Hai-Le Yan

Yu Dong Zhang
email: yudong.zhang@univ-lorraine.fr

Claude Esling

Xiang Zhao
email: zhaox@mail.neu.edu.cn

Liang Zuo

Determination of strain path during martensitic transformation in materials with two possible transformation orientation relationships from variant self-organization

Keywords: martensitic transformation, orientation relationship, transformation strain path, EBSD, crystallography

Determination of strain path across martensitic transformation in materials with two transformation orientation relationships (ORs) is challenging due to the temporal and spatial limitation of the modern techniques. In this work, an analyzing strategy, i.e., the determination of transformation path via the variant organization feature of martensite, was suggested and applied for the Ni-Mn-based alloys as an example, based on the consideration that the different crystallographic symmetries of transformation systems will result in distinct organizations of martensite variants. For the selected Ni-Mn-based alloys, the orientation examination revealed that both the K-S and the Pitsch OR are respected. Further analyses in terms of the strain and stress compatibility condition and the minimum energy criteria showed that, theoretically, the K-S path produces 2 variants as a self-accommodated variant group, whereas the Pitsch path produces 4 variants as a self-accommodated variant group. Compared with the experimental results, the Pitsch path is the energetically favorable transformation path and actually occurs in stress-free austenite of the Ni-Mn based alloys. The significance of this work is multi-fold. It first resolves the long puzzling issue of transformation strain path of Ni-Mn-based alloys.

Moreover, the analyzing scheme can be generalized to determine the transformation characters for martensitic transformation in other systems with multiple possible transformation orientation relationships.

Introduction

Martensitic transformation lies at the origin of fruitful functionalities of the Ni-Mn-based alloys, such as magnetic shape memory effect [START_REF] Kainuma | Magnetic-field-induced shape recovery by reverse phase transformation[END_REF][START_REF] Wang | Tracing memory in polycrystalline ferromagnetic shapememory alloys[END_REF][START_REF] Sun | Magnetic-field-induced strain-glass-to-martensite transition in a Fe-Mn-Ga alloy[END_REF], multicaloric effects [START_REF] Liu | Giant magnetocaloric effect driven by structural transitions[END_REF][START_REF] Gottschall | A multicaloric cooling cycle that exploits thermal hysteresis[END_REF][START_REF] Mañosa | Giant solid-state barocaloric effect in the Ni-Mn-In magnetic shape-memory alloy[END_REF][START_REF] Qu | Simultaneously achieved large reversible elastocaloric and magnetocaloric effects and their coupling in a magnetic shape memory alloy[END_REF], exchange bias [START_REF] Wang | Large exchange bias after zero-field cooling from an unmagnetized state[END_REF], magnetoresistance [START_REF] Sharma | Large magnetoresistance in Ni50Mn34In16 alloy[END_REF][START_REF] Yu | Large magnetoresistance in single-crystalline Ni50Mn50-xInx alloys (x=14-16) upon martensitic transformation[END_REF] and superelasticity [START_REF] Zhang | Giant high temperature superelasticity in Ni53Mn24Ga21Co1Cu1 microwires[END_REF][START_REF] Chen | Unprecedented non-hysteretic superelasticity of [001]-oriented NiCoFeGa single crystals[END_REF][START_REF] Wang | Superelasticity by reversible variants reorientation in a Ni-Mn-Ga microwire with bamboo grains[END_REF]. The energy efficiency of these functions is closely related to the lattice distortion across the structural transition. Therefore, knowledge of the distortion process of martensitic transformation is crucial for materials design aiming at maximizing functionalities at the lowest energy consumption. Among various factors concerning the phase transformation, the transformation strain path is one of the most important factors that possesses both practical importance and theoretical significance [START_REF] Zhao | Effect of nonlinear and noncollinear transformation strain pathways in phase-field modeling of nucleation and growth during martensite transformation[END_REF]. In reality, the transformation strain path is closely related to the resistance of the structural transition, thus, it could play a decisive role in the hysteresis that deteriorates the functionality of the alloys [START_REF] Lexcellent | Two ways for predicting the hysteresis minimisation for shape memory alloys[END_REF][START_REF] Gouné | Overview of the current issues in austenite to ferrite transformation and the role of migrating interfaces therein for low alloyed steels[END_REF]. Solid knowledge on this issue is imperative for application purposes and also crucial for theoretical study or simulation of the phase transformation process, such as phase-field simulations and, in the more general sense, for the further development of martensitic transformation models.

In this regard, the study on the transformation strain path has been frequently conducted both theoretically and experimentally. In theoretical analyses, the Bain strain path {001}A <010>A that results in the Bain orientation relationship (OR) between the parent and the product phase was first proposed as the transformation strain path to describe the structural transition for the Ni-Mn-based alloys [START_REF] Bain | The nature of martensite[END_REF][START_REF] Ayuela | Ab initio study of tetragonal variants in Ni2MnGa alloy[END_REF][START_REF] Entel | Properties and Decomposition of Heusler Alloys[END_REF][START_REF] Mañosa | Anomalies related to the TA2-phonon-mode condensation in the Heusler Ni2MnGa alloy[END_REF][START_REF] Entel | Basic Properties of Magnetic Shape-Memory Materials from First-Principles Calculations[END_REF][START_REF] Bungaro | First-principles study of lattice instabilities in ferromagnetic Ni2MnGa[END_REF][START_REF] Cong | Experiment and theoretical prediction of martensitic transformation crystallography in a Ni-Mn-Ga ferromagnetic shape memory alloy[END_REF]. It has been widely used to evaluate the lattice stability and/or to explore novel alloy compositions by the first-principles calculations [START_REF] Ayuela | Ab initio study of tetragonal variants in Ni2MnGa alloy[END_REF]. The Bain strain path is also convenient to describe several materials properties, such as the energy of twin interface and the magnetocrystalline anisotropy [START_REF] Lexcellent | Phase transformation yield surface determination for some shape memory alloys[END_REF][START_REF] Lexcellent | Shape-memory Alloys Handbook[END_REF]. However, in many materials, the Bain strain is not the true physical path of the transformation although it well explained the structure change. The Bain OR is seldom observed in the real transformations [START_REF] Lagoudas | Shape memory alloys, Part II: Modeling of polycrystals[END_REF][START_REF] Patoor | Shape memory alloys, Part I: General properties and modeling of single crystals[END_REF].

To resolve a more realistic transformation path, the electronic instability of austenite based on the combined studies on the Fermi-surface nesting and the phonon dispersion relation [START_REF] Mañosa | Anomalies related to the TA2-phonon-mode condensation in the Heusler Ni2MnGa alloy[END_REF][START_REF] Entel | Basic Properties of Magnetic Shape-Memory Materials from First-Principles Calculations[END_REF][START_REF] Bungaro | First-principles study of lattice instabilities in ferromagnetic Ni2MnGa[END_REF] have been performed. The transformation path of {110}A <1 ̅ 10> A that results in the Pitsch OR between the parent austenite and the product martensite was proposed. Under this path, many puzzling phenomena for the Bain path, such as the incommensurateness of structural modulation [START_REF] Li | Compositiondependent ground state of martensite in Ni-Mn-Ga alloys[END_REF] and the non-uniform displacement of shuffling plane [START_REF] Pons | Crystal structure of martensitic phases in Ni-Mn-Ga shape memory alloys[END_REF], can be easily understood. It should be noted that theoretical results were obtained under ideal composition and temperature conditions that are far from the practical situation. Moreover, the transformation system of {111}A <110> A that results in the K-S OR between the two end phases [START_REF] Kurdjumov | Over the mechanisms of steel hardening[END_REF] was also suggested for the structural transition of the Ni-Mn-based alloys [START_REF] Cong | Experiment and theoretical prediction of martensitic transformation crystallography in a Ni-Mn-Ga ferromagnetic shape memory alloy[END_REF].

Therefore, these theoretical propositions should be verified by experimental studies.

However, the direct evidence of the transformation strain path by experiments is much more difficult, due to the temporal and spatial limitation of the atomic scaled characterization techniques, as the displacive martensitic transformation occurs at the speeds approaching that of the sound and the relative displacement of atoms is usually much smaller than the length of an atomic band [START_REF] Bunshah | Rate of propagation of martensite[END_REF][START_REF] Mukherjee | On the dynamics of martensitic transformation[END_REF]. Moreover, the extreme sensibility of these materials to the stress-strain state makes the direct experimental observation of transformation path at the atomic scale even more difficult. To date, the investigation of the transformation path of the Ni-Mn-based alloys are mainly confined to the identification of the transformation OR. However, for the martensitic transformation of Ni-Mn based alloys that produces modulated martensite, the Pitsch and the K-S OR are simultaneously satisfied [START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF][START_REF] Li | Determination of the orientation relationship between austenite and 5M modulated martensite in Ni-Mn-Ga alloys[END_REF][START_REF] Zhang | Crystallographic features of the martensitic transformation and their impact on variant organization in the intermetallic compound Ni50Mn38Sb12 studied by SEM/EBSD[END_REF], which bring about ambiguity to the transformation strain path. Moreover, the relation between the microstructural representation and the different possible transformation strain paths, i.e., the organization of the martensite variants, has not been addressed. To this end, a top-down experimental strategy by examining microstructural and crystallographic features of the transformed microstructure combined with crystallographic decoding to determine the transformation strain path could be an effective approach.

Thus, in this work, we conducted a thorough investigation on the transformation strain path of the martensitic transformation of Ni-Mn-In alloys based on a combined study with microstructure characterization and crystallographic analysis by means of SEM electron backscattered diffraction (EBSD) technique. First, the possible transformation strain paths were evaluated by examining the crystallographic orientation relationship (OR) between austenite and martensite. For the various possible transformation paths, their correlated martensite variant combination configurations were then predicted under the strain and stress compatibility conditions and the minimum energy criterion for interface and elastic strain energies. By verifying the predicted microstructural features with the experimental evidence, the transformation strain path of the Ni-Mn-based alloys was determined. The result of this work has multi-folds of significance. It first resolves the long puzzling issue of transformation strain path of Ni-Mn-based alloys and provides solid experimental data for theoretical simulation of phase transformation processes using various novel models. Moreover, the analyzing scheme can be generalized to analyze the structural transition in the diffusional phase transformation of many other alloy systems.

Experimental details

In this work, two alloys, one with a single martensite phase (Ni2Mn1.44In0.56) [START_REF] Yan | Crystal structure determination of incommensurate modulated martensite in Ni-Mn-In Heusler alloys[END_REF] and the other with a mixed austenite and martensite (Ni45Co5Mn36.8In13.2) [START_REF] Yan | Crystallographic insights into Ni-Co-Mn-In metamagnetic shape memory alloys[END_REF] at room temperature, were prepared by arc-melting technique using pure constituent elements Ni (99.97 wt.%), Co (99.9 wt.%)), Mn (99.95 wt.%) and In (99.995 wt.%) under argon atmosphere in a water-cooled copper crucible. In order to achieve composition homogeneity, each ingot was remelted four times under electromagnetic stirring. The ingot was then remelted and injected into water chilled copper mold to obtain a dense cylindrical rod. The rod was first sealed in a quartz tube under argon atmosphere and then annealed at 1173 K for 24 hours and quenched in water. A rectangular parallelepiped sample with the sizes of 5 × 5 × 10 mm 3 was cut out of the middle of the cylindrical rod for microstructure and crystallographic orientation investigation. The inspected surface was first mechanically ground and then electrolytically polished with a solution of 20% nitric acid in methanol at room temperature. A field emission gun scanning electron microscope (Jeol JSM 6500 F) with an electron backscatter diffraction (EBSD) acquisition camera and the Aztec acquisition software package (Oxford Instruments) were used to perform the microstructural examination and crystallographic orientation measurement. The beam control mode was used with a step size of 0.125 m. To avoid the effect of free surface on martensitic transformation, the EBSD measurements were made on the freshly sectioned sample planes after the transformation had terminated in the bulk samples. No further thermal/ mechanical treatment that may affect the self-organization of martensite variants [START_REF] Wang | Experimental evidence of stress-field-induced selection of variants in Ni-Mn-Ga ferromagnetic shape-memory alloys[END_REF] was performed.

Results and discussion

Martensite microstructure and transformation orientation relationship

In Figs. 1a andb, we show the typical SEM/EBSD micrographs of the coexisting austenite and martensite (measured with the Ni45Co5Mn36.8In13.2 sample) and the pure martensite phase (measured with the Ni2Mn1.44In0.56 alloy) of the Ni-Mn-In based alloys. The alloy in Fig. 1a1 is composed of austenite possessing cubic L21 structure [START_REF] Yan | Crystallographic insights into Ni-Co-Mn-In metamagnetic shape memory alloys[END_REF] and martensite with a six-layer modulated (6M) monoclinic structure [START_REF] Yan | Crystal structure determination of incommensurate modulated martensite in Ni-Mn-In Heusler alloys[END_REF][START_REF] Yan | Crystallographic insights into Ni-Co-Mn-In metamagnetic shape memory alloys[END_REF]. Crystallographic orientation examination of the microstructure revealed that the two martensite domains (denoted G1 and G2) are located in one austenite grain. Each domain contains four orientation variants (denoted A, B, C and D), as shown in Fig. 1a2. Misorientation analyses demonstrated that the four variants in one group are twin-related one another, i.e., type-I (A: C and B: D), type-II (A: B and C: D) and compound twin (A: D and B: C), like the cases in some reported Ni-Mn-based alloys [START_REF] Yan | Variant organization and mechanical detwinning of modulated martensite in Ni-Mn-In metamagnetic shape-memory alloys[END_REF]. The interfaces between the variants coincide with their twinning plane K1 [START_REF] Yan | Variant organization and mechanical detwinning of modulated martensite in Ni-Mn-In metamagnetic shape-memory alloys[END_REF]. It should be noted that the martensite variants shown in Fig. 1a were formed in the bulk material and in the interior of austenite grain rather than on the surface or near austenite grain boundaries. The influences of free surface and grain boundaries on the transformation strain path and the organization of the martensite variants were eliminated. The microstructure in Fig. 1b1 revealed that when the martensitic transformation is complete, each initial austenite grain (as outlined with the black lines) transforms into several groups of the plate-shaped martensite variants. In each group, there are four martensite variants.

The variants are inter-related with the above-determined three twin relations. This result indicates that each group with the plate-shaped martensite variants is originated from the variant group in Fig. 1a. Moreover, our experiments showed that one initial austenite grain can produce maximum 6 orientation-independent groups of martensite variants, as shown in Fig. 1b2, hence, in total, 24 martensite variants.

We now focus on the microstructure of Ni45Co5Mn36.8In13.2 alloy (Fig. 1a) since the coexistence of austenite and martensite allows a direct verification of transformation ORs between the parent and the product phase using the ORs reported in the literature [START_REF] Bain | The nature of martensite[END_REF][START_REF] Kurdjumov | Over the mechanisms of steel hardening[END_REF][START_REF] Nishiyama | X-ray investigation of the mechanism of the transformation from facecentered cubic lattice to body-centered cubic[END_REF][START_REF] Wassermann | About the mechanism of α-γ transformation of the iron[END_REF][START_REF] Pitsch | Der orientierungszusammenhang zwischen zementit und austenit[END_REF]. In Fig. 2, we display the possible ORs for the studied alloy, i.e., the Bain (Fig. 2a), the Pitsch (Fig. 2b), the Kurdjumov-Sachs (K-S, Fig. 2c) and the Nishiyama-Wassermann (N-W, Fig. 2d) relations, which were selected based on the crystal structure features of the austenite and the martensite. In this work, the four ORs are discriminated with the angular differences between the theoretical (∆g 0 OR ) and the experimental (∆g exp ) disorientations between the austenite and the martensite under each OR. The details of the calculations are described in Appendix A. The results expressed as the minimal deviation angle (ω) are listed in Table 1. We see that for the Bain OR, the deviation angles for all the variants in G1 and G2 groups (Fig. 1a) are the highest, larger than 3, among the four ORs. A large deviation of the Bain OR was also reported in Ni-Mn-Ga [START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF], Ni-Mn-Sn [START_REF] Lin | Crystallographic study on Ni-Mn-Sn metamagnetic shape memory alloys[END_REF] and Ni-Mn-Sb [START_REF] Zhang | Crystallographic features of the martensitic transformation and their impact on variant organization in the intermetallic compound Ni50Mn38Sb12 studied by SEM/EBSD[END_REF] alloys. Clearly, the Bain OR can be ruled out from being the suitable OR for the Ni-Mn-based alloys. Table 1 Angular deviation of the experimental disorientation ( ∆g exp ) from the theoretical disorientation (∆g 0 OR ) between the austenite and the martensite under the Bain, the N-W, the K-S and the Pitsch relation. Apart from the Bain OR, the N-W OR also demonstrates a large mismatch (deviation angles > 1) for all the four martensite variants. Thus, the N-W path can also be excluded.

Different from the above two ORs, we see from Table 1 that both the K-S and the Pitsch ORs possess the close deviation for all the variants (around 0.6) and also the smallest deviations among the four ORs. Moreover, the values of the deviation for the two ORs are within the limit of the measurement error of the used EBSD technique ( 0.5). Thus, both the K-S and the Pitsch ORs were respected during the structural transformation.

In Fig. 3a, we illustrate the difference in geometry between the K-S and the Pitsch OR by comparing the martensite lattices under these two ORs. For simplicity, the average structure [START_REF] Van Smaalen | Incommensurate crystallography[END_REF] of modulated martensite is used. We can see that the martensite lattices under the Pitsch (green) and the K-S (blue) ORs almost completely overlap. Calculations showed that the disorientation angle between these two lattices is as small as 0.44. This means that the two ORs could be simultaneously satisfied in the present alloy system. A close examination of the OR systems (plane and direction) revealed that the two ORs share the common OR direction, i.e., [01 ̅ 1 ̅ ] A and [3 ̅ 3 ̅ 1] M but different OR planes, as shown in Fig. 3b. It is worth mentioning that such a dual OR phenomenon is not singular only for the present alloy. The same phenomenon has frequently been observed in many other Ni-Mn-based alloys possessing modulated martensite, such as the transformation to 7M modulated martensite in Ni50Mn30Ga20 [START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF], to 5M modulated martensite in Ni50Mn28Ga22 [START_REF] Li | Determination of the orientation relationship between austenite and 5M modulated martensite in Ni-Mn-Ga alloys[END_REF] and to 4O modulated martensite in Ni50Mn38Sb12 [START_REF] Zhang | Crystallographic features of the martensitic transformation and their impact on variant organization in the intermetallic compound Ni50Mn38Sb12 studied by SEM/EBSD[END_REF].

Transformation associated lattice deformation

With the determined possible ORs between the parent and the product phase, the lattice correspondences between the two phases can be established in the OR reference frame. Here, we define the reference system with three mutually perpendicular right-handed unit vectors, the first being perpendicular to both the OR direction and the normal of the OR plane, the second parallel to the OR direction and the third perpendicular to the OR plane, as shown in Fig. 4.

Based on the minimum deformation criterion [START_REF] Yang | Fabrication and crystallographic features of epitaxial NiMnGa ferromagnetic shape memory alloy thin films[END_REF], the deformation gradient tensor (F) associated with the lattice deformation during phase transformation was calculated. F expressed in the respective K-S and Pitsch OR reference frames are shown in Eqs. ( 1) and (2). According to the definition of F, the diagonal elements εii represents the normal strain component in the direction of i, and the off-diagonal elements εij represent the shear strain component in the direction of i and on the plane normal to the direction of j. We can see from

Eqs. ( 1) and ( 2) that the lattice deformation under these two ORs is mainly realized by a shear on the corresponding OR system, as highlighted in bold in Eqs. ( 1) and (2) (0.1002 on the {111}A plane and in the <110> A direction for the K-S OR and -0.1312 on the {110}A plane and in the <1 ̅ 10> A direction under the Pitsch OR), accompanied by the other small structural distortion. Clearly, the OR system functions as the deformation system and represents the strain path. If comparing the corresponding values in the two F, one can find that both the normal strain components (εii) and the shear strain components (εij) are comparable in magnitude for the two paths. With the above quantitative information, the temporal evolutions of the structural change following the respective two paths from the parent austenite to the product martensite were calculated and displayed in Fig. 5. It is seen that by the two paths the transformation can be realized independently and arrives at the same final structure. However, under the two paths, the structure deformation happens on different systems, thus they should have different impacts on variant organization. Therefore, the identification of the true paths could be made by the microstructural fingerprints, i.e., the organization of the martensite variants.

Microstructure prediction and verification

As mentioned above, the K-S and the Pitsch paths possess the common transformation direction <1 ̅ 10> A but different transformation planes (Fig. 3b), i.e., {111}A for the K-S path and {110}A for the Pitsch path. Since the transformation planes of these two paths have different crystallographic symmetries, i.e., three-fold for the K-S path ({111}A) and two-fold for the Pitsch path {110}A, their correlated microstructure features of the low-symmetry phase (martensite) should be different. Thus, we analyzed the variant organization configuration under these two paths.

Martensite variants and their related strain paths under the K-S and the Pitsch paths

The number and the orientation of all possible martensite variants under the K-S and the Pitsch paths were calculated first. The details of the calculation are given in Appendix B. Here, the Bravais lattice frame of the austenite is used as the reference frame. The determined martensite variants under the K-S and the Pitsch paths, henceforth termed as the K-S and the Pitsch variants, are shown in Fig. 6a with the <001>M stereographic projection. We see that one austenite can maximally generate 24 variants (labeled as 1 ~ 24) for both the K-S and the Pitsch paths. This is consistent with our experimental result (Fig. 1b). We see from Fig. 6a that the orientations of the 24 K-S variants are almost identical to the 24 Pitsch variants, which is in accordance with the above OR analyses (Fig. 3a). In Table 2, we listed the individual transformation path and the corresponding symmetry operation for all the K-S and the Pitsch variants. Clearly, the K-S and the Pitsch variants with the similar orientations, such as the K-S variant 1 and the Pitsch variant 1 (Fig. 6a), have exactly the same transformation direction Table 2 Individual transformation paths and their related rotational symmetry elements for all the 24 martensite variants under the K-S and the Pitsch paths. The expression of crystal symmetry follows the notation used in Ref. [START_REF] Humbert | Numbering the crystallographic variants in phase transformation[END_REF]. (x,y,z) x, -z, -y) x,y,) z,x,) (-y, -z, x) (-z, -y, -x)

(1 ̅ 1 ̅ 1 ̅ ) A [1 0 1 ̅ ] A (1 0 1 ) A [1 0 1 ̅ ] A 2 (x, -y, -z) (1 ̅ 1 1) A [1 0 1] A (1 0 1 ̅ ) A [1 0 1] A 3 (-
(1 1 1) A [1 ̅ 1 0] A (1 ̅ 1 ̅ 0) A [1 ̅ 1 0] A 4 (-x, z, y) (1 1 ̅ 1 ̅ ) A [1 ̅ 1 ̅ 0] A (1 ̅ 1 0) A [1 ̅ 1 ̅ 0] A 5 (-
(1 1 ̅ 1) A [1 ̅ 0 1] A (1 ̅ 0 1 ̅ ) A [1 ̅ 0 1] A 6 (-x, -y, z) (1 1 1 ̅ ) A [1 ̅ 0 1 ̅ ] A (1 ̅ 0 1) A [1 ̅ 0 1 ̅ ] A 7 (x, -z, y) (1 ̅ 1 1 ̅ ) A [1 1 0] A (1 1 ̅ 0) A [1 1 0] A 8 (x, z, -y) (1 ̅ 1 ̅ 1 ) A [1 1 ̅ 0] A (1 1 0) A [1 1 ̅ 0] A 9 (z, x, y) (1 ̅ 1 ̅ 1 ̅ ) A [1 ̅ 1 0] A (1 1 0) A [1 ̅ 1 0] A 10 (-
(1 1 ̅ 1) A [1 1 0] A (1 ̅ 1 0) A [1 1 0] A 11 (-y, -x, -z) (1 1 1) A [0 1 ̅ 1] A (0 1 ̅ 1 ̅ ) A [0 1 ̅ 1] A 12 (y, -x, z) (1 ̅ 1 1 ̅ ) A [0 1 ̅ 1 ̅ ] A (0 1 ̅ 1) A [0 1 ̅ 1 ̅ ] A 13 (-z, -x, y) (1 1 1) A [1 1 ̅ 0] A (1 ̅ 1 ̅ 0) A [1 1 ̅ 0] A 14 (z, -x, -y) (1 ̅ 1 1) A [1 ̅ 1 ̅ 0] A (1 1 ̅ 0) A [1 ̅ 1 ̅ 0] A 15 (-y, x, z) (1 1 ̅ 1 ̅ ) A [0 1 1 ̅ ] A (0 1 1) A [0 1 1 ̅ ] A 16 (y, x, -z) (1 ̅ 1 ̅ 1 ) A [0 1 1] A (0 1 1 ̅ ) A [0 1 1] A 17 (y, z, x) (1 ̅ 1 ̅ 1 ̅ ) A [0 1 ̅ 1] A (0 1 1) A [0 1 ̅ 1] A 18
(1 1 1 ̅ ) A [0 1 1] A (0 1 ̅ 1) A [0 1 1] A 19
(1 1 1) A [1 0 1 ̅ ] A (1 ̅ 0 1 ̅ ) A [1 0 1 ̅ ] A 20 (z, y, -x) (1 ̅ 1 ̅ 1 ) A [1 ̅ 0 1 ̅ ] A (1 0 1 ̅ ) A [1 ̅ 0 1 ̅ ] A 21 (y, -z, -x) (1 ̅ 1 1) A [0 1 1 ̅ ] A (0 1 ̅ 1 ̅ ) A [0 1 1 ̅ ] A 22 (-y, z, -x) (1 1 ̅ 1) A [0 1 ̅ 1 ̅ ] A (0 1 1 ̅ ) A [0 1 ̅ 1 ̅ ] A 23 (-z, y, x) (1 1 ̅ 1 ̅ ) A [1 0 1] A (1 ̅ 0 1) A [1 0 1] A 24 (z, -y, x) (1 ̅ 1 1 ̅ ) A [1 ̅ 0 1] A (1 0 1 ) A [1 ̅ 0 1] A
In Figs. 6b andc, we show the stereographic projections of the OR plane, i.e., {013}M of the K-S path and {12 ̅ 3 ̅ } M of the Pitsch path, for all the theoretical K-S and Pitsch variants.

We see from Fig. 6b that the 24 K-S variants gather into four clusters, each containing 6 variants.

The projections of the OR planes of the K-S variants in each cluster exactly overlap with one {111}A pole of austenite, i.e., the pole of transformation plane of the K-S path. Therefore, one transformation plane under the K-S path is associated with 6 martensite variants. As for the Pitsch path, as seen in Fig. 6c, the 24 variants gather into 6 clusters, each containing 4 variants.

The Pitsch variants in each cluster share one {110}A plane of austenite, i.e., the transformation plane of the Pitsch path.

In Figs. 7b1) and 19 (Fig. 7b4). For these two variants, the sign of the normal of the transformation plane is changed. Thus, three transformation directions combined with one transformation plane can totally generate 6 variants under the K-S path. For the Pitsch path, as seen in Fig. 7c, one transformation plane is associated with 4 variants. For these variants, both the signs of the transformation plane and direction are changed. For instance, [101]A direction on (101 ̅ ) A plane can produce variants 2 (Fig. 7c1), 6 (Fig. 7c2), 20 (Fig. 7c3) and 23 (Fig. 7c4).

This difference for the K-S and the Pitsch paths should result in the different variant organization, as depleted next.

Different variant combinations under the K-S and the Pitsch paths

We now derive the theoretical characters of martensite microstructure, particularly the variant organization, under the K-S and the Pitsch paths based on the criteria of the minimum elastic strain and interfacial energies. It is known that the microstructure evolution during martensitic transformation is involved in a self-accommodated process to minimize the transformation strain [START_REF] Bhattacharya | Self-accommodation in martensite[END_REF]. The self-organized martensite variants should simultaneously satisfy the strain and the stress compatibility conditions [START_REF] Patoor | Micromechanical modelling of superelasticity in shape memory alloys[END_REF][START_REF] Chemisky | Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation[END_REF]. The former guarantees that the microstructure after the structural transition is continuous, and no crack nucleates at the interface between the adjacent variants. The latter ensures that the stress in the vicinity of the interface varies continuously and no stress concentration occurs. For the present material, the transformation started from the nucleation of groups of martensite variants (Fig. 1a). The satisfaction of these two conditions requires that the adjacent two self-accommodated variants are transformed from the same strain path plane and direction of austenite, meaning that the spatially adjacent variants should share the same transformation plane and the same in-plane direction during the nucleation process. For the K-S path, since one transformation plane and direction are associated with only two variants, a sandwich microstructure with alternatively distributed two variants should be energetically favorable in terms of transformation strain compatibility. For the Pitsch path, as one transformation plane and in-plane direction is associated with 4 variants, the microstructure should be composed of groups of 4 cotransformation plane variants.

The co-plane variant group should also possess the minimum interfacial energy between variants and minimum volume elastic strain (from volume misfit) between austenite and variant group. Here, the possible combinations for martensite variants generated by one transformation plane, e.g., 6 (111) A plane related K-S variants (Fig. 7b) and 4 (101 ̅ ) A plane related Pitsch variants (Fig. 7c), are discussed. Firstly, the interfacial energy between variants is analyzed by examining their crystallographic orientation relationship [START_REF] Zhang | A general method to determine twinning elements[END_REF][START_REF] Beyerlein | Double twinning mechanisms in magnesium alloys via dissociation of lattice dislocations[END_REF][START_REF] Cong | Determination of microstructure and twinning relationship between martensitic variants in 53 at.%Ni-25 at.%Mn-22 at.%Ga ferromagnetic shape memory alloy[END_REF]. For the K-S path, among the 6 co-transformation plane variants, not all 6 variants can be interrelated with twin relations.

II twin)

. Therefore, the boundaries between these variant pairs could be the so-called invariant twinning plane K1 [START_REF] Zhang | A general method to determine twinning elements[END_REF][START_REF] Beyerlein | Growth twins and deformation twins in metals[END_REF], i.e., the low-energy interface. By contrast, the boundaries for variant pairs 1: 9 and 1: 17 can only be non-coherent high energy boundaries. Consequently, for the K-S path, 3 pairs of twin-related variant combinations (3 individual sandwiches) are favorable in view of interfacial energy. It should be noted that the first two types of twins between variant pairs 3: 1 and 11: 1 have never been experimentally found in the Ni-Mn based alloys. However, for the Pitsch path, all 4 co-transformation plane variants are twin related one another. Thus, all these 4 variants could be interconnected by low-energy coherent interfaces, i.e., the twinning plane.

Apart from interfacial energy, the volume elastic strain for the combinations of the twinrelated variants under the K-S and the Pitsch path is evaluated. As is known, both the volume and the shape changes of the martensite nucleus play important roles in the elastic strain energy during martensitic transformation. The total deformation of a twin related variant pair can be expressed by the following equation:

F = x × F i + (1-x) ×F j (0 ≤ x ≤1), (3)
where F i and F j are the deformation gradient tensor of variant i and j, and x is the relative volume fraction of variant i. find that all 1, 2 and 3 equal to those of the single variant 1 or 19 and stay constant with the variation of the volume fraction (Fig. 8a3). As a result, for the K-S path, among the 6 cotransformation plane variants only one variant pair produces the smallest volume misfit between austenite and martensite and hence is favorable in terms of elastic strain energy. The variants in this pair are also twin related. Thus, under the K-S path, it prefers to form a "sandwich-like" structure with two alternately distributed variants (AB…AB), as illustrated in

Comparison of experimental and theoretical variant organization

The above theoretical analyses demonstrate that the different transformation paths result in different compatible variant organizations. For the K-S path, a sandwich structured variant group with two twin-related variants should be formed (Fig. 9a), whereas, for the Pitsch path, a cluster of 4 inter twin-related variants should be produced by the transformation (Fig. 9b).

Thus, by comparing the predicted variant organization under the two paths with the observed one, the transformation path for the studied Ni-Mn-In alloys can be uniquely determined. As displayed in Fig. 1a and reported in Refs. [START_REF] Yan | Variant organization and mechanical detwinning of modulated martensite in Ni-Mn-In metamagnetic shape-memory alloys[END_REF][START_REF] Li | Evidence for a monoclinic incommensurate superstructure in modulated martensite[END_REF], the martensite variant group or cluster of the modulated martensite in the Ni-Mn-In alloys is self-organized with 4 twin-related variants rather than 2. In Fig. 10, we plot the <001>M stereographic projection of the 4 measured martensite variants in G1 in Fig. 1a and the <001>M pole figures for their corresponding theoretical Pitsch variants. We see that the measured variants A, B, C and D are in exact coincidence with the respective theoretical Pitsch variants 19, 5, 1 and 24. This result suggests that the Pitsch path is the strain path of the formation of the studied 6M modulated martensite in Ni-Mn-In polycrystalline alloys. It should be noted that for the other Ni-Mn-based alloys with different transformation ORs, the transformation strain paths could be different and the martensite variant group configurations could also be different [START_REF] Chulist | Orientation relationship between austenite and non-modulated martensite in Ni-Mn-Ga single crystals[END_REF][START_REF] Cong | Microstructural and crystallographic characteristics of interpenetrating and noninterpenetrating multiply twinned nanostructure in a Ni-Mn-Ga ferromagnetic shape memory alloy[END_REF]. As seen in Fig. 6c and Table 2, these 4 variants are associated with the same Pitsch-type transformation system, i.e., (1 0 1 ) A [1 0 1 ̅ ] A , which is in excellent agreement with the above theoretical analyses. In total, there are 6 distinct Pitsch-type transformation planes <1 0 1 ̅ > A for cubic crystals. Thus, theoretically, one austenite can maximally generate 6 independent martensite groups. This is also in excellent accordance with our experimental observation in Fig. 1b. Furthermore, based on the indirect two-trace method [START_REF] Zhang | Indirect two-trace method to determine a faceted low-energy interface between two crystallographically correlated crystals[END_REF] to determine the interface plane, we find that the Miller indices of the interface plane between variants A: C (or B: D) are {12 ̅ 3 ̅ } M . The interface plane is exactly parallel to the {101}A plane of austenite, i.e., the transformation plane of the Pitsch path. However, no variant interface planes are in coincidence with the {013}M plane that corresponds to the transformation plane of the K-S path. Thus, for the modulated Ni-Mn-In martensite, the Pitsch path is indeed the physical transformation strain path. The mutual satisfaction of the K-S OR by the parent austenite and the product martensite in the studied Ni-Mn based alloys should be a geometrical coincidence. This results from the specific crystal structure systems and the particular lattice parameters of the two end phases of the transformation.

Conclusions

In this work, the ambiguous K-S {111}A <1 ̅ 10> A and Pitsch {110}A <1 ̅ 10> A transformation paths for the Ni-Mn-based alloys with modulated martensite were comprehensively investigated by means of experimental examinations using SEM-EBSD and theoretical analyses in the frame of crystallographic theory. The main conclusions can be drawn as follows:

(1) The modulated martensite of Ni-Mn-based alloys has a self-accommodated microstructure grouped with four inter twin-related martensite variants. The K-S and the Pitsch ORs are mutually respected by the parent and the product phase. Under the two ORs, the OR plane and the OR direction is associated with the major strain component and the OR system is physically the transformation strain path.

(2) Crystallographic analyses showed that by satisfying the strain and stress compatibility condition and the minimum energy criteria, theoretically, the K-S path produces 2 variants as a self-accommodated variant group, whereas the Pitsch path produces 4 variants as a selfaccommodated variant group.

(3) Supported with the experimental results, the Pitsch path is the energetically favorable basis of the corresponding plane and in-plane parallel pairs and crystal structure information of austenite and martensite, respectively. The determined ∆g 0 OR , expressed in terms of the Euler angles (1, , 2) with respect to the austenite lattice reference, is given in Table 1.

The difference between the theoretical and experimental ORs can be evaluated by the rotational difference ∆ε between the theoretical ∆g 0 OR and experimental misorientation ∆g exp :

∆ε = ∆g exp × S l -1 × (∆g 0 OR ) -1 × S j (A.2)
where S j ( j = 1  24) and S l ( l = 1  2) represent the rotation symmetry matrices of the austenite (cubic) and martensite (monoclinic), respectively. These rotational difference ∆ε can also be expressed in terms of rotation angle/axis pairs (ω, d). Among 48×48 possible ∆ε that are equivalent by symmetry, the one with the minimal ω value can be utilized to characterize the difference between the experimental and theoretical ORs.

Appendix B. Possible martensite variants under certain OR

The crystallographic orientations of possible martensite variants (g M i ) with respect to the austenite lattice reference under certain OR can be determined by the follow equation:

g M i = S A i × ∆g 0 OR (B.1)
where S A i ( i= 1  24) are the rotational symmetry matrices of cubic lattice for the austenite phase. ∆g 0 OR represent the theoretical OR matrix from the orthonormal basis of austenite lattice to that of martensite lattice. As show in Eq. B.1, the number of martensite orientation matrices equal to the number of the symmetry operators of the austenite lattice. Thus, for a certain OR, it leads to a maximum of 24 variants in the case of a cubic austenite grain. However, due to the possible symmetry of ∆g 0 OR under certain OR, some variants might coincide in the orientation space [START_REF] Zhang | A general method to determine twinning elements[END_REF], and then the number of the physically distinguishable variants may be less than 24.

Fig. 1

 1 Fig. 1 Phase indexed (a1) and orientation (a2) micrographs of the dual-phase Ni45Co5Mn36.8In13.2 alloy. The solid black lines indicate the phase boundaries between austenite and martensite. The red dotted, red dashed and red solid lines represent the type-I, type-II and compound twin interfaces. Crystallographic orientation (b1) and band quality indexed (b2) micrographs of the single martensite of the Ni2Mn1.44In0.56 alloy. The solid black lines represent the initial austenite grain boundaries. G1 to G6 indicate the distinct martensite groups.

Fig. 2

 2 Fig. 2 Illustrations of lattice correspondences between the austenite and the martensite under the Bain (a), the Pitsch (b), the K-S (c) and the N-W (d) OR. The crystal lattices of the austenite and the martensite are indicated in red and blue, respectively. Subscripts "A" and "M" represent austenite and martensite, respectively.

Fig. 3 (

 3 Fig. 3 (a) Orientations of martensite lattices under the K-S (blue) and the Pitsch (green) relation. (b) Stereographic projection of the OR planes and the OR directions for the K-S and the Pitsch OR in the lattice frame of austenite.

FFig. 4

 4 Fig. 4 Illustration of lattice deformation during martensitic transformation under certain transformation orientation relationship (OR).

Fig. 5

 5 Fig. 5 Illustration of the lattice deformation during martensitic transformation under the K-S (a) and the Pitsch (b) paths. The OR plane and in-plane OR direction parallelism for the austenite and the martensite are depicted by the red and the blue color, respectively. t0, tmid and tterminal indicate the initial, the middle and the final temporal stage of transformation.

[ 101 ̅

 101 ] A but different transformation planes, i.e., the (1 ̅ 1 ̅ 1 ̅ ) A for the K-S variant 1 and the (101) A for the Pitsch variant 1. Thus, the different impacts of the K-S and the Pitsch transformation path on variant organization should be mainly from the transformation plane.

Fig. 6

 6 Fig. 6 Stereographic projections of martensite variants under the K-S and the Pitsch paths. (a) <001>M pole figure for the K-S and the Pitsch variants; (b) {013}M pole figure for the K-S variants; (c) {12 ̅ 3 ̅ } M pole figure for the Pitsch variants. (001)A of austenite is utilized as the projection plane.

  7 a1 and a2, we plot all transformation directions in one transformation plane for the K-S and the Pitsch paths to clarify the relation of the strain paths for martensite variants generated by the same transformation plane. The green and the red arrows indicate the respective normal direction of the transformation plane and the transformation direction. We see from Fig. 7 a1 that there exist three physically distinct transformation directions, for example [101 ̅ ] A , [1 ̅ 10] A and [01 ̅ 1] A , on one transformation plane under the K-S path. As for the Pitsch path, as seen in Fig. 7a2, each transformation plane has only one transformation direction. As revealed above, one transformation plane under the K-S and the Pitsch path can provide 6 and 4 variants. For clarify, in Figs. 7b and c, we display the individual paths for the 6 (111)A plane related K-S variants(1, 3, 9, 11, 17 and 19) and the 4 (101 ̅ ) A plane related Pitsch variants(2, 6, 20 and 23). We see from Fig.7bthat for the K-S path one transformation plane and one direction are associated with 2 variants, for example, [101 ̅ ] A of the austenite can generate the K-S variants 1 (Fig.

Fig. 7

 7 Fig. 7 Illustrations for (a1) the K-S and (a2) the Pitsch path. Individual transformation path for (b) the 6 (111)A plane related K-S variants and (c) the 4 (101 ̅ ) A plane related Pitsch variants. (b1) ~ (b6) represent the K-S variants 1, 17, 9, 19, 11 and 3, and (c1) ~ (c4) the Pitsch variants 2, 6, 20 and 23.

  The three eigenvalues 1, 2 and 3 of F demonstrate the dimension change in the corresponding eigenvector directions and thus can be used as a measure of volume change and shape change of the twin pair. The values lager than 1 mean elongation and the ones less than 1 mean contraction. If they are all close to 1, it means that the volume of the variant pair is very close to the volume of the initial austenite. The evolution of the eigenvalues of F for the combination of the twin-related variant pairs under the K-S and the Pitsch paths are calculated and shown in Figs. 8 a and b. For the K-S path, we can see that for variant pairs 1: 3 and 1: 11 2 and 3 vary with the relative volume fraction of the two variants and are very different from 1, although 1 is constant. The maximum change happens when the two variants possess an equal volume. This suggests that the formation of such variant pairs create large volume and shape change, and thus large volume misfit between the initial austenite and the formed martensite variant pair. Therefore, such combinations are not energetically favorable. For the combination of variants 1 and 19, we can

Fig. 9a .Fig. 9

 9a9 Fig. 9a. In contrast, for the Pitsch path, the three eigenvalues of the combined F for all possible

Fig. 10

 10 Fig. 10 Comparison of the orientations of the measured martensite variants (blue circles) with the theoretical ones (red crosses) generated through the Pitsch path with the stereographic projection of <001>M poles. The inset shows the microstructure of the measured 4 selforganized martensite variants A, B, C and D from G1 in Fig. 1a.

Figure captions:Fig. 1

 1 Figure captions:

Fig. 2 Fig. 3 (

 23 Fig. 2 Illustrations of lattice correspondences between the austenite and the martensite under the Bain (a), the Pitsch (b), the K-S (c) and the N-W (d) OR. The crystal lattices of the austenite and the martensite are indicated in red and blue, respectively. Subscripts "A" and "M" represent austenite and martensite, respectively.

Fig. 4

 4 Fig. 4 Illustration of lattice deformation during martensitic transformation under certain transformation orientation relationship (OR).

Fig. 5

 5 Fig. 5 Illustration of the lattice deformation during martensitic transformation under the K-S (a) and the Pitsch (b) paths. The OR plane and in-plane OR direction parallelism for the austenite and the martensite are depicted by the red and the blue color, respectively. t0, tmid and tterminal indicate the initial, the middle and the final temporal stage of transformation.

Fig. 6

 6 Fig. 6 Stereographic projections of martensite variants under the K-S and the Pitsch path. (a) <001>M pole figure for the K-S and the Pitsch variants; (b) {013}M pole figure for the K-S variants; (c) {12 ̅ 3 ̅ } M pole figure for the Pitsch variants. (001)A of austenite is utilized as the projection plane.

Fig. 7

 7 Fig. 7 Illustrations for (a1) the K-S and (a2) the Pitsch path. Individual transformation path for (b) the 6 (111)A plane related K-S variants and (c) the 4 (101 ̅ ) A plane related Pitsch variants.

(Fig. 8 EigenvaluesFig. 9

 89 Fig. 8 Eigenvalues 1, 2 and 3 of the combined deformation gradient tensor for twin-related variant pairs under (a) the K-S and (b) the Pitsch path as a function of relative volume fraction x. (a1) the K-S variants 1 and 3; (a2) the K-S variants 1 and 11; (a3) the K-S variants 1 and 19; (b1) the Pitsch variants 2 and 6; (b2) the Pitsch variants 2 and 20; (b3) the Pitsch variants 2 and 23.

Fig. 10

 10 Fig. 10 Comparison of the orientations of the measured martensite variants (blue circles) with the theoretical ones (red crosses) generated through the Pitsch path with the stereographic projection of <001>M poles. The inset shows the microstructure of the measured 4 selforganized martensite variants A, B, C and D from G1 in Fig. 1a.

  ̅̅̅̅̅̅̅̅ 0.1251 ̅̅̅̅̅̅̅̅ 4.1157 ̅̅̅̅̅̅̅̅ ] M), 11: 1 (K1=(0.5349 ̅̅̅̅̅̅̅̅ 0.9374 ̅̅̅̅̅̅̅̅ 1.4130 ̅̅̅̅̅̅̅̅ ) M, η1=[2.7804 ̅̅̅̅̅̅̅̅ 3.1890 1.0630 ̅̅̅̅̅̅̅̅ ]M or K1=(0.4702 0.9396 ̅̅̅̅̅̅̅̅ 1.5957)M, η1=[ 3.1230 3.1818 0.9532]M) and 19: 1 (the type-

	Only 3 variants can each establish a twin relation with a fourth variant, i.e., variant pairs 3: 1
	(K1=(0.0200 ̅̅̅̅̅̅̅̅ 0.1204 2.1552)M, η1=[5.7765 0.1929 ̅̅̅̅̅̅̅̅ 0.0643]M or K1=(3.1125 ̅̅̅̅̅̅̅̅ 0.1704 0.0207)M,
	η1=[0.0342

Acknowledgment

This work is supported by the National Natural Science Foundation of China (Grant No. 51801020), the Fundamental Research Funds for the Central Universities (Grant No. N2002005, N2002021), the Liaoning Revitalization Talents Program (Grant No. XLYC1802023), and Programme of Introducing Talents of Discipline Innovation to Universities (the 111 Project of China, No. BP0719037).

transformation path and actually occurs in stress-free austenite of the Ni-Mn based alloys.

The present results shed new light on the physical process of the martensitic transformation that is associated with multiple functionalities of the Ni-Mn based alloys. The obtained knowledge is useful for the efforts in enhancing the martensitic transformation-related functionalities through reducing transformation resistance. The analyzing scheme, i.e., determination of transformation strain path via the microstructure characters of the lowsymmetric phase, could be generalized to determine the transformation characters for martensitic transformation, even for other shear dominated solid-state phase transition, in many other alloy systems.

Appendix A. Difference of the theoretical and experimental ORs

The experimental crystallographic ORs (∆g exp ) can be calculated based on the measured orientations of austenite (g A ) and martensite (g 6M ) by Eq. A.1.

where S i ( i = 1  24) and S k ( k = 1  2) represent the rotational symmetry matrices of the austenite (cubic) and martensite (monoclinic), respectively. The theoretical crystallographic ORs (∆g 0 OR ) of the Bain, the N-W, the K-S and the Pitsch relations can be calculated on the (2007) 436-440.


Dr Christophe Délye
email: christophe.delye@inra.fr

Séverine ; Michel

Fanny Pernin

Véronique Gautier

Marie Gislard

Charles Poncet

Valérie Le Corre

Harnessing the power of next-generation sequencing technologies to the

Keywords: pesticide resistance, detection, next generation sequencing, Illumina, ALS (acetolactate-synthase), AHAS (acetohydroxyacid-synthase), highthrougput, massive screening Acetolactate-synthase (ALS), diagnosis, genotyping-by-sequencing, herbicide, 48 Illumina, resistance

the grass Apera spica-venti, 22 a double mutation at ALS codon 122 causing a Ala-122-Tyr 372 substitution in Raphanus raphanistrum 23 and two combined mutations at codons 102 and 106 373 at the 5-enolpyruvylshikimate-3-phosphate synthase gene that encodes another herbicide target 374 enzyme in the grass Eleusine indica. 24 Double-mutations in one pesticide gene have often been 375 reported to confer an increased resistance level and/or a broader resistance spectrum, especially 376 in fungicides (e.g., 25 ) but also in herbicides. 24 Herbicide sensitivity bioassays are needed to 377 establish the resistance pattern associated to the double mutation identified in groundsel.

378

NGS analysis correctly identified a total of four amino-acid substitutions in ragweed. 379 Three of them were detected in North American ragweed plants used to generate control 380 populations (Table 1). A Trp-574-Leu substitution had previously been identified in this 381 species. 26 An Asp-376-Glu substitution had been identified in 12 species so far, 17 while a Gly-382 654-Asp substitution had only been reported in the grass weed Setaria viridis to date. 27 The last 383 substitution, Ala-205-Thr, was carried by French plants from the field and had never been 384 reported before. Herbicide sensitivity bioassays are underway to establish its associated 385 resistance pattern. 3), even if some differences could be observed (Tables 1 and2). The causes 391 at the root of these discrepancies may be differences in the amount of plant material collected 1,2). Indeed, these mutations 397 were actually detected by NGS, but with an estimated frequency that was below the 0.9% 398 threshold set for reliable mutation detection. This flaw could be overcome by using a 399 proofreading Taq polymerase in the PCRs preceding NGS, which would allow lowering the heterozygous mutants may be of some relevance. However, for resistance management in the 415 field, the vital information is rather the detection of mutation(s) involved in pesticide resistance 416 in one pest population. Such mutations are an unambiguous indicator that resistance is arising, 417 and that steps are to be taken to delay its onset. 418 Herein, we targeted 15 codons in one ALS gene in 96 batches of 50 plants (ragweed) 419 and in two ALS homeologs in 96 other batches of 50 plants (groundsel), which surpasses all 420 preceding studies having applied NGS to pesticide resistance detection. 8,9,10 As it is described here, our NGS-based method only targets mutations at specific codons in the 447 ALS gene. However, the scope of the method can be extended. First, any ALS nucleotide 448 present in the amplicons sequenced can very easily be added to the list of positions to be 449 screened by our pipe-line. This could reveal novel mutations of interest. Second, the pipe-line 450 developed herein can be applied to other weed or pest species. As the level of nucleotide 451 polymorphism varies with the species, this will require to adapt the alignment stringency to the 452 gene(s) and to the weed or pest targeted. This can be done by running the pipe-line on a set of

Pro-197-Leu-2 2 Pro-197-Ser-1 2 Pro-197-Ser-2 2 Pro-197-Thr-1 1 Pro-197-Thr-2 1 Pro-197-Leu-1 + Pro-197-Arg-2 3 Pro-197-Leu-1 + Pro-197-Leu-2 5 Pro-197-Asn-2 + Pro-197-Leu-2 2 Pro-197-Leu-1 + Pro-197-Arg-2 + Pro-197-Leu-2 2 Pro-197-Leu-1 + Pro-197-Asn-2 b + Pro-197-Leu-2 2 Pro-197-Asn-2 b + Pro-197-Leu-2 + Pro-197-Ser-2 1 Pro-197-Leu-1 + Pro-197-Asn-2 b + Pro-197-Leu-2 + Pro-197-Ser-2 1 593 a
The number following the mutation refers to the ALS homeolog (1, ALS1; 2, ALS2). For groundsel analyses, overhang adapter sequences were included at the 5' end of the plants in these populations (Tables 1,4). Thus, a total of eight mutations causing amino-acid that was present with a frequency of 1% was detected with a frequency of 0.63%, i.e., below 307 the 0.9% threshold (Table 2). No mutations were detected in 79 of the 87 field populations 308 investigated. In the remaining eight populations (all from Occitanie), a G-to-A transition at the 309 first nucleotide in codon 205 causing an alanine-to-threonine amino-acid substitution was 310 detected in frequencies ranging from 0.9 to 11.5% (Table 2). Mapping the eight populations 311 from Occitanie investigated herein revealed that six populations were clustered within a radius 312 of roughly one km within one river valley. The other two populations could be "escapees" 313 disseminated by, e.g., agricultural machinery, to different river valleys 2.5 km south and 7.5 314 north from the main resistance focus, respectively (Figure 12). as in the control populations were subsequently compared (Tables 1 and2, Figure 23). For the actually present with a frequency of 1% (i.e., false negatives; Tables 1 and2). In all three cases, 340 the mutations in question had been detected by NGS analysis, but their estimated frequencies 341 ranged from 0.2 to 0.7% and were therefore below the threshold set for reliable mutation 342 detection (0.9%). On the other hand, mutations present with a frequency of 1% were 343 successfully detected by NGS analysis in two groundsel populations and seven ragweed 344 populations (Tables 1 and2). 1,2). 397 Indeed, these mutations were actually detected by NGS, but with an estimated frequency that 398 was below the 0.9% threshold set for reliable mutation detection. This flaw could be overcome preceding studies having applied NGS to pesticide resistance detection. 8,9,10

  of NGS-based quantification of mutations endowing pesticide resistance 388 The frequencies of the ALS mutations assessed by NGS analysis of 50-plants pools matched 389 very closely those determined by analysing the corresponding individual plants in both species 390 investigated (Figure

  392 among individual plants, especially in groundsel where leaf thickness is rather variable, and/or 393 a heterogeneous efficacy of DNA extraction and/or PCR. An unequal contribution of all plants 394 in one pool to the mixture of amplicons generated for NGS is most likely the reason why NGS 395 analysis of plant pools failed to detect mutations present with a frequency of 1% in two ragweed population (false negatives, Tables

  400 mutation detection threshold, and/or by slightly decreasing the number of plants per pool (e.g., 401 40 plants per pool, which would yield a minimum expected mutation frequency of 1.25% on a 402 given gene or homeolog in the pool). Considering the tremendous sequencing depth achieved 403 in this study for every ALS amplicon sequenced, analysis of two pools of 40 plants per 404 population investigated rather than a single pool of 50 plants could be performed for 96 405 populations in one single Illumina run with a codon coverage adequate for mutation detection. 406 This way, reducing the number of plants per pool could largely be compensated for by analysing analysis of plant pools detected and quantified resistance-endowing mutations in 411 9,600 individual plants clustered into 192 pools. This approach did not allow to determine the 412 genotypes of the individual plants constituting the pool. This could be considered a drawback 413 in the case of recessive resistances, where differentiating between homozygous and 414

  extractions followed by the production of three amplicons, each in 422 triplicate PCR reactions per extraction, i.e., 1,728 PCRs, and two Illumina MiSeq runs. (It 423 should be mentioned that, given the sequencing depth achieved, one single such run would have 424 been sufficient to analyse all 192 pools). The same study conducted by the conventional single-425 codon PCR-based genotyping assays used for resistance detection (e.g., 15 ) would have required 426 9,600 DNA extractions. It would have necessitated, first, to set up and validate 15 codon-427 specific genotyping assays for ragweed and 30 homeolog-and-codon-specific genotyping 428 assays for groundsel, then, to carry out and visualise 15 genotyping assays per ragweed plant 429 and 30 per groundsel plant, i.e., a total of 216,000 PCRs (followed by the same number of 430 restriction enzyme digestion reactions in the case of dCAPS). If Sanger sequencing had been 431 used instead of genotyping, this study would have necessitated the production of three 432 amplicons in triplicate PCR reactions in ragweed and six in groundsel (three per homeolog), 433 i.e., 121,500 PCRs, followed by 40,500 Sanger sequencing runs. This clearly illustrates the 434 power of NGS for diagnosing resistance-endowing mutations in numerous samples. 435 In contrast to preceding NGS studies addressing pesticide resistance diagnosis, 9,10 our 436 work was carried out using a rapid DNA extraction procedure based on a non-commercial, lab-437 made extraction buffer. 16 The rough DNA extracts obtained proved perfectly suitable for 438 resistance detection in pools of 50 individual plants. After Illumina sequencing, assignation of 439 the sequence reads to their originating sample was performed using the software attached to the 440 sequencer. This can be done in the case of an in-house facility, or requested from any 441 sequencing supplier. The downstream analyses (read mapping on reference sequences, 442 mutation detection and quantification) required no commercial software, our pipe-line being 443 exclusively based on freely available programs and applications.

  453 previously characterised populations by modifying options for the Bowtie short read aligner 454 (see MutSeeker operating instructions). Third, the sequencing depth achieved by the Illumina 455 technology clearly allows to sequence several genes in a single run. This has been shown herein 456 by our analysing the two ALS homeologs in groundsel. Accordingly, several distinct pesticide 457 targets can be screened in one single NGS run. Resistance can also be due to non-target-site 458 based mechanisms. 28 When the mutations involved in these mechanisms are known, they can 459 be subjected to NGS-based detection. Amplifying and sequencing by NGS as many amplicons 460 as necessary to cover the genome regions including the nucleotide positions of interest is easily 461 feasible, keeping in mind that the length of each amplicon must be lower than that of the NGS 462 reads (i.e., lower than 500 nucleotides for 250 nucleotide pair-end sequences). If many genome 463 regions of interest are targeted, then a compromise is to be found between the number of 464 amplicons to be sequenced per population and the number of population to be sequenced per 465 NGS run so that a satisfactory sequencing depth (e.g., 10× for each amplicon obtained from 466 each individual plant in each pool) is achieved. illustrates the power and throughput of the NGS technologies for the detection of 470 mutations endowing pesticide resistance. The capacity of NGS-based resistance diagnosis exploited for massive resistance surveys (i.e., analysing numerous pest or weed 472 populations) as well as for in-depth resistance detection (i.e., analysing numerous pest or weed 473 individuals in one population to detect to onset of resistance at very early stages, when 474 resistance management practices can still nip resistance evolution in the bud). With the 475 continuously-increasing amount of sequence reads generated by NGS runs and the technical 476 possibility to multiplex hundreds of pools of individuals in one single NGS run, the era of 477 massive resistance diagnosis is clearly just dawning. As shown in our work, the tremendous 478 amounts of sequence reads generated can be analysed without the need for extensive training 479 in NGS data analysis, which should extend the benefit of using NGS diagnosis to a large number 480 of scientists dealing with pest control. Actually, the throughput of assays such as the one 481 described herein is so high that the future main issue with NGS-based resistance detection might 482 well be the possibility to obtain massive numbers of samples from the field. This issue could 483 be overcome by pooling populations of different pests and weed species in shared NGS runs. partly funded by Bayer CropScience France (groundsel sampling), by ANSES 487 via the system for monitoring the adverse effects of plant protection products 488 ('phytopharmacovigilance', established by the French Act on the future of agriculture of 13 489 October 2014) (groundsel sequencing) and by BASF SAS France (ragweed sequencing). We 490 thank the Gentyane facility (Clermont-Ferrand, France [http://gentyane.clermont.inra.fr/]) and 491 the GeT core facility (Toulouse, France [http://get.genotoul.fr]) for providing access to their 492 sequencing equipment.

Figure 1 . 599 Figure 2 .Figure 3 .

 159923 Figure 1. Flow-chart of the NGS-based resistance diagnosis procedure.

  a first PCR as described above. For each population, all three amplicons were 180 pooled in an equimolar mix and tagged with a population-specific index using Nextera XT 181 Index kit (v2) (Illumina). Tagged amplicons were pooled in an equimolar mix, purified with an 182 Agencourt AMPure XP kit (Beckman Coulter, Beverly, MA, USA), quantified using the Qubit 183 HS kit (Invitrogen) and loaded onto one Illumina MiSeq V2 cartridge according to the 184 manufacturer instructions. The quality of the run was checked internally using PhiX. The 185 resulting 250 nucleotide pair-end sequences passing Illumina standard quality controls were 186 assigned to their population of origin on the basis of the population-specific indexes using 187 bcl2fastq v2.20.0.422 (Illumina).188For ragweed analyses, overhang adapter sequences were also included at the 5' end of 189 the three F primers (5'-CTTTCCCTACACGACGCTCTTCCGATC-) and of the three R 190 primers (5'-GGAGTTCAGACGTGTGCTCTTCCGATCT-). Tailed primers were used in a 191 first PCR as described above. For each population, all three amplicons were pooled in an 192 equimolar mix and tagged with a population-specific, home-made six-bp index in a second, 12the population-specific index sequence. Tagged amplicons were purified 197 and loaded onto one Illumina MiSeq V3 cartridge according to the manufacturer instructions.

  the run was checked internally using PhiX. The resulting 250 nucleotide pair-199 end sequences passing Illumina standard quality controls were assigned to their population were analysed using the "MutSeeker", a custom function written in the 204 R programming language and and implementing packages available in the Bioconductor project 205 (bioconductor.org). This function, together with the R script for operating it, detailed operating 206 instructions and one training data set for each of the two species studied here, are available from /data.inra.fr/dataset.xhtml?persistentId=doi:10.15454/BCZF3S 209 Briefly, Tthe 250-nucleotide paired reads were not joined. All rReads were aligned to 210 reference ALS sequences (GenBank/EMBL accession KR024410 and KR024411 for groundsel 211 ALS1 and ALS2 partial sequences, respectively, or KX870184 for ragweed full ALS sequence) 212 using the short read aligner Bowtie as implemented in the package qQuasR. 19 SNP calling was 213 performed using the pileup query in the Rsamtools package. 20 All codons targeted were covered 214 by either the forward or the reverse read in the 250-nucleotide read pairs matching the 215 corresponding amplicon, except codons Asp375, Asp376 and Arg377 that were covered by both 216 reads. For these three codons, SNPs calls obtained from forward and reverse reads were pooled. 217 In a final step, variant counts were calculated at every nucleotide position where mutations 218 would cause amino-acid changes in the 15 ALS codons implicated in herbicide resistance 219 (

  281 substitutions at ALS codon 197 were identified in varying frequencies in the groundsel 282 populations investigated. A Pro-197-Leu substitution at ALS1 detected in 35 populations was 283 by far the most frequent mutation in the populations analysed.

  to-G transversion at the third nucleotide in codon 375 causing an aspartate-to-285 glutamate amino-acid substitution was identified in both ALS1 and ALS2 in 89 of the 96 286 populations analysed, in frequencies systematically comprised between 0.9 and 1.5%. Sanger 287 sequencing in six populations where this substitution was detected by NGS did not allow to 288 confirm its existence. The putative Asp-375-Glu substitution was therefore considered a PCR 289 or NGS artifact, and discarded from the analyses. run generated 20,700,536 250-nucleotide quality reads that could be 293 assigned to one of the 96 populations investigated. The number of quality reads assigned to one 294 population ranged from 147,116 to 274,998, with an average value of 215,631. Each population 295 was analysed as one pool of 50 individual plants, each carrying two ALS gene copies. Thus, in one pool yielded 300 amplicons. The average expected sequencing depth was 297 therefore of 719× for each of the 300 amplicons per pool. 298 The lowest number of reads covering one codon in one population was 15,253 (codons 299 571 to 654, not shown). This allowed an expected sequencing depth of 152× for each of these 300 five codons in each individual plant in the corresponding pool, which was more than sufficient 301 for mutation detection. 302 With the 0.9% threshold for mutation detection, non-synonymous nucleotide 303 substitutions in codons crucial for herbicide sensitivity were identified as expected in the 304 control populations. The only exception was control population C, where a G-to-T transversion 305 at the second nucleotide in codon 574 causing a tryptophan-to-leucine amino-acid substitution 306

  the mutations detected by NGS-based analysis of populations from both 318 species as pools of 50 plants were checked by selecting pools with contrasted frequencies of 319 mutations and analysing each plant in each of these pool individually using a double-blind 320 procedure. In groundsel, the frequencies of the mutations detected at each ALS homeolog in 33 checked by genotyping each plant in each population individually using 322 ALS1-and ALS2-specific dCAPS assays targeting codon 197. dCAPS assays did not 323 discriminate among different mutations occurring at one same codon. 15 Thus, the frequencies 324 estimated by NGS of all mutations identified at codon 197 in each homeolog were cumulated 325 for comparison to the dCAPS results. Similarly, in ragweed, the frequencies of mutations 326 detected in 16 field populations by NGS analysis were checked by Sanger sequencing of the 327 full ALS sequence of each plant in each pool. The frequencies of mutations identified by 328 Illumina sequencing of plant pools and by individual plant analysis in field populations as well 329

  330 34 groundsel populations (33 field populations and one control population) and the for the 25 331 ragweed populations (16 field populations and nine control populations) considered, the 332 frequency of each mutation detected by NGS analysis of one bulk of 50 plants was very strongly 333 correlated to the frequency determined by individual plant analysis (Figure 23; Pearson's 334 correlation coefficients values of 0.996 [P-value < 10 -6 ] and 0.979 [P-value < 10 -6 ] for groundsel 335 and ragweed data, respectively). No false positives were identified, i.e., detection of mutation(s) 336 in one population by NGS analysis of the corresponding plant pool was always confirmed by 337 individual plant sequencing or genotyping. However, NGS-based analysis did not detect 338 mutations in two groundsel populations and one ragweed population where mutations were 339

  in two groundsel and one ragweed population (false negatives, Tables

  399 by using a proofreading Taq polymerase in the PCRs preceding NGS, which would allow 400 lowering the mutation detection threshold, and/or by slightly decreasing the number of plants 401 per pool (e.g., 40 plants per pool, which would yield a minimum expected mutation frequency 402 of 1.25% on a given gene or homeolog in the pool). Considering the tremendous sequencing 403 depth achieved in this study for every ALS amplicon sequenced, analysis of two pools of 40 404 plants per population investigated rather than a single pool of 50 plants could be performed for 405 96 populations in one single Illumina run with a codon coverage adequate for mutation 406 detection. This way, reducing the number of plants per pool could largely be compensated analysis of plant pools detected and quantified resistance-endowing mutations in 411 9,600 individual plants clustered into 192 pools. This approach did not allow to determine the 412 genotypes of the individual plants constituting the pool. This could be considered a drawback 413 in the case of recessive resistances, where differentiating between homozygous and 414 heterozygous mutants may be of some relevance. However, for resistance management in the 415 field, the vital information is rather the detection of mutation(s) involved in pesticide resistance 416 in one pest population. Such mutations are an unambiguous indicator that resistance is arising, 417 and that steps are to be taken to delay its onset. 418 Herein, we targeted 15 codons in one ALS gene in 96 batches of 50 plants (ragweed) 419 and in two ALS homeologs in 96 other batches of 50 plants (groundsel), which surpasses all 420

  control population (artificial population consisting of 50 mutant and non-mutant plants which ALS had been sequenced beforehand, chosen 583 so that the controls contained known frequencies of ALS mutations); F, population collected in the field.

584 3 c

 3 The mutations identified are indicated with their frequency between parentheses.

585 4 d

 4 Number of kilo-reads (i.e., thousands of reads) covering the codons in the interval mentioned (e.g., 121-205: ALS codons 121 to 205). Paired 586 reads were not joined.

Pro

  number following the mutation refers to the ALS homeolog (1, ALS1; 2, ALS2).

594 2 b

 2 Substitution caused by a double mutation.

Figure 1 . 599 Figure 12 .Figure 23 .

 15991223 Figure 1. Flow-chart of the NGS-based resistance diagnosis procedure.

Table 1 .

 1 Groundsel populations used for validation of Illumina-based detection of resistance using dCAPS genotyping.

	ALS1

d Populations with plants containing a double mutation causing a Pro-197-Asn substitution at ALS2. These populations were also subjected to 579 Sanger sequencing of individual plants. Page 27 of 67 http://mc.manuscriptcentral.com/pm-wiley Pest Management Science F o r P e e r R e v i e w 28

Table 2 .

 2 Ragweed populations used for validation of Illumina-based detection of resistance using Sanger sequencing.

	ALS

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Table 4 .

 4 Combinations of mutations detected in the 96 groundsel field populations analysed.

	Mutation(s) a

Table 3

 3

		). Thus, analysis yielded the frequencies of single-nucleotide substitutions in every pool
	220	of 50 plants analysed.

221

The threshold for the detection of mutations was set to 0.9% considering the minimum 222 expected frequency of mutations in a pool of 50 plants of 1% (i.e., one mutation on one ALS 234 the 50 plants in each of the populations used to check NGS results, except the control 235 populations that had been characterised beforehand. 236 In groundsel, mutations conferring resistance to ALS inhibitors were previously

based detection and quantification of the frequency of mutations in groundsel

	272	investigated. In total, eight substitutions occurring exclusively at the first two nucleotides in
	273	codon 197 in ALS1 (three substitutions) and/or ALS2 (five substitutions) were identified, with
	274	up to four different substitutions detected in one same population (Table 4). The frequencies of
	275	the substitutions assessed by the pipe-line ranged from 1.0% to 99.8% (ALS1) and from 0.9%
	276	to 99.7% (ALS2). In six populations, C-to-A transversions at the first and at the second
	277	nucleotide in ALS2 codon 197 were always detected in matching frequencies, suggesting the
	278	occurrence of one double-substitution at codon 197 in ALS2 that would cause a proline-to-
	254 279	ALS asparagine amino-acid substitution. This was confirmed by Sanger sequencing of the individual
	255 280	The groundsel MiSeq run generated 18,084,459 250-nucleotide quality reads that could be F
	256	assigned to one of the 96 populations investigated. The number of quality reads assigned to one o r
	257	population ranged from 35,366 to 498,841, with an average value of 188,380. Each population P
		e e r
	262 263 264	R e v yielded 600 amplicons. The average expected sequencing depth was therefore of 314× for each of the 600 amplicons per pool. The pipe-line assigned the reads to ALS1 or ALS2 on the basis of the homeolog-specific i e w
	265	nucleotide(s) present in all amplicons. The lowest number of reads covering one codon in one
	266	population was 735 (ALS1 codons 571 to 654 in population BZ-67, Table 1), which allowed
	267	an expected sequencing depth of 7.3× for each of these three codons in each individual plant in
	268	the pool. This was deemed sufficient for mutation detection.
	269	With the 0.9% threshold for mutation detection, non-synonymous nucleotide
		12

258

was analysed as one pool of 50 individual plants, each carrying two copies of two ALS 259 homeologs. Three categories of amplicons were generated per ALS homeolog (amplicons 1, 2 260 and 3, Table

1

). As each plant carried two copies of each of two ALS homeologs, one plant 261 yielded four amplicons in each category, i.e., 12 amplicons. Thus, the 50 plants in one pool 270 substitutions were identified at two codons crucial for herbicide sensitivity. Substitutions were 271 identified at codon 197 in the control population and in 45 of the 95 field populations

Table 1 .

 1 As it is described here, our NGS-based method only targets mutations at specific codons in the 447 ALS gene. However, the scope of the method can be extended. First, any ALS nucleotide 448 present in the amplicons sequenced can very easily be added to the list of positions to be Groundsel populations used for validation of Illumina-based detection of resistance using dCAPS genotyping.

	This merely

482

well be the possibility to obtain massive numbers of samples from the field. This issue could 483 be overcome by pooling populations of different pests and weed species in shared NGS runs. Page 59 of 67 http://mc.manuscriptcentral.com/pm-wiley http://mc.manuscriptcentral.com/pm-wiley 574 2 b C, control population (artificial population consisting of 50 mutant and non-mutant plants which ALS had been sequenced beforehand, chosen 575 so that the controls contained known frequencies of ALS mutations); F, population collected in the field.

576 3 c Number of kilo-reads (i.e., thousands of reads) covering the codons in the interval mentioned (e.g., 121-205: ALS codons 121 to 205). Paired Page 62 of 67 http://mc.manuscriptcentral.com/pm-wiley

Table 2 .

 2 Ragweed populations used for validation of Illumina-based detection of resistance using Sanger sequencing.

	ALS

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Table 3 .

 3 PCR primers. Arabidopsis thaliana ALS sequence (Genbank/EMBL accession X51514). Codons in bold have been implicated in herbicide 591 resistance in the field.17 Other codons have been implicated in herbicide resistance in artificial selection experiments.18

	Species Groundsel ALSEN8F Code ALSEN9R Groundsel ALSEN4F ALSEN8R Groundsel ALSEN7F ALSEN7R Ragweed ALAMB9F ALAMB10R TGTTTAGTAATGGAACGTGTTACCTC 720-695 Sequence (3'-5') Target a CTTTGGAACGTGAAGGTGTCACC 42-64 ATTATGTTTAGTAATCGAGCGCG 391-369 CTTCAAATGCTTGGAATGCATGG 761-783 TGCTCATCTAATTCCTTCCTCCAAG 1065-1041 TGAATAATCAGCATTTGGGTATGGTG 1413-1438 CCATCACCTTCAGTAATCACGTC 1722-1700 CTTTGGAACGTGAAGGCGTAACCG 375-398 Ragweed ALAMB10F TTGCATATGCTTGGGATGCATGG 1094-1116 ALAMB4R CAAAATCTCGTTAAGCCCCTGTAAC 1336-1312 Ragweed ALAMB11F TAACAATCAGCATTTGGGTATGGTGG 1747-1772 ALAMB2R CATTCAAAACCGACAAACTGCTTAC >2121-2104 a Nucleotides in GenBank/EMBL accession KR024410 or KR024411 (groundsel ALS1 or ALS2 partial sequences, respectively) or in accession Expected amplicon size ALS codons of interest encompassed b 350 bp (Amplicon 1) Gly121, Ala122, Met124, Val196, Pro197, Arg199, Ala205 306 bp (Amplicon 2) Asp375, Asp376, Arg377 310 bp (Amplicon 3) Val571, Trp574, Phe578, Ala653, Gly654 346 bp Amplicon 1) Gly121, Ala122, Met124, Val196, Pro197, Arg199, Ala205 243 bp (Amplicon 2) Asp375, Asp376, Arg377 383 bp (Amplicon 3) Val571, Trp574, Phe578, Ala653, Gly654 KX870184 (ragweed full ALS sequence). b Numbered after Page 65 of 67 588 589 590 Pest Management Science

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Table 4 .

 4 Combinations of mutations detected in the 96 groundsel field populations analysed.

	Mutation(s) 1a

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ACKNOWLEDGEMENTS

486

This study was partly funded by Bayer CropScience France (groundsel sampling), by ANSES

via the system for monitoring the adverse effects of plant protection products 488 ('phytopharmacovigilance', established