge in vacancy-free layers is the presence of a high amount of Mn 3+ cations [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF][START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF]Lanson et al. 2002a;Gaillot et al. 2004). In the latter case the layers have a C-centered unit-cell with a > b√3 [START_REF] Burns | The mineralogy and crystal chemistry of deep-sea manganese nodules, a polymetallic resource of the twenty-first century[END_REF][START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF][START_REF] Gorshkov | Natural and synthetic birnessites[END_REF]Drits et al. 1997a[START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b;;Gaillot et al. 2003Gaillot et al. , 2004Gaillot et al. , 2005)). Orthogonal layer symmetry results from the distortion of Mn 3+ -octahedra because of the Jahn-Teller effect (Drits et al. 1997a). In Mn 3+ octahedra, two Mn 3+ -O distances are indeed much longer than the other four. For example, in crednerite CuMnO 2 Mn 3+ -octahedra contain two 2.26 Å and four 1.929Å bond lengths with an average <Mn-O> distance of 2.04 Å (Töpfer et al. 1995). Similar distortions of Mn 3+ -octahedra have been reported by Shannon et al. (1975) for α-MnOOH (2.041 Å -Glasser and Ingram 1968), γ-MnOOH (2.037 Å -Dachs 1963) and α-Mn 2 O 3 (2.039-2.045 Å -Norrestam 1967). The random distribution of Mn 4+ and Mn 3+ cations combined with a random azimutal orientation of the long Mn 3+ -O bonds of the Mn 3+ octahedra would lead to unfavorable steric strains, because of the distortion of Mn 3+ -octahedra. An ordered distribution of Mn 3+ -octahedra all having the same azimutal orientation allows minimizing these strains. According to SAED results, in vacancy-free birnessite layers Mn 3+ are distributed in rows parallel to the b axis and have their long Mn 3+ -O bonds parallel to the a axis (Drits et al. 1997a[START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF]Lanson et al. 2002a;Gaillot et al. 2004). Because of the systematic elongation of Mn 3+ -ocathedra along the a axis and because the four short Mn 3+ -O distances (1.92-1.93 Å) are similar to Mn 4+ -O bond lengths (1.912 Å for λ-MnO 2 ), b parameters are similar (2.83-2.85 Å) in most natural and synthetic birnessite samples regardless of the average valency of the Mn layer [START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF]Chen et al. 1996b;Ching et al. 1997a;Drits et al. 1997a[START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b;;Gaillot et al. 2003Gaillot et al. , 2004Gaillot et al. , 2005)).

The transition from birnessite having layers with hexagonal symmetry to that having pseudo-hexagonal symmetry leads to a modification of symbol notation for the corresponding polytypes. Specifically, hexagonal one-, two-, and three-layer polytypes (1H, 2H 1 , 2H 2 , 3H 1 and 3H 2 ) are changed to the corresponding orthogonal ones (1O, 2O 1 , 2O 2 , 3O 1 and 3O 2 ) whereas 3R 1 and 3R 2 are changed to 1M 1 and 1M 2 monoclinic modifications having -a/3 and +a/3 displacements of adjacent layers along the a axis (Table 1). In 1M 1 and 1M 2 birnessite adjacent layers may be shifted along the a axis by values different from ±0.333a [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF]Lanson et al. 2002b).

Cation composition, interlayer structure, and polytype diversity

The arrangement of adjacent layers in different polytypes, the presence or absence of vacant layer octahedral sites, the nature of interlayer cations, and their local environments are interrelated structural characteristics. Therefore, it is reasonable to define possible interlayer structures for each particular layer stacking and specifically to propose optimum positions for interlayer cations as a function of their ionic radius and valency (Table 2). This approach also relies on existing birnessite structure models [START_REF] Chukhrov | Birnessite characterization[END_REF][START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF]Drits et al. 1997a[START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Drits | Structure of heavy-metal sorbed birnessite: Part 2. Results from electron diffraction[END_REF][START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b;;[START_REF] Manceau | Structure of heavy metal sorbed birnessite. Part III: Results from powder and polarized extended X-ray absorption fine structure spectroscopy[END_REF]Gaillot et al. 2003Gaillot et al. , 2005)). To symbolize positions for interlayer water molecules (H 2 O interlayer ) and cations the capital letters A', B', and C', and corresponding lower case a', b', and c' will be used, respectively.

Polytypes with hexagonal layer symmetry. The presence of layer vacancies allows interlayer cations to share one face with vacant octahedra so as to provide local charge compensation to undersaturated O layer . If birnessite interlayers contain relatively small di-or tri-valent cations, such as Mn 2+,3+ , Co 2+,3+ , Cu 2+ , Ca 2+ , and Mg 2+ , then they are commonly octahedrally coordinated by O layer bound to layer vacancies and H 2 O interlayer . Depending on the layer stacking mode the presence of octahedrally coordinated interlayer cations located above and/or below layer vacancies can give rise to three types of bonding between H 2 O interlayer and the nearest O layer from the adjacent layer. In the first [model 1a (polytype 1H)] strong H-bonds link these species as they form empty prisms with short H 2 O interlayer -O layer distances along the prism edges (2.70-2.75 Å -Fig. 3a). In the second [model 2a (polytype 3R 1 ), model 3a (polytype 3R 2 ), and model 4a (polytype 2H 1 )] O layer and H 2 O interlayer are linked by weak Hbonds as they form empty octahedra with long H 2 O interlayer -O layer distances (3.0-3.15 Å -Fig. 3b). In the third interlayer type [model 5a (polytype 2H 2 ), model 6a [polytype 3H 1 ], and model 7a (polytype 3H 2 )] empty prisms and empty octahedra formed by O layer and H 2 O interlayer coexist within a given interlayer, with prisms located on one side of the interlayer and octahedra on the opposite one (Fig. 3c).

The presence of tetrahedrally coordinated interlayer cations located above and/or below the vacant layer octahedra in model 3b (polytype 3R 2 ) is associated with the formation of strong H-bonds between H 2 O interlayer coordinating the interlayer cations and nearest O layer from the adjacent layer. Both species are superimposed in projection on the ab plane and thus located close to each other (Fig. 3d). The coexistence of both octahedrally and tetrahedrally coordinated interlayer cations in model 5c (polytype 2H 2 ) leads to the formation of empty prisms between the H 2 O interlayer and O layer (strong H-bonds) on one side of the interlayer and to short H 2 O interlayer -O layer distances on the other side (not shown).

On the other hand, if birnessite interlayers contain large mono-or di-valent cations, such as K + , Ba 2+ , Sr 2+ , Cs + , then they will be located in the interlayer mid-plane either in octahedra defined by O layer from adjacent layers [model 5b (polytype 2H 2 ), and model 6b (polytype 3H 1 )] or in interlayer prisms [model 2b (polytype 3R 1 )]. In the latter case, interlayer prisms share one face with a layer octahedron and three edges with occupied octahedra of the adjacent layer. Local charge compensation is achieved when interlayer cations are distributed so that prisms share a face with vacant layer octahedra. Random distribution of interlayer cations leads to electrostatic repulsion with Mn layer despite the presence of layer vacancies. Polytypes with orthogonal layer symmetry. The interlayer cations for vacancy-free layers should have six-fold coordination by O layer and H 2 O interlayer , and distributed so as to avoid direct interaction with Mn layer . The 1O, 2O 2 , 3O 1 , and 3O 2 polytypes are thus not suitable to host large mono-or divalent cations as they cannot avoid such interactions. In contrast, the 1M 2 and 2O 1 polytypes can host these cations in the interlayer mid-plane, with octahedral [model 3e (polytype 1M 2 )], or prismatic [model 4c (polytype 2O 1 ), and model 4e (polytype 2O 1 )] coordinations.

Model 2c (polytype 1M 1 ) represents a special case as interlayer cations cannot be located in a' or b' sites because of the interaction with Mn layer . However, smaller interlayer cations, such as Na + , can be located, together with H 2 O interlayer , in the interlayer mid-plane above and/or below O layer of adjacent layers as was described for Na-rich synthetic birnessite, hereafter referred to as NaBi (Lanson et al. 2002b). Similarly, in Na + -saturated 2O 1 polytype the interlayer cations are likely located above and/or below O layer from adjacent layers (model 4e).

Relatively small di-and tri-valent interlayer cations may be located above and/or below empty layer tetrahedra (tridentate cavities) sharing three edges with layer Mn octahedra Vacancy-free birnessite layers can have hexagonal symmetry if the long Mn 3+ -O bonds of the layer Mn 3+ -octahedra are randomly oriented with respect to the a axis by n60° (Gaillot et al. 2005(Gaillot et al. , 2006a)). Interlayer cations in such birnessite layers should be distributed so as to avoid direct interaction with the nearest Mn layer . In this case, suitable interlayer structures are those described for vacancy-free orthogonal layers (Table 2).

CALCULATION OF XRD PATTERNS

The XRD patterns calculated for polytypes with the same layer symmetry and periodicity along the c* axis have the same d-spacings, but differ by their hkl intensity distributions. Characterization of layer silicates has shown that structures can be approximated by models for polytype identification purpose. The influence of the actual layer structure on the hkl intensity distributions is indeed a second-order effect compared to the differences between polytypes [START_REF] Bailey | Structures of layer silicates[END_REF]. Structure models were thus proposed for each birnessite variety and corresponding powder XRD patterns were calculated. All calculations were performed using the program developed by [START_REF] Plançon | CALCIPOW-a program for calculating the diffraction by disordered lamellar structures[END_REF] on the basis of the formalism described by Drits and Tchoubar (1990). No orientation function was considered, and no random stacking faults were introduced for the calculations.

Initial structure models

In all structure models, Mn layer and O layer occupy special sites in the orthogonal Ccentered unit-cell: (0, 0, 0), (0.333, 0, z) and (-0.333, 0, -z), respectively, where z-coordinates (in projection on the c* axis) were equal to 1.00Å [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF][START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b;;Gaillot et al. 2003Gaillot et al. , 2005)). According to the close-packing notation interlayer cations and H 2 O interlayer also occupy special sites. In the initial structure models, the z-coordinates of the interlayer cations (Me) and H 2 O interlayer are the sole variable parameters. The initial z-coordinates of Me and H 2 O molecules can be estimated from typical Me-O and Me-H 2 O bond lengths for four-and six-fold coordinated Me and from elementary geometrical relationships between these bond lengths and corresponding z-coordinates. For example, if an interlayer cation is octahedrally coordinated above and/or below a vacant layer octahedron, then the following equations are deduced from the hexagonal symmetry of the layer (Lanson et al. 2002b):

∆z ) z(O 3 b O) (Me d ) z(O z(Me) layer 2 2 layer + = - - + = and z 2 ) z(O O) z(H layer 2 ∆ + =
In the present work, Me-O and Me-H 2 O interatomic distances were determined from the effective ionic radii given by Shannon (1976). Where applicable the interlayer atomic positions were adapted from published structural determination of synthetic Na-birnessite (Lanson et al. 2002a), Ca-birnessite [START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF]), H-birnessite [START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF], and K-birnessites (Gaillot et al. 2003(Gaillot et al. , 2005)). In the various structure models K, Ca, Mn, Na, and/or Mg were used as interlayer cations. For the different structure models presented in Table 2, corresponding atomic positions and their occupancies are listed in Table 3.

Calculated XRD patterns

Powder XRD patterns calculated for the different polytypes are shown in Figures 5678, whereas d-values and hkl indices of reflections observed on the various patterns are listed in Table 4. Indexing is performed assuming an orthogonal C-centered cell for both hexagonal and orthogonal birnessite. Reflections in the 36-64° 2θ CuKα range have 20l,11l indices (10l and 01l when using a hexagonal unit-cell), whereas they have 31l,02l indices (11l when using a hexagonal unit-cell) over the 64-75° 2θ CuKα range. The XRD patterns shown in Figure 5 correspond to structure models in which interlayer Mn cations are located above and/or below layer sites and are octahedrally coordinated by O layer and H 2 O interlayer ( VI TC sites -Table 3). The calculated XRD patterns (Figure 5) can be used to identify vacancy-bearing birnessite having one-, two-and three-layer periodicity along the c axis and different layer stacking. However, analysis of the XRD patterns calculated for a given birnessite polytype having different interlayer structures shows that for a given birnessite polytype the intensity of hkl reflections also depends on the chemical nature of interlayer cations, their distribution and local environment. For example, interlayer spaces of 3R 2 polytype (models 4a and 4b) may be occupied by Zn cations having octahedral and/or tetrahedral coordination (Manceau et al. 2000c;[START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002a) ) In contrast, the relative intensity of strong, moderate and weak reflections change very little for the 3R 1 polytype when interlayers are occupied by either K + , Ca 2+ , or Mn 3+ . The only significant change in the MnBi XRD pattern compared to KBi is a strong increase of 201/111 intensity (Figs. 8a-b). For the 2H 1 polytype, a strong increase of 200 and 203 intensities and a limited increase of the 206 one is visible on the XRD pattern calculated for MnBi model compared to KBi (models 4and 4b -Figs. 8c-d)

The calculated XRD patterns show the limited influence of the interlayer structure on the hkl intensity distribution for a given birnessite polytype. The intensity distribution is primarily determined by the polytype (Figs. 678). As a consequence, identification of birnessite polytypes having either hexagonal or C-centered orthogonal (a >b√3) unit cells may be performed without a priori details of their layer and interlayer structures.

DISCUSSION

Criteria for determination of birnessite polytypes

Birnessite polytypes having the same periodicity along the c axis, but with different layer symmetry, differ from each other by the number of hkl reflections. For example, the hexagonal birnessite exhibits a single series of 20l/11l reflections, whereas 20l and 11l series of reflections are individualized for birnessite with an orthogonal layer symmetry. In addition, XRD patterns of hexagonal birnessite usually contains a diagnostic 310/020 reflection (110 when using the hexagonal cell) with d = (1.42 ± 0.01) Å whereas for the orthogonal birnessite this reflection is split with d(310) > d(020) = (1.42 ± 0.01) Å.

Birnessites with similar periodicity and layer symmetry can be differentiated by the intensity distribution of hkl reflections. Figures 9a-b show that hkl reflections with l = 2n are more intense for 2H 1 polytype compared to those of 2H 2 polytype. In contrast, 20l/11l reflections (10l and 01l when using the hexagonal cell) with l = 2n + 1 are significantly stronger for 2H 2 polytype. Similarly, 11l and 20l reflections with l = 2n are stronger than those with l = 2n +1 for the 2O 1 polytype (Fig. 9c). XRD patterns from 3R 1 and 3R 2 polytypes also differ from each other by their intensity distributions among hkl reflections. The 20l/11l reflections with l = 3n -1 (01l with l = 3n -1 ones if using the hexagonal cell) are intense for 3R 1 polytype but not for 3R 2 , whereas 20l/11l reflections with l = 3n + 1 (10l with l = 3n + 1 ones if using the hexagonal cell) are intense for 3R 2 polytype and weak for 3R 1 (Figs. 10a-b). 3H 1 and 3H 2 polytypes differ from 3R 1 and 3R 2 by the presence of 20l/11l reflections with l = 3n (Figs 10c-d). Similarly, intensity of 20l/11l reflections with l = 3n (10l with l = 3n if using the hexagonal cell) is significantly lower for 3H 2 than for 3H 1 (Figs. 10c-d).

The intensity distribution among hkl reflections described above for 3R 1 , 3R 2 , 3H 1 and 3H 2 polytypes remain valid for the equivalent birnessite polytypes with orthogonal layer symmetry (1M 1 , 1M 2 , 3O 1 , 3O 2 ). Special attention should be paid to identify one-(1H and 1O) and two-layer (2H 1 and 2O 1 ) polytypes having the same layer symmetry. The presence of a weak 203/113 reflection is the sole distinguishing feature allowing identification of the two-layer polytypes (Figs. 5a-b). Note that the difference between XRD patterns corresponding to these two polytypes is further reduced when 1H layer pairs are present in the 2H 1 polytype (that is when AbC -AbC pairs are present in crystals dominated by AbC = CbA = AbC… sequences) as the intensity of the 203/113 reflection is significantly decreased by the presence of such 1H layer pairs in a mixed-layered structure (not shown).

Stacking faults

The above described method can be used not only for the identification of birnessite polytypes and also to determine the nature of stacking faults which are typically present in natural and synthetic birnessites. Well-defined and random stacking faults significantly alter XRD patterns from defective layer structures (for definition of well-defined and random stacking faults see Drits and Tchoubar, 1990). Well-defined stacking faults correspond to the interstratification of layer pairs having the same thickness but different internal structure and interlayer displacements within a periodic polytype. As the result of such interstratification, hkl reflections are shifted, and their positions become irrational. [START_REF] Drits | The nature of diffraction effects from illite and illitesmectite consisting of interstratified trans-vacant and cis-vacant 2:1 layers: A semi-Golden[END_REF] have shown that Méring's rules, initially proposed for basal reflections [START_REF] Méring | L'interférence des rayons-X dans les systèmes à stratification désordonnée[END_REF], can be generalized to account for the behavior of hkl reflections from defective layer structures. According to these generalized rules, hkl reflections observed from a defective layer structure are located between neighboring hkl reflections of periodic phases whose fragments (layer pairs in the present case) are interstratified. The actual position of hkl reflections corresponding to the defective layer structure depends on the relative proportion of the structure fragments and on relative intensities of the "involved" hkl reflections of the periodic phases.

For example, Lanson et al. (2002b -Fig. 3) showed that reflections of Zn-sorbed birnessite are located between hkl reflections calculated for 3R 2 and 1H polytypes and hypothesized that the main 3R 2 polytype contained some 1H layer pairs (i.e. AbC -AbC pairs are present in crystals dominated by AbC -BcA -CaB -AbC … sequences). As a result, positions of hkl reflections of the main 3R 2 polytype should indeed be shifted from their ideal position towards those of the defect-free 1H polytype. Accordingly, the best agreement between experimental and calculated XRD patterns was obtained for a defective 3R 2 polytype containing 12% of 1H layer pairs (Lanson et al. 2002b). A similar approach may be applied to mixtures containing periodic and defective birnessites. For example, Figure 11 shows the best possible agreement between an experimental XRD pattern and that calculated for a mixture of four birnessites: a periodic 2H 1 polytype and three defective ones (2O 1 /2H 1 , 2H 1 /3R 1, and 3R 1 /2H 1 ). In the three mixed-layered structures, layer pairs of the 2H 1 polytype are randomly interstratified with those of the 2O 1 and 3R 1 polytypes in proportions 1:1, 7:3, and 1:9, respectively. Note on Figure 11 that each of these mixed-layered structures gives a diagnostic contribution to the calculated XRD pattern (Gaillot et al. 2004).

In our experience, one of the most effective way to study defective birnessite is to combine the above rules for polytype identification and interstratification to build up starting models for XRD pattern calculation [START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF][START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al. , 2002aLanson et al. , 2002b;;Gaillot et al. 2003Gaillot et al. , 2004Gaillot et al. , 2005)). Defective birnessite may contain layer pairs which were not reported so far for natural and synthetic periodic birnessite. Therefore, all theoretically possible birnessite polytypes should be considered to determine the nature of stacking faults XRD by comparing experimental and calculated XRD patterns.

Birnessite polytypes reported for natural and synthetic birnessites

1H Polytype. The first detailed structural study of natural birnessite was performed by Chuckhrov et al. (1985) on monomineralic birnessite micronodules dredged from the oceanic floor. The sample has a one-layer hexagonal unit-cell and its structure corresponds to the 1H ploytype (model 1a) in which interlayer Mn 3+ and Mg 2+ cations are octahedrally coordinated above and/or below vacant layer octahedra. Ca 2+ and Na + cations were also present in the interlayer. This structure model was further supported by X-ray absorption spectroscopy data (Manceau et al. 1992a(Manceau et al. , 1992b)). Analysis of published experimental XRD patterns shows that 1H birnessite dominates in Mn-nodules from ocean and lake floors [START_REF] Burns | The mineralogy and crystal chemistry of deep-sea manganese nodules, a polymetallic resource of the twenty-first century[END_REF][START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF]. This 1H polytype occurs also in soil birnessite (Glover 1977).

Birnessite resulting from the equilibration at low pH of NaBi (obtained according to the Giovanoli protocol -Giovanoli et al. 1970b) was studied by [START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]), Drits et al. (1997a) and in more details by [START_REF] Lanson | Structure of H-exchanged hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]. This proton-rich birnessite, hereafter referred to as HBi, has a one-layer hexagonal unit cell and a structure similar to model 1a. HBi can thus be considered a synthetic analogue of natural 1H birnessite. As natural 1H birnessite, HBi layers contain a significant amount of vacant layer octahedra capped by Mn 2+ and Mn 3+ . The negative layer charge of HBi is compensated for by protons and interlayer Mn cations, and the distribution of layer vacancies is inherited from the ordered Mn 3+ distribution in NaBi. The H 2 O interlayer provides octahedral coordination to Mn interlayer and forms empty prisms, and strong H-bonds, with O layer of the adjacent layer. [START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF] and Lanson et al. (2002b) showed that equilibration of NaBi in the presence of aqueous heavy metals (Co, Cd and Pb) leads also to the formation of the 1H polytype (model 1a). When Zn 2+ is present, the resulting Zn-sorbed synthetic birnessite (ZnBi) has a 3R 2 polytype, in which models 3a and 3b coexist. Interlayer Zn 2+ cations are systematically located above and/or below vacant layer sites but can have both octahedral and tetrahedral coordinations. As a result, H 2 O interlayer providing octahedral (model 3a) and tetrahedral (model 3b) coordination of Zn form weak and strong H-bonds, respectively, with O layer of the adjacent layer.

1M 1 Polytype. Na-rich birnessite synthesized at high pH (Giovanoli et al. 1970a) was first described by [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF] as a one-layer monoclinic polytype (1M 1 polytype, model 2c). To refine the structure they used C2/m space group and the Rietveld technique. However, their results were not precise enough to draw definitive conclusions on the origin of the layer charge. Lanson et al. (2002a) showed that NaBi has a one-layer triclinic unit-cell ( 1 C space group) and consists of vacancy-free layers, the layer negative charge arising from the Mn 3+ -for-Mn 4+ substitution within octahedral layers. The orthogonal layer symmetry results from the Jahn-Teller distortion of Mn 3+ -octahedra which all have their long Mn 3+ -O layer bond oriented along the a axis. Structural sites of interlayer Na and H 2 O, and their occupancies, have also been determined. The triclinic character of NaBi originates from a small layer displacement along the b axis.

NaBi varieties with different monovalent and divalent cations that were exchanged for Na + were studied by [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF], [START_REF] Kuma | Crystal structures of synthetic 7 Å and 10 Å manganates substituted by mono-and divalent cations[END_REF] and [START_REF] Bartoli | Contribution à l'étude structurale des birnessites monocliniques saturées au potassium et au rubidium[END_REF]. XRD patterns of these different birnessites can be indexed with a one-layer monoclinic unit-cell whose parameters depend on the interlayer cation. However, essential details of these birnessites remain poorly understood. For example, Mg 2+ cations in Mg-exchanged birnessite (MgBi) are supposedly located almost above or below octahedral sites [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF]. Such a location is possible for interlayer Mg 2+ cations only if the underlying octahedral sites are vacant, NaBi layers being vacancy-free.

Similarly, [START_REF] Bartoli | Contribution à l'étude structurale des birnessites monocliniques saturées au potassium et au rubidium[END_REF] reported in K-exchanged birnessite the location of K + cations in either a' or b' sites, whereas the presence of K + cations in these sites would lead to their direct interaction with Mn layer from adjacent layers, as can be seen from symbolic notations (Model 2c -Table 2). [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF] reported K + positions in KBi that are shifted from the center of the interlayer prism toward its edges.

Ca 2+ -for-Na + exchange in NaBi dramatically modifies the initial one-layer triclinic structure of NaBi (model 2c) leading to a four-layer polytype in which layer pairs having orthogonal stacking are shifted alternately by ± b/2 along the b axis [START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF]. [START_REF] Gorshkov | Natural and synthetic birnessites[END_REF] described an occurrence of natural Ca-bearing birnessite, which was analogous to the synthetic Ca-exchanged variety of NaBi. 3R 1 Polytype. Chen et al. (1996b) synthesized K-rich birnessite (KBi) with a 3R 1 unitcell (model 2b). The KBi layers contain only Mn 4+ and vacancies. From the refinement of integrated intensities they concluded that both K + and H 2 O interlayer were not located in the prism's centers (a' and b' sites) as in the idealized model 2b but rather in the center of the prism's faces. Gaillot et al. (2005) further refined this structure and showed that interlayer prisms contain three possible K sites, each shifted from the faces of the prism toward its center. Similar positions of interlayer cations were found for Cs + , Ba 2+ and Sr 2+ -exchanged KBi (Gaillot et al. 2006b). The Ca 2+ -for-K + exchange in KBi modifies the initial layer stacking from the 3R 1 polytype (model 2b) to the 1H one (model 1a). The driving force for the KBi-to-CaBi transformation is likely the possibility of forming strong H-bonds between H 2 O interlayer providing octahedral coordination of Ca cations and O layer of the adjacent layer (model 1a). Using mild hydrothermal conditions, Chen et al. (1996a) and Gaillot et al. (2005) synthesized directly Na-rich birnessite (NaBi h ) having a 3R 1 unit-cell. According to these authors, these NaBi h layers consist of Mn 4+ cations and vacant octahedra but positions of interlayer Na + were not determined. 2H 1 Polytype. [START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF] synthesized K-rich birnessite (KBi) from the decomposition of KMnO 4 at temperatures ranging from 200-1000°C. Using the Rietveld technique, these authors showed that KBi obtained at 800°C has two-layer hexagonal symmetry because of the regular alternation of octahedral layers rotated with respect to each other by 180° around the axis passing through layer Mn cations (polytype 2H 1 , model 4b). Gaillot et al. (2003) has shown that the actual structure of KBi obtained at 800°C differs from the model of [START_REF] Kim | Preparation of layered MnO 2 via thermal decomposition of KMnO 4 and its electrochemical characterizations[END_REF] by several important details. First, KBi interlayers have heterogeneous cation composition with the coexistence of both K + and Mn 3+ cations; second, because of the layer-to-interlayer migration of Mn 3+ cations KBi layers contain only Mn 4+ cations and vacant octahedra. Finally, interlayer K + is not located in the prism's center. Rather K + is distributed over three possible sites, each of which being shifted from the center of the prism towards it faces. Thus, the idealized KBi structure corresponds to the coexistence of models 4a and 4b (2H 1 polytype). 2O 1 Polytype. KBi synthesized from the thermal decomposition of KMnO 4 at 1000°C has vacancy-free layers and orthogonal layer symmetry (polytype 2O1, model 5c -Gaillot et al. 2005(polytype 2O1, model 5c -Gaillot et al. , 2006a)). Ambiguously determined polytypes. [START_REF] Kim | Factors controlling the stability of O3and P2-type layered MnO 2 structures and spinel transition tendency in Li secondary batteries[END_REF] used the Rietveld technique to determine structures of synthetic K-Li-rich birnessites (Li-K-Bi) obtained from the thermal decomposition of a Mn-KNO 3 -LiOH mixture at 800°C and 1050°C. They concluded that the 800°C Li-K-Bi has a three layer periodicity and hexagonal symmetry of layers whereas the 1050°C Li-K-Bi has an orthogonal layer symmetry and two-layer periodicity due to an ordered rotation of layers by 180°. However, the description of these structures was rather confusing because of technical errors. In particular, symbolic notations for the structures do not correspond to the proposed structure models. For example, the 1050°C Li-K-Bi is described as AaB a' BbA b' instead of the actual notation given for model 4b (AcB a' BcA).

In addition, unit-cell parameters given for the 1000°C Li-K-Bi are not consistent with the proposed space group. Similarly, interatomic Mn-O distances differ significantly from those expected when heterovalent Mn layer cations coexist within the octahedral layers. These authors also describe the structure of the Li-K-Bi sample synthesized at 800°C as AcB a' CbA c' BaC b' (model 3d, polytype 3R 2 ), with octahedrally coordinated interlayer K + cations. However, atomic coordinates reported for this sample (Table 1 - [START_REF] Kim | Factors controlling the stability of O3and P2-type layered MnO 2 structures and spinel transition tendency in Li secondary batteries[END_REF] correspond to polytype 3R 1 (model 2b) with interlayer K + having prismatic coordination. This latter structure model is consistent with the experimental XRD pattern reported for this sample (Figure 4 - [START_REF] Kim | Factors controlling the stability of O3and P2-type layered MnO 2 structures and spinel transition tendency in Li secondary batteries[END_REF] which is similar to those obtained by Chen et al. (1996a) and Gaillot et al. (2005) from 3R 1 polytypes (model 2b) synthesized under mild hydrothermal conditions. All these experimental patterns are similar to the one displayed on Figure 8a. Turbostratic samples. Finally, one has to note that among different natural environments, and especially in soils, turbostratic birnessite is extremely common. For example, turbostratic birnessite has been reported as resulting from the bacterial oxidation of Mn 2+ by different strains [START_REF] Mandernack | Manganese mineral formation by bacterial spores of the marine Bacillus, strain SG-1: Evidence for the direct oxidation of Mn(II) to Mn(IV)[END_REF][START_REF] Villalobos | Characterization of the manganese oxide produced by Pseudomonas putida strain MnB1[END_REF][START_REF] Jurgensen | The structure of the manganese oxide on the sheath of the bacterium Leptothrix discophora: An XAFS study[END_REF][START_REF] Bargar | Biotic and abiotic products of Mn(II) oxidation by spores of the marine Bacillus sp. strain SG-1[END_REF][START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF]) and from abiotic processes [START_REF] Mandernack | Manganese mineral formation by bacterial spores of the marine Bacillus, strain SG-1: Evidence for the direct oxidation of Mn(II) to Mn(IV)[END_REF]. However, so far there is little unambiguous information derived from XRD data on the structural and crystal chemical of these varieties. Most often the structural characterization of disordered birnessite is limited to the description of 00l peak positions as a function of relative humidity to assess the lamellar character of these "poorly crystalline birnessites". The position of hkl reflections has also been used to hypothesize the actual layer symmetry (and thus the origin of the layer charge of these varieties) however without much experimental support [START_REF] Villalobos | Characterization of the manganese oxide produced by Pseudomonas putida strain MnB1[END_REF][START_REF] Jurgensen | The structure of the manganese oxide on the sheath of the bacterium Leptothrix discophora: An XAFS study[END_REF][START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF]).

However, as described, birnessite having different layer symmetry may be unambiguously distinguished from each other from the shape of their hk bands (Fig. 12). A shoulder, resulting from the individualization of 20 and 11 reflections, is indeed visible on the low-angle side of main maximum of the 20,11 band for orthogonal modifications (at ~2.55 Å and 2.45 Å, respectively -Fig. 12b), whereas this shoulder is logically absent for hexagonal modifications (Fig. 12a). Similarly, the 31,02 band of the orthogonal modifications contains two distinct maxima (~1.474 Å and 1.422 Å -Fig. 12b) which are merged for the hexagonal modifications (peak at ~1.422 Å -Fig. 12a). The features described for the orthogonal modifications are like those reported for the Mn oxides resulting from the oxidation of Mn 2+ by Bacillus sp. strain SG-1 (Fig. 3 in [START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF] indicating the presence of a high proportion of Mn 3+ within the octahedral layers of this birnessite. The presence of Mn 3+ -rich rows in vacancy-free layers, as in NaBi, is also supported by the splitting of the 8 Å -1 feature in the EXAFS spectra (Fig. 5 in [START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF]) which has been described as characteristic of the presence of Mn 3+ -rich rows in the octahedral Mn layer leading to its orthogonal symmetry (Fig. 9 in Gaillot et al. 2003;Fig. 6 in Marcus et al. 2004;Fig. 5 in Manceau et al. 2004;[START_REF] Manceau | Natural speciation of Mn, Ni, and Zn at the micrometer scale in a clayey paddy soil using X-ray fluorescence, absorption, and diffraction[END_REF]). To our knowledge, XRD patterns of all other turbostratic varieties reported so far in the literature correspond to hexagonal modifications.

In addition [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF] demonstrated the high sensitivity of XRD profiles to the layer and interlayer structure of turbostratic phyllomanganates. In their study, [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF] observed contrasting experimental modulations of the 20,11 and 31,02 bands, and successfully reproduced them assuming a turbostratic stacking. In this case, the position and profile of the bands depend essentially on the amount and atomic coordinates of both layer and interlayer species, and these authors were able to determine the amount of vacant layer sites, as well as the amount and coordinates of both "heavy" (Mn 3+,2+ ) and "light" (Na + , K + , H 2 O interlayer ) interlayer species. Such calculations also provided them with an estimate of the lateral extension of the octahedral layers (Drits and Tchoubar 1990;[START_REF] Jurgensen | The structure of the manganese oxide on the sheath of the bacterium Leptothrix discophora: An XAFS study[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF]. The influence of the layer and interlayer structure on calculated profiles for 20,11 and 31,02 bands is illustrated in Figure 13. As compared to the structure model shown in Figure 12a (Model 1a), decreasing both the proportion of interlayer Mn and layer vacancies from 0.167 to 0.075 broadens the lineshape of the 20,11 and smoothes out the scattering dip at ~ 45° 2θ CuKα, thus rendering the calculated hump at ~50-55° 2θ CuKα less pronounced (Fig. 12b). Moving interlayer Mn from the VI TC position dramatically modifies the 20,11 lineshape, as observed when the 0.167 interlayer Mn atoms are located above and/or below the tridentate cavities ( VI TE sites -Fig. 13c). The sensitivity of the 20,11 profile to the position of "light" interlayer species is illustrated next by assuming either the presence of Na + above and/or below O layer [(0.333, 0.0, 0.5) -Fig. 13d] or that of K + above/below the tridentate cavities [Position (-0.222, 0, 05) and equivalent positions -Fig. 13e], H 2 O molecules sitting in both cases above and/or below O layer . In the second case, the 20,11 band is broadened and the "hump" observed at ~50° 2θ CuKα in Figure 13d is both shifted towards higher angles and smoothened out. Similar modulations can however result from the partial ordering of the layer stacking (e.g., Ben [START_REF] Ben Brahim | Layer succession and water molecules arrangement in a homogeneous two-water layer Na-smectite[END_REF]Brahim et al. , 1984;;Drits and Tchoubar 1990;[START_REF] Viani | The nature of disorder in montmorillonite by simulation of X-ray powder patterns[END_REF]. Special attention should thus be paid to the structural interpretation of these modulations, and, in this respect, verifying the structural XRD model with independent data from another structural technique, such as EXAFS spectroscopy, is always warranted. quantitative technique for determination of layer-type content. American Mineralogist, 81, 852-863. Drits, V.A., Petrova, V.V., and [START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF] Manganese minerals of Fe-Mn nodules from the sediments of the central part of Pacific Ocean and their post-sedimentation transformation. Lithology and Raw Materials, 3, 17-39. Drits, V.A., Silvester, E.J., Gorshkov, A.I., and Manceau, A. (1997a) The structure of monoclinic Na-rich birnessite and hexagonal birnessite. Part 1. Results from X-ray diffraction and selected area electron diffraction. American Mineralogist, 82, 946-961. Silvester, E.J., [START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF] The structure of monoclinic Na-rich 1H polytype with Mn 3+,2+ in VI TC position (Model 1a). b) 3R 1 polytype with Mn 3+,2+ in VI TC position (Model 2a). c) 3R 2 polytype with Zn 2+ in VI TC position (Model 3a). d) 2H 1 polytype with Mn 3+,2+ in VI TC position (Model 4a). e) 2H 2 polytype with Mn 3+,2+ in VI TC position (Model 5a). f) 3H 1 polytype with Mn 3+,2+ in VI TC position (Model 6a). g) 3H 2 polytype with Mn 3+,2+ in VI TC position (Model 7a).

XRD patterns were calculated using the idealized structure models described in Table 3. a and b unit-cell parameters for the polytypes having a hexagonal layer symmetry are 4.936 and 2.850 Å, respectively, whereas they are 5.180 and 2.850 Å, respectively, for the polytypes having a orthogonal layer symmetry. In all cases the minimum periodicity along the c* axis is 7.10 Å. All calculations were performed assuming a periodic stacking mode devoid of random stacking faults. The radius of the coherent scattering domains in the ab plane was set to 150 Å for all calculations, whereas the mean extent of the coherent scattering domains perpendicular to the layer plane is 7 layers (maximum extent: 35 layers). The distribution of coherent scattering domain size along the c* axis was assumed to be lognormal (Drits et al. 1997b). The values of Debye-Waller thermal factor (B) were 0.5, 1.0 and 1.5 for Mn layer , O layer and H 2 O interlayer , respectively. B factors for Me interlayer were either 1.0 (metal cations Zn 2+ , Mn 3+,2+ , …) or 2.0 (alkali and alkali-earth cations: K + , Ca 2+ , …).

-AbC … 1H 1 O AbC = CbA = AbC … 2H 1 2O 1 AbC -AcB -AbC … 2H 2 2O 2 AbC = CaB = BcA = AbC … 3R 1 1M 1 AbC -BcA -CaB -AbC … 3R 2 1M 2 AbC -AcB -AcB -AbC … 3H 1 3O 1 AbC -AcB -CaB -AbC … 3H 2 3O 2

  hexagonal unit-cell, with a h = b h ≈ 2.85 Å and γ = 120°, or by an equivalent orthogonal Ccentered cell, with a = √3 b, b h ≈ 2.85 Å and γ = 90°. The orthogonal C-centered cell will be used systematically throughout the current manuscript. The birnessite layer consists of two closely packed anion sheets "sandwiching" Mn cations. The anion close-packing formalism can thus be used to describe the mutual arrangement of birnessite layers. As a first step all possible periodic stackings of birnessite layers with periodicity along the c axis of 1, 2, and 3 layers will be considered. Non-equivalent crystallographic sites of the layer oxygen atoms (O layer ) will be hereafter described with capital letters A, B, and C, whereas positions of the Mn cations will be described with corresponding a, b and c letters (Fig.1). It is systematically assumed that the lower surface of the first birnessite layer is an oxygen sheet in which O layer occupy A sites, that Mn cations fill octahedral b positions, and that the upper surface is formed by O layer in C sites. Such a layer can be symbolically represented as AbC. In the simulation of idealized polytypes, it is assumed that the O layer in the lower sheet of the next birnessite layer in a stack can occupy A, B or C positions. If these O layer are located in C sites,

(

  VI TE sites). The H 2 O interlayer provides octahedral coordination to these cations and may form either empty prisms [model 3d (polytype 1M 2 ) -Fig. 4a] or empty octahedra [model 1b, (polytype 1O), and model 4d (polytype 2O 1 ) -Fig. 4b], with O layer from the adjacent layer. Empty prisms and empty octahedra coexist within a given interlayer [model 5d (polytype 2O 2 )] if interlayer cations are octahedrally coordinated. If interlayer cations have both octahedral and tetrahedral coordination then H 2 O interlayer and O layer in model 5e (polytype 2O 2 ) form empty prisms and strong H-bonds on either side of a given interlayer.

  and located in TC sites or TE sites. The replacement of tetrahedrally for octahedrally coordinated Zn cations leads to a significant decrease of 204/114, 208/118 and 20.10/11.10 peak intensity (104, 018 and 10.10 assuming a hexagonal cell), with respect to the strongest 20l/11l reflections (Figs. 6a-b). Location of Zn cations in IV TE sites [model 3c (polytype 3R 2 ) -Fig. 6c] strongly increases the 204/114 and 207/117 reflection intensities, with respect to 201/111. Important redistribution of intensities is observed also for the 2O 1 and 1M 2 polytypes when interlayers are occupied either by large K + (models 4c and 3e) or by smaller Ca 2+ (models 4d and 3d). The transition from model 3e to model 3d significantly increases 201, 110, 112, 203 and 11-2 and decreases the 111 and 113 intensities (Figs. 7a-b). Similarly, the transition from model 4c to 4d is accompanied by redistribution of the 112 and 114 maxima: strong 112 and moderate 114 peaks for model 4c are replaced by strong 114 and moderate 112 ones for model 4d (Figs. 7c-d).

  Drits, V.A., Srodon, J., and Eberl, D.D. (1997b) XRD measurement of mean crystallite tickness of illite and illite/smectite : Reappraisal of the Kubler index and the Scherrer equation.Clays and Clay Minerals, 45, 461-475. Drits, V.A. and Tchoubar, C. (1990) X-ray diffraction by disordered lamellar structures:Theory and applications to microdivided silicates and carbons, 371 p. Springer-Verlag, Berlin.Feng, Q.,Kanoh, H., Miyai, Y., and Ooi, K. (1995) Hydrothermal synthesis of lithium and sodium manganese oxides and their metal ion extraction/insertion reactions.Chemistry ofMaterials, 7, 1226-1232. Feng, Q., Sun, E.H., Yanagisawa, K., and Yamasaki, N. (1997a) Synthesis of birnessite-type sodium manganese oxides by solution reaction and hydrothermal methods. Journal of the Ceramic Society of Japan, 105, 564-568. Feng, Q., Yanagisawa, K., and Yamasaki, N. (1997b) Synthesis of birnessite-type potassium manganese oxide. Journal of Materials Science Letters, 16, 110-112. Gaillot, A.-C., Drits, V.A., Lanson, B., and Manceau, A. (2006a) Structure of synthetic K-rich birnessite obtained by high-temperature decomposition of KMnO4. Structure of a two-layer polytype from 1000°C experiments. Microporous and Mesoporous Materials, submitted. Gaillot, A.-C., Drits, V.A., Plancon, A., and Lanson, B. (2004) Structure of synthetic K-rich birnessites obtained by high-temperature decomposition of KMnO 4 . 2. Phase and structural heterogeneities. Chemistry of Materials, 16, 1890-1905. Gaillot, A.-C., Flot, D., Drits, V.A., Manceau, A., Burghammer, M., and Lanson, B. (2003) Structure of synthetic K-rich birnessite obtained by high-temperature decomposition of KMnO 4 . I. Two-layer polytype from 800 degrees C experiment. Chemistry of Materials, 15, 4666-4678. Gaillot, A.-C., Lanson, B., and Drits, V.A. (2005) Structure of birnessite obtained from decomposition of permanganate under soft hydrothermal conditions. 1. Chemical and structural evolution as a function of temperature. Chemistry of Materials, 17, 2959-2975. -. (2006b) Structure of birnessite obtained from decomposition of permanganate under soft hydrothermal conditions. 2. Variation of the structure as a function of the nature of the interlayer cation. Chemistry of Materials, in preparation. Giovanoli, R., Stähli, E., and Feitknecht, W. (1970a) Über Oxidhydroxide des vierwertigen Mangans mit Schichtengitter. 1. Mitteilung: Natriummangan(II,III)manganat(IV). Helvetica Chimica Acta, 53, 209-220. -. (1970b) Über Oxidhydroxide des vierwertigen Mangans mit Schichtengitter. 2. Mitteilung: Mangan(III)-manganat(IV). Helvetica Chimica Acta, 53, 453-464. Glasser, L.S.D. and Ingram, L. (1968) Refinement of the crystal structure of Groutite, α-MnOOH. Acta Crystallographica, B24, 1233-1236. Glover, E.D. (1977) Characterization of a marine birnessite. American Mineralogist, 62, 278-285. Shannon, R.D. (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica, A32, 751-767. Shannon, R.D., Gumeman, P.S., and Chenavas, J. (1975) Effect of octahedral distortion on mean Mn 3+ -O distances. American Mineralogist, 60, 714-716.

  birnessite and hexagonal birnessite. Part 2. Results from Chemical Studies and EXAFS Spectroscopy. American Mineralogist, 82, 962-978. Stone, A.T., Godtfredsen, K.L., and Deng, B. (1994) Sources and reactivity of reductant encountered in aquatic environments. In G. Bidoglio, and W. Stumm, Eds., Chemistry of aquatic systems: Local and global perspectives, p. 337-374. ECSC, EEC, EAEC, Brussels. Tebo, B.M., Bargar, J.R., Clement, B.G., Dick, G.J., Murray, K.J., Parker, D., Verity, R., and Webb, S.M. (2004) Biogenic manganese oxides: Properties and mechanisms of formation. Annual Review of Earth and Planetary Sciences, 32, 287-328. Tebo, B.M. and He, L.M. (1999) Microbially mediated oxidative precipitation reactions. In D.L. Sparks, and T.J. Grundl, Eds., Mineral-water interfacial reactions, 715, p. 393-414. American Chemical Society, Washington, D.C. Töpfer, J., Trari, M., Gravereau, P., Chaminade, J.P., and Doumerc, J.P. (1995) Crystal growth and reinvestigation of the crystal structure of crednerite, CuMnO 2 . Zeitschrift für Kristallographie, 210, 184-187. Tsuji, M., Komarneni, S., Tamaura, Y., and Abe, M. (1992) Cation exchange properties of a layered manganic acid. Materials Research Bulletin, 27, 741-751. Tu, S., Racz, G.J., and Goh, T.B. (1994) Transformations of synthetic birnessite as affected by pH and manganese concentration. Clays & Clay Minerals, 42, 321-330.

FIGURE CAPTIONS FIGURE 1 .

 CAPTIONS1 FIGURE CAPTIONS

FIGURE 2 .

 2 FIGURE 2. Idealized structure model of birnessite polytypes in projection along the b axis. a)

FIGURE 3 .

 3 FIGURE 3. Idealized interlayer structure model in projection along the b axis for birnessite

FIGURE 4 .

 4 FIGURE 4. Idealized interlayer structure model in projection along the b axis for birnessite

FIGURE 5 .

 5 FIGURE 5. XRD patterns calculated for idealized structure models of birnessite polytypes. a)

FIGURE 6 .

 6 FIGURE 6. XRD patterns calculated for idealized structure models of birnessite 3R 2 polytype. a) With Zn 2+ in IV TC position (Model 3b). b) With Zn 2+ in VI TC position (Model 3a). c) With Zn 2+ in IV TE position (Model 3c).

FIGURE 7 .

 7 FIGURE 7. XRD patterns calculated for idealized structure models of birnessite polytypes. a) 1M 2 polytype with K + in the interlayer mid-plane (Model 3e). b) 1M 2 polytype with Ca 2+ in VI TE sites (Model 3d). c) 2O 1 polytype with K + in the interlayer mid-plane (Model 4c). d) 2O 1 polytype with Ca 2+ in VI TE sites (Model 4d).

FIGURE 8 .

 8 FIGURE 8. XRD patterns calculated for idealized structure models of birnessite polytypes. a) 3R 1 polytype with K + in the interlayer mid-plane (Model 2b). b) 3R 1 polytype with Mn 3+,2+ in VI TC position (Model 2a). c) 2H 1 polytype with K + in the interlayer midplane (Model 4b). d) 2H 1 polytype with Mn 3+,2+ in VI TC position (Model 4a).

FIGURE 9 .

 9 FIGURE 9. XRD patterns calculated for idealized structure models of birnessite polytypes. a) 2H 2 polytype with Mn 3+,2+ in VI TC position (Model 5a). b) 2H 1 polytype with Mn 3+,2+in VI TC position (Model 4a). c) 2O 1 polytype with K + in the interlayer mid-plane

FIGURE 10 .

 10 FIGURE 10. XRD patterns calculated for idealized structure models of birnessite polytypes. a) 3R 1 polytype with K + in the interlayer mid-plane (Model 2b). b) 3R 2 polytype with Zn 2+ in VI TC position (Model 3a). c) 3H 1 polytype with Mn 3+,2+ in VI TC position (Model 6a). d) 3H 2 polytype with Mn 3+,2+ in VI TC position (Model 7a).

FIGURE 11 .

 11 FIGURE 11. Comparison between experimental and calculated XRD patterns for a K-rich

FIGURE 12 .

 12 FIGURE 12. XRD patterns calculated for idealized structure models of turbostratic birnessite. a) Birnessite with Mn 3+,2+ in VI TC position (Model 1a). b) Birnessite with 0.67 Na +

FIGURE 13 .

 13 FIGURE 13. XRD patterns calculated for idealized structure models of turbostratic birnessite

Table 2

 2 lists birnessite polytypes consisting of hexagonal vacancy-bearing layers that differ from each other by stacking modes and interlayer structures, which are reasonable from a crystal chemical point of view.

Table 1 .

 1 List of possible periodic layer stacking modes in birnessite consisting of hexagonal (vacancy-bearing) or orthogonal (vacancy-free) layers

	Layer stacking	Hexagonal layers Orthogonal layers
	AbC

Table 2 .

 2 Symbolic notations of birnessite consisting of hexagonal (vacancy-bearing) and orthogonal (vacancy-free) layers and differing from each other by stacking modes and interlayer structures.

	Hexagonal layer symmetry

Table 3 .

 3 (continued).

	Model		6a	7a
	Polytype		3H 1	3 H 2
	XRD	Fig.	5f, 10c	5g
	pattern
	Mn layer	x a y a	0 0	0 0
		ζ b	0	0
		occ	0.833	0.833
	O layer	x a y a	+/-0.333 0	+/-0.333 0
		ζ b	+/-1.00	+/-1.00
		occ	2	2
	Cat. Inter.	Type	Mn	Mn
		x a	0	0
		y a	0	0
		ζ b	+/-2.15	+/-2.15
		occ	0.0833 x2	0.0833 x2
	H 2 O c	x a y a	-/+0.333 0	-/+0.333 0
		ζ b	+/-3.35	+/-3.35
		occ	0.250 x2	0.250 x2
	Mn layer	x a y a	0.333 0	0.333 0
		ζ b	7.10	7.10
		occ	0.833	0.833
	O layer	x a y a	-0.333/0.000 0	-0.333/0.000 0
		ζ b	6.10/8.10	6.10/8.10
		occ	2	2
	Cat. Inter.	Type	Mn	Mn
		x a	0.333	0.333
		y a	0	0
		ζ b	4.95/9.25	4.95/9.25
		occ	0.0833 x2	0.0833 x2
	H 2 O c	x a y a	0.000/-0.333 0	0.000/-0.333 0
		ζ b	3.75/10.45	3.75/10.45
		occ	0.250 x2	0.250 x2
	Mn layer	x a y a	0.333 0	-0.333 0
		ζ b	14.20	14.20
		occ	0.833	0.833
	O layer	x a y a	-0.333/0.000 0	0.333/0.000 0
		ζ b	13.20/15.20	13.20/15.20
		occ	2	2
	Cat. Inter.	Type	Mn	Mn
		x a	0.333	-0.333
		y a	0	0
		ζ b	12.05/16.35	12.05/16.35
		occ	0.0833 x2	0.0833 x2
	H 2 O c	x a y a	0.000/-0.333 0	0.000/0.333 0
		ζ b	10.85/17.55	10.85/17.55
		occ	0.250 x2	0.250 x2
	Int. shift		0	0

Table 4A .

 4A Calculated d(hkl) values for birnessite polytypes consisting of vacancy-bearing layers having a hexagonal layer symmetry (See Table1). Notes: a and b unit-cell parameters are 4.936, and 2.850 Å, respectively. The minimum periodicity along the c* axis is 7.10 Å for all polytypes.

	Polytype	1H	2 H	3 R/3H
	d(hkl)	hkl	hkl	hkl
	2.468	200,110	200,110	200,110
	2.452	-	-	201,111
	2.432	-	201,111	-
	2.404	-	-	202,112
	2.331	201,111	202,112	203,113
	2.239	-	-	204,114
	2.188	-	203,113	-
	2.136	-	-	205,115
	2.026	202,112	204,114	206,116
	1.917	-	-	207,117
	1.863		205,115	-
	1.810	-	-	208,118
	1.708	203,113	206,116	209,119
	1.613	-	-	20.10,11.10
	1.567		207,117	-
	1.523	-	-	20.11,11.11
	1.441	204,114	208,118	20.12,11.12
	1.425	020,310	020,310	020,310
	1.422	-	-	021,311
	1.418	-	021,311	-
	1.412	-	-	022,312
	1.397	021,311	022,312	023,313
	1.376	-	-	024,314
	1.365	-	-	20.13,11.13
	1.364	-	023,313	-
	1.351	-	-	025,315
	1.329	-	209,119	-
	1.322	022,312	024,314	026,316
	1.295	-	-	20.14, 11.14
	1.290	-	-	027,317
	1.274	-	025,315	-
	1.256	-	-	028,318
	1.231	-	20.10,11.10	20.15,11.15
	1.221	023,313	026,316	029,319

Table 4B .

 4B Calculated d(hkl) values for birnessite polytypes consisting of vacancy-free layers having an orthogonal layer symmetry (See Table1)

	Polytype	1O	1 M 1	1 M 2	2 O 1 /2O 2
	d(hkl)	Hkl	hkl	Hkl	hkl
	2.590	200			200

203/113 -2.331 Å 206/116 -2.026 Å 209/119 -1.708 Å 205/115 -2.136 Å 20.11/11.11 -1.523 Å 20.12/11.12 -1.441 Å 3R 1 -mod 2b 3R 2 -mod 3a 3H 1 -mod 6a

	c 2.404 Å 2.452 Å b a a a	2.331 Å 2.239 Å 204/114 -2.239 Å 2.136 Å 205/115 -2.136 Å 11-1 -2.261 Å 202 -2.329 Å 202/112 -2.404 Å 201/111 -2.452 Å 2.468 Å 201/111 -2.452 Å 201 -2.571 Å 204/114 -2.239 Å 202/112 -2.404 Å	2.026 Å	1.917 Å 207/117 -1.917 Å 207/117 -1.917 Å	1.810 Å 208/118 -1.810 Å 208/118 -1.810 Å	1.708 Å	1.613 Å 20.10/11.10 -1.613 Å 20.10/11.10 -1.613 Å	1.425 Å 1.523 Å 20.11/11.11 -1.523 Å	1.441 Å	1.397 Å 020/310 -1.425 Å 023/313 -1.397 Å	1.365 Å	1.256 Å 3R 2 -mod 3b 3R 2 -mod 3a 1.231 Å 1.221 Å 3R 1 -mod 2a 1H -mod 1a 1M 2 -mod 3e 020/310 -1.425 Å 1.322 Å 1.295 Å 023/313 -1.397 Å
	2.188 Å 2.432 Å d b		112 -2.356 Å			1.863 Å							1M 2 -mod 3d 2H 1 -mod 4a 3R 2 -mod 3a
	e b												2H 2 -mod 5a 2O 1 -mod 4c
	c
	f												3H 1 -mod 6a
	g c d												3H 2 -mod 7a 3R 2 -mod 3c 2O 1 -mod 4d
	30 30 30	35 35 35	40 40 40	45 45 45		50 50 50		55 55 55	60 60 60	65 65 65		70 70 70	75 75 75	80 80 80
					Position (°2θ CuKα) Position (°2θ CuKα) Position (°2θ CuKα)
													Drits et al. Fig. 05 Drits et al. Fig. 06

Identification of birnessite polytypes

ACKNOWLEDGMENTS

VAD is grateful to the Environmental Geochemistry Group of the LGIT (Grenoble, France) and to the Russian Science Foundation for financial support. VAD and BL acknowledge financial support from CNRS/PICS709 program. The manuscript greatly benefited from the remarks of two anonymous reviewers and from the editorial assistance of AE Laurence Garvie.


Ben Kawther

Mabrouk

Thomas H Kauffmann

Hassen Aroui

Marc D Fontana

Raman study of cation effect on sulfate vibration modes in solid state and in aqueous solutions

Keywords: sulfates, cation dependence, calibration, Raman study

Raman spectra of potassium, sodium, and ammonium sulfates (K2SO4, Na2SO4, and (NH4)2SO4) are reported and analyzed. These sulfates have been investigated under two states: solid (anhydrous and hydrated) salts and aqueous solutions. The effects of monovalent ions (K + , Na + , and NH4 + ) and hydration on the position of Raman lines assigned to internal vibrations of sulfate anion SO4 2-are discussed. In solid salts, the line position of each Raman peak is shown to decrease with increasing radius of the cation. The main ν1 mode of sulfate molecule is particularly affected. It is emphasized that this sensitivity in solid sulfates vanishes in aqueous solutions. As a consequence, this mode can be probed by Raman spectroscopy as the main signature of SO4 2-to determine its concentration within a single calibration.

Introduction

Sulfates correspond to a wide family of salts, which are present under different states and compositions in ground, air, and wateron Earth and on Mars as well. Sodium sulfate is used for manufacture of paper and glass and is employed as food additive and detergent while potassium sulfate is a fertilizer. They can befound as anhydrous or hydrated minerals or dissolved insolutions. Their detection and identification are very important in the environment to reveal the source of pollution [START_REF]Health effects from exposure to high levels of sulfate in drinkingwater study, Office of Drinking Water and Ground Water[END_REF] and in geology to study the origin of various physical and chemical transformations. In addition, a variety of sulfates have been identified on Mars through different missions, [START_REF] Bishop | [END_REF] and the hydration states of Mg, Ca, and Fe sulfates are of prime importance for the knowledge of the hydrologic history of Mars. Moreover, Raman spectroscopy measurements are motivated by structural studies, and this technique was shown to be powerful for these investigations, [3] in particular for the comparison between ligated and unligated sulfates. In the first family such as MgSO 4 and Al 2 (SO 4 ) 3 , [4][5][6][7] metal-ligand vibrations were detected in the Raman spectrum, whereas in other sulfates such as Na 2 SO 4 , K 2 SO 4 , and (NH 4 ) 2 SO 4 , solely modes corresponding to the 'free' molecule SO 4 2-were observed in the spectrum. In the second family, it was therefore assumed that the cation has only an indirect effect on vibration modes. In this work, we are interested to analyze this influence in solids and inaqueous solutions.

Numerous Raman studies of sulfates have been undertaken. Recently, Maubec et al. [8] have studied the molecular structure of different minerals of the alunite supergroup. They have reported on the effect of ionic substitutions on the Raman band positions of different vibrations. They showed that the sulfate environment is barely affected by the nature of the cations.

Frost et al. [9] have reported that the peak position of the sulfate band varies with the mineral and that the SO 4 2-symmetric stretching band position increases with increasing hydrogen bond strength.

In the present work, we are interested to Na 2 SO 4 , K 2 SO 4 , and (NH 4 ) 2 SO 4 , under usual conditions (i.e., at room temperature and atmospheric pressure). The influences of cation and water molecule on Raman spectra have been studied, and we successively investigated measurements in unhydrated andhydrated solids, and then solutions of the same compounds. We report and analyze the shift of any band assigned to sulfate anion. It is pointed out that all lines are sensitive to the nature of the cation, but the main line position (ν 1 mode) of SO 4 2-becomes independent of the cation in aqueous solutions, so that this mode can be used to detect the presence of sulfate salts in water and to determine their concentrations, within only one calibration.

Vibration modes of SO 4 2-

According to the T d symmetry of the free anion SO 4 2-, nine modes of internal vibrations of the molecule corresponding to the irreducible representations as A 1 + E + 2F 2 are expected. All modes are Raman active, but only the F 2 modes are infrared active. The ν 1 (A 1 ) is the symmetric stretching mode, ν 2 (E) and ν 4 (F 2 ) modes correspond to the bending vibration, and ν 3 (F 2 ) is an anti-symmetric stretching mode. Figure S1 illustrates the Raman normal modes of this anion.

Line positions depend on the nature of cation as well as environment conditions such as temperature or pressure. The number of lines is defined by the structure of the peculiar sulfate and its state. Then, a symmetry lowering and thus the degeneracy lifting are expected when going from the free molecule corresponding to the sulfate dissolved in water or to the lattice of the solid salt.

For solid sodium sulfate, we give in Table S1 the correlation between the symmetry of the free molecule, its site symmetry in the lattice and the crystal symmetry group. It should be underlined that in the context of our paper, Raman data of various sulfates are compared regardless the substance symmetry. We will refer hereafter to the labels ν 1 , ν 2 , ν 3 , ν 4 of the vibration modes of the 'free' molecule, even in the case of degeneracy lifting of the corresponding lines due to symmetry lowering.

Results and discussion

Experimental conditions

Potassium, sodium, and ammonium sulfate samples used in this work are commercially obtained from Roth with purity higher than 99.9%. Aqueous solutions were prepared by weight.

Spectra were recorded at room temperature (25°C) using a Raman spectrometer RXN-1 from Kaiser Optical System. The spectrometer is equipped with a visible 532 nm laser (Invictus) configured as standard for fiber coupling with FC connectors. The laser beam was brought to the sample through a specific probe with an excitation fiber of 62.5 μm. The m. The laser light is focused on the sample contained in a quartz cell using a 50× long working-distance objective (Olympus) at about 8 mm with a laser power of 71 mW. The Raman light was collected by the same objective in backscattering configuration filtered by a Notch filter and brought through a 100 μm. The m core fiber to the double holographic grating. The scattered light was detected by a charge-coupled device camera of 1024 × 256 pixels cooled using a Peltier device to 40°C. Spectra were recorded over the 150-4300 cm -1 wavenumber range with a spectral resolution of 1 cm -1 .

Spectra analysis of anhydrous sulfates

In Fig. 1 is shown the Raman spectrum of solid sodium sulfate (Na 2 SO 4 ). The main peak corresponds to the ν 1 (A 1 ) mode centered at 992 cm -1 . The ν 2 , ν 4 , and ν 3 modes are detected in the low-wavenumber and in the high-wavenumber sides, respectively. The lifting of triply and doubly degenerate modesof the SO 4 2-ion is clearly seen in the spectrum, as expected by the symmetry lowering according to Table S1. Table S1. Correlation between molecular symmetry, site symmetry and factor group symmetry for SO4 2-vibrations.

Raman spectra recorded in solid ammonium, sodium, and potassium sulfates are compared in Fig. 2. The spectra show some similarities, regardless of the nature of the cation. The ν 2 mode is centered at about 449 cm -1 , the ν 4 mode is between 610-650 cm -1 , then the very intense peak ν 1 is lying in the wavenumber range 970-995 cm -1 , and finally, the triplet ν 3 occurs between 1100 and 1160 cm -1 . Wavenumbers and assignments of lines corresponding to internal vibrations of SO 4 2-are listed in Table 1 and are in good agreement with previous works. [10][11][12][START_REF] Nakamoto | Infrared and Raman Spectra of Inorganic and Coordination Compounds[END_REF][START_REF] Shannon | [END_REF] In this table, we have listed for each sulfate the assignment modes and the measured wavenumbers. The Raman lines are more resolved in the Na sulfate and are more broadened and shifted to lower wavenumber when going to the K-compound and then to NH 4 -compound. The doublet ν 2 and triplet ν 4 appear less resolved in potassium and ammonium sulfates than in sodium compound. Then, deconvolution using 'fityk' software and a Voigt profile of these peaks is necessary to extract the different components of these bands. Figure 3 shows the deconvolution of the ν 2 mode into two component bands. As seen in Table 1 and Fig. 4, the wavenumber of each SO 4 2-vibration exhibits a remarkable decrease when passing from the sodium sulfate to the potassium sulfate and then to the ammonium compound. According to Maubec et al., [8] this shift can be related to the differences of the polarizing power of cations. Because the polarizing power is defined as Z/r 2 , where Z is the ion charge and r the radius, the wavenumber decreasesas the polarizing power decreases. -measured in solid sulfates and the radius of cation. [START_REF] Shannon | [END_REF]

Sodium sulfate in solid state and in aqueous solution

In Fig. 5, we compare the Raman spectra of hydrated andanhydrous sulfate (Na 2 SO 4 .10H 2 O and Na 2 SO 4 ). The incorporation of H 2 O leads to the broadening and to the downshift of all SO 4 2-lines. In Fig. 5(a), the components of the doubly and triply degenerate ν 2 , ν 3 , and ν 4 vibration modes are clearly discernible in the Raman spectrum of the dry Na 2 SO 4 . As seen in Fig. 5(b), for hydrated sulfate, these modes are not resolved. A Voigt deconvolution model has been achieved to extract the wavenumber components of these modes (listed in Table 1 and this figure). The decrease of the wavenumber of each SO 4 2-mode when the sodium sulfate is hydrated (Table 1) is probably related to the increase of interatomic distances due to the presence of OH groups. As a result, the polarizing power of the cation decreases to induce the decrease of sulfate wavenumbers. In Fig. 6 are compared the Raman spectra recorded for hydrated and aqueous solution of sodium sulfate. The characteristic OH vibrations, as the bending mode at about 1633 cm -1 and the stretching mode from 2800 to 3800 cm -1 , are obviously more resolved in the solution. When compared with results obtained for solid sulfates (Table 1 and Fig. 2), the broadening and the downshift of all lines are still enhanced when going from the hydrated crystal to the solution of the same compound. In addition, it should be mentioned that inaqueous solutions, the bands correspond to the free SO 4 2- (symmetry T d ) and degenerate modes (ν 2 , ν 3 , and ν 4 ), contrary to the situation of anhydrous and hydrated solids, in which the degeneracy is lifted by symmetry (according to Table S1).

Behavior of the ν 1 mode in solid and liquid sulfates

In this part, we focus our attention to the ν 1 Raman line of sulfate anion and its sensitivity to the cation type and the presence of water. This mode is well resolved and is very intense in all Raman sulfate spectra. Figure 7(a) shows the relative change according to the state (anhydrous, hydrated, and aqueous solution) of sodium sulfate. In addition to the downshift mentioned previously, the ν 1 mode exhibits a linewidth increasing from the solid to the liquid state (7.6 to 10.4 cm -1 ), which can be attributed to structure disordering, which increases from solid to liquid state. In Fig. 7(b) is plotted the ν 1 peak recorded in various aqueous solutions of Na, K, and NH 4 sulfates. Ammonium spectra recorded at a series of three molarities (0.15, 0.37, and 0.57 mol.l -1 ) illustrate a clear increase of linewidth and integrated intensity with increasing molarity. As seen by this figure, this peak has remarkably the same position in all solutions regardless of the nature of the cation and the SO 4 2-concentration. Compared to solid sulfates, this cation invariance is in contrast with the line position dependences reported in Figs 2 and 7(a). Using the same experimental technique, Rull et al. [15] reported the changes at room temperature of the main Raman internal mode ν 1 of SO 4 2-as function of concentration in several alkali sulfate aqueous solutions. The ν 1 mode position was shown to shift weakly within 2 cm -1 when different dissolved salts are considered. More recently, Matsumoto et al. [16] have performed a similar study in alkali and ammonium sulfate solutions, as function of the temperature, under a pressure of 25 MPa. The cation effect on the main Raman ν 1 mode clearly appeared at high temperature (350°C). Nevertheless, their data are consistent with our results, when considering the room temperature and the same molarities range.

Sulfate calibration

As it is proportional to the concentration, [START_REF] Lewis | Handbook of Raman Spectroscopy[END_REF] Raman intensity is sometimes used to determine the concentration of a substance. This requires at first a suitable calibration of the substance content. Here, thanks to the remarkable property of ν 1 mode inaqueous solutions, a single calibration for all sulfates under study can be achieved. This calibration is illustrated by Fig. 8 for different sulfate solutions with varying dilution. The Raman intensities determined here are in fact integrated over the whole wavenumber range 960-1000 cm -1 covered by the ν 1 mode, and after their normalization by the corresponding intensity of the OH-bending band. This normalization insures that the quantity used in the Raman spectrum -here the integrated intensity -is unaffected by any change in experimental conditions. The integrated intensity is obtained within a precision of 6% estimated as the standard deviation from six samples with the same concentration.

The regression coefficient r 2 of the calibration curve (Fig. 8), equal to 0.992, demonstrates that the same calibration is valid for the three substances Na 2 SO 4 , K 2 SO 4 , and (NH 4 ) 2 SO 4 . Within these conditions our results can be used to probe dissolved sulfates and to determine their concentration in water using Raman sensor. In addition, using the cation dependence of ν 1 mode, one can distinguish between sulfates after drying.

Conclusion

Raman spectra of anhydrous and hydrated sodium, potassium, and ammonium sulfates were reported and compared. The positions of Raman lines attributed to different internal SO 4 2-vibrations in solid sulfates are tabulated, and their shift is attributed to the indirect effect related to the size of cation radius. The hydration gives rise to a similar shift of Raman lines. The cation dependence vanishes when the sulfate is dissolved in water. Then, the Raman spectrum has the same profile in different sulfates regardless of the nature of the cation. Different promising applications in geochemistry and environment can be derived from this study. A Raman sensor could be used to unambiguously identify different sulfate minerals and to distinguish between hydrated and anhydrous states of the same sulfate. Moreover, the intensity of the main Raman peak can be exploited to determine the concentration of sulfate in aqueous solution via a single calibration.

Figure 1 .

 1 Figure 1. The Raman spectrum of solid Na2SO4: (a) 300-700 cm -1 range showing ν2 and ν4 modes and (b) 1060-1200 cm -1 range including ν3 mode.

Figure 2 .

 2 Figure 2. Raman spectra of solid sodium, potassium, and ammonium sulfates within the 200-1200 cm -1 range.

Figure 3 .

 3 Figure 3. Deconvolution of the ν2 mode of SO4 2-into two component bands for the potassium sulfate.

Figure 4 .

 4 Figure 4. Correlation between Raman band positions of SO42-measured in solid sulfates and the radius of cation.[START_REF] Shannon | [END_REF]

Figure 5 .

 5 Figure 5. Raman spectra of (a) anhydrous and (b) hydrated sodium sulfate at 300-1200 cm -1 range.

Figure 6 .

 6 Figure 6. Raman spectra of hydrated sodium sulfate and aqueous solution (0.7 mol.l -1 ) showing the OH bands. The bending band at 1633 cm -1 and the strecthing band in the region 2800-3800 cm -1 .

Figure 7 .

 7 Figure 7. (a) The ν1 mode for anhydrous, hydrated, and the aqueous solution of Na2SO4. (b) The ν1 mode for ammonium, potassium, and sodium sulfate aqueous solutions. For the three sulfates, the three largest peaks correspond to the same weight content of salt in water (100 g.l -1 ) but to notably different molarities.

Figure 8 .

 8 Figure 8. Calibration of peak area (intergrated intensity) of the Raman line ν1 of SO4 2-with the concentration in mol.l -1 .

Table 1 .

 1 Raman bands of various solid sulfates and their assignments to the internal vibrations of SO4 2-.

		Band position (cm -1 )		Assignments
	Na2SO4	K2SO4	(NH4)2SO4	Na2SO4,10H2O
	449	449	449	439
	466	454	451	451
	620	619	613	613
	632	627	624	619	ν4(E)F2)
	647	631	629	642
	992	983	975	988	ν1(E)A1)
	1101	1092	1064	1083
	1131	1106	1083	1113	ν3(E)F2)
	1152	1145	1091	1131

ν2(E)E))

  [START_REF] Bishop | [END_REF]