Florian Semmer

Marie-Charlotte Emperauger

Colin Lopez

Christine Bogicevic

François Treussart

Karen Perronet

François Marquier
email: francois.marquier@ens-paris-saclay.fr

TWO-PHOTON REAL-TIME DEVICE FOR SINGLE-PARTICLE HOLOGRAPHIC TRACKING (RED SHOT) A PREPRINT

Three-dimension real-time tracking of single emitters is an emerging tool for assessment of biological behavior as intraneuronal transport, for which spatiotemporal resolution is crucial to understand the microscopic interactions between molecular motors. We report the use of second harmonic signal from nonlinear nanoparticles to localize them in a super-localization regime, down to 15 nm precision, and at high refreshing rates, up to 1.1 kHz, allowing us to track the particles in real-time. Holograms dynamically displayed on a digital micro-mirror device are used to steer the excitation laser focus in 3D around the particle on a specific pattern. The particle position is inferred from the collected intensities using a maximum likelihood approach. The holograms are also used to compensate for optical aberrations of the optical system. We report tracking of particles moving faster than 30 µm.s -1 with an uncertainty on the localization around 40 nm. We have been able to track freely moving particles over tens of micrometers, and directional intracellular transport in neurites.

Introduction

Single particle tracking has allowed important advances in the understanding of biological domains such as the fast dynamics of biomolecules at cell membrane[LPH + 19], viral infection[LWX + 20] or intraneuronal transport[KIC + 18]. Most of the experiments consist in extracting trajectories from movies after their acquisition by video-microscopy of biological samples using fluorescent emitters [GVG + 17, HMLM + 17] or scattering nanoparticles[KIC + 18, MMC + 20]. Particles? positions are inferred from each frame of the movies with a few 10s nm localization precision, depending on the number of detected photons[DZM + 14]. The timescale is then given by the frame rate of the movie, from 20 to 100 Hz typically. To achieve such high spatio-temporal resolution, most of the studies are limited to tracking in a single plane of observation. Video microscopy can be extended to the third dimension (along the direction of propagation z), as in interferometric scattering microscopy (iSCAT) [START_REF] Hsieh | Label-free, ultrasensitive, ultrahigh-speed scattering-based interferometric imaging[END_REF] or in Point Spread Function (PSF) engineering[OSW + 21] systems. Both those methods can be based on wide-field microscopy allowing parallel tracking of several particles in 3D and the second one allows even multi-color tracking but they operate over an axial range of only a few 10s µm. Another ensemble of tracking technologies consists in inferring the distance of the emitter to a specific excitation pattern. The recent minimal-photon-fluxes method (MINFLUX) presents the smallest nanometer-range localization precision σ that can image single fluorophores in 3D at σ < 1 nm and track single fluorophores in 2D at a typical 30 Hz rate, up to 8 kHz for σ ≈ 20 nm [SWW + 21, WSE + 22], however the accessible volumes are currently small, less than 500 nm in the z-direction, and ≈ 1µm in the x, y-plane, moreover the method remains very demanding in terms of experimental setup. To our knowledge, none of these methods is reported to be used in optically thick samples. To follow the particle over a larger spatial range, other feedback-based 3D real-time single-particle (3D-RT-SPT) tracking methods have been developed [START_REF] Bertus Van Heerden | Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective[END_REF]. Mainly, the spatiotemporal-modulation of the excitation light allows to infer the position of the emitter from the analysis of the resulting collected intensity. A feedback loop makes sure that the emitter stays in a excitation area at the microscale, allowing a localization precision in the 10 nm range. Measuring 2D trajectories on long distances and fast can then be done using a 2D excitation pattern that can be executed very fast using Acousto-Optics Deflector [START_REF] Hou | Real-time 3D single molecule tracking[END_REF] (AOD) or resonant galvo-mirrors[WPT + 19, ADG15]. These methods aim to achieve millisecond time-resolution, and a 5-10 nm localization precision but one of the bottlenecks is to be fast also along the optical axis to scan a 3D thick sample and perform precise 3D-localization. In order to pave the way to thick tissues, RT-SPT has been extended to two-photon microscopy, displaying a nice localization precision of about 15 nm at time scales on the order of 20 ms[Lev05] and more recently at 8 ms [START_REF] Annibale | Electrically tunable lens speeds up 3D orbital tracking[END_REF]. A clever multiplexed illumination allowed to lower the time-response below 5 ms in a two-photon system but the maximum tracked speed is finally limited by the response time of a piezostage[PLH + 15]. Being able to realize a 3D tracking in optically thick tissues at nanometer and millisecond dynamics is still difficult and needs new technologies and strategies.

In this paper, we introduce an original 3D-RT-SPT method based on the use of a digital micromirror device (DMD) and Lee holography [START_REF] Bryngdahl | Laser beam scanning using computer-generated holograms[END_REF][START_REF] Geng | Digital micromirror device-based two-photon microscopy for threedimensional and random-access imaging[END_REF] in a two-photon microscope setup. The use of a DMD allows a fast and precise tracking over an extended range. The DMD is used to (i) create a 3D excitation pattern, allowing the super-localization of a nonlinear nanoparticle (BaTiO 3 nanospheres, ≈ 100 nm diameter), (ii) track the nanoparticle during its motion, changing the 3D excitation-pattern global position, and (iii) correct the wavefront to obtain a diffraction-limited spot at the laser focus. We demonstrate a localization precision lower than 20 nm in the x, y-plane, 40 nm in the z-direction, and we collected position datas up to 1 kHz acquisition rate. We show that our setup is able to efficiently track moving particles whose speed is as large as 30 µm.s -1 . We finally demonstrate the ability of our setup to track particles internalized in living cells (neuroblasts Neuro-2A) over ≈ 20 µm, displaying highly directional trajectories mediated by molecular motors and characterized by fast and slow phases. Coupling two-photon microscopy, holography and real-time single particle tracking, this work paves the way to deep-tissues measurements of molecular-motors dynamics, kinesin or dynein, whose steps have typical size 10 nm at typical frequency of 100 Hz in physiological conditions along hundreds of µm, and eventually of intraneuronal-transport parameters[HMLM + 17, KIC + 18, WPT + 19, PZL + 22, WSE + 22].

Results

Experimental setup

The experiment has been designed to track nanoparticles in biological tissues taking advantage of Second-Harmonic Generation (SHG). This two-photon scattering process allows the conversion of an infrared-light excitation, which is known to be less scattered or absorbed in biological tissues [Gol18], to visible light, for which efficient and sensitive detectors as single-photon counting modules are commonly used nowadays. Such optical probes are expected to be useful in deep tissues.

We used BaTiO 3 nanoparticles (NP), diameter ≈ 100 nm (Fig. 1a) having a large nonlinear susceptibility which leads to a good SHG efficiency (typical two-photon scattering cross section 2.10 3 GM for a 100 nm diameter NP [KSB + 13]). Figure 1b shows a schematic diagram of the setup. It relies on a conventional Lee holography configuration adapted to a two-photon microscope, inspired by a paper from Geng et al. [START_REF] Geng | Digital micromirror device-based two-photon microscopy for threedimensional and random-access imaging[END_REF]. We use an infrared pulsed laser (titanium-doped sapphire laser Ti:Sa, Chameleon Ultra-II; Coherent, USA) having a 80 MHz repetition rate and a pulse width of 140 fs. We tuned its emission wavelength at λ = 1028 nm to excite SHG from BaTiO 3 NP at λ/2 = 514 nm. The excitation laser beam is directed to a DMD (Superspeed V-7001 ; Vialux, Germany) before being sent to an inverted microscope (Eclipse Ti-E; Nikon, Japan) and focused into the sample using a water immersion high numerical aperture microscope objective corrected for a 170 µm glass coverslip (Plan Apo VC 60xA/1.20 WI; Nikon, Japan).

As we use a spectrally broad laser, we need to compensate the DMD chromatic dispersion to avoid an enlargement of the spot at the focus of the microscope objective. We realize a conjugated dispersion with a compensation grating (T-1000-1040, 1000 lines/mm ; LightSmyth, USA) and two lenses L 3 and L 4 . These lenses form an afocal system which optically conjugates the compensation grating with the DMD, and obtain the desired angular magnification to optimally compensate the chromatic dispersion [START_REF] Geng | Digital micromirror device-based two-photon microscopy for threedimensional and random-access imaging[END_REF]. A first telescope (lenses L 1 and L 2 ) is placed before the compensation grating to fit the beam diameter to the DMD active area. Each micromirror on the DMD can be tilted with an angle of ±12 • and the intensity in the desired diffraction order is maximized choosing carefully the angle of incidence on this device to fulfill a blazing criterion. We chose this angle of incidence to be equal to 0 • because it minimizes the sensitivity of the chromatic dispersion to the incident angle on the DMD. The blazed order direction is thus at an angle of 24 • from the incident beam. The beam diffracted by the hologram displayed on the DMD is focused (with L 5 ) onto a pinhole to select only the (-1) order of the displayed diffraction pattern. The lens L 6 associated to L 5 completes a last afocal system which ensure the conjugation of the DMD with the back focal plane of the microscope A near-infrared (NIR) pulsed laser is first slightly expanded (with L 1 and L 2 afocal combination) and then directed towards the DMD after having been pre-compensated for chromatic dispersion with a grating, and enlarged with a telescope (L 3 , L 4 ). After diffraction by the DMD, the -1 order is selected with a diaphragm, recollimated by a lens (L 6 ), and sent to the illumination path of a commercial microscope, the yellow dashed line represent the backfocal plane of the microscope objective which is conjugated to the DMD. The beam is then reflected by a shortpass dichroic beamsplitter into a high numerical aperture microscope objective which focuses the excitation laser in the sample. The latter can be translated with a 3-axis piezoelectric stage to extend the tracking area beyond the field of view accessible with the DMD steering. The SHG signal of the BaTiO 3 nanocrystal is collected through the same objective, transmitted through the BS and focused (L 7 ) on the active area of a single-photon counting module (SPCM). The experiment is interfaced by custom LabVIEW FPGA and LabVIEW programs. (c) Two different beam profile before and after phase correction. Profile imaged after reflection on a mirror in the focal plane of the objective on camera. The intensities are normalized to the maximum intensity of the corrected profile. Scale bar 3 µm.

objective with the adapted magnification. As a result, the spot at the focus of the microscope objective is the Fourier transform of the pattern displayed on the DMD.

The sample is coupled to a 3D piezo-stage (LT3-200 ; Piezoconcept, France) to extend the range of tracking beyond the field of view made accessible with the DMD holograms. The SHG from the tracked non-linear nanocrystal is collected by the same objective, then transmitted through a short-pass dichroic beamsplitter (FF749-SDI01 ; Semrock, USA) and focused (L 7 ) onto a single photon counting module (SPCM-AQRH-13; Excelitas, USA). All the apparatuses are interfaced with a FPGA board (PCIe-7820; National Instrument, USA) and the experiment is controlled by a home-made program written in LabVIEW and LabVIEW FPGA.

Aberration correction

The DMD presents some flatness imperfections that are at the origin of the main laser-beam wave-front deformations and lead to a non-ideal Point Spread Function (PSF). These defects can be observed by placing a mirror in the objective focal plane and conjugating the surface of the mirror to a camera sensor (fixed at one side port of the microscope): the focused laser spot, resulting from the residual excitation light transmitted by the dichroic BS, displays strong astigmatism. Such defects must be corrected before using the device for single-particle tracking. To this aim, we take advantage of digital holography to apply common tools of adaptive optics. We adjust the coefficients of the Zernicke polynomials (mainly the coefficients associated to vertical and horizontal astigmatism) to maximize the peak intensity of the gaussian and obtain ultimately a diffraction-limited PSF. Figure 1c displays the PSF before and after correction of astigmatism.Quantitatively, the corrected PSF has a Strehl ratio of around 0.8, meaning that the standard deviation of the incident wave front is less than λ/14 compared to a flat wave front [vdB00]. In comparison the Strehl ratio obtained without correction is around 0.2. When corrected, the The final excitation intensity can be up to 600 kW.cm -2 . Because we perform 3D tracking, we finally used a single nonlinear nanocrystal to probe the two-photon PSF in 3D via its SHG response, by scanning the crystal position in the (x, y, z) directions with the piezostage (see supplementary figure 1).

Holography and positioning

By changing the spatial frequency of a periodic pattern imprinted on the DMD we can position the laser spot at different locations in the focal plane of the objective. It is also possible to encode a spherical phase in the hologram and thus modify the focusing position along the optical axis [START_REF] Geng | Digital micromirror device-based two-photon microscopy for threedimensional and random-access imaging[END_REF]. The focused spot S of the laser beam can thus be placed at different locations r S = (x S , y S , z S ) within the sample along the three dimensions. S can be seen as the image of a virtual source point C located at r C = (x C , y C , z C ) through the whole optical system. The hologram to be imprinted onto the DMD is the binarized pattern resulting from the interference between the spherical wave that would be emitted by C and a reference laser light (plane wave whose wave vector is denoted k inc ). Such a hologram can be computed at each pixel position r(x, y) of the DMD surface as:

H(x, y) = 1 2 1 + cos 2π λ k inc .r k inc + r -r C -ϕ(r) (1)
Where X is the integer part of X and ϕ(r) the phase map that takes into account aberration corrections. In addition, care must be taken to ensure there is no overlap between the useful diffraction order of the hologram and a natural diffraction order of the DMD grid. It leads to an off-axis configuration which can be interpreted as the choice of a carrier frequency in Lee holography to define the center of the positions attainable by the excitation laser.

Localization precision

The position of the NP is inferred from a set of excitation spots positioned around and in close proximity of it. We first address the precise localization of a fixed emitter. We use a fixed BaTiO 3 NP deposited on a coverglass and covered with water to be in the best working conditions of the microscope objective (Fig. 2a). We sequentially display different holograms on the DMD, each of them focusing the beam at a known position in the vicinity of the NP (Fig. 2b). In the SHG process, the emitted number of photons depends quadratically on the intensity of the excitation laser, hence related to the distance between the excitation point and the position of the NP. Using a maximum likelihood approach [BEG + 17] and the knowledge of the 3D-PSF of the setup, we are able to precisely estimate the location of the emitter in the excitation pattern. The latter consists of 9 spots, distributed as follows: 6 spots are regularly placed on a circle in a plane orthogonal to the optical axis, describing a hexagon, and 3 spots are along the optical axis, located on a segment crossing the hexagon at its center as shown in figure 2b. With numerical simulations discussed in the next paragraph, the radius of the circle encompassing the hexagon has been optimized to be a = 470 nm [START_REF] Wang | Optimal strategy for trapping single fluorescent molecules in solution using the ABEL trap[END_REF], and the distance between two consecutive points on z is dz = 1 µm.

We set first the photon detection integration time at 500 µs at each position of the pattern, so that the total integration time for one localization of the observed NP is 4.5 ms leading to a typical number of 10 3 collected photons (≈ 2.2 × 10 5 photons.s -1 ). We determine the localization precision with repetitive position measurements, as displayed in figure 2b andc. Its value is characterized by the standard deviation of the set locations, yielding 19 nm and 14 nm along the x and y directions respectively and 36 nm in the optical axis z direction (Fig. 2d). Increasing the integration time leads to larger photon numbers and thus a better localization precision. Figure 2e shows the evolution of the position-measurement standard deviation along the y-axis as a function of the total photon number N received from the set of 9 excitation points. We observe the expected 1/ √ N behavior above an asymptotic value of around 10 nm, that we attribute to remaining vibrations of our setup, that could be corrected in the future.

Note that from a temporal point of view, the DMD has a maximum refresh rate of 22 kHz corresponding to a minimum response time of 45 µs. The overall rate results on one hand from the dwell time defined as the sum of the refreshing time and the integration time of the detector (during which the same hologram must be displayed), and on the other hand from the number of holograms needed to infer the position of the NP (9 in this work). As usual, for a targeted localization precision the photon budget is the limiting factor[DZM + 14], hence fixing the maximum measurement rate. In the following, we tracked NP whose SHG maximum emission was between 10 5 photons.s -1 and 5 × 10 5 photons.s -1 .

Tracking strategy

As we cannot perform the maximum likelihood estimation in real time we evaluate the position of the emitter with a centroid computation program embarked on the FPGA board. However, when the NP move too far from the center of the excitation pattern, the localization uncertainty increases and either the emitter needs to be moved toward the center of the pattern or the pattern itself can follow the particle. Most of the existing RT-SPT techniques adopt the first strategy and act on the relative position of the emitter with respect to the pattern at every step of the tracking algorithm using a piezo stage[WPT + 19, BEG + 17, HEW20, PLH + 15]. We chose the second strategy and change the excitation pattern accordingly to the NP position evolution, as it provides a faster scan speed, compared to the piezo stage whose response time is of a few tens of milliseconds (in close-loop). In order to use the DMD at its full speed we preloaded a library of holograms associated to positions regularly spaced in a 3D cubic volume (see Supp. Mat. 4.2)]. The number of excitation positions is limited by the RAM of the DMD control board to 87380 holograms.

A convenient and compact predefined mesh is a hexagonal mesh grid, as the one used for the precision of localization. Considering the parameters a and dz previously defined previously, and easy-to-use memory management, a mesh of 21 × 21 × 5 holograms has been chosen, setting the boundaries of a holographic tracking volume of around 9.9 × 8.5 × 5 µm 3 which limits then the total field of view. When the NP reaches the boundaries of this volume, we use the piezo stage to re-center the NP in the tracking volume. It is finally possible to track the NP over longer distances when it is needed. During the piezo motion, we do not measure the position of the emitter. The tracking algorithm consists finally in the simplified following steps: (i) Localize a NP, (ii) when the NP reaches a given limit into the excitation pattern, use the closest next pattern, (iii) move the piezo-stage if the limit of the field of view is reached. The maximum likelihood estimation of the position at each step is performed afterwards from the recorded intensities to get the best precision from our setup.

Controlled trajectories

We fix the integration time at 500 µs at each excitation point (220 Hz localization rate). To illustrate the spatiotemporal resolution of the setup, we first tracked a NP fixed on a coverglass and moved by the piezo stage along a known predefined trajectory. The tracked NP emits an average of 1.5 × 10 5 photons.s -1 . Figure 3a shows examples of tracks of NP moving along the y-axis with different velocities. We observe that the position measurement match the expected true trajectory of the piezostage represented in plain lines. The distributions of errors is shown on the histograms displayed in figure 3b. Interestingly, the mean error does not strongly depend on the velocity in the range 7 to 31 µm.s -1 . The typical error is most of the time less than 30 nm, in very good agreement with the expected value from localization precision measurements of Fig. 2d, taking into account the difference of photons number emission. For a 100 µs integration time per excitation point (1.1 kHz localization rate), the typical error stays relatively low at 40 nm for the same NP (see Supp. Mat. 4.4). As expected, decreasing the integration time lowers the photon budget and degrades the localization precision so that brighter NP in a two-photon process[LWX + 20, PZL + 22] would definitely help using the full speed of the DMD.

Natural trajectories

Nanoparticles in solution

To check the setup ability to track a NP over a large field of view, we use freely moving NP in a water/glycerine mixture. Tracks can be acquired over tens of micrometer on several minutes. . Figure 4a shows a typical trajectory of a given NP in 3D during 4 min. We observe a clearly diffusing behaviour in the x, y plane, whereas the motion is more directional along the z direction. We first focus on the trajectory in the x, y plane only. We derive the Mean Square Displacement (MSD) from the data sets x i = x(t i ) and y i = y(t i ) at discrete times t i as:

MSD (∆t ij = t j -t i ) = x 2 j -x 2 i + y 2 j -y 2 i - x 2 j -x 2 i + y 2 j -y 2 i 2
Where the braket stands for an average over the same lag times for a given trajectory.

Figure 4b displays the MSD as a function of the lag time ∆t for the typical trajectory depicted in Fig. 4a. As expected from a diffusive motion, we observe a linear behavior whose slope is related to the diffusion coefficient D: MSD(∆t) = 4D∆t. We are thus able to extract a diffusion coefficient from the measurement. We estimate D ≈ 0.011µm 2 .s -1 which is consistent with the NP size and viscosity range considering the Stokes-Einstein relation for a spherical particle D = k B T /(6?ηR NP ) where k B is the Boltzmann constant, η the viscosity and R NP is the NP radius.

Along the z direction, the behavior of the NP is more complex to interpret as the motion becomes directional: the NP goes upwards in the liquid, keeping a random Brownian motion. In that case the MSD can be written as MSD(∆t) = 2D∆t + v 2 ∆t 2 , where D is the diffusion coefficient previously measured in the x, y plane and v is the mean velocity of the directional motion. Simulations show that this behavior is compatible with an effect of the so-called scattering optical force from the excitation laser (see Supp. Mat. 4.3). We measure a velocity of ≈94 nm.s -1 that can be related to an average optical force pushing the NP of F = 6πηR NP = k B T v/D, whose order of magnitude is then ≈ 3.4 × 10 -2 pN, much higher than the weight of the NP, around 0.2 fN. If such a force perturbs the free motion in the fluid, the order of magnitude is negligible compared to the force that a molecular motor could apply to an endosome embedding such a NP, around 10 pN, so that we believe our tracking technique is fully available for measuring directional transport in cells.

Trajectories in living cells

The tracking method has finally been tested on NP internalized in living cells displaying directional trajectories and typical go and stop phases. We used mouse neuroblasts (Neuro-2A) cells 2D cultures and NP were added to the cultured medium of the cell (see Supp. Mat. 4.5). After a few minutes, some NP are likely to be spontaneously internalized in cells by endocytosis[HMLM + 17]. This is confirmed by the trajectories observed for the NP. Figures 5a and5b display two highly directional trajectories, acquired during 2 min, superimposed with microscopy images. The directional behavior cannot be attributed to a diffusive motion in the medium or on the cell membrane[CHL + 16]. In contrast this is the expected motion of an endosome containing a NP and taken over by molecular motors[CWC + 07, HMLM + 17, CAM + 22]. We focus on the latter trajectory on fig. 5c, where the positions of the NP are represented in the x, y plane with a color corresponding to its instantaneous velocity.

We now clearly see slow and fast phases usually associated to stop and go states of the dynamics of endosomes.

The velocities order of magnitude, around 1 µm.s -1 , and up to 2 µm.s -1 are also in the expected range of such processes[KKS + 05]. Depending on the molecular-motors family (kinesin or dynein) predominantly involved in the transport process, we can also observe some back and forth movements (Fig. 5d). During the experiment, no alteration of the cells has been observed. We hence believe that this setup could be used to track NPs in living cells for intraneuronal transport measurements. Due to the two-photon capability, it has the potential to be adapted to the observation of NP transport in more complex tissues as for instance in zebrafish larvae[MMC + 20] in a superlocalization regime and at a very high rate.

Conclusion

In conclusion, we have presented a new two-photon 3D Real-time Single particle tracking method based on digital holography mediated by a DMD. We demonstrated the ability of our setup to localize fixed nanoparticles with a precision of less than 20 nm in x and y directions and 40 nm along the z direction depending on the number of collected SHG photons. We have shown that we can acquire trajectories with a time resolution down to 1 ms and a typical localization precision of 30 nm along x and y directions and 60 nm along z direction. coupled to a piezostage, we tracked free nanoparticles in solution over 10s of micrometer along all directions, test our tracking device on biological sample (living neuroblasts Neuro-2A) and observed typical directional trajectories driven by molecular motors. Aiming to apply the tracking in thick samples we currently work on an adaptive optics loop to compensate for aberration induced by the sample itself.

4 Supplementary materials

3D PSF

The knowledge of the 3D-detection point spread function (PSF) of the setup is crucial to use a maximum likelihood approach [BEG + 17] and to be able to precisely estimate the location of the emitter in the excitation pattern. In order to access this information we scan a single BaTiO 3 nanoparticle fixed on a coverslip by moving it with the piezo stage and collecting the SHG signal.

Excitation pattern

To use the DMD at its full speed we can only display holograms that has already been loaded into the RAM of the DMD controller. This is one of the drawbacks of the use of a DMD because if one wants to acquire fast, it can not ask for a continuous repositioning of the excitation pattern. Hence we need to think about the arrangement of all the possible location we want to focus the laser at. We compute holograms library to form an hexagonal mesh in 3D and we decide to change the holographic excitation pattern, made of holograms from the library, when the particle is 0.6a away from the center or 0.6dz away from the plane of the hexagon. The question of an optimal solution for a and dz seem natural. In comparison, for techniques such as orbital tracking where the excitation spot move continuously along a circular trajectory, the optimum for the parameter a is found to be the value which defines a circular excitation area with uniform power and is w 0 / √ 2. In our case, What we want is to minimize the localization bias during Real-time measurement when the particle it at the boundary to avoid instabilities. We simulate localisation at the boundary for different values of a and dz with different background level and found that a = 470 nm and dz = 1000 nm seemed to be an optimum in our case.

Scattering optical force from the excitation laser

To be updated 4.4 Controlled trajectories

Fast acquisition

Several acquisitions were made increasing the acquisition rate. In Fig7 we tested values of 200Hz, 714Hz and 1,08kHz by choosing integration times of respectively 5 ms, 1.4 ms and 0.9 ms. We observe that the error to the piezo stage position is still around 30 nm until 714Hz, for faster acquisition it raises 44nm. Of course the number of collected photons lower when the frequency rises. We point out that the sequence update takes 8.5 ms approximatively so when we acquire much faster and if the np moves fast, we see that the trajectory is not uniformly measured. Depending on the trajectory expected in biological medium we can adapt the parameters to find a compromise between high spatial resolution and fast acquisition.

x and z trajectories

N2A culture

Neuro-2A cells are mouse neuroblasts with neuronal and amoeboid stem cell morphology isolated from brain tissue. They were divised and deposit on a glass coverslip of 18mm in a culture well with cultured medium (DMEM 10% Fetal Bovine Serum and 10% Pen-Strep antibiotic) on day one. Four days after, the solution of spherical BTO 38 nanoparticules at 300mg/mL was placed into ultrasonic bath during 30 min and added to the cultured medium of the cell. Each well received 20µL of solution and was stored again into incubator for one night. The glass coverslip was deposit on the sample carrier on the 5 th day and was covered by 400µL of new culture medium.

Backmatter

Funding : This work has received financial support from the French National Research Agency ANR (ANR-18-CE09-0027), and by a public grant overseen by the ANR as part of the ?Investissements d?Avenir? program (reference: ANR-10-LABX-0035, Labex NanoSaclay). The research was also supported by a ENS Paris-Saclay scholarship.

Figure 1 :

 1 Figure 1: DMD and nonlinear nanocrystal tracking setup. (a) SEM image of BaTiO 3 nanocrystals used to demonstrate the 3D-tracking. Scale bar 200 nm. (b) Schematics of the DMD-based single particle 3D-tracking setup.A near-infrared (NIR) pulsed laser is first slightly expanded (with L 1 and L 2 afocal combination) and then directed towards the DMD after having been pre-compensated for chromatic dispersion with a grating, and enlarged with a telescope (L 3 , L 4 ). After diffraction by the DMD, the -1 order is selected with a diaphragm, recollimated by a lens (L 6 ), and sent to the illumination path of a commercial microscope, the yellow dashed line represent the backfocal plane of the microscope objective which is conjugated to the DMD. The beam is then reflected by a shortpass dichroic beamsplitter into a high numerical aperture microscope objective which focuses the excitation laser in the sample. The latter can be translated with a 3-axis piezoelectric stage to extend the tracking area beyond the field of view accessible with the DMD steering. The SHG signal of the BaTiO 3 nanocrystal is collected through the same objective, transmitted through the BS and focused (L 7 ) on the active area of a single-photon counting module (SPCM). The experiment is interfaced by custom LabVIEW FPGA and LabVIEW programs. (c) Two different beam profile before and after phase correction. Profile imaged after reflection on a mirror in the focal plane of the objective on camera. The intensities are normalized to the maximum intensity of the corrected profile. Scale bar 3 µm.

Figure 2 :

 2 Figure 2: Measurement of the localization precision of an immobile single non-linear nanocrystal. (a) Configuration of the inverted microscope: NPs (green dots) deposited on a glass coverslip are illuminated by an infrared laser whose focus point varies in time (two configurations represented in dotted lines and in plain fill, The SHG is collected through the objective to a SPCM). (b) The excitation pattern is represented by the red dots, (c) The zoomed scatter plot shows the dispersion of the estimated position of an immobile nanocrystal: each color is a different measurement, for this set of data, each point corresponds to an illumination of 4.5 ms. (d) Histograms showing the distribution of the three position coordinates. The point-dotted line is a gaussian fit whose standard deviation σ is given in each subplot, (e) standard deviation of the y position measurement as a function of the collected photon number N during a set of excitations (sum of the photon numbers collected for the 9 excitation positions). The dotted line decreases as 1 √ N .

Figure 3 :

 3 Figure 3: (a) Tracks of a nanocrystal of BaTiO 3 moved by a piezostage at different velocities, inside the holographic field of view but through several pattern changes. (b) Histograms of the error to the piezo stage position. Standard deviation of the distribution for velocities of 7.7, 10.7, 19.1 and 31.8 µm.s -1 are respectively 26, 29, 25 and 38 nm. The localization precision remains almost constant for velocities up to ≈ 20µm.s -1 .

Figure 4 :

 4 Figure 4: (a) 3D Trajectory of a freely moving particle in a water/Glycerine mixture at a localization rate of around 220 Hz. The colormap corresponds to the time, from blue at the beginning of the trajectory to red at the end of the trajectory. (b) Mean Square Displacement (MSD) in the x, y plane, and in the z direction. The former is fitted with a linear model, whereas the latter is fitted with a parabolic model (solid lines). The linear behaviour is characteristic of a purely diffusive motion.

Figure 5 :

 5 Figure 5: (a and b) Two trajectories observed in living Neuro-2A cells during 2 min. The colormap corresponds to the time from blue at the beginning of the trajectory to red at the end of the trajectory. Trajectories are superimposed with microscopy images of the corresponding cells. The white line is 10 µm. (c) Part of the trajectory from (a), each position of the NP is associated to a color corresponding to its instantaneous velocity. The colorbar is in µm.s -1 . (d) Part of the trajectory from (a) the colors stand for the back and forth movements.

  Fig 6 shows three 2D scans of the same particle and sections of theses scans adjusted with Gaussian function. In this case we observe a little ellipticity in the XY plane with σ x = 251 nm and σ y = 196nm, this difference in the XY can be explain by the shape of this nanoparticle. Along the z direction the standart deviation is

Figure 6 :

 6 Figure 6: a)b)c) 2D Scan of a single BaTiO 3 fixed on a coverslip, colors stand for the collected SHG intensity. d) Gaussian fit of sections of the previous scans,the standard deviations are respectively 251,196,1109 nm.

Figure 7

 7 Figure 7: a) Three trajectories of the same BaTiO 3 nanoparticle at 17 µm.s -1 moved by the pizeo stage along the x direction and with different acquisition rate : 200Hz, 714Hz and 1.08kHz.b) Histograms of the error to the piezo stage position. Standard deviation of the distribution are respectively 27, 29 and 44 nm.

Figure 8

 8 Figure 8: a) Tracks of a nanocrystal of BaTiO 3 moved by a piezo stage along the x direction at different velocities with 200Hz acquisition time. b) Histograms of the error to the piezo stage position. Standard deviation of the distribution are respectively 40,38,32,40 nm.

Figure 9

 9 Figure 9: a) Tracks of a nanocrystal of BaTiO 3 moved by a piezo stage along the z direction at different velocities with 200Hz acquisition time. b) Histograms of the error to the piezo stage position. Standard deviation of the distribution are respectively 62,60,83,146 nm.

Acknowledgments : We thank Christelle Langevin, Guillaume Baffou and Patrick Chaumet for fruitful discussions. We thank Jean-Pierre Mothet, Martina Papa and Baptiste Grimaud for her help in the N2A culture cell. We thank Simon L'Horset and Sebastien Rousselot for their help in electronics and mechanics.

Disclosures : The authors declare no conflicts of interest.

6 References


Prof Masayuki Kawaguchi
email: kawaguti@osakac.ac.jp

Hiromichi Ishikawa

Pascal Berger

Mélissa Fauchard

Sébastien Cahen

Claire Hérold

Kawaguchi

Novel Ca and Ca-Li intercalated B/C and B/C/N materials with layered structures

Keywords: Intercalation of calcium, B/C material, B/C/N material

Osaka Electro-Communication University (OECU) in 1994 and is currently the Dean of the Graduate School of Engineering at OECU. He has worked in the field of syntheses and application of graphite-

Introduction

Boron/carbon/nitrogen (B/C/N) and boron/carbon (B/C) materials with their graphite-like structure and their semiconducting properties are very attractive. Their potential applications and their ability to be considered as host material 1 are attention grabbing in several fields: batteries 2 , capacitors 3 , fuel cells 4 and semiconductors 5,[START_REF] Kawaguchi | Fluorine-Carbon and Fluoride-Carbon Materials[END_REF] . These materials can be used as energy devices due to their physical and chemical properties. Indeed, it is possible to intercalate several metals such as potassium (K), lithium (Li), sodium (Na) and even magnesium (Mg) into this layered structure either by using the vapor phase reaction method or the electrochemical method [START_REF] Kawaguchi | [END_REF][8][9] .

However, the structural organization of B/C/N and B/C materials is poorly known and has never been fully resolved by radio crystallographic studies. In each layer of B/C/N material, 2 carbon atoms are ideally replaced by a boron atom and a nitrogen atom. However, the distance between two successive layers of B/C/N, which is very close to the interplanar distance in graphite, was experimentally determined and reaches 0.340~0.343 nm 10 . On the other hand, boron atoms can replace carbon atoms with the graphite structure to make the composition BC8 10 , although the replaced boron atoms cut off the conjugated double bonds in each layer of B/C material. The distance between two layers of B/C was experimentally determined and reaches 0.340~0.343 nm which is same as that of B/C/N. In this paper we present, after a structural and chemical study of the host B/C/N and B/C materials, the intercalation of calcium (Ca) by using a vapor phase method of Ca, and a solidliquid method in Li-based alloys for the first time with these host materials. The novel Ca and Ca-Li intercalated compounds were studied by X-ray diffraction (XRD) and transmission electron microscope (TEM). Their chemical compositions were determined using usual elemental analyses and nuclear microprobe analysis (NMA).

Experimental 2.1 Syntheses of B/C/N and B/C materials as host materials

B/C/N materials were synthesized at a temperature between 1770 and 2070 K by the chemical vapor deposition (CVD) method 11 using an equimolecular mixture (1:1 or 1:2 as a reference) of acetonitrile and boron trichloride as starting materials 8 . B/C materials were synthesized also by the CVD method at 1170 K using an equimolecular mixture (1:1) of ethylene and boron trichloride 10 . The B/C/N and B/C materials films were obtained on the carbon susceptor as the substrate and then removed from the substrates. The films were formed with an orientation of ab-axis parallel to the susceptor, which were analyzed by using XRD and shown in the results below. The host B/C/N and B/C films were cut into thin platelets whose sizes were 0.5 × 0.5 × 0.01 cm 3 and 1.3 × 0.6 × 0.01 cm 3 for the intercalation by using the vapor phase method and the solidliquid method, respectively.

Intercalation reaction

The intercalation of Ca into B/C/N and B/C host materials were carried out by the vapor phase method 12 . Commercially available Ca pieces (Fujifilm Wako Chemical Co. Ltd.) and B/C/N or B/C platelets were set in a stainless-steel tube, sealed with Swagelok caps at both ends under a high purity argon atmosphere in a glove box, and heated at 1070 K in an electric furnace for 2 weeks.

The intercalation of Ca-Li into B/C/N host material was carried out by the solid-liquid method in lithium-based molten alloy, developed for the intercalation of calcium into graphite 13 . The alloys were prepared in a glove box under a high purity argon atmosphere. Pure lithium and calcium metals were precisely weighed and introduced in a stainless-steel reactor which was heated to get a homogeneous liquid. The B/C/N platelet hanged on a tungsten sample-holder was then introduced in the Ca-Li liquid alloy containing 27 Ca at.%. The reactor was tightly closed and placed into a furnace outside the glove box. The reaction was performed at 620 K for a given duration (from 2 days to 3 weeks).

At the end of the reaction by the both methods, the reactor was opened in the glove box and the intercalated sample was recovered and then placed in a well-adapted air-tight sampleholder for each characterization.

Elemental analysis

Elemental analyses for the host B/C/N and B/C materials were carried out by the usual combustion method for carbon and nitrogen, and ICP emission spectroscopic method for boron using a boron containing solution made by a decomposition of the host materials in an alkali solution.

Ion beam analysis

The host materials and the intercalated compounds were characterized by ion beam analysis using NMA. This technique based on the interactions between a high energy ion beam in the MeV domain and the probed material were used to determine the chemical composition, but also the homogeneity of the samples laterally as well as in-depth 14,15 . A proton beam of 3050 keV and a particle detector at 170° from beam axis were used. To determine the nature and the concentration of the elements likely to be present (B, C, N, Ca, Li), elastic scattering and nuclear reactions were considered. A single spectrum leaded to the whole information for Li, B, C, N, and Ca laterally and in-depth. The analyzed map is typically of 200 × 200 µm², with lateral resolution at a few micrometers level (beam size 3.5 × 4 µm²). Samples composition was determined by adjustment between simulated spectra and experimental data using the SimNRA software. The simulated spectrum was made up of the superimposed contributions of all the interactions, with each isotope of each element of each sublayer of the defined solid. (More information concerning Li, B, C, N, O and Ca crosssections for both backscattering and nuclear reactions are given in Supporting Information 1.) 2.5 X-ray diffraction X-ray diffraction experiments were realized with a XRD apparatus (RIGAKU RINT-Ultima) using Cu-Kα radiation. Since the intercalation compounds were air and water sensitive, a platelet sample was used for the measurement and placed on a sample holder in a sealed equipment with a Be window under pure argon atmosphere or was covered with a polymer film on it.

TEM and EDX

The intercalation compounds were analyzed by using scanning transmission electron microscopy (STEM) and energydispersive X-ray (EDX) as the following. The obtained intercalation compound film was cut into a small piece by using the focused ion beam (FIB) manipulation under argon atmosphere. The small piece was then set in a TEM apparatus (JEOL, JEM-ARM200F). The STEM observation and the EDX analyses were made from the direction of ab-axis for the cross section of the intercalation compound.

Results and Discussion

Host B/C/N materials

The precise chemical composition of this type of material is difficult to determine with the elemental analyses. One of the reasons is due to the combustion difficulty of the materials under oxygen to determine the carbon and nitrogen contents by the usual combustion method. Therefore, we firstly determined boron content by the ICP emission spectroscopy. Then the rest of the contents (100 % -boron content %) was proportionally divided with the carbon and nitrogen contents measured by the combustion method.

We also used the NMA to determine the composition and study the homogeneity of the samples. Table 1 indicates the results of the composition determined by the elemental analyses and the NMA. For the NMA, many samples were studied in several regions and a representative spectrum has been selected and modeled (Figure 1). The numerous recorded spectra are superimposable (not shown), which attests to the good homogeneity of the BCN material. Despite the proximity of the three elements (B, C, N), this spectrum clearly shows three steps. In details, a first step is observed at 2290 keV, which is attributed the 14 N(p,p) 14 N reaction. Then, the signal measured around 2172 keV is attributed to the 12 C(p,p) 12 C reaction. Finally, the last step at 2105 keV corresponding to the 11 B(p,p) 11 B and 10 B(p,p) 10 B reaction is observed. We can also see a small step at 2370 keV characteristic of the presence of oxygen in-depth of the sample. All steps are horizontal and do not present any accident indicating that the sample is homogeneous in depth, which is confirmed by the modeling. The amount of boron, carbon and nitrogen is the same throughout the sample and corresponds to a chemical formula BC2.6N0.55 (indicated in Table 1) with a slight presence of oxygen (6 at. %) in the whole sample. The difference of the compositions analyzed by using the elemental analyses and the NMA could be due to the estimation of carbon and nitrogen contents by using the elemental analyses. Therefore, we represent the compositions of the host B/C/N and B/C materials, and the Ca-Li intercalated B/C/N material by using the NMA in this paper. The crystal structure of this B/C/N material has been studied. For this purpose, a film sample was reduced to powder in order to record an X-ray powder diffraction pattern. The corresponding pattern (Figure 2) reveals a strong and sharp diffraction line at 26.12° in 2θ (d = 0.341 nm), a diffraction line at 53.94° in 2θ (d = 0.170 nm), and a weak diffraction line at 85.72° in 2θ (d = 0.113 nm), which are the positions close to the graphite (002), (004), and (006) diffraction lines, respectively. Weak and broad diffraction lines at 42.28° and 77.12° in 2θ (d = 0.214 nm and 0.124 nm, respectively) were observed in Figure 2, which are the positions close to the (10) and ( 11) diffraction line of graphite with the turbostratic structure 16 . These attributions suggest that the B/C/N material had a layered structure like the graphite. Although the (00l) diffraction index depends on the stacking sequence (AB, AA, or turbostratic stacking), the diffraction line at 26.12° in 2θ (d = 0.341 nm) is called the (002) diffraction line as a usual understandable indexing in this paper.

Host B/C material

In the case of B/C material, we firstly determined boron content by the ICP emission spectroscopy and assumed the rest of the contents (100 % -boron content %) to be carbon content. We analyzed carbon and hydrogen contents by using the combustion method and found negligible amounts of hydrogen in the materials.

We also used NMA to determine the composition and study the homogeneity of the samples. Table 2 indicates the results of the composition determined by the elemental analyses and the NMA. As is the case of B/C/N material, we represent the composition BC6.4 analyzed by using NMA for the B/C material used in the present paper. For the NMA, many samples were studied in several regions and a representative spectrum has been selected and modeled (Figure 3).

Table 2. Composition of B/C material analyzed by elemental analysis and NMA.

The crystal structure of this B/C material has been studied. Figure 4 indicates a powder X-ray diffraction pattern of B/C material (BC6.4). Like that of B/C/N material, it shows very few reflections and are very close to those of graphite. A strong and sharp diffraction line at 26.16° in 2θ (d = 0.341 nm), a diffraction line at 54.02° in 2θ (d = 0.170 nm), and a weak diffraction line at 85.78° in 2θ (d = 0.113 nm), which are the positions close to the graphite (002), (004), and (006) diffraction lines, respectively. Weak and broad diffraction lines at 42.30° and 77.42° in 2θ (d = 0.214 nm and 0.123 nm, respectively) were observed on Figure 4, which are the positions close to the (10) and (11) diffraction lines of graphite with the turbostratic structure 16 . In the similar manner to the B/C/N material, the B/C material had a layered structure 17

Ca intercalated B/C material

The vapor-phase reaction of Ca with the B/C film (BC6.4) resulted in the formation of Ca intercalated B/C material (called as "Ca intercalated BC6.4" thereafter). Figure 5 shows an XRD pattern of the Ca intercalated BC6.4 film (a), compared with that of the original BC6.4 host film (b) 12 . (00l) diffraction lines of the original BC6.4 film were strongly observed in relative to the (10) diffraction (Figure 5b), compared to the relative intensity for the powder (Figure 4). This is because the original film was deposited by the CVD method with an orientation of ab-axis in parallel to the substrate. The (002) and (004) diffraction peaks at 26.16° (d = 0.341 nm) and 53.94° (d = 0.170 nm) of the original BC6.4 film disappeared after the reaction. Then we observed new diffraction peaks at 22.72° (d = 0.391 nm) and 45.84° (d = 0.198 nm) (Figure 5a). These changes in XRD diffraction patterns suggested that the BC6.4 host film reacted with Ca vapor to form the intercalation compound (Ca intercalated BC6.4).

Figure 6 indicates an expected structural view of the c-axis stacking of the compound which has the second stage structure. The layer spacing of the Ca intercalated BC6.4, di : 0.461 nm (= 0.341 + 0.120 nm), is assumed from the Ca intercalated graphite (first stage CaC6: di = 0.455 = 0.335 + 0.120 nm) [START_REF] Bartlett | Intercalation Chemistry[END_REF] . A (002) diffraction peak of the second stage Ca intercalated BC6.4 can be estimated to be 0.401 nm {= (0.461 + 0.341)/2}, which is close to the diffraction peak observed at 22.72° (d = 0.391 nm) in Figure 5a. The diffraction peak at 45.84° (d = 0.198 nm) in Figure 5a should be a (004) diffraction of the second stage compound. The Van der Waals radius of B/C layers overlaps with the Ca δ+ ion can be explained in the same manner as the alkali metal intercalated graphite by using the theory of "nestling" [START_REF] Dresselhaus | [END_REF] .

When we used the B/C material powder as the starting material, we couldn't observe the XRD pattern like Figure 5a, but observed an XRD pattern showing a lot of diffraction lines which couldn't be identified. This means that we couldn't obtain the intercalation compound by using the B/C powder as the starting material. This is probably because the B/C powder having large surface area violently reacted with Ca vapor to form an unexpected compound such as a carbide.

Figure 7 shows the cross-section image of main part of the Ca intercalated BC6. structure was observed on the image. Layers including the heaviest Ca atoms are indicated with the darkest lines, while BC6.4 layers are indicated with the next dark lines. In Figure 7a, two separated Ca layers sandwich two continuous BC6.4 layers, which suggests the second stage structure. Figure 7b indicates the contrast change image in the direction of c-axis. Although the distances measured by STEM are not so accurate as those measured by XRD, the distance between the Ca layers in Figure 7 is approximately 0.75 nm, which is close to the value of 0.80 nm for second stage structure calculated from the XRD result (Figure 5) and shown in Figure 6.

Figure 8 shows the cross-section image of a different part of the Ca intercalated BC6.4 observed with STEM. The first stage structure was observed on the image. In Figure 8a, two separated Ca layers sandwich one BC6.4 layer, which suggests the first stage structure. Figure 8b indicates the contrast change image in the direction of c-axis. An approximate distance between the Ca layers (darkest lines) is 0.41 nm, which is close to the value of 0.46 nm for the first stage structure predicted from the distance of second stage one (Figure 6).

In the XRD pattern of Ca intercalated BC6.4 film (Figure 5a), the (002) diffraction line was broader compared with that of the original BC6.4 (Figure 5b). This result suggests that the crystallinity of Ca intercalated BC6.4 was lower than that of the original BC6.4, and it was composed of several stage structures shown in Figs. 7 and8. Probably Ca intercalated BC6.4 had not only the second stage structure but also the first stage one.

The Ca intercalated BC6.4 had a Ca content in the range between 18 and 27 wt% (6 and 10 at%), which was observed through the EDX analyses. This result is consistent with the metal contents of general graphite intercalation compounds (GICs) with second stage structures (compositions between C12M and C24M, where M is Li, K, or Cs) [START_REF] Bartlett | Intercalation Chemistry[END_REF] .

From the above results made by using XRD, STEM, and EDX analyses, we concluded that the obtained compound "Ca intercalated BC6.4" was composed of the second stage compound as the main product and the first stage one as the sub-product.

We have checked the intercalation of Ca vapor into graphite under the same reaction conditions used in the present study and found that Ca couldn't be intercalated into graphite. Also, we have recognized that Ca intercalation into B/C/N materials under the same reaction condition used in the present study resulted in the formation of intercalation compounds with higher stage structure having a small amount of Ca in the layers. From these results, we found that B/C material with the composition BC6.4 intercalated Ca in their layers more efficiently than the cases of graphite and B/C/N materials.

On the synthesis of GICs, it has long been known that Counts the synthesis of low-stage Na-GIC is difficult compared with those of low-stage other alkali metals-GICs. It has been also known that Mg cannot be intercalated into graphite. On the other hand, Na and Mg have been intercalated into B/C/N materials 8,9 and Na has been intercalated into B/C materials 10 . Several members (Kawaguchi and Ishikawa) of the present authors explained these results in terms of the ionization potentials of the metals and the electron affinities of the host materials 9,17 . They reported that the bottoms of the conduction bands of B/C and B/C/N materials were ca. 1.1 eV lower than that of graphite, which was evaluated from the results of the X-ray absorption near-edge structures (XANES) 17 . This means that the electron affinities of B/C and B/C/N materials are ca. 1.1 eV larger than that of graphite (4.6 eV). Also, Yamada reported that Na could be intercalated more efficiently into B/C materials by using electrochemical method probably because of the larger electron affinity of B/C material compared with that of graphite 10 . The present authors consider that this mechanism can also explain the intercalation of Ca into BC6.4 observed in the present study.

The larger electron affinity of B/C material resulted in the efficient Ca intercalation into the B/C material with the composition BC6.4, compared with the difficult intercalation of Ca into graphite through the solid gas reaction 20 .

Ca-Li intercalated B/C/N material

For the B/C/N host material, intercalation reactions using calcium-lithium alloys were performed using several experimental conditions. After the reaction of a B/C/N film in the Ca-Li alloy (27 Ca at. %) during 2 days at 620 K, the X-ray (00l) diffraction lines of the host structure completely disappeared, indicating that an intercalation phenomenon occurred (Supporting Information 2 represents the (00l) X-ray diffraction pattern of the sample obtained after the reaction of a B/C/N film in the Ca-Li alloy during 2 days at 620 K, compared with that of the B/C/N host structure). The (00l) diffraction lines of the new intercalation compound allow to estimate d-spacings of 0.376 nm and 0.188 nm, although the stage structure hasn't been identified yet. When the reaction time was increased to 5 days, the d-spacings slightly increased to 0.381 nm and 0.191 nm, respectively. However, the d-spacings didn't change any more after 10 days or 21 days, corresponding to the thermodynamic equilibrium. In the case of using graphite host, the intercalation of Ca-Li alloy took longer time to reach the equilibrium 13 . From the comparison of the experimental results between the two kinds of host materials, the B/C/N film reacted with the Ca-Li alloy more smoothly than the case of graphite under the same reaction condition used in the present study. This is probably because the reaction mechanism described in the section 3.3 (Ca intercalated B/C material).

The chemical composition of this new B/C/N intercalation compound was studied by ion beam analysis. Many areas of the sample were analyzed, and a representative spectrum was selected and modelled (Figure 9). Figure 9a indicates a total spectrum showing all parts of analyzed zone. In addition to the boron, carbon and nitrogen steps of the host structure, the spectrum shows the Ca step at 2745 keV and the Li one at 1705 keV. The spectrum shows a characteristic peak of the interaction between protons and oxygen corresponding to the presence of oxygen on the surface of the sample. This oxidation can be explained by the exposure of the sample to the air during its transfer into the analysis chamber of the nuclear microprobe. Since we quickly transfer the sample, oxygen cannot diffuse into the bulk material that is why only a peak is observed (whereas steps are characteristics of the elements present in the bulk material). Figure 9b indicates a high energy part in which Li is recognized. In both spectra Figure 9a and 9b, it is easy in the modelling to distinguish the surface and the bulk of the sample whose chemical composition is Ca0.67Li0.42(BC3.3N0.50). This analysis confirms the intercalation of both lithium and calcium, using the solid-liquid method in lithium-based alloys.

By using B/C film (composition: BC6.4) as the starting material for the intercalation of Ca-Li alloy, a part of the film dissolved in the alloy solution and small pieces of compounds were obtained probably because of a rapid reaction of B/C material with the alloy solution.

The Ca and Ca-Li intercalated B/C and B/C/N compounds were air and water sensitive material, which is like the case of alkali metal or Ca intercalated graphite 21 . The Ca intercalated BC6.4 film slowly decomposed in air to expand in the thickness direction. The Ca-Li intercalated B/C/N film rapidly decomposed in water to show broad X-ray diffraction pattern.

In summary, Ca and Ca-Li were intercalated into B/C and B/C/N materials in this study, while they couldn't be intercalated into graphite under the same experimental condition. The NMA is useful tool to determine the compositions not only the host B/C/N and B/C materials but also the water sensitive Ca and Ca-Li intercalated materials. The efficient intercalation of Ca and Ca-Li into the B/C and B/C/N materials reported in this study suggests the application of these intercalation phenomena to the Ca secondary batteries 22 and superconductors 13,23 as the future energy systems.

Conclusion

The B/C material having the graphite-like layered structure with the composition of BC6.4 can intercalate Ca in their layers to form the second stage compound "Ca intercalated BC6.4". The d-spacing of the intercalated layer was 0.461 nm, which is the value like that of the Ca intercalated GIC CaC6. B/C/N material having the graphite-like layered structure with the composition of BC2.6N0.55 can intercalate Ca-Li metals by using the Ca-Li liquid alloy to form the intercalation compound having the composition of Ca0.67Li0.42(BC3.3N0.50). The intercalation of Ca and Ca-Li into B/C and B/C/N host materials could be explained by considering the relationships between the ionization potentials of metals and the electron affinities of B/C and B/C/N materials. The authors also found that the NMA is one of the most accurate methods for the composition analyses of the host materials and the intercalation compounds. The efficient intercalation of Ca and Ca-Li into the B/C and B/C/N materials, which has been found in the present study, is expected toward the application to the Ca secondary batteries and the superconductors as the future energy systems.

Figure 1 .

 1 Figure 1. NMA(RBS/NRA) spectrum of the B/C/N material, compared with the simulated spectrum. Each elementary contribution to the simulation is individually indicated. Red spots: experimental result. Blue solid line: simulated result.

Figure 2 .

 2 Figure 2. X-ray powder diffraction of B/C/N material (BC2.6N0.55).

Figure 3 .

 3 Figure 3. NMA(RBS/NRA) spectrum of the B/C material, compared with the simulated spectrum. Each elementary contribution to the simulation is individually indicated. Red spots: experimental result. Blue solid line: simulated result.

Figure 4 .

 4 Figure 4. X-ray powder diffraction pattern of B/C material (BC6.4).

Figure 5 .

 5 Figure 5. XRD patterns of (a) the Ca intercalated BC6.4 film and (b) the original BC6.4 host film 12 .

Figure 6 .

 6 Figure 6. Expected structural view of the c-axis stacking of Ca intercalated BC6.4 with the second stage structure.

Figure 7 .

 7 Figure 7. (a) Cross-section image of main part of the Ca intercalated BC6.4 film observed with STEM and (b) contrast change image in the direction of c-axis. These indicate the second stage structure 12 .

Figure 8 .

 8 Figure 8. (a) Cross-section image of the Ca intercalated BC6.4 film observed with STEM and (b) contrast change image in the direction of c-axis. These indicate the first stage structure 12 .

Figure 9 .

 9 Figure 9. NMA(RBS/NRA) spectrum of the Ca-Li intercalated B/C/N material, compared with the simulated spectrum. Each elementary contribution to the simulation is individually indicated. (a) Total spectrum, (b) high energy part. Red spots: experimental result. Blue solid line: simulated result.

Table 1 .

 1 Composition of B/C/N material analyzed by elemental analysis and nuclear microprobe analysis (NMA).

	Synthetic temperature / K	Molar ratio BCl3 : CH3CN	Composition Elemental analysis	NMA
	1770	2:1	BC2.2N0.76	BC1.8N0.69
	2070	2:1	BC2.5N0.79	BC2.0N0.81
	2070	1:1	BC3.6N0.87	BC2.6N0.55

Acknowledgements

The authors are grateful to Dr. N. Emery of Institut de Chimie et des Matériaux de Paris Est for useful discussion about the stage structure of intercalation compounds. The authors also thank M. Maie and T. Furuta of Sumika Chemical Analysis Service, Ltd. for their helpful advice on the TEM and EDX observation of the intercalation compounds.

Supporting Information 1: Li, B, C, N, O and Ca cross-sections for both backscattering and nuclear reactions.

Supporting Information 2: (00l) X-ray diffraction patterns of the compound film obtained after reaction of B/C/N film in the Ca-Li alloy during 2 days at 620 K and the original B/C/N host film.