Micro-XRD and SAED Patterns

Polytypes of Fe-rich biotite can be determined by the characteristic reflections in X-ray diffraction patterns (Takeda & Ross, Reference Takeda and Ross1975). The micro X-ray diffraction  (µXRD) patterns (Figs. 1a and S1a,b) show coexisting 1M and 2M ₁ polytypes and 2M ₁ and 3T polytypes, respectively. The reflections at 34.04°2θ (2.63 Å), 27.52°2θ (3.24 Å), and 54.53°2θ (1.68 Å) in the top μXRD pattern were attributed to the $\overline{1}$ 31, 112, and $\overline{1}$ 35 reflections of the 1M Fe-rich biotite, respectively (PDF card No. 80–1108 CuKα). In the lower μXRD pattern, the diffraction peaks at 26.25°2θ (3.39 Å), 30.62°2θ (2.91 Å), 33.11°2θ (2.70 Å), and 35.84°2θ (2.50 Å) were attributed to the 106, 108, 109, and $\overline{1}\overline{1}$ 4 reflections of the 3T Fe-rich biotite (PDF card No.73–1659 CuKα), respectively. Note that the reflections at 27.28°2θ (3.28 Å), 36.83°2θ (2.44 Å), and 55.09°2θ (1.67 Å) in the two μXRD patterns correspond to the 114, 133, and 139 reflections of the 2M ₁ Fe-rich biotite (PDF card No.83–1366 CuKα), respectively. The 1M, 2M ₁, and 3T polytypes were identified also by SAED patterns recorded from the [110] zone axis (Fig. 1b–d). The μXRD and SAED patterns (Fig. 1) revealed the polytype mixture in the Fe-rich biotite monocrystal, indicating that a complex polytype occurs in the Fe-rich biotite from the rhyolite.

Fig. 1 μ-XRD patterns, SAED patterns, and HRTEM image of biotite crystals: a Representative μ-XRD patterns of biotite samples and standard 1M, 2M ₁, and 3T-polytype PDF cards. b,d SAED patterns of b 1M, c 2M ₁, and d 3T biotite crystals. e,f Representative HRTEM image e and SAED pattern f from [010] zone axis. Arrows in f are the projection of the stacking vectors. The space-fixed azimuthal orientation symbols of Zvyagin in (001) projection is labeled at the lower right, with the length of all stacking vectors being equal to a/3. As the orientation symbols show, when viewed along [010], both stacking vectors 2 and 4 can produce component vectors that are parallel to the [100] direction (a-axis direction) and is equal to + a/6

[010] Zone Axis SAED Pattern and HRTEM Image

The SAED patterns of 1M, 2M ₁, 3T, and the two 4-layer period polytypes taken along the [010] zone axis were identical (Fig. 1e), and the polytypes cannot be distinguished from each other. The representative SAED pattern showed that the h0l reflections fit the characteristics of the subfamily-A biotite (Nespolo, Reference Nespolo1999). In addition, as shown in the HRTEM image from the [010] zone axis (Fig. 1f), the projection of the stacking vectors points to the right, producing a shift of a/6 along the a direction, which agrees well with the SAED patterns along the [010] direction (Nespolo, Reference Nespolo1999). Considering the space-fixed azimuthal orientation symbols of Zvyagin (as labels shown in lower right of Fig. 1f), each stagger of these stacking vectors characterized by a 120° rotation between the adjacent layers produced a vector parallel to the [100] direction and equal to + a/6 for both the stacking vectors 2 and 4 pointing to the right. For stacking vector 6, the stagger could be –a/3 pointing to the left, which is equivalent to + a/6 pointing to the right, when viewed along the [010] zone axis (Fregola & Scandale, Reference Fregola and Scandale2011; Zvyagin, Reference Zvyagin1987, Reference Zvyagin1997). The HRTEM images from the [010] zone axis suggest the occurrence of subfamily-A of mica polytypes in the samples, but the stacking vectors 2, 4, and 6 cannot be discriminated. To obtain the “Ross-Takeda-Wones (RTW)” expression for distinguishing and describing mica polytypes (Ross et al., Reference Ross, Takeda and Wones1966), layer rotations associated with image shifts need to be determined. HRTEM images viewed along the [110] or [1 $\overline{1}$ 0] zone axes provide important information about stacking orientation for the polytypes involving 120° rotations only (Banfield & Murakami, Reference Banfield and Murakami1998; Baronnet & Kang, Reference Baronnet and Kang1989; Fregola & Scandale, Reference Fregola and Scandale2011; Kogure, Reference Kogure2002; Kogure & Banfield, Reference Kogure and Banfield1998; Xu & Veblen, Reference Xu and Veblen1995).

[110] Zone-axis of the two 4-layer Period Polytypes

The SAED patterns along the [110] zone axis (Fig. 2a, b) showed strong diffraction spots in both 00 l and 1 l $\overline{1}$ rows, with a repetition of ~ 1/10 Å⁻¹, and three additional diffraction spots belonging to the 4-layer polytype that occurred between the host strong spots in the 1 l $\overline{1}$ row. The diffraction spot intensities of the two SAED patterns were significantly different (Fig. 2a, b). The diffraction spots in Fig. 2a showed intensity characteristics: strong–weak–weak–weak–strong … (Fig. 2c), corresponding to the [0222] stacking sequences. The diffraction spots in Fig. 2b exhibited intensity distribution: very strong–strong–very weak–weak–very strong … (Fig. 2d), attributed to the [002 $\overline{2}$ ] stacking sequences. Observations and calculations suggested that the intensity distribution of reflections in the reciprocal lattice rows parallel to the c*-axis can be used to infer the stacking sequences corresponding to mica polytypes (Ross et al., Reference Ross, Takeda and Wones1966; Takeda & Ross, Reference Takeda and Ross1975, Reference Takeda and Ross1995). Two 4-layer polytypes that were theoretically speculated by Ross et al. (Reference Ross, Takeda and Wones1966) were identified as 4M ₂ (Fig. 2a) and 4A ₈ (Fig. 2b), and the latter is the first report in natural samples.

Fig. 2 SAED patterns of the two 4-layer polytypes: SAED patterns of a 4M ₂ biotite crystal and b 4A ₈ biotite crystal. c,d Intensity counts of the two repetition periods of hkl reflections, indicated by the yellow dotted boxes in a and b. Red spots and line segments indicate the trend of the intensity changes

The low-magnification TEM image captured along the [110] zone axis of the 4-layer-polytype Fe-rich biotite domain did not show sufficient variations in contrast, and polytype characteristics could not be determined (Fig. S2a). One-dimensional (1D) lattice fringe images were useful for identifying polytypes (Fregola & Scandale, Reference Fregola and Scandale2011; Iijima & Buseck, Reference Iijima and Buseck1978). The TEM image of a tilted Fe-rich biotite specimen (Fig. S2a), rotated ~3° about the [110] direction, showed clear variations in contrast (Fig. S2b). Along the c-axis, distinctions containing four mica layers repeated periodically more than 15 times. The 1D TEM images of Fe-rich biotite monocrystals displayed dozens of four-layer polytype domains, and two representative biotite domains containing 4M ₂ and 4A ₈ polytypes are shown in Fig. 3a, b. The low-magnification 1D TEM images showed regular 4-layer (4 nm) periodicity in the range of hundreds of nanometers (Figs. 3a, b and S3a,b, with enlargements of the yellow dashed squares). The fast Fourier transform (FFT) patterns showed that the repetitive period of both 4M ₂ and 4A ₈ are similar but the sub-cell spot intensities are different for each polytype (Figs. 3a, b and S3a,b, inset at the bottom right), corresponding to different stacking sequences.

Fig. 3 One-dimensional (1D) HRTEM images of representative four-layer biotite domains, with fast Fourier transform (FFT) patterns (bottom right of each image) showing a periodic shift after every four layers. a 1D image of the 4M ₂ biotite domain with the enlarged HRTEM image in the yellow rectangle, and FFT pattern. b 1D image of the 4A ₈ biotite domain with enlarged HRTEM image in the yellow rectangle, and FFT pattern

The stacking sequences of the two 4-layer polytype domains were determined via the atomic-resolution HAADF–STEM images taken along the [110] zone axis (Fig. 4a, b). In the HAADF–STEM (or Z-contrast) images, the intensity (I) of the atom spots is proportional to the atomic number (Z) and the number of atoms (m) along the beam direction (i.e. I ~ mZ ⁿ ) (Pennycook, Reference Pennycook2002). The HAADF-STEM images (Fig. 4a, b) show that the brighter rows were the octahedral sheets (O columns) in the T-O-T sandwiched unit layer, because of the existence of metal cations (i.e. Fe²⁺) with relatively large atomic numbers. Owing to the resolution limit of the measurement instrument, the cations in the O columns could not be distinguished as separated spots. The darker spots adjacent to the O columns represented tetrahedral sheets (T columns), whereas the interlayer K columns are between two T-O-T unit layers, with a distance of ~0.45 nm between the two adjacent K cations when viewed from the [110] zone axis (Fig. 4a, b). The stacking sequences of 4-layer polytypes (Fig. 4a, b) are [0222] and [002 $\overline{2}$ ], which were determined by simulation as 4M ₂ and 4Tc ₈ (i.e. 4A ₈), respectively, in Ross et al. (Reference Ross, Takeda and Wones1966). The 4M ₂ polytype with a stacking sequence of [0222] meant that these Fe-rich biotite domains had monoclinic (C2) symmetry based on 3T (P3₁12 or P3₂12) and 1M, with a preserved twofold axis. On the other hand, the 4A ₈ polytype had a stacking sequence of [002 $\overline{2}$ ] with a monoclinic (C $\overline{1}$ ) symmetry, as a result of the preservation of $\overline{1}$ (e.g. the inversion center) from the packing of 2M ₁ and 1M (off by 60°) only. Both 2M ₁ and 1M have unit-cell parameters of a = 0.53 nm, b = 0.92 nm, and c = 4.00 nm, where β = 95.1°.

Fig. 4 High-resolution, high-angle annular dark-field scanning transmission electron microscopy images of the two 4-layer long-period biotite domains (4M ₂ and 4A ₈). The stacking sequences with the RTW symbols are a [0222] and b [002 $\overline{2}$ ]. The ball-and-stick model displays the corresponding structures of biotite along the [110] zone axis. The purple, green, red, and yellow spheres represent K, (Si, Al), O, and (Mg, Fe), respectively

Composition Analysis

Each Fe-rich biotite domain was analyzed using EDS (see Materials and Methods). The average electron probe microanalysis (EPMA) result was used as the standard mica composition to obtain the k-factors of each element (Table S1). The formulae calculated using the chemical compositions of several 4M ₂ and 4A ₈ Fe-rich biotite domains, corrected by k-factors, are listed in Table 1. The elemental distribution in a domain was generally homogeneous for a specific polytype (Table 1) but slightly different for other polytypes (Table 1, Figs. 5a and S4-5). The average structural formulae of the two 4-layer Fe-rich biotite polytypes were calculated based on 11 oxygen atoms as follows:

1. EPMA:

   ${\left(K_{0.89}{\mathrm{Na}}_{0.08}\right)}_{\sum =0.97}{\left({\mathrm{Ti}}_{0.27}{\mathrm{Mn}}_{0.03}{\mathrm{Fe}}_{1.61}{\mathrm{Mg}}_{0.95}\right)}_{\sum =2.86}{\left({\mathrm{Si}}_{2.84}{\mathrm{Al}}_{1.16}\right)}_{\sum =4.00}{O}_{10}{\left(F_{0.08}{\mathrm{Cl}}_{0.02}{\mathrm{OH}}_{1.90}\right)}_{\sum =2.00.}$

2. EDS:

   $\begin{array}{c}4M_2-{\left(K_{0.91}{\mathrm{Na}}_{0.08}\right)}_{\sum =0.99}{\left({\mathrm{Mg}}_{0.93}{\mathrm{Fe}}_{1.66}{\mathrm{Mn}}_{0.03}{\mathrm{Ti}}_{0.27}\right)}_{\sum =2.89}{\left({\mathrm{Si}}_{2.84}{\mathrm{Al}}_{1.16}\right)}_{\sum =4.00}{O}_{10}{\left(\mathrm{OH}\right)}_2,\\ 4A_8-{\left(K_{0.86}{\mathrm{Na}}_{0.08}\right)}_{\sum =0.94}{\left({\mathrm{Mg}}_{0.97}{\mathrm{Fe}}_{1.58}{\mathrm{Mn}}_{0.03}{\mathrm{Ti}}_{0.27}\right)}_{\sum =2.84}{\left({\mathrm{Si}}_{2.85}{\mathrm{Al}}_{1.15}\right)}_{\sum =4.00}{O}_{10}{\left(\mathrm{OH}\right)}_2.\end{array}$

Table 1 Biotite formulae of 1M-, 4A ₈-, and 4M ₂- biotite based on EDS ratios

Fig. 5 a Diagram showing the relationship between the K and Fe contents of 4M ₂ and 4A ₈ biotite crystals, as calculated using the cation coordination number. b HRSTEM image showing screw dislocations (indicated by the black triangles) throughout a 4A ₈ biotite domain. Enlarged red box in b shows a screw dislocation with layers on both sides of the dislocation indicated by means of a black dotted line and the dislocation line indicated with a dotted yellow line

In this calculation, the Fe was assumed to exist as Fe²⁺, which is the dominant valence state of Fe ions in the samples (Metz & Mahood, Reference Metz and Mahood1991), and share the octahedral sites with Mg ions. The estimated standard deviations (ESD) of Fe, K, Si, and Mg were calculated based on compositional data from EPMA (Table S2), with the formula (Hooper & Eloranta, Reference Hooper and Eloranta1986):

(1) $\mathrm{ESD}\left(z\right)={\left(\frac{1}{N},\sum _{i=1}^N,{\left(P,\left(z\right),{\mathrm{iz}}^2,-,\overline{P\left(z\right)z^2}\right)}^2\right)}^{1/2}$

where N, z, and P are the number of compositional data, the element type, and specific content value (stoichiometry used here), respectively. After correction, the EDS calculation results, on average, agreed well with the EPMA test results. The ESD of elements calculated and reported in Table S2 showed that all estimated standard deviations were <5.70%. The effect of thickness and local inhomogeneity had been eliminated as much as possible. A comparison of the elemental composition showed that the Fe and K contents of the 4M ₂ Fe-rich biotite were apparently greater than those of the 4A ₈ Fe-rich biotite, whereas the contents of other elements showed only a very small difference between the two polytypes (Table 1, Figs. 5a and S5a,b).