Ateba Yanick

Anne-Laure Betanda

François Helbert

Marie-Hélène Brisset

Thierry Mathon

Thierry Waeckerlé

Baudin

Yanick Ateba Betanda
email: yanick.ateba-betanda@u-psud.fr

Anne-Laure Helbert

François Brisset

Marie-Hélène Mathon

Thierry Baudin

Measurement of stored energy in Fe-48%Ni alloys strongly cold-rolled using three approaches: Neutron diffraction, Dillamore and KAM approaches

Keywords: EBSD, Neutron diffraction, Dillamore, KAM, Stored energy

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Introduction

The stored energy during the plastic deformation is an important feature for the optimization of texture, microstructure and then the mechanical properties of a given material. During the cold rolling, the energy is accumulated in the material. A large amount of this energy is dissipated as a heat and the rest is stored in the material as dislocations [START_REF] Hu | proceedings of the seventh RisØ International Symposium[END_REF][START_REF] Doherty | [END_REF]. In the literature, several techniques have been used to measure the stored energy as calorimetry, diffraction and microscopy techniques. These techniques estimate the stored energy as a function of crystallographic orientation except from the calorimetry which measures the stored energy of a set of orientations. By calorimetry technique, Knudsen et al. [3] found value of 126J/mol in the Nickel 98% coldrolled. Guiglionda et al. [4] studied the stored energy in the hot deformed Al-2.5%Mg by X-ray diffraction and shows that the S component has the highest stored energy compared to the Brass, Goss and Cube orientations. Furthermore, Branger et al. [5] showed that the stored of these components estimated by neutron diffraction in the Fe53%Ni 50% cold rolled vary as EC (28J/mol) > ES (18J/mol) = EB (18J/mol) > ECube (10J/mol) while Theyssier et al. [6] found that the stored energy of the texture components vary as ES (22.2J/mol) > EC (18.4J/mol) > EB (15.5J/mol) > ECube (10.4J/mol) in the pure aluminium bicristal using microscopy technique (Dillamore).

Values of stored energy depend on the measurement techniques which are based on different approaches. Thus, in the IF steel 40% cold-rolled, Samet-MEZIOU et al. [7] have measured the stored energy for different texture components using Dillamore and neutron diffraction methods. For the {111}<110> component, the authors reported values of 3J/mol and 5J/mol, respectively. In their investigations, Taheri et al. [8] calculated the stored energy in a commercial cold-rolled aluminum (AA1050) by Dillamore and calorimetry approaches, and found different values between the two methods.

In the present study, two cold rolled Fe-48%Ni alloys were used to measure the stored energy of the main deformation components, which are the Brass (B: {110}<112>), the Copper (C: {112}<111>) and the Aluminum (S: {123}<634>). Moreover, the stored energy of Cube ({100}<001>) component was also measured. The difference between both alloys is the sulfur content.. These two alloys have not the same texture and microstructure after recrystallization, thus, the effect of sulfur addition (0 and 40 ppm) on the driving force of recrystallization (stored energy) was studied.. The stored energy was calculated on one hand with the neutron diffraction method, which is based on the diffraction peak broadening measurement, and on the other hand by the KAM (Kernel Average Misorientation) and the Dillamore approaches both based on the use of EBSD data (misorientations, dislocation cell size). The results of the three measurement techniques were compared and discussed for the first time in the litterature.

Experimental procedure

The Fe-48%Ni studied samples were elaborated by Aperam alloys Imphy and exhibit the chemical compositions showed in table 1. After melting, casting (bar) and hot-rolling, samples underwent a cold rolling of 99% of thickness reduction. The obtained samples have the form of thin tapes of 50µm of thickness. The samples analyzed by EBSD were firstly mechanically polished and then electro-polished. For KAM and Dillamore approaches, the microstructure and texture parameters were analyzed by EBSD and OIM TM software (Orientation Imaging Microscopy) in the rolling surface (RD, TD) where RD is the rolling direction and TD is the transverse direction. The scans explored an area of 1500 x 800µm with 0.1µm step size. The scanning electron microscope FEG-SEM SUPRA 55 VP operating at 25 kV was used to collect results. For neutron diffraction measurements, the samples were stacked to form 1cm 3 cube volume (200 thin tapes). The neutron measurements were performed at the Laboratoire Léon Brillouin (Saclay/France) on the four circles diffractometer 6T1.

Determination of stored energy by neutron diffraction

The stored energy determination by neutron diffraction is a based on the diffraction peak broadening measurement. Many studies on the stored energy estimation have been done by using either X-ray diffraction [9][10][11] or neutron diffraction [5,[12][13]. The diffraction peak broadening of both X-ray and neutron diffractions is mainly due to the local modification of inter-reticular distance [14]. This modification may be related to the dislocations and the heterogeneous distribution of chemical elements in the material. In the present materials, 99% cold-rolled, the peak broadening is mainly due to the existence of dislocations. Thus, the broadening enables directly the measurement of the elastic deformation in the crystal lattice, which leads to the measurement of stored energy. Neutrons have a high capacity of penetration in a bulk material. This capacity allows the measurements to be non-sensitive to the effect of the surface and moreover, to be statistically representative of all of the material volume.

The orientation distribution function (ODF) was calculated from four complete pole figures {111}, {200}, {220} and {311} using the discrete ADC method [15]. In the present work, samples were cold-rolled and exhibit an orthotropic symmetry. For this purpose, stored energy measurements were performed on quarter of pole figures only. Many scans were achieved in each pole figure quarter to obtain stored energy for a large number of orientations and in particular to provide accurate values for the deformation texture orientations. The scans (   2  ) were measured for various values    , on each quarter of pole figure, using a 5x5(°) grid, completed by the positions where the diffracted intensity is significant.

The neutron diffraction pattern of sample cubic terbium garnet was measured and refined by Rietvield profile program [START_REF] Rodriguez-Carvajal | Abstracts of the Satellite Meeting on Powder Diffaction of the XV Congress of the IUC[END_REF] to determine exactly the resolution curve of the diffractometer. Then the u,v and w parameters, which depend on the diffractometer geometry, were calculated and related to the Full Width at Half Maximum of the peaks [START_REF] Caglioti | [END_REF]. The peak broadening was fitted using a Gaussian distribution to determine the integral width of the peak. The integral method has been developed to separate the domain size and the strain effects from the diffraction peak broadening [18]. Thus, the normalized integral width   s b m of the measured diffracted peak is described as sum of the two gauss functions depending on the size domain D and on the

strains 2  . 2 2 2 2 2 1 ) ( s D s b m     (1)
D is the average size of the diffracting domains and s , which is equal to

  / ) sin 2 (
, is the diffusion vector.

Assuming that for a given reduction R, the term of deformation 2

 remains constant for the same family of planes and that D is constant whatever is the plan, the average size of diffracting domain deducts easily from two successive orders of the same family of planes, as {111} and {222}.

For a crystallographic orientation "j" diffracted in the position (α, β), where, α and β are the azimuthal and radial angles of a point from the pole figure, respectively, the stored energy is given by the following equation [13] for each position in the pole figure.

          , ) 2 1 ( 2 3 ,

Determination of stored energy by Dillamore approach

Calculation of stored energy by Dillamore approach is based on the fact that the deformation energy of a grain is accumulated into the dislocation cell walls [19]. The principle of this technique consists in measuring the cells size d and the average misorientation angle  between them and then deduct the stored energy (Figure 1). The stored energy according to Dillamore is given by the following equation 3 [5]:

d KV E s   (3)
Where, K is a constant which depends on the cell shape (K = 3.31 for the equiaxed cells), V is the molar volume, s  is the boundary energy which is given by Read and Schockley relationship (equation 4) [START_REF] Read | Dislocation in crystals[END_REF].

                  m m m s       ln 1 (4)
m  is the maximal energy of a grain boundary, which corresponds to the maximal misorientation value m  .

Determination of stored energy by the KAM approach

The local variations in misorientation is a good indicator of strain in crystalline materials and thus of the stored energy. Kernel Average misorientation (KAM) is an OIM analysis tool that characterizes the local misorientation. For a given point, the average misorientation

KAM  of that
point with all of its neighbors in the kernel is calculated with the priso that misorientations exceeding some tolerance value (maximum misorientation) are excluded from the calculation. In this study, only the points at the perimeter of the kernel were used (Figure 2).The kernel size is defined according to the searched information. From misorientation, the dislocation density is estimated by the following equation [START_REF] Takayama | [END_REF][22][23].

Xb KAM    (5)
Where,  is a parameter which depends on the grain boundary type and is equal to two for tilt boundaries, four for the twist ones and three for the mixt of the two types b is the burgers vector (b=0.253nm for Fe50%Ni alloy [24]) and nd X  is the kernel size ( n the defined nearest neighbor and d is the scan step) (Figure 2). Then, the stored energy can be formulated as:

2 2 1 b E   (6)
Where,  is the shear modulus.

Results

The stored energy of two Fe-48%Ni samples cold-rolled to 99% of thickness reduction, containing different sulfur contents (S-0 and S-40), has been measured by the three approaches described above.

Stored energy calculated from neutron diffraction measurements

The measurement of the stored energy was performed on the B, C, S and Cube orientations. As it can be observed in figure 3, the stored energy of the S and C orientations increases with the sulfur addition. However, the one of the Cube orientation remains quasi-stable and exhibits the lowest value. This low energy of the Cube component favors its development despite of the other orientations, during recrystallization [9].

Stored energy calculated by the Dillamore approach

For each orientation (B, C, S and Cube of the deformed state), the average size of dislocation cells and the average misorientation between cells have been measured on EBSD scans by using OIM TM software. In order to get more statistic results, many misorientation profiles (about 20 profiles by orientation) between cells were done on the whole EBSD scans and average results are shown in table 2. From the data of  and d, the stored energy was calculated by the Dillamore method. It should be noted that cells were equiaxed (K = 3.31). The evolution of the stored energy of the different components (B, C, S) for the two sulfur contents is similar to the one obtained from neutron diffraction, the stored energy values obtained by the Dillamore approach being lower.

Stored energy calculated by the KAM method

In order to get a good precision of the stored energy values by the KAM method while the cell size is about [0.7-1µm], a scan step size of 0.1µm, a kernel size of 0.3µm (n=3) and a maximum misorientation of 15° have been chosen for the KAM calculation. Moreover, the boundaries were supposed to be of flexion type. Once again, the stored energy found by this method varies in the same way than the one measured by neutron diffraction depending on the orientation and on the sulfur content.

Discussion

In the literature, the calculation of the stored energy after plastic deformation is not unanimous. Experimental results were often dispersed, and even contradictories. The influence of the crystallographic orientation on the stored energy has been confirmed by different authors [26][27][28]. For copper single crystals deformed by tension, Steffen et al. [27] showed that the stored energy measured by calorimeter of the {111} orientations is higher than that one of the {110} orientations. While Nakada [28] showed that these two orientations have the same energy.

Moreover, even for the same studies, results are difficult to be interpreted, thus, for aluminum single crystals deformed by compression, Nakada [28] found that the {100} exhibits lower stored energy than that of the {111} orientations, but in the case of silver single crystal, the author found inverted results. In their study, Jakani et al. showed that the stored energy measured by neutron diffraction for the copper alloys (38% deformed) inside the {111} orientations (3.6J/mol) is higher than inside the {001} orientations (1.8J/mol) [29].

The aim of the present study is to compare the values of stored energy obtained by the three approaches. For the two investigated samples, a comparison of the calculated stored energy of each orientation is shown in figure 4. The evolution of the stored energy follows the same trend:

) ( ) ( ) ( ) ( Cube E B E C E S E   
for the three techniques. Furthermore, this trend is reproducible in both samples with or without sulfur. These results are in agreement with those of Etter et al. [12] who found that, for Fe53%Ni alloy cold-rolled to 77% and 95% of thickness reduction, In spite of the similar evolution of the stored energy with the crystallographic orientation, the values of this energy are very different from a technique to another. The global analysis of the results shows that the stored energy calculated from neutron diffraction is higher than the one measured by KAM, which itself is higher than the one calculated by the Dillamore approach

) ( ) ( ) ( ) ( Cube E B E C E S E    .
( Dillamore KAM Neutron E E E  
). A significant difference between the stored energy calculated by the Dillamore and the other methods is found. This energy gap between methods can be induced by the ability for the different methods to measure the different types of dislocations (SSD (Statistically Stored Dislocations) and GND (Geometrically Necessary Dislocations)) and also to measure the dislocations located in the cell interiors and in the cell walls. In plasticity, dislocations can be separated into two different categories, geometrically necessary dislocations (GND) which appear in strain gradient due to geometrical constraints of the crystal lattice, and statistically stored dislocations (SSD) which evolve from random trapping processes during plastic deformation [30] (Figure 5). Figure 5 shows that, misorientation is principally due to GND dislocations. In the case of the neutron diffraction, the dislocation walls and cells both contribute to the diffraction peak broadening [31,32] which is due to the distortion of the crystal lattice. The crystal lattice distortion is generated by all of the volume dislocations (SSD+GND), where the presence of GND polarizes the field distortion. As a conclusion, the measurement of stored energy by neutron diffraction takes into account dislocations in the entire microstructure (cells and walls) and all types of dislocation (GND and SSD).

Contrary to the neutron diffraction method, the Dillamore approach takes into account only the dislocations within cell walls [19] and only one type of dislocations (GND). Indeed, this last approach is based on the misorientation between dislocation cells which is the result of the presence of the GND. Then, this method under-estimates the stored energy. Both the interior of cells and the SSD are not taken into account in the calculations.

The measurement of stored energy by KAM method is also based on misorientation but between one point and its neighbors. As the Dillamore approach, the misorientation is due only to GND dislocations. The present calculation of the misorientation by KAM method takes into account dislocations within cells and walls since the KAM parameters have been chosen

according to the dislocation sub-structure. Indeed, the kernel size of 0.3µm is smaller than the cell size (d<1µm) and the KAM calculation excludes misorientations greater than 15° to avoid the contribution of grain boundaries.

Contrary to the Dillamore approach, values of stored energy calculated by KAM method are closed to those calculated by neutron diffraction. Nevertheless, a slight underestimation is observed.

The energy gap observed between the neutron and KAM methods which is about 1.2J/mol, is due to the fact that the KAM approach does not take into account the SSD in both the cell interiors and walls.

The energy gap between KAM and Dillamore approaches is about 7J/mol. This gap is due to the fact that the Dillamore approach misses the dislocations in the cell interiors. As regards to the comparison between neutron and Dillamore methods, the energy gap is about 8.5 J/mol.

The comparison of stored energy measurements by the different methods are summarized in the following equations:

These results show that the SSD dislocations contribute slightly (~ 8%) to the global stored energy value (Equation 10).

(

) 10
At the same time, the effect of sulfur addition on the stored energy was also investigated.

Results show that the stored energy increases by sulfur addition (Figures 3 and4). This could be explained by the effect of alloying elements which increase the strain hardening of the material and then the stored energy. Moreover, it was observed that the sulfur element combines with Manganese element in the S-40 sample to form MnS precipitates of size 100-200µm. These precipitates lead to a hardening of the material and then increase the stored energy. Thus, the presence of sulfur in the Fe-48%Ni alloy implies an increase of the stored energy [33] which is clearly evidenced by the three techniques investigated in the present work.

Conclusion

This investigation consisted in studying two main subjects: a comparison between the measurements of stored energy by different approaches and the effect of sulfur addition on the stored energy, of two highly cold-rolled Fe-48%Ni (99% of thickness reduction) alloys containing different sulfur contents.

First, it was demonstrated that Dillamore approach highly underestimates the stored energy while the one calculated by KAM method is slightly underestimated. Nevertheless, the one calculated by neutron diffraction approach, based on the diffraction peak broadening, exhibits the best estimation. Dillamore approach considers only the GND dislocations, blocked in the cell walls. The KAM method takes into account only the GND in all of the microstructure (cells and wall). However, the neutron diffraction method takes into consideration all of the dislocation types present in all of the microstructure features. As a conclusion, for the measurement of the stored energy in Fe-48%Ni alloys, the neutron diffraction remains the most complete technique. Furthermore, values of stored energy obtained by KAM approach are very close to the one obtained by neutron approach. This implies that the quantity of the SSD are not significant in the cold-rolled samples (equation 10). However, it is important to choose the correct parameters in the KAM calculation to consider dislocations in cells and in walls.

Second, whatever the different techniques, it was found that the addition of sulfur in the Fe-48%Ni alloys increased the stored energy. The sulfur combines with manganese to form precipitates (MnS). That implies a hardening of the material and then increases the stored energy.

2 

 2 modulus and Poisson coefficient of the material, respectively. is the micro-deformation which is obtained from the width of the broadening peak   s b m . This parameter   s b m is expressed by the equation (2).

Fig. 1 .

 1 Fig. 1. (a) Dislocation cells and walls inside of a deformed grain. (b) Microstructure of the deformed state.

Fig. 2 .

 2 Fig. 2. Principal of KAM technique. i  is the misorientation between the first point (the central point) and a

Fig. 3 .

 3 Fig. 3. Stored energy of S, C, B and Cube components in the deformed state of the two S-0 and S-40 samples, measured by neutron diffraction.

Fig. 4 .

 4 Fig. 4. Comparison of stored energy of S, C, B and Cube components in the deformed state of the two S-0 and S-40 samples, calculated by the three approaches.

Fig. 5 .

 5 Fig. 5. Schematic process of GND dislocations accumulation in the crystal. In figures (a) to (c) GND accumulation increase misorientation between two crystal and in (d) to (e), GND accumulation lead to the crystal lattice distortion [30].

Table 1 :

 1 Chemical composition of the studied samples (%Wt).

	Samples	Fe	Ni	Mn	S
	S-0	51.7	48	0.3	0
	S-40	51.696	48	0.3	0.004

Table 2 :

 2 Average misorientation, cell size and stored energy of the different orientations for the S-0 and S-40

				samples.
				S-0				S-40
	Orientation	S	C	B	Cube	S	C	B	Cube
	 (°)	3.60	4.70	2.80	2.78	3.85	3.67	2.57	2.74
	d (µm)	0.80	1.01	0.78	0.91	0.80	0.82	0.73	0.91
	Stored enegy (J/mol)	8.03	7.26	7.16	6.12	8.31	7.91	7.30	6.06

Table 3 :

 3 Stored energy of the different orientations for the S-0 and S-40 samples estimated by KAM.

			S-0				S-40
	Orientation	S	C	B	Cube	S	C	B	Cube
	Stored enegy (J/mol)	15.00 14.55 14.51 13.62 16.00 15.33 15.2 13.65

Acknowledgements

The authors would like to thank Aperam alloys Imphy, Pierre MATERA for providing materials. "Le ministère de l'enseignement supérieure (France)" is gratefully acknowledged for the founding of the Ph.D. project.


K Dia

V L Coli

L Blanc-Féraud

J Leblond

L Gomart

D Binder

Applications of Learning Methods to imaging issues in Archaeology, regarding ancient ceramic manufacturing

Keywords: Machine Learning algorithms, Convolution Neural Network, Support Vector Machine, Image classification and analysis, Hough transform, Archaeology, Neolithic Pottery

Archaeological studies involve more and more numerical data analyses. In this work, we are interested in the analysis and classification of ceramic sherds tomographic images in order to help archaeologists in learning about the fabrication processes of ancient pottery. More specifically, a particular manufacturing process (spiral patchwork) has recently been discovered in early Neolithic Mediterranean sites, along with a more traditional coiling technique. It has been shown that the ceramic pore distribution in available tomographic images of both archaeological and experimental samples can reveal which manufacturing technique was used. Indeed, with the spiral patchwork, the pores exhibit spiral-like behaviours, whereas with the traditional one, they are distributed along parallel lines, especially in the experimental samples. However, in archaeological samples, these distributions are very noisy, making analysis and discrimination hard to process. Here, we investigate how Learning Methods (Deep Learning and Support Vector Machine) can be used to answer these numerically difficult problems. In particular, we study how the results depend on the input data (either raw data at the output of the tomographic device, or after a preliminary pore segmentation step), and the quality of the information they could provide to archaeologists.

Introduction

Back in the seventh and sixth millennia BC, when farming was introduced to Europe, pottery was a central practice for storing and food processing. For the archaeologists, the techniques used to manufacture ancient pottery can act as a powerful marker of the social identity of their producers. A previously unrecognised pottery manufacturing technique was recently identified [START_REF] Gomart | Spiralled patchwork in pottery manufacture and the introduction of farming to Southern Europe[END_REF] at the Pendimoun rock shelter (early Neolithic layers dated to the early 6th millennium BCE) in southeastern France (Alpes-Maritimes) and named spiralled patchwork technology (SPT). The construction of pottery using SPT relies on juxtaposing and fusing circular patches, see Figure 1, right. This manufacturing technique is contemporary to the coiling technology (CoT), which is often observed in European early farming contexts [START_REF] Salanova | Methods of study of large ceramic complexes: series and sets of Neolithic pottery from Kovachevo (Bulgaria)[END_REF][START_REF] Gomart | Traditions techniques et production céramique au Néolithique ancien. Étude de huit sites rubanés du Nord-Est de la France et de Belgique[END_REF][START_REF] Gomart | Variabilité technique des vases du Rubané récent du Bassin parisien (RRBP) et du Villeneuve-Saint-Germain (VSG) : un cas d'étude dans la vallée de l'Aisne[END_REF] and is characterised by superimposition of coils, see Figure 1, left.

Micro-computed tomographic (µ-CT) 3-D images of pottery sherds formed using these techniques were acquired, revealing their internal structure. In particular, in 2-D cross-sections, the distribution of pores (i.e., voids trapped inside the clay forming the sherd structure during the building process) revealed curvilinear patterns for the SPT sherds and mainly parallel linear patterns for the CoT sherds, see Figure 2 (mostly visible in the first and second columns).

The goal of the present work is to analyse and classify pottery manufacturing sequences using the images acquired by µ-CT from available archaeological sherds and from experimental sherds that were recently manufactured in controlled conditions using both coiling and spiral patchwork techniques. These scans allow to access the complete internal structure of these sherds and, after a segmentation process, to isolate the regions corresponding to pores, showing their spatial distribution, see Figure 2, bottom line.

The purpose of this work is to provide a quantitative characterisation of Neolithic pottery forming techniques using 3-D datasets. To the authors knowledge, it represents a first attempt to achieve this goal.

The dataset considered in this study is composed of sixteen sherds:

• four CoT sherds (one archaeological and three experimental sherds);

• twelve SPT sherds (five archaeological and seven experimental sherds).

The first and second columns of Figure 2, which show 2-D cross-sections images of CoT and SPT experimental sherds, reveal that pore distribution varies according to the manufacturing technique used. The third and fourth columns of Figure 2, which represent archaeological CoT and SPT sherds, show that manufacturing technique is much more difficult to detect in archaeological samples as patterns are not visually distinguishable, most probably because of fragment alteration through time. The pore distribution of both archaeological and experimental sherds is accessible by analysing the segmented images (as in Figure 2, bottom line). Detecting pore alignments, which are visible in Figure 2 down-left image, allows to identify the CoT technique. This is obtained by using the Hough transform as in [START_REF] Coli | Microcomputed tomography for discriminating between different forming techniques in ancient pottery: New segmentation method and pore distribution recognition[END_REF], an automatic way to detect aligned patterns in images. We first select the lines that intersect the highest quantity of pore regions, and we analyse their parallelism by computing the scalar product between their directional vectors.

As expected, CoT-like images reveal parallel lines characterised by values of the scalar products close to 1, whereas other techniques as SPT show other / random distributions, see [START_REF] Dia | Machine learning for imaging issues in archaeology[END_REF]. To classify ceramic sherd images, we investigate in this work classical Machine Learning (ML) algorithms. The Support Vector Machine (SVM) method [START_REF] Widodo | Support vector machine in machine condition monitoring and fault diagnosis[END_REF] is applied to preliminary features given by the scalar products between the detected lines, while Deep Learning (DL) method is initially run on the segmented images (extracted pores). We use Convolutional Neural Network (CNN) [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF] with the pre-trained network GoogLeNet [START_REF] Szegedy | Going deeper with convolutions[END_REF] for transfer learning to classify segmented images. Finally, as CNN-based methods result in automatic feature extraction, the pore segmentation step appears not be necessary. The same CNN based classification procedure, with the learning phase, has been applied directly on the 2D slices of tomographic images and good classification results have been obtained. Below, we describe the data, the considered analytical protocol and classification methods, and show how they can answer archaeological questions. In Section 2 we precise some information on data acquisition and treatments. Section 3 is devoted to a brief overview of the exploited learning algorithms (ML/SVM and DL/CNN). In Section 4, classification results for the above dataset including both pottery forming techniques are given and analysed. Finally, a brief conclusion is provided in Section 5.

Data processing

We describe here the data acquisition process, the pre-processing step of the images, that consists in pore segmentation, and the way we proceed to feature extraction, using Hough transform.

Image acquisition

The experimental and archaeological pottery sherds were scanned using a SkyScan-1178 X-ray µ-CT system (Bruker) with two 1280x1024 X-ray cameras, beam energy of 60kV, a 0.5mm thick aluminium filter, 0.

Image processing

The spatial distribution of pores inside pottery depends on the manufacturing sequence used, as air tends to be trapped between building elements during the forming process. Thus, CoT sherds are characterised by pores showing linear patterns, while SPT sherds reveal more dispersed patterns, which in some cases suggest circular dispositions by visual interpretation. Therefore, the segmentation of pores inside tomographic images reveals useful information for the characterisation of the building technique.

The procedure we use to segment pore regions is as follows. First, the pixels with low intensity grey-scale values are selected as corresponding to air. Then, a volume binarisation is applied to separate air pixels from the rest of the materials characterising the pottery (i.e. clay and mineral inclusions). Finally, a connected components detection is performed in order to remove unwanted connected components corresponding to the air surrounding the sherd. This procedure is applied to 3-D stack of tomographic images and more details can be found in [START_REF] Coli | Microcomputed tomography for discriminating between different forming techniques in ancient pottery: New segmentation method and pore distribution recognition[END_REF]. The 2-D cross-section images which we chose to use in this work are successively extracted from the 3-D stack. In Figure 2, bottom line, we show examples of results of this segmentation process, where only the porosity contrast is kept visible in the images. In the rest of this work, we refer to these images as segmented images. After segmentation, the images show mostly aligned patterns for the pores in the CoT sherds, while the distribution appears to be more circular and random for the SPT ones (Figure 2, bottom line). Then, the distribution of pores is investigated by means of the Hough transform.

Feature extraction

The Hough transform is a classical technique which is often used to detect alignments or other patterns in images [START_REF] Ballard | Generalizing the Hough transform to detect arbitrary shapes[END_REF][START_REF] Beltrametti | Hough Transform of Special Classes of Curves[END_REF][START_REF] Mukhopadhyay | A survey of Hough Transform[END_REF]. In order to detect lines in 2-D images, the Hough transform relates points in the image to sinusoidal curves in an associated Hough space. The intersections between sinusoids account for the presence of points along lines in the original image. Keeping the points where most sinusoids intersect provides us with the main alignment directions of pores. In the analysis of the segmented images, only the five lines which have the greater amount of aligned pore pixels are retained in each image for both classes (e.g., see Figure 3). The parallelism between these five lines is tested by computing the scalar products between their directional vectors [START_REF] Dia | Machine learning for imaging issues in archaeology[END_REF][START_REF] Coli | Microcomputed tomography for discriminating between different forming techniques in ancient pottery: New segmentation method and pore distribution recognition[END_REF]. These scalar products constitute the main feature which will be provided to the SVM classifier.

A second feature is provided by the number of intersection points between the recovered lines in the image. Indeed, these lines are almost parallel for CoT sherds and may intersect outside the image region, while this is not the case for SPT sherds for which these lines admit quite a few intersection points close to the image centre (see Figure 3).

Classification with learning algorithms

In this section, we briefly introduce the two classical ML methods we used to classify the dataset. The Support Vector Machine (SVM) [START_REF] Widodo | Support vector machine in machine condition monitoring and fault diagnosis[END_REF] and Convolutional Neural Network (CNN) [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF][START_REF] De Rezende | Exposing computer generated images by using deep convolutional neural networks[END_REF], both are supervised learning methods, meaning that they require a labeled dataset to be trained. In this study, labels correspond to CoT and SPT techniques. The big difference between these two methods is that a feature extraction procedure is essential for the SVM in order to classify the data. These features may also provide important additional information in view of archaeological interpretations. In this archaeological sherd study, features are based on the alignments in the pores structure. While, CNN do not require this preliminary process, instead the algorithm detects and extracts necessary features throughout its hidden layers. In the following two sections we provide a short overview of these standard methods in the context of this sherd study.

Support Vector Machine

Support Vector Machine is a ML method used to perform classification tasks. It was initially introduced as a two-class classification technique, which can be extended to multiple-class classifier [START_REF] Widodo | Support vector machine in machine condition monitoring and fault diagnosis[END_REF][START_REF] Abe | Support Vector Machines for Pattern Classification[END_REF]. For data in a n-dimensional space with two classes, the objective of the SVM classifier is to find a hyperplane in the n-dimensional space that separates the two classes. Among all possible hyperplanes, the objective is to find the one that has the maximum margin, i.e. the maximum distance to data points of both classes (see Figure 4, left). Usually, real-life problems contain noisy data and may not be efficiently separated by such a hyperplane. Indeed, if it exists, this hyperplane may have a very small margin (minimal distance to the points, see Figure 4, left). To deal with this problem, an additional term weighted by a parameter C ∈ R + is introduced in the SVM, in order to specify how many errors can be accepted in the classification. The parameter C allows to tune the trade-off between having a wide margin and the number of admitted errors (that correspond to the slack variables in Figure 4, right).

Moreover, data may not be separable by a hyperplane (see an example Figure 5). In such general cases, they are projected onto a higher dimensional feature space, where linear classification is possible. This is done by the use of a kernel transformation such as linear, polynomial and Gaussian Radial Basis Function (RBF) [START_REF] Widodo | Support vector machine in machine condition monitoring and fault diagnosis[END_REF].

Based on the archaeological question of identifying the CoT or SPT manufacturing techniques on the basis of sherds, it seems natural to first detect alignment of pores in segmented images and then classify data from these lines. More precisely, the considered features for SVM classification are line intersections points and dot products between the Hough-detected lines, as described in Section 2.3. Due to non-linearity of the data, a RBF Kernel, depending on a parameter γ, is used to increase the accuracy rate. See Section 4 for technical details and values. We choose to use a transfer-learning procedure with a pre-modeled and pretrained network, specifically the GoogLeNet architecture [START_REF] Szegedy | Going deeper with convolutions[END_REF].

Convolutional Neural Network

The architecture and huge quantity of parameters of the first two parts of this CNN network which compute image characteristics (e.g. bias, coefficients of the convolution filters) remained unchanged. Only the parameters of the third fully connected layer part were estimated and tested using our dataset, which is one of the main advantages of using such a network. For this estimation, we used the DL Matlab toolbox1 .

All parameters of SVM and CNN are provided in Section 4. This section presents the classification results obtained on lines, segmented images (see Section 2.2), and 2-D cross-sections of raw tomographic images. The considered datasets are as follows:

Classification results

• 360 segmented binary images (130 from CoT sherds and 130 from SPT sherds), used for SVM and CNN classification.

• 460 grey-scale images (230 from CoT sherds and 230 from SPT sherds), used for CNN classification.

Note that the dataset of segmented images is smaller than the dataset of tomographic images, because the pore segmentation process can produce empty images (dark images, which correspond to a slice where no pores were detected).

As Figure 2 (first line) shows, the CoT experimental sherds usually have a squared shape, while the SPT ones are round-shaped. Since this shape is not relevant for manufacturing characterisation, it may induce bias in the classification. To avoid this phenomenon, only the central part of each grey-scale image is considered in the experiments (see Figure 7).

Whatever the classification methods and the input data, the learning step is performed on 80% of the dataset and the remaining 20% are used for testing.

Results Support Vector Machine

As mentioned in Section 3.1, a cost parameter C and the Kernel parameter γ must be tuned in order to prevent under-or over-fitting phenomena. A grid search is performed to determine the optimal values of these parameters. From these multiple tests, C was set to 100 and γ to 10. The dataset is randomly shuffled 1000 times and different learning and testing sets are picked for each run. The prediction accuracy results averaged over 1000 runs on 72 test images are shown in Table 1.

Results with Convolutional Neural Network

The second method we consider is the classification by CNN, first on segmented images, and then on raw images. As presented in Section 3.2, we use a transfer-learning procedure with GoogLeNet network which requires three-dimensional 224 × 224 × 3 images as inputs; the images are thus resized accordingly. As the images of our dataset are either binary or grey-scale, each image is replicated three times to obtain the desired form. The training and validation set is composed by 80% of the images of each dataset (more precisely, 64% of the dataset is used for training and 16% for validation), while the testing set is composed by the remaining 20% of the images.

The CNN classifier was tested multiple times with different input parameters, in order to determine their suitable values for our data. The following parameters are set for each run: number of epochs (number of complete passes through the training dataset) = 15, batch size (number of training samples that are fed to the classifier at once to reduce the computational time) = 40 images, validation frequency (number of iterations after which the validation set is fed to classifier to test its accuracy and update the weights of the fully connected layers) = 20 iterations, and learning rate (step size) = 0.0001. These parameter values are the same for both experiments described below, i.e. for segmented and grey-scale images.

Segmented images

The CNN classifier was first tested on segmented images, in order to take into account the fact that we are interested in pore alignments for CoT while random/spiral distribution are expected in SPT. The prediction accuracy results on 72 test images are shown in Table 1.

Grey-scale images

As the CNN classifier showed remarkable improvement in classification with respect to the SVM performances, the classifier is tested on the more challenging set of grey-scale images of Figure 7. The prediction accuracy results on 92 test images are shown in Table 1.

Discussion

We first want to point out that one of the challenges we faced during the training procedure was the small size of the dataset. Indeed, we had to work with a reduced number of available samples.

Considering the methods applied to segmented images, the CNN method appears more accurate than the SVM one. Indeed, the accuracy rates for SVM roughly hit less than 80%, while they are higher than 90% for CNN for most of the tested situations (see Table 1). Despite the differences between the classification methods, it could be that the features captured by CNN on segmented images are richer than those extracted from the lines obtained by the Hough transform on pores.

From these results, it appears that the Deep Learning method is more competent than the SVM Machine Learning method in classifying the testing set, where it provided significantly more accurate results. Moreover, CNN automatically performs the feature detection / extraction steps with transfer learning, whence only the classification network needs to be trained. For SVM however, each image had to be pre-processed in order to extract the retained features. Finally, SVM is 5 times more computationally costly (in time) than the CNN one.

Ultimately, the CNN procedure gives slightly better classification results from grey-scale images than from segmented images. Yet, some information might be lost during by the segmentation / pore extraction procedure.

Conclusion

Promising results were obtained with Machine Learning and Deep Learning algorithms for classification of ancient pottery samples, running on 2-D cross-sections extracted from a set of µ-CT images. This will be useful to classify archaeological sherds which are often damaged and difficult to distinguish from noisy images. As CNN methods give good results, different configurations of these techniques can be further investigated. To improve the classification, we also plan to acquire more samples and images, with other modalities and at different resolutions.

However, one of the most important drawbacks of CNNs is their lack of interpretation in terms of modelling. The advantage of the more traditional image analysis approaches (like the SVM one) is that it provides archaeologists with visual and quantitative elements for image interpretation (e.g. the quantity of parallel pore lines in CoT sherds) that are very useful for their analysis of the manufacturing process. Many additional features can also be considered, as for example the positions of lines intersection points.

With the same goal, the Hough transform can be adapted in order to catch circular or spiral-like behaviour of pores in SPT images, see [START_REF] Coli | Microcomputed tomography for discriminating between different forming techniques in ancient pottery: New segmentation method and pore distribution recognition[END_REF]. Finally, note that higher dimensional versions of the Hough transform are able to detect surfaces in 3-D images, see [START_REF] Beltrametti | Hough Transform of Special Classes of Curves[END_REF][START_REF] Ballard | Generalizing the Hough transform to detect arbitrary shapes[END_REF]. They could provide good results on sherd images.

The quantitative analysis proposed here to discriminate between CoT and SPT manufacturing techniques using pore distribution in µ-CT scans of sherds can be applied to other pottery building processes. These promising results address similar issues concerning other markers of the micro-structures inherited from the building process. More specifically, the spatial organisation of mineral inclusions also reflects the technical gestures implemented during pottery making. The present approach may provide useful complementary classification results on such inclusions, though their segmentation from µ-CT images is more difficult than those of the pores due to the variety of materials (hence of intensities in images). Next step will be to jointly process these different markers in order to refine the diagnostic and to furnish more robust and accurate information.

Figure 1 :

 1 Figure 1: Coiling Technology (superimposition of coils, left), Spiral Patchwork Technology (juxtaposed spiral patches, right).

Figure 2 :

 2 Figure 2: Pores segmentation results. The first line shows 2-D tomographic images and the second line the corresponding segmented images. From left to right: CoT and SPT experimental sherds, CoT and SPT archaeological sherds.

  7 • rotation. Each reconstructed image has a resolution of 81 µm. To reduce the data size, a box volume surrounding each sherd is cropped from the 3-D stack and used in the analysis. In this work we considered central 2-D cross sections of tomographic images of sherds (see Figure 2, first row, for an example of CoT and SPT experimental and archaeological sherds).

Figure 3 :

 3 Figure 3: Hough transform results. The red lines represent the detected alignments. From left to right: CoT and SPT experimental sherds, CoT and SPT archaeological sherds .

Figure 4 :

 4 Figure 4: Left: an example of how a dataset is separated in two different classes by a hyperplane. Right: a non-separable case, with an example of slack variables.

Classification

  Figure 6: CNN architecture.

Figure 7 :

 7 Figure 7: Grey-scale tomographic images, cropped central regions. Left: the 230 images composing the CoT dataset. Right: the 230 images composing the SPT dataset. The 10 black images displayed in the bottom-left corners of each set are not included in the datasets.

Table 1 :

 1 Prediction accuracy for each object category and all considered classification methods. The number of images in the testing dataset is indicated between parentheses. The results are averaged over 1000 runs for the SVM method.

	Object category SVM (segmented images + features) CNN (segmented images) CNN (grey-scale images)
	SPT	77.7% (36)	88.8% (36)	100% (46)
	CoT	79.5% (36)	100% (36)	93.4% (46)
	Overall accuracy	78.6% (72)	94.4% (72)	96.7% (92)

https://it.mathworks.com/help/deeplearning/ref/trainnetwork.html

Acknowledgements

This work was supported by the French National Research Agency, with the reference number ANR-15-IDEX-0001, IDEX UCA JEDI "Multiscale Tomography: Imaging and Modelling Ancient Materials, Technical Traditions and Transfers -TOMAT" project and through the 3IA Cte dAzur Investments, with the reference number ANR-19-P3IA-0002.

We thank the reviewers for their comments and suggestions.


Sébastien Thomine
email: sebastien.thomine@i2bc.paris-saclay.fr

Sylvain Merlot
email: sylvain.merlot@i2bc.paris-saclay.fr

Manganese matters: Feeding manganese into the secretory system for cell wall synthesis

Main text

Manganese (Mn) is an essential element for plants, playing major roles as a co-factor of enzymes involved in photosynthesis and oxygen species detoxification [START_REF] Schmidt | The Biochemical Properties of Manganese in Plants[END_REF]. Mn acts in various plant cell compartments and need to be transported in chloroplast and mitochondria [START_REF] He | Transport, functions, and interaction of calcium and manganese in plant organellar compartments[END_REF]. The Mn/Ca efflux transporters of the UPF0016/GTD family [START_REF] Demaegd | Molecular Evolution of a Novel Family of Putative Calcium Transporters (C Beh[END_REF], PAM71 and CMT1 have been shown to allow Mn transport at the thylakoid and inner membranes of the chloroplast, respectively (Fig. 1) [START_REF] Schmidt | Chloroplast Transition Metal Regulation for Efficient Photosynthesis[END_REF].

In this issue of New Phytologist, Yang et al. (pp. 000-000) investigated the function of another member of the UPF0016/GTD transporter family, PML3, in Arabidopsis thaliana. Using a functional GPF tagged protein, they showed that PML3 localizes in the cis-Golgi compartment as previously proposed by [START_REF] Hoecker | Homologous Proteins of the Manganese Transporter PAM71 Are Localized in the Golgi Apparatus and Endoplasmic Reticulum[END_REF](Fig. 1). In agreement with the role of UPF0016/GTD in Mn transport, the growth of pml3 mutant is impaired under Mn limitation.

The authors further determined that the pml3 phenotype is mainly caused by a defect in protein glycosylation and cell wall biosynthesis. Although it was known that Mn acts as a co-factor for glycosyl transferases, this publication provides the first genetic evidence that Mn loading in the Golgi is essential to sustain this process and that PML3 plays a dominant role in Mn loading into this cell compartment when Mn availability is limited. These results support a highly conserved role of PML3 and its homologues in distant organisms in Mn influx into the Golgi for protein glycosylation [START_REF] Potelle | Glycosylation abnormalities in Gdt1p/TMEM165 deficient cells result from a defect in Golgi manganese homeostasis[END_REF].

Before this study, it was assumed that the main effect of Mn deficiency on growth was the consequence of decreased PSII efficiency. However, photosynthesis does not appear to be affected in the pml3 mutant. Furthermore, even with ample Mn supply, the plm3 mutant is still strongly affected in reproductive functions, probably as a direct consequence of a defect in pectin deposition during the fast elongation of the pollen tube [START_REF] Zhang | A Golgi-Localized Manganese Transporter Functions in Pollen Tube Tip Growth to Control Male Fertility in Arabidopsis[END_REF]. This result provides a cellular basis for the essential role of Mn in fertility.

The study of PML3 demonstrates the importance of Mn influx into the secretory system. It establishes a link between Mn entry in the Golgi, the presence of Mn dependent glycosyl transferase in this compartment and the formation of the cell wall. Both protein glycosylation and glycosylation of cell wall polymers such as homogalacturonans, rhamnogalacturonans, xylogalacturonans and xyloglucans involve Mn-dependent glycosyl transferases [START_REF] He | Transport, functions, and interaction of calcium and manganese in plant organellar compartments[END_REF]. The data presented show that arabinose, xylose and mannose contents are specifically decreased in the pml3 mutant cell walls under Mn deficiency. This supports the notion that Mn plays an important role in the synthesis of secreted cell wall polymers. Yang et al. also demonstrates a strong decrease in the levels of glycosylation with xylose and fucose. Especially the amount of RSW2, a protein involved in cell wall organization which is the target of Mndependent MNS1/2 glycosyl transferase, is decreased in the pml3 mutant under Mn limiting conditions. Together, these defects indirectly affect cellulose deposition and ultimately cell wall expansion accounting for the growth defect of pml3 under Mn deficiency, while photosynthesis apparently remains unaffected.

Previously, other Mn transporters have been implicated in Mn loading into the secretory system.

The Ca/Mn pump ECA3 resides in the Golgi and endosomes (Fig. 1) [START_REF] Mills | ECA3, a Golgi-Localized P 2A -Type ATPase, Plays a Crucial Role in Manganese Nutrition in Arabidopsis[END_REF][START_REF] Li | A Distinct Endosomal Ca 2+ /Mn 2+ Pump Affects Root Growth through the Secretory Process[END_REF]. Like pml3, the eca3 mutant displays growth defects under Mn deficiency. The CDF transporter MTP11 localizes in the Golgi and in the PCV/late endosome [START_REF] Peiter | A secretory pathway-localized cation diffusion facilitator confers plant manganese tolerance[END_REF][START_REF] Delhaize | A role for the AtMTP11 gene of Arabidopsis in manganese transport and tolerance[END_REF]. However, in contrast to plm3 and eca3, the A. thaliana mtp11 mutant is more tolerant to Mn deficiency. All 3 genes PML3, ECA3 and MTP11 are involved in the tolerance to Mn excess. This raises the question of the respective functions of these transporters.

Each transporter may act in different tissues or developmental stages. Furthermore, these transporters could act at different steps of the secretory pathway. Our knowledge of this complex and dynamic system has considerably evolved in the last decade with the identification of functional sub-compartments within the trans-Golgi network (TGN). In this view, it would be useful to refine the localization of ECA3 and MTP11 and compare it to that of PML3. It would also be interesting to test whether ECA3 or MTP11 loss of function affects protein glycosylation and cell wall formation as observed in pml3. Since these transporters play roles in both Mn deficiency and excess, it would be important to further test if their localization is affected by fluctuation of Mn supply, as recently shown for the Mn uptake transporter NRAMP1 [START_REF] Castaings | Manganese triggers phosphorylation-mediated endocytosis of the Arabidopsis metal transporter NRAMP1[END_REF].

Once in the secretory system, Mn will end up either in the apoplast or in the vacuole following membrane fusion (Fig. 1). It thus appears necessary to recover Mn from the secretory system for other functions (eg photosynthesis) at least under Mn deficiency. In contrast to the loading step, only one transporter involved in Mn retrieval has been identified so far. The NRAMP2 transporter was shown to reside in the TGN [START_REF] Alejandro | Intracellular Distribution of Manganese by the Trans -Golgi Network Transporter NRAMP2 Is Critical for Photosynthesis and Cellular Redox Homeostasis[END_REF][START_REF] Gao | NRAMP2, a trans-Golgi network-localized manganese transporter, is required for Arabidopsis root growth under manganese deficiency[END_REF]. The nramp2 mutant is more sensitive to Mn deficiency for root growth and photosynthesis.

Accordingly, the mutation of NRAMP2 also affects Mn supply to chloroplasts. Interestingly, NRAMP1, that functions in Mn uptake at the plasma membrane, was also localized in the TGN under sufficient Mn supply and could thus be also involved in Mn release from this compartment [START_REF] Agorio | Phosphatidylinositol 3-phosphate-binding protein AtPH1 controls the localization of the metal transporter NRAMP1 in Arabidopsis[END_REF][START_REF] Castaings | Manganese triggers phosphorylation-mediated endocytosis of the Arabidopsis metal transporter NRAMP1[END_REF]. The pml3 mutation partially rescues the root growth phenotype and the chlorophyll content of the nramp2 mutant under Mn deficiency. This underlines the functional link between Mn loading in the Golgi and its downstream retrieval from the TGN due to the dynamic nature of the secretory pathway (Figure 1).

The import of Mn in the secretory pathway and the higher tolerance of the pml3 mutant to Mn excess raise the question of the role of the secretory pathway in the sequestration of Mn. The mtp11 mutant accumulates more Mn in roots. The MTP11 transporter was proposed to mediate Mn secretion leading to increased tolerance. However, this role is expected to be deleterious under Mn deficiency. Downstream of the TGN, the flux of vesicles might also be targeted to the vacuole. This pathway would contribute to the storage of Mn in the vacuole together with Mn transporters that reside on the vacuolar membrane such as MTP8 and CAX2 [START_REF] He | Transport, functions, and interaction of calcium and manganese in plant organellar compartments[END_REF]. Collectively, these transporters are required for tolerance to Mn excess. Conversely, under Mn deficiency, Mn needs to be remobilized from the vacuole to provide Mn to photosystem II in chloroplasts [START_REF] Lanquar | Export of Vacuolar Manganese by AtNRAMP3 and AtNRAMP4 Is Required for Optimal Photosynthesis and Growth under Manganese Deficiency[END_REF].

The study by Yang et al. provides an important piece in the jigsaw puzzle of Mn homeostasis in plant cells. It highlights the need to load Mn in the Golgi as a cofactor for glycosyl transferases that are essential for cell wall formation. This model is inferred from genetic and biochemical evidence. However, it would need to be substantiated by direct detection of Mn in organelles using Mn specific fluorescent sensors or high resolution XRF microscopy [START_REF] Das | Manganese Mapping Using a Fluorescent Mn 2+ Sensor and Nanosynchrotron X-ray Fluorescence Reveals the Role of the Golgi Apparatus as a Manganese Storage Site[END_REF]. These approaches may allow to visualize a Mn concentration gradient through the secretory pathway and how it is spatially modulated by the activities of PML3, MTP11, ECA3 and NRAMP2. Different members of UPF0016/GTD family are thus involved in targeting Mn in two different organelles hosting enzymes that require this element as cofactor. Differential regulation and differences in affinity for Mn of PAM71 and CMT1 or PML3 could provide means to prioritize Mn use for photosynthesis or cell wall synthesis according to plant needs.

Finally, further research is needed to delineate the pathways for the supply of Mn for other important functions, as the superoxide dismutase in mitochondria and peroxisomes.

Figure 1 :

 1 Figure 1: Transporters involved in the intracellular distribution of Mn in plant cells. The transporters involved in influx and efflux from the secretory pathway (PML3, MTP11, ECA3, NRAMP2), into the plastids and thylakoids (CMT1, PAM71) and in the vacuole (MTP8, CAX2, NRAMP3 and NRAMP4) are shown. Straight arrows through the transporters indicate the direction of the transport. Curved arrows indicate the flow of vesicles through the secretory pathway. Created in BioRender.c