aDivision of Materials Science and Engineering, Nanyang Technological University, Singapore, bLaboratoire de Minéralogie et Cosmochimie du Muséum National d'Histoire Naturelle, UMR-CNRS 7202, CP52, 61 Rue Buffon, 75005 Paris, France, cChemical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH, England, dISIS User Office, Building R3, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 OQX, England, and eCentre for Advanced Microscopy, Australian National University, Canberra, ACT 2601, Australia
*Correspondence e-mail: firstname.lastname@example.org
Certain complex structures are logically regarded as intergrowths of chemically or topologically discrete modules. When the proportions of these components vary systematically a polysomatic series is created, whose construction provides a basis for understanding defects, symmetry alternation and trends in physical properties. Here, we describe the polysomatic family A5NB3NO9N + 6XNδ (2 ≤ N ≤ ∞) that is built by condensing N apatite modules (A5B3O18Xδ) in configurations to create BnO3n + 1 (1 ≤ n ≤ ∞) tetrahedral chains. Hydroxyapatite [Ca10(PO4)6(OH)2] typifies a widely studied polysome where N = 2 and the tetrahedra are isolated in A10(BO4)6X2 compounds, but N = 3 A15(B2O7)3(BO4)3X3 (ganomalite) and N = 4 A20(B2O7)6X4 (nasonite) are also known, with the X site untenanted or partially occupied as required for charge balance. The apatite modules, while topologically identical, are often compositionally or symmetrically distinct, and an infinite number of polysomes is feasible, generally with the restriction being that an A:B = 5:3 cation ratio be maintained. The end-members are the N = 2 polysome with all tetrahedra separated, and N = ∞, in which the hypothetical compound A5B3O9X contains infinite, corner-connected tetrahedral strings. The principal characteristics of a polysome are summarized using the nomenclature apatite-(A B X)-NS, where A/B/X are the most abundant species in these sites, N is the number of modules in the crystallographic repeat, and S is the symmetry symbol (usually H, T, M or A). This article examines the state-of-the-art in polysomatic apatite synthesis and crystallochemical design. It also presents X-ray and neutron powder diffraction investigations for several polysome chemical series and examines the prevalence of stacking disorder by electron microscopy. These insights into the structure-building principles of apatite polysomes will guide their development as functional materials.
Keywords: polysomatic series; apatite; powder diffraction.
Apatites are an important crystal family. In addition to the traditional use of phosphate varieties for bone and teeth replacement (Weiner & Wagner, 1998) their diverse applications span hazardous waste fixation (Lutze & Ewing, 1988), soil amendment (Manecki et al., 2000), laser materials (Payne et al., 1994) and clean energy (Nakayama et al., 1995). The archetype has the general formula AF4AT6(BO4)6X2 (A = large cations; B = metals or metalloids; X = anion) and a zeolitic topology where a AF4(BO4)6 framework (F) creates tunnels (T), whose diameter adjusts to the filling characteristics of the AT6X2 component. Less well known are the apatite polysomes ganomalite (Dunn et al., 1985; Carlson et al., 1997) and nasonite (Frondel & Bauer, 1951; Giuseppetti et al., 1971).
The concept of polysomatism was extensively developed by Thompson (1978) and Veblen (1991) for the crystallochemical analysis of rock-forming silicates and is a widely applied taxonomic principle for the description of condensed matter. The numerous polysome families include perovskite derivatives such as layered high Tc superconductors (Park & Snyder, 1995), fluorite superstructures found in high-level nuclear ceramics (White et al., 1985), and β-alumina-hibonite materials that are encountered in superionic conductivity (Yao & Kiemmer, 1967) and presolar mineralogy (Ireland, 1990; Nittler, 2003). In every case polysomes are derived by the regular alternation of geometrically commensurate, and usually compositionally distinct, slices that share a coherent interface lattice. Polysomatic descriptions accentuate common crystallographic features in families of related compounds (Hyde et al., 1979), illuminate linkages between structure and functionality (Mellini et al., 1987), and guide the optimization of physical properties in advanced materials (Leonyuk et al., 1999).
There is growing interest in apatites as functional materials enablers for clean energy, environmental, catalytic and electronic technologies, but a comprehensive assessment of polysome crystal chemistry has not been undertaken. This article consolidates our present understanding of apatite polysomatism, beginning with the formalization of building principles, followed by a review of definitive chemistries and structural analyses, and concluding with crystallographic refinements and microscopic examination of several new family members.
1.1. Polysome construction and nomenclature
Following the description of Povarennykh (1972) the apatite framework contains larger cations (AF) that are ideally coordinated to six oxygens in the disposition of AFO6 metaprisms corner-connected to isolated BO4 tetrahedra. Twisting opposing (001) triangular prism faces by varying degrees (φ) creates two apatite aristotypes where φ = 0° leads to  face-sharing AFO6 trigonal prism pillars, while φ = 60° yields octahedral columns (White & ZhiLi, 2003). The magnitude of φ is regulated by the extent of channel filling with tunnel cations (AT) and anions (X), such that when the AT3X portion is relatively small or sub-stoichiometric the tunnel diameter contracts through larger metaprism twisting. In this scheme apatite is represented by the general formula [AF4][AT6][(BO4)6]X2. Generally, φ adopts values ranging from ∼ 15 to 25°, but in certain varieties the twist angle is smaller, as exemplified by hedyphane [Ca4][Pb6][(AsO4)6]Cl2 (Rouse et al., 1984), where φ = 5.2° because the tunnel not only accommodates a relatively large halide, but also the stereochemically active electron lone pairs of lead ions that strongly partition to the AT positions.
As the metaprism twist angles of apatite polysomes are usually quite acute, it is practical to adopt φ = 0° as an idealized polysome module having the composition AF2AT3B3O18X and a thickness of ∼ 3.5 Å with the disposition of trigonal prisms and tetrahedra shown in Figs. 1 and 2. These modules can occupy a hexagonal unit cell in two orientations, designated the α and β layers, that are rotated 60° with respect to each other, with condensation leading to the elimination of oxygen from the coincident lattice positions. Layers joined without rotation create corner-connected BnO3n+1 (n = ∞) tetrahedral strings that can be broken through introducing a rotated layer. Thus, if the modules are placed directly one upon the other in the sequence …α(α)α… the hypothetical compound AF2AT3B3O9X is created that contains continuous chains of corner-connected tetrahedra (Fig. 2b). In this case, nine O atoms are duplicated in the co-incident lattice – three from two triangular prism faces and one from each of the three tetrahedra at the conjoined module boundary. Alternatively, if every module is rotated 60° (rotationally twinned) with respect to its neighbours in the order …β(αβ)α…, six oxygen per layer pair are duplicated in the trigonal prisms, and the overall composition of the polysome is AF4AT6B6O24X2. In this configuration, the BO4 tetrahedra remain isolated and the familiar [AF4][AT6][(BO4)6]X2 apatite motif results as in [Pb4][Pb6][(Si/SO4)6](Cl/OH)2 mattheddleite (Fig. 2a).
An infinite number of arrangements intermediate to …α(α)α… and …β(αβ)α… are possible, and the ideal compositions of the apatite polysomes can be expressed as (2 ≤ N ≤ ∞), where N is the number of modules () in the crystallographic repeat. All the tetrahedral sequences for the polysomes with N = 2 to 8 are collated in Table 1 and Fig. 3, and evidentially, longer period structures can in principle adopt compositionally equivalent but structurally distinct configurations. The AT cations within the polysome tunnel also have discrete configurations such that for N = 2 face-sharing columns of AT6 octahedra appear, while for N = ∞ these are transformed to trigonal prisms, with intermediate members showing mixed intergrowths (O'Keeffe & Hyde, 1985). The X anions are located in the centres of the AT3 triangles if small enough, but more often are displaced along the module stacking direction to partially occupied crystallographic sites (Fig. 4).
The silicate mineral ganomalite is an example of the N = 3 polysome with the module sequence …β(ααβ)α… and ideal formula [AF6][AT9][(B2O7)3(BO4)3]X3. The composition is Pb9Ca5.44Mn0.56Si9O33 (Carlson et al., 1997) that when rearranged as [Ca5.44Mn0.56][Pb9][(Si2O7)3(SiO4)3]□3 emphasizes the common crystallochemical characteristics of apatite polysomes (Fig. 5a). Strong, and in this case complete, partitioning of lead to the tunnel is often observed in the polysomes, as in the absence of X anions the lone-pair electrons of Pb2+ occupy the space released. The AFO6 metaprisms at the αβ boundaries are fully occupied by larger Ca2+ (1.00 Å) and have a relatively large twist angle of φ = 17.2°, while those adjacent to the Si2O7 αα modules contain smaller Mn2+ (0.83 Å) with the (Mn0.56Ca0.44)O6 trigonal prism having φ = 0° (Fig. 6b). In common with all N odd structures, the highest possible symmetry space group is ideally .
Nasonite with N = 4 adopts the configuration …β(ααββ)α…, where the ideal formulation [AF8][AT12][(B2O7)6)]X4 is mimicked compositionally as [Ca8][Pb12][(Si2O7)6)]Cl4 (Giuseppetti et al., 1971) in the type mineral (Figs. 5c and 6c). Again, lead enters the tunnel exclusively, but unlike ganomalite the channel accommodates chlorine, in addition to the lone-pair electrons, and must expand almost completely across both the αβ and αα module boundaries leading to φ = 6.2 and 0°. As this polysome has N even the space group is ideally P63/m. For N = 4 the alternate module arrangement …β(αααβ)α… (Fig. 5b) is possible in principle, but has not been verified in apatite polysomes, possibly because Si3O10 chains prove less stable than Si2O7 owing to the high electrostatic repulsions between the closely spaced Si4+ ions. Clearly, the longer the stacking repeat, the greater the possibility for polysomatic intergrowth.
A nomenclature to describe the essential characteristics of the polysomes has been adapted from the recommendations of the Commission on New Minerals, Nomenclature and Classification (CNMNC) for the naming of apatite minerals (Pasero et al., 2010).1 In this scheme, naming takes the general form apatite-(A B X)-NS; the generic family appellation can be replaced by the specific mineral if known for a particular composition; (A B X) are the most abundant constituents on these sites; N is the number of modules in the crystallographic repeat and S the lattice symmetry. Thus, for N = 2 polysomes (with conventional apatite structures) the hexagonal vanadate Pb10(VO4)6Cl2 would be written as vanadinite-(Pb V Cl)-2H (Dai & Hughes, 1989), monoclinic chlorapatite Ca10(PO4)6Cl2 as chlorapatite-(Ca P Cl)-2M (Mackie et al., 1972), while triclinic svabite Ca10(AsO4)6F2 is svabite-(Ca As F)-2A (Baikie et al., 2007). By extension, the minerals ganomalite and nasonite described above are ganomalite-(Pb Si □)-3H (Carlson et al., 1997) and nasonite-(Pb Si Cl)-4H (Giuseppetti et al., 1971).
1.2. Polysome chemistry
1.2.1. N = 2
The crystal chemistry of …β(αβ)α… apatite-2S structures is diverse and there is little need to add to several extensive reviews (White et al., 2005; Hughes et al., 1989; Pan & Fleet, 2002; Piccoli & Candela, 2002). Of the total number of chemical end-members somewhat less than 60% of this polysome are hexagonal P63/m, while a further third crystallize in hexagonal and trigonal subgroups (P63, and ), with the balance monoclinic (P21/m or P21; Elliott et al., 1973) or triclinic (; Baikie et al., 2007). Almost every element in the periodic table can be accommodated in apatite-2S. In addition, oxidized and reduced varieties exist with the B cations in triangular [e.g. finnemanite Pb10(AsO3)6Cl2; Baikie et al., 2008] and penta-coordination [e.g. Ba10(ReO5)6Cl2; Besse et al., 1979], rather than BO4 tetrahedra; hybrid varieties such as [Ca9Na0.5][(PO4)4.5(CO3)1.5](OH)2 (Feki et al., 1999) and [La10][(GeO4)5(GeO5)]O2 (Pramana et al., 2007) have been described. Non-stoichiometry can appear in the framework (e.g. [La3.33][La6](SiO4)6O2; Sansom et al., 2001) or tunnel [e.g. Cd10(PO4)6Br(I)2 − δ; Alberius-Henning et al., 2000], which gives rise to modulated structures, or the common P21/b variant with inter-channel order correlation of the statistically occupied X position (Bauer & Klee, 1993). Transition metal ions can also be located in the X sites, for example in A10(PO4)6MxOyHz [A = alkaline earth metal; M = Cu (Kazin et al., 2003; Baikie et al., 2009), Ni, Co Zn (Kazin et al., 2007)]. Furthermore, cation [e.g. [Nd3.33][La2Nd4](SiO4)6O2]; Malinovskii et al., 1990] and anion [e.g. Ca10(PO4)6I2/3O2/3; Alberius-Henning et al., 1999] ordering can yield superstructures, which retain bimodular periodicity along the stacking direction and modify translational periodicity in (00l).
1.2.2. N = 3
The mineral ganomalite from Långban, first described by Nordenskiöld (1876, 1877), was erroneously identified as the hydroxyl analogue of nasonite, i.e. Ca8Pb12(Si2O7)3(OH)4. Ganomalite was subsequently redefined as [Ca5Mn][Pb9]Si9O33 (Dunn et al., 1985) with P3 as the most likely space group, since refinements in gave large positional errors, unrealistic site occupancies, non-physical atomic displacement parameters (ADPs) and unreasonable bond lengths. A more recent single-crystal study (Carlson et al., 1997) of ganomalite-(Pb Si □)-3H from the same locality yielded and the chemical formula [Ca5.44Mn0.56][Pb9][(Si2O7)3(SiO4)3]□3. This study found that P3 offered no improvement in the refinement residuals.
Generally, synthetic N = 3 polysomes are less well characterized than their N = 2 counterparts, although [Pb6][Pb9][(Ge2O7)3(GeO4)3]□3 has received significant attention because of its ferroelectric and pyroelectric functionality, and reversible optical activity (Iwata, 1977; Iwata et al., 1973; Kay et al., 1975; Iwasaki et al., 1971; Iwasaki, Miyazawa et al., 1972; Iwasaki, Sugii et al., 1972; Nanamatsu et al., 1971; Wu et al., 2004; Newnham et al., 1973). As for the natural species, there was initial debate regarding the space-group assignment, with ganomalite-(Pb Ge □)-3H first reported in (Newnham et al., 1973). However, a re-determination suggested P3 ganomalite-(Pb Ge □)-3T (Iwata et al., 1973), later corroborated by powder neutron diffraction (Kay et al., 1975). A separate study re-confirmed P3 for Pb15(Ge2O7)3(GeO4)3 and the isomorphous material Pb15(Ge2O7)3(SiO4)3 from the X-ray extinction conditions (Iwasaki, Miyazawa et al., 1972). At room temperature these materials are ferroelectric, however, above the Curie temperature (∼ 450 K), changes in X-ray extinction suggested the paraelectric phases undergo a transformation to , as subsequently confirmed by a neutron study (Iwata, 1977). The trigonal to hexagonal transition was attributed to the twisting and displacement of the Ge2O7 double tetrahedra. The influence of substitutions over the Pb and Ge sites on the dielectric properties of Pb15Ge3O33 has been studied. For example, polycrystalline and single-phase Pb15-xAxGe9-yByO33, A = Ca (Misra et al., 1995; Goswami et al., 2001), Sr (Misra et al., 1998), Ba (Choudhary & Misra, 1998) and Cd (Engel, 1972), B = Si (Eysel et al., 1973; Iwasaki, Miyazawa et al., 1972), Ti (Goswami, Mahapatra et al., 1998; Goswami, Choudhary et al., 1998b) and Zr (Goswami et al., 1997, 1998a), and more recently, coupled aliovalent substitutions of Nd3+/K+ (Wazalwar & Katpatal, 2001, 2002) or Bi3+/Cs+ (Otto et al., 1980) for Pb2+ have been reported (see also Table 2). Whilst the ganomalite polysome persists upon doping, the introduction of smaller cations at the Pb sites decreases the ferroelectric transition temperature and appropriate substitutions over Pb and Ge sites gave 243 ≤ Tc ≤ 573 K. However, detailed crystallographic investigations were not carried out and only lattice parameters were reported. B-site substitutions with cations of a different charge, and without counter-ion substitution at the A site, have been attempted but lead to the formation of lacunar-type apatite-2H with the tunnel site X anions absent, e.g. Pb10(GeO4)4(CrO4)2□2 (Engel & Deppisch, 1988), Pb10(GeO4)4(SO4)2□2 (Engel & Deppisch, 1988), Pb10(GeO4)2(VO4)4□2 (Ivanov, 1990) and Pb10(SiO4)2(VO4)4□2 (Krivovichev et al., 2004). In these examples, the Si or Ge was replaced by higher valence cations, with charge compensation by oxygen ions that stabilized A10B6O24□2, N = 2 polysomes, rather than A15B9O33□3, N = 3 phases. There is a single example where the 3H (or 3T) polysome is maintained via a coupled A and B site substitution. In an attempt to induce oxygen interstitials in Pb15Ge9O33 via replacement of Pb2+ by Bi3+ i.e. Pb15-xBixGe9O33+x/2, a solid solution limit was found (x = 0.09), beyond which apatite-2H forms. However, a combined bismuth (Bi3+) and boron (B3+) substitution in (Pb15-xBixGe9-xBxO11) extended the solubility limit to x = 0.6 (Otto & Loster, 1993). The synthesis was fortuitous as B2O3 was introduced to control melt viscosity and promote the growth of large single crystals. The resultant material is pyroelectric and could be used for IR radiation detection.
1.2.3. N = 4
Nasonite-type polysomes are currently poorly represented, and the compositional ranges and nature of structural variants less well understood. The mineral was first described by Penfield and Warren (1899) and later by Palache (1935) as a rare species found in the Franklin Mine. Subsequently, Aminoff (1916) identified its occurrence at Långban. A Weissenberg X-ray study (Frondel & Bauer, 1951) recognized the structural relationship between nasonite and pyromorphite [Pb10(PO4)6Cl2] and reported the lattice parameters a = 10.06 and c = 13.24 Å, cell contents as Pb12Ca8(Si2O7)6Cl4, and postulated the space group as P63/m or P63. A later single-crystal X-ray diffraction study found P63/m (Giuseppetti et al., 1971), but high-resolution electron microscopy (HRTEM) of the same sample failed to locate the twofold axis and a deviation from hexagonal symmetry was suspected (Brès et al., 1987). This was ascribed to sampling differences between techniques and the presence of non-hexagonal micro-domains that on average gave the appearance of P63/m. In §3.3 we report the first preparation and crystal structure refinement of synthetic …(βααββ)α… apatite-4H polysomes.
1.2.4. N > 4
In addition to nasonite (N = 4) and ganomalite (N = 3) longer sequence polysomatic members are feasible. For example, Pb40(Si2O7)6(Si4O13)3O7 was proposed for a metastable lead silicate (Stemmermann, 1992), with reflection indexing yielding a = 17.196 (1), b = 9.928 (1), c = 28.744 (2) Å, β = 90.36 (1)°. Several possible polysomes were suggested but the exact nature of this phase is unresolved. The same study intimated that the true structure of the partially characterized phase Ca3Si2O7·1/3CaCl2 was actually a nasonite-type (N = 4) of composition Ca20(Si2O7)6Cl4 and the orthorhombic cell a = 3.763 (1), b = 34.70 (1) and c = 16.946 (5) Å assigned (Hermoneit et al., 1981), but subsequently a monoclinic metric (P21/a) with a = 18.665 (1), b = 14.107 (1), c = 18.139 (1) Å, β = 111.65 (1)° was suggested (Ye et al., 1986; Stemmermann, 1992). In addition, Sr substitution for Ca was reported and Ca12Sr8(Si2O7)6Cl4 can be indexed with a slightly dilated monoclinic cell. More recently, Eu2+ has been introduced to the Ca site of Ca20-xEux(Si2O7)6Cl4 as such phases show promise as phosphors (Ding et al., 2007), but a crystallographic analysis is lacking.
Nassau et al. (1977) confirmed the existence of a metastable `Pb5Ge3O11', first identified by Hasegawa et al. (1977) during recrystalization of vitreous `Pb5Ge3O11' at 723 K, and assigned the hexagonal lattice parameters a = 10.19 and c = 19.34 Å (no standard deviations were reported). Heating to 823 K produces the stable crystalline form of `Pb5Ge3O11' with the hexagonal lattice parameters a = 10.251 and c = 10.658 Å. We can identify the stable crystalline phase as Pb15(Ge2O7)3(GeO4)3□3 or ganomalite-(Pb Ge □)-3H (or 3T) and predict from the lattice parameters that the metastable phase is an N = 6 polysome. Furthermore, it is suggested from the reported non-ferroelectric properties of the metastable `Pb5Ge3O11' that its structure contains a centre of symmetry consistent with the stacking sequence …β(αααβββ)α… apatite-(Pb Ge □)-6H and the crystallochemical formula is [Pb12][Pb18][(Ge3O10)6]□6 (Table 1); however, experimental confirmation is required.
2. Experimental methods
Several new chemistries of the ganomalite and nasonite structure types were investigated to better understand the structural relationships between these polysomes. To this end, two ganomalite solid solutions were prepared – Pb15-xBix/2Nax/2(Ge2O7)3(GeO4)3□3 and Ca6Pb9(Si2-yGeyO7)3(Si1-zGezO4)3□3 to explore co-doping across the A-site and isovalent B-site substitutions. The nasonite phases Ca8Pb12(B2O7)6Cl4 (B = Si and Ge) were also synthesized. The primary characterization tool was powder X-ray diffraction, with selected materials examined by neutron diffraction and transmission electron microscopy.
All polysomes were synthesized via conventional solid-state reaction techniques. The reagents PbO (Fisher, 99%), CaCO3 (Aldrich, 99.9%), Bi2O3 (Aldrich, 99.9%), Na2CO3 (Fisher, 99%), GeO2 (Aldrich, 99.99%), SiO2 (Alfa, 99.99%) and CaCl2 (Jebchem, 99%) were mixed in appropriate stoichiometric quantities according to the reactions shown in (1), (2) and (3). Ganomalite samples were synthesized with x = 0, 3 and 6 [see (1)] and x = 0, 2, 4.5, 7 and 9 (x = y + z) [see (2)], while the nasonites were silicate and germanate end-members [see (3)].
For (1)–(3) the powders were ground in a ball-mill (20 min at 150 r.p.m.), pressed into pellets and heat treated in air in alumina crucibles from 873–1073 K for 12 h. The samples were reground, pressed into pellets and re-heated for 48–120 h until a single-phase or near single-phase product was obtained. In the case of nasonite (3), care was needed to avoid chlorine loss and the pellets were placed in covered alumina crucibles containing excess NH4Cl (1 g for 5 g of sample) to create a chlorine rich atmosphere.
2.2. Crystallographic characterization
Sample purity was established and preliminary structural refinements carried out from powder X-ray diffraction (PXRD) patterns collected with a Shimadzu Lab XRD-6000 diffractometer (Bragg–Brentano geometry) equipped with a Cu Kα X-ray tube operated at 40 kV and 40 mA. The crushed powders were mounted in a top-loaded trough and data accumulated from 10–140° 2θ using a step size of 0.02° with a dwell time of 10 s per step. Under these conditions the intensity of the strongest peak was 30 000–40 000 counts. Rietveld refinement of the X-ray data was carried out with TOPAS (Bruker, 2008), using the fundamental parameters approach (Cheary & Coelho, 1992) and a full axial divergence model (Cheary & Coelho, 1998). The specimen-dependent parameters refined were the zero error, a user-specified number of coefficients for Chebyshev polynomial fitting of the background, and the `crystallite size' to model microstructure-controlled line broadening. Only isotropic atomic displacement parameters (ADPs) were refined. A common ADP was assumed for all O positions and Ge and Si (the BO4 unit), and Pb/Bi/Na/Ca/Na occupying the same site. Individual isotropic ADPs were refined for the Pb/Bi/Na/Ca/Cl when it was clear that any site was solely occupied by one of these elements. Owing to the almost identical X-ray scattering factors the site preferences of Pb and Bi could not be established. To ensure reasonable Si/Ge—O bond lengths within the Si/GeO4 and Si/Ge2O7 units, a soft-constraint was implemented using the `Parabola_N' penalty function of TOPAS with values for the expected bond lengths consistent with the standard ionic radii of Shannon (1976).
Time-of-flight (TOF) powder neutron diffraction patterns were recorded on the HRPD diffractometer, at ISIS, Rutherford Appleton Laboratory, England, from approximately 2 cm3 of sample loaded into vanadium cans. Data sets from two banks of detectors were used for the refinement; the first was the data from the back-scattering bank (average 2θ ≃ 145°) and the second was the data from the 90° detector bank. Structure refinement was performed using the GSAS suite of Rietveld refinement software (Larson & Von Dreele, 1987). No constraints were imposed on the Ge/Si—O bond lengths using the neutron diffraction data owing to the greater sensitivity of the technique towards oxygen. In addition, individual isotropic ADPs were refined for each oxygen site. Experimental details are given in Table 3.
Transmission electron microscopy (TEM) was conducted on powders deposited on holey-carbon copper grids and loaded in an analytical double tilt holder. Data were obtained at 200 kV using a Jeol JEM-2010 electron microscope (Cs = 0.5 mm) equipped with an EDAX EDS X-ray microanalysis system and three field-limiting apertures for selected-area electron diffraction (SAED; 5, 20 and 60 mm diameter). High-resolution images were collected using an objective aperture (100 µm), corresponding to a nominal point-to-point resolution of ∼ 1.7 Å. Electron diffraction patterns were calibrated against external standards to derive reliable values for both the electron wavelength and camera length. Lattice parameters were determined repeatedly to check for hysteresis of the electromagnetic lenses leading to errors < ± 1%. For convergent-beam electron diffraction (CBED), the spot size at the specimen was nominally 10 nm, obtained in the nanoprobe mode.
3.1. Pb15 − xBix/2Nax/2(Ge2O7)3(GeO4)3, x = 0, 3 and 6: ganomalite-(Pb/Bi/Na Ge □)-3S
Single-phase materials were produced for x = 0, 3 and 6, but attempts to prepare lead-free ganomalite Bi7.5Na7.5Ge9O33 (x = 15) were unsuccessful and the substitution limit is x ≃ 6, i.e. Pb9Bi3Na3Ge9O33. For x > 6 Bi4Ge3O12 begins to form together with other poorly crystallized phases, as indicated by broad X-ray diffraction reflections. The optimal reaction temperature was 973 K, although mixtures with high Bi/Na content melted congruently.
3.1.2. Structure of x = 0
Refinement of Pb15Ge9O33 (x = 0) neutron data was initially attempted in , however, it was clear from the reliability factors and germanium and oxygen isotropic displacement parameters that P3 yielded a superior fit (P3: wRp = 0.043, RF = 0.036, χ2 = 2.001; : wRp = 0.066, RF = 0.074, χ2 = 4.214), in agreement with the room-temperature structure of Kay et al. (1975). As with previous studies, the Pb5F position was fixed to define an origin along z and yield reasonable atomic coordinates, bond distances and angles (Fig. S1a, and Tables S1a and S1b of the supplementary material).2 Using the space group the Ge2, O2 and O3 sites that are associated with the isolated GeO4 tetrahedra yielded either negative or unreasonably large isotropic displacement parameters and a short Ge—O bond length [1.69 (1) Å] and an inferior difference profile fit (see Fig. S1b, and Tables S1c and S1d).
3.1.3. Refinement Strategy for x = 3 and 6
For the Bi-/Na-doped polysomes PXRD and neutron data were refined sequentially, as it was anticipated that Pb, Na and Bi would be distributed non-statistically across the AF and AT sites. Pb (Z = 82) and Bi (Z = 83) have very similar X-ray scattering factors and PXRD refinements assumed Bi as Pb, before examining the distribution of Na (Z = 23) across the A sites, with the Ge—O bonds soft-constrained to ∼ 1.7 Å (Shannon, 1976). The refined Na occupancies were then transferred to the structural model for refinement of the neutron data, where they were fixed and the Pb and Bi occupancies refined. This approach will suffer from minor errors as Pb and Bi do not have identical form factors, but can be independently checked by comparison against the expected stoichiometry.
The refinements of both the x = 3 and 6 Bi/Na polysomes required application of a `strain' function during XRD analysis, and an L33 parameter to the peak-shape function for neutron data. This indicates c-axial strain, presumably due to distortions caused by different ionic sizes and a preference for certain sites or module stacking disorder.
The PXRD Rietveld refinements slightly favoured P3 over , as indicated by the reliability factors, and the sodium occupancies gave values close to the nominal compositions. Neutron refinements were also attempted using both space groups, which on the basis of derived occupancies and overall stability (refinements in tended to result in Pb and Bi occupancies with non-physical values) confirmed P3 as most probable. The lower symmetry is possibly favoured as it provides a greater number of discrete cation acceptor sites to accommodate the site preferences of Pb/Bi/Na.
In both Pb12Bi1.5Na1.5Ge9O33 (x = 3) and Pb9Bi3Na3Ge9O33 (x = 6) Na ions strongly partition to the framework. A5F and A6F were the most favoured cation-acceptor sites for sodium (from the Pb15Ge9O33 parent), A2F the second most favoured site, with the A1F/3F/4F positions showing similar affinity for Na occupancy; the preferred sites (A5F and A6F) are located next to the (αα) double tetrahedral units. For x = 3 sodium was excluded from the tunnel, with only very partial inclusion in the x = 6 sample. This is consistent with the requirement for stereochemically active Pb2+ lone-pair electrons to stabilize the channels, and may explain why the solid-solution upper limit is x ≃ 6. The possible occurrence of oxygen within the channels was tested by placing low occupancy ions at several trial positions; however, this yielded poor reliability factors and non-convergence, indicating that the tunnel is indeed empty.
3.1.4. Structure of x = 3
Bi3+ was tenanted in the AF sites, rather than the AT positions, even though this ion also possesses stereochemically active lone-pair electrons that could in principle mimic Pb2+ for stabilizing the empty channels. This suggests that ionic size ultimately determines their location within the 3T polysome – [Pb2+ is larger (1.29 Å) than both Bi3+ (1.17 Å) and Na+ (1.18 Å)] – with a distribution different from apatite-2H, where the Bi3+ was found from X-ray work to be located in the AT sites, e.g. Pb7.4Bi0.3Na2.3(PO4)6□2 (Hamdi et al., 2007) and Pb4.6Bi0.4Ca2.6Na2.4(PO4)6□2 (Hamdi et al., 2004). For Pb12Bi1.5Na1.5Ge9O33 bismuth entered A5F and A6F preferentially with lead favouring A1F and A2F. The site occupancies of A3F and A4F were ambiguous with either all the Bi at A3F with all the Pb located at A4F, or vice versa, and no differentiation by the reliability indices. Therefore, Pb/Bi were distributed evenly and fixed. The final refined Bi content was higher than anticipated (1.81 compared to the ideal value of 1.50). It is noted that the presence of AF/AT cation vacancies could not be probed as the refinement strategy required full occupancy of all sites. An alternative explanation for Na+ and Bi3+ occupying the framework is the need to locally conserve charge.
3.1.5. Structure of x = 6
The investigation of Pb9Bi3Na3Ge9O33 (x = 6) was straightforward; once the Na occupancies were determined by PXRD the remainder of the framework sites were filled with Bi; Na entered the AT sites (∼ 0.36Na per unit formula) to a minor extent with the majority located in the framework sites. Bi3+ was introduced to the tunnel sites but the refinement was unconvincing, with ready convergence achieved with Bi3+ on AF positions to yield a total of 3.32 Bi3+ per unit formula, compared with the ideal value of 3. An unrealistically high ADP for A1F (Uiso = 0.058 Å3) was improved (Uiso = 0.025 Å3) by introducing 0.32 Pb at this site in an attempt to improve the overall stoichiometry and charge balance. The absolute values for the refined occupancies should be treated with some caution owing to the nature of the refinement; they do however offer a good indication to the preferred location of the different chemical species. Nevertheless, all of the ADPs were high, which may arise from module stacking disorder. It is noted that the AF—O bond lengths of the A6F site (occupied by Na) are quite distorted compared with the other refinements, perhaps owing to the influence of nearby Bi3+ lone pair electrons.
The refined atomic positions, site occupancies and selected bond lengths are shown in Figs. S2 and S3, and Tables S2(a)–(c) and S3(a)–(c). The structure drawing of Pb9Bi3Na3Ge9O33 emphasizes the clear preference of Bi and Na for the framework (Fig. 7) and the general formula of this series can be written as [Bix/2Nax/2][Pb15-x](Ge2O7)3(GeO4)3□3.
3.2. Ca6Pb9(Si2 − xGexO7)3(Si1 − xGexO4)3□3: ganomalite-(Pb Si/Ge □)-3S
Powder X-ray diffraction confirmed ganomalite-(Pb Si/Ge □)-3S could be synthesized across the entire series, with minor Pb3(Si,Ge)3O7 and/or Ca(Si,Ge)O3 impurities removed by repeated grinding and heat treatments. The optimal reaction condition was 1073 K for 36 h, divided into three sintering stages (12 h) with intermediate grinding. Higher temperature or prolonged heating resulted in partial product decomposition presumably owing to lead volatilization.
3.2.2. Structural characterization
Close inspection of the sharp XRD diffraction peaks revealed anisotropy, particularly the 00l reflections, suggestive of phase segregation. Similar observations in (Ca10-xPbx)(VO4)6F2 apatites were shown to be due to the non-equilibrated partitioning of calcium and lead over AF(4f) and AT(6h) sites (P63/m), which favoured Pb2+ preferentially entering the larger AT site (Dong & White, 2004a); prolonged heating (4 weeks at 1073 K) was required to obtain the equilibrium structures (Dong & White, 2004b).
Pawley fits showed all the materials were three-phase assemblages (see Table 4). Single-phase refinements were attempted with the inclusion of a function to model anisotropic peak broadening; however, this offered little improvement in the residuals indicating that the samples contained more than one phase.
For preparations of nominal compositions Ca6Pb9(Si2O7)3(SiO4)3□3 and Ca6Pb9(Ge2O7)3(GeO4)3□3 the polysomes had similar a cell edges but the c parameters showed slightly larger variations. The compounds having the largest and smallest volumes are presumably rich in Pb2+ and Ca2+, while the phase with the intermediate c parameter was nearer equilibration. Preparations containing mixed Si/Ge occupancies (x = 2, 4.5 and 7) showed a greater variation in their lattice parameters, especially along the  module stacking direction, indicating a more complex cation distribution and a delay in ordering (see Fig. 8 and Table 4). As Si (IR = 0.40 Å) is displaced by Ge (IR = 0.53 Å) unit-cell dilation is expected (Fig. 8), and for the polysomes closest to equilibration (B phase) the expansion was essentially linear, in agreement with Vegard's law. Discontinuities of equivalent plots for the non-equilibrated A and C phases indicate a more complex partitioning behaviour.
3.2.3. Convergent-beam electron diffraction (CBED) of [Ca6][Pb9][(Si2O7)3(SiO4)3□3
Most ganomalite samples were electron-beam sensitive and decomposed rapidly. However, for a single composition it was possible to collect CBED patterns for ganomalite-Ca6Pb9(Si2O7)3(SiO4)3 and unambiguously distinguish between P3 and by examining special projections along  that will conform to plane symmetry p1 and p11m, respectively. Several  CBED patterns were collected under different conditions to verify the presence of a mirror plane parallel to  as anticipated in symmetry. In addition to experimental zero-order Laue zone (ZOLZ) CBED, Bloch wave simulations with 1.2 mrad half-convergent illumination and 150 nm thickness for P3 and were calculated using the JEMS simulation program (Stadelmann, 2003). The clear absence of a mirror plane (Fig. 9) confirms this ganomalite polysome belongs to P3. This is particularly evident when comparing high-angle reflections (far from the direct beam) where over-exposure effects are less pervasive (Fig. 9a) and dynamical contrast distributions are not related by mirroring (Figs. 9b and c).
3.2.4. Disequilibrium, phase separation and functionality
The fact that for each sample three distinct phases were found in approximately equal quantities, but containing different cation distributions and crystal sizes may explain the anomalies found in previous ganomalite-3S structural determinations, i.e. space-group assignment and atomic displacement parameters. Furthermore, natural ganomalite may also contain micro-domains with similar hexagonal matrices, which would contribute to ambiguous structural studies. This may not be an unusual feature in apatites, as, for example, a natural crystal of a Brazilian gem-grade apatite was found to contain micro-domains of F and Cl enriched apatites each with similar c parameters but with differing a lattice parameters (Ferraris et al., 2005).
Multi-phase ganomalite samples might also have been encountered in studies of their ferroelectric properties where diffuse transitional temperatures were reported (Goswami et al., 1997, 2001; Goswami, Mahapatra et al., 1998; Choudhary & Misra, 1998; Misra et al., 1999). Although indexing the XRD patterns indicated single-phase products, the materials could be similar to those obtained here and contain mixtures with comparable lattice parameters, but differing cation distributions. In contrast, a report on the ferroelectric properties of a single-crystal sample of Pb15Ge9O33 and no phase segregation, showed a sharp transition temperature. Interestingly, measurement of the transition temperature of a `single crystal' of Pb15Ge6Si3O33 was broad, which may be indicative of the existence of micro-domains (Iwasaki, Miyazawa et al., 1972), as in apatite gems (Ferraris et al., 2005).
3.3. Ca8Pb12(B2O7)6Cl4 (B = Si and Ge): nasonite-(Pb Si/Ge Cl)-4H
Nasonite-(Pb Si Cl)-4H was prepared as a single phase, while the synthesis of the germanate analogue was partially successful, with PXRD revealing several unidentified reflections. The optimal synthesis temperature for the silicate polysome was 873 K, with 973 K required to form the germanate nasonite. The higher-synthesis temperature resulted in excessive Cl loss whereby nasonite converts to ganomalite. In addition, the impurity phase Pb2(Si,Ge)3O9 (margarosanite) was found in the reaction products. Due to its multiphase nature only lattice parameters of Ge nasonite are reported.
3.3.2. Structure of Ca8Pb12(Si2O7)6Cl4
Neutron diffraction refinements for Ca8Pb12(Si2O7)6Cl4 were attempted in P63/m and P63, with the former being the preferred model (Figs. 10 and S4). The refinement proceeded directly to give lattice parameters and atomic positions close to those previously reported, however, the chlorine sites yielded an occupancy slightly less than 1. In addition, moving the Cl ions off the special positions along the channel to partially occupied split sites lowered their ADPs to more realistic values, although still quite high. A difference-Fourier map also indicated a small excess of nuclear density between the Cl atoms close to (0, 0, 1/8). This site is commonly occupied by oxygen in apatite-2S, and therefore a comparable site was introduced between the chlorine ions. Oxygen ions were initially placed at (0, 0, 1/8), however, their stability was improved by site splitting, suggesting channel disorder as commonly encountered in the N = 2 polysomes (White & ZhiLi, 2003). The occupancy of the tunnel O5 oxygen site was initially refined without constraint; however, a restriction of chemistry (4 − xCl− + x/2O2− to give an overall charge of −4) was ultimately applied to ensure overall charge neutrality. It is possible that the O5 is OH, but this could not be confirmed owing to the low occupancy.
A structural model was developed that gave a good fit to the data (Table S4a), however, the ADPs, although tolerable, were slightly high, particularly for Pb. This may be indicative of polysynthetic module rotation twinning (as confirmed subsequently by HRTEM below). Selected bond lengths and angles (Table S4b) are also in good agreement with the single-crystal mineral (Giuseppetti et al., 1971); however, in this work the structure was refined with substantially higher accuracy.
3.3.3. TEM analysis
Microscopy of N = 4 Ca8Pb12(Si2O7)6Cl4 nasonite shows disordered stacking sequences of α and β layers along  in an estimated 5 vol% of crystals.  SAED patterns from an area containing disorder (Fig. 11a) contains, in addition to dynamically forbidden (00l) reflections with l ≠ 2n, pronounced * streaking. Lower magnification images possess evident bands of dark and light contrast (Fig. 11b) arising from extensive defect intergrowths. In a detailed analysis of a HRTEM segment N = 4 and N = 3 unit cells often regularly alternate along c* in a …3(34)4… sequence. Intercalation of N = 5 or 7 polysomes is also recognisable (Fig. 11c) but rare, suggesting SinO3n+1, n ≥ 4 are stereochemically unfavourable.
3.3.4. Structure of Ca8Pb12(Ge2O7)6Cl4
The lattice parameters for Ca8Pb12(Ge2O7)6Cl4 [a = 10.3144 (3) and c = 13.5342 (4) Å] were obtained from a Pawley fit in P63/m. Owing to the multiphase nature of this sample no structural refinement was attempted, nor is further discussion presented here. It is anticipated that a single-phase product of the germanium nasonite could be prepared using a hermetically sealed system to prevent chlorine loss.
4.1. Expanded phase space for the apatite family
The initial crystal-structure determination of hexagonal (P63/m) fluorapatite-(Ca P F)-2H almost 80 years ago (Naray-Szabo, 1930) was followed by several decades of solid-state investigations from which around 100 chemical analogues arose (Wyckoff, 1965), generally described within the constraint of the prototype symmetry. In parallel with the examination of synthetics, a range of minerals including the aesthetic mimetite-(Pb As Cl)-2H (Calos & Kennard, 1990) and vanadinite-(Pb V Cl)-2H (Dai & Hughes, 1989) varieties were reported. The seminal study of Elliott et al. (1973) first validated the monoclinic P21/b 2M dimorph of hydroxyapatite and served as a prelude to the structural re-determination of many apatites and the conspicuous expansion of their subtle crystallochemical complexities (Pramana et al., 2008). It is now recognized that the apatite family exploits seven adaptive mechanisms including:
These fundamental crystallographic principles can operate cooperatively, and when apatite phase space is viewed in total it is evident that substantial opportunities exist to formulate new derivatives through the creation of AF4AT6(BO3/BO4/BO5)6X2 hybrids that may display polysomatic character (Fig. 12). Although this study has focused on intergrowth of tetrahedral strings, there is no reason to exclude BO3/BO5  intergrowths, and preliminary electron diffraction of Ba10(ReO5)6O2 shows diffuse scatter indicative of (00l) polysome disorder (Pramana & White, 2009).
4.2. Future polysome chemistries
All apatite polysomes reported to date are predominantly plumbous, and it is clear that Pb2+ partitions to the AT sites so that stereochemically active lone-pair electrons stabilize these phases by occupying the volume normally containing X anions. It is therefore intriguing that Bi3+, which also possesses electron lone pairs, partitions to AF positions and does did not play a similar role to Pb2+. This suggests the size difference between Bi3+ (1.17 Å) and Pb2+ (1.29 Å) and/or the requirement for localized charge balance with Na+ are overriding factors. However, such analyses are non-trivial as Hyde & Anderson (1989) suggest the lone-pair distance in Bi3+ (0.98 Å) is greater than Pb2+ (0.86 Å), which would a priori favour entry of bismuth in the AT sites. Some clarity could be gained by synthesizing monovalent thallium-bearing polysomes where the Tl+ ion is relatively large (1.59 Å), but its lone-pair distance is short (0.69 Å). Were Tl+ to completely replace Pb2+ in the tunnel, and assuming the B sites are occupied by +4 ions, charge-balance considerations would require the AF sites to have a charge of +3.5 per site, as for example in hypothetical N = 3 [Ce4+3Bi3+3][Tl+9](Ge2O7)3(GeO4)3□3 or N = 4 [Ce4+4Bi3+4][Tl+12](Si2O7)6Cl4. However, Tl+ may display characteristics similar to a large alkali (e.g. Rb+ or Cs+) and show a strong preference for the AF positions. Clearly, the relative importance of size, charge and stereochemically active lone pairs in limiting polysome chemistry requires further study. Given the extensive chemistries of apatite-2S polysomes, it would be extraordinary if it proved impossible to formulate new longer period polysomes that are lead free. As noted earlier, several workers have suggested Ca20(Si2O7)6Cl2 is an N = 4 polysome (Stemmermann, 1992; Hermoneit et al., 1981; Ye et al., 1986; Ding et al., 2007).
4.3. Polysomes as functional materials
Apatite polysomes with identical chemistries, such as (Pb Ge □)-2H, (Pb Ge □)-3H and (Pb Ge □)-4H, will display unique physical properties and functionalities. For example, silicate and germanate apatites are promising low-temperature solid-oxide fuel cell electrolytes. Crystallographic (Pramana et al., 2007) and computational (Kendrick et al., 2007) studies suggest that oxide ion mobility is mediated via the SiO4 and GeO4 tetrahedra, and consequently, longer-period tetrahedral strings that reduce metaprism twisting and expand the primary ion-conducting channel may prove beneficial for ion transport and conductivity (Pramana et al., 2009). At the very least, measurements of physical properties across polysomatic series can be used to better understand mechanistic features, as used to good effect in the Ruddlesden–Popper homologous series (An+1BnO3n+1) superconducting cuprates where it was predicted, and observed experimentally, that longer-period polysomes yielded higher high Tc (Skakle, 1998).
Moreover, outstanding questions remain regarding the extensively studied structures of the cation-deficient La9.33(SiO4)6O2 and La9.67(SiO4)6O2.5 apatite electrolytes. Powder neutron-diffraction studies have shown that lowering the symmetry from P63/m to P63 (Tolchard & Slater, 2008) or (Sansom et al., 2001) led to improved fits, as the removal of the mirror plane better represented static oxygen disorder. From this study, it can be proposed that the static disorder may be a consequence of polysynthetic twinning on the unit-cell scale that provides a means to accommodate cation vacancies at the La framework sites. These stacking faults would produce cages from Si2O7 units, as shown in Fig. 13(a), which have already been observed in Na3YSi2O7 (Merinov et al., 1981). This proposed structural arrangement is also supported by recent 29Si NMR studies (Sansom et al., 2006; Orera et al., 2008), which show lanthanum silicate apatites containing La vacancies and/or excess oxygen give chemical shifts consistent with Si2O7 dimers, together with the expected chemical shift for SiO4 units. In addition, chemical shifts for Si2O9 were found, which would be consistent with oxygen interstitials. In contrast, fully stoichiometric samples show a single Si environment for SiO4 units. It is proposed that La9.33(SiO4)6O2 could be re-expressed as an N = 6 polysome with the general formula [La10□2][La18][(SiO4)6(Si2O9)3(Si2O7)3]O6 (Table 5). In this idealized structure the La vacancies occur at every sixth stacking layer (Fig. 13b), and while structural studies thus far are consistent with a disordered apatite-2H average structure, it may be that the powdered samples and single crystals were not equilibrated. In other apatite systems (Dong & White, 2004a,b) and in La—Si—O apatites (Li et al., 2009) several weeks annealing were required to stabilize vacancy sequences. Similarly La9.67(SiO4)6O2.5 could be expressed as an N = 12 polysome with the formula [La22□2][La36][(SiO4)18(Si2O9)6(Si2O7)3]O12. The principle of describing apatite non-stoichiometry as polysome intergrowths is general and, for example, the cation-deficient hybrid phosphate apatite [Ca9Na0.5][(PO4)4.5(CO3)1.5](OH)2 might be formally described as an N = 8 polysome of the type [Ca12Na2□2][Ca24][(PO4)6(CO3)6(P2O9)3(P2O7)3](OH)8. In this case, future 31P MAS-NMR may shed light on the correctness of this proposed structure where three distinct phosphorus environments are expected.
Although `apatites' are important biomaterials their precise nature remains speculative because the chemistry is incompletely defined (especially the role of protons; Pasteris et al., 2004), the crystallinity may be poor or they appear as multiphase assemblages. It is believed that amorphous calcium phosphate (ACP) is a precursor of hydroxyapatite and the mechanism of transformation is presumed via an intermediate Ca2P2O7 pyrophosphate on the basis of 31P NMR that revealed P2O7 units (Tropp et al., 1983). However, P2O7 groups are also consistent with disordered polysome fragments. In other developments, apatites are seen as low temperature and selective catalysts for a range of reactions including CO oxidation (Matsumura et al., 1997) and volatile organic combustion (VOC; Matsumura et al., 1994). In the latter case, where apatite-(Ca P OH)-2H has been used to destroy formaldehyde (HCHO), it is believed that CaT and OH− proximity are critical to promoting the adsorption/activation of HCHO. It has been suggested that oxygen absorption may be enhanced by replacement of Ca2+ and P5+ by Ce4+ and Si4+, that may favour the creation of SinO3n+1 polysome domains. While our understanding of the technological applications of polysomes is rudimentary, we believe the demonstration of module building principles is sufficiently compelling to warrant their consideration in the design of apatite-based advanced materials.
A formal description of apatite (2 ≤ N ≤ ∞) polysomes has been developed in which moduless are arranged by 60° rotation twinning to generate long-period structures. This group of compounds has not received significant attention, although the N = 3 germanate polysome displays useful ferro- and pyroelectric properties. It is probable that the chemistry of N > 2 compounds is substantially broader than currently recognized. Electron microscopy has recorded disordered intergrowths of the apatite modules, demonstrating that these are stable structure building entities, rather than abstract crystallographic constructs. As with all polysomatic families, these structural units can be arranged with distinct chemistries, that in apatites controls the relative size of the (AF2(BO4)3) framework with respect to the tunnel contents, leading to systematic adjustments of the AFO6 metaprism twist angles (φ), which ultimately control channel diameter and polysome symmetry. Furthermore, oxidized and reduced varieties exist where BO4 tetrahedra are replaced by BO5 and BO3 entities. With this range of adjustable parameters to hand, it will be feasible to tune and optimize a variety of functionalities including electrical properties, ion conduction, radiation resistance and repair, cation and anion exchange, and magnetic susceptibility amongst others. Nonetheless, exploiting this expanded apatite phase space will not be without challenges. For example, it was found here that polysome powders are often multiphase assemblages of chemically differentiated structural analogues, as observed in ganomalite-(Pb Ge/Si □)-3T. Designing enhanced synthesis methods that intimately mix constituents to promote rapid equilibration will be a prerequisite to the development of apatite polysomes as practical functional materials.
Crystal structure: contains datablocks Pb15Ge9O33, Bi1.5Na1.5Pb12Ge9O33, Bi3Na3Pb9Ge9O33, Ca8Pb12Si12O42Cl3.8O0.1. DOI: https://doi.org/10.1107/S0108768109053981/bk5091sup1.cif
Neutron/X-ray diffraction profiles and tables of crystal data. DOI: https://doi.org/10.1107/S0108768109053981/bk5091sup2.pdf
Neutron TOF powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Pb15Ge9O33sup3.rtv
X-ray powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Pb12Na1.5Bi1.5Ge9O33sup4.rtv
Neutron TOF powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Pb12Na1.5Bi1.5Ge9O33sup5.rtv
X-ray powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Pb9Na3Bi3Ge9O33sup6.rtv
Neutron TOF powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Pb9Na3Bi3Ge9O33sup7.rtv
X-ray powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Ca8Pb12Si12O42Cl3.8O0.1sup8.rtv
Neutron TOF powder data file (CIF format). DOI: https://doi.org/10.1107/S0108768109053981/bk5091Ca8Pb12Si12O42Cl3.8O0.1sup9.rtv
|Mr = 4289.47||V = 966.23 (1) Å3|
|Hexagonal, P3||Z = 1|
|a = 10.22887 (1) Å||Neutron radiation|
|c = 10.66337 (2) Å||T = 298 K|
|ISIS HRPD |
|Data collection mode: transmission|
|Specimen mounting: vanadium can with He exchange gas||Scan method: time of flight|
|Rp = 0.036||4540 data points|
|Rwp = 0.043||96 parameters|
|Rexp = 0.030||0 restraints|
|Pb1||0.3333||0.6667||0.3346 (11)||0.019 (2)|
|Pb2||0.3333||0.6667||0.6581 (11)||0.006 (1)|
|Pb3||0.6667||0.3333||0.3241 (9)||0.014 (1)|
|Pb4||0.6667||0.3333||0.6715 (11)||0.02 (1)|
|Pb7||0.2700 (3)||0.2714 (3)||0.1771 (9)||0.0171 (6)|
|Pb8||0.2569 (3)||0.2532 (3)||0.8110 (9)||0.0099 (6)|
|Pb9||0.2512 (3)||0.9939 (4)||0.5111 (9)||0.0135 (6)|
|Ge1||0.0195 (3)||0.3960 (3)||0.1422 (9)||0.0094 (1)|
|Ge2||0.0042 (5)||0.3859 (4)||0.8380 (9)||0.015 (9)|
|Ge3||0.3944 (4)||0.3869 (3)||0.4970 (9)||0.0094 (5)|
|O1||0.0959 (5)||0.3218 (6)||0.2556 (10)||0.021 (1)|
|O2||0.0880 (6)||0.3297 (6)||0.7300 (10)||0.015 (1)|
|O3||0.1229 (5)||0.5963 (6)||0.1531 (11)||0.023 (1)|
|O4||0.0842 (5)||0.5850 (6)||0.8358 (10)||0.014 (1)|
|O5||0.8290 (5)||0.3272 (5)||0.1625 (10)||0.021 (1)|
|O6||0.8096 (6)||0.2890 (6)||0.8332 (9)||0.014 (1)|
|O7||0.0666 (4)||0.3551 (4)||0.9886 (11)||0.0134 (9)|
|O8||0.2950 (4)||0.4840 (5)||0.4991 (11)||0.013 (1)|
|O9||0.5859 (6)||0.5036 (6)||0.5317 (9)||0.021 (1)|
|O10||0.3729 (6)||0.2879 (6)||0.3613 (10)||0.020 (1)|
|O11||0.3185 (6)||0.2420 (6)||0.6146 (10)||0.021 (1)|
|Mr = 4015.83||V = 935.65 (1) Å3|
|Hexagonal, P3||Z = 1|
|a = 10.13385 (3) Å||Neutron radiation|
|c = 10.52045 (6) Å||T = 298 K|
|ISIS HRPD |
|Data collection mode: transmission|
|Specimen mounting: vanadium can with He exchange gas||Scan method: time of flight|
|Rp = 0.040||4540 data points|
|Rwp = 0.040||96 parameters|
|Rexp = 0.017||0 restraints|
|Pb1||0.3333||0.6667||0.312 (2)||0.025 (2)||0.893|
|Na1||0.3333||0.6667||0.312 (2)||0.025 (2)||0.107|
|Pb2||0.3333||0.6667||0.646 (2)||0.009 (1)||0.844|
|Na2||0.3333||0.6667||0.646 (2)||0.009 (1)||0.156|
|Pb3||0.6667||0.3333||0.301 (2)||0.027 (2)||0.469|
|Na3||0.6667||0.3333||0.301 (2)||0.027 (2)||0.062|
|Bi3||0.6667||0.3333||0.301 (2)||0.027 (2)||0.469|
|Pb4||0.6667||0.3333||0.674 (2)||0.024 (2)||0.468|
|Na4||0.6667||0.3333||0.674 (2)||0.024 (2)||0.065|
|Bi4||0.6667||0.3333||0.674 (2)||0.024 (2)||0.467|
|Na6||0.6667||0.3333||−0.012 (4)||0.025 (2)||0.522|
|Bi6||0.6667||0.3333||−0.012 (4)||0.025 (2)||0.478|
|Pb7||0.2593 (7)||0.2603 (8)||0.170 (2)||0.017 (2)|
|Pb8||0.2632 (8)||0.2633 (9)||0.809 (2)||0.024 (2)|
|Pb9||0.2483 (4)||0.9970 (5)||0.493 (2)||0.023 (2)|
|Ge1||0.0079 (9)||0.3903 (8)||0.142 (2)||0.023 (2)|
|Ge2||0.0170 (8)||0.3971 (8)||0.837 (2)||0.013 (1)|
|Ge3||0.3963 (4)||0.3910 (5)||0.489 (2)||0.016 (2)|
|O1||0.0811 (4)||0.3118 (10)||0.249 (2)||0.035 (3)|
|O2||0.0870 (12)||0.3291 (9)||0.722 (2)||0.018 (2)|
|O3||0.0993 (11)||0.5951 (13)||0.144 (2)||0.029 (3)|
|O4||0.1210 (11)||0.5962 (13)||0.820 (2)||0.018 (2)|
|O5||0.8211 (14)||0.3167 (14)||0.151 (2)||0.020 (2)|
|O6||0.8168 (10)||0.3171 (11)||0.838 (2)||0.023 (2)|
|O7||0.0706 (5)||0.3573 (5)||0.989 (2)||0.041 (3)|
|O8||0.2858 (6)||0.4807 (6)||0.493 (2)||0.026 (3)|
|O9||0.5931 (8)||0.5079 (8)||0.514 (2)||0.018 (2)|
|O10||0.3706 (11)||0.2766 (12)||0.357 (2)||0.027 (3)|
|O11||0.3313 (9)||0.2558 (10)||0.613 (2)||0.033 (3)|
|Mr = 3742.18||V = 916.93 (1) Å3|
|Hexagonal, P3||Z = 1|
|a = 10.08745 (3) Å||Neutron radiation|
|c = 10.40506 (7) Å||T = 298 K|
|ISIS HRPD |
|Data collection mode: transmission|
|Specimen mounting: vanadium can with He exchange gas||Scan method: time of flight|
|Rp = 0.053||4540 data points|
|Rwp = 0.045||96 parameters|
|Rexp = 0.018||0 restraints|
|Pb1||0.3333||0.6667||0.326 (5)||0.025 (2)||0.320|
|Na1||0.3333||0.6667||0.326 (5)||0.025 (2)||0.173|
|Bi1||0.3333||0.6667||0.326 (5)||0.025 (2)||0.507|
|Na2||0.3333||0.6667||0.643 (6)||0.023 (2)||0.323|
|Bi2||0.3333||0.6667||0.643 (6)||0.023 (2)||0.677|
|Na3||0.6667||0.3333||0.296 (5)||0.032 (3)||0.198|
|Bi3||0.6667||0.3333||0.296 (5)||0.032 (3)||0.802|
|Na4||0.6667||0.3333||0.684 (5)||0.017 (1)||0.253|
|Bi4||0.6667||0.3333||0.684 (5)||0.017 (1)||0.747|
|Na6||0.6667||0.3333||−0.034 (6)||0.032 (3)|
|Pb7||0.2648 (9)||0.2666 (10)||0.167 (5)||0.017 (2)||0.995|
|Na7||0.2648 (9)||0.2666 (10)||0.167 (5)||0.017 (2)||0.005|
|Pb8||0.2574 (10)||0.2621 (11)||0.810 (5)||0.016 (2)||0.901|
|Na8||0.2574 (10)||0.2621 (11)||0.810 (5)||0.016 (2)||0.099|
|Pb9||0.2443 (5)||0.9969 (7)||0.489 (5)||0.025 (2)||0.975|
|Na9||0.2443 (5)||0.9969 (7)||0.489 (5)||0.025 (2)||0.015|
|Ge1||0.0127 (12)||0.3971 (12)||0.142 (1)||0.021 (2)|
|Ge2||0.0169 (13)||0.3959 (12)||0.833 (5)||0.017 (2)|
|Ge3||0.3994 (6)||0.3932 (6)||0.486 (5)||0.014 (2)|
|O1||0.0707 (14)||0.2950 (10)||0.248 (5)||0.025 (2)|
|O2||0.0888 (15)||0.3331 (13)||0.718 (5)||0.021 (2)|
|O3||0.119 (2)||0.597 (2)||0.165 (5)||0.044 (4)|
|O4||0.1158 (18)||0.6002 (18)||0.830 (5)||0.033 (3)|
|O5||0.8245 (14)||0.3306 (15)||0.150 (5)||0.022 (2)|
|O6||0.8128 (16)||0.3126 (16)||0.831 (5)||0.026 (3)|
|O7||0.0677 (7)||0.3550 (7)||0.989 (6)||0.023 (2)|
|O8||0.2906 (8)||0.4852 (7)||0.491 (6)||0.027 (3)|
|O9||0.5961 (9)||0.5108 (10)||0.514 (5)||0.029 (3)|
|O10||0.3751 (17)||0.2795 (16)||0.354 (5)||0.041 (4)|
|O11||0.3334 (16)||0.2534 (16)||0.609 (5)||0.029 (3)|
|Mr = 3952.35||V = 1168.24 (1) Å3|
|Hexagonal, P63/m||Z = 1|
|a = 10.0898 (1) Å||Neutron radiation|
|c = 13.2506 (1) Å||T = 298 K|
|ISIS HRPD |
|Data collection mode: transmission|
|Specimen mounting: vanadium can with He exchange gas||Scan method: time of flight|
|Rp = 0.070||4540 data points|
|Rwp = 0.059||71 parameters|
|Rexp = 0.017||0 restraints|
|Ca1||0.3333||0.6667||0.9953 (6)||0.020 (2)|
|Pb1||0.2475 (2)||0.2660 (2)||0.1085 (1)||0.027 (3)|
|Si1||0.0253 (4)||0.4185 (4)||0.3639 (3)||0.025 (2)|
|O1||0.0774 (4)||0.3300 (4)||0.4442 (2)||0.025 (2)|
|O2||0.8606 (3)||0.3956 (3)||0.6206 (2)||0.026 (3)|
|O3||0.8508 (3)||0.3702 (3)||0.3709 (2)||0.024 (2)|
|O4||0.0718 (5)||0.3825 (5)||0.25||0.027 (3)|
|Cl1||0||0||0.242 (1)||0.021 (2)||0.45 (1)|
|Cl2||0||0||−0.009 (1)||0.027 (2)||0.5 (1)|
1This nomenclature was reviewed by the IMA Commission to address inconsistencies in naming apatite minerals (see also Nickel & Mandarino, 1987).
2Supplementary data for this paper are available from the IUCr electronic archives (Reference: BK5091). Services for accessing these data are described at the back of the journal.
3We have chosen the term pseudomorphism in preference to the more cumbersome, but strictly correct, pseudopolymorphism. This crystallographic use of pseudomorphism is distinct from the geological meaning that describes a mineral altered in a manner that preserves the external form but the internal structure and chemical composition is modified.
The authors would like to thank Fui Ling Lew and Yu Yan Liang for sample preparation and the Rutherford Appleton Laboratory for access to neutron beam time. In addition, the authors gratefully acknowledge Professor Stefan Merlino (University of Pisa) for useful discussion regarding silicate framework topologies. This work was funded by A*STAR SERC Grant `Optimization of Oxygen Sublattices in Solid Oxide Fuel Cell Apatite Electrolytes' number 082 101 0021.
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