High-resolution imaging of biotite using focal series exit wavefunction restoration and the graphene mechanical exfoliation method

Abstract We have applied mechanical exfoliation for the preparation of ultra-thin samples of the phyllosilicate mineral biotite. We demonstrate that the 'scotch tape' approach, which was made famous as an early method for production of single-atom-thick graphene, can be used for production of sheet-silicate specimens that are sufficiently thin to allow high-resolution transmission electron microscope (HRTEM) imaging to be achieved successfully while also being free from the specimen preparation artefacts that are often caused by ion-beam milling techniques. Exfoliation of the biotite parallel to the (001) planes has produced layers as thin as two structural TOT units thick (∼2 nm). The minimal specimen thickness enabled not only HRTEM imaging but also the application of subsequent exit wavefunction restoration to reveal the pristine biotite lattice. Exit wavefunction restoration recovers the full complex electron wave from a focal series of HRTEM images, removing the effects of coherent lens aberrations. This combination of methods therefore produces images in which the observed features are readily interpreted to obtain atomic resolution structural information.


Introduction
RECENT improvements in the resolution of transmission electron microscopes (TEMs) have demonstrated a need for increasingly thin highquality samples, with thicknesses <~10 nm often being preferred (Urban, 2008). Specimen thickness is particularly important when operating the TEM at a lowered accelerating voltage to reduce beam-induced knock-on damage or when performing electron energy loss spectroscopy (EELS), but reaching the required thickness while retaining the perfect crystal structure is very challenging. Thinning of a material in preparation for HRTEM is often achieved by bombardment with high-energy argon ions. However, this can lead to significant lattice damage and surface amorphization, even on robust phases such as silicates (McCaffrey et al., 2001), and may lead to the development of artefacts as well as difficulties in the identification of original lattice deformation features or defects. Phyllosilcates, such as micas and clays are built of sheets of oxygen-bonded tetrahedral silica and octahedral metal layers (TOT), weakly held together by interlayers containing high coordination cations, such as K, water or electrostatic charges. Biotite is a 2:1 phyllosilicate which, like many sheet silicate minerals, has a strong tendency for basal-plane cleavage. The structure of biotite comprises TOT layers containing mainly Mg, Ti and Fe, bonded by interstitial K atoms (Fig. 1). This structure allows the easy cleavage of the structure parallel to these TOT layers. This weak interplanar bonding has been exploited in this work to produce ultra-thin crystal flakes via mechanical exfoliation. This cleavage approach is also referred to as the 'Scotch Tape' method and has attracted considerable attention from its successful use for the preparation of single-layer graphene (Novoselov et al., 2004) and more recently for other twodimensional inorganic crystals .
In this study we demonstrate the use of the mechanical exfoliation method for the preparation of phyllosilicate samples suitable for HRTEM lattice imaging. The method has the considerable advantage of avoiding damage induced by other specimen-preparation techniques such as argon ion-beam polishing or focussed ion beam (FIB) milling. This absence of sample preparation artefacts is particularly important when studying point defects or structural degradation produced as a result of radiation damage, extreme environmental conditions or chemical attack (Ma et al., 1998).

Biotite characterization
The mineral we have used to demonstrate this technique is biotite, taken from a 2 Ba almandinegrunerite-biotite sample from near Tunaberg, Sweden. The sample was chosen because the host rock was well characterized (Pattrick et al. 2013) and consisted of large single crystals (~2 cm in diameter). X-ray diffraction (XRD) analysis using a Bruker D8 Advance diffractometer confirmed the mineral as biotite mica (Cruciani and Zanazzi, 1994;Brigatti et al., 2008). The bulk chemistry of the biotite was established by means of electron probe microanalysis (EPMA) (Reed, 2010), using a Cameca SX100 microsonde with a beam current of 20 nA and an acceleration voltage of 15 keV. Standards used for biotite were fayalite (Fe), tephroite (Mn), wollastonite (Ca and Si), rutile (Ti), K-feldspar (K), cordierite (Al), jadeite (Na), periclase (Mg) and rutile (Ti  Fleet, 2003). Flakes of mica~20À30 mm thick, were extracted from the rock for this study.

Exfoliation of biotite
In this work we report use of the mechanical exfoliation sample preparation technique, as described for graphene in Novoselov et al., to produce ultra-thin layers of biotite. In this method, a high tack/low stain adhesive tape is pressed and peeled onto itself repeatedly so as to pull off increasingly thinner layers of material. The tape with the thinnest layers of material is then stuck down onto an oxidized silicon substrate. Following this, the tape is then dissolved in methyl isobutyl ketone heated to 80ºC, leaving the exfoliated flakes on the silica. A final tape peel is employed to remove the thickest flakes from the substrate although the remaining material contains biotite flakes with a range of thicknesses. Optical imaging was used to identify which regions of the exfoliated material were ultra-thin from their characteristic violet-blue colour (Fig. 2a). Very thin flakes are often highly transparent so have poor contrast in the optical microscope. However, the correct choice of optical wavelength and the added path of the SiO 2 substrate shifts the optical interference pattern, allowing even monolayer graphene to be clearly visible (Blake et al., 2007); a similar effect was expected and found for biotite. A wavelength of 90 nm and crossed polars was chosen so as to give optimal contrast for the thinnest flakes when supported on a silica wafer with a 300 nm surface oxide.

Atomic force microscopy analysis of ultrathin biotite
An atomic force microscope (AFM) (Binning et al., 1986) was used to measure the height of the exfoliated biotite films relative to the silica substrate (see Fig. 2). The machine used was a Digital Instruments Multimode IIIA operated in tapping mode. The tips were Veeco RTESPA10 which are p(n) doped Si 1À10 ohm·cm with a nominal frequency of 280 kHz, a nominal force constant of 40 N/m, a mean tip radius of 10 nm and Al reflective back coating. Transverse AFM scans across the surface of two of the thinnest flakes revealed average step heights of 2.180Ô0.2 and 1.826Ô0.2 nm respectively. These values are close to the thickness of two complete~1 nm biotite TOT layers. The sharp peak visible in Fig. 2c is considered to be a region where the biotite has folded or creased. When other thicker flakes of the sample were measured, thicknesses increased in units of~2 nm in height, with no evidence of fragments 1, 3, 5 or 7 nm thick. We suggest that surface charges may be the reason for the observation of flakes with even numbers of TOT layers (whole unit cells).

Flake transfer
Transfer of the flakes from the silica substrate onto a support grid suitable for transmission electron microscope (TEM) imaging was achieved by the method described by Meyer et al. (2008) as summarized in Fig. 3. The exfoliated sample was coated in a thin poly(methyl methacrylate) (PMMA) protective film, then heated to 110ºC for a few minutes to improve adhesion. After checking the position of the region of interest in an optical microscope, a circle was scribed into the PMMA around the biotite flakes chosen for transfer. KOH was then used to chemically etch away the underlying SiO 2 layer so that the biotite-PMMA composite film could be floated free from the Si wafer in distilled water. After rinsing in distilled water the sample was transferred to a quantifoil TEM carbon support grid. The PMMA support layer was then removed by dissolving in acetone. Finally the sample was dried using a Critical Point Dryer (CPD), with acetone as an intermediate agent, before being replaced with liquid CO 2 and heated to 40ºC. The successful transfer of a flake only a few TOT layers thick, identified using optical microscope imaging, onto a support grid to enable high-resolution TEM imaging is illustrated in Fig. 3. It is difficult to distinguish the ultra-thin flake region optically after transfer (Fig. 3cÀe), but its location on the grid can be deduced from the position of the thicker flakes, as the relative locations of the flakes are largely preserved after transfer. The thin biotite region is easily identified at low magnification in the TEM using a small objective aperture to increase contrast (Fig. 3f).

High-resolution imaging
The ultrathin biotite flakes were analysed at high resolution using the Titan 2 G2 80-200 (S) TEM in the School of Materials, University of Manchester. The instrument was operated in the conventional TEM imaging mode using an accelerating voltage of 200 kV. Imaging conditions were chosen to obtain a reasonable signalto-noise ratio while limiting beam-induced radiation damage (specimen pixel size of 0.0216 nm, beam current of 3.5 nA, exposure of 1 s and an imaging dose of~100 electrons Å À2 ). Using these imaging parameters it was possible to acquire >30 images without seeing any electron beam-induced sample damage although significant damage was observed after 100 images (Fig. 4). The images here were all acquired for biotite viewed along TEM specimen holder or by taking advantage of folds and creases in the sheets. High-resolution TEM images often suffer from the effects of high spatial frequency oscillations in the contrast transfer function due to coherent aberrations of the objective lens. When the sample is sufficiently thin, exit wavefunction restoration from a series of TEM images allows these effects to be compensated providing local structural information in the phase of the exit wavefunction (Coene et al., 1992(Coene et al., , 1996. Focal series data sets consisting of 10À20 high-resolution transmission electron microscope images with a uniform focal step (~10 nm) were recorded close to the Scherzer defocus (À39 nm for 200 kV electrons and a spherical aberration of 0.6 mm). Highresolution lattice images acquired at the same defocus value before and after a 20 image focal series are compared in Fig. 4a and b. No beaminduced damage is visible as a result of focal series data acquisition and the inset Fourier Transforms (FTs) for the images appear identical, demonstrating no loss of information transfer. However, after the acquisition of~100 images, damage to the crystal was clearly visible (Fig. 4c). Exit wavefunction restorations were calculated from the focal series data sets using a Wiener filter approach (Saxton, 1988) implemented using the FTSR commercial software (www.hremresearch.com) within the Gatan Digital Micrograph program. Prior to exit wavefunction restoration the images were aligned using a phase correlation function/ phase contrast index function to correct for specimen drift and to determine the precise focal step variations between images (Meyer et al., 2002(Meyer et al., , 2004. The modulation transfer function for the CCD camera was determined independently and compensated as part of the restoration process (Meyer et al. 2000). The phase of the exit wavefunction restored using the focal series data set acquired between the images in Fig. 4a and b is shown in Fig. 5a. An advantage of restoring the full complex exit wavefunction is that the uncertainty of comparison to image simulations is reduced. Image simulations were performed using the multislice method (Goodman and Moodie, 1974;Lynch and O'Keefe, 1972) for the phlogopite crystal structure (Takeda and Ross, 1975). These confirmed that the images and restored exit wavefunction had the contrast expected from the phyllosilicate structure with a specimen thickness of <20 nm (inset Fig. 5b). It is interesting to note that restoration of the exit wavefunction has the additional advantage of improving the signal-to-noise ratio in the images and that this enables the weaker {110} and {020} reflections to appear in the FT of the restored exit wavefunction (Fig. 5c) even though they are not visible above the noise in the FT of an individual HRTEM image (inset Figs 5a,b). The diffraction pattern from the same sample region has a similar contrast to the FT of the restored exit wave (Fig. 5c,d) with {110} and {020} reflections having considerably weaker intensity than {200} (consistent with dynamical diffraction effects for sample thicknesses of <20 nm).

Summary
Our results demonstrate that mechanical exfoliation combined with identification of the thinnest FIG. 4. High-resolution TEM images demonstrating the absence of electron beam-induced radiation damage during focal series acquisition. Images were acquired at nominally the same defocus (a) before and (b) after the acquisition of the 20 image focal series data used to restore the exit wavefunction shown in Fig. 5(a). The Fourier transforms of the images (inset in a and b) show there was no loss of lattice information during image series acquisition. (c) The same area after >100 images: the mottled appearance of the image indicates that the sample is damaged severely. flakes using optical imaging and transfer to standard TEM support films can provide specimens suitable for high-quality lattice imaging in phyllosilicates. This sample-preparation approach avoids the need for argon-ion polishing and hence the possibility of artefacts introduced as a result of ion-beam milling. The samples were found to be sufficiently stable to allow the routine use of highresolution focal series data acquisition and exit wavefunction restoration. This novel approach is suitable for any sheet silicates with weak interlayer bonding. The properties of clay minerals are very dependent on structure and there is considerable interest in the use of clay in retaining radionuclides in a Geological Disposal Facility. Radiation damage investigations involving synchrotron radiation have implied that there are major effects on the "metal layers, including breakdown of OH groups, Fe-redox changes, defect generation and amorphisation" (Ewing et al., 2000;Pattrick et al., 2013). In using the TEM to assess structural damage to the clays induced by deliberate radiation exposure, it is essential to eliminate the possibility that the observed changes are sample-preparation artefacts. This necessitates the production of thin, defect-free crystals and has motivated this work but we recognize that the ability to produce very thin, high-quality TEM samples from sheet silicates has much wider applications.