Peter T Hutchins

Olivier Leynaud

Luke A O'dell

Mark E Smith

Paul Barnes
email: p.barnes@mail.cryst.bbk.ac.uk

Paul F Mcmillan
email: p.f.mcmillan@ucl.ac.uk

Time-Resolved in situ Synchrotron X-ray Diffraction Studies of Type 1 Silicon Clathrate Formation

Keywords: silicon clathrate, Na 8 Si 46, Zintl phase, NaSi, solid state synthesis, synchrotron radiation, Xray diffraction, NMR spectroscopy, in situ studies

Silicon clathrates are unusual open-framework solids formed by tetrahedrally-bonded silicon that show remarkable electronic and thermal properties. The type I structure has a primitive cubic unit cell containing cages occupied by metal atoms to give compositions such as Na 8 Si 46 or Na 2 Ba 6 Si 46 . Although their structure and properties are well described there is little understanding of the formation mechanism. Na 8 Si 46 is typically produced by metastable thermal decomposition under vacuum conditions from NaSi, itself an unusual structure containing Si 4 4-poly-anions. In this study we used in situ synchrotron X-ray diffraction combined with rapid X-ray detection on samples taken through a controlled temperature ramp (25-500 o C at 8 o /min) under vacuum conditions (10 -4 bar), to study the clathrate formation reaction. We also carried out complementary in situ high temperature solid state 23 Na NMR experiments using a sealed tube loaded under inert gas atmosphere conditions. We find no evidence for an intermediate amorphous phase during clathrate formation. Instead we observe an unexpectedly high degree of structural coherency between the Na 8 Si 46 clathrate and its NaSi precursor, evidenced by a smooth passage of several X-ray reflections from one structure into the other. The results indicate the possibility of an unusual, epitaxial-like, growth of the clathrate phase as Na atoms are removed from the NaSi precursor into the vacuum.

Introduction

Semiconductor clathrates, based on tetrahedrally-bonded networks of elements in groups 13-15 of the periodic table, form a large family of unusual open-framework structures that exhibit remarkable and potentially useful electronic and thermal properties. [1][2][3][4][5][6][7][8][9][10][11][12][13][START_REF] Shevelkov | Structure & Bonding[END_REF][START_REF] Horie | [END_REF] The framework composed from sp 3 bonded atoms is intrinsically semiconducting. However the structures usually contain electropositive metal atoms located within the clathrate cages that inject electrons into the conduction band to produce metallic or narrow-gap semiconducting phases. The result is a wide range of materials with electronic properties ranging from metallic to wide-gap-semiconducting, depending on the cage and framework site occupancy.

In addition to the electronic behavior, "rattling" vibrations of metal guest atoms affect the phonon propagation properties resulting in lowered thermal conductivity and potentially useful thermoelectric properties. Sharp peaks near the Fermi level in the electronic density of states result in large Seebeck coefficients and also superconductivity for Ba-containing members. 3,4,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] Two main structural types were described during the initial studies of Si and Ge clathrate materials. [1][2][3][4][5][6][7][8][9] The type I clathrate has a primitive cubic structure (Pm3n: a o ~ 10.2 Å) based on dodecahedral [5 12 ] and tetrakaidecahedral [5 12 6 2 ] cages that are occupied by metal guest atoms to produce metallic Na 8 Si 46 whose formation is studied here. Studies on Ge and Sn clathrates gave rise to narrow gap semiconducting materials with compositions like K 8 Ge 44 or Rb 8 Sn 44 , where the metal oxidation is compensated by formation of vacancies in the clathrate framework. Compound clathrates such as Sr 8 Ga 16 Ge 30 have fully occupied frameworks and achieve charge balance by introduction of group 13 elements. Metal-deficient clathrates such as K 7 Si 46 are also known. It was recently shown that molecular H 2 can be incorporated in the clathrate cage sites to form materials such as Na 8-x (H 2 ) x Si 46 . 31 In addition to the type I structure, type II clathrates can also be formed. These have an fcc structure containing 136 framework (T) atoms within the cell (a o ~14.6 Å), with 16 "small" ( [5 12 ]) and 8 "large" ([5 12 6 4 ] cages that are completely or partially filled to yield clathrates such as Na x Si 136 (x = 0-24) or Cs 8 Na 16 Si 136 . Examples of further clathrates with a hexagonal structure have now also been described. 10,13,[START_REF] Shevelkov | Structure & Bonding[END_REF] The structure and chemistry of these materials is compatible with existing semiconductor technology and it is essential to understand and control their synthesis in bulk and thin film Growth of the NaSi precursor on Si has now been demonstrated, leading to the possibility of thin film synthesis. 33 In this study we have used in situ synchrotron X-ray diffraction techniques, combined with rapid collection of the full pattern obtained during temperature ramp and vacuum conditions, to investigate the formation of Na 8 Si 46 clathrate from NaSi. We have also carried out 23 Na solid state NMR experiments to study the NaSi phase at high temperatures immediately preceding the clathrate formation reaction. The results provide a unique view of the clathrate formation process and suggest an unusual epitaxial-like relationship between the NaSi phase at high temperature, as it loses its Na component into the vapor phase, and the Na 8 Si 46 clathrate that grows at the sample surface.

Experiment and Methods Section

The synthesis of clathrate phases, including Na 8 Si 46 as well as type II Na x Si 136 (x = 4-24) materials, typically involves a metastable thermal decomposition reaction under dynamic vacuum conditions starting with the Zintl compound NaSi: The reactant and product structures have very different architectures and it has therefore been generally assumed that nucleation and growth of the clathrate phase proceeds heterogeneously, perhaps via an amorphous Na x Si layer formed at the Zintl phase surface as Na atoms are removed into the vacuum. Here we have exploited recently-developed in situ synchrotron X-ray diffraction techniques to obtain time-resolved structural data during the course of clathrate synthesis reaction. In earlier work of this kind, where tailor-made environmental cells were necessary to deliver highly specialized conditions to the sample, in situ data collection was more conveniently carried out by exploiting the adaptability of either white beam energy-dispersive X-ray diffraction 34 or neutron diffraction 35 techniques.

However similar capabilities can now be achieved with angle-scanning X-ray diffractometers using specially designed capillary-based environmental cells and rapid detector systems that can deliver time-resolved X-ray diffraction data of sufficient time and angular resolution to permit meaningful dynamic structural refinement. The high-vacuum and controlled hightemperature in situ conditions required for following the clathrate formation from NaSi were achieved here by designed adaptation of a capillary-based in situ environmental reaction cell. 36 The resulting combination offered a unique opportunity to study the clathrate formation mechanism directly.

The starting material, NaSi, was prepared from mixtures of the elements (Si, 99.999%; Na, 99.95%) in a dry box. 15 mol% excess Na was added to counter evaporation loss during synthesis. The mixture was placed in a Ta crucible and heated in a steel autoclave at 600 °C for 24 hours. In situ time-resolved X-ray diffraction experiments were carried out at station 6.2 37 of the synchrotron radiation source (SRS) at Daresbury, UK using an incident beam energy of 8.856 keV ( = 1.42λ Å). The RAPID2 38 position-sensitive detector enabled medium-high angular resolution data (Δ(2θ) ~ 0.06°) to be collected on a timescale of a few seconds at each temperature using the high-T (high temperature) in situ cell. For this study the environmental cell was configured to provide controlled entry of the air-/moisture-sensitive samples into the capillary which was also coupled to a vacuum (10 -4 mbar) system. During data collection the sample was heated at 8°C/min up to 500 o C after which the temperature was held constant. The computational package FullProf/WinPLOTR program 39,[START_REF] Roisnel | Proc.7th Europ. Powder Diffraction Conf. (EPDIC[END_REF] was used for Le Bail [START_REF] Bail | [END_REF] and Rietveld 42 unit cell/structural refinements which were applied in interactive mode across the whole time/temperature-resolved diffraction data set using the multi-phase refinement option assigned to the NaSi and Na 8 Si 46 clathrate structures. The structures reported by Witte et al. 43 and Ramachandran et al. 9 were used as starting points for refinements of the two phases. The multi-phase analysis option permitted us to examine whether the synthesis proceeded via a continuous route or else involved sharp transitions between two or more structure types. The obtained R Bragg values were typically around 10-25% but increased to 40% or more for temperatures where one phase was much less-well defined. The X-ray diffraction patterns of both structures show unusual and remarkable convergence between several of the peak positions, as the temperature is increased. This result suggests some structural coherency exists between the two apparently unrelated phases. We have discussed possible models for this behavior below. However, the in situ nature of the experiment, with both NaSi and clathrate phases present together and evolving during the high-T synthesis study, precluded the detailed level of structural refinement that is achieved during normal crystallographic structure determination studies on pure phases under constant conditions. In this case the in situ data are complicated yet further by peaks shifting rapidly due to the very high thermal expansion of the NaSi phase. However, the results are within normal bounds for multiphase in situ data refinement across a continuous reaction sequence and, provided fine structural details are not being sought, they are easily of sufficient quality to provide thermal expansion data or to identify major features such as a phase transformation occurring during synthesis.

For high-T NMR studies we developed a specialized probe [START_REF] Hutchins | PhD thesis[END_REF][START_REF] O'dell | [END_REF] based on an L-shaped SiO 2 glass sample holder that was loaded and sealed in the inert (Ar) atmosphere of the dry-box.

Static 23 Na NMR spectra were recorded at 7.05 T: the chemical shift reference was 1M aqueous NaCl (79.386 MHz). Heating was achieved via a Ni/Cr coil wound with its axis parallel to the magnetic field. Temperature calibration to within ±5°C was achieved beforehand using a thermocouple embedded in MgO powder placed within the RF coil. After adjusting the power, one hour was allowed for the sample temperature to equilibrate. Single pulse excitation was used with a 3 s pulse width (approximately λ0° tip angle). A 1s recycle delay was used to achieve an acceptable signal to noise ratio in the experiment (~30 minutes).

Results and Discussion

Single Temperature Ramp Experiments

A typical in situ dataset, obtained during high-T treatment of NaSi and resulting in production of Na 8 Si 46 clathrate, is shown in Figure 1. The data were recorded over 512 detector wires and interpolated to 4096 channels over a 2θ-range of 5-65° with absolute 2θ positions calibrated against the Si powder standard. The in situ conditions were set to generate a temperature ramp of 8°C.min -1 from room temperature to the target 500°C under a vacuum of 10 -4 bar. Diffraction data were collected every 30 seconds for the first 3 hours, and then every minute thereafter. Figure 1a Figs. 1b and1c present expanded views of important regions of the data that demonstrate the appearance of clathrate peaks after 59-60 minutes, just as the target 500°C is reached. The most striking aspect of the data during the initial heating phase is the remarkable shift with temperature of the NaSi peaks to lower 2θ, during the initial period before the onset of the reaction, indicating a very large thermal expansion coefficient (4.54x10 -5 °C-1 ) for the Nasilicide phase, which is comparable with those observed for ionic conductors. Another main feature is the lack of any reduction in crystalline peak intensities and the absence of amorphous scattering in the range over which clathrate formation takes place. This observation indicates that the clathrate synthesis proceeds smoothly from the Zintl phase. In fact the evidence is that the clathrate formation occurs continuously and with a structural relationship to the Zintl phase; that is, several reflections that are indexed as part of the NaSi pattern at room temperature appear to become attributable to the Si-clathrate phase; examples of such peaks with apparent "dual ownership" are listed in Table 1.

The variations in unit cell parameters for the NaSi and Si-clathrate phases during the vacuum heating and synthesis process were studied using Le Bail and Rietveld approaches to refine the powder X-ray diffraction data. All diffraction patterns were first fitted to the NaSi and Na 8 Si 46 clathrate phases using le Bail refinement and, after inspection, the le Bail output was then used to provide initial starting cell parameters for multi-phase Rietveld refinement for the two structures. Figure 2 shows an example of this procedure carried out for the end point of the synthesis at 500°C when the composition is predominantly of a clathrate nature. The structural/refinement data, for three representative stages of the overall synthesis process.

Figure 3 charts the overall variations in unit cell volume over the synthesis; variations in other thermal/structural parameters are also illustrated in the Supplementary Information. As already noted, the NaSi phase exhibits unusually large thermal expansion, up to the point of onset of clathrate formation (~60 min., 500°C). After this there is an anomalous reduction in the unit cell volume; this point also coincides with a drop in vacuum observed in the system. Although these observations do not provide absolute proof, together they do indicate that Na is lost in the form of vapor from the structure from around and after the point of clathrate formation, as expected from reaction (1), Sodium loss from the NaSi structure must be accompanied by reduction of Na + to Na o species and Si-Si bond formation. [START_REF] Cabrera | [END_REF][47][START_REF] Kauzlarich | Chemistry, Structure and Bonding of Zintl Phases and Ions[END_REF] It is likely that the cages in the clathrate structure are formed around the remaining Na atoms that then act as templates for the microporous crystalline solid.

Comparison of the evolution of selected features of the NaSi silicide and Na 8 Si 46 clathrate diffraction patterns provides new clues as to the nature of the solid state reaction process. The NaSi structure contains isolated Si 4- 4 tetrahedra separated by Na + ions, in contrast with the Na 8 Si 46 clathrate structure with its open-framework cages. The respective space groups are monoclinic C2/c (NaSi) and cubic Pm3n (type 1 clathrate). The two compounds have different stoichiometries and so it is not possible to identify a true crystallographic group/subgroup relationship between the two structures. In Figure 4a,b we compare the overall structural features of the two phases. We first consider the NaSi (-202) planes and clathrate (200) planes that have already been linked because of their similar lattice spacing and apparent propagation of one into the other as the synthesis reaction proceeds (Figure 1, Table 1). The -202 planes for NaSi pass through Na + sites that then become the centers of pentagonal dodecahedral and tetrakaidecahedral cage sites occupied by Na atoms in the clathrate structure. Figure 4c shows that this is both feasible and likely: the occupation of the NaSi (-202) planes by Na + cations is such that they effectively constitute "sodium sheets" providing an easy transfer route to the new composition and cage environment, following Na loss to the vacuum from the initial Zintl phase structure. The results of Rietveld refinements of the X-ray data support this idea in that, as the temperature is raised, large excursions of the Na + cations around their starting positions occur, accompanied by flattening and elongation of the Si 4 4-tetrahedra. This trend can also be perceived from the change in behavior of Na thermal parameters after 80 min with the temperature at 500°C (see Supporting Information).

However, due to the highly correlated nature of thermal/occupancy parameters from X-ray refinement, we sought independent confirmation from high-T 23 Na NMR spectroscopy.

The in situ high-T NMR studies were therefore undertaken to further investigate the response of Na in the NaSi structure to increasing temperature. The spectra were obtained using a specially designed probe that permitted examination of NaSi samples in situ at high temperature, inside a pre-sealed vacuum tube; useful data could be obtained up to T = 400 o C.

At room temperature, the static 23 Na signal from NaSi occurs at ~0 ppm consistent with ionic Na + species. The broad asymmetric peak shape occurs due to quadrupolar effects associated with the asymmetry of the local electric field gradient surrounding the spin I=3/2 nucleus. [START_REF] Smith | [END_REF][50][51] The slight baseline distortion to the left of the main peak is due to the single pulse experiment that caused some signal loss at the start of the free induction decay; attempts were made to carry out spin echo experiments but there was too little signal to yield useful data. Above T ~ 250°C, a considerable reduction in peak width along with an increase in peak symmetry occurs (Figure 5). This observation is consistent with a time-averaged increase in local site symmetry around the Na + ions in the NaSi structure at high temperature, and perhaps even the onset of Na + mobility between sites indicating possible ionic conduction behavior. No further change in the peak shape or intensity was observed following heating at 400°C for up to 10 hours, until the NMR signal was finally lost due to degradation of the glass tube and the Cu coil, just as the NaSi sample began to undergo significant Na loss and form clathrate material.

The combined data from the in situ X-ray diffraction and 23 interface. This view is supported by the cell expansion data (Figure 3) which show that in the early stages of clathrate formation (e.g. after 10 minutes heating at 500°C) the unit cell volume of the clathrate is anomalously low (by ~0.14 %) compared with even the room temperature value, but it then rises to the constant value expected for bulk clathrate material as the formation reaction progresses. This behavior is consistent with the quasi-epitaxial growth scenario suggested above. As new clathrate material forms at the Zintl phase surface it becomes structurally coherent with it and is constrained by the unit cell parameters of the substrate, whereas material produced later in the reaction grows out and away from the NaSi surface and therefore adopts the normal bulk clathrate unit cell value. This effect could also be associated with a slight compositional change in the type I clathrate as it forms. Böhme et al. 52 have recently reported formation of a Na-deficient variety of Na

Thermal cycling experiments

In this case temperature ramp-cycling experiments were carried out to further investigate the high temperature behavior of NaSi and the clathrate formation process. In these experiments repeated heating and cooling cycles were introduced into the synthesis time-temperature profile such that the end-temperature of each successive cycle progressively approached a final target temperature which was set at the same 500°C; the resultant temperature profile resembles a "sawtooth" shape (Figure 6). These experiments were carried out in a closed tube environment placed under vacuum before the cycling stage rather than under dynamic pumping conditions, so that Na vapor exsolved from the NaSi remained inside the sample chamber and could re-react with the solid phase during the cooling part of the cycle.

However, after several cycles to progressively higher T values, some Na reacted with the glass walls of the container and was removed from the system. The X-ray patterns remain dominated by NaSi throughout, even to the highest temperatures examined (500 o C), indicating the high thermal stability of the Zintl phase in a Na-rich atmosphere. The repeated cycles of large thermal expansion/contraction of the NaSi phase are clearly observed in the figure. However, a new diffraction peak begins to emerge between 28-28.5 o 2θ following several temperature cycles (Figure 6). Because of the high expansions involved and correlations between the silicide and clathrate phases, it is difficult to unambiguously identify this peak with the formation of Na 8 Si 46 , or indeed to any other clathrate phase or polymorph of elemental Si (Si-I, Si-III, Si-IV etc) that might form metastably under these conditions.

Throughout the ramp cycles the peak positions match the high thermal expansion behavior of the NaSi substrate, indicating an intimate structural relationship between the two. In the earlier cycles, the new peak disappears during the highest temperature part of the ramp, when it merges with a NaSi reflection, and re-appears during the lower T part of the ramp, giving an appearance like that of Barchan dunes marching across a desert landscape. After 6 cycles (when the top temperature reaches 450 o C or higher) the new peak becomes a permanent feature of the pattern. The same behavior is mirrored by a second new peak appearing near 33 o 2θ (Figure 6). During this period, the NaSi reflections at 26.7 o and 28.1 o 2θ undergo weakening, first reversibly during the earlier cycles then permanently after further cycles, which could correspond to the timing of the perceived Na loss from the Zintl phase. We do not yet have a structural interpretation for this new diffraction feature but suggest that, apart from the probability of having clathrate origins, it could correspond to a Na-deficient NaSi

Zintl phase or to a new type of ordered Na x Si (x < 1) structure formed at the surface; many examples of crystalline Zintl compounds with partly polymerized sheet or network polyanions are known, 50,51 although none have yet been described in the Na-Si system.

Regardless of the complete explanation, the unusual appearance of these cyclic ramps serves to highlight the thermal complexity of these systems, the important role played by Na loss and possible templating actions from the NaSi precursor phase during the earlier stages of the clathrate-forming reaction.

Conclusions

The results reveal a remarkable formation scenario for Na (the 400 cannot be accurately assigned so all three potential candidates are given)

Captions for Figures

  provides an overall view of the diffraction patterns showing that most changes occurred during the first 75 minutes, i.e., within the first 10 displayed patterns (corresponding to a full set of 150 collected patterns), during which time the temperature had reached the 500°C target plateau. During this period the NaSi pattern exhibited substantial shifts in peak positions and changes in relative intensities due to large thermal expansion and loss of the Na-component at higher T, followed by onset of peaks due to Na 8 Si 46 clathrate formation. Once the clathrate phase had formed and become established within the sample, little further change occurred until the sample capillary was destroyed, following attack by the evolved sodium vapor, and the diffraction pattern was then lost.

  Na NMR studies indicate that clathrate formation is linked to thermally-induced Na + motions occurring within the expanded NaSi lattice, leading to loss of Na + ions that undergo reduction to form Na o species in the vapor phase which is pumped away during the vacuum experiment. The Na +  Na o reduction is accompanied by formation of new Si-Si bonds between the highly distorted Si 4 4tetrahedra of the Zintl phase structure. The data and analysis indicate this process can occur directly, linking the two apparently unrelated structures and without invoking the formation of any intermediate amorphous material. A notable feature is the continuity of X-ray diffraction features between the NaSi and clathrate phases which indicates some type of growth process in which there is structural continuity between elements of both phases at the NaSi/Na 8 Si 46

  Figure 1. (a) Powder X-ray in situ diffraction patterns obtained during the heating of NaSi in vacuum (10 -4 bar) to produce Na 8 Si 46 clathrate. The diagram shows every 15 th 30 s pattern in a stacked plot, so the spacing between the displayed patterns represents 7.5 minutes. The temperature was ramped from room temperature up to 500 o C at 8°C/min after which it was held constant. The small data gap, at just over halfway, is due to a necessary interruption of the X-ray beam while the vacuum system liquid nitrogen was being topped up. The loss of diffraction intensity with the last four patterns was due to the destruction of the sample capillary following attack by Na vapor released during the synthesis reaction. It is clear that all the significant structural changes occur during the first 10 patterns which corresponds to a time period of 75 minutes and a top temperature of 500 o C. (b,c) More detailed views of the time-resolved diffraction data collected within the regions indicated by the two boxes shown in Figure 1a (here, every 8 th 30 s pattern is shown, giving a spacing of 4 minutes between the displayed patterns; the 2θ-angle ranges are: (a) 12-26º; (b): 24-38º). The continuous shifting of peaks, from NaSi precursor to Si-clathrate product, is very clear.

Figure 2 .

 2 Figure 2. A "Rietveld" diffraction plot (Intensity in arbitrary units versus 2θ (°)) from the sample at 500 o C after 150 minutes, this being the end point of the synthesis. The data are fitted as a two-phase model to the NaSi and Si-clathrate structures: points = Y obs = observed diffraction data; upper line = Y calc = calculated diffraction data from the model; lower line = Y obs -Y calc = difference between these two; vertical bars are the predicted positions of the Bragg diffraction peaks (upper = clathrate, lower = NaSi peaks) showing significant peak overlap with the two structures. Further examples of Rietveld plots, together with associated refinement/structural data, can be found in the Supplementary Information.

Figure 3 .

 3 Figure 3. In situ thermal expansion data, over the ranges of existence of the NaSi and Siclathrate phases, during the clathrate synthesis: The unit cell volumes are shown against time or temperature using the displayed temperature ramp profile and probabilistic error bars (as derived from the obtained unit cell refinement) are given for representative points on both data sets. The NaSi exhibits unusually large expansion up to the synthesis point (near 500 o C) after which it drops to lower values; by comparison, the Si-clathrate cell increases slowly

Figure 4 .

 4 Figure 4. Structural graphics for the NaSi and Si-clathrate phases obtained using the CCDC (Cambridge Crystallographic Data Centre) Mercury Structure Visualization Program, with standard slice/ packing/depth parameters; some atoms have been interactively removed at the fringes so as to aid viewing: (a) View of the NaSi structure down the [-202] direction such that one is looking down onto (-202) planes which are related, diffraction-wise, to the clathrate (200) planes indicated in Figure 4b. (b) View of the Si-clathrate (Na 8 Si 46 ) structure such that the (200) planes (indicated) are seen "sideways on". (c) An alternative "sideways" view (to (a)) of the NaSi structure (looking down the [C2/c] direction) which clearly shows the -202 plane effectively cutting through the "sheet" of Nacations.

Figure 5 :

 5 Figure 5: 23 Na NMR spectra obtained during heating of the NaSi phase from ambient to 400°C as for the synthesis of the Si-clathrate phase. The spectra are stacked and arbitrarily separated by temperature for comparison.

Figure 6 :

 6 Figure 6:In situ diffraction patterns stacked upwards, covering ca 9 cycles of heating/cooling ramps, applied to the NaSi pre-curser phase as would be used in a Si-clathrate synthesis. The temperature "sawtooth" profile is indicated on the left sideμ each "tooth" represents a separate ramp from ambient to a target temperature, which is initially 300ºC but then increases each cycle by 25ºC until the full synthesis 500ºC maximum is reached, i.e. the sawteeth size progressively increases (20→300→20→325→20→350→20→375→….500ºC).Each pattern represents 59 seconds and every 4 th pattern is shown; the diffraction intensity scale is arbitrary. The large arcs described by each diffraction peak reflect the large thermal expansions/contractions of NaSi during the thermal cycling. The new diffraction peaks (e.g. between 28º-29º and 32º-33.5º) begin to be observed above ~300 o C but only become permanent after ~6 cycles to T>425 o C, after which they track more closely the NaSi expansions/contractions.

  Figures

  Figure 4aFigure4b

  Figure 4c

  Fd 3 m form to develop future applications. However, although much is known about their structures and physical properties, there is little understanding of the clathrate formation mechanisms.The Si and Ge materials are usually prepared by partial thermal decomposition of Zintl compounds like NaSi under vacuum conditions. Clathrates such as Na 8 Si 46 (type I) and Na x Si 136 (type II: x = 4-24) are produced with varying target temperature and ramp rate, vacuum conditions etc. The clathrate compounds are metastable under the synthesis conditions, with respect to diamond-structured Si at ambient pressure, but it has been suggested that slightly negative pressures achieved under tensile strains, that are readily achieved during epitaxy on Si surfaces, could result in stabilization of the clathrate phase.32

  8-x Si 46 clathrate with x = 1.8, produced by reaction between NaSi and HCl, with a unit cell volume of 1060.6 Å 3 which is significantly smaller than that obtained with the clathrate produced here. However, experimental and theoretical work on type II Na x Si 136 clathrates has shown that the unit cell volume remains virtually unchanged as the Na content is varied.8,9,53

Table 1 .

 1 8 Si 46 clathrate under high temperature -high vacuum conditions from the Zintl NaSi phase, suggesting an unusual kind of epitaxial relationship between lattice planes of the two apparently dissimilar structures following indications of sudden Na loss and high temperature structural distortion of the Zintl phase precursor. They help us understand why the Type I Na 8 Si 46 clathrate phase is produced under relatively low vacuum conditions whereas Type II Na 24-x Si 136 materials are formed with greater Na loss under higher vacuum or rapid heating conditions. The in situ X-ray diffraction data and uncovering of the formation mechanism will help guide further investigations towards producing clathrate phases in thin film form on semiconductor substrates33 and to design new clathrates from Zintl phase precursors, including incorporation of H 2 into the clathrate cage structures.31 (52) Böhme, B.; Guloy, A.; Tang, Z.; Schnelle, W.; Burkhardt, U.; Baitinger, M.; Grin, Y. J. Related reflections between the two structures, starting as NaSi phase reflections (left 2 columns) and propagating eventually into Si-clathrate reflections (right 2 columns).

	Amer. Chem. Soc. 2007, 129, 5348.
	(53) Beekman, M.; Nenghabi, E. N.; Biswas, K.; Myles, C. W.; Baitinger, M.; Grin, Y.;
	Nolas, G. S. Inorg. Chem. 2010, 49, 5338.
	Tables
	NaSi		Na 8 Si 46
	hkl	2θ (°)	hkl	2θ (°)
	-202	16.0996	200	15.7358
	-221	28.1222	222	27.4309
	-314	31.9186
	-404	32.0165	400	31.7786
	221	32.0175

Acknowledgements

This work, including PhD and PDRA support to PTH, was enabled by the EPSRC Portfolio grant EP/D504782 to PFM and PB in collaboration with CRA Catlow, and an EPSRC Senior Research Fellowship GR/T00757 to PFM. LAO thanks EPSRC for funding and MES thanks EPSRC and the University of Warwick for partial funding of NMR equipment. J. Gryko is thanked for invaluable advice on clathrate synthesis and the Daresbury SRS staff are praised for their considerable help with the in situ synchrotron experiments.

Supplementary Information gives similar Rietveld plots, together with the associated

Supporting Information

Additional data are presented in this section, including further Rietveld diffraction refinement plots, structural data and variations in certain structural/thermal parameters during the main stages of the synthesis reaction. This information is available free of charge via the Internet at http://pubs.acs.org/.

Figure 5

Rapid in situ synchrotron X-ray diffraction data suggest an unusual epitaxial synthesis of type-I Na 8 Si 46 clathrate: the precursor NaSi, on losing Na, provides a template for clathrate formation. Cyclic diffraction-heating data give a "barchan dune" appearance resulting from the large thermal expansion of the Zintl and derivative phases.


R Quesada Cabrera

A Sella

E Bailey

O Leynaud

P F Mcmillan
email: p.f.mcmillan@ucl.ac.uk

High-Pressure Synthesis and Behaviour of Sodium Orthonitrate Na 3 NO 4

Keywords: Sodium orthonitrate, sodium oxide, sodium nitrate, high-pressure synthesis, diamond anvil cell, pressure-induced amorphization

Sodium orthonitrate (Na 3 NO 4 ) can be prepared rapidly and in high yield from NaNO 3 and Na 2 O at high pressure in a multianvil press. The acceleration is atributed to a substantially negative molar volume of reaction, and provides a much faster route compared to the synthesis at ambient pressure. The high-pressure behaviour of sodium orthonitrate has been studied in a diamond anvil cell up to 64 GPa. At the upper end of the pressure ranges we see evidence for incipient pressure-induced amorphization. Similar processes are also discussed for Na 2 O and NaNO 3 .

Introduction

Structures based on tetrahedrally-bonded oxoanions form a wide range of important minerals and materials including sulphates, phosphates, and especially the orthosilicates ,containing isolated SiO 4 4-, groups that are major components of the Earth's upper mantle. Such silicate anions are well known to polymerize to form chains, sheets, and threedimensional network structures. The high-pressure behaviour of these tetrahedrally coordinated species has been studied extensively because of density-driven transitions to higher coordinated structures that are important for mantle mineralogy. For example, (Mg, Fe) 2 SiO 4 olivines transform to spinel structures containing silicon in octahedral coordination and this marks the passage between the upper and lower mantle within the Earth. Octahedrally coordinated silicon also occurs in other high-pressure mantle minerals including silicate perovskite, ilmenite, and garnet structures and SiO 2 polymorph stishovite. Unusual five-fold coordinated silicate species have been identified in glasses prepared at high pressure and these play an important role in the densification and viscous flow of the molten materials [START_REF] Stebbins | Structure, Dynamics and Properties of Silicate Melts[END_REF]. Compression of (Mg,Fe) 2 SiO 4 crystals and glasses results in pressure-induced amorphization and formation of such highly-coordinated species and linkages between the orthosilicate anions.

It is notable that tetrahedral oxoanion species are generally formed with atoms of the second or higher rows of the periodic table (Si, P, S, Cl, Ge, As etc). By contrast, the first row elements tend to form trigonal species (BO 3 3-, CO 3 2-, NO 3 -), behaviour attributed to their small size and to somewhat nebulous ideas such as octet expansion related to orbital energies. However, a tetrahedral oxoanion chemistry does occur for boron, either copolymerized with other species or as isolated B(OH) 4 -anions (e.g., LiB(OH) 4 ). A longstanding question in solid state chemistry and geochemistry has therefore been whether structures based on tetrahedral NO 4 3-or CO 4 4-units can be prepared at all, and the extent of their thermodynamic or indeed kinetic stability. The occurrence of tetrahedral orthocarbonate species would have implications for carbon storage within mineral or melt species within the Earth.

Ab initio cluster calculations have indicated that tetrahedral units based on light element species should be thermodynamically stable with respect to decomposition to simpler ions [2]. For carbon, unambiguous proof of such structures has remained elusive. A tetrahedrally-bonded structure analogous to the SiO 2 polymorphs, was observed by high-P,T synthesis from CO 2 [3]. Other high-P,T studies on CO 2 have indicated formation of glassy "carbonia" that could contain even higher-coordinated carbonate species [4]. Recent experiments found that MCO 3 (M= Sr, Ca) can be transformed into polymeric chain structures containing linked CO 4 tetrahedra at high pressure [5]. Ionic orthocarbonate species containing CO 4 4-groups have not been synthesized yet. Nonetheless, theoretical calculations [6] indicate that a very low energy barrier hinders the orthocarbonate structure from being a global minimum and molar volume considerations suggest the synthesis via high-pressure conditions, due to the smaller volume of the orthocarbonate structure as compared to the carbonate and oxide precursors mixture.

For nitrogen on the other hand, the first solid-state orthonitrate was synthesised by Jansen [7], who obtained sodium orthonitrate Na 3 NO 4 containing isolated NO 4 3-units, by reaction of Na 2 O with NaNO 3 at high temperature over a period of months (Fig. 1). This compound is therefore an attractive testing ground to explore the stability of high coordinate structures under extreme conditions.

In the present study, we have synthesized Na 3 NO 4 via high-pressure conditions and investigated the high-pressure behaviour of Na 3 NO 4 using synchrotron X-ray diffraction and Raman spectroscopy in the diamond anvil cell (DAC).

Experimental

The ambient pressure synthesis of Na 3 NO 4 was conducted by reaction between Na 2 O and NaNO 3 as described in ref. [7]. The reactants (Na 2 O 80%, Aldrich, main impurity Na 2 O 2 ; NaNO 3 99.9%, Aldrich) were ground together in an approximately 3:1 ratio under dry box conditions (<10 ppm O 2 /H 2 O, N 2 atmosphere) and loaded into a silver capsule that was crimped shut then transferred to a glass tube and sealed under vacuum before heating in a furnace at 380 ºC (10 ˚C h -1 ) for periods between 14-90 days.

For in situ high-pressure Raman and synchrotron XRD experiments, Na 3 NO 4 samples were loaded into a screw-driven DAC without any pressure-transmitting medium under N 2 or Ar glove box conditions (H 2 O/O 2 < 10 ppm). Diamond culet diameters were 300-150 μm. Preindented rhenium gaskets were drilled with 80-μm diameter holes. Ruby chips were added to estimate the pressure inside the sample chamber [8].

The home-built Raman system is based on Kaiser supernotch filters, an Acton spectrograph and a LN 2 cooled back-thinned CCD detector [Soignard, Chem Mater]. An Ar + laser (514.5 nm, ~1 mW entering the cell) was focused onto the sample using a 50x Mitutoyo objective and Raman scattering was collected using backscattering geometry. Angle-dispersive X-ray diffraction data were obtained at station 9.5 HPHT, Daresbury SRS using = 0.444 Å. Two-dimensional X-ray patterns were obtained and then integrated around the diffraction rings and converted into 1D plots using FIT2D software [9]. The Xray beam was collimated and focused to 30 m inside the cell using a Laue optical system [10]. Additional X-ray diffraction data were obtained at ESRF BM01A (Swiss-Norwegian beam Lines) using angle-dispersive techniques ( = 0.7 Å).

Results and Discussion

High-Pressure Synthesis of Na 3 NO 4 from Na 2 O + NaNO 3 : characterisation by X-ray diffraction and Raman spectroscopy

The synthesis of Na 3 NO 4 at room pressure allows the detection of Na 3 NO 4 traces after 7-14 days [7]. According to these authors, a single crystal can be obtained only after 240 days. After several attempts, we obtained nearly pure Na 3 NO 4 samples only after 90 days (Fig. 2). The main impurity was excess Na 2 O, but traces of Na 2 O 2 were sometimes detected by Raman spectroscopy. Runs carried out on samples containing Na 2 O and NaNO 3 impurities allowed the X-ray patterns and Raman spectra of this antifluorite-structured compound to be obtained for the first time at high pressure. The precursors mixture (3:1 molar ratio, ~5 mm 3 ) was sealed inside a Pt capsule in the glove box and pressurized up to 4 GPa in a 1,000-ton Walker-type multianvil press (Fig. 3). W/Re thermocouples were used for temperature measurement and control. Then, the mixture was heated up to 500 ºC (10 ˚C h -1 ) and held for 50 hours before quenching by turning off the furnace power. Fig. 3. Multianvil assembly. The capsule containing the precursors mixture was sealed by welding at one end, with a combination of Pt disc and BN plug at the other. This allowed easy loading in the glove box. The Pt disc had a slightly larger diameter than the capsule and was bowed slightly before assembly. Careful assembly produced gas tight sample environments without the need for welding at both ends. This greatly facilitates loading of temperature and atmosphere sensitive samples.

Simple molar volume considerations for the reaction:

Na 2 O + NaNO 3  Na 3 NO 4 (Na 3 NO 4 (V m = 57.20 cm 3 mol -1 ), Na 2 O (V m = 27.31 cm 3 mol -1 and NaNO 3 (V m = 36.95 cm 3 mol -1 ) suggest a significantly negative value volume of reaction (ΔV = 7.06) associated with the reaction. Hence the equilibrium is strongly shifted in favour of orthonitrate at high pressure. This is also reflected in the rate of the reactionpeaks associated with Na 3 NO 4 could be seen within 2 days at 500˚C (Fig. 2). Thus the application of pressure provides a useful route to the orthonitrate material.

The presence of Na 3 NO 4 following syntheses at ambient and high pressure was first observed by Raman spectroscopy (Fig. 4). The Raman spectrum of Na 3 NO 4 at room conditions is dominated by a strong peak at 843 cm -1 (υ 1 ) due to symmetric NO 4

3stretching vibrations. The antisymmetric NO stretching bands are observed at ~1000 cm -1 (υ 3 ). Symmetric and antisymmetric ONO bending modes appear between 650-670 cm -1 (υ 4 ) and at 540 cm -1 (υ 2 ), respectively [7]. The Raman studies also demonstrate the presence of Na 2 O and NaNO 3 remaining within the samples. The band at 240 cm -1 corresponds to the triply degenerate stretching mode of Na 2 O, whereas the band at 1058 cm -1 along with a shoulder at 1067 cm -1 are due to the dominant NO 3 stretching vibrations of NaNO 3 (Fig. 4).

Raman spectroscopy at high pressure

The high-pressure behaviour of Na 3 NO 4 was monitored by Raman spectroscopy up to 61 GPa (Fig. 5). Using our microbeam technique (3-4 m) we could obtain spectra of Na 3 NO 4 alone from regions where Na 2 O or NaNO 3 grains were absent. Little change was observed in the Na 3 NO 4 spectrum throughout the pressure range studied, indicating that the orthonitrate structure is remarkably resistant to compression. The vibrational frequencies plotted versus pressure show that a new band is clearly observed among the υ 4 bending modes above 21 GPa (Fig. 5), which indicates minor structural changes occurring within this pressure range. Compression above 40 GPa results in the appearance of additional weak spectral features in the region between 300-450 cm -1 . However, all these spectral changes are fully reversible upon decompression at room temperature.

Fig. 5 -Raman spectra of Na 3 NO 4 during compression at room temperature. We typically avoided those regions contaminated with any precursor in this study, but illustrate in some spectra the presence of Na 2 O and NaNO 3 in the sample (symbols).

Fig. 6 -Raman shifts of Na 3 NO 4 during compression (full circles) and decompression (empty circles) runs. All pressure-induced changes were found to be fully reversible.

Synchrotron X-ray diffraction at high pressure

The X-ray diffraction experiments sampled a much larger volume of the material within the DAC compared with the microbeam Raman results described above. The X-ray beam could only be collimated to 30 m and the diameter of the DAC gasket hole was ~80 m, so features from Na 2 O and NaNO 3 were present along with the Na 3 NO 4 reflections in the patterns and these had to be taken into account during the analysis of the data. The diffraction patterns are dominated by Na 2 O reflections. The absence of a pressuretransmitting medium meant that compression was non-hydrostatic and peak broadening for all phases was expected to occur arising from pressure gradients and internal strains in the sample. Selected X-ray diffraction patterns of the reaction components upon compression are shown in Fig. 7.

There are no significant changes between the patterns recorded at 7 and 10 GPa, except for an intensity increase of the NaNO 3 peaks, which reflects the inhomogeneity across the sample (Fig. 7). However, a closer observation of intensity ratios suggest that the peak at 2 ~10.3 ˚ may arise from a superposition of reflections from NaNO 3 and Na 3 NO 4 , as it can be confirmed in the diffraction pattern obtained at 13 GPa. Indeed, above 10 GPa reflections associated with Na 2 O broadened and vanished while a broad signal was observed at 2~13.5 ˚. The NaNO 3 features also seem to undergo dramatic peak broadening and intensity decrease. The broadening and vanishing of the peaks from the precursors mixture will be discussed below. The peak at 10.3˚ in the pattern at 13 GPa must now correspond to the [023] reflection from Na 3 NO 4 as its intensity is comparable with other peaks from the ambient-pressure structure (Fig. 7).

A minor rearrangement of the Na 3 NO 4 structure seem to occur between 13-25 GPa, as suggested by the changes observed within the 11-13˚ region of the corresponding patterns (Fig. 7). This is consistent with our Raman results (Fig. 6). Unfortunately, the broadening of the peaks was so severe as to preclude structure solution for any possible high-pressure modification.

Beyond 25 GPa, the diffraction patterns are dominated by the broad peak due to Na 2 O. However, the Na 3 NO 4 diffraction peaks are still visible up to 64 GPa although they are significantly broadened, that might be due to the non-hydrostatic pressurization conditions, or could indicate the initial steps of some disordering mechanism operating at higher pressure. The broadening and/or vanishing of those reflections due to the precursors may seem to contradict theoretical studies on alkaline oxides predict a very rich landscape for pressureinduced phase transitions in pure Na 2 O [11] or experimental observations in which pure NaNO 3 remained crystalline beyond the pressure range observed in this work [12]. However, it is plausible that both compounds undergo pressure-induced amorphization due to geometrical instability in the mixture. The reduced diffusion of atoms in the mixture at high pressure may hinder the rearrangement of the corresponding structures into new crystalline phases, and thus a phase transition would be kinetically impeded. This is consistent with the pressure-induced amorphization process observed for Ca(NO 3 ) 2 /NaNO 3 mixture above 9 GPa [13].

Conclusion

We saw no evidence for pressure-induced amorphization or appearance of new bands that might signal a coordination increase or polymerization among the orthonitrate groups within the pressure range studied. On the other hand, the broadening or vanishing of precursor peaks above 13 GPa have been explained in terms of pressure-induced amorphization in the sample mixture, as a consequence of a possible kinetically-hindered phase transition.

Fig. 1 .

 1 Fig. 1. Two views of the orthorhombic (Pbca) Na 3 NO 4 structure reported in ref. [3] at ambient conditions. View along a (left) and b axes (right). The NO 4 3-groups are indicated by filled tetrahedra surrounded by Na + ions (circles).

Fig. 2 -

 2 Fig. 2 -Powder X-ray diffraction patterns at ambient P,T conditions from (a) precursors mixture, Na 2 O (black) and NaNO 3 (grey), (b) calculated Na 3 NO 4 from ref. [7], (c) pure Na 3 NO 4 found after synthesis at 380°C/90 days at room pressure, (d) Na 3 NO 4 after synthesis in the multianvil cell at 4 GPa/500°C/2 days. The pattern shown in (c) was obtained using = 0.7 Å at BM01A, the Swiss-Norwegian Beam Lines (ESRF) but with 2 values recalculated for Cu 1 radiation for comparison with other patterns.

Fig. 4 -

 4 Fig. 4 -Raman spectra of Na 3 NO 4 at ambient conditions after synthesis at (a) 380°C/90 days at room pressure and (b) 4 GPa/500°C/2 days. The corresponding vibrational modes are indicated [7]; the extra bands indicate the presence of precursors, Na 2 O and NaNO 3 .

Fig. 7 .

 7 Fig. 7. Powder X-ray diffraction patterns from Na 3 NO 4 upon pressure under non-hydrostatic conditions. The symbols mark those reflections corresponding to NaNO 3 () and Na 2 O ().

Acknowledgements

Fellowship details. We thank Alistair Lennie, 9.5 HPHT, SRS (now at Diamond Light Source) for his support during the diffraction runs and the Swiss-Norwegian Beam Lines (BM01A) for the pattern of the sample at room conditions.


Cyril Legrand

Philippe Richard

Vincent Benard

Frédéric Vanderhaegen

Patrice Caulier

Ifsttar -Estas Villeneuve D'ascq

France Frédéric Vanderhaegen

Diagnosis of human operator behaviour in case of train driving: interest of facial recognition

Keywords: human factors, human stability, facial recognition, railway safety

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Thanks to technological progress with regards to systems safety, accidents/incidents due to technical failures become less frequent. In spite of this, serious or even catastrophic accidents continue to occur in transportation field such as the train collision at Hal in Belgium [START_REF] Frédéric Vanderhaegen | Rapport d'enquête technique sur la collision survenue le 9 Juin 2005 au passage à niveau 83 à Saint Laurent Blangy[END_REF].

It highlights, through the feedbacks (REX data), the essential role of human operator for this kind of accidents/incidents in the field of guided systems in particular transport. This role can be harmful in the case of human error (violation or unconscious error) or beneficial like in the accident of TER Lille-Rouen at Saint Laurent Blangy [START_REF] Era | Railway Safety Performance in European Union[END_REF] underlining the inconsistent of some safety procedures. That is why, it is necessary to consider human factors, not only, during the design of a guided transport system but also throughout its life-cycle in order to evaluate its safety and improve its performances. In this context, a diagnostic model of human operator behaviour is proposed and allows to attain these targets. In order to observe precursor signs of emotional state changing, the facial recognition can be used.

Using facial recognition in the service of railway safety

The first application of the face recognition is the people identification, used, for example, by the police in order to compare faces with a database of criminals and arrest them. This technology has greatly increased in recent decades. It is developed in a lot of field like telephony with the famous smartphone iPhone of Apple. In this case, it will be applied in transports. Some manufacturers like BMW or Mitsubishi Motors (EMIRAI Concept car) have worked on cars with face recognition on-board in order to display information about driver's behaviour. Contrary to automobile domain, the recognition topic is useful in railway transport for safety. The facial recognition is used for human operator impact analysis. The rate of facial expressions recognition is very high on a fixed position and in delayed time. Nevertheless, if the goal is to detect a change of emotional state, it must be realized on line i.e. during a driving simulation. This diagnostic will be done in four steps.

Step 1: face detection (Viola and Jones algorithm)

The Viola and Jones algorithm [START_REF] Viola | Rapid Object Detection using a Boosted Cascade of Simple Features[END_REF] is very used in face recognition. In fact, this method is more efficient than the others similar. The detection can be done in real time. The procedure is based on the classification of pictures. It is logical to think that it can be possible with computing sums of pixels but Viola and Jones, for constraints of computing speed, use features (see Figure 2-1) based on Haar-like features [START_REF] Papageorgiou | A General Framework for Object Detection[END_REF]. To compute them, some masks are used. They scan a picture and define the difference of sums of pixels of areas inside rectangles to find a change of texture or a contour. After converting the picture into grayscale, these areas are extracted from the detected face and several treatments are used on each area.

The Canny filter (see Figure 234) is a contours detector often used in computer vision. This filter is chosen for its performances. Other filters exists (Sobel, Prewitt, …) but they are less efficient. This filter is applied to LE, RE and Mouth areas. Then, some ellipses are drawn on these areas depending of the detected contours (see part 3 for results). The mouth and eyes shape is similar to an ellipse. With these ellipses, the features (perimeter, length of axis, angles, etc…) of eyes and mouth can be computed easily.

Step 3: interpretation of facial expression

With the distances compute in step 2, facial expressions can be founded. Regarding to eyes, it has to distinguish between simple blinking and sleepiness. The blinking is an unconscious and necessary function of eye which consists of open/close of eyelid in order to avoid eye dryness. It can be detected and misinterpreted. On one hand, contrary to this, the beginning of a drowsy state is a long phenomenon; the upper eyelid slowly closes. On the other hand, an increasing of the frequency of blinking can indicate that the operator go into a sleepiness state. Like eyes, an ambiguity is possible between yawns and speech. Indeed, both are defined by an opening of the mouth. A yawn can be distinguished between speech by the opening amplitude of the mouth and the opening time of this action. It is a long and large opening whereas the lips movements are more variables during a speech. However, in the train driving context, the operator is not supposed to speak in the cab except if he/she is called. In this case, he/she places the microphone in front of his/her mouth and it is not detected anymore.

Step 4: diagnostic of impact on railway safety

The sleepiness is one of the states of human operator which is the most critical during rail driving. The surprise state is important: it can be signified that the operator has seen something whereas the system can not detect. So, it is interesting to know the state of the two entities to ameliorate safety. However, detect these human states is not enough. This impact on the railway safety must be known. To better understand it, the concept of human stability [START_REF] Richard | Contribution à la formalisation et à la détection de la stabilité humaine au regard de la sécurité : application aux systèmes de transport guidé[END_REF] will be used. It is characterized by several states (stable, instable, indeterminate) and transitions between two states (leap, break, indeterminate). Stability sequences can be detected regarding the occurrence of a disturbance. Two kinds of stability were defined: recommended signature (in the case of the disturbance can be control) and risked signature (in the contrary case). The human stability criteria are clearly asserted and classified in three facets: State, Performance, and Behaviour. The object of this study is focused on the facet State. In fact, the monitoring of variations in facial expression allows to define a leap or a break of stability in terms of emotional state like sleepiness.

To apply these different steps, experimentations have been led.

Experimental results

To carry out these different algorithms, a library of functions for real time computer vision, OpenCV, is used [START_REF]Open Source Computer Vision (OpenCV[END_REF]. The experimentations are divided in two steps. First, the BioID database [START_REF]BioID face database[END_REF] is used to test the face detection. This database contains 1521 grayscale pictures of 23 different people (men/women, wear glasses or not, bearded or not…) with a 384x286px resolution. These pictures were caught with different room's brightness and distance between video camera and people.

Fault detections

No detection Correct Detection Results 3,3 % 3 % 93,7 %

These results coincide with detection rates advanced by Viola and Jones [START_REF] Viola | Rapid Object Detection using a Boosted Cascade of Simple Features[END_REF]. Throughout this test, some factors have been identified:

-If a part of a face is hidden or not be in shot, the face is not detected, -If the face is over/underexposed (too and not enough bright), the face is not detected, -Some elements of decor can be associated with a face (some inscription on a wall…) corresponding with fault detections in the table 3- Debe is computed by the center of ellipses corresponding with eyebrow and eye. Dm is simply the axis of the ellipse and corresponds with the opening of the mouth.

Debe and the perimeter of eye -corresponding to the contour drawn by upper and lower eyelid -are observed. If a decreasing then a constancy of these features are noticed, a sleepiness state can be interpreted. Inversely, an increasing can signify that the operator is in a surprise state.

Conclusion and perspectives

The facial recognition is a possible method to detect changes of human operator states in terms of emotions. It is a good solution to observe external signs of intrinsic states. Nevertheless, the results coming from this method are not enough. In addition to the fault detections and some people characteristics (wear glasses, haired people, etc), each operator do not react in the same way. This facial expressions recognition can bring some clues to identify states of human stability but it must be a complementary method to reach this goal. Other non-intrusive means of detection exist: measure of breath and heart rates, infrared for the body temperature. A fusion of all output data is necessary and a multicriteria study must be led. This base of human factors impacts diagnostic allows to identify the state of the human operator. The operator and the system do not apprehend the situation in the same way. Endsley [START_REF] Endsley | Toward a Theory of Situation Awareness in Dynamic Systems[END_REF] defines in her work the concept of situation awareness (see The Situation Awareness is divided in three steps: first the human operator perceives a given situation, then, comprehends it and, finally, acts in consequence. His/her representation of the situation is able to give some information of an emotional state. A perception can correspond with a stability signature [START_REF] Richard | Contribution à la formalisation et à la détection de la stabilité humaine au regard de la sécurité : application aux systèmes de transport guidé[END_REF] given and leads to an action. At this moment, warnings can be displayed on the operator interface. Some barriers can be put between the moment when the operator senses the situation and he/she acts.

Figure 2 - 1 :

 21 Figure 2-1 : Example of masks used in Viola and Jones algorithm

Figure 2 - 2 :Figure 2 - 3 :

 2223 Figure 2-2 : Facial expressions retrievalAt this moment, a face is detected but the facial expressions must be extracted from this face.

Figure 2 - 4 :

 24 Figure 2-4 : Canny filter in operation

1 .Figure 3 - 5 :Figure 3 - 6 :

 13536 Figure 3-5 : Example on an eye

Figure 4 Figure 4 - 7 :

 447 Figure 4-7).

Table 3 -

 3 1 : Detection results

30th European Annual Conference on Human Decision-Making and Manual Control, Braunschweig, Germany, sptembre 2012


Olivier Emile
email: olivier.emile@univ-rennes1.fr

Morgane Le Meur

Janine Emile

Light angular momentum of a plane wave diffracted by a two-dimensional simple object

Keywords: numbers: 42.50.Tx, 03.65.Vf, 42.87.-d, 42.25.Fx

The question of the transfer of angular momentum from light to objects is a key issue in optical tweezers and thus raises issues in physics, chemistry and biology. Most of the attempts have been performed either with spin angular momentum using light's polarization or using orbital angular momentum with twisted beams. We experimentally demonstrate here the exchange of angular momentum from a linearly polarized plane wave to a two dimensional asymmetric object. More precisely, we show that the diffracted light from a snail-shaped mask, carries orbital angular momentum which topological charge depends on the symmetry of the object. This opens the way to new means to produce micrometer-sized twisted beams from high power laser or even pulsed beams.

Since 1992, there has been a revival of interest for the angular momentum of light [1][2][3]. Apart from fundamental considerations, they are many potential applications as, for example, in astrophysics [4], microwaves [5], atom optics [6,7], rotation of particles [8,9], manipulations of objects of biological interest [10,11], telecommunications [12,13], quantum entanglement [14,15], acoustics [16], or electron beams [17]. These beams are generally produced either from dedicated optical elements [1,18,19], or from the diffraction of particular gratings [20][21][22].

Such beams have been recently shown to be able to interfere in the shadow of a circular disk, thus generating non-diffracting beams with micro-meter dimensions [23]. In particular, since the disk is symmetrical, the beam in its shadow keeps the same topological charge as the incident beam. On the other hand, one may seek for new, simple, and effective ways to produce twisted beams with micrometer size in the context for example of atom guiding [24,25] or for broadband sources that can be adapted to high power continuous, pulsed light beams, or white light sources. One may then wonder what would the diffracted light look like in the shadow of a simple asymmetrical disk, illuminated by a single plane wave. The aim of this work is to investigate such diffracted light, and to look for possible connexions with twisted beams.

Let us consider the experimental set-up depicted in figure 1. A collimated red laser beam (λ = 633 nm) illuminates a 2 mm diameter two-dimensional (2D) object. We have used four different objects, (i) a circular disk that is fully symmetrical under rotation. (ii) a snail shaped 2D object or single cam (wheel used in mechanics) with one notch that has a 2π/l (l = 1) symmetry, we will call it a l = 1 object in the following. (iii) a double snail or double cam with two notches that has a 2π/l (l = 2) symmetry, we will call it a l = 2 object. (iv) a triple snail or triple cam with three notches that has a 2π/l (l = 3) symmetry, we will call it a l = 3 object. By analogy, the symmetrical disk will be called a l = 0 object. Actually, we show below that the l object generates twisted beams with a l topological charge. These objects are drawn with a computer and printed in black on a transparency.

The diffracted beam in the shadow of the object is best observed on a screen, at a distance d = 6 m, with the naked eye or with a camera. For a l = 0 object, one recognizes on figure 1, the usual Arago-Poisson non-diffracting bright spot [26], as expected. Surprisingly, for l = 1, 2, 3 objects, the Arago-Poisson bright spot is replaced by a small dark spot surrounded by bright light. It strongly resembles the dark spot recently observed [23] in the shadow of a perfect symmetrical disk that was illuminated by a twisted beam generated from a spiral phase plate. This suggests that a single plane wave diffracted by a simple asymmetric object may have the same spatial distribution as a twisted beam diffracted by a symmetrical object. It has already been shown that in the case of gratings, the wave generated by asymmetrical sources [5] or diffracted by asymmetrical gratings [20][21][22] is indeed twisted. However it has never been explored in the case of simple asymmetrical objects.

We have developed numerical simulations based on Fresnel diffraction [27], to investigate the structure of such diffracted beams. Using exactly the same masks as the ones printed for the experiments (1 st input parameter), we calculate the diffracted field from a plane wave, for a wavelength λ (2 d input parameter), at a distance d (3 d input parameter) from the diffracting object. From the simulations, we can either extract the light intensity or the phase distribution of the light field.

The comparison between our simulations and the experimental observations on the intensity of the diffracted beam shows a very good agreement (see figure 1).

We have experimentally changed the various input parameters, starting with the wavelength of the beam, using different lasers (see figure 2a). At a given distance d, where the image is clear, the size of the dark spot increases linearly with the wavelength, as usual for diffraction patterns [23,26], for every value of l.

We have then changed the distance d between the diffracting object and the screen. We have measured the size of the dark spot versus d (see figure 2b), for l = 1, 2, 3. One distinguishes four zones: zone1 2 m< d < 4 m, zone2 4 m< d < 5m, zone3 5 m< d < 10 m and zone4 d > 10 m. Zone2 seems to be a transition zone: the diffracted beam undergoes specific deformations and the dark spot is hardly noticeable. In zone4, the dark spot slowly disappears and evolves into the usual Arago-Poisson bright spot for d > 20 m (not shown in figure 2b). Let us thus focus on zone1 and zone3. We clearly identify a dark spot surrounded by bright light in the shadow of the disk. Its diameter increases linearly with the distance, as usual for diffraction patterns [23,26]. However, the slope of its variation is divided by a factor of two between zone1 and zone3. The straight line in zone1 for l = 1, matches the straight line in zone3 for l = 2, with a transition zone in between.

Thus, it seems impossible to find an analytical expression describing the size of the dark spot for the different input parameters.

Finally, we have modified the shape of the diffracting object. Figures 2a and2b show that the diameter of the dark spot varies linearly with the number of notches (l). We have checked that the observation of this dark spot is not specific to the dimensions of the cam we used. A smaller diameter of the cam or a smaller notch only shifts the various zones towards smaller d values.

Are these diffracted beams actually twisted? Let us extract the phase of the beam from the simulations (figure 3). For l = 0 one evidences a supraluminal propagation as already demonstrated [26], thus validating our phase simulations.

For l = 1, 2, 3 and d=6 m, the phase of the beam varies from 0 to 2πl in one turn.

The diffracted beam carries angular momentum with a topological charge equal to the number of notches l. However, for d = 3 m, the phase of the diffracted beam varies from 0 to 4πl in one turn. The diffracted beam thus carries angular momentum with a topological charge equal to 2l, confirming the differences observed between zone1 and zone3 in figure 2b. For d >20 m, we have checked that the phase is constant, then the topological charge equals zero. Since the topological charge of the diffracted beam varies from 2l to 0, the topological charge is not a conserved quantity along propagation.

Let us focus on the transition zone, zone2, in order to understand how the topological charge of the diffracted beam by a single snail changes from l = 2 to l = 1. We have simulated on Fig. 4 with 2π per turn. This explains why it was so difficult to evaluate the size of the dark spot since the beam has lost its cylindrical symmetry. The jump from l = 2 to l = 1 is not sudden. Since this diffracted beam is not an eigen solution of the equation of propagation, it thus could be that the topological charge is not conserved along propagation.

Actually, is it possible to experimentally evidence the twisted nature of the beam? Among the various existing techniques, we choose to measure the topological charge using the interference pattern from Young's double slit set-up [28]. We now use a green laser (λ = 532 nm), since the human eye is much more sensitive to green than to red. One clearly sees in figure 5 that the fringes are shifted by one order of interference from the top to the bottom of the figure. The diffracted spot behind the cam thus carries orbital angular momentum with a l = 1 topological charge. For a distance d = 3 m, the topological charge is l = 2, as expected.

Besides, one can easily reverse the 2D asymmetrical object from a right to a left snail, just by turning it over. The interference pattern is reversed (see figure 5).

The handedness of the diffracted laser beam is thus reversed to l = -1. Indeed one can simply generate a left-handed or a right-handed twisted beam with a plane wave and a 2D asymmetrical object just by turning it over. The diffracted twisted waves are thus chiral, with a size of the order of few micrometers. Recently, it has been suggested that such twisted waves could induce chirality [29,30]. As 2D objects and plane waves are not chiral whereas twisted beams are, the generation of chiral quantities (twisted beams) from non chiral quantities (diffraction of plane waves and asymmetrical 2D objects) may then shed some new light in the unsettling problem of the homochirality of life [31,32].

We have thus been able to generate twisted beams from a linearly polarized plane wave diffracted by asymmetrical objects. We have checked numerically that the diffracted light from an inverted cam (the cam only is transparent), complementary to the cam we used, doesn't carry angular momentum in its shadow.

There is thus no light carrying orbital angular momentum out of the cams shadow.

We have also verified that the spin angular momentum has no influence since the polarization of the diffracted light is the same as the incident light. The angular momentum carried by the diffracted light from a cam is of orbital nature and lies in the shadow of the object, only. Then, due to the conservation of the angular momentum, the diffracting object must have acquired angular momentum.

In principle, it should be possible to rotate asymmetrical 2D objects using plane waves.

To conclude, we have experimentally evidenced the generation of a twisted beam from the diffraction of a plane wave by a 2D simple asymmetric object.

The topological charge corresponds to the symmetry of the diffracting object and is not conserved along propagation. One may now try to optimize the shape of the diffracting object depending on the applications. Such an experiment could be a way to generate twisted beams in a wide variety of lasers as in high power beams or pulsed lasers for example. Indeed, in high power instable cavity lasers, an intense Arago-Poisson spot arises in the shadow of the output mirror [33]. Using an asymmetrical output coupler would lead to a high power twisted beam behind the mirror. Besides, since the dark spot only slightly varies with the wavelength, one could create twisted beams on the whole spectrum of light with a single-easy-torealize diffracting object. Thus, pulsed lasers, or light electroluminescent diodes, or even white light twisted beams could be generated.

  the phase variation of the beam, for various distances d between the diffracting object and the observation, with a step of 0.25 m. For d = 3 m, the topological charge clearly equals 2, and for d = 6 m the topological charge equals 1. Actually, the phase distribution on a circle of d = 3 with 4π per turn slowly moves into a spiral (d = 4) that then starts to close (d = 5)

  The authors thank L. Pruvost, D. Bloch, B. Viaris de Lesgno and C. Brousseau for valuable discussions, and J. R. Thébault, and A. Faisant for technical assistance.

FIG. 1 .

 1 FIG. 1. Experimental and simulated diffracted beams. Diffracted pictures of a red laser beam diffracted by 2D objects recorded at a distance d = 6 m from the object. The red laser has been collimated using two lenses. In the case of a symmetrical object, one recognizes the well-known Arago-Poisson spot. In the case of an asymmetrical object, a strange hole appears in the diffracted bright spot in the shadow of the object.

FIG. 2 . 2 FIG. 3 . 1 FIG. 5 .

 22315 FIG. 2. Variation of the dark spot size. Variation of the diameter of the dark spot, a) versus the laser wavelength, for various asymmetrical 2D objects, and b) versus the distance between the diffracting object and the screen. The grey zone corresponds to distances where the dark spot is hardly noticeable.