René Brusetti

Helmut Schober

Pierre Bordet

Stefan Eibl

Jacques Bossy

Superconductivity in the tungsten bronze RbxWO3 in connection with its structure, electronic density of states and phonon density of states

Keywords: numbers: 75.20.-g, 61.12.-q, 74.70.Ad, 74.25.Kc, 71.15.Mb, 74.62.-c superconducting state stability, Magnetic susceptibility, Structural properties, Phonon density of states

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

I. INTRODUCTION

The transport properties of the tungsten bronzes of general formula M x WO 3 (M = alkali atoms) and, particularly, the ability of some of these oxides-those having the "tetragonal I" or hexagonal symmetry 1 -to form superconducting ground states, have given rise to large numbers of investigations and interpretations for more than forty years. In this system, like in many others, a lot of confusion has been introduced by contradictory results, to be principally attributed to inadequate characterization of the samples. Now that this point has been improved, it is possible to see more clearly what features the tungsten bronzes share with other superconductorsoften much more documented because displaying higher transition temperature T c -and, on the contrary, to what extent they pose a specific problem. First it seems clear that a parallel can be drawn with the barium bismuthate system because both systems are built from a parent insulating oxide-WO 3 and BaBiO 3 respectively-via a kind of heavy doping (which, in the case of the bronzes is somewhat reminiscent of an intercalation process). In both systems the doping range where a metallic but highly resistive behaviour is observed is rather narrow and corresponds to a structure with a higher symmetry than the neighbouring phases. In this narrow range, T c strongly depends on the doping level and is the highest at the lowest level compatible with the stability of the phase. Another feature these two systems have in common is the type of building blocks that make up the lattice i.e. the corner-bound WO 6 and BiO 6 octahedra, which can connect together in many ways, but can also accommodate various kinds of distortions, in connection with the electron population. It is, therefore, not surprising to observe polaronic effects in the non-metallic phases. Since up to now, no traces of magnetism have been found in these oxides, in which the electronic density of states is quite low, it is generally concluded that very special electron-lattice interactions are involved in the stabilization of the superconducting ground state. In the case of Ba 1-x K x BiO 3 (BKBO) which has given rise to the most extensive studies (maximum T c ≈ 35 K), it seems that this robust stabilization can be accounted for-in the framework of the Eliashberg strong coupling theory-by the particular strength of the electron coupling with high-energy oxygen phonons, probably those corresponding to bond-stretching modes. However, it has still not been established what are the more effective among these modes within the 30-70 meV energy range [2][3][4] . Considering now the M x WO 3 system and, more precisely, the superconducting "tetragonal I" and "hexagonal" phases, we distinguish first-leaving apart the lower T c -the specific role of stoichiometry: in these compounds, doping is achieved by intercalating the M atoms in some cages or tunnels available between a skeleton of WO 6 octaedra. Only in the "hexagonal" tungsten bronzes (HTB) one can speak about a "stoichiometric" composition M 0.33 WO 3 for which all the (tunnel) sites are occupied by alkali atoms of appropriate size (K, Rb and Cs). Reducing the doping creates vacancies on these sites and opens up the possibility of disorder. This vacancy disorder differs in its nature from the substitutional disorder in the BKBO system where barium is partially replaced by potassium. Both have in common that order can be established rather easily. In K x WO 3 and Rb x WO 3 this happens near room temperature or slightly below, respectively. The effect on T c of ordering among the doping population in BKBO 5 has still not been studied. In the high-T c cuprates (YBaCuO), it sensibly increases T c [START_REF] Jorgensen | For a review, see for instance[END_REF] . Ordering of the vacancies in the rubidium and potassium HTB drastically destabilizes superconductivity 8 . In principle, this opens the opportunity of identifying out the signature(s) of electronphonon coupling by comparing the relevant properties (structure, electronic density of states and phonon density of states) in superconducting disordered and in nonsuperconducting ordered M x WO 3 . Actually, no such straightforward comparison is possible in the BKBO system, for instance, because the non-superconducting parents have very different structures and electron populations. On the contrary, in the HTB, superconductivity can settle or not in two very similar landscapes. We have focused our investigations on the rubidium HTB (maximum T c ≈ 5.5 K) which is the most suited for the comparison we had in mind as it stands just between K x WO 3 -in which the ordering leaves no much place to superconductivity-and Cs x WO 3 in which no ordering occurs. After a short description of the experimental techniques we have used in this study, we shall present below: -the results of our magnetic susceptibility measurements, from which we can judge the relevance of the electronic density of states to the stability of the superconducting state, -the structural information obtained from our elastic neutron diffraction experiments-complementing the previous X-Rays study on a single crystal 7 , -finally, the generalized phonon density of states we have deduced from our inelastic neutron scattering (INS) experiments. These data will be compared to the results of our density-functional calculations. A general discussion will follow in which we consider the new pieces of information provided by our study and how they orientate further investigations.

II. EXPERIMENTAL AND CALCULATION

A. Samples

All the measurements we are to report have been made on micro crystallized samples which had been prepared by the usual solid-state reaction of high purity W, WO 3 and Rb 2 WO 4 in sealed quartz tubes as described in Ref. 8. We focused our attention on three Rb x WO 3 compounds with quite different behaviours as far as super-conductivity is concerned. The first compound is the stoichiometric one (x = 0.33), in which all the tunnel sites are occupied, its T c is about 2.2 K; the second one has 1/4 of the tunnel sites vacant (x = 0.25), these vacancies are ordered below about 240 K and the superconducting state only appears below about 0.2 K. The third compound has a vacancy content (about 40%) which places it very close to the boundary of the HTB phase, where T c is the highest (about 5 K) and where the destabilizing effect of the vacancy ordering can be easily shown. Its nominal rubidium content corresponds to x = 0.20 9 ; however the X-ray scattering spectrum of this preparation reveals it contains approximately 5% of the intergrowth tungsten bronze (ITB) whose formula is probably Rb 0.10 WO 3 10 .Therefore, the majority HTB phase is likely to have a Rb content corresponding to x = 0.205 11 . As discussed later, this small amount of ITB in the x = 0.20 preparation cannot significantly affect its magnetic properties; it should have no influence either on the generalized phonon density of state G(ω) deduced from the inelastic neutron scattering experiments. However, it will not allow us to carry out any crystal structure refinement from the elastic neutron scattering experiments performed on this sample.

B. Magnetic susceptibility

We performed magnetic susceptibility measurements with a MPMS XL Quantum Design superconducting quantum interference device (SQUID) magnetometer. In this kind of apparatus, the sample is positioned between the detection coils by fixing it on a straw. As the magnetic moments, which we had to measure, were quite weak, we choose to minimize the sample holder contribution by preparing composite samples in the following way: the crystallized powder was mixed with epoxy and moulded to obtain a cylinder which could be maintained within the straw by friction only. As this straw is much longer than the distance between the detection coils it should give no signal provided it is perfectly homogeneous. However, even by using always the same straw we did not achieve a reproducibility of our measurements better than about 2%. This could be due to the imperfect homogeneity of the straw or/and to the fact that the lateral centring of the sample cannot be guarantied with sufficient accuracy. Since the susceptibility of the epoxy (Vishay 610 in this case) is more than an order of magnitude larger (about -5.5 × 10 -7 uem/g) than the susceptibility χ x of the bronzes, we reduced its content in the composite samples to the minimum (about 5% of the total mass). The resulting absolute accuracy of our determination of χ x is estimated at about 10 -9 uem/g whereas the sensitivity of the measurements is better than 10 -10 uem/g. In order to check the isotropy of the magnetic properties, we also prepared oriented samples by mixing the bronze powder with a special epoxy, introducing the mixture (60:40 mass ratio) into a 15 T magnetic field and hardening the mixture by raising its temperature to 120 • C for 6 mn. The orientation of the Rb x WO 3 micro-crystals with their c axis parallel to the applied field is clearly observed under a microscope and confirmed by an X-ray observation-which indicates that the susceptibility is larger along this direction 12 . However, this method of orienting the powders did not give us quantitative results as we were unable to estimate the epoxy content in the samples and, therefore, the epoxy contribution to χ-which now largely overcomes that of Rb x WO 3 -with sufficient accuracy . Moreover, this process has the potential of introducing some parasitic magnetic moments, as it was observed in some high-T c cuprates 13 .

C. Elastic neutron scattering experiments

These experiments were performed on the highresolution neutron powder diffractometer D2B of the ILL, Grenoble, France 14 . The samples were placed in a 10 mm diameter cylindrical vanadium can inside a closedcycle pulse-tube cryostat. Diffractograms were recorded between 2θ = 0 • and 160 • at a constant step of 0.05 • , at different temperatures between 5 K and 300 K, using the λ = 1.594 Å wavelength obtained from the (335) reflection of the Ge monochromator. In order to improve the spatial resolution, we also collected two diffractograms with λ = 2.4 Å at T = 5 K for the x = 0.25 and 0.20 samples, for which additional superstructure reflections due to ordering of the Rb cations were expected. All refinements were carried out using the WinPLOTR software suite [START_REF] Roisnel | Materials Science Forum[END_REF] .

D. Inelastic-neutron-scattering-experiments

The inelastic neutron scattering (INS) measurements were performed on the cold neutron time-of-flight spectrometer IN6 of the ILL. The incident wavelength was 4.12 Å and neutrons were detected over the scattering angles from 13 • to 114 • . We used a slightly inelastic focusing (E focus = 2.7 meV) to improve resolution at large energy transfers in up-scattering (neutron energy gain mode). The raw data were corrected for empty container scattering and normalized to a vanadium standard. The spectra thus obtained were converted into generalized phonon density of states (GDOS) G(ω) using the incoherent approximation. Multiphonon corrections were performed self-consistently. The neutron-weighted GDOS is related to the true partial phonon density of states g i (ω) (i = Rb, W and O) according to:

G(ω) = i=Rb,W,O (c i σ i /m i )g i (ω) i=Rb,W,O (c i σ i /m i ).
Where c i indicates the concentration, σ i the total bound scattering cross section for atoms i and m i is its mass.

Consequently, G(ω) is related to the true total phonon density of states g(ω) by a frequency-dependent factor f (ω) = g(ω)/G(ω) which has no simple expression here as the σ i /m i are very different.

E. Density-functional calculations

We have calculated the phonon dispersion relations and phonon density of states of the stoichiometric compounds Rb 0.33 WO 3 and Cs 0.33 WO 3 using the software PHONON [START_REF] Parlinski | Phonon software[END_REF] . PHONON uses the direct method to set-up a dynamical matrix from Hellmann-Feynman forces. In our case the Hellmann-Feynmann forces were provided by ab initio calculations performed within the density functional theory (DFT), using the PAW potentials [START_REF] Blöchl | [END_REF]18 and the generalized gradient approximation (GGA), as implemented in the VASP software 19,[START_REF] Kresse | Software VASP, Vienna[END_REF] . We choose a 2s 2 1p 4 , 4p 6 5s 1 , 5s 2 5p 6 6s 1 , 5d 4 6s 2 valence electron configurations for O, Rb, Cs and W, respectively. The maximum energy cut-off was 283 eV. The Hellmann-Feynmann forces are calculated with respect to a completely relaxed structure with no residual forces acting on the various atoms (F residual ≤ 0.005 eV/ Å; 1 eV/ Å = 0.01602 nN). In the first stage of the relaxation process we optimized the structural parameters of the primitive cell. In a second step the supercell parameters were obtained using a k: 1×1×1 mesh for the wavevector summation over electronic states. The optimized theoretical structure was then used to determine the Hellmann-Feynmann forces for symmetry independent displacement with the amplitude of 0.05 Å. The use of a rather extended supercells containing more than 200 atoms is mandatory as the force constants fall of rather slowly with distance. All phonon calculations on single cells predict, therefore, unstable crystals, i.e. their dynamical matrix D( q) for some q possesses negative eigenvalues leading in theory to relaxational modes. The Rb 0.33 WO 3 calculations in the C222 1 symmetry group were e.g. carried out on a supercell containing 208 atoms with a dimension of roughly 12.9 × 14.9 × 15.3 Å3 . We also calculated the neutron-weighted phonon DOS G(ω) and the weighting factor f (ω).

III. RESULTS

A. Magnetic properties

We can summarized the main results of these measurements as follows: -At low field, the magnetic susceptibility of our samples is field dependent, even at room temperature, showing a paramagnetic contribution χ p saturating below 1 T; this contribution is noticeably larger in the oriented samples and probably results from a pollution by ferromagnetic particles-representing less than 10 -6 of the sample mass in the case of Fe particules. This contribution has been removed in the data presented below.

-The temperature dependence of χ is only sensible below 100 K where it resembles the contribution of magnetic impurities 22 . We fitted the low-temperature behaviour (T 120 K) with a Curie-Weiss term C T -θ and found it could correspond to about 30-50 ppm of Fe 3+ . These impurities are probably coming mostly from the Rb 2 WO 4 starting powder ; however the C values derived from this fit are not clearly correlated with the Rb content, x 23 . The characteristic temperature θ seems to increase with x, between (0 K±0.5 K) and (6.8 K±1.5 K) [START_REF]Curie-Weiss expression does not imply we believe these impurities can directly magnetically interact, but they could interact via the conduction electrons[END_REF] . By removing these Curie-Weiss terms from our data we obtain the "intrinsic" susceptibilities χ x plotted in Fig. 1.

-The order-disorder transition of the rubidium atoms is clearly seen in Rb 0.25 WO 3 at T OD ≈ 250 K. It has been also observed at about 220 K in another experiment, on a sample (N • 2) coming from another batch (see insert in Fig. 1). It has been shown previously 8 that the order- disorder transition becomes more and more continuous as the rubidium content deviates from x = 0.25, which explains it cannot be observed in Rb 0.20 WO 3 . It should also be mentioned that the order-disorder anomaly occurs at a lower temperature in sample N • 2. This shift of T OD comes from slightly different x and, incidentally, confirms the rapid lowering of T OD with the departure from the optimal x = 0.25 rubidium content. The larger ordering-induced susceptibility increase in sample N • 2, however, cannot be explained in the same way. It is more probably related to the use of a lower field (1 T) and this is born out by the still higher anomaly observed in the same sample with a 0.1 T field. -As displayed in Fig. 2, the magnetic susceptibility does not depend significantly on the Rb content, which confirms the previous data of Wanlass and Sienko [START_REF] Wanlass | [END_REF] . Our data, however, are about 10 -8 emu/g above those of the Cornell University group, on average, i.e. well beyond the estimated accuracy of both results [START_REF] According | Inorg[END_REF] . Such a discrepancy is quite common when low-susceptibility samples of different origins, measured with different techniques are compared. It probably indicates that some random errors have been overlooked. This is illustrated, for instance, by the case of WO 3 we shall have to refer to below.

B. Structural properties

In a previous work 7 , we have examined the structure of the stoichiometric Rb 0.33 WO 3 compound using X-ray single crystal diffraction. The observation of unexpected (h0l), l = 2n + 1 reflections for the reported P6 3 /mcm space group had lead us to search for a lower symmetry. Two solutions yielding structure refinements with reasonable agreement factors were proposed with the P6 3 and P3 space groups. The presence of at least a 3-fold axis along c was supported by the absence of detectable unit cell distortion or twinning. The neutron diffraction experiments we are to present were meant to complement these investigations. The first attempts to perform a full pattern matching of the x = 0.33 data at T = 5 K rapidly demonstrated that they could not be fitted using a hexagonal unit cell. This was evidenced by large discrepancies in the reflection positions indicating a unit cell distortion. A χ 2 agreement factor of 10.8 was obtained for a pattern matching refinement with the P3 space group. The data could be successfully fitted by using monoclinic symmetry, yielding a χ 2 of 2.2 for a pattern matching refinement with the P2 1 space group. The structure was then solved and refined in P2 1 symmetry, with agreement factors R p = 9.70%, R wp = 10.3% and χ 2 = 3.69 and the unit cell parameters: a = 7.37263(6) Å, b = 7.53091(4) Å, c = 7.3650(2) Å and β = 120.043(2) • . Similar refinements were then carried out for all temperatures up to 300 K. One observes that the very small difference between a and c and the deviation of β from 120 • gradually decrease on heating and vanish at room temperature. This explains why the distortion could not be detected by single crystal X-ray diffraction at room temperature. It is also worth noting that the structure description in P2 1 symmetry requires 13 independent atoms, (3 tungsten, 1 rubidium and 9 oxygen atoms) all on a general position, resulting in 38 positional parameters (the y parameter of Rb was kept equal to 0 in order to fix the origin along the b-axis). This leads to strong correlations between parameters in this pseudo-symmetric structure description and makes it difficult to obtain a proper convergence of the refinements-especially close to room temperature were the distortion vanishes. Therefore, we searched for solutions with a higher symmetry and which would provide more stable refinements. We found that a satisfactory fit to the 5 K data could be found by using the C-centered orthorhombic unit cell with:

a o = a + 2 b b o = -a c o = c leading to a o = a √ 3, b o = b and c o = c.
The volume of this cell is twice that of the original hexagonal cell (and of the monoclinic cell given above). The best result for the Rietveld refinement of the structure was obtained with space group C222 1 ,(χ 2 = 2.6) for which only 8 independent atoms (2 tungsten, one rubidium and 5 oxygen atoms) and 18 positional parameters are required. Similar refinements were carried out on the diffractograms obtained at higher temperatures without noticing any deterioration of the convergence up to 300 K, which confirms this model does not induce excessive correlations between positional parameters. Here again, the very small structural distortion (which can be represented by the difference (b o -ao √ C. Phonon density of states and generalized phonon density of states

An overall picture of the generalized phonon density of states G e (ω) deduced from our INS experiments is presented in Fig. 4. These data have been obtained on Rb 0.33 WO 3 and Rb 0.20 WO 3 samples which where simply wrapped in an aluminum foil and placed directly in the beam at ambient temperature and atmosphere. Getting rid of the cryostat allows to reduce the error introduced by subtracting the background scattering [START_REF]All the GDOS data we present have been normalized to have R 120meV 0 Ge(ω)[END_REF] . In order to describe and discuss more conveniently the GDOS spectra, we will distinguish therein four main regions covering approximately the following energy ranges:

region I region II region III region IV 0→10 meV 10→25 meV 25→60 meV 60→120 meV
The more obvious difference between the GDOS observed in the two compounds concerns region I where the well defined peak observed in the stoichiometric compound just above 5 meV seems to have collapsed in Rb 0.20 WO 3 . Simultaneously, the first minimum is shifted from ∼7.5 meV to ∼ 9.1 meV and replaced by a blunt maximum between 6.5 and 7.5 meV. Among the other small differences between the two spectra we shall notice the slightly larger GDOS observed in Rb 0.20 WO 3 in the ∼(20-27 meV) and ∼(45-55 meV) ranges, as well as a sensible hardening in region IV. Although less accurate, the data obtained with the samples inside the cryostat (Fig. 5) indicate that these Rb-content-related differences seem to develop continuously and does not make Rb 0.25 WO 3 (T c 0.2 K) significantly different from Rb 0.20 WO 3 (T c 5 K). From our measurements at T = 100 K on the three samples, we have derived the generalized density of states shown in Fig. 6, where they are compared to the room-temperature results obtained under the same experimental conditions. The energy range is restricted here to below ≈ 3k B T ≈ 30 meV due to the sharply decreasing thermal occupation of the phonons.

In order to check for a possible effect of the Rb ordering in Rb 0.20 WO 3 , we compared the spectral response of the same sample after it has been slowly cooled, on the one hand, and after it has been cooled down to 100 K in about 1 min by immersion in liquid N 2 and consecutive transfer at this temperature into the cryostat, on the other hand. No difference could be detected between these two experiments, within the data statistics.

D. DFT calculations

In Fig. 7 we compare the calculated g(ω) for Rb 0.33 WO 3 in C222 1 symmetry with the experimental data.

The agreement is very good even down to small details. We e.g. exactly reproduce the four peaks in g(ω) measured between 8 and 25 meV (region II). It is as already mentioned not possible to stabilize the structure of Rb 0.33 WO 3 in P3 symmetry. This changes when we go to Cs 0.33 WO 3 . Due to the large size of the Cs ion the hexagonal P6 3 /mcm is stable, provided we use a supercell of similar size as that employed for the calculations vectors describing collective rotations of the WO 6 octahedra. As the frequency increases there are more and more distorting contributions to these rigid-unit modes. At intermediate frequencies (region II and III) distortion takes place perpendicular to the strong W-O covalent bond. At the high-frequency end (region IV) the W-O bonds are solicited in W-O stretching modes. The frequency of these stretching modes depends crucially on the W-O bond length distribution. In Fig. 9 we compare the calculated density of states for two (P3 and C222 1 ) Rb 0.33 WO 3 and one Cs 0.33 WO 3 (P6 3 ) structure. The fact that the calculations are unable to produce a stable Rb 0.33 WO 3 crystal within the P3 symmetry group and thus produce negative values of the dynamical matrix is of no importance for the high-frequency end of the spectrum. We clearly observe important shifts of the oxygen bands, in particular of the stretching modes in region IV. This is not surprising as the WO 6 octahedra in Rb 0.33 WO 3 in P3 can be characterized as more distorted, giving in particular larger extremes for the smallest and largest W-O distance, respectively. The calculated O spectrum of Cs 0.33 WO 3 (P6 3 ) is to the contrary rather close to that in Rb 0.33 WO 3 (C222 1 ).

(d i -d) 2 n.d
1. Generalized and "true" phonon DOS

In the preceding section we have presented a true density of states obtained from the experimental data. We shall concisely establish how we determine the conversion factor f (ω) relating the two quantities. In principle it could be fully calculated from the DFT results. Actually, the acoustic part of the spectrum, below about 4 meV, is not very well described by our density-functional calculations: this is a quite usual shortcoming and results in overestimating the ratio f (ω) in this range. This ratio should approach unity as ω tends to zero, however, the experimental G e (ω) is also overestimated below about 1.5 meV, due to spurious detection of elastic contributions. Consequently, the ratio-we shall call it f e (ω)between the "true" experimental g e (ω) and the measured G e (ω) will decrease below unity as ω goes to zero. A more precise estimate of the low-energy behavior of f e (ω) can be derived from a comparison between the lattice specific heat (C p ) obtained from g e (ω) and the direct experimental determinations by Bevolo 415 K±15 K: a ω 2 fit of our g e (ω) below ∼ 2 meV should give us a similar value of θ D . Finally, a corrected f e (ω) which satisfies the specific-heat requirements is displayed in the inset of Fig. 7. It yields the experimental g e (ω) = f e (ω)G e (ω) displayed in the same figure. Our derivation is also confirmed by the number of modes one can count within the (4 to 9 meV) range an which is now consistent with what is expected from the Rb population (7.7%). It is the preponderance of the Rb modes in this range which explain the large low-energy maximum in f e (ω).

IV. DISCUSSION

A. Magnetic Properties

Let us first review the different contributions entering the measured magnetic susceptibility χ x , considering first the stoichiometric compound Rb 0.33 WO 3 :

• The diamagnetic core component χ core is usually identified with the ionic contributions which have been compiled by Klemm 29 : this gives -20 × 10 -6 emu/gramion for Rb +30 . Similarly, following Klemm would give -49 × 10 -6 emu/mole for the diamagnetic core contribution of WO 3 ; however this compound is much less diamagnetic due to a significant Van Vleck paramagnetism, χ vv . As a first approximation, we shall suppose that χ core and χ vv are the same in WO 3 and in Rb 0.33 WO 3 . Accordingly, we take for the susceptibility χ loc of the localized electrons in Rb 0.33 WO 3 : χ loc (Rb 0.33 WO 3 ) ≈ χ core (Rb + .33 ) + χ (WO 3 ) Unfortunately, χ (WO 3 ) is not known very precisely and the published values 32 range between -13 × 10 -6 emu/mole and -21 × 10 -6 emu/mole 33 .

• Another paramagnetic contribution is expected from the spin susceptibility of the conduction electrons χ spin (or Pauli susceptibility).

As far as Rb 0.33 WO 3 is concerned, χ spin can be roughly determined by using the electronic coefficient of the specific heat γ which has been estimated between 2.2 mJ/K 2 mole 35 and 1.9 mJ/K 2 mole 36 . The corresponding electron density of states at the Fermi level D FE would be about 0.87 ± 0.07 state/eV molecule and χ spin ≈ 7.8±0.6×10 -7 emu or 28±2×10 -6 emu/mole. These values are about two times larger than expected from a free-electron band containing x electron per W atom and it is also what is observed, on average, in the other alkali tungsten bronzes 37 . The composition dependence of χ x which would result only from the x dependence of χ spin is plotted on Fig. 2.

• Finally, an orbital contribution of the conduction electrons, χ L is expected from the Landau mechanism: it partly compensates the Pauli susceptibility when we are dealing with a free electron gas (χ L = -1/3χ spin ), but its absolute value is higher the smaller the electron effective mass. Comparing the contributions estimated above to the total measured susceptibilty (χ x = -7.4 ± 0.3 × 10 -6 emu/mole for Rb 0.33 WO 3 at 280 K), gives χ L = χ x -(χ loc + χ spin ) = -7.8 ± 2.3 × 10 -6 emu/mole-taking χ = -21×10 -6 emu/mole for the susceptibility of WO 3 38 . Such a value for χ L seems to confirm the quasi-free-electron-like behaviour. This agreement could be somewhat fortuitous, considering our poor knowledge of the other contributions, however it is supported by the fact that all the investigations carried out on the tungsten bronzes have never revealed a more complex behaviour. In particular, we have no experimental or theoretical 39,40 indication that D FE could increase noticeably when x and the electron population decrease.

As an aside, we can notice that a similar decomposition should hold for the ITB phases of Rb x WO 3 , therefore a few per cent of these phases should not have a sensible effect on the susceptibility of the Rb 0.20 WO 3 sample. Let us now consider the main problem raised by our data, namely the effect of the order-disorder transition. The small susceptibility increase at the transition toward the ordered state in Rb 0.25 WO 3 could be attributed to a corresponding increase of the electronic density of states D FE but this would contradict the drastic destabilization of the superconducting state in this compound. Another possibility is that the ordering of the rubidium vacancies simultaneously modifies both χ spin and χ L (and eventually χ vv ): an increase of χ L (and eventually χ vv ) compensating for a decrease of D FE and χ spin . This hypothesis seems to be supported by the electronic band structure study of K.-S. Lee et al. 39 according to which a part of the Fermi surface is quasi one-dimensional (1D) in the disordered state: the superstructure accompanying the ordering could create electron and hole pockets in place of the initial warped sheets, therefore reducing D FE and generating possible mechanisms for an increase of χ L . However, in the framework of the BCS model, a reduction of D FE by about 40% 41 would be necessary to explain, on its own, the corresponding destabilization of the superconducting state. This seems implausible, first because the main part of the Fermi surface is threedimensional (3D) and should not be perturbed by the ordering. Second, because the ordering only concerns a small part of the atoms (1/4 of the Rb atoms are missing in Rb 0.25 WO 3 i.e. only 2% of the total population). We are therefore prone to conclude that if there is any reduction of D FE induced by the ordering it cannot be large enough to explain the drastic reduction of T c , contrary to most of the previous interpretations.

B. Structural properties

The main result of this structural study is the improvement brought by adopting a description of slightly lower symmetry than before, the better one compatible with the low-temperature data. Moreover, it appears now that the rubidium bronze is farther from the strict hexagonal symmetry the lower is the temperature. On the contrary, they probably recover the full hexagonal P6 3 /mcm symmetry above room temperature, as we shall discuss below. It is worth underlying that our attribution of the C222 1 symmetry to these bronzes has been remarkably confirmed by the density-functional calculations we have performed to describe the lattice dynamics of these compounds (see Section III D). Actually, this symmetry allows to produce a not only completely relaxed structure (no residual forces acting on the atoms) but equally stable structure (no negative eigenvalues of the dynamical matrix), whereas the formerly proposed symmetries P6 3 /mcm and P3 lead to an unstable lattice. By comparing our C222 1 description with the previous ones, we can notice a slightly different oxygen environment around the rubidium atoms: instead of twelve nearest neighbours at 3.30 Å plus six second nearest at 3.52 Å corresponding to the P6 3 /mcm configuration, we find the twelve nearest neighbours between 3.26 Å and 3.36 Å and two O5 oxygen at 3.434 Å in the stoichiometric bronze at 300 K. This coordination is illustrated in Fig. 10. The large amplitude of the Rb vibrations within this oxygen cage is manifested in the large associated atomic displacement parameter at room temperature: B ≈ 3.5 Å. It should be noted that this value is higher than that observed in RbOs 2 O 6 , where it has attracted considerable attention and been associated with some tattling mode 45 . Except for the superstructure which accompanies the vacancy ordering in Rb 0.25 WO 3 , no drastic structural changes are observed between this non-superconducting compound and the stoichiometric superconducting Rb 0.33 WO 3 . The principal differences are illustrated in Figs. 3 and11, and can be summarized as follows:

• at 300 K, the reduction of the Rb content notably increases the distortion of the WO 6 octahedra around W1, whereas it slightly reduces the distortion around W2. Therefore, in Rb 0.25 WO 3 , the W1 population is distinguished very clearly from the numerically equivalent W2 population, whereas in Rb 0.33 WO 3 this distinction is small enough that it could pass unnoticed in the previous works. Although the difference between the two compounds lessens as the temperature decreases (cooling reduces the distortion in Rb 0.25 WO 3 whereas the opposite happens in Rb 0.33 WO 3 ), the distinction between the W1-centred and the W2-centred octahedra is still well marked in Rb 0.25 WO 3 at 5 K.

• Lowering the temperature has an opposite effect upon the oxygen cage surrounding the rubidium, which leads, at 5 K, to a quite spherical cage in Rb 0.33 WO 3 but to a much more distorted one in Rb 0.25 WO 3 .

• The small distortion associated with the (b o -ao √ 3 ) difference is more stable in Rb 0.25 WO 3 , than in Rb 0.33 WO 3 : more precisely, the differences plotted in Fig. 3 vanish at 375 K and 295 K respectively when extrapolated with a second-order polynomial. This is clearly reminiscent of the structural phase transition observed by Sato et al., although the transition temperatures T c1 above which they found the rubidium tungsten bronzes recover the P6 3 /mcm symmetry are markedly higher (420 K≤ T c1 ≤ 450 K).

• The ordering of the Rb vacancies in Rb 0.25 WO 3 clearly appears through an increase of the atomic displacement parameter B of the rubidium, but also of the oxygen atoms. This ordering is also manifested in an opposite effect on the distortion of the oxygen cage around W1 and W2, whereas it increases the distortion around Rb (Fig. 11).

C. Lattice dynamics and phonon density of states

As discussed in Section III D, the DOS g c (ω) deduced from our density-functional calculations on Rb 0.33 WO 3 compares remarkably well with our measurements and allows us to characterize precisely the four energy ranges distinguished above: -the Rb vibrations only contribute to region I, -the W vibrations are spread between the second half of region I and region III, with a maximum contribution between about 7 and 25 meV , -the oxygen vibrations contribute to the whole spectrum but dominate region III and take up alone the highestenergy region IV-in which the oxygen vibrations are directed towards the tungsten atoms. An energy gap, centered around 60 meV, separates these modes from the softer ones for which the oxygen vibrations are not directed towards the tungsten atoms. Our calculations also bring to the fore that the oxygen contribution largely dominates the GDOS (94 %) whereas the Rb and W atoms participate for only about 3% each, due to their much lower σ i /m i coefficients. Consequently, as the tungsten modes are spread in a rather large energy range they share with oxygen modes, they are completely masked by the latter. The Rb modes are fortunately more visible because concentrated at lower energies in a narrower range. More precisely, the peak at about 5 meV in Rb 0.33 WO 3 is to be attributed to the motion of the Rb ions in the x-y i.e. equatorial plane of the cavities these ions fill within the WO 3 skeleton. The vibrations along the channels which link these cavities along the c axis are spread between ∼ 5 meV-corresponding to in-phase motion of the alkali ions-and ∼ 10 meV-corresponding to their outof-phase motion-in an energy band with a tuning fork shape. The highest energy spike of this fork coincide with the shoulder observed in G e (ω) at ∼ 10 meV.

Dependence of the phonon DOS spectrum on the rubidium content

Let us now consider how these features evolve when the Rb population decreases, leaving vacant sites in the tunnels. As we noticed in Section III C, the sharp peak at ∼ 5 meV broadens and shifts to higher energies; concomitantly, the hump at ∼ 10 meV disappears. This is illustrated in Figs. 4 and5. The broadening is clearly related to the disorder within the Rb sublattice and to the corresponding distribution of local environments seen by the Rb-ions. A part of the equatorial band is simultaneously shifted to higher energies, which probably results from the following mechanism: the Rb-ions which have lost one of their neighbors should tend to get closer to these vacancies and the WO 3 matrix to readjust around them-reacting both to the missing charge transfer and to the shifts of the remaining Rb-ions. In this defective environment, the Rb-ions are a little more tightly bound in the equatorial plane and the corresponding vibrations are slightly stiffer. On the contrary, the out-of-phase motion of these ions towards the neighboring vacancy, i.e. along the channels, is easier and the corresponding vibrations are softer. Since increasing the vacancy content also reduces the difference between the in-phase and out-of-phase motions along the c axis, its global effect on the phonon DOS in region I is to attenuate the well defined structures observed in the absence of vacancies-the sharp peak at ∼ 5 meV and the shoulder at ∼ 10 meV-and to fill in the formerly low-density-of-states region in between. In regions II and III of the phonon DOS spectra, the changes induced by an increasing deviation from stoichiometry are not very pronounced and not easy to interpret since many different modes are involved here and non-stoichiometry cannot be taken into account by our calculations. However, in region IV, the clear hardening which is observed on the rising edge of the band (by ∼ 5 meV) when up to one third of the Rb-ions is removed, can be explained by the shortening of the mean W-O distance.

Dependence of the phonon DOS on temperature

Within the limited energy range accessible experimentally, the more important modifications induced by lowering the temperature are observed between 4 meV and 9 meV, where the Rb modes are predominant (see Fig. 6). The most impressive effect is the softening and concomitant narrowing of the band of equatorial Rb-vibrations at ∼ 5 meV in Rb 0.33 WO 3 . Usually the anharmonic terms that enter the atomic potentials render them softer at larger displacements. This is why, in general, the restoring forces an ion experiences become stronger as the mean square displacement decreases with temperature leading to higher frequencies. A particularly strong hardening of this type is e.g. observed for the C 60 librations in superconducting Rb 3 C 60 48 . It is not associated with a broadening of the band. Softening is possible if the potential has a trough-like character or if in the extreme case the particle is confined geometrically in a stiff environment described theoretically by a potential well. Such phenomena are observed in many guest host systems where a small molecule is loosely bound in a cage. An instructive example is N 2 hydrate clathrate 49 . While the N 2 molecules are vibrating against the cage walls at elevated temperatures they perform a tumbling motion in a trough-like potential at low temperatures. However, in such a case the softening is accompanied by pronounced damping. A very narrow band in Rb .33 WO 3 at 100 K indicates that the Rb-ions experience both a harmonic and homogeneous environment -a fact which already emerged from our Rietveld analysis of the structure (see IV B and Fig. 11). In addition a narrow band does not allow for band dispersion. Therefore, at 100 K the Rb-ions vibrate in the equatorial plane harmonically and decou-pled from each other like perfect Einstein oscillators. The softening is, therefore, to be explained purely by the evolution of the Rb ions environment leading to a fine tuning of the force constants. It is interesting to note that the DFT calculations produce always a tiny splitting within the narrow Rb-band (see Fig. 7 and 12), which even if real would be difficult to observe in the experimental spectra. No softening of the equatorial Rb-band is observed in the non-stoichiometric compounds. However, in Rb 0.25 WO 3 cooling seems to promote a second peak at ∼ 7.6 meV, in agreement with what Sato et al observed on a sample of approximate composition Rb 0.27 WO 3 . As this effect is not found in Rb 0.20 WO 3 it is tempting to relate it to the ordering of the Rb vacancies which is optimal when 1/4 of the alkali are missing. In the case of Rb 0.20 WO 3 the only clear sign of anharmonicity is a small low-frequency shoulder that appears in the 100 K spectrum at about 4 meV. This is also the only feature that could recall a contribution from local structural excitations and the LSE model proposed by Ngai and Silberglitt 47 . This clue seems too tenuous-confronted to the "T c (x) paradox"to support this model.

V. GENERAL DISCUSSION

If we consider the totality of our results, then it turns out that what favors or destabilizes superconductivity in the Rb x WO 3 system is much more subtle that thought up to now. First, we have shown in Section IV A that there is no sign of a sensible increase of the electronic density of states D FE near x = 0.20-the low-rubidium-content boundary-where the highest T c is observed. Nor is there a significant decrease of D FE induced by the ordering of the Rb vacancies-which destroys superconductivity in Rb 0.25 WO 3 ; quite to the contrary, this ordering may even lead to a slight increase in D FE . Second, the crystallographic structure of this compound displays only minor differences if compared to that of the stoichiometric Rb 0.33 WO 3 . They can principally be summarized as a slightly more marked difference between the oxygen octahedra surrounding the W1 and W2 sites, respectively. Unfortunately, we have not been able to extend this comparison up to Rb 0.20 WO 3 but, even if this difference should keep growing, we notice that it does not seem to affect D FE . Third, reducing the rubidium content does not yield a global softening of the lattice ; on the contrary, it leads to a loss of low-energy Rb xy modes which are redistributed at higher energy. Moreover, even the high-energy O vibrations in region IV are shifted to higher energy. No sign of softening distinguishes Rb 0.20 WO 3 from its nonsuperconducting neighbor. This lack of softening does not contradict the fact that, below this Rb content, the HTB phase is no more stable. Actually, it is replaced by a mixture with the ITB (pseudo)phases which themselves consist of mutually intercalating WO 3 and HTB slabs. Therefore it seems that what drives superconductiv-ity in this system must be traced back to a very specific electron-phonon (e-p) interaction, involving closely defined electron states and phonons. This is a quite common issue which pertains to the field of the strong-coupling theory. The Ba, K-bismuthates, the M 3 C 60 fullerides and MgB 2 are among the systems in which this question has been thoroughly investigatedexperimentally and theoretically-without always receiving definitive answers. At present, our case is much less documented and we have to rely on our own results for interpretation. We shall note first that we cannot discard the possibility that the low-energy phonon band associated with the alkali xy vibrations contribute to a significant electronphonon coupling in the stoichiometric HTB. This was initially proposed by Kamitakahara et al. 42 , considering some correlation between T c and the energy of the Einstein-like peak deduced from the specific-heat excess it generates. Our density-functional calculations a priori support this correlation since they find that this peak is shifted up by about 2 meV when substituting Cs for Rb in M 0.33 WO 3 , compatible with the lower T c of the Cs bronze (about 1 K). If we consider only the mass m A of the alkali ions then their frequencies should scale with 1/ √ m A . It is, however known that in guest host systems the size of the guest atom can play a decisive role on determining physical quantities. We should not forget that this size effect stabilizes the hexagonal structure against distortion. The DFT calculations confirm this stabilizing effect and give a slightly stronger restoring force for Cs if compared to Rb. The lattice stabilizing effect has already been discussed by K.-S. Lee et al. 39 .

It has been argued against a strong electron-phonon coupling of the alkali modes that the alkali-ions were too far from the t 2g orbitals involved at the Fermi level and which emerge from the W 5d-O 2p interaction. However, we have seen that the oxygen displacement parameter B and the distortion of the WO 6 octaedra are quite sensitive to the vacancy content and to their ordering (cf. Fig. 11). The magnetic susceptibility-and therefore the conduction band-are also affected by this ordering. To a lesser extent, the neighboring WO 6 octraedra probably feel the alkali vibrations and this may influence the conduction band by modulating the W 5d-O 2p hybridizations. The softening of the Einstein-like vibrations at low temperature (cf. Fig. 6) could be a symptom of this contribution to the electron-phonon coupling.

A similar contribution to the electron-phonon coupling has been put forward in the β-pyrochlore osmates AOs 2 O 6 , in which the large-amplitude motion of the alkali-metal ions A has been considered to deserve a new qualifier and to be responsible for the superconductivity of these compounds 46 . However this may be in the osmates, we observe in the tungsten bronzes that reducing the alkali content x causes the associated Einsteinlike peak to collapse; nevertheless, T c increases unless ordering takes place. This means that, even if we accept that the Rb vibrations play a role in the superconductivity, they cannot be made responsible for it on their own. Another part of the phonon spectrum has to be involved in the electron-phonon coupling . However, no clear indication of this mechanism appears in the phonon DOS at 300 K or below 30 meV at 100 K. Two possibilities seem to be left: first, the enhancement of the e-p coupling with decreasing x concerns such a restricted energy range that it cannot be resolved in our experiment; second, the softening it induces at low temperature occurs above 30 meV-an energy range to which the technique we used gives no access. Such a situation is reminiscent of the significant softening of the oxygen "bond stretching" modes observed in Ba 0.6 K 0.4 BiO 3 around 30 and 60 meV 3,4 . It is tempting to suppose a similar process in M x WO 3 where we have the following indications that the e-p coupling could involve high-energy oxygen modes: i) Walkingshawet al. 43 have performed a densityfunctional study of charge doping in WO 3 ; considering only the effect of the addition of electronic charge (without the inclusion of M ions and the associated size effects). They show that reducing the doping level leads to rotations of the WO 6 octahedra and displacement of the W ion from the center of its octahedron. ii) It also emerges from our calculations (see Section III D) that the energy of an oxygen stretching or breathing mode, above the 60 meV gap, is quite sensitive to the W-O distance involved-which appears when the C222 1 structure of Rb 0.33 WO 3 is replaced by the previously considered P 3 symmetry, or when Rb is replaced by Cs (P 6 3 /mcm symmetry). iii) We observed such a sensitivity of vibrations to the W-O distance in Rb x WO 3 at 300K, near 80 meV (Fig. 5). Further experiments should be undertaken at low temperature to extend the investigation of the phonon DOS to the region beyond 30 meV. They could be guided by the following remarks: the T c increase with decreasing x would be similar in Cs x WO 3 and Rb x WO 3 if ordering could be prevented in the latter. This could indicate that similar parts of the phonon spectra are involved, despite the somewhat different lattice structure. According to our density-functional calculations, fair coincidences between these spectra occur between 75 and 85 meV for the oxygen (bond stretching) vibrations, and also between 40 and 57 meV (bond bending vibrations), as it appears in Fig. 12. Other coincidences have to be noticed between 30 meV and 35 meV for the W xy vibrations, between 30 and 56 meV for the Wz vibrations. One last question must be considered again, i.e. the detrimental effect of the Rb-vacancy ordering on the stability of the superconducting state. Although this ordering does not lead to a significant depression of D FE , it becomes manifest in the magnetic susceptibility (Fig. 1), in the tungsten environment and in the oxygen displacement parameter (11). It therefore generates some alterations in the conduction band. Moreover, it could partly remove (condense) the phonons engaged in a strong e-p coupling, as suggested by K.-S. Lee et al. 39 , and reduce drastically this coupling via a perhaps fortuitous cooperation of these two mechanisms.

VI. CONCLUSION

The data we have presented allow to address in more realistic terms the questions raised by superconductivity in Rb x WO 3 and, more generally, in the hexagonal tungsten bronzes. Our magnetic susceptibility measurements confirm that the increase of T c with the Rb impoverishment is not due to an increase in electronic density of states D F E . They contradict the previously admitted postulate according to which the drastic decrease of T c accompanying the Rb ordering results from a deep reduction of D F E . Our structural study has led us to abandon the previous hexagonal description for the C222 1 lower symmetry. Incidentally, these results emphasizein agreement with the density-functional calculations 43 how much the precise arrangement of the WO 6 octahedra within the WO 3 skeleton is sensitive to the concentration of conduction electrons brought by the alkali ions. The oxygen cage surrounding a Rb ion is rather large and allows large amplitude displacements, as noticed in the previous studies. This leads to Rb vibrations which are well decoupled from the rest of the lattice and, particularly, to well defined Einstein-like modes in the equato- rial xy plane-at least when all the Rb ions are present because these features rapidly attenuate when the vacancy content increases. The phonon spectra derived from our INS experiments extends up to a rather high energy (120 meV), due to the rigidity of the WO 6 octahedra, in front of which the BiO 6 octahedra of BKBO look quite soft. The lattice stability and dynamics of the stoichiometric bronzes are very well described by our density-functional calculations which are able to confirm that the stability of Rb 0.33 WO 3 is ensured by the C222 1 structure and not by the hexagonal symmetry, whereas the stability of Cs 0.33 WO 3 is compatible with the more symmetric P6 3 /mcm structure. Our INS data also indicate that decreasing the alkali content does not soften the structure at room temperature and that softening could also be ruled out at low temperature, below 30 meV-except for the Rb xy vibrations in the stoichiometric compound. We are tempted to conjecture that a reason why underdoping favors superconductivity could lay in the fact it slightly remodels the WO 6 octahedra and makes some associated phonons more active in the e-p coupling. Such phonons are to be searched for above 30 meV, i. e. in an rather unusual energy range but which yields strong contributions to the e-p coupling in BKBO, MgB 2 and the fullerides, for instance. The lower T c obtained in the tungsten bronzes, compared to the above materials, could partly result from the particular stiffness of the WO 6 octhaedra, the building bocks of these bronzes. Conversely, the stabilization of the SC state at higher temperatures, which has been observed in some marginal situations [START_REF]Extrinsic (probably interfacial) superconductivity has been observed in RbxWO3 at ∼8 K (Ref. 8 and the nucleation of high-Tc superconducting regions on the surface of Nadopped WO3 has been claimed by Levi et al[END_REF] could have something to deal with exotic rotations of the WO 6 octahedra at the surface or interface, due to reduced atomic coordination. In order to get more insight upon the "T c (x) paradox" we should need to complete our INS experiments at lower temperature and higher energy. Refining the lattice structure near the x = 0.20 limit could also be fruitful as well as extending similar investigations to the order-free and more symmetrical Cs x WO 3 . This could also help us to understand why superconductivity is destroyed by the slight modulation here produced by the alkali ordering: a phenomenon for which the HTB offer the unique illustration and which deserves particular theoretical efforts since it has all the potential to tell us something fundamental about the superconducting state.

FIG. 1 :

 1 FIG.1: Magnetic susceptibility of the RbxWO3 powder samples as a function of temperature. The difference between the data obtained on two samples of the same batch, for x = 0.25 and 0.33, gives an estimate of their absolute accuracy. The impurity contributions have been subtracted (see text). The inset corresponds to a measurement on a sample from another batch, with another magnetometer and a different sample holder, for which the absolute accuracy cannot be guarantied. Lines are only guides to the eye.

FIG. 2 :

 2 FIG. 2: Magnetic susceptibility of the RbxWO3 powder samples at 280 K and 120 K as a function of the rubidium content x. The previous data of Wanlass and Sienko 25 have been included ( ). The dashed line represents what would be the x dependence of a Pauli contribution χspin in a quasi-freeelectron model with an effective mass two times the electron mass mo (a diamagnetic contribution has been added to χspin in order to obtain χx ≈ -3.3 × 10 -8 emu/g for x = 0.33 ). Other lines are guides to the eye.

FIG. 3 :

 3 FIG. 3: (Color online) Temperature dependence of the C2221 cell parameters in Rb0.25WO3 (squares) and Rb0.33WO3 (circles); empty symbols correspond to bo = b, full symbols correspond to ao/ √ 3. Lines are second-order polynomial fits.

FIG. 4 :

 4 FIG. 4: (Color online) Generalized phonon density of states in Rb0.33WO3 ( ) and Rb0.20WO3 ( in red color) deduced from INS experiments at 300 K in the absence of cryostat; the inset displays a blow-up of the low-energy range.

2 ,FIG. 6 :

 26 FIG. 6: (Color online) Generalized phonon density of states in RbxWO3 at T = 300 K: (in red color) and T = 100 K: (in blue color).

FIG. 7 :

 7 FIG. 7: (Color online) Phonon density of states of Rb0.33WO3: DFT calculations (in red color) and IN6 experiment at T = 300 K (in blue color) deduced from the measured GDOS displayed in Fig. 4. The inset shows the weighting factor relating DOS and GDOS (see III D 1)..

  FIG. 9: (Color online) Calculated phonon density of states for two (P3 and C2221) Rb0.33WO3 and one Cs0.33WO3 (P63) structure.

FIG. 10 :

 10 FIG. 10: (Color online) Crystallographic structure of Rb0.33WO3 at 5 K.

FIG. 11

 11 FIG. 11: (Color online) Temperature dependence of the isotropic atomic displacement parameter B (parts (a) and (b)) and distortion (part (c)) in Rb.33WO3 and Rb.25WO3.

FIG. 12

 12 FIG. 12: (Color online) Partial phonon density of states in Rb0.33WO3 separated into contributions arising by projecting the eigenvectors into and perpendicular to the basal xy plane of the channels. Only the x-component is shown as it is indistinguishable from the y-component.

TABLE I :

 I Structural parameters refined for RbxWO3 with space group C2221 at 5 K (third, fifth and seventh columns) and 300 K (fourth, sixth an eighth columns). In each row, the upper data correspond to Rb0.33WO3 and the lower data to Rb0.25WO3.

	Atom Pos.	x		y		z
	W1 4	0.0000	0.4794(7) 0.481(2) 0.0000 0.4768(2) 0.472(2)	0.0000	0.0000
	W2 8	0.7596(3) 0.758(1) 0.7580(8) 0.759(3) 0.2473(6) 0.2492(8) 0.7583(9) 0.759(1) 0.759(2) 0.758(2) 0.254(1) 0.251(1)
	Rb 4	0.0097(2) 0.0065(5) 0.0015(9) 0.0022(8)	0.0000	0.0000	0.0000	0.0000
	O1 8	0.6065(3) 0.607(1) 0.8138(7) 0.815(2) 0.270(1) 0.2571(8) 0.6071(8) 0.6084(7) 0.816(1) 0.816(1) 0.266(2) 0.262(1)
	O2 8	0.7883(2) 0.7919(5) 0.0039(8) 0.004(3) 0.2233(4) 0.2230(7) 0.7895(5) 0.7907(5) 0.004(2) 0.004(2) 0.223(1) 0.2317(7)
	O3 8	0.6031(3) 0.6055(9) 0.1845(7) 0.181(2) 0.273(1) 0.2696(9) 0.6031(8) 0.6044(7) 0.182(1) 0.182(1) 0.269(2) 0.269(1)
	O4 4	0.5178(2) 0.5094(7) 0.5171(5) 0.5132(4)	0.0000	0.0000	0.0000	0.0000
	O5 8	0.

2333(1) 0.2400(3) 0.2286(3) 0.230(1) 0.0000(6) -0.0007(9) 0.2353(3) 0.2385(3) 0.2283(8) 0.2335(9) 0.0079(9) 0.0030(8)

TABLE II :

 II Agreement factors, cell parameters and atomic displacement parameters of Rb0.33WO3 and Rb0.25WO3 at T = 5 K and 300 K.

		Rb.33WO3	Rb0.25WO3
		T = 5 K T = 300 K T = 5 K T = 300K
	Rp (%)	9.79	12.2	17.2	11.6
	Rwp(%)	10.4	11.9	17.8	11.7
	χ 2	3.71	3.78	6.43	4.01
	RBragg(%)	4.15	5.29	9.58	5.74
	a( Å)	12.7509(1) 12.7887(2) 12.7766(4) 12.8056(4)
	b( Å)	7.37259(6) 7.3835(2) 7.3853(2) 7.3959(2)
	c( Å)	7.53086(5) 7.56749(6) 7.5037(1) 7.53745(8)
	BO ( Å2 ) 0.488(13)	0.83(2)	0.76(3)	0.88(2)
	B Rb ( Å2 ) 0.93(3)	3.51(6)	3.4(1)	4.60(8)
	BW ( Å2 )	0.33(2)	0.60(2)	0.2(3)	0.71(3)

TABLE III: Cation-anion distances for Rb0.33WO3 and Rb0.25WO3 at T =5 K and 300 K from the Rietveld refinement results given in Tables I and II; distortion is defined as P n i=1

TABLE IV :

 IV Calculated and experimental lattice parameters (from 21 for the Cs bronze). Rb 0.33 WO 3 . For both compounds and structures the calculated lattice parameters agree very well with the measured values, as displayed in TableIV. The dynamic response of M 0.33 WO 3 (M = Rb, Cs) is clearly separated into various vibrational bands. Using the fact that the DFT calculation provides us with the complete set of phonon eigenvectors we may decompose the density of states into its partial components. A further characterization is obtained by separating the partial DOS into contributions that arise by projecting the eigenvectors either into the basal x-y plane of the channels or perpendicular to it. In Fig.8we show the partial phonon DOS for Cs 0.33 WO

	Model Cs0.33WO3	a [ Å] 7.480	b [ Å] 7.480	c [ Å] b -a 7.687	√	3 [ Å]
	Experiment 7.4116(3) 7.4116(3) 7.5981(5)
	Rb0.33WO3 12.938	7.473	7.660	-0.0059
	Experiment 12.751	7.373	7.531	-0.0188

on 3 . The low-frequency part of the spectrum (region I) is dominated by the motion of the guest ion within the cage. This motion is characterized by a strong anisotropy. The motion within the basal plane has very little dispersion leading to a sharply peaked and narrow

)) decreases on heating and vanishes at room temperature as shown in Fig.3. Due to its higher symmetry and the better stability of the refinements, we chose to use the structure description with the symmetry of space group C222 1 . It was also applied to the data obtained for the x = 0.25 sample. Good quality Rietveld refinements were obtained at temperatures above 240 K (χ 2

= 4.01 at 300 K), indicating that the same type of structural distortion is present for this composition. In this sample, the ordering of Rb cations occurs between 200 K and 240 K as shown by the appearance of small superstructure peaks similar to those first observed by Sato et al.[START_REF] Sato | [END_REF] . Below 200 K, the agreements become slightly worse (χ 2 = 6.43 at 5 K) because the superstructure is not taken into account in this structural model. A summary of the refined parameters and principal interatomic distances are given in Tables I, II and III for T = 5 K and 300 K.

Acknowledgments

The authors would like to thank Jacques Marcus for his help in the preparation of the samples, André Sulpice for his contribution to the magnetic susceptibility measurements, Emanuelle Suard for assistance with experiment on the D2B diffractometer and Mark Johnson for his invaluable help with the computer codes.


Natalia I Vargas-Cuentas

Daniela Hidalgo

Avid Roman-Gonzalez

Michael Power

Robert H Gilman

Mirko Zimic
email: mirko.zimic@upch.pe

A Diagnosis of Autism Using an Eye Tracking System

Keywords: Autism spectrum disorders, eye tracking, diagnosis, M-CHAT

Autism Spectrum Disorders (ASD) are characterized by a deficit in social integration, language development, and restricted interests. ASD is defined as a prevalence development life disability. However, children who are early diagnosed and intervention improve long-term prognosis. This project proposes to detect autism in children at a first level (preclinical stage) using a tool "eye tracking" highly cost-effective and embedded in a tablet. The results obtained with this system have been compared with the outcomes of the Modified Autism in Children M-CHAT questionnaire.

I. INTRODUCTIÓN

CCORDING to some data presented in [START_REF]Prevalence of autism spectrum disorders: Autism and Developmental Disabilities Monitoring Network, 14 Sites, United States[END_REF], the prevalence of autism is 1 in every 88 people. In this sense, ASD is a permanent problem that affects a high percentage of the population. In the aftermath, the families of children with autism have some difficulties about the diagnosis because they are the ones who identify the first signs or suspicions in delaying the development of your child. The potential impact of this situation not only for the individual but also for the family and the government points to a significant need to identify tools for early diagnosis.

There are some aspects considered to refer to the difficulties of early detection of autismµ. The logical and likely problem of parents to detect subtle symptoms like those that characterize autism in their early stages (especially if it is the first child); lack of information from most pediatricians and other professionals to detect autism early, and the inadequacy of development assessment tools currently in use by specialists [START_REF] Mendizábal | Actas del VII Congreso de Autismo[END_REF] Currently, the diagnosis must be based on at least two levels of performance; at a first level is to looking within the healthy population for a child with series of signs of a high probability of ASD. These people go into a second phase where they held a series of diagnostic tests to rule out other diseases, and finally, register the case to have a clinical diagnosis [START_REF] Paz | Investigación epidemiológica en el autismo: una visión integradora[END_REF].

Currently, in Peru, there are not detection instruments of autism spectrum disorders adapted to the context of primary health care services. According to Diez-Cuervo, et al. (2005) [START_REF] Díez-Cuervo | Guía práctica para el diagnóstico de los trastornos del espectro autista[END_REF], specialized diagnosis is a complicated and costly procedure, under a clinical trial, reported. However, early detection of cases in which the diagnosis is indicated is a simple and inexpensive process, which will streamline performance.

For all above reasons, the present project aims to propose a method for early diagnosis of autism, noninvasive, efficient and the majority of Peruvians. This proposal will ensure screening in health systems and, therefore, increase the likelihood of early diagnosis and intervention in each case.

The project introduces an innovative tool, which generates a significant impact from its simplicity, allowing use in poor remote communities where there is a lack of specialists to diagnose autism in younger children, in which clinical symptoms are not evident. Furthermore, it is intended that this tool is accessible nationwide, seeking to be a resource for mass use and can be used by doctors not specialized in any pediatric unit or health center. The idea also is to develop a database of patients diagnosed with the aim to review each case and maintain adequate control.

The previous diagnosis will develop a particular model of intervention and a better outlook. For example, giving an early intervention for children with autism, 86% can develop a verbal communication skill, in contrast to 50% who do not receive any intervention [START_REF] Harris | Age and IQ at intake as predictors of placement for young children with autism: A four-to six-year follow-up[END_REF]. The interest in the early identification is due to the evidence accumulated over the last ten years; that establish that a particular, personalized early intervention for children and their families leads to an improvement in the prognosis for most children with ASD [START_REF] Díez-Cuervo | Guía práctica para el diagnóstico de los trastornos del espectro autista[END_REF]

II. BACKGROUND

The diagnosis of ASD is made from deficits in social and communicative behavior; besides the presence of repetitive and restricted behaviors. In the diagnostic assessments with standardized instruments such as ADOS, where direct observation of the child and ADI-R, where the child's parents are interviewed, it is required medical experts on the subject. Studies conducted in the US by the Centers for Disease Control indicate that the ADI-R and ADOS are used in less than 0.1% and 2.1% respectively for the diagnosis of autism made in the community. Other instruments and parent questionnaires and checklists are used in only 30% of these assessments while 67% use nonstandardized or validated tools [START_REF] Klin | Social visual engagement in infants and Toddlers with Autism: Early developmental transitions and a model of pathogenesis[END_REF].

As noted, one of the deficits that come with autism diagnosis is the social gap. Within this situation, the development of mutual look and preferential attention to the social interaction; in a study presented in [START_REF] Jones | Absence of preferential looking to the eyes of approaching adults predicts level of social disability in 2-year-old toddlers with Autism Spectrum Disorder[END_REF], where participated 66 children, of which 14 had a diagnosis of the autism spectrum, 36 children with normal development and 15 children with developmental delay but not autism. One shows ten videos to the children, in these videos an actress looking directly at the camera and developing a caregiving role. It found that children with ASD did not have a preferential binding in the eyes of adults who approach and prefer to see the region of the mouth. Setting the relationship between the eyes and the level of social deficit is also presented suggesting that could be useful for quantifying the social phenotype in early autism early within the development. The results indicate that the skills present in typical children were not found in children with autism at age two; notes atypical development that generates failures in social commitment. A child with ASD is learning in a world dominated by a particular world instead of social events [START_REF] Warren | Heterogeneity and homogeneity across the autism spectrum: the role of development[END_REF].

III. AUTISM DIAGNOSIS TOOL

A) Cost-Effective Portable System

Pierce, K., et al. (2011) tried to determine, in children with ASD from 14 to 42 months, the existence of a tendency towards geometric repetitions (for example, fixing the wheels of the car). The study provided strong evidence of some babies at risk for ASDs begin with an unusual preference for geometric repetition [START_REF] Pierce | Preference for geometric patterns early in life as a risk factor for autismo[END_REF].

The tool used in this research is based on "eye tracking" system that seeks to identify early changes in the visual preference of the child. The video that we use is divided into two scenes where a scene was composed of children participating in different games and social activities, and the second scene was composed by abstract in motion forms and curves with attractive colors. Finally, the idea is to have a Web server that automatically centralize information allowing store text files containing the personal data of each child, diagnostic data and other material that may be important to create an electronic health record. This record will allow monitoring and control of each child.

The block diagram of the "eye tracking" algorithm is given as shown in Figure 2. In Figure 2, one can observe the workflow step that the algorithm will follow to reach a final result, for this reason, three primary processes will be described below:

B) Modified Childhood Autism Questionnaire (MCHAT)

Considering the need to compare and validate the results obtained in this research, one will use a tool applied internationally to detect autism spectrum disorders in children aged between 18 and 60.

IV. TEST PROTOCOL

A) Procedures

After validation of judges screening survey, they settled and formed the different participating groups, contacted them and finally carried out the necessary psychological evaluations and confirmation procedures or diagnosis according to the results of the M-CHAT test.

B) Constitution of groups for evaluation:

As a result of preliminary tests that were conducted, it was identified that the sample size of this project should be 8 case children and 24 control children. So, it may reach 84% of statistics power to detect a difference of 55% between the null hypothesis of both ratios. Group 1, control children is 10% and the alternative hypothesis of proportion in Group 2, case children, is 65% using a one-sided chi-squared test with continuity correction, and a significance level of 5%.

The characteristics of the control children are male and female children between 18 months and 7 years old. No previous diagnosis of mental or neurological disease.

The case children were derived from the Instituto Nacional de Ciencias Neurologicas (National Institute of Neurological Sciences), they have a previous diagnosis of ASD and are receiving therapy within the Institute.

C) Evaluation:

Evaluations were performed in the "Instituto Medico del Lenguaje y Aprendizaje" -IMLA (Medical Institute of Language and Learning). The first provided information was the ethical considerations; at this stage, it was stressed that participation is voluntary, that there is complete confidentiality of personal data of the child, and the objectives of the research were explained. All it summarized in an informed consent that parents authorize the participation of their youngest child.

As a next step, we proceeded to the implementation of MCHAT/ES, which was developed by parents. It was necessary to gather additional information summarized in a sociodemographic poll. For example: environment where the child grows, sex, age, weight, height, district of origin, people living at home, marital status of the parents, level of education of father and mother, place for medical care, rooms in the home, materials floors, and a family history with a diagnosis ASD.

Finally, we proceeded to the assessment using the algorithm tool where the first visual stimulus presented to the child was a video. This video has a duration of one minute, which contains two scenes on the same screen: the left side is a social scene, and the right side is colorful moving objects. Webcam device made a video recording of the child watching two scenes. This video is the material that the software must process to quantify the percentage of time of child watching a scene or another.

V. RESULT ANALYSIS

A) Results of the analysis of the discriminative ability obtained by our diagnostic tool

The participating children had to watch five Videos of one minute. Each video contains a 10-second introduction, consisting of a lively current attractive and sound design.

On the other hand, the principal part of the video is 50 seconds long, composed of a divided screen into two without sound scenes, one social scene, and an abstract object scene.

Regarding the observation of the videos, one obtains the following results: As shown in Figure 4, only one could not see any video, this child belonged to the group of clinical cases. As shown in Table 3, diagnosis video 2 has a P value of 0.015. The P value should normally be in the range of 0.01 to 0.05 to be significant. For this reason, we can say that the Video 2 is one that contributes to achieving better discrimination of clinical case and control children.

Reasons for distraction

Number of children

B) Results of the analysis of the discriminative ability obtained by the MCHAT

For the evaluation process, the participating children were divided into two categories as seen in Table 3.

Category Diagnostic

No suspect Suspect M-CHAT (-) M-CHAT(+) TGD AUTISM Normal Development TOTAL Table 4 also shows the existence of a 16.6% (4 children) of control children who result as positive (+) in the M-CHAT test. One of them, within their sociodemographic record, recorded family history of ASD within the family (older sister).

VI. DISCUSSION

 On the MCHAT results, the negative subject (-) with a previous diagnosis, could be explained by the continuous therapy following since its first diagnosis, this probably is improving their prognosis and consequently result in an overlap in the outcome of the test M-CHAT.  Between the five videos used in the tests, according to the statistical analysis, it was observed that the Video 2 is the best for contributing to discrimination between autistic and non-autistic children.  The visual preference of the child, regarding social or abstract scenes, helps to determine the risk of autism in children. However, one need to determine the contribution percentage of distractions in the result.  For future tests, we will take into account the fact that children can always be in the company of his parents because, in this way, they feel safer to see the videos.

Fig. 1

 1 Fig. 1 Block diagram of the ASD diagnosis tool

Fig. 2

 2 Fig. 2 Workflow of the diagnosis algorithm a) Pre-processing: In this stage, one use techniques to improve the quality of the obtained image, a filter is performed to smooth, enhance edges and remove noise from the image. One converts images to grayscale values; finally, a contrast correction is performed. b) Processing: At this stage one make an extensive enhancement of the features of the image. Also, one performs a face coding of a child to adequately recognize that photography provided a face as input to the algorithm. On the other hand, a cascade algorithm was implemented with the primary objective of face detection, detection of both eyes, and eye detection for each of the child's eyes. c) Feature extraction: In this stage, one makes an ocular edge detection for correctly identifying the eye iris and eventually quantifying or counting the black pixels of the identified iris to discriminate what is the direction of gaze.

Fig. 3

 3 Fig. 3 Graphical User Interface (GUI)

Fig. 4

 4 Fig. 4 Number of watched videos vs. number of children vs. controls and cases

Table 1 :

 1 Number of children per number of watched videosAs shown in Table1, a higher rate of clinical controls and clinical cases could observe the five videos displayed by the software.

	Children	Number of	Control	Case
	number	watched videos	Childs	Childs
	14	5 Videos	11	3
	4	4 Videos	4	0
	5	3 Videos	4	1
	7	2 Videos	4	3
	1	0 videos	0	1

Table 2 :

 2 On the other hand, during the tests, one can identify the existence of different reasons that could cause disruption in the child as shown in Table2: Reasons for distraction and number of children As shown in Table2, the reason causing the disturbance in a greater number of children was boredom, as children had a tendency to get bored after seeing, at least, three videos. As we can see, other reasons for distraction with a high percentage of occurrence among children participating in the test occurred because the child was alone or a different person to her/his mother at the time of testing front video diagnostic tool.Finally, doing a statistical analysis of the obtained results, it was possible to get the following P values for each diagnosis video:

	Boredom	4
	Tiredness of the child	2
	Child sitting alone	3
	Testing child without his mother	3
	A disturbance in the environment
	(object or mom sitting incorrectly)	3
	Misbehavior	2
	Video	P Valium
	1	0.046
	2	0.015
	3	0.923
	4	0.223
	5	0.070

Table 3 :

 3 Diagnosis video vs. P valium

Table 4 :

 4 Distribution of participants according to diagnostic categoriesIn Table4, we can see that 87.5% of cases children were confirmed with the MCHAT diagnosis.

	1 (12.5%)	7 (87.5%)
	20 (83.3%)	4 (16.6%)
	21	11

Acknowledgements

This work was supported by INNOVATE Peru, 'Contrato N° 153 PNICP-PIAP-2015'; and FONDECYT -'01-2013-Fondecyt Financiamiento de Subvención para Investigación Postdoctoral'.


Avid Roman-Gonzalez
email: roman-gonzalez@ieee.org

Natalia I Vargas-Cuentas
email: natalia.i.vargascuentas@ieee.org

DESIGNING A WEB PLATFORM PARADIGM FOR SATELLITE IMAGES BASED ON USER PREFERENCES

The current satellite imagery management platforms are useful tools, but they assign labels with fix priorities to each patch of a satellite image based on the contents of the image. These tags with fixed priorities do not respond to all needs since each user is different and the uses given to the satellite images depend on the work carried out. Faced with this, we propose a new paradigm in which the priorities of the labels change according to the user who makes the request for the satellite image. For this purpose, we use machine learning and artificial intelligence techniques. With this proposal, one could have a platform that will give a better result at the time of search and manage satellite imagery.

I. INTRODUCTION

Satellite images give a very helpful, useful, relevant, and complete information in different fields such as environmental monitoring, disaster management, security and defense, mapping, marine monitoring, agriculture, cartography, and many other applications.

Currently, several platforms are providing the service to search, share, analyze, and manage satellite images. Typically, satellite images on these platforms are divided into patches, and each patch has different labels representing their content, these labels could be: 'water', 'forest', 'urban', 'field', among others.

Each of these labels has a particular priority according to their predominance in the patch of the satellite image that they represent.

With the described above paradigm, users are subject to these labels and must use the priority order of labels established in the database. However, each user is different, and everyone seeks and applies satellite images according to their needs, so the priorities are different from one to other users.

That is why in this paper we propose a new paradigm for an adaptive platform on which labels of the satellite images patches may be changing their priorities according to each user and application in which the satellite image will serve. The priority of the labels will be adapted in a personalized way depending on the activity and history search for each user. In that sense, a patch labels will have different priorities depending on the user requirements.

To implement this paradigm platform one must apply machine learning and artificial intelligence techniques.

One proposes this work motivated by the fact that the Space Agency of Peru (CONIDA) has made the purchase of a remote sensing satellite that was put in orbit last September 15th.

On April 24th, 2014, Peru signed the contract for the acquisition of an Earth observation satellite system. This agreement was signed with the French company Airbus Defence & Space.

It should be emphasized that Peru was not only acquiring a satellite, but Peru bought all satellite system that includes:

• Ground segment (ground station).

• Space Segment (satellite itself).

• Access to the constellation of French submetric, metric, and radar satellites. • It also includes technology transfer for Peruvian engineers.

This acquisition is a significant step for Peru in its foray into the space age. It has acquired technology with a sub-metric resolution satellite. With this technology, Peru becomes the first Latin American country to have a satellite with a capacity to detect objects smaller than one meter.

Among the many applications (both civilian and national security), we can mention: The beneficiaries of these services are public entities of government as well as regional and local governments, contributing to the socio-economic development, poverty reduction, and social inclusion; in addition to promoting scientific and technological research in the country.

The PeruSat-1 was launched on September 15th from French Guyana at 8:43 pm (Peruvian time). It is possible to see in Figure 1 an image of the launch.

By the above reasons, the acquisition of this satellite system is a significant contribution to the development of the country, and we must be prepared to take advantage of all the information we can provide our images. The continuation of this article is organized as follows: Section II shows the state of the art about platform paradigms related to satellite images. In Section III, the description of our proposal is presented. Finally, in Section IV the discussion and our conclusions will be mentioned.

II. STATE OF THE ART

This section describes the background of this study. The different management systems of satellite images across different platforms is presented.

The authors of [START_REF] Datcu | Information mining in remote sensing image archives: system concepts[END_REF] demonstrate a concept of a knowledge-driven content-based information mining system produced to manage and explore large volumes of remote sensing image data. The concept consists of an offline part and an online interface. The offline part aims the feature extraction, compression, generation of an unsupervised image content-index, and the ingestion of the catalog entry in the database management system.

In [START_REF] Datcu | Humancentered concepts for exploration and understanding of earth observation images[END_REF], a novel advanced remote sensing data processing system knowledge-driven information mining (KIM) is proposed. KIM system uses humancentered concepts (HCCs). HCC implements new features and functions (semantic level, collected knowledge, interactive knowledge discovery, and new user interfaces) for improving feature extraction.

In [START_REF] Aloisio | A dynamic earth observation system[END_REF], the authors present the SARA/Digital Puglia (Synthetic Aperture Radar Atlas). SARA is a remote sensing environment that uses grid technologies and high-performance computing for building a dynamic Earth observation systems for management data coming from space missions. SARA/Digital Puglia was developed in a joint research project with CACR/Caltech, ISI/USC, and the Italian Space Agency.

The authors of the work [START_REF] Gudivada | Content based image retrieval systems[END_REF] show a content-based image retrieval (CBIR) to effectively and efficiently use information from satellite image repositories. CBIR helps users retrieve relevant images based on their contents.

The research presented in [START_REF] Durbha | An information semantics approach for knowledge management and interoperability for the global earth observation system of systems[END_REF] shows an end-to-end process for collecting and distributing Earth observation (EO) data to suppliers and consumers worldwide. This process is prepared for the Global Earth Observation System of Systems (GEOSS). The authors explore the possibility of using modular ontologies for formulating smaller interconnected ontologies.

In [START_REF] Albrecht | User requirements for an Earth Observation (EO)-based landslide information web service[END_REF] the author present a user requirements analysis for an Earth Observation Based Landslide Information Web Service. The idea is to have a fast and efficient provision landslide information products.

The classical approach for designing a management platform for satellite images is to use a feature extraction technique for automatic labeling of the satellite image patches. Each satellite image patch can have many labels, each label with a different priority according to the picture content as the result of the feature extraction and classification process.

In Figure 2, one can observe a diagram block for a classical web platform paradigm. An example of the use in remote sensing application could be presented in [START_REF] Camps-Valls | A Special Issue on Advances in Machine Learning for Remote Sensing and Geosciences [From the Guest Editors[END_REF]. Using this artificial intelligence/ machine learning block, try to change the priorities of the satellite image patch according to the preferences of each user. Each user is different, and the application for which he will use the satellite image also is different. The label of a satellite image patch changes depending on the application. Would necessary to have a database and a control of the access to the system for each user. Using this historical database, the system must learn which label is most important for the user. In that sense, a patch labels will have different priorities depending on the user requirements. In Figure 3 one can see the block diagram of our proposal including all the strategic block and steps to develop the platform.

IV. DISCUSSION Y CONCLUSIONS Satellite images have many application, both, civil and military applications.

PeruSat-1 will provide around 300 images per day, so, a platform to manage this pictures, would be necessary.

Each satellite image user is different, and the application for which he needs the image also is different. So, the label priorities depend on the application.

Using an adaptative platform that changes de priority of the labels regarding the user, would increase the user satisfaction.

Fig. 1

 1 Fig. 1 Launch of the first peruvian remote sensing satellite PeruSat-1 viewed from the CNOIS (Centro Nacional de Operaciones de Imagenes Satelitales -National Center of Satellite Images Operation) in Pucasana -Peru via a big screen.

Fig. 2

 2 Fig. 2 Clasical aproach for a satellite image management platform

Fig. 3

 3 Fig. 3 Diagram block for the proposed paltfarm