Short-Range Stacking Disorder in Mixed-Layer Compounds: A HAADF STEM Study of Bastnäsite-Parisite Intergrowths

: Atomic-scale high angle annular dark ﬁeld scanning transmission electron microscopy (HAADF STEM) imaging and electron diffractions are used to address the complexity of lattice-scale intergrowths of REE-ﬂuorocarbonates from an occurrence adjacent to the Olympic Dam deposit, South Australia. The aims are to deﬁne the species present within the intergrowths and also assess the value of the HAADF STEM technique in resolving stacking sequences within mixed-layer compounds. Results provide insights into the deﬁnition of species and crystal-structural modularity. Lattice-scale intergrowths account for the compositional range between bastnäsite and parasite, as measured by electron probe microanalysis (at the µ m-scale throughout the entire area of the intergrowths). These comprise rhythmic intervals of parisite and bastnäsite, or stacking sequences with gradational changes in the slab stacking between B, BBS and BS types (B—bastnäsite, S—synchysite). An additional occurrence of an unnamed B 2 S phase [CaCe 3 (CO 3 ) 4 F 3 ], up to 11 unit cells in width, is identiﬁed among sequences of parisite and bastnäsite within the studied lamellar intergrowths. Both B 2 S and associated parisite show hexagonal lattices, interpreted as 2 H polytypes with c = 28 and 38 Å, respectively. 2 H parisite is a new, short hexagonal polytype that can be added to the 14 previously reported polytypes (both hexagonal and rhombohedral) for this mineral. The correlation between satellite reﬂections and the number of layers along the stacking direction ( c* ) can be written empirically as: N sat = [(m × 2) + (n × 4)] − 1 for all B m S n compounds with S (cid:54) = 0. The present study shows intergrowths characterised by short-range stacking disorder and coherent changes in stacking along perpendicular directions. Knowing that the same compositional range can be expressed as long-period stacking compounds in the group, the present intergrowths are interpreted as being related to disequilibrium crystallisation followed by replacement. HAADF STEM imaging is found to be efﬁcient for depiction of stacking sequences and their changes in mixed-layer compounds, particularly those in which heavy atoms, such as rare-earth elements, are essential components.


Introduction
Advanced electron microscopy of foils prepared by focused ion beam-scanning electron microscopy (FIB-SEM) allows atomic-scale insight into patterns of element distribution in minerals, with significance for both petrogenesis and the minerals industry [1]. High angle annular dark  [24] * Layers 1 (after [17] are: CeF; CO 3 ; Ca(CO 3 ) of thickness = 2.24 Å except the latter which is 4.25 Å; ** Layers 2 (after [15]): d = LnF layer; e: CO 3 layer between 2 LnF layers; f = Ca layer; g = CO 3 layers between a CeF (or LnF) and Ca layers; # = both R and H polytypes documented from TEM studies [16,21,22]. c(×n) values for named mineral from [15] and for unnamed species calculated according for 1-period of layers in the stacking sequence (Layers 2). Other polytypes for parisite and B 2 S reported in the literature are given in Table S4. N sat -number of satellites according to: N sat = [(m × 2) + (n × 4)] − 1 for all B m S n compounds with S = 0. H-hexagonal, O-orthorhombic; R-rhombohedral.

Background
Syntaxy and epitaxy are concepts used to describe crystals that show X-ray spectra indicating oriented intergrowths between species that are compositionally either the same (e.g., carborundum [25]), or closely related [15], and references therein). The term 'polycrystal' was suggested since most specimens analysed contain intergrowths of two species, with every pair observed except bastnäsite-synchysite [15]. The individual species share a pronounced pseudo-hexagonal centred lattice which is the basis for defining structures with common sub-motifs in terms of a = a/2cos30 • and c = c/n (n-integer), where there is a linear relationship between c and the chemical composition, i.e., decreasing a and c from bastnäsite to synchysite [15]. Subsequent TEM studies have confirmed these findings and increased the number of species by adding seven unnamed polysomes (Table 1), which are recognisable as long-range stacking periods as well as their rhombohedral and/or hexagonal polytypes [16,18,19].
The crystal structure of minerals in this group was qualitatively described in terms of four types of layer, which are parallel to the hexagonal (000l) plane: (d) LnF ionic layers; (e) layers containing CO 3 groups between two LnF layers; (f) layers with Ca ions; and (g) layers containing CO 3 groups between a Ca-and a LnF-layer [15]. Such notation allows for representation of different structures in terms of stacking sequences as shown in Figure 1. The arrangement of CO 3 groups in the (g) layers can be either perpendicular or diagonal to the layer stack defining hexagonal or rhombohedral lattice points.  [15]. Numbers in brackets represents the width of the sequence shown as: one period of the layer sequence except for bastnäsite and synchysite, which are shown as 2 periods (corresponding to 2 × a" and 4 × a , respectively in (a)); (b) shows polysomes and their polytypes in the range between B 2 S and parisite [16,18]. H-hexagonal; R-rhombohedral.
The extensive syntaxy between the various species was recognised at a very fine scale in the first TEM study that addressed the mixed-layer model for structures of Donnay and Donnay [15], using both direct lattice imaging (in bright and dark field modes) and electron diffractions [16]. The study underpins the systematic variation between the number of satellite reflections on (000l)* rows (between strong reflections defining the pseudo-period c , c.f. [15]), and the number of layers within the two blocks/slabs, B and S. For example, parisite consisting of simple BS slabs shows five weak reflections leading to d 0006 = c/6, corresponding to the six layers in the stacking sequence, i.e., two (de) and four (dgfg) layers in the B and S slabs, respectively (Table 1).
Despite the predictions that syntaxy among BSG phases is the governing rule, pure specimens were also found and used for crystal structure refinement using X-ray diffraction (XRD). These investigations confirm hexagonal symmetry for bastnäsite-(Ce) [17] but not for the two Ca-bearing species examined, synchysite-(Ce) and parisite-(Ce). These are instead interpreted to have monoclinic symmetry [23,24]. Furthermore, these XRD studies led to a different structural model whereby intergrowths of bastnäsite slabs with general formula: (CeF) n (CO 3 ) n+1 (n = ∞ in bastnäsite, 1 in synchysite, 2 in parisite) are linked by (Ca) layers, the latter introducing a structural offset from hexagonal to monoclinic symmetry [23]. In complex mixed-layer BSG compounds or domains with large unit cells, 'n' can take different values [26].
The coplanar geometry of the Ca layer in both synchysite and parisite resembles that observed in vaterite, a CaCO 3 polymorph [27]. Ni et al. [23] contend any compounds richer in Ca than synchysite are not possible as this would require Ca-Ca links resulting in vaterite-like slabs, unstable under geological conditions. Polytypism in both compounds is presumed by analogy with 2M micas [23,24].
The most recent structural interpretation of the bastnäsite-synchysite group, with the general formula: Ca m (REE) n (CO 3 ) n+m (F,OH) n (bastnäsite, m = 0, n = 1; synchysite, m = 1, n = 1; parisite, m = 1, n = 2; röntgenite, m = 2, n = 3 [28]), considers order-disorder (OD) formalism akin to that seen in vaterite [29]. In this case, the polytypism and OD phenomena are attributed only to the Ca-based layer (as in vaterite) whereas the REE-layers, although analogous to the Ca-based OD layer, has a p32 layer symmetry and thus their stacking does not lead to polytypism and OD phenomena.
As such, HAADF STEM imaging has not been applied to mixed-layer compounds in general, or to REE-fluorocarbonates specifically despite the potential of the technique for underpinning the layer complexity in long-period stacking sequences.

Experimental
The thin polished section from which the TEM samples are obtained was initially examined in backscatter electron (BSE) mode using an FEI Quanta 450 Field Emission Gun scanning electron microscope (FEI, Eindhoven, The Netherlands), equipped with a silicon-drift energy-dispersive X-ray spectrometer.
Electron probe microanalytical data on the REE-fluorocarbonate intergrowths was collected using a Cameca SX-Five electron probe microanalyzer (EPMA; Cameca, Paris, France) at Adelaide Microscopy, The University of Adelaide. The reader is referred to Supplementary Material Tables S2 and S3 in Schmandt et al. [11] (www.mdpi.com/2075-163X/7/10/202/s1) for full details of elements analysed, peak/background positions, count times, reference standards, set-up parameters, elemental overlap corrections and minimum limits of detection. The instrument was operated at 15 kV and 20 na and with a spot size of 1 µm.
Preparation of thinned (<100 nm) foils from the polished blocks for TEM investigation was performed using a FEI-Helios nanoLab (FEI, Hillsboro, OR, USA) Dual Focused Ion Beam and Scanning Electron Microscope (FIB-SEM) in the same laboratory. Extraction and thinning procedures followed [30]. Each TEM foil was attached to a copper grid.
Initial High-Resolution (HR)-TEM imaging in Bright Field mode (BF) and electron diffraction (illuminated area of 200 nm) were performed on a Philips CM200 TEM (Philips, Eindhoven, The Netherlands). The instrument is equipped with a LaB6 source, utilises a double-tilt holder and a Gatan Orius digital camera (Gatan Inc., Pleasanton, CA, USA) and was operated at 200 kV. Energy-dispersive X-Ray spectra (EDS) were acquired using an Oxford Instruments X-Max 65T SDD detector (Oxford Instruments, Abingdon, U.K.) running Aztec software. Diffraction measurements were performed using DigitalMicrograph™ 3.11.1 (Gatan Inc., Pleasanton, CA, USA) and Winwulff© 1. All HAADF STEM imaging and EDS measurements reported here were performed using an ultra-high resolution, probe-corrected, FEI Titan Themis S/TEM (FEI, Hillsboro, OR, USA) operated at 200 kV in the same laboratory. The spot size was 6 and the gun lens was 7 for this analysis. This instrument is equipped with the X-FEG Schottky source and Super-X EDS geometry. The Super-X EDS detector provides geometrically symmetric EDS detection with an effective solid angle of 0.8 sr. Probe correction delivered sub-Ångstrom spatial resolution and an inner collection angle greater than 50 mrad was used for HAADF experiments using the Fischione HAADF detector.

Samples and Compositional Range of BSG Phases
In this study, we use two FIB-prepared TEM foils obtained from BSG intergrowths (Figure 2a-c) which occur as filling of a mm-sized grain of replaced feldspar [13]. The intergrowths are cut across sets of lamellae with varying composition, expressed by different contrast on BSE images. The intergrowths can be divided into those that are: (i) long (up to~100 µm in length) and parallel to one another and with molybdenite (Foil 1; also documented in Kontonikas-Charos et al. [12]), and; (ii) shorter (<50 µm) sets of the same lamellae types but with variable orientation (Foil 2). In both cases, the brightest species on the BSE images (Ca-poor, bastnäsite) is subordinate to the darker one. The latter is often 'pitted' as it hosts sub-µm-sized inclusions of Fe-oxides ( Figure 2b; [12]).
The bastnäsite is, in contrast, relatively clean. Some of the shorter and narrower lamellae appear distinct in that they feature rhythmical bands of bright and dark contrast within the same crystal/lamella ( Figure 2c). HAADF STEM images of the two foils mimic the BSE images, whereas the BF TEM images show an inversed contrast with such images (e.g., Foil 2 in Figure 3 and Figure S1, respectively). The epitaxial associations between minerals in Foil 1 (BSG species, molybdenite and minor hematite), as well as HR-TEM images of lattice-scale intergrowths between bastnäsite and parisite, were discussed by Kontonikas-Charos et al. [12]. In Foil 2, the lamellar intergrowths between BSG phases are broadly oriented in two directions. At low magnification, most lamellae appear 'composite', either with gradational changes in colour, or contrasting bright and dark domains ( Figure 3b). More homogenous parts of lamellae (Figure 3c), or stubby grains with well-defined edges are also identified ( Figure 3e). In some cases, such lamella can display a rhythmic banding with bright and dark appearance representing bastnäsite and parisite, respectively ( Figure 3f). For comparison with HAADF STEM imaging, Foil 2 and areas of interest are also imaged in BF TEM mode ( Figure S1). Electron probe microanalysis was carried out across the intergrowths around the areas with the FIB-cuts to compositionally constrain the brighter (Ca-poor) and darkest (Ca-richer) phases within the lamellar intergrowths ( Figure 2d; Tables S1-S3). Microanalysis confirms predictions based on the stacking sequences and EDX spectra revealed in the preliminary TEM study in terms of the compositional range restricted to the compositional range between bastnäsite and parisite. EPMA data indicate that all species are Ce-dominant. The compositional data (32 individual analyses) plotted as Figure 2d defines compositions at the scale of the microprobe beam close to end-member bastnäsite and parisite but also within compositional space between parisite and B 2 S, and to a lesser extent between B 2 S and bastnäsite. Apart from REY, Ca and F, elements present at measurable concentrations were Sr and K (<0.05 wt % SrO and K 2 O), Th (up to 0.15 wt % ThO 2 ), Fe (0.1-0.25 wt % FeO) and Cl (<0.1 wt %). Analyses with Fe concentrations > 0.3 wt % were not considered as this was readily attributed to mineral inclusions; Fe was not included in the formula calculation.

Stacking Sequences
Identification of stacking sequences was undertaken using electron diffractions and HAADF STEM imaging on identical areas. These were selected for the range of intergrowths and their heterogeneity as observed from TEM imaging.

Electron Diffractions and TEM Imaging
TEM BF imaging of both foils ( Figure S2) shows that the lamellar intergrowths among BSG species vary widely in terms of the bright and dark rhythms (tens to hundreds of nm), rarely also displaying domains of an intermediate grey colour (identified in Foil 2). Other observed features include the cuspate edges of lamellae that show dark and bright sides, changes in the colour of the sequence along the lamella, as well as smaller, stubby grains or thin, single lamella that crosscut the regular lamellar sequences ( Figure S2a-d). The latter are often typical of the darkest species on the BF TEM images, bastnäsite. Image contrast is mostly attributable to variation in chemistry as monitored by TEM EDS spectra giving a range of Ca-bearing BSG phases (brighter phases) and darkest phases with little or no Ca (bastnäsite). Such data is in agreement with [12]. In some cases, however, the variation in colour is also due to differences in orientation of lamellae from the same bundle.
Electron diffractions were obtained from the BSG phases tilted on the [−1100] and [10 − 10] zone axes, which are pertinent for interpreting stacking sequences from periodicity along the c* axis and their expression in 2-dimensional reciprocal space, respectively (Figures 4 and 5). Although the [11 − 20] zone axis is similar or equivalent to the [10 − 10] zone axis, the latter will be used here for simplicity. Both ordered and disordered patterns were observed over the~200 nm diameter of the selected area of electron diffraction (SAED). All SAEDs have orthogonal geometry indicating hexagonal lattices on both zone axes, whereby the smallest ac subcells are marked as strong (Bragg) reflections, and the supercells are marked by satellite reflections with different periodicity along the c* axis (Figures 4 and 5). The ordered supercells show 2-, 6-and 8-fold periodicities on the c* axis and correspond to stacking layers for c in bastnäsite, parisite and the unnamed B 2 S compound (hereafter called 'B 2 S'; Table 1; Figure 4a).
The 8-fold periodicity on the c* axis (c' = 8c ~37 Å) is attributable to B 2 S (Table 1; [19]) and was observed in areas of SAEDs that are otherwise representative of disordered bastnäsite (Figure 4f). These were obtained from lamellae that display domains with brightness intermediate between bastnäsite and parisite. The satellite reflections have generally the same intensity. Higher numbers of satellites, with variable intensity, as well as changes between bastnäsite and parisite along the c* axis, were also observed (Figure 4g,h).
All the SAEDs on [10 − 10] zone axis of the BSG species in the two foils show hexagonal symmetry (Figure 5a) but only the a2c bastnäsite is well ordered (Figure 5b). The other SAEDs show a range of satellite reflections, variable in both number and intensity, along c* and parallel directions, suggesting intergrowths between different BSG species. For example, sequences with 6-fold periodicities along c* and parallel 3n rows displaying the ac superlattice of parisite are intercalated with 2 rows showing 2-fold (a2c bastnäsite) periodicity, or with rows marked by strong disordering (Figure 5c,d). The latter are shown as streaks and satellite reflections of variable intensity, nonetheless marking a rectangular pattern indicating a hexagonal lattice. Comparable intergrowths are observed for SAEDs with 8-fold periodicities on the c* axis (Figure 5e). Such results require high-resolution imaging to reach a conclusion as to whether the stacking sequences represent (long period) polysomes of various types, or lattice-scale intergrowths between parisite, bastnäsite and B 2 S.

HAADF STEM Imaging
Several areas from Foil 2 were studied in closer detail (Figure 3) after low-magnification imaging both foils in HAADF STEM mode. The image contrast reveals banding within lamellae of various sizes, the smallest being a few hundred nm (Figure 6a,b). These low magnification images also show variation in the rhythms over several orders of magnitude, from just a few nm in width up to hundreds of nm within the same lamella. The colour variation due to orientation of the lamellae is highlighted by a decrease in contrast (e.g., Figure 6a). Wider parts of lamellar packages can have a homogenous appearance across widths of hundreds of nm (e.g., bastnäsite in Figure 6c). The mutual boundaries between individual lamellae within such aggregates show growth with imbricated relationships (Figure 6a-c), or triple junctions (Figure 6d). In the latter, the scale of banding is below tens of nm.
The stacking code for compounds in compositional range considered here is illustrated by atomic-scale HAADF STEM imaging of phases that contain both Ln(F) and Ca layers as, for example, in parisite. When tilted on [1 − 100] zone axis, this reveals bright atoms, attributable to Ln and Ca in order of decreasing intensity (d and f layers, respectively), forming parallel arrays along hh − 2h0 directions with~3.6 Å distances between them (Figure 7a). These atomic arrays are separated from one another by darker strips at~4.7 Å along c attributable to the lighter CO 3 layers, e and g. Combinations of 'de' and 'dgfg' stacks form the B and S slabs along c with a BS repeat of~14 Å, corresponding to one period of layer stacking in parisite (as shown in Figure 1a). The stacking code in HAADF STEM imaging is in good agreement with the distribution of atoms within the crystal structure of parisite (Figure 7b). Longer sequences of regular B and BS slabs (up to tens of slab repeats in either case), and representing bastnäsite and parisite, respectively (Figure 8a,b), were imaged from many areas in both foils with the specimens tilted to [1 − 100] zone axis. Darkening of B slabs within bastnäsite (Figure 8a) is a common feature and could be interpreted as variation in the proportions of different Ln atoms (more La or Nd relative to Ce giving lesser or greater average atomic mass, respectively). Single slab defects are always present, as for example, SS slabs within parisite (Figure 8b).
The same stacking code is valid for HAADF STEM imaging of BSG phases on the [10 − 10] zone axis, as shown for parisite and the B 2 S phase (Figure 8c,d). In this case, however, the shortest distances along 0k − k0 directions are much smaller,~2.1 Å, corresponding to the thickness of individual LnF or Ca layers (=a /2). The B 2 S phase is identified from gradational sequences in area 1 of Foil 2 (Figure 3a,b). This consists of BBBS stacks with smallest width at~38 Å (Figure 8d). Defects are present along both the c and b axes, as variable n × B stacks, or changes of layers from LnF to Ca, respectively. In the latter case, these can be recognised as an array of jogs accounting for a decrease in thickness of the B slabs (Figure 8d).   Irrespective of such single slab defects, longer stacking sequences in the 20 to 50 nm range can be recognised as regular bastnäsite, parisite and B 2 S intervals such as those imaged from area 1 in Foil 2 (Figure 9a-c). Such intervals can alternate with one another or form rhythms with decreasing widths (Figure 9a). The boundaries of longer intervals of parisite are marked by slab defects towards intervals of bastnäsite (Figure 9b). Likewise, the boundaries between B 2 S and parisite are marked by sequences with a greater abundance of B slabs alternating with BS (parisite) stacks (Figure 9c).
In closer detail, the stacking disorder observed over 20-30 nm intervals in parisite shows strips of 2-3 units of bastnäsite alternating with irregular sequences of B and S slabs (Figure 9d). Comparably, single S-stack defects within 5 or 6 × B slabs, as well as irregular sequences of B and S slabs over intervals of~10 nm, are observed in bastnäsite (Figure 9e). Such stacking disorder most likely accounts for the SAEDs with streaks along c* (Figure 4b) observed in bastnäsite from lamellar intergrowths with parisite.
Lamellar intergrowths with strong contrast on HAADF STEM images such as those in area 6 ( Figure 3f) are illustrative of one of the stacking sequence (~1 µm), in which longer rhythms of bastnäsite and parisite, tens to hundred nm in width, are seen (Figure 6a,c and Figure 10). This profile was imaged across the middle part between the two bastnäsite lamellae of 100-200 nm thickness forming the margins of the sequence (Figure 6a,c). The specimen was tilted on the [10 − 10] zone axis and representative SAEDs are shown in Figure 5c,d. The imaging shows three main domains of 320 nm each: (i) on one side, one of the longest parisite intervals (>200 nm); (ii) in the middle part, short-range (tens of nm), irregular rhythms of bastnäsite and parisite with one interval including also the B 2 S ( Figure 10); and (iii) at the other side, an interval of bastnäsite and parisite with gradational changes in the dominant component from the former to the latter ( Figure 10). Throughout each of these intervals, stacking disorder is expressed either as single B or S slab defects, or as short range stacking irregularities as shown above (Figure 9). Aside from changes in phase speciation via stacking disorder along the c axis, the BSG species also show changes in slab stacks and composition along other directions ( Figure 11). The junctions between BSG phases in lamellae with slight offset to one another show relatively sharp boundaries (Figure 11a). In this case, co-crystallisation is suggested by the stepwise adjustment of B slabs on the longer side of a bastnäsite lamella matching the edges (between sets of S-slabs) of individual lamellae of disordered bastnäsite on the other side of the junction. Such an interpretation is also supported by the absence of open spaces and continuation of single S slabs, albeit with a kink, across the boundary.
Changes between B and S slabs on directions perpendicular to the c axis can lead to apparent transformation of bastnäsite into B 2 S or parisite stacking sequences across the c axis (Figure 11b,c). Such transformations are associated with aspects suggestive of overprinting rather than growth at equilibrium. These include layer-wide jogs between S and B slabs in the B 2 S and parisite sequences, slab darkening indicating absence of Ln or Ca cations (Figure 11c), as well as irregular interfaces associated with lattice strain in the slabs (Figure 11d).

Discussion
The present study provides further insights into: (i) the definition of species and crystal-structural modularity in mixed-layer REE-fluorocarbonate compounds in the bastnäsite-synchysite group; and (ii) the significance of short-range stacking disorder and coherent changes of stacks for genetic interpretations.
We report here a second occurrence of the B 2 S phase found among sequences of parisite and bastnäsite within the studied lamellar intergrowths. The longest BBS sequence (~19 Å wide) contains up to~22 repeats, or 11 × B 2 S unit cells if we consider that 2 × BBS repeats represent a single unit cell with hexagonal symmetry. Indeed, both B 2 S and associated parisite show hexagonal lattices, as documented from electron diffractions and HAADF STEM imaging from the two zone axes (Figure 4d-f,  Figures 5c-e and 8b-d) obtained by tilting the specimen around the c* or c axis, respectively, at the same location. The lattice vectors defining the reciprocal space with distances at (~2 Å × 3) and (~4.7 Å × 6) do not give orthogonal solutions for indexing the electron diffractions when using the monoclinic cell for parisite [17].
Parisite and B 2 S species documented here are most likely 2H polytypes with c = 28 Å (c = 6 × c ) and c = 38 Å (c = 8 × c ), respectively. 2H parisite is a new, short hexagonal polytype that can be added to the 14 polytypes (both hexagonal and rhombohedral) that have been reported so far (Table S4; [16,21,22]). The 2H B 2 S polytype is a species among the seven variants reported from the occurrence in China (Table S4; [19]).
Two polytypes of bastnäsite are identified (Figures 4b,c and 5b): the 2H polytype with P-62c space group [15,17], and a new species in which the presence of 000l reflections with l = 2n indicates the absence of 2-fold operators along c. This is possibly a 1H polytype with P − 62m as one of the compatible space groups.
The specific features of diffraction patterns for mixed-layer compounds can be interpreted using a model superstructure in which two layer/slab types, although with different structures, fit epitaxially along the planar interfaces between the slabs [3]. Based on previous and present data, the correlation between satellite reflections and the number of layers along the stacking direction (c*) can be written empirically as: N sat = [(m × 2) + (n × 4)] − 1 for all B m S n compounds with S = 0 ( Table 1). The number of satellites can vary; however, due to extinctions associated with symmetry elements in certain space groups, e.g., the number is half for phases within P − 62c space group due to the reflection condition 000l, l = 2n.
Variation in satellite intensity can occur due to lattice-scale intergrowths as interpreted here, or from the complexity of blocks within a given polysome. For example, the stacking sequence in the hexagonal polytype representing the B 10 S 6 polysome can be written either as (3 × BBS)·(BS)·(BBS)·(BS), or the equivalent hierarchical sequence: B 7 S 4 ·B 3 S 2 (Figure 1b). The number of satellite reflections is predictable from the layer stacking (Table 1) but not the variation in the intensity of satellite reflections displayed along c* [18]. Its significance lies, however, within polysomatism in the group, requiring further studies with respect to modularity concepts akin to mixed-layer compounds. For example, a model of displacive modulation vectors have shown that the diffraction patterns, with two brightest reflections about the middle of d 1 *, are described by monotonic decrease of two modulations with increase in Bi in mixed-layered compounds from the tetradymite group in the compositional range Bi 2 Te 3 -Bi 8 Te 3 [31].
Overall, the lattice-scale intergrowths account for the compositional range between bastnäsite and parisite revealed by electron probe microanalysis (Figure 2d; Tables S1-S3). In detail, the compositional range, which is almost continuous between parisite and B 2 S, is covered either by rhythmic intervals of parisite and bastnäsite, or by stacking sequences with gradational changes in the slab stacking between B, BBS and BS types as exemplified by the~1 µm profile image shown as Figure 10. As shown in this study, HAADF STEM imaging is a well-suited tool for direct imaging of the stacking sequences as these are readily depicted by the arrays of heavier atoms (Ln and Ca). None of the polysome sequences defining the four species in the compositional range between the B 2 S phase and parisite (B 7 S 4 , B 10 S 6 , B 3 S 2 and B 8 S 6 ; Table 1, Figure 1b) were identified, although random blocks of variable B, BS, BBS or S slab widths are seen across any of the gradational intervals in the~1 µm profile ( Figure 10).
In contrast, the compositional interval between the B 2 S phase and parisite is covered by long-range polysomes and their polytypes, as known from the reported occurrence in China [18,19,21,22]. Such differences between the two occurrences may indicate that the same compositional range can be expressed by epitaxial intergrowths between either short-or long-range stacking polysomes/polytypes. In the present study, short-range stacking disorder occurs across blocks tens to hundreds of nm in size, precluding ordering of long-range period phases. Whereas both types of sequences can be presumed to originate via primary growth mechanisms, the growth rates differ depending upon the state of disequilibrium or (close-to-) equilibrium, respectively, of the thermodynamic system. We suggest that such phenomena, typical of syntaxial intergrowths, may be mechanisms for Ca-CO 3 layer adjustment within hexagonal/rhombohedral lattices as opposed to the monoclinic shift interpreted from X-ray diffraction (XRD) studies of pure compounds [23,24].
In addition to the short-range stacking disorder, HAADF STEM imaging shows changes between different stacking sequences across grain boundaries, or along directions perpendicular to the stack (c axis; Figure 11). In the latter case, the interface between such changes is either straight or irregular (Figure 11c,d, respectively), inferring adjustment of the layers due to sharp chemical gradients. The irregular boundaries between bastnäsite and parisite, nonetheless preserving the coherence of atom arrays along the c axis, can be attributed to atom-scale replacement reactions whereby Ca-CO 3 layers are converted into LnF-CO 3 layers or vice versa. This can be attributed to processes responsible for chemical changes without open spaces such as metasomatism, with mechanisms of atom exchange invoking either diffusion across chemical gradients, or fluids that can infiltrate at lattice-scale. Such a process, imaged here at the atomic scale, is part of a broader spectrum of replacement reactions that advance by sharp fronts of fluid-mineral reaction by coupling dissolution with reprecipitation rates (CDRR; [32,33]). The importance of CDDR-driven mechanisms of mineral replacement throughout the hydrothermal evolution at Olympic Dam has been emphasised previously for different minerals and/or mineral pairs, including feldspars [12,13], uraninite ± Cu-Fe-sulphides [34][35][36], and hematite [37].

Implications and Outlook
In contrast to the lattice-scale intergrowths discussed here, end-member bastnäsite and synchysite have been documented from hematite-sericite-altered breccias hosting the Olympic Dam orebody [11]. On the other hand, the intimate, lattice-scale, relationships between BSG minerals and hematite [12] are not unique to this occurrence, a prospect distal to the deposit, but are also observed within the orebody, in which hematite hosts inclusions of BSG species [37]. These will be documented and discussed in further detail elsewhere. They are important for understanding the link between Fe-and REE-metasomatism at Olympic Dam, and for IOCG deposits in general. The present occurrence clearly carries significance in defining the early stage of magmatic feldspar alteration in deposits belonging to the IOCG clan, whereby Ca can be inferred to be derived from albitization and REE, F, and CO 2 are introduced by hydrothermal fluids. The fact that such changes are mediated via CDRR (pseudomorphic replacement of feldspars) rather than open-fracture fluid circulation suggests that these elements are derived from the host granite rather than any other external source. The lattice-scale intergrowths documented here show that the compositional space between parisite and bastnäsite is accommodated by species within this interval without any synchysite present, supporting thermodynamic modelling of phase equilibria that indicate stepwise changes in composition between the two end-members in the group [4].
As shown here, HAADF STEM imaging is most appropriate for depiction of stacking sequences and their changes in mixed-layer compounds, particularly those in which heavy atoms (Ln) are essential components. This technique is however not readily applicable to visualisation of the lighter atoms; in this case, the internal geometry of the CO 3 layers responsible for polytype identification. In follow-up studies, we will investigate if such atoms can be imaged by HAADF STEM at lower kV. REE-fluorocarbonates are an exemplary group among other mixed-layer compounds which include shear structures, long-period antiphase boundary structures, polysynthetic twins, and in general periodic interface modulated structures [3]. Crystal structure modularity in such groups can be defined by different formalism concepts, as exemplified here by the polysomatic descriptions of BSG minerals [15][16][17]29]. Other examples of mixed-layer compounds that would benefit from atomic-scale HAADF STEM imaging of the stacking sequences include the NC-pyrrhotites, recently redefined by translation modulation interface ( [38] and references therein), or the layer-module types which are considered to explain polysomatism in Bi-and Bi-Pb-chalcogenides of the tetradymite group and related aleksite series [31,[39][40][41].