Ran Liu

Xing Gao

Mario Barbatti
email: mario.barbatti@univ-amu.fr

Jun Jiang

Guozhen Zhang
email: guozhen@ustc.edu.cn.

Promoting Intersystem Crossing of Fluorescent Molecule via Single Functional Group Modification

Pure light-atoms organic phosphorescent molecules have been under scientific scrutiny because they are inexpensive, flexible, and environment friendly.

The development of such materials, however, faces a bottleneck problem of intrinsically small spin-orbit couplings (SOC), which can be addressed by seeking a proper balance between intersystem crossing (ISC) and fluorescence rates. Using Nsubstituted naphthalimides (NNI) as the prototype molecule, we applied chemical modifications with several electrophilic and nucleophilic functional groups, to approach the goal. The selected electron donating groups actively restrain the fluorescence, enabling an efficient ISC to the triplet manifold. Electron withdrawing groups do not change the luminescent properties of the parent species. The changes in ISC and fluorescence rates are related to the nature of the lowest singlet state, which changes from localized excitation into charge-transfer excitation. This finding opens an alternative strategy for designing pure light-atoms organic phosphorescent molecules for emerging luminescent materials applications.

Molecular phosphorescence has a high potential in information processing applications, including sensors, biological imaging, and LEDs, which has promoted a vivid search for efficient, low-cost, and environment-friendly phosphorescent materials. [START_REF] He | White Light Emission from a Single Organic Molecule with Dual Phosphorescence at Room Temperature[END_REF][START_REF] Zhao | Rational Molecular Design for Achieving Persistent and Efficient Pure Organic Room-Temperature Phosphorescence[END_REF][START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF][START_REF] Lee | Deep Blue Phosphorescent Organic Light-Emitting Diodes with Very High Brightness and Efficiency[END_REF][START_REF] Zhen | Ultralong Phosphorescence of Water-Soluble Organic Nanoparticles for in Vivo Afterglow Imaging[END_REF][START_REF] Baryshnikov | Theory and Calculation of the Phosphorescence Phenomenon[END_REF] Naturally, a crucial point in this search is to develop molecules with efficient intersystem crossing (ISC), the nonradiative transition between electronic states with different spin multiplicity. [START_REF] Kwon | Suppressing Molecular Motions for Enhanced Room-Temperature Phosphorescence of Metal-Free Organic Materials[END_REF][START_REF] Hedley | Ultrafast Intersystem Crossing in a Red Phosphorescent Iridium Complex[END_REF][START_REF] Rothe | Long-Range Resonantly Enhanced Triplet Formation in Luminescent Polymers Doped with Iridium Complexes[END_REF][START_REF] Acharya | Effect of Selenium Substitution on Intersystem Crossing in Pi-Conjugated Donor-Acceptor-Donor Chromophores: The LUMO Matters the Most[END_REF][START_REF] Samanta | Up-Conversion Intersystem Crossing Rates in Organic Emitters for Thermally Activated Delayed Fluorescence: Impact of the Nature of Singlet Vs Triplet Excited States[END_REF][START_REF] Lucenti | H-Aggregates Granting Crystallization-Induced Emissive Behavior and Ultralong Phosphorescence from a Pure Organic Molecule[END_REF][START_REF] Bai | Excited States of a Significantly Ruffled Porphyrin: Computational Study on Structure-Induced Rapid Decay Mechanism Via Intersystem Crossing[END_REF][START_REF] Ma | Efficient and Long-Lived Room-Temperature Organic Phosphorescence: Theoretical Descriptors for Molecular Designs[END_REF] In organometallic LEDs, for instance, the interaction between the singlet metal-to-ligand charge transfer ( 1 MLCT) and the lowest triplet metal-to-ligand charge transfer ( 3 MLCT) states leads to robust ISC, resulting in high phosphorescence quantum yield. [START_REF] Vlček | Modeling of Charge-Transfer Transitions and Excited States in D6 Transition Metal Complexes by Dft Techniques[END_REF][START_REF] Thomas | Energy Dependence of the Ruthenium(Ii)-Bipyridine Metal-to-Ligand-Charge-Transfer Excited State Radiative Lifetimes: Effects of Pipi*(Bipyridine) Mixing[END_REF] To date, many phosphorescent molecules are either organometallic molecules or organic molecules with halogen atoms. [START_REF] Xu | Recent Progress in Metal-Organic Complexes for Optoelectronic Applications[END_REF][START_REF] Mukherjee | Recent Advances in Purely Organic Phosphorescent Materials[END_REF] Such dominance has two causes, both well-documented. First, heavy, occasionally magnetic metal ions help to strength the spin-orbit coupling (SOC), which is the root of ISC. [START_REF] Mcclenaghan | Excited-State Equilibration: A Process Leading to Long-Lived Metal-to-Ligand Charge Transfer Luminescence in Supramolecular Systems[END_REF][START_REF] Yushchenko | Ultrafast Intersystem-Crossing Dynamics and Breakdown of the Kasha-Vavilov's Rule of Naphthalenediimides[END_REF] Secondly, charge transfer (CT) processes contribute to tuning the relevant excited energies favorably. [START_REF] Joo | Model-Independent Determination of the Degree of Charge Transfer in Molecular and Metal Complexes[END_REF][START_REF] Niehaus | Charge-Transfer Excited States in Phosphorescent Organo-Transition Metal Compounds: A Difficult Case for Time Dependent Density Functional Theory[END_REF][START_REF] Han | Phosphorescent Mechanism for Single-Dopant White Oled of Fpt: Electronic Structure and Electron Exchange-Induced Energy Transfer[END_REF] That is, the poor superposition of the orbitals from the metal center and ligand results in tiny singlet-triplet energy gap ( ST E  , the energy difference between the lowest singlet excited state and neighboring triplet state). [START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF] Thus, the ISC efficiency can be improved by either reducing ST E  or enlarging the SOC matrix element [START_REF] Yang | Recent Advances in Organic Thermally Activated Delayed Fluorescence Materials[END_REF][START_REF] Yang | Aggregation-Induced Intersystem Crossing: A Novel Strategy for Efficient Molecular Phosphorescence[END_REF] (see also eq. ( 1)).

It has been reported that small ST E  led to efficient ISC and thereby strong phosphorescence in dibenzothiophene-S,S-dioxide and 2-biphenyl-4,6-bis(12phenylindolo[2,3-a]carbazole-11-yl)-1,3,5-triazine complexes. [START_REF] Dias | Triplet Harvesting with 100% Efficiency by Way of Thermally Activated Delayed Fluorescence in Charge Transfer Oled Emitters[END_REF][START_REF] Endo | Efficient up-Conversion of Triplet Excitons into a Singlet State and Its Application for Organic Light Emitting Diodes[END_REF] In suitable conditions, the metal-ligand compounds may emit phosphorescence thanks to the ligand-localized nature ( 3 IL * or 3 π-π * ) of the lowest triplet state and the relaxation of [START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF] LMCT/ 3 MLCT to 3 πLC * . [START_REF] Chabera | A Low-Spin Fe(Iii) Complex with 100-Ps Ligand-to-Metal Charge Transfer Photoluminescence[END_REF] However, the risk of toxicity and instability of organometallic or halo-organic molecules limits their applications. [START_REF] Bolton | Activating Efficient Phosphorescence from Purely Organic Materials by Crystal Design[END_REF] By comparison, pure light-atoms organic molecules could be an alternative because of their low cost, potentially low toxicity, and high engineering flexibility.

Recently, pure light-atoms organic materials have emerged as a promising type of phosphorescent materials. Their luminescent properties were modified through crystallization and aggregation-induced emission enhancement to reduce nonradiative losses. [START_REF] Bolton | Activating Efficient Phosphorescence from Purely Organic Materials by Crystal Design[END_REF][START_REF] An | Stabilizing Triplet Excited States for Ultralong Organic Phosphorescence[END_REF][START_REF] Qian | Aggregation-Induced Emission Enhancement of 2-(2'-Hydroxyphenyl)Benzothiazole-Based Excited-State Intramolecular Proton-Transfer Compounds[END_REF][START_REF] Ravotto | Aggregation Induced Phosphorescence of Metal Complexes: From Principles to Applications[END_REF][START_REF] Mei | Aggregation-Induced Emission: Together We Shine, United We Soar![END_REF] Nevertheless, the designing of pure light-atoms organic phosphorescent chromophores has still been a significant challenge because of their tiny SOC, ranging from around 1 cm -1 in El-Sayed [START_REF] El-Sayed | Spin-Orbit Coupling and the Radiationless Processes in Nitrogen Heterocyclics[END_REF] forbidden transitions to typically 50 to 100 cm -1 in El-Sayed allowed transitions. [START_REF] Gao | Evaluation of Spin-Orbit Couplings with Linear-Response Time-Dependent Density Functional Methods[END_REF][START_REF] Dinkelbach | Assessment of Interstate Spin-Orbit Couplings from Linear Response Amplitudes[END_REF] Such SOC values are truly too small compared to those above 500 cm -1 observed in organometallic systems, [START_REF] Sayfutyarova | A State Interaction Spin-Orbit Coupling Density Matrix Renormalization Group Method[END_REF] especially considering that the ISC rate depends on their squared values.

Despite their tiny SOCs, specific chemical modification to pure light-atoms organic fluorescent molecules with functional groups have successfully activated phosphorescence. This is the case, for instance, of N-substituted naphthalimides (NNI), whose luminescent properties can be fundamentally altered when the functional group -OCH3 is added, as reported by Chen et al. [START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF] Specifically, NNI is fluorescence active but phosphorescence inactive. By contrast, NNI-OCH3 is phosphorescence active but fluorescence inactive (see Figure 1 We have found out that EDG substitutions strongly enhance the triplet population, while EWG substitutions have little effect compared to the parent system.

As proposed by Chen et al., [START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF] the CT character of the S1 state in NNI-EDG is the crucial piece to understand the enhanced ISC in these systems. Nevertheless, the reason underlying the ISC enhancement is not a reduction of Based on the semiclassical Marcus theory, the ISC rate,

1 ISC ISC k  - =
, from S1 to a neighbor triplet state Tm can be estimated as 38 ( )

2 2 21 exp 4 4 v ST ISC SOC B B G kV kT kT       =-   (1)
where SOC V is the spin-orbit coupling (SOC) matrix element,  is the reorganization energy, and

( ) ( ) 1 1 1 min min m v ST ST T S S S G E E E    = - RR .
The SOC matrix elements of selected singlet-triplet channels were calculated at the optimized structure of S1. They were evaluated adopting the Breit-Pauli (BP) spin-orbital Hamiltonian with effective-charge approximation, 39 using Casida's wavefunction Ansatz. [START_REF] Casida | Time-Dependent Density Functional Response Theory for Molecules[END_REF] Given proper approximations (See details in the Supporting Information), the simplified rate model in Eq. ( 1) is supposed to deliver a qualitative estimate of the ISC rate. This limitation is not a major impediment for us, as the rates here are only needed for a qualitative comparison between different photophysical processes.

Meantime, the fluorescence rate,

1 FL FL k  - = , was estimated as 41 2 2 32 0 2 FL e e k E f mc  = ( 2
)
where 0 is the vacuum permittivity, me is the electron mass, e is the electron charge, c

is the speed of light.

( ) ( )

0 1 1 1 min min S S S S E E E  = -

RR

and f are the S1-S0 energy gap and the oscillator strength calculated at the S1 minimum.

The chemical structures of NNI and its four derivatives with single parasubstitution are collected in the upper half of Figure 2. We first examined the ground states of all species. Intriguingly, regardless of the substituent added to NNI, the benzene and naphthalimide groups are always perpendicular to each other in optimized structures (See Cartesian coordinates in Supporting Information). Further, vertical excitation calculations based on optimized S0 geometries show that the S1 states of all species are almost the same (See Table S1 in Supporting Information). Thus, for NNI-OCH3 and NNI-OH, there may be some configurational change during the relaxation of S1 that can induce the change of its nature.

The electron-hole distributions of their respective S1 and T2 states based on optimized S1 structures are collected in the lower half of The occurrence of an S1 state with CT character in NNI-EDG has major consequences for the photophysics of these molecules. While the S1→T2 ISC rate in the EWG substitutions is not significantly altered in relation to the parent NNI (Table 1), in the case of the EDGs, it shows an increase of three times for -OCH3 and doubling for -OH. Thus, the ISC lifetime shortens from 23 -26 ns in NNI and NNI-EWG to about 8 -11 ns in NNI-EDG. The data in Table 1 also show that the ISC rate variation is caused by the increase of the VSOC, from 0.5 to 1.3 cm - upon EDG substitution, which compensates the small but unfavorable growth of EST.

Curiously, the reason VSOC is so small in either NNI-EWGs or NNI-EDGs is not the same. In NNI-EWGs (and in the parent NNI), the singlet-triplet transition between * states is unfavorable by the El-Sayed rule. [START_REF] El-Sayed | Spin-Orbit Coupling and the Radiationless Processes in Nitrogen Heterocyclics[END_REF] In NNI-EDGs, VSOC is tiny due to the local nature of the spin-orbit coupling Hamiltonian, [START_REF] Marian | Spin-Orbit Coupling and Intersystem Crossing in Molecules[END_REF] which tends to return vanishing elements for non-local transitions, as in CT states.

Table 1. S1-T2 energy gap (EST) at the S1 minimum, reorganization energy (), and SOC (VSOC). ISC rate (kISC), ISC rate relative to that of NNI (krel), ISC lifetime (ISC).

All quantities calculated for NNI and its para-and meta-substituted derivatives with electron withdrawing (-F and -COOH) and electron donating (-OCH3 and -OH) groups.

EST (eV)  (eV)

VSOC (cm -1 ) kISC (10 [START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF] Nevertheless, the effect of the EDG substitutions on the fluorescence is more impressive. In NNI and NNI-EWGs, the fluorescence rate is about 210 8 s -1 (Table 2). In NNI-EDGs, this value is strongly reduced by a factor ~35.

Thus, the fluorescence lifetime is elongated from 5 ns in NNI and NNI-EWGs to about 180 ns in NNI-EDGs. This substantial shift in the fluorescence rates caused by the EDG substitutions is a direct result of the CT character of the S1 state, which reduces the S1-S0 oscillator strength. In addition, large S1-S0 energy gaps at the S1 minimum (Table 2)

suggests that nonradiative decay of S1 are not significant for these molecules, even though we have not explicitly investigated nonradiative decay pathways in this work.

Table 2. S1-S0 energy gap E and oscillator strength f at the S1 minimum. Fluorescence rate (kFL), fluorescence rate relative to that of NNI (krel), and fluorescence lifetime (FL).

All quantities calculated for NNI and its para-and meta-substituted derivatives with electron withdrawing (-F and -COOH) and electron donating (-OCH3 and -OH) groups.

E (eV) f kFL (10 8 s -1 ) krel FL (ns) NNI -     Para -F -     -COOH -     -OCH3 -     -OH -     Meta -F -     -COOH -     -OCH3 -     -OH -    
In short, we show that substitution of selected EDGs in NNI results in the enhancement of ISC rate between its lowest singlet excited states and adjacent triplet excited states thanks to a larger SOC induces discernable configuration change of the lowest singlet excited state, resulting in a larger SOC between S1 and adjacent T2 and ensuing enhancement of ISC rate. In contrast to the hypothesis in the experimental work which emphasizes the decisive role of reducing singlet-triplet gap to boost ISC, we show that it follows an alternative mechanism for NNI species. Moreover, the dark nature of the S1 state in the NNI-EDG, which also roots from the structural change of S1, strongly elongates the fluorescence lifetime, making it slower than ISC and favoring the phosphorescence in these species. Thus, our theoretical results suggest the significance of configuration tuning of chromophores on their luminescent properties, casting new physical insight into the hypothesis proposed in the precedent work of Chen et al. [START_REF] Chen | Versatile Room-Temperature-Phosphorescent Materials Prepared from N-Substituted Naphthalimides: Emission Enhancement and Chemical Conjugation[END_REF] To further exploit this design strategy, we studied the effect of substitutions in the meta-position. Our results, presented below, revealed the general relationship between the mechanism of intersystem crossing and the charge-transfer excited-state process.

Figure 3 shows the chemical structures of NNI and its four derivatives with single meta-substitution, and the electron-hole distributions of their S1 and T2. They are like their counterpart species of para-substitution in both geometric and electronic structures.

Figure 3. Upper half: chemical structures; lower half: the electron-hole distribution of S1 and T2 of NNI and its meta-substitution derivatives.

The S1-T2 energy gaps of each meta-substituted species are almost invariant compared to their para-substituted counterpart, as seen from the data in Table 1 and Table 2. The natures of S1 are barely changed as well. (See Table S2 and Table S3 in the Supporting Information). The main reason for the insensitivity to the substitution position on the excitation energy of S1 lies in that the region the electron moves out during the S0→S1 excitation does not directly involve the added group.

The effects of the substitutions on the ISC and fluorescence rates are also qualitatively the same as those observed in the para-substitutions. Nevertheless, there are some interesting quantitative variations.

The ISC rates of the meta-NNI-EDGs are about 6 to 7 times larger than that of NNI (Table 1). In the para-NNI-EDGs, this growth was no larger than 3. The reason for this additional enhancement is once again in VSOC, which reaches 2.2 cm -1 in meta-NNI-EDGs against 0.5 cm -1 in NNI and 1.3 cm -1 in para-NNI-EDGs. Although all these values are within the error bar our methodology for VSOC calculation, [START_REF] Gao | Evaluation of Spin-Orbit Couplings with Linear-Response Time-Dependent Density Functional Methods[END_REF] we can speculate that the slightly larger value upon meta-substitutions are due to the asymmetry it introduces, helping to mix the singly-occupied orbitals in the singlet and triplet states.

The fluorescence rates are also more significantly impacted by the meta-than by the para-substitutions. While in the latter, they are reduced by a factor 35 compared to NNI, in upon a meta-substitution this reduction is between 64 and 77 times. Thus, the fluorescence lifetime is elongated up to 408 ns. Once more, the reduction of the fluorescence rates is due to the dark nature of S1.

Efficient ISC is the prerequisite for photoinduced phosphorescence process. It is crucial to enhance ISC in molecular design towards organic phosphorescence. [START_REF] Ma | Efficient and Long-Lived Room-Temperature Organic Phosphorescence: Theoretical Descriptors for Molecular Designs[END_REF] In this theoretical study, we showed that for specific fluorescent molecules like NNI, chemical modification by adding an electron donating group (EDG) could appreciably shift the balance between fluorescence and ISC, favoring the latter. In NNI and NNI with electron withdrawing group (EWG), ISC occurs within ~25 ns, while fluorescence is faster, occurring within 5 ns. Thus, these molecules tend to show strong fluorescence.

In NNI-EDG, however, ISC becomes faster, between 3 and 11 ns, while fluorescence becomes much longer, between 185 and 408 ns. Therefore, these molecules efficiently populate the triplet manifold and, under adequate conditions, may become phosphorescent. It is encouraging to see that the EDG substitution enhances the transference from singlet to triplet states and enables phosphorescence, even in systems with very small spin-orbit couplings (~1 cm -1 ), as it is often the case of pure light-atoms organic molecules.

The strong photophysical shift between NNI and NNI-EWG on the one hand and NNI-EDG on the other is related to the nature of the S1 state. In the former molecules, the lowest singlet state has a localized character, while upon an EDG substitution it becomes a charge-transfer (CT) state in response to the configurational change of molecules. The CT state has a slightly stronger coupling to T2. Although the spin-orbit coupling is still tiny, about 2 cm -1 , it is enough to enhance the ISC rate by up to a factor 7 compared to the parent NNI. Concerning fluorescence, while the localized S1 state is strongly dipole-coupled to S0, with oscillator strength near 0.4, the CT S1 state has a vanishing coupling to S0, with an oscillator strength not larger than 0.01.

Therefore, the fluorescence rate reduces by up 77 times.

These are systematic findings observed in the comparison between the parent NNI and NNI functionalized by -F and -COOH EWGs and-OCH3 and -OH EDGs.

Substitution of these groups in either para or meta locations does not change the qualitative results, although the population of triplet states is even more favorable after a meta-substitution.

In short, we have shown that ISC can be promoted by restrained fluorescence due to low-lying CT singlet states. The triplet population formed in this way may fluoresce as long as conventional conditions are met: nonradiative rates are small, and the chromophore is in an oxygen-depleted atmosphere. Restrained-fluorescence ISC turns out to be so efficient that it can deplete the singlet population even in systems with spin-orbit couplings as small as those in El-Sayed forbidden transitions.

This study cast new insight into the design of pure light-atoms organic phosphorescent molecules via chemical modifications of functional groups. By exploring more organic molecules using the same strategy and employing more comprehensive theoretical framework that can compute phosphorescent radiative decay rate, [START_REF] Peng | Correlation Function Formalism for Triplet Excited State Decay: Combined Spin-Orbit and Nonadiabatic Couplings[END_REF][START_REF] Minaev | Principles of Phosphorescent Organic Light Emitting Devices[END_REF] we are on the way of rational design of new organic phosphorescent molecules.

  (a)). The proposed mechanism 3 explaining the phosphorescence activation in NNI-OCH3 claims that both the first singlet excited state (S1) and the closest triplet excited state of NNI-OCH3 have charge-transfer (CT) characters, reducing ST E  and, consequently, enhancing the ISC rate (see Figure 1(b)).

Figure 1 .

 1 Figure 1. (a) The luminescence properties of NNI and NNI-OCH3. The addition of -OCH3 turns the fluorescent NNI into a phosphorescent molecule. (b) A previously proposed mechanism to explain NNI-OCH3 phosphorescence is based on a small EST due to low-lying CT states. 3 (c) The mechanism proposed in this work is based on restrained fluorescence also caused by low-lying CT states.

  rather a strongly- restrained fluorescence due to transition dipole moment reduction (Figure1(c)), which compensates for the small SOCs.

Figure 2 .

 2 Compared to the NNI molecule, the EDGs concerned in the work (-OH and -OCH3) alter the nature of S1 and T2 from locally excited states to charge-transfer (CT) states, with an electron transfer from the benzene to the naphtalimide group. Noticeably, this shift is closely related to the conformational change of S1 and T2. For NNI, the benzene and the naphthalimide groups are perpendicular to each other, while for NNI-X (X= -OH or -OCH3), they are not. Also, the S1 of NNI-OH and NNI-OCH3 is a dark state because the two molecular orbitals involved in S1 (see TableS2in the Supporting Information) are poorly π-conjugated as the two corresponding molecular fragments appreciably deviated from co-planarity.[START_REF] Gong | Optical Excitation in Donor-Pt-Acceptor Complexes: Role of the Structure[END_REF] Meanwhile, the EWGs groups -F and -COOH left almost unchanged the nature of S1 and T2.

Figure 2 .

 2 Figure 2. Upper half: chemical structures; lower half: the electron-hole distribution of S1 and T2 of NNI and its para-substituted derivatives. (The blue and green regions represent the hole and electron, respectively.)

Acknowledgments

This work was financially supported by MOST (No. 2016YFA0400904), NSFC (21703221, 21633006), and the Fundamental Research Funds for the Central Universities (WK2060030027). RL and GZ are grateful for the computing resources from University of Science and Technology of China High Performance Computing Center. MB thanks the support of the Excellence Initiative of Aix-Marseille University (A*MIDEX) and the project Equip@Meso (ANR-10-EQPX-29-01), both funded by the French Government "Investissements d'Avenir" program. MB also acknowledges funding from the WSPLIT project (ANR-17-CE05-0005-01).

AUTHOR INFORMATION

Corresponding Author *(G.Z.) E-mail: guozhen@ustc.edu.cn. *(M.B.) E-mail: mario.barbatti@univ-amu.fr.

ORCID

Guozhen Zhang: 0000-0003-0125-9666 Mario Barbatti: 0000-0001-9336-6607

Note

The authors declare no competing financial support.

Supporting Information Avaliable

The computational details, transition energies, transition related molecular orbitals and corresponding electron-hole distribution of the lowest singlet excited state, the energy level diagrams of low-lying excited states, the Cartesian coordinates of all optimized molecules.


J.-F Girres

G Touya

Cartographic Generalisation Aware of Multiple Representations

Introduction

Cartographic generalisation helps deriving maps at smaller scales from a detailed geographical dataset. It is more and more frequent to have at disposal several datasets at different levels of detail in a web mapping application. For instance, a source dataset is used for deriving maps from 1:50k to 1:250k and another less detailed dataset is used to derive maps below 1:250k. Deriving intermediate scales can be helpful to generate intermediate zoom levels in a multi-scale geoportal. However, current solutions only use one dataset as input, which may lead to inconsistencies when the user switches to maps derived from a different source dataset (Figure 1).

Scenarios for Handling Multiple Representations during Generalisation 2.1 Post -processing Strategy

The first possible strategy for handling multiple representations during generalisation is to apply post-processing corrections that modify the generalised data in order to preserve consistency. There are two alternatives: a simple one and a complex one. The simple alternative is to identify the inconsistencies in the generalised output (Figure2a) and then use the next level representation to enrich the generalised output. In Figure 2, the inconsistency is a missing river that is added in the post-process.

Figure 2: Post-processing strategy: the forgotten river (a) is added after generalisation at 1:150k from the 1:250k level data (b). This scenario tends to increase the amount of data in the generalised output, which is not desirable. The second alternative is a more complex post-process that deals with this problem by reducing the amount of data after consistency has been achieved. In Figure 2, it would remove another river that is not present at the 1:250k level.

Pre-processing Strategy

The second strategy seeks to handle consistency between scale levels before generalisation. Once again, two alternatives are discussed. The first one consists in identifying the objects in the initial level that are linked to an object in the upper levels, and then apply generalisation only on those objects that are not linked (Figure 3): matched objects cannot be deleted as they are not processed by generalisation. selection is computed on unmatched objects only (5 is deleted and 9 is kept).

The second alternative is quite different from all other strategies, as it involves the modification of the generalisation process, while the others just provided adaptations to what a generalisation process can achieve. With this strategy, the matched objects are a complementary input of the process that has been changed to cope with a set of matched objects and a set of unmatched objects. For instance, instead of just simplifying the geometry of a matched object, the modified process will instead compute an intermediate geometry between the detailed and the undetailed matched geometries.

Scenarios Comparison

All four scenarios have advantages and drawbacks. They are analysed in relation to the quality of the MR-aware generalisation they can provide, and to the cost of their implementation in a given multi-scales generalisation system. The best scenario in terms of output quality is the last one that modifies the generalisation processes to take matched objects into account. Unfortunately, it is also the most costly scenario as it requires the reimplementation of each generalisation process, which is sometimes not possible, for instance in a system based on external generalisation web services [START_REF] Regnauld | Process Modelling, Web Services and Geoprocessing[END_REF]). On the other hand, the simpler scenario is the post-processing addition of missing objects. We believe that the worst theoretical scenario in terms of output quality is the first pre-processing strategy where only the unmatched features are generalised. As generalisation is a holistic process, removing the neighbours of an object may lead to poor generalisation results. Finally, the most balanced scenario is the post-processing strategy that preserves consistency as well as the final amount of data in the map. All four scenarios are sensible to the errors of the matching process, but the sensibility of each scenario to omission and commission has to be studied further.

Experiments

To illustrate MR-aware generalisation (using post-processing strategy), an experiment is provided on a sample of road networks extracted from datasets at 1:50k and1:250k (Figure 4). A preliminary matching of homologous road objects was achieved using the [START_REF] Mustière | Matching Networks with Different Levels of Detail[END_REF] algorithm. In order to generalise an intermediary road network at the scale 1:150k, strokes-based generalisation is carried out [START_REF] Thomson | Efficient generalisation and abstraction of network data using perceptual grouping[END_REF]. The process is applied with and without MR-aware generalisation. Figure 5 shows the roads which have been preserved (in green) by MR-aware generalisation, but would have been eliminated without (in red). To quantify these differences, Table 1 exposes the difference in object numbers and roads total length, between both original datasets and the generalised road network with or without MR-aware generalisation. The results show that more than 400 km would have been deleted by not applying MR-aware generalisation. A second experiment was carried out on railroad network generalisation (Touya & Girres 2014) with a comparison of the strategy where only unmatched features are generalised and the previously tested post-processing strategy (Figure 6). Both strategies provide better results than only generalisation, and in this case, pre-processing deletes more features as removing the matched features damages the geographic context used by generalisation.

Conclusion and Further Work

This paper proposed different scenarios to enable the derivation of consistent intermediate cartographic representations between existing multi-scale levels. Two of the scenarios have been implemented and tested on real datasets, with promising results. As the presented work is on-going research, there is much to explore. First, both implemented scenarios were tested with simple generalisation processes, and further testing should be made with more complex processes. For instance, polygon to line collapse (Figure 6) should be hard to handle with the post-processing strategy. Then, all four strategies should be tested and compared to get a clearer view on the best strategies. Generalisation is a holistic process that requires the modelling of the geography around each object, notably the spatial relations with neighbours. Roads are drawn in a map to show they allow the access to some place, so geographical context has to be integrated to MR-aware generalisation to improve the quality of intermediate levels.

Finally, the proposed scenarios do not handle inconsistencies between levels, which occur with real datasets. In Figure 4, the bottom left road of the 1:250k dataset does not exist at 1:50k. It is not possible here to preserve consistency.

Figure 1 :

 1 Figure 1: The intermediate scale (1:200k) is generalised from 1:50k but inconsistently with 1:250k. The aim of the on-going research presented in this paper is to derive consistent intermediate cartographic representations to enable smooth transitions in a multi-scales geoportal. We call Multi-Representation Aware (MR-Aware) generalisation such generalisation. This work requires two major hypotheses:  a multi-scales generalisation system to compute intermediate scales is available, like the ScaleMaster2.0 by Touya and Girres (2013), or the vario-scale model by van Oosterom et al. (2014),  a data-matching system (e.g. Mustière and Devogèle 2006) has been used to link objects at different levels that represent the same real world entity. The second part of the paper describes different scenarios to achieve MR-Aware generalisation. The third part describes experiments on real data and the fourth one draws some conclusions and explores further work.

Figure 3 :

 3 Figure 3: Pre-processing strategy: (a) the unmatched objects (5 and 9) are identified (b)selection is computed on unmatched objects only (5 is deleted and 9 is kept).

Figure 4 .

 4 Figure 4. Road networks extracted from 1:50k and 1:250k datasets

Figure 5 .

 5 Figure 5. A road network (1:150k) without (red) and with (green) MR-aware

Figure 6 .

 6 Figure 6. (a) railroad network at initial scales (1:50k in blue, 1:250k in magenta). (b) generalisation without MR-aware process. (c) post-processing MR-aware generalisation.(d) pre-processing MR-aware generalisation.

Figure 6 .

 6 Figure 6. Rivers represented by lines and polygons at 1:50k and by only simplified lines at 1:250k.

Table 1 .

 1 Comparison of generalised roads with or without MR-aware.

Dataset Number of objects Length (km) Roads 1:50k 6512 5039,76 Roads 1:150k (without MR-aware) 2264 2041,64 Roads 1:150k (with MR-aware)

		2713	2476,88
	Roads 1:250k	812	1768,39


LCFC Marc Borsenberger
email: marc.borsenberger@ensam.eu.

Abdelkader Benabou

Cyrille Baudouin

Régis Bigot

Pierre Faverolle

Jean-Claude Mipo

Characterization of massive magnetic parts with a dedicated device

Keywords: FE-Simulation, magnetic characterization, massive sampling, material properties

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Usually, in electrical machines, the magnetic core is made from stacked laminations in order to limit the eddy current losses and improve the efficiency of the energy conversion. Nevertheless, for special electrical machines, due to cost reasons in mass production, massive magnetic parts such as the rotor can be incorporated. In that case, the magnetic field is free to circulate in all the bulk, selecting the trajectory that minimizes the energy consumption, or in other words the trajectory with the minimal global reluctance in the electrical machine. This may lead to complex three dimensional trajectories of the flux in the material requiring a specific design of electrical machines with non-trivial geometries of some components of the magnetic circuit. Then, as the performances of electrical machines are strongly related to the magnetic properties of the employed materials, the use of massive magnetic parts requires to pay special attention to the bulk properties of the material [START_REF] Li | Influence of Magnetic Materials on Claw Pole Machines Behavior[END_REF]. In practice, when designing such electrical devices, numerical tools, such as the finite elements analysis, are usually employed. The material magnetic properties implemented in these tools may not correspond to the real behavior as they are mostly considered as homogeneous and consequently the performances of the simulated electrical device may be different from the experimental one. In fact, the magnetic parts can be issued from complex manufacturing processes that may lead to inhomogeneous properties within the same magnetic part. Therefore, for a more accurate study and/or design of the device, the characterization of the magnetic behavior, by considering the influence of the manufacturing processes, is necessary.

Regarding the massive magnetic parts, they are usually manufactured with a succession of operations including hot forging which impact on the magnetic permeability has been illustrated by Ghodsi and Loghmanian [START_REF] Ghodsi | Effect of forging on ferromagnetic properties of low-carbon steel[END_REF]. However, the scientific literature content is mostly dedicated to the study of laminated electrical steels and the related manufacturing processes. For example, the rolling process impact in terms of rolling direction and plastic strain on the magnetic properties has been studied by Landgraf et al. [START_REF] Landgraf | Effect of grain size, deformation, aging and anisotropy on hysteresis loss of electrical steels[END_REF] or Hou and Lee [START_REF] Hou | Effect of rolling strain on the loss separation and permeability of lamination steels[END_REF]. Also, different cutting processes (shearing, laser and wire electric discharge machining) have been compared by Kurosaki et al. [START_REF] Kurosaki | Importance of punching and workability in non-oriented electrical steel sheets[END_REF] in terms of specific losses and magnetizing force to reach 1.5 T. In all these works, phenomenological approaches are adopted and the results may be extended with difficulty to other applications or for numerical modelling.

Another approach consists in considering the inherent material properties, such as the microstructure, mechanical stress or plastic strain, in order to understand the related magnetic properties. In the literature, a correlation between grain size and specific core losses has been revealed in several works [START_REF] De Campos | The optimum grain size for minimizing energy losses in iron[END_REF][START_REF] Premkumar | Relative effect(s) of texture and grain size on magnetic properties in a low silicon non-grain oriented electrical steel[END_REF][START_REF] Gutiérrez-Castañeda | Effect of annealing prior to cold rolling on magnetic and mechanical properties of low carbon non-oriented electrical steels[END_REF]. Regarding the iron losses, an optimum grain size exists for a given material at a given operating frequency because of the antagonist effects of eddy currents and hysteresis losses. Other studies focus on the effect of mechanical stress and plastic strain on magnetic properties [START_REF] Iordache | Magnetic behaviour versus tensile deformation mechanisms in a non-oriented Fe-(3 wt.%)Si steel[END_REF][START_REF] Bernard | Effect of Stress on Magnetic Hysteresis Losses in a Switched Reluctance Motor: Application to Stator and Rotor Shrink Fitting[END_REF][START_REF] Vandenbossche | Impact of mechanical stresses on the magnetic performance of non-oriented electrical steels and its relation to electric machine efficiency[END_REF]. They demonstrate experimentally that slight tensile stresses (for non-pre-stressed laminations) can improve the magnetic properties whereas compression stresses and severe tensile stress deteriorate the magnetic properties. Furthermore, plastic strain, in cold deformation, results in a general flattening of the hysteresis loop and consequently in a deterioration of the magnetic properties.

These observations have largely been made in case of laminated steels because of their large use in magnetic core applications. Moreover, magnetic characterizations are most of the time performed on laminations with techniques such as those described by the IEC 60404 standard [START_REF]Magnetic materials -Part 2: Methods of measurement of the magnetic properties of electrical steel sheet and strip by means of an Epstein frame[END_REF] (Epstein or Single Sheet Tester). Other non-destructive techniques have also been proposed [START_REF] Arbenz | Characterization of the local incremental permeability of a ferromagnetic plate based on a four needles technique[END_REF], but remain limited in terms of magnetization level and are not adapted to detail material parameters effect on magnetic properties. For massive magnetic parts, a first approach is the extraction of ring-shaped samples. In that case, the sample may be larger than the zone of interest in the product. Moreover, for this kind of sample, the trajectory of the magnetic flux is circumferential which makes the study of material anisotropies difficult to realize.

In the present work, a dedicated characterization procedure is proposed in order to investigate massive samples properties. The proposed approach consists in extracting, from magnetic steel billets, parallelepipedic samples, which are relatively massive in order to avoid potential mechanical stress relieving and also to limit the impact of edge or surface effects induced by the sampling process. Then, the characterization is performed while the magnetic flux goes though the bulk material and is supposed unidirectional along the sample, allowing the consideration of material anisotropies.

First, the experimental device is described, along with its numerical study to verify the feasibility and the relevance of the measurement setup. Then, the measurement validation is performed on the basis of a sensitivity and repeatability analysis together with a reference measure. Finally, measurements are performed on selected samples, with different mechanical and material anisotropies, to reveal the impact on the magnetic properties.

Description of the experimental device

General description

The magnetic properties of a material describe the evolution of the magnetic polarization J in function of the excitation magnetic field H inside the considered sample. In the proposed approach, the sample is placed between the magnetic poles of an electromagnet device (Fig. 1). A controlled current source composed of a function generator (National Instrument USB-6353) and an amplifier (Toellner TOE 7621-60) is connected to the primary winding of the electromagnet device. The amplifier is controlled to generate an alternative current to generate an alternative magnetic field inside the sample.

First, to measure the polarization J of the sample, a secondary coil is placed on a plastic support in which the sample can be inserted. This way, the eventual dispersion in measurements, due to different windings placed directly on the different samples, is limited. The electromotive force v 2 is measured with a voltage probe thanks to Lenz-Faraday induction phenomenon. From this measure the magnetic polarization of the sample J is determined with the compensation of the flux in the air:

J = 1 S sample 1 n 2 ∫ v 2 (t) dt -µ 0 HS winding (1)
where S sample is the cross section of the sample, n 2 and S winding are respectively the number of turns and the cross-section of the secondary winding, µ 0 the magnetic permeability of the vacuum and H the magnetic field estimated in the sample. The magnetic field H is supposed homogeneous in the region enclosed by the secondary winding, that is to say the ferromagnetic sample and the air-gap between the winding and the sample.

To measure the magnetic field H, two Hall probes are placed above the sample. They deliver a voltage proportional to the magnetic field H at two known locations in the air around the sample. As a first approach, a linear extrapolation is chosen to estimate the magnetic field at the surface of the sample: where H probe i and z probe i are respectively the magnetic field measured by the probe i and its distance to the sample surface. The direct output of such a fluxmetric technique is an hysteresis loop whereas generally, the electromagnetic numerical tools require the use of a single-valued behavior law of the materials. Therefore, from the measured hysteresis loops, the normal polarization curve will be extracted. This curve is drawn from the maximum magnetic fields and polarizations of centered inner loops measured at different levels of polarization, as illustrated in Fig. 2.

H = H probe 1 z probe 2 -H probe 2 z probe 1 z probe 2 -z probe 1 (2)
In addition, the specific core losses are determined in our case for a given applied magnetic field H:

P H[kA/m] [W/kg] = f ρ HdB ( 3
)
where f is the frequency in Hz, ρ the material density in kg/m 3 and B the magnetic flux density in T . Several considerations are observed regarding the experimental device. First of all, the standards recommend to measure a sinusoidal magnetic flux density whereas in the proposed technique the input current is sinusoidal. In fact, in the quasi-static conditions, the hysteresis behavior is more dependent on the extreme values of the magnetic field than on its waveform. Moreover, the sample is 25 mm length and has a square basis of 8 mm wide, which is considered massive regarding the dimensions of steel sheets used in Epstein frames. In addition, the extreme surfaces of the parallelepipedic sample must be as parallel and as flat as possible to limit the parasite air gaps which would increase the leakage flux around the sample and introduce a strong gradient of the magnetic field H between the poles of the electromagnet device. Eventually the frequency must remain low (< 0.5 Hz) because of the design of the electromagnet and also to avoid skin effects in the sample. Since the material investigated is a soft magnetic steel grade, these considerations lead indeed to a skin depth of about 10 mm which is sufficient, regarding half of the width of the sample, to neglect the skin effect.

Numerical study of the device

A first study of the experimental device is performed through a numerical modelling approach. The three dimensional electromagnetic problem is solved thanks to a time stepping finite element (FE) method and using electric potential formulation to consider the electrical conductivity in the sample. The magnetic behavior law of the sample used in the model is similar to what is expected for the considered material.

From this model, an investigation on several hypotheses can be performed in order to improve the understanding of the different sources of errors. The first hypothesis considers that the magnetic field H and the magnetic flux Φ are measured at the same position. In fact, the Hall probes measure the magnetic field at two points in the space surrounding the sample and along a given direction, whereas the secondary winding gives the average magnetic flux density which passes through the surface of the winding and on a given length of the winding. The Eq. ( 1) also supposes that the magnetic field in the sample and in the air gap between the winding and the sample is the same.

The numerical simulation shows that the magnetic field surrounding the sample is not homogeneous. In Fig. 3, the distribution of the magnetic field is shown in a cross-section located in the middle of the sample between the electromagnet poles.

The homogeneous center of this distribution (≈ 5300 A/m) represents the sample. Then, by increasing the distance to the sample, the magnetic field increases to a maximum and decreases. This calculated magnetic field profile is verified experimentally by moving the Hall probes along the Z-axis (back to Fig. 1).

The scatter plot of Fig. 4 (blue diamonds) represents, for a given level of the excitation field, the measured profile of the magnetic field H above the sample, from the upper surface of the sample (origin, vertical green line) to the limit of the flat surfaces of the pole (vertical dashed line). In this particular configuration, the magnetic field H inside the sample is estimated with more accuracy thanks to a polynomial fitting. The corresponding reference value of the magnetic field H inside the sample is the evaluation of the polynomial function at the origin.

During the magnetic characterization, the linear extrapolation from Eq. ( 2) is made from the two positions of the Hall probes represented by the two red points in Fig. 4. The relative error with the reference value is estimated at 1.32%. However, the air gap between the electromagnet poles and the sample is inevitable. A simulation has been performed to verify the impact of the air gap on the magnetic field H and its estimation.

Figure 5 shows the simulated profile of the magnetic field above the sample for an air gap of 0.15 mm between each electromagnet pole and the two extreme surfaces of the sample. The magnetic field H is estimated either with linear extrapolation according to Eq. ( 2) or with a third-order polynomial Lagrangian extrapolation and using four virtual measures of the magnetic field. In that specific case, the error on the estimation of the magnetic field can be reduced from 425% to 105%.

Eventually, another assumption is a uniform distribution of the magnetic flux density in the sample in every cross section along the length of the secondary winding which is confirmed by the simulation.

Uncertainty analysis of the measure

Sensitivity and repeatability

To evaluate the uncertainty of the measure, two steps are performed: a qualitative analysis and a comparison with the classical ring core characterization technique.

The qualitative analysis is represented by the ability of the characterization protocol to give always the same result (precision according Standard ISO 5725-1). The major source of errors is related to the relative positions of the sample, the electromagnet device, the probes and the secondary winding. A preliminary experimental sensitivity analysis has been performed. The effect of the following parameters has been investigated:

-The Hall probes position regarding the sample: along X, Y and Z-axis (Fig. 1), -The secondary winding position: centered or in contact with a pole (along X direction), -The sample position in the magnetic poles It has been observed that the secondary winding position has a minor impact on the measures whereas the relative position of the Hall probes, sample and electromagnet poles must be accurate. Indeed the Hall probes must be as close to the sample as possible in order to limit the error due to the linear extrapolation to estimate the magnetic field at the sample surface.

To go further in the qualitative analysis, a set of ten measurements are performed on the same sample under repeatability conditions. The following protocol is applied for each measurement:

-Positioning the sample between the magnetic poles, -Compensating the remnant induction in the magnetic circuit for a given amplitude of the excitation field, -Recording the monitored quantities for ten different levels of the input current, -Post-processing of the measures.

The results associated to the normal curves are shown in Fig. 6 and those associated to the losses, at an excitation field of 16 kA/m, in Fig. 7.

Qualitatively the Fig. 6 shows slight variations on the normal curves. Considering the ± 2 σ interval, where σ is the standard deviation, the variations in the result is mostly due to the uncertainty on the measure of the magnetic field H. For example, to compare numerically the normal curves, and as a first approach, the chosen criterion is the required magnetic field H 1.5 to reach a magnetic polarization of 1.5 T. Considering a cubic interpolation between the measured points, the repeatability of the measurement can be qualified with an average value of H1.5 = 2370 A/m and a standard deviation of σ = 99 A/m, representing a coefficient of variation σ/ H = 4.2%. Concerning the specific losses at 16 kA/m shown in Fig. 7, the coefficient of variation σ/ρ, with ρ the average loss value, represents 2.13%. Note that, to distinguish the effect of material parameters on the magnetic properties, the calculated error of precision must be significantly inferior to the variations observed on samples with different magnetic properties.

Comparison with another characterization methodology

The precision of the measure has been investigated in the previous section. The next parameter to be considered to estimate the uncertainty of the measure with the characterization device is the trueness (according Standard ISO 5725-1). This parameter describes the deviation between the measured and the true value.

To estimate the trueness of the measure, the results of magnetic characterization with the presented device are compared to the standard ring core measurement. Measures with both techniques have been performed on reference samples, taken from the same hot rolled bar in two consecutive slices as presented on the diagram from Fig. 8.

The material anisotropies and eventual variations in the material properties, due to hot rolling and impact of the sampling technique, must be taken into account. In this kind of billet, mechanical anisotropy is often qualified with the grain flow, that is to say the elongation of the malleable inclusions in the matter in the same direction as the flow of matter during the forming process [START_REF]ASM Handbook: Volume 11, Failure analysis and prevention[END_REF]. Hence the reference samples are taken in a way, described in Fig. 8, that the magnetic flux has a similar trajectory orientation regarding the grain flow in the billet. Also, the locations of the samples and the ring core are chosen at a similar radius in order to limit the impact of an eventual variation of the material properties (such as the microstructure) along the radius. These samples are furthermore obtained using wire electric discharge machining, which is assumed to have a repeatable and limited impact on the magnetic properties [START_REF] Kurosaki | Importance of punching and workability in non-oriented electrical steel sheets[END_REF]. The experimental protocol consists in repeating three times the measurements for each parallelepipedic sample at twelve levels of the input current. The normal curves obtained for the samples are shown in Fig. 9 where R i stands for the sample number and M i for the measure repetition. The magnetic field needed to reach a polarization level of 1.5 T has an average value of 2190 A/m and a standard deviation of 142 A/m over these twelve measurements, that is to say a coefficient of variation of 6.7%. The average value of the specific losses is 0.248 W/kg and the associated standard deviation is 0.011 W/kg over the twelve measures, representing a coefficient of variation of 4.4%. This represents slightly more variation than the repeatability measures. The conclusion is that the parallelepipedic reference samples are slightly different from each other in terms of specific losses and magnetic field H 1.5 .

Regarding the ring core samples, the measure has been performed to investigate about the relevancy and limits of the dedicated characterization device. Three ring cores of dimensions D50 mm × d42 mm × h6 mm have been extracted from the same bar as the parallelepipedic samples (Fig. 8). The primary and the secondary windings have been designed to reach a comparable magnetic field range. Each ring core is measured three times. The characterization has been made using a Brockhaus MPG200 measurement equipment which controls the magnetic flux density B in closed-loop. Nine levels of amplitudes are reached from 0.2 T to 1.8 T at 3 Hz. In that case the skin depth is about 4 mm which is still acceptable to neglect this effect regarding the sample dimension. From the measured hysteresis loops, the bench gives the information on the normal curve directly. In this kind a measurements, the magnetic quantities are usually evaluated according to the following formulas:

H = n 1 i l m (4)
J = 1 n 2 S Sample v 2 (t)dt -µ 0 H (5)
where n 1 and n 2 are the number of turns of respectively the primary and secondary winding, l m the Fig. 10. Comparison between the reference samples and the ring core.

characteristic length of a magnetic core according to Standard IEC 60205. Here the secondary winding cross section is assumed to be the same as the sample cross section. The comparison between the normal curves from the used dedicated device and standard ring core characterizations are shown in Fig. 10.

In the standard measures (ring core), the required field to reach 1.5 T is H 1.5 = 1425 A/m. In that case, the specific characterization gives a value about 50% superior. This difference can be explained by different sources of deviations. Firstly, the samples are not exactly the same. Despite the sampling methodology presented before, they have not been taken exactly at the same place, so that their material properties, in terms of grain size, plastic strain or grain flow may differ from one sample to another. Moreover after the sampling process the residual stresses can be relaxed in a different way due to the closed shape of the ring core and the open shape of the parallelepipedic sample.

Secondly, the main source of deviation is due to the characterization procedure. On the one hand, at high level of magnetic field i.e. in the saturation zone, the standard ring core measure becomes inaccurate, for instance because of the inter-turns leakage flux and the axial component of the magnetic field. Furthermore, for these measures the compensation of the flux in the air gap between the sample and the secondary winding is not taken into account, and the compensation of the axial magnetic field is not guaranteed. In the other hand, the error can be imputed to several hypotheses enounced in the case of the specific characterization. First one major source of deviation is the linear extrapolation which overestimates the magnetic field H at the sample surface inside the sample whereas the profile shape is parabolic. The difference increases with a more significant gradient of the magnetic field H between the electromagnet poles. This is the case at low levels of magnetic field H (< 1000 A/m) or if the magnetic flux is not well channeled through the sample, for example if the air gap between the sample and the poles increases or if the magnetic properties are not sufficiently high. Secondly, the magnetic flux is averaged on the total length of the secondary winding. This leads to an uncertainty on the estimation of the magnetic polarization J which can shift the normal curve from the reference normal curve. In conclusion, a deviation between the ring core measurement and the presented technique has been observed. However comparative studies can be performed with this device considered the evaluated repeatability error. Consequently characterizing different samples using this technique reveals the impact of material parameters on magnetic properties.

Application to massive magnetic samples having different material properties

As explained in the introduction, the manufacturing process, like hot forging, has a strong impact on material and mechanical properties. The proposed characterization approach is now used to study the impact of these inherent properties on magnetic properties. The sensitivity of the device is illustrated with selected material parameters. On one hand, the grain size influence on magnetic properties, especially the specific losses, is verified and on the other hand, the influence of grain flow on the magnetic properties is investigated.

Grain size

Three sets of samples are investigated in this section. The first one (set A) is directly sampled in a hot rolled cylindrical bar, the corresponding grain size index is 6 ASTM (45 µm). The two other are obtained after different heat treatments. The set B has been obtained with a normalizing heat treatment, at a temperature of 900 • C during 10 minutes with air cooling. The obtained grain size index is 9 ASTM (15 µm). The set C has been obtained with a grain growth heat treatment, at a temperature of 1100 • C during 20 hours and furnace cooling. The obtained grain sized index is about 0 ASTM (350 µm). The grain size is evaluated using the intercept segment method according the standard ISO 643. The corresponding micrographs are shown in Fig. 11.

The samples have been magnetically characterized with the proposed technique. The results concerning the magnetic field needed to reach a polarization of 1.5 T are shown in Table 1.

Considering only the mean values, these results may show a trend that the larger the grain is, the lower the magnetic field H 1.5 is, which describes better magnetic properties. However, the standard deviation of these measures prevents an evident conclusion. Regarding the specific losses, the results in Fig. 12 show a clear trend that these losses decrease with larger grains. Considering the given frequency of 0.5 Hz, the eddy current losses seems not significant and a diminution of the hysteresis losses with larger grain size is expected as found in the literature [START_REF] De Campos | The optimum grain size for minimizing energy losses in iron[END_REF].

Grain flow

As discussed in the introduction, the shows difference in terms of magnetic properties according to the direction of characterization regarding the rolling direction for electrical steel laminations. The phenomenon is significant between the two cross direction 0 • and 90 • [START_REF] Landgraf | Effect of grain size, deformation, aging and anisotropy on hysteresis loss of electrical steels[END_REF]. In this case, due to the hot rolling process, the fiber is oriented in the same direction as the cylindrical bar axis. To evaluate the impact of the grain flow, two sets of samples are taken from the billet according different directions represented in Fig. 13.

These samples have been characterized with the presented device at 0.5 Hz and the same 12 levels of input current. The Table 2 shows the specific losses at 16 kA/m for the two sets of investigated samples. The distance between the two sets is not significant regarding the associated standard deviations.

The Fig. 14 shows the mean normal curves for the two sets of samples. For the direction θ = 0 • , the magnetic field required to reach 1.5 T of polarization is H The proposed specific protocol allows to verify that, for this steel grade (with a very low content of element of addition) for the frequency of 0.5 Hz, grain flow has no significant impact on magnetic properties.

Conclusion

The present work introduces the investigation of a dedicated magnetic characterization device to assess the influence of material properties. The literature shows many results in terms of impact of the material properties and processes on magnetic properties for laminated samples. The objective of the proposed approach is to extend all these results to massive samples, and keeping the possibility to investigate material anisotropies.

The presented device rests on a classic method of magnetic flux measurement and magnetic field estimation. The Section 3.1 confirms that the device is able to give repeatable measures. Nevertheless, the difference with the measure on ring cores revealed that the magnetic field H seems to be overestimated and the measures are not quantitative yet. Several trays of improvement of the characterization technique can be tested. The addition of more Hall probes to estimate the quadratic profile of the magnetic field within the electromagnet poles can reduce the error due to the linear extrapolation. Modifying the magnetic circuit topology or adding a magnetic shielding can also positively impact the spatial evolution of the magnetic field and make the linear extrapolation relevant.

At the end of this work, an application of the device has been proposed in order to study the impact of material properties on magnetic properties. Among the different sets of samples investigated, the standard deviation of the magnetic field H 1.5 remains slightly greater than the error of repeatability. The samples inside a same set have consequently similar magnetic respectively material properties. For the studied material, the influence of the material properties on the normal curves and the magnetic field H 1.5 are not significant for the investigated parameters. However, it has been shown that the grain size has a significant impact on specific losses, which is in accordance with the literature.

The illustration can be extended to other material parameters which are also investigated in the literature, such as crystallographic texture, plastic strain or residual stress. Investigating other steel grades with more element of addition result in more pronounced inclusions and may show differences of magnetic properties according to grain flow.

The immediate perspective of the work consists in improving the protocol with the proposed solutions and to apply the methodology to other material parameters in order to establish empiric models to predict their influence on magnetic properties.

Fig. 1 .

 1 Fig. 1. Schematic of the characterization equipment.

Fig. 2 .

 2 Fig. 2. Normal curve extraction from centered loops.

Fig. 3 .

 3 Fig. 3. Distribution of the magnetic field H between the poles of the electromagnet according to the FE simulation.

Fig. 4 .

 4 Fig. 4. Magnetic field distribution above the sample : experimental measures, polynomial fitting for the reference value and current linear extrapolation method during characterization.

Fig. 5 .

 5 Fig. 5. Estimation of magnetic field with different extrapolations (Simulation results, air gap = 2 × 0.15 mm).

Fig. 6 .

 6 Fig. 6. Normal curves under repeatability conditions for the considered test sample.

Fig. 7 .

 7 Fig. 7. Specific losses under repeatability conditions for the considered test sample.

Fig. 8 .

 8 Fig. 8. Position of the reference samples in two consecutive slices, flux direction during characterization and grain flow direction.

Fig. 9 .

 9 Fig. 9. Normal curves for the parallelepipedic reference samples.

Table 1 MagneticFig. 11 .

 111 Fig. 11. Micrographs for the two different sets of samples (left: set A; middle: set B; right: set C).

1 . 5 =

 15 2250 A/m with a standard deviation of 160 A/m. Concerning the direction θ = 90 • , the respective values are 2190 A/m and 142 A/m.

Fig. 13 .

 13 Fig. 13. Sampling with different angles to grain flow direction.

Fig. 14 .

 14 Fig. 14. Normal curve for different direction of sampling.

Table 2

 2 Specific losses at 0.5Hz and 16kA/m for different directions

	θ	0 •	90 •
	P16	0.240 W/kg	0.247 W/kg
	σ (P16)	0.015 W/kg	0.011 W/kg

Fig. 12. Influence of the grain size on specific losses.