Polysomatic apatites

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 A_5NB_3NO_9N + 6X_Nδ (2 ≤ N ≤ ∞) that is built by condensing N apatite modules (A₅B₃O₁₈X_δ) in configurations to create B_nO_3n + 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.

1. Introduction

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 A^F₄A^T₆(BO₄)₆X₂ (A = large cations; B = metals or metalloids; X = anion) and a zeolitic topology where a A^F₄(BO₄)₆ framework (F) creates tunnels (T), whose diameter adjusts to the filling characteristics of the A^T₆X₂ 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 T_c 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 (A^F) that are ideally coordinated to six oxygens in the disposition of A^FO₆ 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 [001] face-sharing A^FO₆ 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 (A^T) and anions (X), such that when the A^T₃X 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 [A^F₄][A^T₆][(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 A^T 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 A^F₂A^T₃B₃O₁₈X 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 B_nO_3n+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 A^F₂A^T₃B₃O₉X 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 A^F₄A^T₆B₆O₂₄X₂. In this configuration, the BO₄ tetrahedra remain isolated and the familiar [A^F₄][A^T₆][(BO₄)₆]X₂ apatite motif results as in [Pb₄][Pb₆][(Si/SO₄)₆](Cl/OH)₂ mattheddleite (Fig. 2a).

Figure 1 Schematic representation of α and β, A5B3O18X2 apatite modules (assuming a hexagonal basal plane) that are related by [001]hex 60° rotation twinning. The principal idealization is that the A^FO6 polyhedron is represented as a trigonal prism, but in real polysomes, twisting of the triangular faces through an angle φ creates metaprisms.

Figure 2 Stacking of α and β modules for the construction of …β(αβ)α… apatite-2H, A10(BO4)6X2 (a) and the hypothetical structure …α(α)α… apatite-1H, A5(B3O9)X (b) polysome end-members. The coincident lattice where condensation and elimination of oxygen takes place is emphasized by brackets. For clarity the A^T and X ions are not included.

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 A^T cations within the polysome tunnel also have discrete configurations such that for N = 2 face-sharing columns of A^T₆ 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 A^T₃ triangles if small enough, but more often are displaced along the module stacking direction to partially occupied crystallographic sites (Fig. 4).

Table 1
Stacking sequences and compositions of polysomatic apatites

N	Crystallochemical formulae	Chemical formulae	Stacking sequence
2	A10(BO4)6X2δ	A10B6O24X2δ†	…β(αβ)α…
3	A15(B2O7)3(BO4)3X3δ	A15B9O33X3δ‡	…β(ααβ)α…
4	A20(B3O10)3(BO3)3X4δ	A20B12O42X4δ	…β(αααβ)α…
	A20(B2O7)6X4δ	A20B12O42X4δ§	…β(ααββ)α…
5	A25(B4O13)3(BO4)3X5δ	A25B15O51X5δ	…β(ααααβ)α…
	A25(B3O10)3(B2O7)3X5δ	A25B15O51X5δ	…β(αααββ)α…
6	A30(B5O16)3(BO4)3X6δ	A30B18O60X6δ	…β(αααααα)α
	A30(B4O13)3(B2O7)3X6δ	A30B18O60X6δ	…β(ααααββ)α
	A30(B3O10)6X6δ	A30B18O60X6δ	…β(αααβββ)α…
7	A35(B6O19)3(BO4)3X7δ	A35B21O69X7δ	…β(ααααααβ)α…
	A35(B5O16)3(B2O7)3X7δ	A35B21O69X7δ	…β(αααααββ)α…
	A35(B4O13)3(B3O10)3X7δ	A35B21O69X7δ	…β(ααααβββ)α…
8	A40(B7O22)3(BO4)3X8δ	A40B24O78X8δ	…β(αααααααβ)α…
	A40(B6O19)3(B2O7)3X8δ	A40B24O78X8δ	…β(ααααααββ)α…
	A40(B5O16)3(B3O10)3X8δ	A40B24O78X8δ	…β(αααααβββ)α…
	A40(B4O13)6X8δ	A40B24O78X8δ	…β(ααααββββ)α…
∞	A5(B3O9)Xδ	A5B3O9Xδ	…α(α)α…

†Apatite.
‡Ganomalite.
§Nasonite.

Figure 3 Possible tetrahedral stacking sequences for polysomes with N > 4.

Figure 4 Arrangement of the A^T octahedra and/or trigonal prisms in (a) apatite-2S, where a small X anion is positioned in the A3^T triangle, (b) ganomalite-3S with the X-site vacant and (c) nasonite-4S that contains a large X anion centred in the A^T6 polyhedra.

The silicate mineral ganomalite is an example of the N = 3 polysome with the module sequence …β(ααβ)α… and ideal formula [A^F₆][A^T₉][(B₂O₇)₃(BO₄)₃]X₃. The composition is Pb₉Ca_5.44Mn_0.56Si₉O₃₃ (Carlson et al., 1997) that when rearranged as [Ca_5.44Mn_0.56][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 A^FO₆ 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 (Mn_0.56Ca_0.44)O₆ trigonal prism having φ = 0° (Fig. 6b). In common with all N odd structures, the highest possible symmetry space group is ideally .

Figure 5 Polysome stacking sequences for (a) N = 3, (b) N = 4 without a centre of symmetry and (c) N = 4 with a centre of symmetry.

Figure 6 Polyhedral drawings shown in [100] (left) and [001] (right) of (a) N = 2 Pb10(Si/SO4)6Cl2 − x(OH)x mattheddleite-(Pb Si/S Cl)-2H, (b) N = 3 Ca5.44Mn0.56Pb9(Si2O7)3(SiO4)3□3 ganomalite-(Pb Si □)-3H and (c) N = 4 Ca8Pb12(Si2O7)6Cl4 nasonite-(Ca/Pb Si Cl)-4H with associated twist angles of the individual modules. The A^FO6 twist angles across (αα) boundaries are always smaller than (αβ) boundaries.

Nasonite with N = 4 adopts the configuration …β(ααββ)α…, where the ideal formulation [A^F₈][A^T₁₂][(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 [Ca₉Na_0.5][(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. [La_3.33][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)₆M_xO_yH_z [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. [Nd_3.33][La₂Nd₄](SiO₄)₆O₂]; Malinovskii et al., 1990] and anion [e.g. Ca₁₀(PO₄)₆I_2/3O_2/3; 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 [Ca_5.44Mn_0.56][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 Pb_15-xA_xGe_9-yB_yO₃₃, 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 ≤ T_c ≤ 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. Pb_15-xBi_xGe₉O_33+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 (Pb_15-xBi_xGe_9-xB_xO₁₁) 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.

Table 2
Reported lattice parameters for N ≥ 3 apatite polysomes (e.s.d.s shown where reported)

Phase	Crystal data (Å)	Reference
Ca5MnPb9(Si2O7)3(SiO4)3	a = 9.82, c = 10.13	Dunn et al. (1985)
Ca5.44Mn0.56(Si2O7)3(SiO4)3	a = 9.8456 (3), c = 10.1438 (4)	Carlson et al. (1997)
Pb15(Ge2O7)3(GeO4)3	a = 10.19, c = 10.624	Kay et al. (1975)
Ca6Pb9(Si2O7)3(SiO4)3	a = 9.849 (2), c = 10.152 (2)	Engel (1972)
Pb9Bi3Na3(Si2O7)3(SiO4)3	a = 9.876 (1), c = 10.175 (1)	Engel (1972)
Cd6Pb9(Si2O7)3(SiO4)3	a = 9.810 (4), c = 10124 (4)	Engel (1972)
Cd6Pb9(Ge2O7)3(GeO4)3	a = 10.104 (1), c = 10.379 (1)	Engel (1972)
Pb9Bi3Na3(Ge2O7)3(GeO4)3	a = 10.084 (1), c = 10.398 (1)	Engel (1972)
Pb15(Ge2O7)3(TiO4)3	a = 10.294 (7), c = 10.730 (5)	Goswami, Mahapatra & Choudhary (1998)
Ca0.15Pb14.85Ge7.5Ti1.5O33	a = 10.2574, c = 10.6706	Goswami et al. (1998b)
Sr0.15Pb14.85Ge7.5Ti1.5O33	a = 10.2625, c = 10.6772	Goswami et al. (1998b)
Sr0.15Pb14.85Ge7.5Ti1.5O33	a = 10.2727, c = 10.6905	Goswami et al. (1998b)
Pb15(Ge2O7)3(ZrO4)3	a = 10.2818, c = 10.7168	Goswami et al. (1997)
Ca0.6Pb14.4(Ge2O7)3(GeO4)3	a = 10.293 (8), c = 10.665 (9)	Misra et al. (1995)
Sr0.3Pb14.7(Ge2O7)3(GeO4)3	a = 10.229 (5), c = 10.67(4)	Misra et al. (1998)
Sr0.6Pb14.4(Ge2O7)3(GeO4)3	a = 10.220 (8), c = 10.661 (4)	Misra et al. (1998)
Sr0.9Pb14.1(Ge2O7)3(GeO4)3	a = 10.216 (1), c = 10.654(3)	Misra et al. (1998)
Ba0.3Pb14.7(Ge2O7)3(GeO4)3	a = 10.2465, c = 10.6758	Choudhary & Misra (1998)
Ba0.6Pb14.4(Ge2O7)3(GeO4)3	a = 10.2507, c = 10.6790	Choudhary & Misra (1998)
Ba0.9Pb14.1(Ge2O7)3(GeO4)3	a = 10.2540, c = 10.6847	Choudhary & Misra (1998)
Pb14.7Bi0.3Ge8.7B0.3O33	a = 10.219 (1), c = 10.667 (2)	Otto & Loster (1993)
Pb14.4Bi0.6Ge8.4B0.6O33	a = 10.212 (2), c = 10.664 (2)	Otto & Loster (1993)
Ca8Pb12(Si2O7)6Cl4	a = 10.08, c = 13.27	Giuseppetti et al. (1971)

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 Ca_20-xEu_x(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 `Pb<sub>5</sub>Ge<sub>3</sub>O<sub>11</sub>', 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 `Pb<sub>5</sub>Ge<sub>3</sub>O<sub>11</sub>' with the hexagonal lattice parameters a = 10.251 and c = 10.658 Å. We can identify the stable crystalline phase as Pb<sub>15</sub>(Ge<sub>2</sub>O<sub>7</sub>)<sub>3</sub>(GeO<sub>4</sub>)<sub>3</sub>□<sub>3</sub> 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 – Pb_15-xBi_x/2Na_x/2(Ge₂O₇)₃(GeO₄)₃□₃ and Ca₆Pb₉(Si_2-yGe_yO₇)₃(Si_1-zGe_zO₄)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.

2.1. Synthesis

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 BO<sub>4</sub> 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/GeO<sub>4</sub> and Si/Ge<sub>2</sub>O<sub>7</sub> 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.

Table 3
Experimental details

For all structures: Z = 1. Experiments were carried out at 298 K with neutron radiation. Refinement was with 0 restraints.

	Pb15Ge9O33	Bi1.5Na1.5Pb12Ge9O33	Bi3Na3Pb9Ge9O33	Ca8Pb12Si12O42Cl3.8O0.1
Crystal data
Chemical formula	Pb15Ge9O33	Bi1.5Na1.5Pb12Ge9O33	Bi3Na3Pb9Ge9O33	Ca8Pb12Si12O42Cl3.8O0.1
Mr	4289.47	4015.83	3742.18	3952.35
Crystal system, space group	Hexagonal, P3	Hexagonal, P3	Hexagonal, P3	Hexagonal, P63/m
a, c (Å)	10.22887 (1), 10.66337 (2)	10.13385 (3), 10.52045 (6)	10.08745 (3), 10.40506 (7)	10.0898 (1), 13.2506 (1)
V (Å^3)	966.23 (1)	935.65 (1)	916.93 (1)	1168.24 (1)
Specimen shape, size (mm)	Cylinder, 10 × 10 × 100	Cylinder, 10 × 10 × 100	Cylinder, 10 × 10 × 100	Cylinder, 10 × 10 × 100
Data collection
Diffractometer	ISIS HRPD	ISIS HRPD	ISIS HRPD	ISIS HRPD
Specimen mounting	Vanadium can with He exchange gas	Vanadium can with He exchange gas	Vanadium can with He exchange gas	Vanadium can with He exchange gas
Data collection mode	Transmission	Transmission	Transmission	Transmission
Scan method	Time-of-flight	Time-of-flight	Time-of-flight	Time-of-flight
Time-of-flight (TOF) values (µs)	TOFmin = 30, TOFmax = 125, TOFstep = 0.005	TOFmin = 30, TOFmax = 125, TOFstep = 0.005	TOFmin = 30, TOFmax = 125, TOFstep = 0.005	TOFmin = 30, TOFmax = 125, TOFstep = 0.005
Refinement
R factors and goodness of fit	Rp = 0.036, Rwp = 0.043, Rexp = 0.030, χ^2 = 2.045	Rp = 0.040, Rwp = 0.040, Rexp = 0.017, χ^2 = 5.523	Rp = 0.053, Rwp = 0.045, Rexp = 0.018, χ^2 = 6.250	Rp = 0.070, Rwp = 0.059, Rexp = 0.017, χ^2 = 11.560
No. of data points	4540	4540	4540	4540
No. of parameters	96	96	96	71

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. Results

3.1. Pb_15 − xBi_x/2Na_x/2(Ge₂O₇)₃(GeO₄)₃, x = 0, 3 and 6: ganomalite-(Pb/Bi/Na Ge □)-3S

3.1.1. Products

Single-phase materials were produced for x = 0, 3 and 6, but attempts to prepare lead-free ganomalite Bi_7.5Na_7.5Ge₉O₃₃ (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: wR_p = 0.043, R_F = 0.036, χ² = 2.001; : wR_p = 0.066, R_F = 0.074, χ² = 4.214), in agreement with the room-temperature structure of Kay et al. (1975). As with previous studies, the Pb5^F 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 A^F and A^T 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 Pb₁₂Bi_1.5Na_1.5Ge₉O₃₃ (x = 3) and Pb₉Bi₃Na₃Ge₉O₃₃ (x = 6) Na ions strongly partition to the framework. A5^F and A6^F were the most favoured cation-acceptor sites for sodium (from the Pb₁₅Ge₉O₃₃ parent), A2^F the second most favoured site, with the A1^F/3^F/4^F positions showing similar affinity for Na occupancy; the preferred sites (A5^F and A6^F) 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 A^F sites, rather than the A^T 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 A^T sites, e.g. Pb_7.4Bi_0.3Na_2.3(PO₄)₆□₂ (Hamdi et al., 2007) and Pb_4.6Bi_0.4Ca_2.6Na_2.4(PO₄)₆□₂ (Hamdi et al., 2004). For Pb₁₂Bi_1.5Na_1.5Ge₉O₃₃ bismuth entered A5^F and A6^F preferentially with lead favouring A1^F and A2^F. The site occupancies of A3^F and A4^F were ambiguous with either all the Bi at A3^F with all the Pb located at A4^F, 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 A^F/A^T 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 A^T 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 A^F positions to yield a total of 3.32 Bi³⁺ per unit formula, compared with the ideal value of 3. An unrealistically high ADP for A1^F (U_iso = 0.058 ų) was improved (U_iso = 0.025 ų) 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 A^F—O bond lengths of the A6^F 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 [Bi_x/2Na_x/2][Pb_15-x](Ge₂O₇)₃(GeO₄)₃□₃.

Figure 7 Polyhedral representation of …β(ααβ)α… ganomalite-(Bi/Na/Pb Ge □)-3T [Bi3Na3][Pb9][(Ge2O7)3(GeO4)3]□3 including the twist angles (φ) for the αα and αβ boundaries. The metaprisms at the α–α boundary are primarily occupied by smaller Na^+ and have an acute φ, while at the α-β boundary Bi^+ is dominant and φ is larger. Pb^2+ partitions almost exclusively to the tunnel sites where lone-pair electrons occupy the channel. The substantial distortion of the BiO6 metaprisms may imply that stereochemically active lone-pair electrons are operative.

3.2. Ca₆Pb₉(Si_2 − xGe_xO₇)₃(Si_1 − xGe_xO₄)₃□₃: ganomalite-(Pb Si/Ge □)-3S

3.2.1. Products

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 (Ca_10-xPb_x)(VO₄)₆F₂ apatites were shown to be due to the non-equilibrated partitioning of calcium and lead over A^F(4f) and A^T(6h) sites (P6₃/m), which favoured Pb²⁺ preferentially entering the larger A^T 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.

Table 4
(a) Pawley fit residuals (R_wp) for different number of ganomalite-3H(T) phases contained in samples of Ca₆Pb₉Si_9 − xGe_xO₃₃ with x = 0, 2, 4.5, 7 and 9; (b) refined lattice parameters and volumes determined from the Pawley fits

The phase with intermediate lattice parameters or the `equilibrated' phase is designated as `B' in all cases.

(a)
x	1 phase	2 phase	3 phase
0	12.24	6.82	5.36
2	11.59	6.13	4.88
4.5	16.11	8.76	6.43
7	14.86	9.53	7.70
9	16.90	13.22	10.31

(b)
	x = 0			x = 2
Phase	0A	0B	0C	2A	2B	2C
a (Å)	9.8783 (1)	9.8820 (1)	9.8870 (2)	9.9038 (2)	9.9181 (2)	9.9480 (3)
c (Å)	10.1891 (2)	10.2163 (2)	10.2406 (3)	10.2232 (3)	10.2399 (3)	10.2653 (4)
Vol (Å^3)	861.05 (3)	864.00 (3)	866.93 (4)	868.40 (4)	872.34 (4)	879.79 (6)
Crystal size (nm)	280 (15)	350 (40)	180 (8)	265 (20)	193 (15)	68 (1)

	x = 4.5			x = 7
Phase	4.5A	4.5B	4.5C	7A	7B	7C
a (Å)	9.9447 (3)	9.9998 (2)	10.0517 (3)	10.0198 (7)	10.0777 (2)	10.0922 (2)
c (Å)	10.2651 (5)	10.3054 (3)	10.3494 (5)	10.3351 (10)	10.3649 (2)	10.4114 (3)
Vol (Å^3)	879.17 (7)	892.44 (5)	905.58 (7)	898.60 (15)	911.64 (4)	918.35 (5)
Crystal size (nm)	93 (3)	100 (3)	92 (3)	46 (1)	132 (5)	188 (10)

	x = 9
Phase	9A	9B	9C
a (Å)	10.1061 (2)	10.0991 (2)	10.1108 (2)
c (Å)	10.3817 (2)	10.4234 (3)	10.4710 (3)
Vol (Å^3)	918.26 (4)	920.69 (4)	927.02 (5)
Crystal size (nm)	314 (20)	200 (11)	179 (7)

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 [001] 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.

Figure 8 Refined lattice parameters for the three phase assemblages in Ca6Pb9Si9 − xGexO33 polysomes. Disequilbrium is reminiscent of that observed previously in (Ca,Pb)10(VO4)6F2 apatites where several weeks high-temperature annealing were required to obtain a stable phase assemblage (Dong & White, 2004a,b). Over the whole compositional range the greater span of the c axis, compared with the basal plane, may reflect module, chemical or stacking disorder.

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 [210] that will conform to plane symmetry p1 and p11m, respectively. Several [210] CBED patterns were collected under different conditions to verify the presence of a mirror plane parallel to [20] 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).

Figure 9 (a) Convergent-beam electron diffraction (CBED) pattern of [Ca6][Pb9][(Si2O7)3(SiO4)3]□3 aligned along [210]. The absence of a mirror plane parallel to [20] is clear from the non-equivalence of the indexed reflections and is consistent with trigonal symmetry. (b) and (c) are simulated CBED for P3 and . In hexagonal symmetry the mirror plane (vertical line) is evident as, for example, in the mirror relationship of 004 and 00 reflections.

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

3.3.1. Products

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.

Figure 10 Rietveld refinement of the neutron time-of flight (TOF) data for Ca8Pb12(Si2O7)6Cl4.

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 [001] in an estimated 5 vol% of crystals. [100] SAED patterns from an area containing disorder (Fig. 11a) contains, in addition to dynamically forbidden (00l) reflections with l ≠ 2n, pronounced [001]* 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 Si_nO_3n+1, n ≥ 4 are stereochemically unfavourable.

Figure 11 Disordered module intergrowth (polysynthetic twinning) in nominal N = 4 Ca8Pb12(Si2O7)6Cl4 was observed in ≃ 5% of crystal fragments. (a) [100]* SAEDs from areas containing α, β module disorder are characterized by the presence of dynamical forbidden (00l) reflections with l ≠ 2n and pronounced streaking. (b) Low magnification images show modulated contrast indicative of disorder. (c) HRTEM can be interpreted as mainly N = 4 and N = 3 polysomes with intercalation of N = 5 or 7 recognized less frequently.

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. Discussion

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:

• (i) cation ordering in chemically complex members with minimal A^F₄(BO₄)₆ framework distortion (metaprism twist angle φ < 25°) that is accommodated in the P6₃, and maximal isomorphic subgroups of P6₃/m;

• (ii) intra- and inter-tunnel anion ordering that leads to P2₁/b varieties, possible modulation and extension of the (001) basal plane;

• (iii) framework topological tuning where the A^T₆X₂ tunnel contents are sufficiently small or sub-stoichiometric that the framework must constrict by increasing the A^FO₆ metaprism twist angle (φ) to > ∼ 25° that is accompanied by a reduction to P2₁/m, P2₁ or symmetry;

• (iv) framework hybrid intergrowth in which oxygen super- and sub-stoichiometry leads to partial or complete replacement of BO₄ tetrahedra by BO₅ and BO₃ polyhedra, sometimes accompanied by a reduction in symmetry;

• (v) polymorphic transformations initiated by the application of temperature/pressure that changes relative ionic sizes to drive framework tuning;

• (vi) pseudomorphism³ whereby quite small compositional adjustments lead to breaches in the critical limits of the metaprism twist angle and a change in symmetry; and

• (vii) polysomatism that arises by rotational twinning of A₅B₃O₁₈X_δ modules in ordered and disordered sequences.

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 A^F₄A^T₆(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 [001] intergrowths, and preliminary electron diffraction of Ba₁₀(ReO₅)₆O₂ shows diffuse scatter indicative of (00l) polysome disorder (Pramana & White, 2009).

Figure 12 An expanded apatite phase space containing all permutations of polymorphs, pseudomorphs, polysomes and hybrid structures that may be feasible.

4.2. Future polysome chemistries

All apatite polysomes reported to date are predominantly plumbous, and it is clear that Pb²⁺ partitions to the A^T 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 A^F 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 A^T 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 A^F 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 A^F 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 (A_n+1B_nO_3n+1) superconducting cuprates where it was predicted, and observed experimentally, that longer-period polysomes yielded higher high T_c (Skakle, 1998).

Moreover, outstanding questions remain regarding the extensively studied structures of the cation-deficient La_9.33(SiO₄)₆O₂ and La_9.67(SiO₄)₆O_2.5 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 La_9.33(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 La_9.67(SiO₄)₆O_2.5 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 [Ca₉Na_0.5][(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.

Table 5
Interpretation of silicate apatite electrolytes as ordered polysomes

Note the conventional representation does not include the Si₂O₇ and Si₂O₉ entities identified by ²⁹Si NMR.

Composition	Conventional representation	Polysome representation	N
La9.33Si6O26	[La3.33□0.67][La6][(SiO4)6]O2	[La10□2][La18][(SiO4)6(Si2O9)3(Si2O7)3]O6	6
La9.67Si6O26.5	[La3.67□0.33][La6][(SiO4)6]O2.5	[La22□2][La36][(SiO4)18(Si2O9)6(Si2O7)3]O12	12

Figure 13 (a) Postulated topology of Si2O7 constructed cages surrounding La^3+ vacancies in the LaO6 prismatic columns of lanthanum silicate oxyapatite electrolytes. Also indicated in blue are Si2O9 dimers, which can be formed with interstitial oxygen ions. (b) Idealized, and to date hypothetical, [La10□2][La18][(Si2O7)3(Si2O9)3(SiO4)6]O6 structural arrangement in equilibrated La9.33Si6O26, where the La^3+ vacancies condense as Si2O7 cages (αα), with interstitial oxygen ions between some (αβ) boundaries, to create an N = 6 polysome.

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 Ca^T 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 Si_nO_3n+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.

5. Conclusions

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 (A^F₂(BO₄)₃) framework with respect to the tunnel contents, leading to systematic adjustments of the A^FO₆ 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.

Supporting information

Computing details

(Pb15Ge9O33)

Crystal data

Mr = 4289.47	V = 966.23 (1) Å^3
Hexagonal, P3	Z = 1
a = 10.22887 (1) Å	Neutron radiation
c = 10.66337 (2) Å	T = 298 K

Data collection

ISIS HRPD diffractometer	Data collection mode: transmission
Specimen mounting: vanadium can with He exchange gas	Scan method: time of flight

Refinement

Rp = 0.036	4540 data points
Rwp = 0.043	96 parameters
Rexp = 0.030	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
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)
Pb5	0.3333	0.6667	0.997	0.006 (1)
Pb6	0.6667	0.3333	−0.0048	0.015 (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)

(Bi1.5Na1.5Pb12Ge9O33)

Crystal data

Mr = 4015.83	V = 935.65 (1) Å^3
Hexagonal, P3	Z = 1
a = 10.13385 (3) Å	Neutron radiation
c = 10.52045 (6) Å	T = 298 K

Data collection

ISIS HRPD diffractometer	Data collection mode: transmission
Specimen mounting: vanadium can with He exchange gas	Scan method: time of flight

Refinement

Rp = 0.040	4540 data points
Rwp = 0.040	96 parameters
Rexp = 0.017	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
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
Na5	0.3333	0.6667	0.997	0.008 (1)	0.607
Bi5	0.3333	0.6667	0.997	0.008 (1)	0.393
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)

(Bi3Na3Pb9Ge9O33)

Crystal data

Mr = 3742.18	V = 916.93 (1) Å^3
Hexagonal, P3	Z = 1
a = 10.08745 (3) Å	Neutron radiation
c = 10.40506 (7) Å	T = 298 K

Data collection

ISIS HRPD diffractometer	Data collection mode: transmission
Specimen mounting: vanadium can with He exchange gas	Scan method: time of flight

Refinement

Rp = 0.053	4540 data points
Rwp = 0.045	96 parameters
Rexp = 0.018	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
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
Na5	0.3333	0.6667	0.997	0.035 (3)	0.726
Bi5	0.3333	0.6667	0.997	0.035 (3)	0.274
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)

(Ca8Pb12Si12O42Cl3.8O0.1)

Crystal data

Mr = 3952.35	V = 1168.24 (1) Å^3
Hexagonal, P63/m	Z = 1
a = 10.0898 (1) Å	Neutron radiation
c = 13.2506 (1) Å	T = 298 K

Data collection

ISIS HRPD diffractometer	Data collection mode: transmission
Specimen mounting: vanadium can with He exchange gas	Scan method: time of flight

Refinement

Rp = 0.070	4540 data points
Rwp = 0.059	71 parameters
Rexp = 0.017	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ca1	0.3333	0.6667	0.9953 (6)	0.020 (2)
Ca2	0.3333	0.6667	0.25	0.025 (2)
Ca3	0.6667	0.3333	0.25	0.015 (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)
O5	0	0	0.181 (6)	0.025	0.025

 

Footnotes

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.