E Hug

O Hubert

M Clavel

Some aspects of the magnetomechanical coupling in the strengthening of non oriented and grain oriented 3% SiFe alloys

An investigation has been carried out on the effect of plastic strains on the magnetic properties of grain oriented and non oriented 3%SiFe alloys. A drastic degradation of these properties with increasing deformations is observed for magnetic field amplitudes ranging between 0 and 2000 A/m. Empirical relationships between plastic strain and magnetic characteristics are obtained. Materials exhibit a Lüders strain state under tensile loading in a low plastic deformation range. Meanwhile, the classical Ramberg-Osgood law is verified. The observation of the dislocation features at various plastic strain levels shows three typical configurations : hexagonal cells in the Lüders strain state, small tangles and isolated screw dislocations at medium values of strain, and finally high density tangles at higher deformations. In the same way, the densities of main and secondary magnetic domains follow an evolution in three stages with increasing strains. It is shown that the transverse domain patterns take place to counterbalance the increase of magnetoelastic energy due to the strengthening. The evolution of the coercivity and the initial relative permeability with the strains

I. INTRODUCTION

The prediction of total core losses in magnetic media used for the manufacture of transformers and rotating electrical machines requires a numerical approach. To this end, standard magnetic characteristics of the materials, i.e. core losses versus flux density and magnetization curve under an ac supply, obtained with classical techniques of measurement (standard Epstein facility or Single Sheet Tester), need to be known with high precision. These standard tests are generally implemented with laminated sheet strips annealed after cutting. Hence, the magnetic properties are expected to be independent of any residual stresses which could exist inside the metal die.

Yet, there is a great difference between direct magnetic measurements on electrical machines and standard characteristics. For some machines, this implies total power losses twice or more higher than losses measured with standard frames, especially for high flux density levels. These differences result from several parameters : electromagnetic factors (distorsion of the wave forms, harmonics, ...) and mechanical factors (residual stresses after punching, elastic stresses in service, ...) in particular.

In the present work, the influence of plastic deformation on the magnetic behaviour of grain oriented (GO) and non oriented (NO) 3% SiFe alloys is investigated. Section 2 describes the magnetic frame used to measure magnetic properties directly on stress-strain test pieces. Experimental results showing the evolution of the magnetic characteristics with plastic strains are then given. The mechanical behaviour of 3% SiFe alloys submitted to various tensile test levels is presented in section 3. The microstructural aspects (dislocation feature evolution with plastic strain, coupled with magnetic domain structure observations) are reported in section 4. Finally, the validity of some models describing the interactions between dislocations and domain walls and the influence of plastic stresses on coercive field strength are discussed in section 5.

II. MAGNETIC PROPERTIES OF PLASTICALLY STRAINED 3% SIFE ALLOYS

A. Experimental Procedure

Standard apparatus for measuring the magnetic properties of ferromagnetic steel sheets (Epstein frame or Single Sheet Tester) are not able to study stress-strain pieces.

A magnetic measurement frame has been then built [START_REF] Hug | Etude des dégradations des propriétés magnétiques d'alliages Fe-3%Si avec les déformations plastiques. Application à la mise en oeuvre des tôles utilisées dans la conception des moteurs électriques[END_REF] (Fig. 1a). It consists of a ferromagnetic yoke where a magnetic flux Φ(t) is created by a field winding. This flux crosses over the strained specimen which is held in position at the ends of the yoke. A locking system (screws and springs) ensures a small and constant airgap between the sample and the ferromagnetic frame. The dimensions of the latter have been computed in order to always neglect its reluctancy face to this of the sample. The flux rate variations are detected through a secondary winding concentrated in the middle of the tensile test specimen.

The magnetic frame is supplied with an imposed 50Hz sinusoidal current i(t). The electromotive force e(t) induced in the secondary winding and i(t) are stored. e(t) is then numerically integrate. It gives the magnetic flux inside the sample :

Φ(t) = - 1 n ⌡ ⌠ 0 t e(t)dt (1)
with n the number of turns of the secondary winding. The magnetic flux density B(t) is then given by the following relationship :

B(t) = Φ(t) S (2)
S is the cross section of the sample. The Ampere's law is applied along the medium magnetic circuit (Fig. 1b) in order to compute the magnetic field strength H(t) :

H y (t)L y + 2H a (t)L a + H(t)L = Ni(t) (3)
L is the effective length of the specimen crossed by the flux lines, calculated thanks to a numerical simulation of the frame. L y and L a are respectively the medium length of the yoke and the airgap length. This latter can be measured by optical microscopy (L a ≈ 6µm on average). N is the number of turns of the field coil. This experimental system has been numerically validated and it is reliable up to H = 6000A/m. The total flux Φ(t)

is then supposed to be invariant along the magnetic circuit. This allows us to use the following relationships :

H y (t) = Φ(t) µ y (H y (t))S y (4) H a (t) = Φ(t) µ 0 S a (5)
S y and S a are respectively the yoke and airgap sections. S y is thousand time higher than S so H y is much smaller than H (H y ≤ 50 A/m). µ y is also considered as a constant permeability of the yoke estimated as µ y = 1000µ 0 , with µ 0 = 4π10 -7 H/m.

Consequently, relations (3), ( 4) and ( 5) give raise to the magnetic field strength H(t) inside the specimen * :

H(t) = N L . i(t) - Φ(t) L .       L y S y µ y + 2L a S a µ 0 (6)
The maximum magnetic flux density B m is plotted against the maximum magnetic field H m in order to obtain the magnetization curve of the specimen under ac supply excitation. Furthermore, the area of the hysteresis loop is proportional to the total core losses P of the material, for a given value of B m . coercivity, retentivity and initial permeability are obtained under quasi-static (f=0.1Hz) conditions.

Materials investigated are GO and NO 3%SiFe alloys. Specimens consist in 200mm long, 20mm wide and 0.35mm thick strips cut along the rolling direction of the sheets. They have been annealed (720°C, 2h, P O2 = 0,027Pa) and then plastically deformed at various plastic strain levels ε p , up to fracture. Tensile tests have been performed at room temperature and at a constant plastic rate dε p /dt = 6.67 10 -4 s -1 .

B. Experimental Results

* Nevertheless, we have observed that H(t) ≈ (N/L)i(t) whatever the magnetomotive strength Ni(t) and the plastic strain level applied to the specimen. The magnetic flux density B(t) is sinusoidal for the lower values of H(t) and become trapezoidal for higher levels.

Figure 2 shows the evolution with ε p of the magnetization curves and the loss characteristics for the two alloys. Plotting various magnetic properties against ε p (Fig. 3)

shows a marked dependence for low and medium values of magnetic field amplitude i.e. between 0 and 2000 A/m. This phenomenon is weaker when high magnetic field amplitudes are reached.

Simple empirical relations can be found between the main magnetic properties and plastic strains [START_REF] Hug | Influence de l'écrouissage sur les propriétés magnétiques d'alliages Fe-3%Si non-orientés[END_REF], [START_REF] Hubert | Influence of plastic strain on magnetic behaviour of non-oriented Fe-3Si and application to manufacturing test by punching[END_REF]. The maximum magnetic flux density decreases according to the law :

B m = B m0 (H m ). k mc (H m ) k mc (H m ) + ε p nmc(Hm) (7)
B m0 (H m ) is the initial magnetization curve at ε p = 0%, k mc and n mc are parameters functions of H m and representative of the material. Furthermore, the following relation gives the increase of the total power losses versus plastic strains :

P = P 0 (B m ). [ ] 1 + k p (B m ).ε p np(Bm) (8)
P 0 (B m ) is the initial power loss characteristic. k p , n p are parameters depending on B m and representative of the alloy too. The retentivity of the materials and their initial relative permeabilities µ ri strongly decrease according to :

B r = B r0 1 + ε p nr (9)
µ ri = µ ri0 1 + ε p nµ [START_REF] Vicena | On the influence of dislocations on the coercive force of ferromagnetics[END_REF] Finally, the coercive field strength markedly increases :

H c = H c0 .(1 + ε p nc ) (11)
B r0 , µ ri0 and H c0 are respectively the values of retentivity, initial permeability and coercive field strength without plastic strains. n r , n µ and n c are constants representative of the studied alloys. Numerical values of the various parameters which appear in relations ( 7) to ( 11) can be found in [START_REF] Hug | Etude des dégradations des propriétés magnétiques d'alliages Fe-3%Si avec les déformations plastiques. Application à la mise en oeuvre des tôles utilisées dans la conception des moteurs électriques[END_REF], [START_REF] Hug | Influence de l'écrouissage sur les propriétés magnétiques d'alliages Fe-3%Si non-orientés[END_REF].

III. TENSILE TEST BEHAVIOUR OF 3% SIFE ALLOYS

Monotonous stress-strain curves σ(ε) are shown in figure 4 for the two SiFe alloys. Both exhibit a Lüders strain state at the beginning of straining (σ remains constant on a range of deformation L p , length of the Lüders level). Moreover, materials often exhibit a discontinuity of the yield point ∆σ e .

After the Lüders strain state, classical strengthening is observed. This phenomenon is well marked for the NO alloy and less sensitive for the GO. Non homogeneous deformation occurs after the maximal stress σ m preceding rupture. This can be characterized by A%, the rupture elongation of the sample.

The true stress-strain curves σ v (ε v ) follow a classical Ramberg-Osgood law [START_REF] Lemaitre | Mécanique des matériaux solides[END_REF] :

σ v = C + K y .ε v n ( 12
)
with C≈0 for weakly alloyed steels, K y and n are respectively the plastic strength and the strain hardening coefficients.Table 1 summarizes the several mechanical parameters representative of tensile tests carried out on NO and GO alloys.

IV. MICROSTRUCTURAL ASPECTS

Transmission Electron Microscopy observations of strained specimens were performed. Colloid techniques have been also used to observe ferromagnetic domains.

Magnetic domain patterns are strongly dependent of the dislocation structure. This microstructural study gives helpful informations about the harmfulness of some dislocation configurations and about the interactions between domain walls and dislocations in 3% SiFe alloys.

A. Behaviour of Dislocations with Plastic Strains

Typical configurations of dislocations for the non oriented alloy were previously reported [START_REF] Hug | Influence de l'écrouissage sur les propriétés magnétiques d'alliages Fe-3%Si non-orientés[END_REF]. For unstrained specimens, the basic dislocation arrangement consists of long screw dislocations lying in a {110} glide plane and with a Bürgers vector b=a/2<111>. These dislocations are either isolated or get some trend to accumulate close to grain boundaries. Between 0 and 0.5% of plastic strain, a strongly heterogeneous dislocation structure was observed in the Lüders domain. This later structure consists in hexagonal cells with mean size of 26µm. This structure was no longer observed at higher strains. In the range 1 to 10% of plastic strain roughly homogeneous dislocation structure is observed. In this range, small tangles of relatively low density are progressively created (about 0.1µm in length), with isolated glissile dislocations in the channel. Above ε p =10%, the dislocation structure becomes strongly heterogeneous. Tangles of high density are created, with a typical dimension of (0.2µmx1µm). In this channel, the dislocation density remains very low.

Similar dislocation structures have been reported for the grain oriented alloy by ourselves and recently for soft steels by Hou and Lee [START_REF] Hou | Effect of rolling strain on the loss separation and permeability of lamination steels[END_REF]. All these structures are characteristic of the strengthening process of body centered cubic alloys. Only the critical plastic strains are modified, due to the different rupture elongation of the two alloys. The three main dislocation features are summed up in figure 5.

The average density of statistically stored dislocation were previously computed using a method reported elsewhere [START_REF] Hirsch | Electron microscopy of thin crystals[END_REF], [START_REF] Dumas | Etude du comportement magnétique d'alliages Fe-3%Si non orientés utilisés dans la conception de machines électriques[END_REF]. It was oberved that the two alloys follow the linear relationship :

ρ d = ρ d0 .(1 + β.ε p ) ( 13
)
ρ d0 is the initial dislocation density (6.10 8 cm/cm 3 for the NO and 2.10 8 cm/cm 3 for the GO), β being a constant representative of the alloy.

B. Magnetic Domain Structures and Plastic Strains

Observations of the magnetic domain patterns were carried out on deformed grain oriented samples, thanks to a colloidal method. Several configurations of magnetic domains may be observed [START_REF] Hug | Evolution of the magnetic domain structure of oriented 3% SiFe sheets with plastic strains[END_REF] with increasing strain levels.

It is well known that grain oriented sheets have a Goss texture that implies boundaries of main domain structures more and less parallel to the easy direction <001>. This main domain structure can be represented by the surface density Ω 1 , following the definition given by Shilling and Houze [START_REF] Shilling | Magnetic properties and domain structure in grain-oriented 3% Si-Fe[END_REF]. When ε p ranges from 0 to 2% (Lüders strain state of the GO sheet), strong increase of the supplementary structure density happens (this density we may call Ω 2 ). This secondary structure is composed of reverse spikes of opposite magnetization on grain boundaries, lancet networks or firtree patterns. Around 5% of plastic deformation, transverse domains suddenly appear into slab domains and at some grain boundaries. What is more, a relative stabilization of Ω 1 and Ω 2 after this strain rate is noticed. For ultimate values of ε p , bowing of slab walls occurs and so Ω 2 increases again at the expense of Ω 1 .

A statistical analysis of the magnetic domain structures observed on strained GO samples indicates that the evolution of Ω 1 and Ω 2 versus ε p clearly shows three distinct stages (Fig. 6), each of them corresponding to a typical magnetic domain structure.

These experimental results show the role played by the transverse domain structures which counterbalance the increase of the magnetoelastic energy brought with the strengthening process.

Observations of magnetic domain structure on strained NO samples using colloid techniques is very difficult because of the smaller grain size of these alloys (80µm against 500µm for GO on average) and the strong initial density of the secondary structure. Measurements of Ω 1 and Ω 2 don't give reproductible results. Nevertheless, bowing of the main domain structure occurs only after 10% of plastic strains, when dislocations tangles of high densities are present in the metallic matrix.

V. DISCUSSION

A. Dislocations / Bloch Walls Interaction Models 1) Presentation of the models:

The modelling of the movement of domain walls in crystals containing pinning centers like dislocation features remains very difficult.

These approaches need a statistical treatment, which generalizes the former models of interaction between one single domain wall and one single dislocation [START_REF] Vicena | On the influence of dislocations on the coercive force of ferromagnetics[END_REF], [START_REF] Kleman | Contribution à l'étude de l'intéraction entre une dislocation vis et l'aimantation[END_REF], [START_REF] Seeger | Effect of Lattice defects on the magnetization curve of ferromagnets[END_REF],

and between one domain wall and an array of dislocations [START_REF] Brown | The effect of dislocations on magnetization near saturation[END_REF], [START_REF] Brown | Dislocations, cavities and the approach to magnetic saturation[END_REF]. Typically, the main models may be classified into two categories i.e. the potential models [START_REF] Chen | Magnetism and metallurgy of soft magnetic materials[END_REF], [START_REF] Jiles | Introduction to magnetism and magnetic materials[END_REF] and the domain wall bowing models [START_REF] Dietze | Theorie der Blochwandwölbung mit Streufeldeinfluß[END_REF].

In the first category, it is thought that the domain walls are rigid. Local potential energy fluctuations drive their movements. Subjected to an outside magnetic field H, the displacement of a domain wall is function, as first approximation, of two energies :

the field energy and the domain wall energy. This latter is generally supposed to be dependent of the position of the wall. When reversible movements of domain walls occur (Rayleigh zone), the initial relative permeability µ ri is the main magnetic parameter. On the other hand, irreversible displacements of the walls are controlled by the coercive field strength H c . However, in a real strained crystal, domain wall displacements are perturbated by the elastic stress field of dislocations. The theoretical approach of Kronmüller, Seeger and co-workers [START_REF] Seeger | Effect of Lattice defects on the magnetization curve of ferromagnets[END_REF], [START_REF] Kronmüller | Statistical theory of Rayleigh's law[END_REF], [START_REF] Kronmüller | Magnetic techniques for the study of dislocations in ferromagnetic materials[END_REF] shows that H c may be written as a function of the dislocation density :

H c = C te . ρ d ( 14
)
and the initial permeability of the material obeys to the law :

µ ri = C te ρ d (15)
The product H c .µ ri is assumed to be constant to verify the potential theory. Since a linear relation exists between ρ d and ε p in the range [0-10]% (relation ( 13)), then H c .µ ri must be independant of the applied plastic strain. Using the relations ( 10) and ( 11) :

H c .µ ri = H c0 . ( ) 1 + ε p nc . µ ri0 1 + ε p nµ = C te . 1 + ε p nc 1 + ε p nµ (16)
We must have n c =n µ to apply the potential theory to 3%SiFe alloys.

In the second class of models, the dislocation structures act as pinning centers with variable strength amplitudes. Under the influence of an outside magnetic field, the variation of magnetization in the sample is performed by the bowing of the free segments of walls. Irreversible jump occurs for a critical value of the radius of curvature. Based on this hypothesis, Labush [START_REF] Labusch | Calculation of the critical field gradient in type II superconductors[END_REF] developed a statistical model concerning flexible walls and pinning center density. The author obtains the relationship :

H c = C te .ρ d 2/3 (17)
Thus, according to relation [START_REF] Brown | The effect of dislocations on magnetization near saturation[END_REF], H c must be proportional to ε p 2/3 to verify bowing walls models.

2) Experimental results: Figure 7 gives the evolution of H c .µ ri with ε p for the GO and NO alloys when a linear relationship between ρ d and ε p is verified. An evolution in two stages of H c .µ ri against ε p is observed for the oriented material and a monotonous decrease of H c .µ ri with ε p occurs for the non oriented alloy. Furthermore, fitting H c against ε p with the help of relation [START_REF] Dumas | Etude du comportement magnétique d'alliages Fe-3%Si non orientés utilisés dans la conception de machines électriques[END_REF] gives n c = 0.23±0.05 for the NO alloy and n c = 0.18±0.05 for the GO alloy. Confrontation of these tendencies with the microstructural investigations gives us the following conclusions (these various effects are listed in figure 8) :

• For Non Oriented Materials : Potential Models do not apply between 0 and 10% of plastic strains because of the variation of the H c .µ ri product. Furthermore, bowing models seem more able to explain our experimental results after 10% of plastic strains, but cannot explain the behaviour of the material between 0-10% of plastic strains because relation ( 17) is here not verified.

• For Grain Oriented Materials : Potential Models do not apply to samples deformed between 0 and 2% (Lüders strain state) because of the variation of the H c .µ ri product. between 2 and 8% of plastic strains, H c .µ ri remains constant and no bowing of main domain structure is observed: potential models could then successfully be applied.

After ε p =8%, bowing of 180° domain walls occurs and then bowing models must be used.

3) Discussion: The last results relative to the coercive field strength are based on the hypothesis that dislocation features are the only source of pinning for the domain walls.

In fact, the phenomenon could be more complex if grain boundaries are taken into account. In this case, H c could be written as the sum of two components :

H c = H cb + H cd ( 18
)
with H cb an almost constant contribution from grain boundaries and H cd a variable contribution from dislocations. So, (H cb + H cd )µ r is not constant, while H cd µ r can be constant. Nevertheless, our experimental results are related to the total coercive field strength of polycrystalline alloys. The potential models seem hardly applicable in the range of plastic strains where H c µ r is not a constant. In fact, potential models are entirely valid only in the case of strained single crystals [START_REF] Seeger | Effect of Lattice defects on the magnetization curve of ferromagnets[END_REF]. In this case, the displacements of magnetic walls are hindered by the same obstacles (dislocations) and it has been shown that the two models (potential and bowing) are the limit cases of a more general model of interaction [START_REF] Hilzinger | Statistical theory of the pinning of Bloch walls by randomly distributed defects[END_REF]. Previous experimental works on polycristalline Ni and Permalloy have given similar results than those obtained on 3% SiFe alloys [START_REF] Bostanjoglo | Microscopical test of current theories of magnetic wall motion[END_REF].

B. Influence of Plastic Stress on Coercive Field Strength

To explain the evolution of magnetic properties with strengthening, several authors prefer to use ∆σ=σ-σ e instead of the plastic strain ε p [START_REF] Astie | Predictions of the random potential energy models of domain wall motion : an experimental investigation on high-purity iron[END_REF]. We have shown elsewhere that ∆σ is representative of the total strengthening of the alloy at each step of the straining process [START_REF] Hug | Influence de l'écrouissage sur les propriétés magnétiques d'alliages Fe-3%Si non-orientés[END_REF]. It is interesting to compare the evolution of H c with ∆σ for our alloys and for high-purity iron as it was determined by Degauque [START_REF] Degauque | Les pertes d'énergie dans les ferromagnétiques métalliques doux : origines physiques[END_REF] (figure 9).

A variation of H c following two linear stages for each SiFe alloy is shown. The first stage encountered for high purity iron does not exist in our case. Each stage can be tied to a specific configuration of dislocations. For instance, for the high purity alloy, the first stage (H c =c te ) corresponds to isolated and mobile dislocations, the second stage (strong increase of H c ) is associated to small isotropic tangles and isolated dislocations, and the third stage to high dislocation density tangles. For SiFe alloys, the first stage (strong increase of H c for ∆σ≈0) corresponds to the cell structure observed on Lüders strain state and the second stage to the formation of tangles. The first stage present for high-purity iron does not exist in 3%SiFe because no configuration of purely isolated dislocations is encountered.

On the other hand, it is worth noting that the evolution of H c against ∆σ is the same for GO and NO alloys. The magnetomechanical interactions in these alloys are rather complex but seem to be more function of short range interactions than function of the long range ones.

VI. CONCLUSION

In this paper, some experimental results concerning the evolution of magnetic properties of grain oriented and non oriented 3%SiFe alloys have been presented.

Experimental laws between magnetic properties and ε p have been achieved.

Correlations between these results, mechanical properties and microstructural observations of dislocations and domain structures have been carried out. It has been shown that the formation of transverse domain patterns counterbalances the increase of magnetoelastic energy brought with the strengthening. Then, the degradation of magnetic properties is less sensitive.

H c and µ ri measurements with increasing ε p have shown that potential model theories do not apply to non oriented SiFe but could explain the magnetic behaviour of grain oriented SiFe in the range [2-8]% of plastic strains. For both materials, domain wall bowing theories seem more able to explain our experimental results at the ultimate stages of deformation. The relationship between coercivity and strengthening displays two linear stages for both 3%SiFe alloys, instead of the three stages reported in the case of a polycristalline high purity iron [START_REF] Degauque | Les pertes d'énergie dans les ferromagnétiques métalliques doux : origines physiques[END_REF]. Consequently, the magnetomechanical interactions could be strongly correlated to microstrains surrounding around dislocation features.

These results need to be generalized to different mechanical tests (tensile tests along several directions lying in the sheet plane, fatigue tests, ...) but can be applied with some success to the study of the degradation of magnetic properties of soft magnetic materials after punching. Microhardness measurements can be carried out to obtain the equivalent plastic strain profile near the cutting edge of a punched material [START_REF] Hubert | Influence of plastic strain on magnetic behaviour of non-oriented Fe-3Si and application to manufacturing test by punching[END_REF]. Magnetic properties profiles versus distance from the cutting edge followed, which can be introduced into finite element modelling models of rotating electrical machines.

Results concerning the computation of iron losses for a wound rotor synchronous motor and a buried magnet synchronous motor were exposed elsewhere [START_REF] Hug | Influence des déformations plastiques sur le comportement magnétique d'alliages fersilicium[END_REF]. These simulations have shown a significant majoration of the losses when the punching deformation is taken into account . and for high purity iron as determined in [START_REF] Bostanjoglo | Microscopical test of current theories of magnetic wall motion[END_REF].

  FIGURE 1(a)Author : E. HUG

Figure 1 :

 1 Figure 1 : Principle of magnetic properties measurements on stress-strain test pieces. (a) The experimental frame ; (b) corresponding magnetic circuit.

Figure 2 :

 2 Figure 2 : Magnetic properties of non oriented and grain oriented 3%SiFe samples with various plastic strain levels. (a) magnetization curves for NO alloys ; (b) magnetization curves for GO alloys ; (c) loss characteristics for NO alloys ; (d) loss characteristics for GO alloys (experimental conditions of magnetic tests are given in text).

Figure 3 :

 3 Figure 3 : Relationship between magnetic properties and plastic strain levels for NO and GO SiFe alloys. (a) induction versus ε p for several values of the applied magnetic field ; (b) retentivity versus ε p ; (c) coercive field strength versus ε p ; (d) power losses versus ε p for various induction levels.

Figure 4 :

 4 Figure 4 : Tensile test properties of NO and GO SiFe alloys. (a) monotonous stress-strain curves ; (b) Lüders strain state ; (c) rational stress-strain curves and Ramberg-Osgood models.

Figure 5 :

 5 Figure 5 : Typical dislocation patterns with plastic strains for NO and GO alloys.

Figure 6 :

 6 Figure 6 : Relationship between the surface densities Ω 1 , Ω 2 and plastic strain levels.

Figure 7 :

 7 Figure 7 : Product µ ri .H c plotted against ε p , GO and NO alloys. Linear relationship between plastic strains and dislocation density.

Figure 8 :

 8 Figure 8 : Abstract of the experimental results concerning dislocation structures, magnetic domain patterns, coercivity and (H c .µ ri ) product for NO and GO alloys at various stages of plastic deformation. Validity of potential and bowing models for domain walls / dislocations interactions.

Figure 9 :

 9 Figure 9 : Evolution of H c with the plastic stress level ∆σ for NO and GO alloys,

TABLE 1

 1

	Author : E. HUG

TABLE CAPTIONS LISTTable 1 :

 CAPTIONS1 typical values of the mechanical parameters representative of the tensile test behaviour of the two SiFe alloys.


Member, IEEE Anna Guerra

Member, IEEE Francesco Guidi

Senior Member, IEEE Davide Dardari

On the impact of beamforming strategy on mm-wave localization performance limits

Keywords: Position Error Bound, Millimeter-wave, Massive array, 3D localization

In this paper we investigate the localization performance limits of massive arrays working at millimeter-wave (mm-wave) frequencies and adopting two different beamforming strategies. In the first one, array weights are set in order to point towards a precise direction (classic beamforming), whereas in the second one, such weights are randomly chosen (random beamforming). Thanks to the large set of measurements as well as the high angular resolution provided by massive arrays, only one single anchor node can be used for localization estimation, thus avoiding over-sized infrastructures dedicated to positioning. Accounting for such beamforming strategies, performance is evaluated by taking into account the effects of arrays orientation and beamforming weights non-idealities arising when the number of antennas is high and low-complex components are adopted. Results reveal that classical beamforming outperforms the random one which still remains a feasible solution when the system complexity has to be kept affordable.

I. INTRODUCTION

Fifth generation personal devices will be required to perform self-localization in indoor environments as well as to share a huge amount of data at extremely high rates [START_REF] Dardari | Location-aware communications for 5G networks: How location information can improve scalability, latency, and robustness of 5G[END_REF]. To face these challenges, massive arrays and mm-wave frequencies emerge like potential candidates for including a large number of antennas in a small size with the possibility to focus the array beam in a precise direction in space [START_REF] Chin | Emerging technologies and research challenges for 5G wireless networks[END_REF]- [START_REF] Swindlehurst | Millimeter-wave massive MIMO: The next wireless revolution?[END_REF]. In this context, an access point (AP) equipped with a massive array could be in principle used as a single-anchor node, i.e., a node whose position is a-priori known, permitting the mobile users to be aware of their positions, and, thus, enabling new applications such as those related to augmented reality and cyber-physical systems, as depicted in Fig. 1. Moreover, when operating at such high frequencies, the portable devices can also adopt massive arrays as the reduced wavelength permits to pack a large number of antennas in small spaces, as for example smartphones or tablets [START_REF] Razavizadeh | Three-dimensional beamforming: A new enabling technology for 5G wireless networks[END_REF]- [START_REF] Garcia | Direct localization for massive MIMO[END_REF].

Different works deal with the derivation of the Cramer-Rao Lower Bound (CRLB) as a tool to investigate the ultimate performance of a localization system [START_REF] Shen | On the accuracy of localization systems using wideband antenna arrays[END_REF]- [START_REF] Guerra | Position and orientation error bound for wideband massive antenna arrays[END_REF]. Notably, the CRLB can be considered as an asymptotic lower bound for all estimators and it can be asymptotically achieved, for example, by the maximum likelihood estimator (MLE) operating in high signal-to-noise ratio (SNR) regime. Therefore, here we aim at Anna Guerra and Davide Dardari are with the Dipartimento di Ingegneria dell'Energia Elettrica e dell'Informazione "Guglielmo Marconi" -DEI, University of Bologna,Via Venezia 52, 47521 Cesena, ITALY.

(e-mail: anna.guerra3@unibo.it, davide.dardari@unibo.it).

Francesco Guidi is with CEA, LETI, MINATEC Campus, 38054 Grenoble, France. (e-mail: francesco.guidi@cea.fr). presenting the localization performance as a benchmark for real estimators without providing new localization techniques as done, for example, in some our previous works [START_REF] Guidi | Joint energy detection and massive arrays design for localization and mapping[END_REF]. In [START_REF] Shen | On the accuracy of localization systems using wideband antenna arrays[END_REF], [START_REF]Fundamental limits of wideband localizationpart I: A general framework[END_REF], the Position Error Bound (PEB) is derived for a wideband sensors network composed of several anchors and multipath effects are taken into account in the analysis. Nevertheless, in these works, beamforming strategies are completely neglected as anchors were considered equipped with a single antenna unable to perform beamsteering operations. Moreover, even if considered as a virtual array, anchors operate independently to each other as in multiple-input multiple-output (MIMO) systems. In our previous work [START_REF] Guerra | Position and orientation error bound for wideband massive antenna arrays[END_REF], some preliminary results on positioning accuracy have been presented for different fractional bandwidth and spherical arrays.

Stimulated by this framework, in this paper we propose a PEB study to compare the localization capabilities of mm-wave massive arrays operating different beamforming strategies. More specifically, classical and random beamforming will be compared in terms of positioning performance. In both cases, a phased array composed of phase shifters (PSs) is considered, as reported in Fig. 2. In the first strategy, all the beamforming weights are set in order to point towards a precise direction, e.g., the AP, while in the second one, the weights are randomly chosen. From a radiation pattern pointof-view, classical beamforming permits to accurately shape the radiation pattern radiation pattern with a main narrow beam in the intended direction. Differently, random beamforming results in a non-defined pattern shape but, at the same time, it permits to maintain a certain level of diversity gain while keeping the architecture complexity lower. In fact, as shown in [START_REF] Kaouach | Wideband low-loss linear and circular polarization transmit-arrays in V-band[END_REF]- [START_REF]Wideband 400-element electronically reconfigurable transmitarray in X band[END_REF], where transmitarrays (i.e., a particular type of phased arrays consisting of a focal source illuminating a planar array) have been proposed, PSs are usually realized using switches. Therefore, as it is often unfeasible to obtain a continuous phase value ranging from 0 • to 360 • with real antennas, the resulting quantization errors should be taken into account in the analysis. Thus, this paper proposes a CRLBbased investigation on how a proper choice of the beamforming strategy can lead to different levels of localization accuracy and of array complexity.

The rest of the paper is organized as follows. In Sec. II we describe the considered array configurations, whereas in Sec. III we discussed an ad-hoc signal model for the analyzed multi-antennas schemes. Sec. IV shows the PEB derivation, where results are given in Sec. V. Final conclusions are successively drawn in Sec. VI.

II. ANTENNA ARRAY GEOMETRIC CONFIGURATION

We consider a 3D localization scenario consisting of a N rx -sized receiving array located in known position (i.e., p r = [x r 0 , y r 0 , z r 0 ] T = [0, 0, 0] T ) and a transmitting array with N tx antennas whose position,

p t = [x t 0 , y t 0 , z t 0 ] T = [x, y, z]
T , is to be inferred by the estimation process. We indicate with θ = [θ, φ]

T the direction-of-arrival (DOA), i.e., the angle formed between the two arrays geometric centers. Moreover, if classical beamforming is considered, the steering angles will be indicated with θ 0 = [θ 0 , φ 0 ]

T . In both arrays, the antennas coordinates with respect to the array centroid can be expressed as

p t/r i/m (ϑ t/r ) = x t/r i/m , y t/r i/m , z t/r i/m T = ρ t/r i/m R ϑ t/r d T θ t/r i/m (1)
with i = 1, 2, . . . , N tx , m = 1, 2, . . . , N rx being the 1D transmitter (TX)/receiver (RX) antenna index, R ϑ t/r being the 3D rotational matrix with ϑ t/r = ϑ t/r , ϕ t/r T being the transmitting/receiving array orientation with respect to its geometric center. The direction cosine in ( 1) is given by

d (θ) = [sin(θ) cos(φ), sin(θ) sin(φ), cos(θ)] . (2)
Finally,

ρ t/r i/m = p t/r i/m (ϑ t/r ) -p t/r 2 and θ t/r i/m = θ t/r i/m , φ t/r i/m
T represent the transmitting/receiving spherical coordinates.

Having indicating with D the maximum diameter and with d = p rp t 2 the distance between the two arrays, we suppose that they are sufficiently far from each other, i.e., D ≪ d, in order to assume an identical angle of incidence at all the array antennas. Note that this hypothesis is especially verified at mm-wave where the array dimensions are very small thanks to the reduced wavelength. Given this assumption, it is possible to express the propagation delay and the amplitude between the mth receiving and the ith transmitting antenna, respectively, as

1) τ im ≈ τ + τ t i (θ, ϑ t ) -τ r m (θ, ϑ r ) 2) a im ≈ a (3)
where τ im p r mp t i 2 /c is the time-of-arrival (TOA) between the mth receiving and the ith transmitting antenna,

√ E P (f ) √ E P (f ) µ t 1 (θ 0 ) + δ t 1 υ 1 µ t i (θ 0 ) + δ t i υ i µ t Ntx (θ 0 ) + δ t Ntx υ Ntx
τ p r -p t 2 /c = d/c
is the TOA between the arrays centers and τ t/r i/m (θ, ϑ t/r ) is the transmitting/receiving interantenna delay given by

τ t/r i/m (θ, ϑ t/r ) = 1 c d (θ) p t/r i/m ϑ t/r (4)
with c being the speed of light.

III. BEAMFORMING SCHEMES AND SIGNAL MODEL

In this section, the two array beamforming strategies present in Fig. 2 will be analysed from a signal processing point-ofview and by focusing on how the different signaling phasing schemes translate in different localization capabilities.

A. Transmitted Signal Model and Beamforming

The transmitted signal at the ith transmitting antenna is denoted with g(t) = √ E ℜ p(t) e j 2 πfct with p(t) being the unitary energy equivalent low-pass signal, and f c the carrier frequency. We consider a constraint on the total transmitted energy E tot which is uniformly allocated among antennas, thus E = E tot /N tx represents the normalized energy at each antenna element. We introduce the Fourier transform of p(t) as P (f ) = F {p(t)}, with F {•} denoting the Fourier transform operation in a suitable observation interval T obs . For further convenience, the vector p(f ) = P (f ) 1 Ntx×1 contains all the baseband transmitted signals with 1 Ntx×1 being a N tx -sized vector of all ones.

In multi-antenna systems, beamforming is obtained by applying different weights at each array element. In classical beamforming, the objective of this operation is to coherently sum up signals towards the intended steering direction, i.e. θ 0 . Considering the signal bandwidth W , when W ≪ f c holds, this process can be realized using only PSs. The corresponding array structure is referred as phased array. Contrarily, in random beamforming, weights are randomly generated resulting in a non-directive radiation pattern but in an extremely low-complexity array design. In both cases, the beamforming weights are collected in a matrix that can be defined as

B = diag (ω 1 , ω 2 , . . . , ω i , . . . ω Ntx ) (5)
where the ith PS generic element can be written as

ω i = e j 2 π fc τ t i (θ0) = e jµ t i (θ0) Classical Beam. e j υi Random Beam. ( 6
)
with υ i uniformly distributed between 0 and 2 π, i.e., υ i ∼ U (0, 2π).

In addition, even when classical beamforming is adopted, some technological issues could induce errors in the beamforming vector resulting in an increased side-lobe level (SLL), decreased array maximum gain and angular resolution. In fact, in practical implementations, digitally controlled PSs are often adopted in place of their high-resolution analog counterparts inducing quantization errors, to be accounted for in the localization performance analysis [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF].

In the presence of such non-perfect weights, a matrix accounting for non-idealities is introduced

Q = diag (ς 1 , ς 2 , . . . , ς i , . . . , ς Ntx ) (7)
where ς i takes into account the i th beamforming weight quantization error, i.e., ς i = exp (jδ t i ) with δ t i being the phase error. For further convenience, let indicate with ωi = exp (j(µ t i (θ 0 ) + δ t i )) the quantized weights in classical beamforming; whereas ωi = ω i in random beamforming.

B. Received Signal Model

All the received signals are gathered in a vector

r(f )=[R 1 (f ), . . . , R m (f ), . . . , R Nrx (f )]
T , where R m (f ) = F {r m (t)} is evaluated in T obs and r m (t) is the equivalent low-pass received signal at the mth receiving antenna. Specifically, the received signal vector can be written as r(f ) = x(f ) + n(f ), where the set of useful received signals is

x(f ) = [X 1 (f ), . . . , X m (f ), . . . , X Nrx (f )] T = √ E a r (f, θ, ϑ r ) c(f, τ ) A t (f, θ, ϑ t ) Q B p(f ) (8)
and n(f

) = [N 1 (f ), . . . , N m (f ), . . . , N Nrx (f )]
T is the noise vector with N m (f ) = F {n m (t)}, with n m (t) ∼ CN (0, N 0 ) being a circularly symmetric, zero-mean, complex Gaussian noise. The receiving and transmitting direction matrices for the inter-antennas delays and TX orientation are a r (f, θ, ϑ r ) = e j γ r 1 , . . . , e j γ r m , . . . , e j γ r Nrx T (9)

A t (f, θ, ϑ t ) = diag e -j γ t 1 , . . . , e -j γ t i , . . . , e -j γ t N tx [START_REF] Han | Performance limits and geometric properties of array localization[END_REF] with

γ t/r i/m = 2π (f + f c ) τ t/r i/m (θ, ϑ t/r ). The channel vector is indicated with c(f, τ ) = α 1 1×Ntx being the 1 × N tx , whose generic element is α = a exp (-j 2 π (f + f c ) τ ).
For further convenience, define ν t = E t /N 0 = ν N tx , with ν = E/N 0 . The SNR at each receiving antenna element is SNR t = N tx SNR 1 , where SNR 1 = a 2 ν represents the SNR component related to the direct path between a generic couple of TX-RX antenna elements.

IV. POSITION ERROR BOUND

In the following, we will derive the asymptotic limits of the TX position (i.e., p t ) estimation error starting from the set of received waveforms r(f ). Thus, we define the unknown parameters vector as ψ = (p t )

T , a T . We assume that an initial search between the TX and RX is conducted in order to coarsely infer the TX position and to allow the TX setting its own beamforming weights to point towards the RX in the case in which classical beamforming is operated.

The performance of any unbiased estimator ψ = ψ (r (f )) can be bounded by the Cramér-Rao bound (CRB) defined as [START_REF] Van Trees | Detection, estimation, and modulation theory[END_REF] E r,ψr ψψ ψψ

T J -1 ψ = CRB (ψ) (11)
where J ψ is the Fisher Information Matrix (FIM) given by

J ψ -E r,ψr ∇ 2 ψψ ln f (r|ψ) = J pp J pa J ap J aa (12)
with the symbol ∇ 2 ψψ = ∂ 2 /∂ψ∂ψ indicating the second partial derivatives with respect to the elements in ψ and

J pp =   J xx J xy J xz J yx J yy J yz J zx J zy J zz   , J pa =   J xa J ya J za   . ( 13
)
Since the observations at each receiving antenna element are independent, the log-likelihood function ln f (r|ψ) can be written as

ln f (r|ψ) ∝ - 1 N 0 Nrx m=1 W |R m (f ) -X m (f )| 2 df. (14)
According to ( 12)-( 14), it is possible to compute the elements of the FIMs as

J p b pa = 8 π 2 ν a 2 mij ℜ {ω ij ξ ij χ ij (2) } ∇ pa (τ im )∇ p b (τ jm ) J a a = 2 ν mij ℜ ωij ξ ij R p ij (∆τ ij ) J p b a = 4 π a ν mij ℑ { ωij ξ ij χ ij (1)} ∇ p b (τ im ) = 0 (15)
where p a/b indicate two elements in the set {x, y, z}, mij =

Nrx m=1

Ntx i=1 Ntx j=1 , ωij = ωi (ω j ) * , ξ ij = e -j 2 π fc ∆τij with ∆τ ij = τ imτ jm , and

χ ij (2) = W (f + f c ) 2 e -j 2 π f ∆τij |P (f )| 2 df χ ij (1) = W (f + f c ) e -j 2 π f ∆τij |P (f )| 2 df R p ij (∆τ ij ) = W e -j 2 π f ∆τij |P (f )| 2 df. ( 16
)
The derivatives translating the TOA and DOA in position information can be expressed as

∇ p (τ im ) = 1 c c ∇ p (τ ) + ∇ p (d (θ)) p t i (ϑ t ) -p t m (ϑ r ) (17)
with

∇ p (d (θ)) =∇ p (θ) cos(θ)   cos(φ) sin(φ) -tan(θ)   T + ∇ p (φ) sin(θ)   -sin(φ) cos(φ) 0   T . ( 18
) ∇ pp (τ im , τ jm ) =   ∇ x (τ im ) ∇ x (τ jm ) ∇ x (τ im ) ∇ y (τ jm ) ∇ x (τ im ) ∇ z (τ jm ) . . . ∇ y (τ im ) ∇ y (τ jm ) ∇ y (τ im ) ∇ z (τ jm ) . . . . . . ∇ z (τ im ) ∇ z (τ jm )   = d 2 ant (c y) 2    (m x -i x ) (m x -j x ) y dant (m x -i x ) (m x -i x )(j z -m z ) . . . y 2 d 2 ant y dant (j z -m z ) . . . . . . (i z -m z ) (j z -m z )    (19)
Moreover, by further analyzing [START_REF] Guidi | Joint energy detection and massive arrays design for localization and mapping[END_REF], one can notice the dependence of the FIM from the beamforming weights given by the coefficients ωij .

Finally, by using the Schur complement, the PEB expression can be easily derived as

PEB = tr (CRB (p t )) = tr J pp -J pa J -1 aa J H pa -1 = tr J -1 pp ( 20
)
where tr (•) is the trace operation. Equation ( 20) is a general bound valid for any beamforming strategy and accounting for signal weights quantization effects. Specialized expressions can be derived from [START_REF] Van Trees | Detection, estimation, and modulation theory[END_REF] for specific cases to get insights on the key parameters affecting the performance as it will be done in the following.

A. Absence of Quantized Weights in Classical Beamforming

Here we provide an example on how the general expression (20) can be simplified in absence of beamforming weights errors. Given the FIM in [START_REF] Guidi | Joint energy detection and massive arrays design for localization and mapping[END_REF], it can be easily found that for classical beamforming it is

PEB = tr G -1 J-1 pp (21)
where we have separated the effect of signal design Jpp (i.e., that related to ( 16)) from that of the geometry G (i.e., that related to [START_REF] Clemente | 1-bit reconfigurable unit cell based on pin diodes for transmit-array applications in-band[END_REF]). Specifically for phased arrays, we have

Jpp = 8π 2 SNR 1 β 2 + f 2 c (22) G = mij ∇ pp (τ im , τ jm ) (23)
where ∇ pp (τ im , τ jm ) is a 3 × 3 matrix and β 2 is the squared baseband effective bandwidth of p(t).

The matrix G provides, through derivatives, the relationship between the TOA-DOA at each TX-RX antenna element couple and the TX position. To improve the comprehension of [START_REF]Revision of Part 15 of the Commissions Rules Regarding Operation in the 57-64 GHz Band[END_REF], in the next paragraph the particular case of planar arrays will be discussed considering a fixed orientation ϑ t = ϑ r = [0, 0] T .

1) Special Case: Planar Array: For squared arrays with antennas spaced of d ant , we can compute a simplified version of [START_REF] Clemente | 1-bit reconfigurable unit cell based on pin diodes for transmit-array applications in-band[END_REF]. Specifically, it is possible to obtain:

∇ p (τ im ) = 1 c [c ∇ p (τ ) + d ant ((i x -m x )∇ p (φ) +(m z -i z )∇ p (θ))] (24)
with

m x = m z = - √ Nrx 2 , . . . , √ Nrx 2 and i x = i z = j x = j z = - √ Ntx 2 , . . . , √ Ntx
2 . From (24), it is straightforward to derive [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF]. Then, by considering the summations present in (22), it is possible to obtain the elements of the position CRB matrix as

CRB (x) = CRB (z) = CRB 0 12 S 1 N tx (N rx -1) CRB (y) = CRB 0 N tx N rx ( 25
)
where CRB 0 represents the CRB of the ranging error one would obtain using single antenna which can be written as

CRB 0 = c 2 8π 2 SNR t (β 2 + f 2 c ) (26)
and S = A r /y 2 with A r = N rx d ant .

From (25) it is possible to remark that the CRB of the estimation error in the y-coordinate is inversely proportional to N tx and N rx : in fact, the N tx term accounts for the SNR enhancement due to the beamforming process while the N rx term accounts for the number of independent measurements available at the RX.

V. NUMERICAL RESULTS

In this section, numerical results are reported considering the two discussed beamforming schemes. For what the antennas spatial deployment is regarded, planar arrays are accounted for as they represent the most conventional structure to be integrated in small-sized devices. Differently from Sec. IV-A1, here we compare results with fixed and averaged RX orientations, thus giving the possibility to appreciate the impact of the array rotation on the localization performance.

We consider a scenario with a single RX with the centroid placed in p r = [0, 0, 0] T , and a TX located in p t = [0, 5, 0] T (d = 5 m). As previously assumed, the RX has a perfect knowledge of the TX steering direction.

Results are obtained for f c =60 GHz and W =1 GHz (the signal duration is τ p = (1 + β)/W = 1.6 ns) in free-space conditions. Root raised cosine (RRC) transmitted pulses centered at frequency f c = 60 GHz and roll-off factor β = 0.6 are adopted, being compliant with the Federal Communications Commission (FCC) mask at 60 GHz [START_REF]Revision of Part 15 of the Commissions Rules Regarding Operation in the 57-64 GHz Band[END_REF]. A noise figure of N F = 4 dB and a fixed transmitted power of P t = 10 mW are considered, if not otherwise indicated.

The performance is evaluated in terms of PEB averaged over N cycle = 500 Monte Carlo iterations. For each cycle, a different 3D RX array orientation is generated. The antennas are spaced apart of d ant = λ L /2, where λ L = c/f L and f L = f c -W/2. When present, the PSs quantization errors are δ t i ∼ U (-π/4, π/4) and the random beamforming weights υ i ∼ U (0, 2π).

A. Results

Results have been obtained in free space conditions as a function of the number of antennas; of the beamforming schemes (i.e., classical vs. random); of the presence or absence of quantization errors; and as a function of arrays orientation.

In Fig. 3, the PEB performance is reported as a function of N tx , for N rx = 25 and averaged over different RX's orientations, apart for results refering to the fixed orientation (i.e., ϑ r = [0, 0] T ). It can be observed that classical beamforming is very sensitive to the particular geometric configuration chosen when compared with its random counterpart, and performance can drastically decrease when a rotational angle is considered. On the other side, the impact of quantization errors is not much appreciable both in fixed and averaged RX orientations.

For what random beamforming is regarded, it shares the structure simplicity of phased arrays but it does not allow the formation of a high gain main beam pointing towards the RX, and thus, the positioning accuracy results degraded with respect to that achievable with classical beamforming. Nevertheless, as previously mentioned, it results more insensitive with respect to the RX orientation. Consequently, if the localization accuracy required by the application of interest is not so stringent, random beamforming can be an interesting option to guarantee both a sub-centimeter positioning accuracy (e.g., for N rx = 50 and N tx = 25, PEB ≈ 1 cm) and an easy implementation in future devices operating at mm-wave frequencies. For example, it could be employed for an initial coarse users localization estimation useful as a preliminary step before a precise beamforming operation. For what the number of TX antennas is concerned, it can be observed that the localization performance for N tx > 25 is almost constant for all the configurations, and thus, it can be relaxed in order to guarantee an easy integration in portable devices. In Fig. 4, the PEB results are reported as a function of the receiving antennas with N tx fixed to 25. The same considerations drawn for Fig. 3 hold with the exception of those regarding the dependence on N rx . Indeed, in this case, a higher number of antennas translates in a higher number of collected measurements and thus, in an increased localization accuracy.

VI. CONCLUSION

In this paper, we have considered a new scenario where a single-anchor localization exploiting mm-wave massive arrays has been put forth for next 5G applications. The theoretical PEB has been evaluated for different beamforming strategies, i.e., classical vs. random beamforming. Moreover, phase quantization errors and arrays orientation have been taken into account in the analysis.

From numerical results, we can conclude that classical beamforming permits to achieve a better localization performance thanks to the capability of focusing the power towards a precise direction in space; nevertheless, random beamforming attains a sub-centimeter accuracy even when the number of antennas is not extremely massive. Finally, the impact of quantization errors can be considered negligible. Consequently, whenever the localization requirements are not too stringent, it is possible to relax the implementation constraints (i.e., adoption of switches instead of analog PSs) without severely degrading the localization performance.

Fig. 1 .

 1 Fig. 1. Single AP localization scenario.

Fig. 2 .

 2 Fig. 2. Classical and random beamforming schemes.

Fig. 3 .

 3 Fig. 3. Classical and random beamforming PEB vs. Ntx, Nrx = 25.

Fig. 4 .

 4 Fig. 4. Classical and random beamforming PEB vs. Nrx, Ntx = 25.

ACKNOWLEDGMENT

This work has been supported by the H2020 project XCycle (Grant 635975) and in part by the H2020-EU.1.3.2 IF-EF Marie-Curie project MAPS (Grant 659067).


Eugénie Granado

Emelyne Gervais

Guillaume Gotti

Sandrine Desclaux

Martine Meireles

Pierre Gros

David Evrard
email: evrard@chimie.ups-tlse.fr

Influence of Coating Process on Surface Reactivity and Analytical Performances

Keywords: Chemically prepared gold nanoparticles, drop-casting, deposit morphology, electrochemical reactivity, mercury(II) trace detection

published or not. The documents may come

INTRODUCTION

Since the middle of the 20 th century, heavy metals represent a growing environmental [1,2] and health [3,4] problem. They are considered to be a major ecological issue due to their wide dispersion in natural media [5], including fresh and marine waters, air and soils [6]. Heavy metals mainly originate from human activities, namely atmospheric emissions from coal-burning plants, smelters, waste incinerators, process waste from mining, industrial and urban runoff, and so on [7,8]. Once released into the environment, they are a persistent threat for decadal or even longer time scales since they are not biodegradable. Amongst all heavy metals, mercury (Hg) is of particular interest and global importance. Hg is present in natural media as inorganic and organometallic species, the latter one being the toxic and bioaccumulating methylmercury (MeHg) form [9,[START_REF] Fitzgerald | Geochemistry of mercury in the environment[END_REF]. Acute MeHg exposure can cause adverse health effects for mammals including humans, such as eyesight problems, trembling, paresthesia or ataxia [START_REF] Mergler | [END_REF][START_REF] Sakamoto | A review of mercury toxicity with special reference to methylmercury[END_REF]. Chronic MeHg exposure, even at lower levels, has been related to developmental neurotoxicity of the fetus and is thus far considered to be the most critical endpoint [START_REF] Sonke | [END_REF]. MeHg production relies on the concentration and (bio-)availability of inorganic Hg(II) [14]. Due to the bioaccumulation phenomena, this latter may be dangerous even at very low levels [9,15,16]. Consequently, the World Health Organization has delivered a guideline value of 1 µg L -1 (ca. 5 nM) for drinking water [17]. In Europe, the implementation of the European Water Framework Directive [18] requires all states to monitor hazardous substances in surface, ground and coastal waters throughout Europe. Thus, there is an urgent need for in situ, real-time and highly-sensitive Hg(II) sensors in order to multiply monitoring points dedicated to early warning pollution alert [19].

Hg(II) traces are routinely quantified in analytical laboratories by spectroscopic techniques such as cold-vapor atomic absorption spectrometry or cold-vapor atomic fluorescence spectrometry [20][21][22]. This latter offers selectivity and quite good sensitivity, reaching 0.2 pM for total Hg(II) [23]. However, these techniques suffer important limitations since they involve expensive material and require complex and time-consuming procedures, thus limiting any in situ or on line and operando analysis. Moreover, rigorous sampling and storage conditions are necessary to avoid any external Hg contamination or speciation changes [24,25].

In this context, electrochemistry affords an interesting alternative due to its manifold advantages over other detection techniques: electrochemical devices are usually cheap, user-friendly, require only few energy and simple procedures. They are also mostly reagentless and well-suited for miniaturization and automatic in situ measurements with minimal sample changes, and quite fast analyses may be achieved with experimental data obtained in real time or with a few minutes time-lag. Finally, limits of detection (LOD) in the pM range can be reached using a combination of a preconcentration step like anodic stripping voltammetry (ASV) and pulsed techniques such as differential pulse (DPV) or square wave voltammetry (SWV) [26,27]. Another strategy for the improvement of the analytical performances concerns electrode surface functionalization. The wide range of possibilities reported in the literature has been recently reviewed [27,28]. Amongst all modifiers, gold nanoparticles (AuNPs) have received a particular attention with respect to Hg(II) trace determination [29][30][31][32][33]. This is mainly due to the fact that Au exhibits a strong affinity for Hg that enhances the preconcentration effect and to the specific physicochemical properties of nanoparticles (NPs) [34]. These include enhanced diffusion rate of electroactive species based on high effective surface area of NPs, catalytic activity, higher signal-to-noise ratio and unique optical properties [35]. AuNPs may be prepared either via chemical route [36,37] followed by physicochemical deposition onto the electrode surface or by direct electrodeposition [38,39]. In the latter case, AuNPs are often electrodeposited using a given electrochemical method without providing any justification nor checking the influence of the deposit morphology on Hg(II) detection [30][31][32]. On the contrary, we have recently reported on Hg(II) trace determination on a GC electrode (AuNPs-GC) functionalized by AuNPs deposited using cyclic voltammetry [40], and proved the analytical performances to be strongly correlated to both the density and size of the NPs, the best responses being obtained on AuNPs-GC electrodes exhibiting high density of rather small, spherical-shaped NPs. This was further verified by studying different AuNPs electrodeposition modes, namely constant potential electrolysis (CPE) and potentiostatic double pulse (PDP) [41]. In this latter work, it was shown that the best results in terms of LOD were obtained with AuNPs electrodeposited onto GC by CPE. In order to further optimize the analytical performances, we also examined the physicochemical phenomena which occur at the electrode/solution interface during SWASV and showed that chloride anions adsorption on Au surface was a key parameter [42]. As a consequence, further improvement was brought by adding a chloride desorption step in the analytical procedure and the applicability of the AuNPs-GC electrode to Hg(II) trace analysis in natural waters was demonstrated [43]. In particular, a Hg(II) value of 19 pM was measured using the AuNPs-GC electrode for a submarine groundwater discharge sample, and confirmed by CV-AFS. In the case of chemically prepared AuNPs, the use of soundly chosen, complicated capping ligand such as polystyrenesulfonate doped poly(hydroxymethyl 3,4ethylenedioxythiophene) [44] or 1,2-bis[5,2-thiolmethyl-sulphide-1,3,4-oxadiazol-2-yl]-ethane [33] is often required to ensure AuNPs stabilization and adsorption onto the electrode surface. In an alternative strategy, Li et al. have taken advantage of the highly porous feature of the specific threedimensional fibril-like carbon fiber mat substrate (CFME) [32] to adsorb their chemically-prepared AuNPs. Finally, the group of Mandler has operated a pretreatment to indium-tin oxide substrates by dipping the electrodes in polyethylenimine prior to colloidal AuNPs deposition [45]. However, none of these works provide any information correlating the deposits morphology and the analytical performances with respect to Hg(II) trace determination.

In the present work, we explore a simple procedure to functionalize GC electrodes by colloidal AuNPs. These latter were prepared by using the classical method described by Turkevich [46] and refined by Frens [47]. The resulting AuNPs were then filtered and deposited onto GC by simple dropcasting at different temperatures. The corresponding AuNPs-GC electrodes were characterized by CV in H 2 SO 4 , Pb underpotential deposition (UPD) and field emission gun scanning electron microscopy (FEG-SEM), and their response to low Hg(II) concentration examined. In particular, a correlation between the activation step of the AuNPs and the sensitivity of the functionalized electrode was evidenced. Finally, a comparison with our previous results obtained using electrodeposited AuNPs and other reports from the literature was provided.

EXPERIMENTAL

Chemicals and apparatus

All the solutions were prepared using ultra-pure water (Milli-Q Millipore, 18.2 MΩ cm). HAuCl 4 x3H 2 O (pro analysis grade) was purchased from Acros Organics. Trisodium citrate (C 6 H 5 Na 3 O 7 ) anhydrous was obtained from Alfa Aesar. 95 % H 2 SO 4 (normapur grade) was supplied by VWR Prolabo. 30 % HCl and NaNO 3 (suprapur grade) were obtained from Merck. A standard stock solution of 4.99 ± 0.01 µM Hg(II) was prepared by dilution of 1001 ± 2 mg L -1 Hg(NO 3 ) 2 NIST standard solution (certiPUR grade, Merck) and acidified to pH 2 with concentrated 65 % HNO 3 (suprapur grade, Merck), and then used as it for further dilution.

All the electrochemical experiments were performed at room temperature in a classical threeelectrode glass cell (Metrohm) by using a µ-Autolab II potentiostat (Metrohm Autolab, Utrecht, Netherlands) interfaced to a personal computer and controlled with GPES 4.9 software package (Metrohm). A Metrohm Ag/AgCl/KCl 3 M electrode, separated from the electrochemical cell by a Teflon PTFE capillary containing a 0.1 M NaNO 3 solution and terminated by a ceramic diaphragm (D type), and a Metrohm glassy carbon (GC) wire were used as reference and counter electrodes, respectively. Working electrodes were GC rotating disk electrodes from Radiometer (3 mm diameter, A = 7.07 mm 2 ) or AuNPs-modified GC (AuNPs-GC). The electrochemical cell was maintained in a Faraday cage in order to minimize the electrical interferences. When necessary, working electrodes were rotated using a rotating system Model EDI 101 interfaced to a CTV 101 speed control unit from Radiometer. When indicated, the solutions were deaerated using a N 2 stream for 10 min. A N 2 atmosphere was then maintained over the solution during the corresponding experiments.

Total Hg analyses were performed by cold-vapor atomic fluorescence spectrometry (CV-AFS) following a method from the Environmental Protection Agency (EPA-1631) that was extensively described in one of our previous work [43].

AuNPs synthesis and filtration

Gold nanoparticles were prepared using a previously reported procedure [48], in accordance with the classical method described by Turkevich [46] and refined by Frens [47]. Briefly, 22 mg (8.5×10 -5 mol) of sodium citrate was dissolved in 30 mL of Milli-Q water. The solution was heated under reflux and 20 mL of an aqueous solution of HAuCl 4 (9.9 mg, 2.5×10 -5 mol) was quickly added. The mixture was kept under reflux for 20 min and then cooled to room temperature to afford a ruby red solution. Because nanoparticles are prone to aggregate in suspension even when a stabilizer such sodium citrate is present in solution, for some experiments the suspension was filtered using a 0.45-µm cutoff polyethersulfone membrane filter (VWR) prior to drop-casting in order to assess the influence of the occurrence of aggregation in the suspension on the deposit morphology.

Electrode preparation and modification

All the working electrodes were carefully polished prior to use. They were first polished by silicon carbide grinding paper (grit 1200) for 10 s. GC surfaces were further polished successively by a 9 µm, 3 µm, 1 µm and 0.25 µm diamond suspension (Presi) on a cloth polishing pad during 2 min for each size. Between each polishing step, the surfaces were cleaned with Milli-Q water. Finally, the electrodes were rinsed in an ultrasonic 96 % ethanol bath (three times for 10 min) and cleaned with Milli-Q water. After drying, the quality of the polishing step was verified by checking the surface state using a Nikon Eclipse LV150 optical microscope.

Electrode functionalization was achieved by using the drop-casting technique. Briefly, 50 µL of the colloidal AuNPs solution was dropped on the GC surface and evaporated overnight either at room temperature or in an oven at 100 °C. All the electrodes were then carefully rinsed using Milli-Q water and then activated by cyclic voltammetry between 0.2 and 1.4 V in a deaerated 0.5 M H 2 SO 4 solution.

AuNPs characterization

AuNPs were characterized by transmission electronic microscopy (TEM) at the Centre de Microscopie Electronique Appliquée à la Biologie (CMEAB, Toulouse) using a HT 7700 Hitachi equipment with an accelerating voltage of 80 kV. Average diameter measurements were carried out by micrograph analysis with Origin 8, using between 1500 and 3000 nanoparticles for each sample.

Zeta potentials were obtained from electrophoretic measurements on a Malvern Zetasizer Nanoseries ZS90 controlled by integrated software. Calculations were performed using the Smoluchowski model [49,50].

The AuNPs-GC surface was characterized by field emission gun scanning electron microscopy (FEG-SEM) at the CMEAB using a Quanta 250 FEG FEI equipment with an accelerating voltage of 5 kV and a working distance between 3 and 8 mm depending on the sample. Image analysis was carried out using a LGC homemade program for particles counting (density estimation) and average diameter measurement developed using MatLab image processing toolbox software.

Pb underpotential deposition (UPD) experiments were conducted in a 0.01 M HClO 4 solution containing 1 mM Pb(NO 3 ) 2 . A potential step of -0.4 V was applied for 10 s before stripping from -0.35 V to 0.3 V at 50 mV s -1 .

Stripping voltammetric detection of Hg(II)

The analytical procedure dedicated to Hg(II) trace determination was the same as that reported in previous works from our group [40,41], in order direct comparison to be made. Electrochemical detection and assay of Hg(II) on AuNPs-GC electrodes were performed in a deaerated (N 2 ) 0.01 M HCl solution by using square wave anodic stripping voltammetry (SWASV) in the following conditions: cleaning potential = 0.80 V, cleaning time = 15 s; preconcentration cathodic potential = 0.00 V, preconcentration time = 300 s; pulse amplitude = 25 mV, step amplitude = 5 mV, frequency = 200 Hz; anodic scan from 0.00 to 0.80 V. During the preconcentration step, the solution was stirred by means of the rotating working electrode (2000 rpm). A second scan was recorded immediately after the first one using the same conditions except the preconcentration time which was set to 30 s, and considered as a blank. Hg oxidation peak heights were measured from the curves obtained after subtraction of the blank. This procedure, called "subtractive ASV method", has been previously reported in the literature [51]. It allows the analytical results to be released from background vagaries. It is noteworthy that the subtractive anodic signals recorded with low Hg(II) concentrations were noisy so that the use of a Savitzky-Golay smoothing function was required. Figure 1 depicts the TEM micrographs of AuNPs before and after filtration and their corresponding size distribution (Table 1). Micrographs showed a gaussian size distribution of spherical NPs with a 18 nm average diameter in both case. One can notice a very small proportion of ovale objects which could correspond to the aggregation of small nuclei. Zeta potential calculations gave a value of -46.1 mV and -43.3 mV respectively. Together with the size distribution, these results comfort the idea that the synthesis ensure a dispersion containing a large proportion of spherical NPs stable in solution. Moreover, the filtration step proved not to affect the NPs. Once characterized, both unfiltered and filtered AuNPs were deposited onto glassy carbon (GC) electrode substrates by using the drop-casting technique according to two different protocols: in the former one, the colloidal solution drop was left to dry at room temperature overnight; in the second one, the drying step was operated overnight in a stove at a given temperature of 100 °C. For the sake of clarity, the 4 different resulting deposits will be referred to as AuNPs(X)-GC with X = A, B, C and D as stated in Table 2. The AuNPs(X)-GC deposits were characterized by field emission gun scanning electron microscopy (FEG-SEM) and cyclic voltammetry (CV) in a deaerated 0.5 M H 2 SO 4 solution. Table 2 summarizes the corresponding results.

RESULTS AND DISCUSSION

AuNPs synthesis and characterization

AuNPs-GC electrodes characterization

AuNPs(A) formed a dense deposit onto GC with big beads of NPs, resulting in a nonhomogeneous distribution of the deposit over the entire surface (Fig. 2A). Calculations were undertaken including and excluding these bead structures, producing two sets of values (see Table 2 for features). The values obtained for NPs diameter and density were systematically higher while including the bead structures, but remained in the same order of magnitude when compared to the data set for which they are excluded. AuNPs(B)-GC deposits exhibited an almost similar morphology, however with a slightly lower NPs density. Less and smaller beads were observed in this case (Fig. 2B). Contrary to the former two deposits, AuNPs(C)-GC electrode showed significantly lower NPs density and no beads (Fig. 2C). Note that the large, bright objects in the middle of the micrograph are NaCl crystals from salt remaining in solution after NPs synthesis. These different observations may be accounted for considering the high evaporation rate associated with the drying procedure. The deposit lacked homogeneity, especially in the vicinity of the NaCl crystals where AuNPs aggregated. Finally, it has to be noticed that AuNPs(D) which were filtered after synthesis and deposited at 100 °C did not allow any exploitable FEG-SEM image nor voltammogram to be recorded. This experiment was repeated several times with a similar result, the reason for such a behavior remaining unclear to us.

In order to get more information upon AuNPs structuration, Pb underpotential deposition (UPD) experiments were performed in 0.1 M HClO 4 on AuNPs(X)-GC (X = A, B, C) (Fig. 2D). All three stripping voltammograms showed comparable shapes. AuNPs(C)-GC afforded much lower currents than AuNPs(A)-GC and AuNPs(B)-GC, in accordance with the corresponding deposit morphology observed by FEG-SEM: a less dense deposit of bigger NPs is expected to afford a lower active surface area. For all three deposits, a well-defined peak around -0.25 V associated to a shoulder was recorded. This split system is typical of (111)-oriented terraces with different size domains, the peak being commonly associated to wide Au(111) faces, whereas the shoulder is indicative of narrower Au(111) domains. Another broad signal centered around -0.05 V was noticed, which corresponds to Au(110) faces. It has to be noticed that, whatever the deposit to be considered, no signal characteristic of Au(100) faces was recorded in the potential range from -0.2 to -0.1 V. Thus, nor the filtration step neither the drop-casting temperature seemed to have a significant influence on the AuNPs crystallographic structure.

All the deposits were then activated by CV in a deaerated 0.5 M H 2 SO 4 solution. Fig. 3A depicts the 10 th and 60 th consecutive cyclic voltammograms (CVs) recorded for AuNPs(X)-GC (X = A, B, C). After 10 cycles, AuNPs(A)-GC exhibited the typical shape for such a CV at potentials higher than 1.1 V, with several oxidation peaks corresponding to the formation of different kinds of Au oxides (solid, blue line). However, another oxidation peak was also noticed at lower potential, ca. 1.05 V. This latter peak, which was significantly smaller than those at higher potentials, was assigned by Angerstein-Kozlowska et al. [52] and the group of Compton [53] to the formation of a sublattice of OH species deposited between specifically adsorbed anions. It is noteworthy that this peak (referred to as "OA1" following the nomenclature proposed by Angerstein-Kozlowska et al.), the appearance of which was random, had never been observed in our previous studies dealing with electrodeposited AuNPs [40,41,43,54]. Since Kolb et al. reported a correlation between OA1 peak current and the density of surface defects [55,56], this latter observation suggested that chemically prepared AuNPs contain more surface defects than electrochemically generated ones. On the backward scan, the characteristic reduction peak of Au oxides located at 0.92 V was recorded, together with a small, illdefined post-peak around 0.8 V which actually corresponded to the OA1 oxidation peak. This latter result is also in accordance with the report by Angerstein-Kozlowska et al. [52]. The integration of the reduction peak at 0.92 V Q oxides is reported in Table 2. In the same experimental condition, i.e. 10 consecutive scans, AuNPs(B)-GC electrode afforded a similar CV, but most of the time without the presence of OA1 and its associated reduction peak (solid, red line). It has to be noticed that the shape and location of the oxidation peaks at potentials higher than 1.1 V were always different from that recorded on AuNPs(A)-GC, suggesting different AuNPs surface reactivity. As discussed before, for unfiltered suspensions, some large beads were observed in the resulting deposit. We may infer that the presence of these structures modify in some way the surface reactivity. On the backward scan, the typical reduction peak of Au oxides was present, although at a potential slightly more cathodic (ca. 40 mV) than that recorded on AuNPs(A)-GC. This latter peak also exhibited systematically higher magnitude (around 19 %, see Q oxides values in Table 2), indicating a larger active surface area for filtered AuNPs. AuNPs(C)-GC electrode afforded a very different CV (solid, green line). Indeed, only one small, broad peak was noticed in the region 1.15 -1.4 V for the formation of Au oxides, with a small reduction peak located at 0.9 V on the backward scan. The corresponding Q oxides value was only 25 % of that of AuNPs(A)-GC. It is worth noting that the global shape of this CV actually compared better to a bulk Au electrode as reported by the group of Compton [53] than to AuNPs (electro)deposited onto GC. The fact that peak currents were much lower than that of AuNPs(A)-GC and AuNPs(B)-GC was consistent with the FEG-SEM data showing a less dense deposit of bigger AuNPs and confirmed the observation provided by the UPD experiments.

In order to get further information on the three deposits, new series of CV scans were recorded in the same deaerated 0.5 M H 2 SO 4 solution.

Fig. 3A, dashed lines, depicts the 60 th scan recorded for each deposit (dashed lines). As can be seen from the comparison between solid and dashed lines for a given deposit, the CV shapes experienced a strong evolution while scanning in acidic medium. For AuNPs(A)-GC, only a single, large peak was recorded around 1.2 V, and the peak current corresponding to OA1 increased. According to Angerstein-Kozlowska et al. [52,57], the increase in OA1 peak current is indicative of a reconstruction process which accompanies the electrooxidation of Au. On the backward scan, the reduction peak around 0.9 V decreased following an almost linear trend of about 60 % (Fig. 3B). This decrease in peak current while cycling is consistent with nanoparticle aggregation and/or Au material loss by Au dissolution that both lead to a decrease in active surface area [58]. As a consequence of the increase of OA1 peak current, the reduction post-peak around 0.8 V also increased. In the case of AuNPs(B)-GC, a similar trend was observed: the oxidation peaks located at potential higher than 1.1 V decreased and the global shape of the CV flattened, whereas a small peak at 1.05 V corresponding to OA1 appeared. On the backward scan, the reduction peak located around 0.9 V decreased of about 45 % (Fig. 3B, red data) while a small post-shoulder corresponding to OA1 oxides reduction appeared. These results compared well with the report by Steven et al. [58] concerning AuNPs of 2.9 and 3.1 nm diameter, which showed a decrease in active surface area while scanning in H 2 SO 4 . However, they significantly differ from the behavior of 4.5 nm diameter AuNPs described in the same work, the electrochemical response of which remained stable over 100 scans in H 2 SO 4 . For AuNPs(C)-GC, the broad oxidation peak shifted to less anodic values and its shape became closer to that observed for AuNPs(A)-GC and AuNPs(B)-GC, whereas the whole peak current remained almost constant. On the backward scan, the reduction peak located at 0.9 V decreased of about 30 % (Fig. 3B, green data) and split, leading to the appearance of a new, broad reduction peak at 0.76 V. Thus, for all three deposits the cycling in H 2 SO 4 proved to have an influence on the surface reactivity. This results contrasts with what we previously observed in the case of electrodeposited AuNPs [40,41,43], for which the CVs in H 2 SO 4 showed no longer evolution after 10 scans.

Since HSO 4 -and SO 4 2-anions are known to compete for adsorption with the OH species involved in Au oxidation [57,59], we also investigated the evolution of the CVs obtained on the different deposits in H 2 SO 4 vs. time. The result for AuNPs(B)-GC is depicted in Fig. 4.

In this case the functionalized electrodes were left in the solution between each scan. Clearly, the evolution of the CVs shape was more marked compared to that observed when cycling continuously. The oxidation peaks located at the highest potentials shifted to lower potential values and their corresponding peak currents decreased, while the OA1 peak strongly increased. This is indicative of surface rearrangement leading to more surface defects. It is noteworthy that this increase was significantly higher than that recorded upon continuous cycling. On the backward scan, the peak around 0.9 V decreased and the second reduction peak around 0.8 V appeared, the overall peak area remaining nearly constant over the experiment. This latter peak slowly shifted to more cathodic value with time, ca. from 0.77 V to 0.70 V between 1.5 and 4.5 hours. Thus, the way the activation of AuNPs deposits onto GC by scanning in H 2 SO 4 is performed has a strong impact on the NPs surface reactivity since an evolution of the CVs was noticed vs. both the number of scans recorded and the duration of the dipping in the solution. Keeping in mind that no stabilization of the resulting electrochemical response was obtained even after 100 scans, the activation conditions were expected to strongly impact the analytical performances of the chemically prepared AuNPs deposits towards Hg(II).

Hg(II) trace determination and assay

The response of AuNPs(X)-GC electrodes (X = A, B, C) towards increasing amounts of Hg(II) was examined in 0.01 M HCl solution, using a SWASV procedure the optimized parameters of which were described in a previous study [41]. For the sake of comparison with this latter work, the AuNPs activation process was performed by running 10 scans in a 0.5 M H 2 SO 4 solution between 0.20 and 1.40 V at a scan rate 100 mV s -1 . Fig. 5 depicts the SWASV signals obtained on AuNPs(B)-GC.

The peak observed around 0.67 V corresponded to preconcentrated Hg(0) reoxidation in Hg(II). Compared to our previous results on electrodeposited AuNPs [40,41], the signal was much broader and located at slightly higher potential (ca. 0.1 V anodic shift). Moreover, the peak potential shifted to more anodic values while increasing the Hg(II) amount in the solution, and a pre-peak shoulder concomitantly appeared around 0.6 V. Both phenomena were not observed in the case of electrodeposited AuNPs [40,41,43]. The amperometric response followed a linear trend with respect to Hg(II) concentration up to 3.6 nM, after what it became nearly constant, suggesting a saturation effect of the active surface area of the NPs (Fig. 5, inset). From the slope of the calibration plot, the normalized sensitivity of AuNPs(B)-GC electrode was found to be 0.49 µA nM -1 min -1 . This is a little more than twice better than the value obtained in our previous work with electrodeposited AuNPs and using exactly the same experimental conditions (ca. 0.23 µA nM -1 min -1 ) [41]. Thus, given the AuNPs exhibited similar diameter using both preparation methods but higher density when electrodeposited, this result suggested a much higher reactivity towards Hg(II) in the case of chemically prepared AuNPs. It has to be noticed that varying the AuNPs activation parameters (i.e. total number of CVs in H 2 SO 4 ) did not allow any significant change in the amperometric response towards Hg(II) in the nM range to be observed (not shown). AuNPs(A)-GC and AuNPs(C)-GC afforded comparable analytical performances (not shown), which may be surprising since the active surface area of the three deposits were very different (see Q ox values in Table 2 and discussion above). This may be accounted for considering that in this Hg(II) concentration range, the electrode surfaces were all three close to saturation.

These results together with the latter consideration encouraged us to check the amperometric response of the functionalized electrodes in the pM range. The results obtained for AuNPs(A)-GC are given in Figure 6.

In this concentration range, the impact of the activation parameters was much more marked, this latter showing a strong influence both on the linear range and on the normalized sensitivity. It was not possible to provide error bars in this concentration range due to a slight increase in Hg(0) reoxidation peak current while repeating measurements (not shown). This phenomenon suggests that all the deposited Hg is not redissolved during the stripping step. b Carbon paste electrode. c (ch.) stands for "chemically prepared AuNPs"; (elect.) stands for "electrochemically generated AuNPs". d Reduced graphene oxide. e 1,2-bis[5,2-thiolmethyl-sulphide-1,3,4-oxadiazol-2-yl]-ethane. f (3-mercaptopropyl) trimethoxysilane-multi-walled carbon nanotubes. g The value of the normalized sensitivity was obtained by dividing the slope of the linear response by the preconcentration time. h As the corresponding sensor was impedimetric, the sensitivity value is meaningless here.

From the analysis of the different calibration plots on Fig. 6, one may invoke a bell-shape influence of the number of activation scan on the amperometric response of AuNPs(A)-GC electrode towards very low Hg(II) concentration. Although the reproducibility of the results was not good enough in order to ascertain and sustain this hypothesis, it is interesting to notice that it could be supported by the observation made on the basis of activation CVs, which showed a decrease in activate surface area upon scanning. The best response in terms of sensitivity was recorded on AuNPs activated in the same conditions than before, i.e. by recording 10 scans in a 0.5 M H 2 SO 4 solution between 0.20 and 1.40 V at a scan rate 100 mV s -1 . In this case a linear response was found in the range 2 -12 pM with a normalized sensitivity of 0.296 µA pM -1 min -1 . A limit of detection (LOD) of 1 pM was calculated for a signal-to-noise ratio of 3 [60]. These analytical performances compared favorably with recent reports found in the literature dealing with AuNPs prepared either by electrochemical or chemical route (see comparative features in Table 3).

Indeed, only the works by Ramezani et al. [33] and Ratner et al. [45] allowed a LOD in the few pM range to be reached. It is noteworthy that the common point to these latter two works with the present one is the use of chemically prepared AuNPs, which confirms once again the great reactivity of these nanoobjects.

CONCLUSION

In this work, AuNPs were prepared using the Turkevich method, filtered and deposited onto GC by drop-casting either at room temperature or at 100 °C. The results showed that the filtration step, prior to drop-casting did not exhibit a strong influence on the resulting NPs deposits morphology. On the contrary, evaporation rate has a dramatic effect on AuNPs by favoring aggregation phenomema. Activation of the AuNPs by cycling in H 2 SO 4 lead to significant evolution of their reactivity and decrease in active surface area consistent with NPs growth and/or Au material loss by Au dissolution. With respect to Hg(II) detection, the activation step and more precisely the number of activation scans also showed an influence while measuring Hg(II) in the pM range. Finally, chemically-prepared AuNPs exhibited a better sensitivity than electrogenerated ones, and allowed a LOD down to 1 pM to be reached. However, the results lacked repeatability due to a memory effect, i.e. all the reduced Hg is not reoxidized while stripping. Efforts will now focus on this latter point together with the long-term stability of the interface.

Figure 1 .

 1 Figure 1. TEM micrographs and corresponding size distribution of AuNPs prepared using the Turkevich method and (A) unfiltered, (B) filtered after synthesis.

  b Q oxides corresponds to the amount of charge consumed during the reduction of Au oxides (peak around 0.9 V) produced by CV in 0.5 M H 2 SO 4 (scan rate: 100 mV s -1 ).

Figure 2 .

 2 Figure 2. (A, B, C) FEG-SEM images of (A, C) unfiltered and (B) filtered AuNPs drop-casted onto GC electrode surface. Temperature used for the deposition: (A, B) room temperature; (C) 100°C. (D) Lead UPD in 0.1 M HClO 4 (scan rate: 50 mV s -1 ).

Figure 3 .

 3 Figure 3. (A) Evolution of the CVs recorded in 0.5 M H 2 SO 4 between 0.2 and 1.4 V at 100 mV s -1 vs. the number of scans for: (blue) AuNPs(A)-GC; (red) AuNPs(B)-GC; (green) AuNPs(C)-GC. Solid line: 10 scans; dashed line: 60 scans. (B) Evolution of the amount of charge consumed during Au oxides reduction (deduced from integration of the reduction peak around 0.9 V) vs. the number of CV scans.

Figure 4 .

 4 Figure 4. Evolution of the CVs recorded with AuNPs(B)-GC in 0.5 M H 2 SO 4 at 100 mV s -1 vs. time.

Figure 5 .

 5 Figure 5. SWASV responses obtained in a 0.01 M HCl solution for increasing Hg(II) concentrations (blank subtracted) on a AuNPs(B)p vs. [Hg(II)] and corresponding linear regression.

Figure 6 .

 6 Figure 6. Calibration plots obtained in the pM range on AuNPs(B)-GC electrode activated by using various number of cyclic scans in 0.5 M H 2 SO 4 .

Table 1 .

 1 Physicochemical characterization of AuNPs prepared using the Turkevich method before and after filtration of the colloidal solution by using a 0.45-µm cutoff polyethersulfone membrane filter.

	AuNPs filtration	Diam TEM (nm)	Zeta potential (mV)
	No	17	-46.1
	Yes	19	-43.3

Table 2 .

 2 Characterization of the AuNPs deposited onto the GC electrode surface by drop-casting.

	AuNPs(X)-GC X =	Filtration step	Drying temperature (°C)	Average diameter (nm)	Average density (particles µm -2 )	Q oxides (µC) b
	A	No	RT	11 (14) a	246 (251)	48.7
	B	Yes	RT	15 (20)	195 (241)	57.9
	C	No	100	18 (22)	166 (193)	12.9
	D	Yes	100	-	-	-

a Numbers in brackets correspond to values obtained including the dense beads.

Table 3 .

 3 Comparison of the analytical performances of electrochemical sensors with respect to Hg(II) trace detection.

	Substrate	Functionalization	Normalized sensitivity	LOD	Ref.
			(µA pM -1 min -1 ) g	(pM)
	ITO a	AuNPs (ch.) c	-	5	[45]
	CPE b	Composite Bi-AuNPs (elect.) c	2.58×10 -6	1400	[61]
	Au	RGO d / polyaniline / DNA	-h	35	[62]
	CPE	RGO / Au nanocomposite	1.20×10 -5	1250	[63]
	CPE	BTMSOE e / AuNPs (ch.) / SH-MWCNTs	5.53×10 -8	1.7	[33]
		f
	GC	Ag / 4,4'-bypyridine polymer	1.42×10 -4	450	[64]
	GC	AuNPs (ch.)	0.296	1	This work
	a Indium-tin oxide.

ACKNOWLEDGEMENT

The authors thank the Laboratoire de Génie Chimique for financial support. They are grateful to Dr. Teddy Hezard for his help in MATLAB programming.