J Herrero-Martín

J García

G Subías

J Blasco

C Mazzoli

M C Sánchez

Charge and orbital ordering in Fe and Mn perovskite oxides far from half-doping by resonant x-ray scattering

The emergence of superlattice periodicities at metal to insulator transitions in hole doped perovskite oxides responds to a rearrangement of the local atomic structure, and electron and spin density distribution. Originally, the ionic model based on a checkerboard-type atomic distribution served to describe the low temperature charge and orbital ordered (COO) phases arising in half-doped manganites. In the last years, the exploitation of resonant x-ray scattering (RXS) capabilities has shown the need to revisit these concepts and improve the picture. Yet, we have realised that COO is a more common phenomenon than expected that can be observed in a wide range of doping levels. Here we compare the experimental data recently collected by RXS on La 0.4 Sr 1.6 MnO 4 (x=0.60) and La(Pr) 1/3 Sr 2/3 FeO 3 (x=0.67). The first shows a COO phase similar to that found in the x=0.5 sample but angular peak positions vs. T denotes the incommensurability of superlattice reflections. Meanwhile, the analysis of the commensurate CO phase in the studied ferrite underlines the role of the structural changes also involving La(Sr) and O atoms.

Introduction

The metal-insulator (MI) phase transition in transition metal (TM) oxides continues to draw the attention of the scientific community in condensed matter physics. Within the assumed linkage of this process to lattice structure, charge distribution and spin and orbital magnetic moments, the precise role of the any of the corresponding order parameters has not been fully detailed yet. Among these materials, Mn-based compounds are one of the most studied families due to the interest on the colossal magnetoresistive properties they can exhibit. An ionic model was proposed by Goodenough [1] to explain the different magnetic structures present in La 1-x A x MnO 3 (A: alkali-earth) as a function of hole doping (x), i.e. the relation of Mn 3+ : Mn 4+ ions. For the particular case of x=0.5, this ratio is 1:1 and would facilitate their periodic array in the crystal lattice in the low temperature charge localised phase thus leading to the so-called charge ordering (CO) and orbital ordering (OO) phenomena. Since this figure reproduced reasonably well many of the macroscopic properties of these materials it did not significantly changed so far. Nevertheless, the development of new experimental techniques such as the resonant x-ray scattering (RXS) currently allows us to characterise the local geometry and electronic structure of TM atoms in charge localised phases, combining the atomic selectivity that provides x-ray absorption and crystal sites contrast characteristic of diffraction [START_REF] Materlik | Resonant Anomalous X-Ray scattering[END_REF]. The pioneer works on half-doped perovskites such as La 0.5 Sr 1.5 MnO 4 and Nd 0.5 Sr 0.5 MnO 3 [3,4] confirmed the existence of two well differentiated sites occupied by two Mn ions (approximated as Mn 3+ and Mn 4+ ) in the CO phase (below ~200 to 250 K). In agreement with previous results by x-ray diffraction [5], they showed that these sites order in the crystal lattice following zig-zag chains (as a checkerboard) propagating in the ab plane and leading to the appearance of a superlattice modulation originated in the charge segregation. Associated to it and with a doubled periodicity, single occupied e g orbitals of Mn 3+ ions would order following a CE-type scheme. This model has been generalised for half-doped MnO 7 series and similarly to other Co or Ni based oxides [6,7]. Nevertheless, in the last years an increasing number of both theoretical and experimental works have cast doubts on the validity of the ionic approximation. There have been detected two main problems. First, the charge segregation between dissimilar TM sites has been found to be much smaller than one electron at the time that the covalence with nearest O atoms has been remarked [8][9][10]. And secondly, CO phases have been found in doped manganites out of half-doping condition where the number of crystallographic sites do not match with the calculated expected ratio of +3/+4 ionic states [11]. It is convenient to remark here that the term CO is commonly used in the broadest sense, i.e. it comprehends the cases of a charge segregation between sites, no matter its magnitude. In spite of these results, CO systems based on different TMs continue to be generally described in terms of integer ionic states (TM n+ /TM m+ ), those where m-n=1 being the most widely studied. In this sense, focusing on systems showing CO phases with a ratio of sites ≠1 and/or m-n≠1 appears to be a direct way towards a better knowledge of the physics of electron localisation.

R 1-x A x MnO 3 (R: lanthanide), layered (or ~2D structure) R 1-x A 1+x MnO 4 compounds, intermediate R 2- 2x A 1+2x
Electron and x-ray diffraction results on La 1-x Ca x MnO 3 and La 1-x Sr 1+x MnO 4 have shown that the CO and OO modulations become incommensurate with the crystal lattice for x>0.5 [12,13] except for x~0.67 or 0.75, probably due to the fact that it can be expressed as a simple rational number (2/3, 3/4) and facilitates the array of two Mn sites with dissimilar oxidation state in a 1:2 or 1:3 relation. For 0.5<x<0.67, the modulation vector depends approximately linearly on x, which has been interpreted in terms of a charge density wave (CDW) of Mn e g electrons. Indeed, electron diffraction results have discarded the existence of charge stacking faults (i.e. a bimodal distribution of Mn sites) and indicated the presence of a superlattice with a uniform periodicity [14].

Charge ordering has also been subject of deep investigations in Fe oxides, where we can find a similitude with manganites. First studies by Mössbauer and neutron diffraction [15,16] showed that the T driven charge localised phases in La 1-x A x FeO 3 (A: Ca, Sr) occur in a wide doping range (x<0.7). Further results obtained by transmission electron microscopy demonstrated that the superlattice propagation vector q direction is found to be locked to (1/2 0 0) for x<0.5 and parallel to the [111] cubic perovskite direction for x>0.5 [17]. For x=2/3, it becomes commensurate with a (1/3 1/3 1/3) periodicity and it was postulated to be originated in a …AABAAB… sequence of two differentiated Fe ions, identified as A=Fe 3+ and B=Fe 5+ . Yet, the same propagation vector would be obtained if we consider B'=Fe 4+ , leading to a …AB'B'AB'B'… sequence. As we show further through this paper, the charge localisation is here strongly coupled to the stabilisation of lattice distortions affecting not only Fe atoms but also R and O.

In this work we summarise resonant x-ray scattering data collected on the over-doped layered manganite La 0.4 Sr 1.6 MnO 4 (x=0.6) at the Mn K edge and La(Pr) 1/3 Sr 2/3 FeO 3 (x=2/3) at the Fe K edge. We analyse the CO and OO phases with respect to the half-doped and under-doped systems. In the first case, superlattice reflections are found for the wave vectors q v,h+ ~(h+ε, h+ε, 0) and q w,h+ ~(h+2ε, h+2ε, 0), where 2ε=1-x, h is integer and considering the tetragonal I4/mmm space group. In particular, we present data for h=1, 2. For ferrites, using the primitive cubic perovskite structure notation (though real structure is discussed later) q' CO,h' =(h'/3 h'/3 h'/3) p , equivalent to q' CO,h' =(0 0 2h') hex in hexagonal coordinates (R-3c space group). Though expected to be equivalent, different spectra are recorded for H=2, 4, 5. A structural model here presented explains these divergences.

Experimental details

Single crystals of La 0.4 Sr 1.6 MnO 4 (LSMO-214) and R 1/3 Sr 2/3 FeO 3 (R: La, Pr) (L(P)SFO) were grown by the floating zone method as described elsewhere [18,19]. They were characterised by x-ray powder diffraction and electrical and magnetic measurements to control their quality. For RXS experiments, the Mn crystal was carefully cut along a surface normal to the [110] direction. Meanwhile, the ferrites were cut perpendicular to the [111] p . Data were recorded at the ID20 beamline in the ESRF in Grenoble, France. Incident x-rays were monochromatised to energies close to the Mn and Fe K absorption edges by means of a Si (1 1 1) crystal. Samples were mounted on a four (+1) circles diffractometer working in vertical scattering configuration (i.e. incident σ polarization) and equipped with a He close-cycle refrigerator for low T measurements. The additional circle in the diffractometer serves for φ azimuthal angle rotation around the scattering vector Q. The origin corresponds to crystallographic [001] and [-110] p parallel to the incident beam direction for LSMO-214 and LSFO, respectively. Polarisation of the scattered radiation was analysed (σ' or π') by means of a Cu (2 2 0) (Mn K) and MgO (2 2 0) (Fe K) single crystals at ~45 deg., radiation collection being performed by an avalanche photodiode. All spectra have been corrected for absorption. Figure 1. Left panel: (1.6 1.6 0) σσ' at φ=-5° (solid line), -50° (dashed) and -80° (dotted). The inset shows the intensity at the maximum of the resonance as a function of φ. Right panel: q v,1(2)+ reflections in σ-π' channel. Fluorescence (circles) is also shown. Inset: azimuthal evolution at the pre-peak (crosses) and main resonance (circles). Minima are zero. All spectra have been recorded at 80 K.

Results and discussion

Energy dependent spectra for the q w,2-~(1.6 1.6 0) reflection in the σ-σ' channel and the four possible q vi+ (i=1,2) in the rotated σ-π' channel in LSMO-214 (ε=0.2) at the Mn K edge are shown in Figure 1. I σ-σ' was absent in the latter reflections while a very weak σ-π' contribution (near the detection limit) cannot be discarded in the (1.6 1.6 0) once having subtracted the analyser crystal leakage (not shown here). The left panel shows that there exist both a resonant and off-resonant signal for q w,2-in the whole studied range of φ. The intensity at the resonance is ~ 10 -6 that of the Bragg (220) reflection at the same energy. By analogy to checkerboard model as established for the half-doped compound, this reflection would be the counterpart of the (h/2 h/2 0), with h odd, associated to CO. The results indicate the existence of a small charge disproportionation between Mn sites and a Thomson contribution due to little shifts of atoms from their ideal crystallographic positions in the I4/mmm system. The intensity at the maximum of the main resonance (after off-resonant contribution subtraction) shows little variations with the azimuthal angle as plotted in the inset. This is in contrast to the observations reported in other half-doped compounds [10]. These changes could be ascribed to either the different dimensionality or the incommensurate character of this reflection. In the right panel, q v,1(2)+ ~(0.8 0.8 0), (1.2 1.2 0), (1.8 1.8 0) and (2.2 2.2 0) are shown after normalisation to the

Intensity (arb. units) E (keV)

same scale. Following the analogy to the x=0.5 case, these would be ATS reflections [20] whose origin might be in the x 2 -z 2 /y 2 -z 2 OO. The identical main resonances confirm their same dipolar character while at the pre-peak a Q dependence is observed. Thus, it is interesting to note that its shape can be grouped into couples, q v,1+ ~ q v,2+ and q v,1-~ q v,2-. On the other hand, the inset shows that the azimuthal evolution at both the pre-peak and main peak follows a ~sin 2 φ dependence with coincident zero minima as reported for the half-doped compound [3].

Figure 2 plots temperature dependences of the diffraction angle 2θ of the superlattice (1.8 1.8 0) and the Bragg (2 2 0) atomic reflections. First, OO-kind reflection (1.8 1.8 0) peak is broadened, which is indicative of a shorter correlation length than for nuclear reflections. Second, we notice on their commensurability. The contraction of a tetragonal lattice parameter when lowering T is reflected in the drift of the angular position of (220) reflection to larger angles, about 0.2° from 240 to 100 K. In contrast, any variation is hardly detectable in (1.8 1.8 0). This would mean that Miller indexes are incommensurate to the crystal lattice and T dependent. Indeed, the actual (h k l) found in the experiment for q v and q w are typically deviated ~10 -2 Å -1 from ideal rational values. A lock-in to the latter has not been observed in the range from 80 to 220 K. It turns out evident that these results make difficult the direct applicability of the checkerboard model as understood for manganites with x=0.5 but rather agree with a picture where the electronic charge density is strongly coupled to the lattice, propagating as a CDW.

We do not discuss here on the magnitude of the formal charge segregation between inequivalent Mn sites. It remains as the subject for a future deeper analysis. In the case of La(Pr) 1/3 Sr 2/3 FeO 3 , the variation of 2θ in (4/3 4/3 4/3) p superstructure confirms the commensurate character of the CO phase (not shown here). In Figure 3 (a) we see the q' CO,H =(h'/3 h'/3 h'/3) p energy scans in the σ-σ' channel for h'=2, 4, 5 in PSFO. Resonances are observed at the Fe K edge energy for h'=4, 5, while (2/3 2/3 2/3) p shows a "valley". Off-resonant intensities are also highly dependent on Q. It is maximal for h'= 4 and much weaker for h'= 2, relative intensity for h'=2 is quite different. A smaller resonant signal correlates to previous results arguing that the charge segregation between different Fe sites decreases proportionally to R cation size [22]. We recently demonstrated that a lattice modulation involving not only Fe but also La(Sr) and O atoms is necessary in order to reproduce RXS spectra in LSFO. Furthermore, these results combined to x-ray absorption data permitted to discard the integer CO model based on a …+3+3+5+3+3+5… sequence. Simulations converged to a real average charge disproportionation of 0.6 e -, i.e. formal Fe +3.3 and Fe +3.9 ordered along the [111] cubic direction in a 1:2 ratio in combination with a displacement of La(Sr)O atomic planes in antiphase to Fe [21,23]. Spectra in figure 3 suggest that a similar but not identical structural model would be necessary to fit PSFO curves. All studied superlattice reflections disappear at T~180 K. Compared to Mn oxides, no OO-kind superstructure has been found in R 1/3 Sr 2/3 FeO 3 ferrites. Moreover, energy scans of the (h'/3 h'/3 h'/3) p reflections are identical as a function of the azimuth angle in R 1/3 Sr 2/3 FeO 3 ferrites, as demonstrated in figure 3(b). In manganites, the appearance of the OO-kind superstructure is usually explained in terms of the partial occupation of lowest energy e g orbitals, in direct correlation to the development of a Jahn-Teller distortion in Mn atoms that increases a Mn-O pair bond length. This type of distortion seems to be absent in ferrites. The description of Fe 4+ (3d 4 ) as a low spin system without e g electrons is in agreement. The comparison of CO/OO phases in layered and non-layered samples can help to decouple the role of geometrical and electronic order parameters. Actually, due to the different dimensionality of the lattice, the e g orbitals involved in the OO formation in R 0.5 A 0.5 MnO 3 and La 0.5 Sr 1.5 MnO 4 are thought to be different [24].

Conclusions

We have investigated the charge and orbital ordered phases in La 0.4 Sr 1.6 MnO 4 and La(Pr) 1/3 Sr 2/3 FeO 3 by RXS at the Mn and Fe K absorption edges. The transition metal is in a formal intermediate oxidation state in both samples, i.e Mn +3.60 and Fe +3.67 , respectively. In the case of the Mn oxide, recorded CO and OO spectra show reminiscences from the well known half-doped (x=0.5) parent compound. However, in comparison to the latter, peaks intensities are strongly reduced (a factor ~10 2 ) and considerably broadened (unpublished data) due to a shorter correlation length. A Mn bimodal distribution model considering charge-stacking faults or COO phase correlated "melting" islands would be then plausible. Though, the incommensurate character these superlattice reflections appear to have (fig. 2) seems hardly reconcilable with a model where CO is only supported by Mn atoms. Other experimental results point also to discard this possibility and support a continuous charge modulation, i.e. a CDW model [14]. This could commensurate to the lattice for particular rational values of hole doping, as x=1/2 and 2/3. CO is also observed in R 1-x S x FO in a wide range of hole-doping, where similar commensurateincommensurate coupled electron-lattice modulations have been proposed to explain the observed phenomenology. For x=2/3, we have shown that Pr based sample modulated crystal structure in the CO phase must be very similar to that we proposed for the La sample [21]. Here we argued that small cooperative displacements of Fe, La(Sr) and O atoms are necessary to account for the measured RXS spectra and that Fe charge segregation was not very significant.

We realise that the rich phenomenology of COO phases in mixed valence transition metal oxides still leaves open questions, and further experimental and theoretical efforts must be done in order to improve the actual picture.

Figure 2 .

 2 Figure 2. Temperature dependence of 2θ angular position in (220) Bragg and (1.8 1.8 1.8) superlattice reflections. Color (arbitrary units) varies linearly with intensity from blue to red scale.

  5. The comparison to LSFO [21] reveals a similar shape in all spectra though resonances (h'=4, 5) are less marked in Pr sample and

Figure 3 .

 3 Figure 3. (a) Energy dependence of superlattice reflections in PSFO at 100 K. (b) Energy profile of LSFO (4/3 4/3 4/3) p for φ=-15 (solid), 30 (dashed) and 75 (dotted) degrees.

Acknowledgements

The authors wish to thank ESRF for beamtime granting and financial support from Spanish MICINN FIS2008-03951 and DGA Camrads projects.


J Àn Galdun

Jean-Marc Thiriet

AND J ÀN Ligu Š

STUDY OF DIFFERENT LOAD DEPENDENCIES AMONG SHARED REDUNDANT SYSTEMS *

Keywords: Shared redundancy, Dependability, Networked control systems

Study of different load dependencies among shared redundant systems

1. Introduction. To be able to obtain relevant results of reliability evaluations for complex systems, it is necessary to describe the maximum of specific dependencies within the studied system and their influences on the system reliability. Different methods or approaches for control systems' reliability improvement are developed in order to be applied to specific subsystems or to deal with dependencies among subsystems. A classical technique consists in designing a fault-tolerant control [START_REF] Spooner | Fault-Tolerant Control for Automated Highway Systems[END_REF] where the main aim is to propose a robust control algorithm. Guenab and others in [START_REF] Guenab | Fault-tolerant control system design: A reconfiguration strategy based on reliability analysis under dynamic behaviour constraints[END_REF] deal with this approach and reconfiguration strategy in complex systems, too.

On the other side is the design of reliable control architectures. Probably the most used technique is to consider the redundant components which enlarge the system structure and its complexity too. Active and passive redundancy is the simplest way how to improve dependability attributes of the systems such as reliability, maintainability, availability, etc [START_REF] Laprie | Dependability: Basic Concepts and Terminology[END_REF]. However, as it was mentioned the control structure turns to be more complex due to an increasing number of components as well as the number of possible dependencies among components, it is in particular the case for Networked Control Systems [START_REF] Mechraoui | Co-design for wireless networked control of an intelligent mobile robot[END_REF] [START_REF] Ghostine | A Framework for the Reliability Evaluation of Networked Control Systems[END_REF].

The paper introduces complex networked control architecture based on cascade control structure. The cascade structure was chosen purposely due to its advantages. This structure is widely used in industrial applications thanks to positive results for quality of control which are already described and generally known [START_REF] Brosilow | Techniques of Model-Based Control[END_REF]. On the other side it offers some possibilities of system reliability improvement. There are potentially redundant components such as controllers (primary, secondary). If more than one network is implemented we could consider them as potentially redundant subsystems too. Finally if the physical system allows it, it is possible to take profit from sensors. The cascade structure and other features are introduced in more details in the third part.

The paper is organised as follows. After bringing closer the research background, the shared redundancy is introduced. The controllers and networks are presented in more details in order to show some dependencies which could be appeared when a shared redundancy approach is implemented. In the next part are presented networked topologies considered as cascade control (CC) structure of the 4-rotor minihelicopter (drone) model [START_REF] Castillo | Real-Time Stabilisation and Tracking of a Four Rotor Mini-Rotorcraft[END_REF]. Using Petri nets were prepared the models of the introduced quasi-redundant components as well as drone's control structure. A simple model of the two quasi-redundant subsystems is evaluated. Finally, are proposed the simulation results of the mentioned simple two components model as well as the model of the complex drone's structure with short conclusion.

2. Research Background. Control architecture design approach was taken into account by Wysocki, Debouk and Nouri [START_REF] Wysocki | Shared redundancy as a means of producing reliable mission critical systems[END_REF]. They present shared redundancy as parts of systems (subsystems) which could replace another subsystem in case of its failure. This feature is conditioned with the same or similar function of the subsystem. Wysocki et al. introduce the shared redundant architecture in four different examples illustrated on "X-by-Wire" systems used in automotive applications. Presented results shown advantages of this approach in control architecture design.

The shared redundancy approach involves the problematic of a Load Sharing [START_REF] Bebbington | Reliability of Modules with Load Sharing Components[END_REF]. Thus, some of the components take part of the load of the failed components in order to let the system in functional mode. Consideration of the load sharing in mechanical components is presented by Pozsgai and others in [START_REF] Pozsgai | Models to Consider Load-Sharing in reliability Calculation and Simulation of Systems Consisting of Mechanical Components[END_REF]. Pozsgai and others analyze this type of systems and offer mathematical formalism for simple system 1-out-of-2 and 1out-of-3. Also there are some mathematical studies [START_REF] Bebbington | Reliability of Modules with Load Sharing Components[END_REF] of several phenomena appeared on this field of research. Bebbington and others in [START_REF] Bebbington | Reliability of Modules with Load Sharing Components[END_REF] analyze several parameters of systems such as survival probability of load shared subsystems.

3. Shared Redundancy. Specific kind of redundant subsystems which have similar features such as active redundancy however gives us some additional advantages which will be introduced in further text. This kind of spares represents another type of redundant components which are not primary determined as redundant but they are able to replace some other subsystems if it is urgently required. This type of redundancy is referred as shared redundancy [START_REF] Wysocki | Shared redundancy as a means of producing reliable mission critical systems[END_REF] or quasi-redundancy [START_REF] Galdun | Reliability increasing through networked cascade control structure -consideration of quasi-redundant subsystems[END_REF]. Due to its important advantages it is useful to describe this kind of spares in order to show several non-considered and non-evaluated dependencies which could have an influence to the system reliability. Identification and description of this influence should not be ignored in order to obtain relevant results of the reliability estimation of the systems which involve this kind of spares.

As it was mentioned above, the shared redundancy (SR) mentioned by Wysocki and others in [START_REF] Wysocki | Shared redundancy as a means of producing reliable mission critical systems[END_REF] is in further text taken into account in the same meaning as a quasiredundant (QR) component. Thus, quasi-redundant components are the parts of the system which follow their primary mission when the entire system is in functional state. However, when some parts of the system fail then this function could be replaced by another part which follows the same or a similar mission, thus by quasiredundant part. The quasi-redundant components are not primary determined as active redundant subsystem because each one has its own mission which must be accomplished. Only in case of failure it could be used. In NCS appears the question of logical reconfiguration of the system when the data flow must be changed in order to replace the functionality of a subsystem by another one. For example, some new nodes will lose the network connection and the system has to avoid the state when packets are sent to a node which does not exist. Thus, the main features of the shared redundancy could be summarized as follows: "Quasi-redundant component is not considered as primary redundant component such Generally in networked control systems, three kinds of quasi-redundant components (subsystems) could be considered:

• QR controllers.

• QR networks.

• QR sensors. Hence, a necessary but not sufficient condition is that a control structure where SR could be considered has to be composed at least of two abovementioned subsystems (controllers, networks, actuators). The subsystems should have similar functionality or construction in order to be able to replace the mission of another component. In case of quasi-redundant components there are several limitations. In order to take profit of quasi-redundant networks, it is necessary to connect all nodes in all considered QR networks. Thus, in case of different networks the components should have implemented all necessary communication interfaces. In case of QR controllers the hardware performance has to allow implementing more than one control task.

Third mentioned components are sensors. Consideration of the sensors as QR components has important physical limitations. In order to be able to replace a sensor for measuring a physical value X by another one for measuring Y it is necessary to use "multi-functional" smart sensors. We can suppose that some combination of the physical values can not be measured by using one sensor due to the inability to implement the required functionality in one hardware component.

Other limitation is the distance between failed sensor and its QR sensor which could have a significant influence to the possibility of its replacing. Generally, implementation of the QR sensors within control system structure could be more difficult than the application of the SR approach on controllers or networks.

There are several naturally suitable control structures which could implement the shared redundancy approach without other modifications such as cascade control structure (Fig. 3.1). This structure is often used in industrial applications thanks to its important features which improve the quality of control. With using cascade a control structure there are several constraints [START_REF] Wysocki | Shared redundancy as a means of producing reliable mission critical systems[END_REF]. The main condition requires that the controlled system must contain a subsystem (secondary subsystem FS(s) -Fig. 3.1) that directly affect to the primary system FP(s). Thus, the cascade structure composes of two independent controllers which can be used in order to implement the shared redundant approach.

Usually for secondary subsystems there is a condition of faster dynamics than primary process. This condition must not be fulfilled [START_REF] Wysocki | Shared redundancy as a means of producing reliable mission critical systems[END_REF]; in this case, some modifications of conventional cascade structure (Fig. 3.1) and control laws must be provided.

3.1. Quasi-redundant controllers. In the previous text, several suitable control structures were briefly introduced. As it was shown the controllers covered by these structures could be considered as quasi-redundant components by default. Thus, the hardware of both components could be shared in order to implement a shared redundant approach.

Let's consider the networked cascade control system shown in figure 3.2. The system is composed of five main components (Sensor S 1 , S 2 , controllers C 1 , C 2 and actuator A) and two networks. The communication flow among components is determined by its cascade control structure. Thus, sensor S 1 sends a measured value to controller C 1 (Master), the controller C 2 (Slave) receives the values from the sensor S 2 as well as the controller C 1 in order to compute an actuating value for the actuator A.

Each part of the system (components and networks) presents independent subsystem. However, when quasi-redundant components are studied, the system is not considered as composed of independent components. Depending on the performance parameters of the used hardware equipment in the control loop, a specific influence on the system reliability should be taken into account. Thus some dependencies should not be ignored in the dependability analysis. In the NCCS shown in Fig. 3.2 we could consider controllers C 1 and C 2 as the quasi redundant subsystems (components). Both QR controllers have a primary mission which should be followed. Thus, a controller C 1 controls outer control loop and controller C 2 stabilizes inner control loop. However in case of failure of one of them, we could consider the second one as a kind of spare.

As it was mentioned previously, the controllers follow their primary mission stabilization or performance optimization of the controlled system. Therefore, in regards to the similar hardware, it allows sharing the computing capacity and executing different tasks. Thus, in order to implement the SR approach, both controllers have to encapsulate both control tasks -for the outer and the inner control loop (see the cascade control structure in figure 3.1).

In non-failure mode the primary task is executed in both controllers. However, in case of controller's failure (primary or secondary) non-failed controller starts execute both tasks and computes actuating value for primary as well as secondary subsystems. In this case we can suppose two scenarios.

The first one supposes that the controller is able to execute all the necessary tasks within the required sample periods (Fig. 3.3a). Thus, no delays or other undesirable consequences are expected. In this case the behavior of the quasi-redundant com- ponent is similar as in the case of active redundant components. Thus, in the case of failure of one of the components, the second takes care about its mission until its failure.

Figure 3.3b shows a second case when time to execute both necessary tasks is greater than the required sampling period. Thus, the controller will cause the delays which have significant influence to the system stability [START_REF] Galdun | Definition and modelling of the communication architecture for the control of a helicopter-drone[END_REF] [START_REF] Ligusova | Effect of Element's Initialization in Synchronous Network Control System to Control Quality[END_REF]. Therefore, this delay could be known which allows its partially compensating by using several methods [START_REF] Nicolescu | Stabilité systèmes à retard -Aspects qualitatifs sur la stabilité et la stabilisation[END_REF]. Thus, we can suppose that the system destabilization will not occur immediately after the first delay and we are able to compensate it for some time interval. Thus, quasiredundant controller does not fail immediately but its reliability decreased.

There are several situations when this scenario could be considered. In critical systems where the failure of an important component could cause undesired damages or other dangerous consequences, the shared redundancy approach could help to allocate some time interval in order to maintain the system in a safe state. Thus, the SR approach can be a significant technique to secure the system before a damage risk.

3.2.

Quasi-redundant networks. The second part of the NCS which could be taken into account as SR subsystems are networks. Let's suppose a system with two networks (Fig. 3.2) where all components could communicate (connect) on these networks (N 1 and N 2 ) if it is needed. In this case we can apply the SR approach on this system.

Considered functionality of the quasi redundant networks is as follows. Both networks transmit required data -network N 1 transmit data from S 1 to C 1 and from C 1 to C 2 such as network N 2 from S 2 to C 2 and from C 2 to A. Thus both networks are active and allocated during the system mission. The same as in the case of QR controllers: when a network failed, the second one can take its load after a system reconfiguration. Thus, all required data are sent through the second network. Hence, two similar scenarios as with the controller task execution could be described. The amount of transmitted data on the network with a specified bit rate has logically influence on the probability of failure of the network (of course this depends on the network type and other parameters mentioned). This influence could be ignored when the network performance parameters are sufficient. However, we can suppose that the probability of network failure is increasing simultaneously when the network load increases.

The characteristic between network loading and its bit rate depends on the net-work type and have to be measured in real network conditions in order to determine the type of dependency -linear or nonlinear. Not only the network bit rate can be important however other network limitations such as maximal number of nodes connected to the network, etc. All limits of the QR subsystems can create dependencies with direct influence on the system reliability. Primary, we could consider these dependencies as undesirable but in case of critical failures this SR approach gives some time to save the system.

When NCS with an SR approach are analyzed, this characteristic should be included in the prepared model and further evaluated in order to determine its influence to the reliability of the whole NCS.

3.3. Different scenarios in shared redundancy. When certain dependencies are ignored we could regard on the control system with QR components as a control structure with active redundant components. However, there are several important scenarios when the reliability of the system could be decreased in order to prevent dangerous consequences or other undesirable events.

These scenarios could appear when some conditions could not be fulfilled (insufficient execution time or network bit rate) but the system need some time in order to take a safe state. Hence, it is necessary to identify and describe the influence of these dependencies which leads to more relevant results. Thus, prevent from too pessimistic or too optimistic results of the reliability analysis of the considered systems. The dependencies could be distinguished as follows:

• active redundant dependency,

• single step change of the nominal failure rate λ n ∈ 0; 1 increased once by a constant value -step load change, • time depend change of the nominal failure rate λ n -functional dependency-the load of the subsystem is changed with time passed from speared subsystem failure, 1. linear, 2. nonlinear. Let's assume that the destabilization of the system does not occur immediately after the first delay on the network caused by insufficient controller's hardware or network's parameters. Thus, the quasi-redundant controller does not fail immediately but in this case its failure rate increases which correspond consequently to a decreased reliability.

Thus, in case of the active redundant dependency we suppose that a quasiredundant subsystem has sufficient capacities in order to follow its primary mission as well as the mission of the failed subsystem (or subsystems).

A single step change of the nominal failure rate of the subsystem is considered in the case of subsystems where the failure rate of the quasi-redundant subsystem is changed (increased) once by a constant value (Fig. 3.4) during its life time. Thus, the new increased failure rate λ remains constant during further life time of the subsystem. For example, let's suppose a NCS with two Ethernet networks where one of them has failed and consequently the system is reconfigured and all nodes (components) start to communicate through the non-failed network which has a sufficient bit rate capacity in order to transmit all the required data. However, the amount of data has been increased which consequently increases the probability of packets' collisions (under the assumption of a classical CSMA/CD protocol, for instance). Thus, the probability of failure (failure rate) has been increased up to the new value λ .

A third case considers the change of the nominal failure rate λ n which depends on the time passed from the moment of the failure until current time of the working of the quasi-redundant subsystem which encapsulates the executing necessary tasks (own tasks as well as tasks of the failed subsystem). Thus, a functional dependency has to be considered. This dependency of the change of the failure rate λ n could be described by a linear or nonlinear dependency / function. We could study the previous example of the system with two networks. However, in this case the bit rate of the second (nonfailed) network is not sufficient. Consequently delays in data transmission as well as other consequential undesirable problems such as system might be caused. We can suppose that the non-failed network will fail in some time. Thus, the nominal failure rate λ n of the second network is now time dependent and is linearly or nonlinearly increased until the system failure. Mentioned examples with related equations are further discussed in more details. Let's suppose that the reliability of the system R(t), probability of the failure during time interval 0; t , is characterized by a nominal failure rate λ n ∈ 0; 1 . Let's suppose a system with two subsystems S 1 and S 2 (such as the networks in the previous examples) whereas the subsystem S 1 will fail at first and then the quasi-redundant subsystem S 2 will follow both missions (S 1 and S 2 ). In figure 3.4 are shown two above mentioned scenarios when the nominal failure rate λ n of the subsystem is increased by a constant value or by a value which could be described as a linear or nonlinear function (functional dependencies).

At first increasing the failure rate λ n one time by a constant value (see Fig. 3.4) will be dealt. It corresponds to the reliability reduction of the quasi-redundant subsystem S 2 by increasing the failure rate, during its mission, from its nominal value λ n up to new λ . Consequently, the system will follow its primary mission thanks to the QR subsystem S 2 but its failure rate is already increased and consequently the probability of failure of S 2 is higher. The difference between nominal λ n and increased λ failure rate will be called decrease factor d R . Thus, the mentioned constant value is characterized by the decrease factor d R of the QR subsystem and a new changed failure rate λ at the fail time t f is given by the followed simple formula:

λ = λ n + d R (3.1)
The failure rate increases only one time by the specified value and the QR subsystem S 2 with a new constant failure rate λ will follow both missions of its own mission and mission of the failed subsystem S 1 .

The second case shown in figure 3.3 considers the reliability reduction where the failure rate λ n is increased during the working of the subsystem S 2 by a specified decrease factor. This change of the nominal failure rate depends on time whereas with time extending the failure rate of the S 2 is got near to 1 (system failed). Thus, a decrease function f d R (t) is represented by a linear or nonlinear characteristic and depends on the real subsystem which is considered as quasi-redundant. Thus, an increased failure rate λ of the subsystem S 2 depends on time t and is given by the following formula:

λ (t) = λ n + f d R (t) (3.2)
As it was mentioned, the decrease function f d R (t) can be represented by a simple linear function, for example,

λ (t) = λ n + d R 10 -3 (t + 1 -t f ) (3.3)
where t + 1 allows changing the nominal failure rate λ n at the moment of the failure at time t f .

On the other side a nonlinear exponential function can be considered as follows:

λ (t) = λ n + e d R (t-t f ) (3.4)
where λ is the value of the increased failure rate, λ n is the nominal failure rate of the component, t f is the time of the failure of the component, d R is the decrease factor which has a direct influence on the increased failure rate.

Application to a mini-drone helicopter.

The NCC structure is applied for the control of a four rotors mini-helicopter (Drone, Fig. 3.5). The proposed control structure for this real model is as follows. The NCC architecture is composed of one primary controller (Master) and one secondary controller (Slave), thirteen sensors, four actuators and two communication networks.

The Master is designed for attitude stabilization (control) through Slave controller for angular velocity control for each propeller. The aim of the control is to stabilize coordinates of the helicopter [START_REF] Pozsgai | Models to Consider Load-Sharing in reliability Calculation and Simulation of Systems Consisting of Mechanical Components[END_REF].

The controllers are used as quasi-redundant components within the presented networked cascade control system (further only NCCS). They use the same control algorithm (propeller's angular velocity control) but with different input data (set point, system output, etc.) Hence, in case of failure, one of them could retransmit all the required data to another one, whereas pre-programmed control algorithm should compute the actuating value. Thus, the failed controller is replaced by a second one which starts to compute the actuating value.

Other quasi-redundant parts of this control structure are networks (Fig. 3.6). As in the case of controllers, one of the networks can compensate another one after a system reconfiguration. Usually, two networks are primary designed due to reduction amount of transmitted data. However, in case of network failure all data could be retransmitted through the second one.

The described approach for subsystem's failure compensation by using the shared redundancy requires a logical reconfiguration of the NCCS. Thus, in case of failure the hardware configuration is non-touched but communication ways must be changed in order to transmit the data to a non-failed component or through a non-failed network. 4. Simulation and results. All the presented networked control architectures (Fig. 3.5, 3.6) were modelled by using Petri nets. This tool was chosen thanks to its ability to model different types of complex systems and dependencies within them. To provide the reliability analysis, the Monte Carlo simulation (further only MCS) method was used. The multiple simulations of the modelled architecture [START_REF] Spooner | Fault-Tolerant Control for Automated Highway Systems[END_REF] are provided to obtain the reliability behavior of the basic two quasi-redundant components (for example two controllers in structure).

Model of the system covers the simulation of the random events of the basic components of the system such as sensors, controllers and actuators as well as the network's random failures. Software used for model preparation is CPN Tools which allow multiple simulation of the model in order to obtain statistically representative sample of the necessary data to determine the reliability behavior of the studied model.

As it was mentioned, the simulation of the simple two quasi-redundant compo- We can see there are five curves. Two non-dashed curves show the studied system as a system with two active redundant components (thus, d R is equal to zero -first curve from the top) and as system without redundant components (thus, the system composes of two independent components without redundant relation -first curve from the bottom). These two curves determine borders where the reliability of the studied system can be changed depending on the value of the decrease factor d R .

As we can see from figure 4.1, a single increasing of the nominal failure rate λ n of the non-failed components by the same value as was nominal failure rate λ n up to λ = 0.002 (d R = 0.001) cause a significant reduction of the reliability. Table 4.1 show several values of the life time (parameter MTTFF) for the studied system. Each table (Table 4.1, 4.2, 4.3) shows the life time of the studied components as active redundant subsystems (d R = 0) and as independent subsystems (d R = 0.999). From the value of the decrease factor d R = 0.01 the life time of the system significantly improves (18% and more). The results of the linear and nonlinear failure rate increasing are shown in tables 4.2 and 4.3. In all tables are noted the percentual value of the increased life time corresponding to the decrease factor. Table 4.1 shows the MTTFF parameters of both complex mini-helicopter structures. In the first drone structure (Fig. 3.5) two quasi-redundant controllers are considered. In the second structure (Fig. 3.6) two groups of quasi-redundant subsystems are considered and simulated -the controllers and the networks. In all simulated systems was observed the influence of the single step of the failure rate by a value specified by the decrease factor d R . The same as in tables 4.1 -4.3,

λn = 10 -3 Act. red. d R = 0 d R = 0.001 d R = 0.005 d R = 0.01 d R = 0.1 (λ = 10 -3) (λ = 0.002) (λ = 0.006) (λ = 0.011) (λ = 0.101) MTTFF[Tu]
1503 (+ 300%) 1002 (+200%) 667(+34%) 589(+18%) 509(+2%) λn = 10 -3

No red. d R = 0.999 (λ = 1) MTTFF [Tu] 499 there are shown the life time of system corresponding to different decrease factors 2.10 -3 , 10 -2 , 59.10 -3 . We can see that increasing the component's nominal failure rate λ n by a decrease factor equal to 59.10 -3 , which represents approximately 59 times higher the failure rate, has a significant influence to decreasing the life time of the system. The results are a little bit better than in the case of the system without redundant components (d R = 0.999), but we could see that they are almost the same. The drone's structure composes of twenty (twenty-one -structure with two networks) components -thirteen sensors (3 gyro-meters, 3 magneto-meters, 3 accelerometers, 4 rotors' angular velocity sensors), two controllers, four actuators and one (two) networks. Due to the high ratio of independent components and shared redundant components within the drone's structure (18 independent and 2 quasi-redundant -Fig. 3.5) there is a difference between life times for minimal and maximal d R is significantly smaller (about 11% and 22%) than in the case of a basic two components subsystem (Table 4.1, 4.2, 4.3).

The Mean Time Before First system's Failure is significantly longer in the case of a basic two component subsystem than in the drone's case. As it was mentioned above this is caused by the difference in complexity between basic and drone's NCC architecture. In case of comparison between two drones structures (Fig. 3.5, 3.6) the results are better for architecture with two networks which is composed of two quasi-redundant subsystems -controllers (Master, Slave) and networks when the decrease factor is smaller than 59.10 -3 . The increasing of the nominal failure rate by the decrease factor greater than 59.10 -3 significantly decreases the life time of the drone. On the other side, even if the controller loading will change its failure rate approximately ten times (d R = 10 -2 ) the system's life time is about 7% longer than in the case of the system without a shared redundant approach implementation.

Reliability approximation.

In previous article states we focused on the description of the dependencies among QR components and their influence to the final reliability of the systems. The aim of this research is to propose a simple analytical method which describes the reliability behavior of the shared redundant subsystems with dynamically changed failure rate. Hence, in next states we introduce an an- alytical equation which allows approximating the reliability of the two component system. Of course, a quasi-redundant approach is considered. Thus, a finally simple method for the dependability analysis is proposed as an extension of the common known methods for the dependability analysis. The proposed method for reliability behavior approximation supposes that both quasi-redundant components have the same or similar nominal failure rate where differences are small and could be ignored.

As it was mentioned above, the system composed of two QR components is considered. In this case study, we introduce only the results for reliability approximation where a single step change of the failure rate (further only FR) is considered. This FR behavior is described in the previous part of the article (3.3) by equation 3.1. Thus, let's suppose two QR components with the nominal failure rate λ n and define the decrease factor d R , then the reliability R 2qr (t) behavior of the QR subsystem composed of both components can be described as follows:

R 2qr (t) = 1 - 2 i=1 (1 -e -(λn+kid R )t ) (4.1)
where k i is the approximated coefficient. The parameter decrease factor d R and approximated coefficients of equation 4.1 are shown in table 4.5. In each row of the table is shown the decrease factor with the corresponding value of the coefficients k 1 and k 2 . The table shows several different values of the decrease factor whereas non-mentioned values can be easily approximated by using an appropriate method.

The maximal error of the approximation given by the parameters of the equation 4.2 is less than 1

R 2λn (t) = 1 - 2 i=1 (1 -e -(λn+ d R 2 )t ) (4.2)
where d R is the decrease factor and λ n the nominal failure rate of the QR components. It is necessary to explain that the error of all the approximations converge to the highest mentioned limits (1% for table's coefficients) in the bottom part of the reliability curves where the reliability of the system is smaller than 0.4. Thus, in live period when a component replacement could be already too delayed. 4.2. MTTF parameter approximation. Each quasi-redundant subsystem does not exceed the limits of the bound of the minimal (M T T F min ) and maximal time life (M T T F max ) of the quasi-redundant subsystem. The parameter M T T F max represents the maximal time life of the QR subsystem which could be obtained when the conditions are equal to the conditions of the subsystem with active redundant components. Thus, the nominal failure rate of the non-failed component is not changed when its load has been increased -the case when the decrease factor is equal to zero. The lowest life time limit could be defined by the parameter M T T F min which characterizes the subsystem composed of the independent components. Thus, when one of the components fails the system is considered as failed. In term of the decrease factor, it is equal to 1 or (1-λ n ) for a single step FR change. Let's suppose the system life time limited by the bound defined by the MTTF parameter such as M T T F min ; M T T F max . These two parameters could be found by solving the simple following equations [START_REF] Stary | Spolehlivost systmu[END_REF]:

M T T F min = ∞ 0 n i=1 R i (t)dt (4.3) and M T T F max = ∞ 0 (1 - n i=1 (1 -R i (t)))dt (4.4)
where R i (t) is the reliability of each component.

In the final part of the results presentation we described the life time increasing of the two component QR subsystem with regard to the life time parameter M T T F min whereas various values of the decrease factor d R are considered. We consider it as a simple and fast method for life time approximation. The results are shown in table 4.5. As in the previous part of this case study, we consider only the influence of the single step increasing of the nominal failure rate to the final life time of the two components QR system characterized by its MTTF parameter. In the first line, the failure rate of 4.5 are rounded, hence the method error is about +/-2 for the multiple of the nominal failure rate smaller or equal to 40.λ n (decrease factor d R < 40). For higher value of the decrease factor, the approximated error is about +/-1 of values shown in the table. Thus, in the case of very similar analysis result of considered complex structures it is necessary to prepare the exact model in order to obtain a more exact MTTF parameter reduction. This method could be used for the QR subsystems with the same failure rate or for the system when difference among the nominal failure rate λ n of the components is very small and can be ignored. In the case of a nominal FR smaller than 10 -2 , the increased value 100.λ n should represent approximately 0.1 whereas the error could be higher. Then, it could be useful that the value of nominal FR determined for a time interval T transforms to the greater value for a shorter time interval (unit).

Conclusion.

The paper shows the influence of additional reliability decreasing of the quasi-redundant component to entire reliability of the studied system. The description of this dependency is getting closer to show the behavior of the system reliability when a shared redundancy approach is implemented. The results shown in tables 4.1 -4.3 could be very helpful in order to approximate the life time of the quasiredundant subsystems under different conditions of the failure rate increasing. The presented cascade control architecture is suitable for a shared redundancy approach implementation and could be applied to similar systems. For example, Steer-by-Wire control [START_REF] Leen | Expanding Automotive Electronic Systems[END_REF] of two front wheels in a car, etc. In addition the paper has shown the conventional cascade control structure within conditions of networked control systems as naturally suitable to profit from quasi-redundant subsystems as networks, controllers and potentially sensors if the physical process allows it. Despite of some constraints for using this type of control, the cascade architecture is widely used in industrial control applications. Hence, only the reconfiguration algorithm should be implemented to take profit from quasi-redundant subsystems.

The case study presented in parts 4.1 and 4.2 (results section) extends the field of common methods for reliability approximation. Equations (4.1, 4.2) are considered as simple and fast analytical method in order to evaluate the reliability of the systems which covers two-component QR subsystems with single step FR change.

The main advantages of the quasi-redundant components could be summarized as follows:

• The system is composed only of necessary components (parts) for following the primary mission of the system whereas higher system reliability is ensured without using any additional active redundant components.

• Following the first point we could suppose less number of components used for saving the control mission. Thus, the economic aspect could be significant. • Prevention of the system's critical failure when a QR subsystem has no sufficient hardware capacities.

Fig. 3 . 1 .

 31 Fig. 3.1. Main structure of the cascade control

Fig. 3 . 2 .

 32 Fig. 3.2. NCCS with two networks and alternative network connections

Fig. 3 . 3 .

 33 Fig. 3.3. Possible scenarios for quasi-redundant controllers

Fig. 3 . 4 .

 34 Fig. 3.4. Possible failure rate curves for the subsystem S 2 during its mission

Fig. 3 . 5 .

 35 Fig. 3.5. Cascade control structure of a mini-helicopter with one network

Fig. 4 . 1 .

 41 Fig. 4.1. Influence of the increased failure rate of the component by a constant decrease factor d R to the reliability of the system composed of two quasi-redundant components

Table 4 .

 4 1 MTTFF OF SIMULATED CONTROL STRUCTURES WITH DIFFERENT DECREASE FACTORS

	Decrease factor -d R	MTTFF -Drone (Fig. 3.5) MTTFF -Drone (Fig. 3.6)
	0	55(+11%)	58(+22%)
	2 * 10 -3	54(+9%)	56(+17%)
	10 -2	53(+7%)	54(+13%)
	59 * 10 -2	50.5(+2%)	49(+3%)
	0.999	49.6	47.6
		Table 4.2
	MTTFF OF THE TWO QUASI-REDUNDANT WITH SINGLE STEP CHANGE OF THE
	FAILURE RATE

Table 4 .

 4

	3

Table 4 .

 4 5 PARAMETERS OF EQUATION 4.1 FOR A SINGLE STEP FR CHANGE

	Decrease factor -d R	k 1	k 2
	λn	0.44	0.52
	2λn	0.39	0.395
	3λn	0.28	0.393
	4λn	0.198	0.434
	5λn	0.154	0.46
	6λn	0.13	0.4653
	7λn	0.11	0.46
	8λn	0.099	0.471
	9λn	0.09	0.46
	10λn	0.081	0.463
	20λn	0.0445	0.38
	30λn	0.0296	0.377
	40λn	0.0225	0.385
	50λn	0.0182	0.3518
	70λn	0.0133	0.3284
	80λn	0.011625 0.32475
	100λn	0.0094	0.3332

Table 4 .

 4 6 APPROXIMATED VALUES OF THE MTTF REDUCTION OF THE TWO-COMPONENT QR SUBSYSTEM WITH DIFFERENT SINGLE STEP CHANGE OF THE NOMINAL FAILURE RATE λn failed QR component characterized by the multiple of the nominal failure rate λ n . The second line shows the corresponding MTTF parameter percentage reduction within the limits defined by the abovementioned interval of the maximal and minimal life times (MTTF). The MTTF values introduced in table

	Single step	2 λn	3 λn
	change	(d R = λn )	(d R = 2λn )	4 λn	5 λn	7 λn	10 λn	20 λn	40 λn	100 λn
	of λn
	Extended	50%	35%	25%	20%	15%	10%	5%	2%	1%
	M T T F min
	the non-


Sujuan Wu

Pascal Brault
email: pascal.brault@univ-orleans.fr

Cong Wang

Deposition and diffusion of plasma sputtered platinum nanoparticles in porous anodic alumina oxide

Keywords: Anodic aluminum oxide, Sputtering, Platinum, Anomalous diffusion, RBS

Plasma sputtering deposition of Platinum thin films is studied on porous anodic aluminum oxide (AAO) template. The size effect of AAO cylindrical pores is shown to influence the diffusion of atoms in the porous layer. The resulting maximum reached depth of platinum varied from 2 μm to 20 μm, and the density on the surface is lowered from 23 µg.cm -2 to 5 µg.cm -2 as the pore diameter increased from 40 nm to 320 nm. The pore diameter is decreasing as Pt is deposited. Sputtered Pt is observed to grow as clusters on the surface and along the pore walls.

Introduction

Plasma sputtering deposition of precious metals on porous substrate, such as porous materials, membranes with nanochannels and nanoarrays, is important in physical process and applications [1][2][3][4]. The advantage of controlling growth and depth concentration profiles is particularly useful in the field of catalysis, which is helpful to increasing the efficiency and reducing the waste of noble metal catalyst [5][6]. Earlier experiments [7][8][9] have shown great promise for this technique and the deposition into porous materials, but a clear description of Pt penetration into the nanochannels membranes and resulting concentration profiles remains to be established. In order to obtain more detailed information of Pt deposition in nanochannels, a porous anodic alumina oxide (AAO) membrane has been used as substrate.

AAO membrane is a typical self-ordered nanochannel material formed by anodization of Al in an appropriate acid solution. The structure of AAO is a close-packed array of columnar cells, each containing a central cylindrical pore of which the diameter and interval can be controlled by changing the forming conditions.

Normally, the pore diameter can be adjusted from 25 to 350 nm and aspect ratio can be changed by controlling the anodizing time [10][11][12]. It has already been used as hard-template to control the growth of nanotubes, nanowires and nanodots using chemical methods. Up to now, the Pt [13,14], Si [15], Bi [16], PbO [17], SnO 2 [18], NiO [19], LiMn 2 O 4 [20] nanowires and nanotubes have already been successfully prepared. Unfortunately, controlled growth of nanowires in the template by plasma sputtering technology is difficult to achieve, due to the isotropic distribution of the sputtered atoms reaching the template. Herein, to study the distribution of sputtered particles in the template and to control the distribution of the nanoparticles, is not only helpful for studying the diffusion process, it is also advantageous for controlling the growth of nanostructures.

Since the sputtered platinum atoms are deposited on the surface and penetrate into the pore of the AAO template, the morphology of the surface and the pore size of the template may have a drastic impact on the deposition and diffusion process. The goal of the experiments is to characterize the morphology and to determine the depth-density profiles of Pt coated templates having different cylindrical pore diameter.

Experimental

A low pressure, high frequency (VHF) inductive plasma sputtering system has been applied as displayed in Fig 1 . An argon plasma is created in the stainless steel deposition chamber by using an external planar antenna (TCP) at 100 W input power and an argon pressure of 2.4*10 -3 mbar. The excitation antenna is powered by a radiofrequency generator operating 13.56 MHz. The electrodes are placed on a movable/rotating grounded substrate holder in front of the sputtering target with a target-substrate distance of 8 cm. A base pressure of P 0 =2.7*10 -7 mbar is achieved using a primary/turbomolecular pump combination. The argon flow is fixed to 5 sccm using a mass flow meter.

The coated Pt AAO templates were analyzed by high resolution scanning electron microscopy (SEM) (ZEISS) to determine pore size and evolution of the porosity at the surface. The line scan profile on the EDX (energy dispersive X-ray spectrometry) was carried out to observe the presence of platinum along the pores. Rutherford Backscattering Spectroscopy), with a Van de Graaf accelerator (CEMHTI-CNRS, Orleans, France) using a 2 MeV 4 He + ion beam, was used to measure the total Pt content and to quantify Pt penetration into pores. RBS measurements were performed to determine the Pt content depth profile in the AAO templates. Figure 5 shows a typical RBS spectrum of a plasma electrode after 5

min Pt deposition time. The left side of the spectrum corresponds to AAO membranes substrate contributions, whereas on the right side, the asymmetrical peak originates from α particles scattered by Pt atoms. The area under this Pt peak is directly related to the number of platinum atoms deposited on both surface and in the pores. The tail on the left side of the Pt peak indicates that the Pt atoms have diffused into AAO pores.

Moreover, it is possible to deduce the Pt depth profile from this spectrum. By fitting the experimental spectrum with a simulated spectrum (using SIMNRA software) the depth profile can be recovered by an iteration process until the simulated spectrum matches the experimental spectrum. We observed that the resulting depth profile is similar as Pt depth profile in porous carbon layer [1,2]: a growing layer above the porous medium, with the constant density Z1(t) and the mean thickness h (t) = z 0 (t) ( z<0); a diffusion layer in the porous medium, which extends in the z > 0 domain; and the interface between the growing layer and porous media, where the density profile is continuous (z=0). In porous layer, the Pt depth profile corresponds to the known solution of anomalous diffusion processes that can be defined by Eq .1 [1]. Hence, we still use this equation to define the diffusion process in AAO channels and fit the depth profile with different pore size.

ρ (z,t) = Z 1 (t), -z 0 <z≤0 ρ (z,t) = Z 1 (t)exp[-z 2+θ /Z 2 (t)] z>0
θ is the dimensionless coefficient which characterizes the anomalous diffusion behaviour. If θ<0 then the behaviour is superdiffusive else if θ>0 it is subdiffusive. The deduced depth profiles of Pt deposited on the template, with different pore size, are displayed in Figure 6. The density on the surface is decreasing, but the thickness is increasing as the pore size increasing. The best fits correspond to θ changing between -1.76 to -1.6, which means that Ar plasma exposure during Pt deposition induces superdiffusion and the diffusion rate is different in different pore size. When the pore size increasing from 40 to 320 nm, the density on the surface is lowered from 23 µg.cm -2 to 5 µg.cm -2 and the maximum reached depth of Pt is from 2 µm to 20 µm. Pt atoms diffused more efficiently into the pores with largest size, which is consistent with the results from SEM. So combined SEM, EDX and RBS measurements suggest that Pt atoms arriving with a relatively high kinetic energy [6] undergo multiple scattering and diffusion on the surface of the inner walls of AAO ending by cluster growth.

Conclusions

In conclusion, the morphology and depth concentration profile of sputtered Pt atoms into porous AAO templates has been observed. The pore size is decreasing as the Pt is deposited. The morphology of the surface has a dramatically effect on the transport process in the pores. So, a concentration gradient extended as deep as 20 μm into the diffusion layer, depending on the pore size. Pt clusters are evidenced along the pore walls as resulting from transport/diffusion/adsorption/clustering process.

Figure 1 :Figure 2 :

 12 Figure 1: Schematic of the plasma sputtering reactor called "CataPulP".

Figure 3 :

 3 Figure 3: Various Pt coated AAO showing the structure of the deposit on and in the pores. (a) Pt deposited on smooth AAO surface (b) Pt deposited on the AAO surface which looks like a funneled pore surrounded the holes (c) cross section view showing Pt diffusion along inner pore walls.

Figure 3 Figure 4 :

 34 Figure 3 displays some selected SEM views of the Pt coated AAO. After Pt deposition, the Pt atoms are stacked on the smooth surfaces of the AAO (Figure 3 (a)). Kai-TzeHuang et al also have reported that the AAO surface is used to provide the nucleation and growth sites for the formation of Pt nanorods[21]. In figure3(b), the surface of the templates looks like a funneled pore surrounding the vacant space. When the templates were exposed to the flux of sputtered Pt, Pt atoms were driven to travel across this surface and fall into the holes. A zoom on the cross section shows that the pore walls are coated by Pt clusters with a size of 10 nm (figure3(c)), implying that Pt atoms are subject to transport/diffusion/adsorption on the inner walls and cluster growth. The rate of diffusion and absorption on the AAO surface are not consistent with the sputtering rate. Usually it is higher than the diffusion and absorption rate that caused most of Pt particles concentrated on the surface.

Figure 4 (Figure 4 Figure 5 :

 445 Figure 4(a) is displaying the Al, O and Pt concentrations along the selected straight line crossing some pores drawn below the diagram in Figure 4(a). On the other hand, Figure 4(b) reports the Pt, Al, O concentration profiles along the inner surface of a pore. The amounts of Pt and Al are obviously dropped simultaneously at the position of the holes (Figure 4(a)). The distribution of Pt in the pores is visualized in Figure 4(b), the Pt amount is decreasing as increasing the depth. The particle flux delivered by the plasma sputtering cannot be absorbed directly by the porous AAO template. Part of Pt particles is deposited on the surface between pores and part of the Pt is diffusing into the porous and adsorbed on the inner walls.

Figure 6 :

 6 Figure 6: The density depth profile of Pt