M Gonzalez
email: michel.gonzalez@coria.fr

Analyzing the effect of dilatation on the velocity gradient tensor using a model problem

Keywords: Variable mass density, Velocity gradient tensor, Pressure Hessian, Strain properties, Flame fronts

The effect of variable mass density on the velocity gradient tensor is addressed by means of a model problem. An equation system for both the velocity gradient and the pressure Hessian tensor is solved assuming a realistic expansion rate. The model results show the evolution of the velocity gradient tensor as the density front is approached and are relevant to the physics of flame fronts.

Introduction

The influence of local mass density variations upon the properties of the velocity gradient tensor is especially significant in compressible flows or in reacting flows with heat release. Intensity and orientation of both strain and vorticity may be altered, which eventually plays on the growth rate and alignment of scalar gradients. Through the velocity gradient, mass density gradients may thus influence the mixing process, a phenomenon addressed in compressible turbulence [START_REF] Danish | Influence of flow topology and dilatation on scalar mixing in compressible turbulence[END_REF][START_REF] Boukharfane | Evolution of scalar and velocity dynamics in planar shock-turbulence interaction[END_REF] and in turbulent flames [START_REF] Swaminathan | Interaction of turbulence and scalar fields in premixed flames[END_REF][START_REF] Dopazo | The physics of scalar gradients in turbulent premixed combustion and its relevance to modeling[END_REF][START_REF] Zhao | Dynamics and kinematics of the reactive scalar gradient in weakly turbulent premixed flames[END_REF].

Such indirect effects often stem from an intricate interaction. For instance, there is now some evidence that, to a large extent, the small-scale physics of turbulent flames is governed by the interplay of the respective gradients of velocity, concentration, and mass density. Explaining the resulting phenomena may thus requires, as a first step, analyzing each underlying mechanism separately. The present work is based on this kind of approach.

The basic model problem is the evolution of the velocity gradient tensor undergoing a given expansion rate. This is a one-way coupling in which heat release, for instance, is forced in a restricted flow region, and subsequently affects the velocity gradient properties. The equation system for the velocity gradient tensor, including the enhanced homogenized Euler equation (EHEE) model of Suman and Girimaji [START_REF] Suman | Dynamical model for velocity-gradient evolution in compressible turbulence[END_REF] for the pressure Hessian tensor, is solved in a two-dimensional Euler flow (Sect. 2). The evolution of strain structure is analyzed for large and low values of the density ratio (Sect. 3).

Model problem

In an Euler flow, the evolution of the velocity gradient tensor, A = ∇u, is described by the following equation:

DA ij Dt = -A iα A αj -Π ij , (1)
where the Π ij 's are the components of the pressure Hessian tensor, Π = ∇[(∇p)/ρ], with p and ρ being respectively the pressure and the mass density.

In the two-dimensional case, Eq. ( 1) can be expressed by a four-equation system:

Dσ n Dt = -δσ n + Π 22 -Π 11 , (2)
Dσ s Dt = -δσ s -Π 12 -Π 21 , (3)
Dω Dt = -δω + Π 12 -Π 21 , (4)
DP Dt = - 1 2 (σ 2 -ω 2 + P 2 ) -Π 11 -Π 22 , (5)
where δ(t) is the expansion -or dilatation -rate, δ(t) = -1/ρ Dρ/Dt, σ n = A 11 -A 22 and σ s = A 12 + A 21 are, respectively, the normal and shear components of strain, σ = (σ 2 n +σ 2 s ) 1/2 is the strain intensity, ω = A 21 -A 12 is the vorticity, and P = A 11 + A 22 is the velocity divergence which -as a result of mass conservation -coincides with the dilatation rate: P ≡ δ.

The model problem is based on assuming the expansion rate as:

δ(c) = 4δ m c(1 -c), (6)
with

c(t) = (ρ o /ρ(t) -1)/(ρ o /ρ ∞ -1) where ρ o ≡ ρ(0), and ρ ∞ ≡ lim t→∞ ρ(t);
the density ratio is defined by ρ o /ρ ∞ . The parabolic function modelling δ(c) is inspired from numerical simulation data for the velocity divergence across a flame front [START_REF] Dopazo | Strain rates normal to approaching iso-scalar surfaces in a turbulent premixed flame[END_REF]. From the definitions of c(t) and δ(t):

Dc Dt = c + 1 q δ, (7)
with q = ρ o /ρ ∞ -1. In this study, we state δ m = q, with q > 0, which means ρ ∞ < ρ o -and δ > 0 -as a result, for instance, of heat release. Note that from the approach of Tien and Matalon [START_REF] Tien | On the burning velovity of stretched flames[END_REF] δ ≃ q/τ f in the reaction zone of a flame front, where τ f is the flame timescale. Stating δ m = q thus comes to normalize δ m by 1/τ f . This choice is convenient, for it makes δ(c) depend on a single parameter.

Figure 1 shows c(t) and δ(t) for q = 5 and q = 1. Fig. 1 Evolution of c and δ; (1) c(t) for q = 5; (2) for q = 1; (3) δ(t) for q = 5; (4) for q = 1

The evolution of the velocity tensor is computed from Eqs. ( 2)-( 4), with the EHEE modelled equation for Π 12 , Π 21 , and Π 22 [START_REF] Suman | Dynamical model for velocity-gradient evolution in compressible turbulence[END_REF]:

DΠ ij Dt = -A αj Π iα -A αi Π αj -(n -1)A αα Π ij , (8)
-in which n is the ratio of specific heats -, while component Π 11 is computed from Eq. ( 5) with P derived from Eqs. ( 6) and [START_REF] Dopazo | Strain rates normal to approaching iso-scalar surfaces in a turbulent premixed flame[END_REF].

A study spanning a range of initial conditions is not within the scope of this work. As a first step, the physical relevance of the model is checked with a single set of initial conditions, namely: c(0) = 10 -4 , σ n (0) = -δ m , σ s (0) = 0.1|σ n (0)|, ω(0) = σ(0), together with isotropy of tensor Π, namely Π 12 (0) = Π 21 (0) = 0, and Π 11 (0) and Π 22 (0) derived from Eq. ( 5) at t = 0, with Π 11 (0) = Π 22 (0).

In Fig. 2, A 11 , A 22 and δ/A 22 are plotted against c, for q = 5. Interestingly, the behaviour shown in Fig. 2 is akin to the structure of normal strain (a N ≡ A 11 ) and tangential strain (a T ≡ A 22 ) across a flame front [START_REF] Chakraborty | The scalar gradient alignment statistics of flame kernels and its modelling implications for turbulent premixed combustion[END_REF][START_REF] Dopazo | Strain rates normal to approaching iso-scalar surfaces in a turbulent premixed flame[END_REF].

Effect of dilatation on strain structure

The evolution of strain tensor properties, namely strain eigenvalues, λ 1 = (-σ + δ)/2 and λ 2 = (σ + δ)/2 [START_REF] Gonzalez | Effect of variable mass density on the kinematics of the scalar gradient[END_REF] as well as orientation of the strain eigenvectors, e 1 and e 2 , is examined for both q = 5 (large density ratio) and q = 1 (low density ratio ) with the same latter initial conditions.

Large density ratio

Because it determines the sign of the lowest strain eigenvalue, the ratio of dilatation rate to strain intensity, δ/σ, is a significant parameter of the dynamics of a scalar gradient in a non-solenoidal flow [START_REF] Gonzalez | Effect of variable mass density on the kinematics of the scalar gradient[END_REF]. As shown in Fig. 3, dilatation makes the smallest eigenvalue, λ 1 , positive -which thus means two extensional strain directions -over most of the c-range, where δ/σ > 1. It is only at the edges (c < 0.12, and c > 0.92), where δ/σ < 1, that λ 1 < 0, which thus leads to one compressional and one extensional strain directions.

c δ/σ 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 λ 1 < 0 λ 2 > 0 λ 1 < 0 λ 2 > 0 λ 1 > 0, λ 2 > 0 0.12 0.92
Fig. 3 Ratio δ/σ and sign of strain eigenvalues vs. c; q = 5

The orientation of strain eigenvectors is shown by Φ = arctan(σ n /σ s )/2 -π/4, the angle between axis x 1 and the direction of the largest strain, e 2 (Fig. 4). For small c, Φ < -π/4, which means that direction x 1 mostly undergoes the influence of the smallest strain. As c increases, counterclockwise rotation of strain axes brings the direction of the largest strain near x 1 , and this orientation is hold all over the intermediate c-range. As c reaches the upper range, rotation of strain axes is reversed, and the direction of the lowest strain comes back close to x 1 . These changes in strain axes orientation, in particular, alignement of the largest strain with the direction of anisotropy, are consistent with the evolution of strain approaching a flame front [START_REF] Zhao | Dynamics and kinematics of the reactive scalar gradient in weakly turbulent premixed flames[END_REF][START_REF] Steinberg | Statistics and dynamics of turbulenceflame alignment in premixed combustion[END_REF]. In this two-dimensional Euler flow, rotation of strain principal axes is promoted by anisotropy of the pressure Hessian tensor [START_REF] Lapeyre | Does the tracer gradient align with strain eigenvectors in 2D turbulence?[END_REF]. The rotation rate of strain eigenvectors is indeed given by Ω = 2DΦ/Dt = σ -2 (σ s Dσ n /Dt -σ n Dσ s /Dt), and then, from Eqs. ( 2) and [START_REF] Swaminathan | Interaction of turbulence and scalar fields in premixed flames[END_REF], 5 clearly shows the anisotropy of Π revealed by Π 11 prevailing over the other components, and the resulting rotation rate, Ω.

Ω = σ -2 [σ s (Π 22 -Π 11 ) + σ n (Π 12 + Π 21 )]. Fig- ure

Low density ratio

Similar features of strain evolution are retrieved for q = 1 with, however, a lesser influence of expansion rate. The lowest strain eigenvalue again gets positive for intermediate c values as expansion rate exceeds strain intensity, but this time over a somewhat shorter range (Fig. 6). The influence of density ratio is more obvious in strain axes orientation (Fig. 7). The direction of the largest strain comes much less close to x 1 over the intermediate c-range, and the latter is more narrow as well. This directly results from a weaker rotation rate, Ω, for q = 1 (not shown). Indeed the lower q, the smaller the respective magnitudes of strain components, σ n and σ s , and of anisotropic terms, Π 22 -Π 11 and Π 12 + Π 21 ; and the level of σ -2 -greater for q = 1 than for q = 5 -is not enough to balance this difference.

Conclusion

The mechanisms underlying the influence of dilatation on the velocity gradient tensor can be reliably addressed with a model problem. Assuming a likely evolution of the expansion rate, the solution of an equation system for the components of the velocity gradient and of the pressure Hessian includes a number of features regarding the evolution of the dynamic field as a density front is approached.

The ratio of dilatation rate to strain intensity, a critical parameter in the variable-mass-density kinematics of scalar gradient, is derived. More specifically, the evolution of normal and tangential strains is reminiscent of strain structure at the crossing of a flame front. Finally, the pressure Hessian anisotropy resulting from forcing the expansion rate promotes the rotation of strain principal axes, which subsequently aligns the largest strain with the direction of anisotropy, a result relevant to questions at issue in the physics of flames. Extension of the approach to the three-dimensional case as well as to the coupling of the velocity gradient dynamics with the physics of a reacting scalar gradient is a work in progress. Fig. 7 Angle Φ between x 1 and the direction of largest strain, e 2 , vs. c; q = 1; a solid arrow indicates compressional strain, while a dashed arrow indicates extensional strain; direction of the largest strain is shown by a bold dashed arrow

Fig. 2

 2 Fig. 2 Diagonal components of A, (1) A 11 , (2) A 22 ; (3) ratio δ/A 22 , vs. c, for q = 5

2 Fig. 4

 24 Fig.4Angle Φ between x 1 and the direction of largest strain, e 2 , vs. c; q = 5; a solid arrow indicates compressional strain, while a dashed arrow indicates extensional strain; direction of the largest strain is shown by a bold dashed arrow

Fig. 5

 5 Fig. 5 Rotation rate of strain principal axes, Ω, and components of pressure Hessian tensor, Π ij , vs. c; q = 5; (1) Ω; (2) Π 11 ; (3) Π 12 and Π 21 ; (4) Π 22

Fig. 6 1 c

 61 Fig. 6 Ratio δ/σ and sign of strain eigenvalues vs. c; q = 1

Acknowledgement

This is a post-peer-review, pre-copyedit version of an article published in Springer Nature Applied Sciences. The final authenticated version is available online at: http://dx.doi.org/10.1007/s42452-020-03513-4

Conflict of interest statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.


Louis Tsakou

Célia Vicari

Laura Helou

Vivek Keshri

Sabyasachi Das

Yves Bigot

Pierre Pontarotti
email: pierre.pontarotti@univ-amu.fr

Chapter 14 DDE Transposon as Public Goods

DDE Transposons have been recruited at least four times as site-specific recombination activating gene allowing programmed DNA elimination in eukaryotes. The described cases are RAG in jawed vertebrates, Kat 1 and Alpha 3 in the Kluyveromyces lactis yeast and Piggymac/TPB1 TPB2 and TPB6 in ciliates. The domesticated RAG is the most known case. It constitutes the enzymatic core of the Jawed vertebrates V(D)J recombination machinery. It directs random assembly and joining of gene segments during the development of B and T cells helping in the generation of the enormous gene diversity encoding antibodies or T cell receptors. It was shown in the case of RAG that the shift from DDE transposon to site-specific recombination activating gene is an evolutionary phenomenon that did not require dramatic changes. This explains why the co-option of DDE transposon as site-specific recombination activating gene can occur in a convergent manner. As numerous genes coding for DDE transposases are widespread through numerous members of the life tree, it is expected that several of them might correspond to domesticated transposons involved in programmed DNA elimination and maybe in the generation of receptor diversity. The domestication of DDE transposon could have been and still be of an extreme importance for organisms' evolution.

Preamble

Eukaryotes and prokaryotes do not have the same DNA content in their genome over AQ1 stages of their cell differentiation. Indeed genomes are modified during development or cell differentiation. This phenomenon is called developmentally regulated genome rearrangement (DRGR) [START_REF] Zufall | Evolution of developmentally regulated genome rearrangements in eukaryotes[END_REF]. DRGRs start by a DNA breaks either due to a specific endonuclease activity or specific chromatin structure that is related to a mechanisù inducing a DNA recombination event.

Developmentally Regulated Genome Rearrangement via a Specific Endonuclease

All the reported cases so far correspond to the domestication of selfish DNA that displayed at the minimum an endonuclease activity derived from a DDE transposase, a homing endonuclease, or a prophage recombinase.

The homothallic switching endonuclease (HO) is a domesticated homing endonuclease (Fig. 14.1). The HO endonucleases are mobile genetic elements that correspond to DNA fragments encoding these proteins over all their length, from their first 5' to the last 3' nucleotide. These DNA fragments use the homing endonuclease they encode to mediate their mobility [START_REF] Keeling | The selfish pursuit of sex[END_REF][START_REF] Koufopanou | Degeneration and domestication of a selfish gene in yeast: molecular evolution versus site-directed mutagenesis[END_REF]. Homing endonucleases specifically recognize and cleave a specific oligonucleotide motif that is generally located within a very conserved motif of some house-keeping protein-coding sequence. After DNA cleavage, a DNA fragment coding an HO endonucleases specifically inserts in frame with the parasitized gene in the middle of its own recognition sequences (Fig. 14.1). In a diploid cell that AQ2 is heterozygous for a homing endonuclease, the gene lacking the parasitic element becomes cleaved at the recognition site, and the broken chromosome is invaded by the parasitic DNA fragment by homologous recombination using the homing endonuclease-containing gene as a template. The mating type in budding yeasts is derived from the domestication of one of these parasitic DNA fragments. The mating types in budding yeasts are encoded by the mating-type (MAT) loci MAT a and MAT α.

Some yeasts have the ability to change their mating type (mating-type switching) without going through mating or meiosis." In Saccharomyces cerevisiae, switching is initiated when the homothallic switching (HO) endonuclease induces a DNA doublestrand break (DSB) in the MAT locus. Next, the replacement is completed through a gene conversion, in which transcriptionally silent copies of MAT genes, known as "hidden MAT left, HMLα" and "hidden MAT right, HMRa," are copied into the expressed MAT locus.

Prophage excision involved in the specific rearrangement. (Feiner et al. 2015, Fig. 14.2) During the differentiation process in procaryote, prophages and derived prophages are excised from the genomic region using a prophage recombinase in order to . a Temperate phages enter a cycle in which their phage genome is first going to be integrated into the bacterial chromosome to become a prophage that is going to persist in what is considered a phage latent or dormant state in which bacterial cells will be viable and will not produce of phage particles. Prophages are replicated together with the bacterial host chromosome during host-cell replication and switch into lytic production upon exposure to stress. Chronologically, the entry in the lytic phase starts with the excision of the phage genome, its gene transcription then the production of phagie capsid and tail proteins that are thereafter assembled in phage particles. The last step is the lysis of the bacteria that releases phages and kills the bacteria. b Regulation of mother cell-specific genes during sporulation in Bacillus subtilis. A phage regulatory switch (phageRS), named skin, is inserted within the sigK gene. SigK encodes a protein, σK, that regulates the expression of late-stage sporulation genes in the mother cell. skin excises itself at the initiation of the sporulation process, leaving an intact sigK gene able to encode a functional σK protein. Post excision, σK expression activates the mother cell's late-stage sporulation genes. Following excision, the excised skin element is eventually lost in the mother cell, which dies late during sporulation. By contrast, the forespore, which did not undergo element excision, gives rise to an endospore that still encodes the skin element within its sigK gene. This figure was constructed from derived information and graphic elements from Heterocysts in cyanobacteria are specialized cells with a role in nitrogen fixation.

They provide nitrogen to vegetative cells. Differentiation in a heterocyst is due the excision of fragments that interrupt three different loci: nitD, fdxN, and hupL that encodes a dinitrogenase alpha subunit, a ferredoxin and an uptake hydrogenase large subunit, respectively. The excised fragments have prophage origins and include at least the recombinase gene [START_REF] Hilton | Surveying DNA elements within functional genes of heterocyst-forming cyanobacteria[END_REF].

Finally, to promote phagosomal escape, Listeria monocytogenes need to excise a temperate prophage integrated into the comK locus during bacterial phagocytosis in order to activate the comk expression [START_REF] Feiner | A new perspective on lysogeny: prophages as active regulatory switches of bacteria[END_REF] 14.3 Programmed Break Specified by Chromatin Signals

Mating-Type Switching in the Fission Yeast S. pombe

As in the case of S. cerevisiae, the yeast Schizosaccharomyces pombe is able of mating-type switching. This mechanism occurred in an independent manner, the two species that belong to two highly divergent clades of yeast. The S. pombe genome contains one active (mat1) and two silenced (mat2 and mat3) mating-type loci that share similarities with the S. cerevisiae MAT proteins. However, the mechanism of switching is different from that involved in S. cerevisiae. Instead of cleavage mediated by an HO endonuclease (Fig. 14.2), a fragile chromosomal site consisting of an epigenetic mark at the mat1 locus in switching-competent cells leads to a dsDNA break during replication [START_REF] Klar | A unique DNA recombination mechanism of the mating/celltype switching of fission yeasts: a review[END_REF].

Immunoglobulin Switching

Immunoglobulin isotype class switching is a mechanism that changes a B cell's production of immunoglobulin from one type to another. It involves an intrachromosomal deletional rearrangement that focuses on the region of 1-10 kb of repetitive switch (S) located upstream of each heavy chain isotype gene. Class switch recombination is induced by a break done by cytidine deaminase AID (AID-APOBEC family) on accessible chromatin which is expressed during the B cell development [START_REF] Yu | Current insights into the mechanism of mammalian immunoglobulin class switch recombination[END_REF].

The variable lymphocyte receptors (VLRs) system (Fig. 14.3). In agnathes (cyclostomes), the VLR system involved in adaptive immunity includes a germline VLR that do not code for functional protein but instead encodes the only portion of the amino and carboxyl termini of the mature VLRs. The sequences encoding those portions are separated by non-coding intervening regions. In lymphocytes, the germline VLRs are assembled by somatic DNA rearrangement into a mature VLR that encodes the functional receptor via the insertion of LRR cassette that flank the germline VLR. The germline VLR is broken by the AID-APOBEC enzyme at the intervening sequences between the C-terminal and N-terminal portions of the VLR genes where the chromatine is accessible. Then gene conversion starts thanks to sequence identity between the intervening sequence and sequences surrounding the LRR cassettes [START_REF] Boehm | Evolution of alternative adaptive immune systems in vertebrates[END_REF].

Immunoglobulin Diversity Driven by Gene Conversion in Birds and Some Mammals

In birds and some mammals, only one pair of functional V and J segments is found for both the Ig light and heavy chain loci. Therefore, the diversity generated by V(D)J recombination is limited. However, several pseudo-V coding segments are found upstream the functional V segment in genes coding light and heavy chains. Several DDE transposons have been domesticated by their hosts retaining their DNA binding capacity (see for review [START_REF] Sinzelle | Molecular domestication of transposable elements: from detrimental parasites to useful host genes[END_REF][START_REF] Jangam | Transposable element domestication as an adaptation to evolutionary conflicts[END_REF])) and in some cases, the transposase and their related TIR as site-specific recombination activating gene. The few well-studied examples will be presented in the next sections.

Shift from a DDE Transposon to a Mechanism of Programmed DNA Elimination

DDE transposons have been recruited as site-specific recombination activating gene at least four times as programmed DNA elimination system, mediating biological differentiation processes: RAG (RAG1-RAG2) in jawed vertebrates, Kat 1 and Alpha 3 in K. lactis yeast and PiggyBac (TPB1 TPB2 and TPB6) in the ciliate Tetrahymena.

The first described and best known example is the V(D)J RAG.

The Recombination Activating Gene (RAG) Paradigm

Jawed vertebrates has a specific adaptive immune system based on lymphocytes In conclusion, biochemical functions of the DDE transposon and the sequencespecific recombination activating system are very similar, hence the biochemical shift from a transposon to a sequence-specific recombination activating system corresponds an easy evolutionary step requiring a very limited number of events to pass form a "wild" state to a domesticated one (Fig. 14.3). This is also supported by the fact that many other DDE transposons have been co-opted as recombination activating site-specific endonuclease as described in the next paragraphs. Piggymac/TPB2/TPB1/TPB6 domesticated transposon evolved in the two lineages:

tetrahymena and paramecium Piggymac and TPB2/TPB1/TPB6. In the case of tetrahymena, a duplication gave rise to TPB2 in one part and TPB1/TPB6 ancestor in the other. TPB2 lost the possibility to recognize its TIR but gained the possibility to interact with the scan RNA. TPB1/TPB6 represent maybe the ancestral state and TPB2 could represent another state in the domestication process.

Kat 1 and MAT alpha3 [START_REF] Barsoum | α3, a transposable element that promotes host sexual reproduction[END_REF][START_REF] Rajaei | Domesticated transposase Kat1 and its fossil imprints induce sexual differentiation in yeast[END_REF] As we said above, some yeasts have the ability to change their mating type.

In In conclusion, DDE transposons evolved as site-specific recombination activating genes many times during evolution and therefore this is a case of isoconvergent evolution of site-specific recombination activating genes.

Simple Evolutionary Shift Can Explain Convergent Evolution

Isoconvergent evolution, the independent evolution of similar features from the same ancestral state in different evolutionary lineages [START_REF] Pontarotti | Road map to study convergent evolution: A proposition for evolutionary systems biology approaches. Evolutionary biology: convergent evolution, evolution of complex traits, concepts and methods[END_REF], could be explained in part by natural selection where the new feature gave an advantage to the individual. Isoconvergent evolution could be due to the limited number of evolutionary pathways resulting from developmental and functional constraints on the evolutionary process (Losos 2011)-Functional constraints imposing a finite number of accurate adaptations, a finite number of mechanisms can be used to answer functional problems. Finally, isoconvergent evolution can be explained in part by the ease of transition from ancestral state to a derived state. This last aspect is not really discussed in the literature. [START_REF] Losos | Convergence, adaptation, and constraint[END_REF] pointed out that the wings powering flight in vertebrates have been built in different ways in birds, pterosaurs and bats. In all these cases, the wings represent modified forelimbs. The combination of wings and forelimbs, in theory, would be not very useful in real life. He concluded that this was due to lack of constraints; however, we underline here that besides the constraints, it was easier to modify forelimbs to get wings than to start from nothing. The same reasoning could be applied for the DDE transposon co-option as sequence-specific recombination activating systems and the biochemical shift from a transposase to a sequence-specific recombination activating endonuclease is an easy evolutionary step.

Transposases Form the Largest Family in the Diverse

Genomes of Life

Transposase-encoding genes are greatly over-represented in sequenced genomes and metagenomes relative to other coding sequences [START_REF] Aziz | Transposases are the most abundant, most ubiquitous genes in nature[END_REF]. Some of the transposase coding genes could correspond to domesticated transposons, active transposons and maybe to fossilized ones. From this and the chapter developed above, we hypothesize that many DDE transposons have been recruited as recombination activating site-specific endonuclease systems. Many domesticated candidates have already been described in the literature, some of them lost the endonuclease domain butand conserved the DNA binding domain and they could be involved in novel chromatin-modifying complexes [START_REF] Feschotte | Transposable elements and the evolution of regulatory networks[END_REF]) while others are involved in centromere binding, chromosome segregation, meiotic recombination [START_REF] Sinzelle | Molecular domestication of transposable elements: from detrimental parasites to useful host genes[END_REF]). Some articles also described large-scale systematic analysis to search for domesticated transposons including DDE transposons [START_REF] Hoen | Discovery of novel genes derived from transposable elements using integrative genomic analysis[END_REF][START_REF] Bouallègue | Molecular evolution of piggyBac superfamily: from selfishness to domestication[END_REF]). In the human genome 26 putative DDE transposases has been described [START_REF] Arnaoty | Novel approach for the development of mew antibodies directed against transposase-derived proteins encoded by human neogenes[END_REF], among these putative domesticated transposases as far as we know other than the RAGs, only the function of one of them, PBGD5 was really investigated, and its nuclease activity has been shown, however we do not know whether it recognizes specific sequences and if it is really involved in recombination [START_REF] Henssen | Genomic DNA transposition induced by human PGBD5[END_REF][START_REF] Henssen | Forward genetic screen of human transposase genomic rearrangements[END_REF][START_REF] Henssen | Forward genetic screen of human transposase genomic rearrangements[END_REF]. Another candidate has been tested for its transposase activity [START_REF] Majumdar | The human THAP9 gene encodes an active P-element DNA transposase[END_REF] where the authors show that THAP9

gene encodes an active DDE DNA transposase.

We need to test further the hypothesis that many transposons have been recruited

as recombination activating site-specific endonuclease. If our hypothesis is true, many domesticated DDE transposons acting as specific DNA endonucleases should be found throughout the life diversity.

Search for Domesticated Transposons Involved in Programmed Recombination. Test of the Hypothesis

This paragraph is a small guideline. The strategy to search for domesticated transposons involved in programmed recombination can be performed by two complementary approaches: Look for the candidate domesticated transposase and look for a somatically rearranged genomic region.

Look for the Candidate Transposase Co-opted as Site-Specific Endonuclease Involved in Genomic Recombination

Different strategies have been developed in particular by [START_REF] Hoen | Discovery of novel genes derived from transposable elements using integrative genomic analysis[END_REF] and [START_REF] Bouallègue | Molecular evolution of piggyBac superfamily: from selfishness to domestication[END_REF]. The strategy described here was adapted from these publications. We first have to look for the sequence that codes for complete transposase;

these can be done by profile search using an alignment with a known transposase [START_REF] Eddy | Accelerated profile HMM searches[END_REF].

The ORF found needs to be checked for a bona fide catalytic site and the conservation of the DDE motif. Then in order to be sure that the transposase is likely to be active it is necessary to show that the protein evolved under constraint. This can be done by calculating the ratio of non-synonymous to synonymous substitutions (dN/dS) which is a useful measure of the strength and mode of natural selection acting on protein-coding genes [START_REF] Jeffares | A beginners guide to estimating the nonsynonymous to synonymous rate ratio of all protein-coding genes in a genome[END_REF].

The next step is to differentiate between transposase belonging to an active transposon from site-specific recombination activating gene (domesticated transposase).

The following criteria must be present in the case of site-specific endonuclease. The domesticated transposase must be in single copy without pseudogene like sequences that could correspond to recent transposition events. The next criteria is based on the fact that the domesticated transposase should be unable to transpose thus the domesticated transposase should remain in the same genomic region in different speciesconserved synteny- [START_REF] Rascol | CASSIOPE: an expert system for conserved regions searches[END_REF]). The higher the number of divergent species display conserved synteny, the higher is the probability that the transposase has been domesticated. For example, PGBD5 is present in all chordate genomes and belongs to a conserved synteny [START_REF] Pavelitz | PGBD5: a neural-specific introncontaining piggyBac transposase domesticated over 500 million years ago and conserved from cephalochordates to humans[END_REF] indicating that it is likely to have been domesticated. transposase, as this is the case for the RAG transposon and the domesticated RAG (see [START_REF] Kapitonov | RAG1 core and V(D)J recombination signal sequences were derived from Transib transposons[END_REF][START_REF] Huang | Discovery of an active RAG transposon illuminates the origins of V(D)J recombination[END_REF][START_REF] Poole | The RAG transposon is active through the deuterostome evolution and domesticated in jawed vertebrates[END_REF]. The TIR like sequences can then be searched in the genome(s) coming from the cells where the "domesticated" transposase is transcribed. It should be noted that the endonuclease could recognize RNA intermediates as this is the case for TPB2 inciliates where the TIR recognition has been lost and instead a chromatin structure is recognized.

Look for Somatically Rearranged Genomic Regions

The next step is to look for rearranged genomic regions, and this can be done in several ways. The first way would be to sequence the genome from the cell or the tissue where the domesticated transposase is expressed (sequence 1) compare this genome with a reference genome (sequence 2) from the same species (same individual) in order to look for the rearranged sequence in sequence 1. Another way is to use high throughput genome translocation sequencing methodology based on the ability of a double-strand break to translocate to a fixed 'bait' double-strand break generated by a nuclease [START_REF] Hu | Detecting DNA doublestranded breaks in mammalian genomes by linear amplification-mediated high-throughput genome-wide translocation sequencing[END_REF].

In both cases, the genomic region, where the rearrangement occurred, should be flanked by terminal repeats; these terminal repeats corresponding to the RSS should be compared to the TIR of the active transposon (the most similar one).

Candidate regions using the second methodology have been described by [START_REF] Wei | Long neural genes harbor recurrent DNA break clusters in neural stem/progenitor cells[END_REF]. They described 27 recurrent double-strand breaks that occurred during neural stem/progenitor cell differentiation and they named it as recurrent doublestrand break cluster. The authors hypothesized that the break region will be joined to the distal break region thus potentially leading to new genetic information via for example a novel exon combination that can be generated by recombination between intronic regions at the DNA level via "exon shuffling." [START_REF] Alt | DNA double-strand breaks as drivers of neural genomic change, function, and disease[END_REF] In the case where the double-strand break followed by a recombination occurs via the action of domesticated DDE transposon a possible candidate could be PGBD5.

Indeed PGBD5 seems to be expressed in the brain and fetal brain and therefore possibly in the neural stem/progenitor cells [START_REF] Pavelitz | PGBD5: a neural-specific introncontaining piggyBac transposase domesticated over 500 million years ago and conserved from cephalochordates to humans[END_REF] and PGBD5 is able to induce double double-strand breaks in non-physiologic condition [START_REF] Henssen | Genomic DNA transposition induced by human PGBD5[END_REF][START_REF] Henssen | Forward genetic screen of human transposase genomic rearrangements[END_REF].

Are There Other Domesticated Transposases that Are

Able to Generate Diversity?

One important question concerns the possibility that some domesticated transposase and their TIRs could create diversity through the rearrangement of distinct tandem repeat paralogous gene segments (such as in V(D)J recombination). These processes correspond to an excision between at least 2 sets of paralogous fragments with a combinational joining. In these cases, the paralogous fragments should be flanked by the TIR like sequences located 3 from each of the first paralogous fragments family and 5 to each of the second fragment paralogue family. Such genomic rearrangement can be searched. The corresponding transposon can be searched as described above.

Conclusion

We discussed in this chapter the possibility that DDE transposons have been recruited

several times as systems involved in programmed DNA elimination and perhaps in the generation of receptor diversity. This is due to the fact that the functional shift is an easy one and that the huge number of transposase domains are present and across the tree of life. Therefore, DDE transposons along with other so-called selfish element encoding nucleases (homing nuclease and prophage) could have been major players in the evolution of biodiversity. The co-option of DDE transposons as the regulatory element is also very important. This has been largely discussed, Justin Goodrich this Issue) [START_REF] Sinzelle | Molecular domestication of transposable elements: from detrimental parasites to useful host genes[END_REF][START_REF] Jangam | Transposable element domestication as an adaptation to evolutionary conflicts[END_REF]. Another important role of DDE transposons is the one in the horizontal gene transfer (HGT). Horizontal transfer of DDE transposons (HTT) has been widely reported in eukaryotes [START_REF] Baidouri | Horizontal transfers and the new model of TE-driven genome evolution in Eukaryotes[END_REF]. However, in most cases, the literature discusses HGT and HTT in a non-integrated manner. However, the role of DDE transposons as the carrier of additional antibiotic resistance genes is well known in bacteria [START_REF] Babakhani | Transposons: the agents of antibiotic resistance in bacteria[END_REF], and at least the role of DDE transposon as carrier one case in yeast is also known. [START_REF] Mcdonald | Transposon-mediated horizontal transfer of the host-specific virulence protein ToxA between three fungal wheat pathogens[END_REF]. It is likely that most of the HGT are driven by transposons, but as most of the studied cases HGT corresponds to ancient events the transposase and the corresponding TIR has been lost so an effort in the analysis of recent HGTs should be done. Therefore, DDE transposons could have been major players in organismal evolution because it helps in genetic exchange between species.

The DDE transposon evolutionary trajectory should be included in the public goods hypothesis for the evolution of life on Earth [START_REF] Mcinerney | The public goods hypothesis for the evolution of life on Earth[END_REF]. According to this hypothesis, nucleotide sequences are simply seen as goods, passed from one organism to another through both vertical and horizontal transfer. The interesting things about DDE transposons are that they evolved in vertical and horizontal manner and they should be seen as goods since they increase the possibility of transfer and can be co-opted for example as recombination activating site-specific endonucleases involved in programmed DNA elimination.

  Fig. 14.1 Organization, expression, splicing, and mobility from one allele occupied by an intein to an unoccupied allele. The main steps of the intein mobility and homing are numbered. Step 1 is the RNA transcription. Black lines indicate DNA strands of the occupied and unoccupied alleles by an intein-coding DNA fragment, and cyan blue and light green bars indicate the coding-frame of the DNA region transcribed for each allele kind. Blue and red lines indicated regions coding for the intein (blue) and the homing endonuclease (HEN) moieties (red) in the DNA and the corresponding RNA transcripts. Step 2 is translation into protein. "pacmans" HEN moieties are shown in red and blue ellipses are N-and C-terminal intein moieties. Step 3 is site-specific recognition of an unoccupied allele by HEN. Blank spaces indicated the insertion site specifically cleaved by the HEN in both alleles. Step 4 is specific cleavage by the HEN. Finally, steps 5 and 6 depicted the invasion of a DNA fragment encoding intein from an occupied allele toward an unoccupied one by DNA strand invasion at DNA replication. This figure was constructed from derived information and graphic elements from Piègu et al. (2015)

  frame. In addition to sigK, many other examples of sporulation-specific gene rearrangement occur, suggesting that this phenomenon is widespread and common in spore-forming bacteria (the intervening sequence can correspond to only a recombinase of prophage origin. The recombinase has two functions: it catalyzes the DNA cleavage at the recombination site and join the DNA molecule ends of the restored protein-coding genes(Abe et al. 2017b) (Fig. 14.2)

  Fig. 14.3 Variable lymphocyte receptors (VLRs) system. Schematic diagram of a germline VLR gene and the postulated gene conversion-like (copy choice) mechanism for VLR assembly. The germline VLR gene is incomplete and contains invariant regions encoding for 5'-end of the Nterminal LRR (5 LRRNT) and 3 -end of the C-terminal LRR (3 LRRCT) and stalk. Hundreds of different LRR cassettes are located upstream and downstream of a pre-assembled germline VLR gene.The non-coding intervening sequence between 5 LRRNT and 3 LRRCT is replaced by the donor LRR cassettes that are sequentially copied either from 5 to 3 or 3 to 5 direction. At the beginning of the gene assembly process, a cytosine deaminase (CDA) converts cytosine (C) to uracil (U) in the germline VLR gene. The uracil is then removed by uracil-DNA glycosylase (UNG), leaving an apurinic (AP) site. The AP site activates nicking activity of AP endonuclease (APE) which leads to a DNA double-strand break. To repair this break, homologous recombination starts based on the sequence homology of 10-30 bp between the donor and acceptor LRR cassettes. This process is repeated along with deletion of the intervening sequence until the completion of a mature VLR gene. The diversity region of a mature VLR is composed of a 3'LRRNT, LRR1, multiple LRRVs, connecting peptide (CP), and a 5'LRRCT

  Fig. 14.4 RAG implication in the V(D)J recombination mechanism in jawed vertebrates. The chordates consensus tree shows the position of jawed vertebrates among chordates. The V(D)J mechanism was adapted from Janeway et al., 2001

  Fig. 14.5 Taxonomic distribution of the RAG and RAG-like sequences known in Deuterostomes. This is a deuterostomes consensus tree with the clades presenting RAG in the V(D)J recombination in the adaptive immune system, the clades presenting RAG-like sequences and the clades presenting no RAG-like sequences until today. described in Morales Poole et al. (2017)

  Saccharomyces cerevisiae, switching is initiated by homothallic switching (HO) endonuclease. In the related yeast Kluyveromyces lactis HO has been replaced by two domesticated DDE transposons: MATalpha 3 involved in the switch d MAT α to MATa.Kat1 involved in the switch de MATa to MATα. MAT α3 which was domesticated from transposable elements belonging to the Mutator Like Element Family MULEs. Regulated excision of this element results in a double stranded DNA break, (DSB) that stimulates recombination from the genome and initiates mating-type switching from MAT α to MATa. It has to be noted that in the case of this domesticated transposon the TIR-like sequences have been replaced by other sequences which are different on the left and right sides. The left side is a low complexity sequence with a long stretch of T and A. The right side contains a conserved motif that is conserved in sibling species-species of the Kluyveromyces genus. The other domesticated transposon named Kat1 evolved from hAT (hobo/Activator/Tam3) transposases and is involved in the switching from MAT a to MAT α. Kat1 cleaves the MAT a locus at two different positions, resulting in DSBs that stimulate recombination. Kat1 recognizes a TIR like sequence. In both cases, the intervening DNA is joined into a circle.

  The following step is to search the domesticated sequence recognition signal: find RSS/TIR like sequence. One way to search for the sequence recognition signal is to perform Chip-Seq experiment (Park 2009), and the other, that could be complementary to the Chip-Seq experiment is to be guided by sequence data. This could be done by looking for the active transposon which is the most similar to the domesticated transposon and to determine the TIR sequence of the transposon. The TIR sequence should be similar to the site-specific DNA sequence recognized by the domesticated 491382_1_En_14_Chapter TYPESET DISK LE CP Disp.:13/8/2020 Pages: 22 Layout: T1-Standard

DDE Transposon as Public Goods

Acknowledgements This work was supported by the French Government under the «Investissements d'avenir» (Investments for the Future) program managed by the Agence Nationale de la Recherche (ANR, fr: National Agency for Research), (reference: Méditerranée Infection 10-IAHU-03).

U N C O R R E C T E D P R O O F

14 DDE Transposon as Public Goods


François Rouzé L'alzit

Tiphaine Bazin

Angéline Poulon-Quintin

Eric Champion

Caroline Bertrand

Thierry Cardinal

Aline Rougier

Issam Mjejri

Véronique Jubera

Manuel Gaudon
email: manuel.gaudon@icmcb.cnrs.fr

THERMOCHROMOLUMINESCENT Mn 2+ -DOPED OXIDES AS THERMAL SENSOR FOR SELECTIVE LASER SINTERING

Mn 2+ -doped Zn 3 (PO 4 ) 2 and Mn 2+ -doped ZnAl 2 . 2 O 4+ compounds were prepared from solid state route and Pechini process, respectively. The luminescent properties evolution of both asprepared powder compounds versus the annealing temperature (for 10 min annealing treatments) was studied, in the range 500-1400°C. In parallel, Doctor Blade was used to prepare few micron-thick films for laser irradiation with the 1m wavelength laser of our SLS process (Selective Laser Sintering process). The ultra-rapid heating produces by laser irradiation induces on the films very different optical properties evolution in comparison to what was observed for the powder samples annealed into furnaces for the Mn-doped zinc phosphate. On the opposite, for the spinel compound, whatever the heating process (laser on film or furnace for powder samples), the modification of the luminescence properties is directly linked in a same way to the maximum temperature gained during the thermal history. The idea is to use thermal sensor to extract the temperature map of a film while it is subjected to laser irradiation as during SLS process. The study shows that thermal sensors must rely on mechanisms which remain effective even for ultra-rapid heating: a cationic redistribution versus temperature as occurring into spinel matrix is one solution proposed. But changes in the chromaticity resulting from phase transition between different allotropic forms as occurring into the zinc phosphate compound cannot be directly exploited.

Introduction

The development of 3D-printing (or additive manufacturing) has encouraged the manufacture of small-scale parts while reducing production time of limited or custom series since certain steps such as mould making are no longer useful [START_REF] Frazier | Metal additive manufacturing: a review[END_REF]. Coupling of the shaping technique with numerical modelling and simulation tools allows the production of complex shapes, whether geometrically or hierarchically: objects with cavities, inclusions or alveolar structures can be easily printed. The manufacturing is therefore called "additive process" in the sense that the shaping of a three-dimensional piece results from the addition of matter thanks to powder sintering, layer by layer. Among, additive synthesis processes, the selective laser sintering process involves the sintering of powder particles (metal, ceramics, polymer, glass) using a laser heating. Each powder layer undergoes a two-dimensional structuring before being covered with a new layer. Most of the commercially available SLS machines are equipped with Nd:YAG laser or ytterbium doped laser [START_REF] Ferrage | Dense yttria-stabilized zirconia obtained by direct selective laser sintering[END_REF][START_REF] Ferrage | A review of the additive manufacturing (3DP) of bioceramics: alumina, zirconia (PSZ) and hydroxyapatite[END_REF][START_REF] Yadroitsev | Parametric analysis of the selective laser melting process[END_REF][START_REF] Shirazi | A review on powder-based additive manufacturing for tissue engineering: selective laser sintering and inkjet 3D printing[END_REF][START_REF] Stansbury | 3D printing with polymers: challenges among expanding options and opportunities[END_REF].

The interaction of the laser beam with the powder produces a local heating at a temperature close or higher than the powder melting point; this causes the particles to partially fuse, allowing the powder to be consolidated thanks to sintering phenomenon.

On one hand, the transferred energy depends on both the thermal conductivity and melting point of the powder and its optical absorption at the wavelength of laser radiation. If the applied energy is too weak, the consolidation between the particles themselves and the different layers will be insufficient leading to porous and brittle objects [START_REF] Simchi | Direct laser sintering of metal powders: Mechanism, kinetics and microstructural features[END_REF]. However, too much energy causes the total melting of particles that rearrange themselves to minimize their surface energy forming solidified droplets: this phenomenon being sometimes named "balling effect" [START_REF] Ho | Effects of graphite powder on the laser sintering behaviour of polycarbonate[END_REF][START_REF] Hao | Selective laser melting of a stainless steel and hydroxyapatite composite for load-bearing implant development[END_REF] and or with modification of the composition and porosity formation. Delamination of the sintered layers and the formation of cracks can also be observed due to high cooling rates and so, residual stresses [START_REF] Simchi | Direct laser sintering of metal powders: Mechanism, kinetics and microstructural features[END_REF]. Each compound will have to be studied to determine the optimal Laser regime to apply, directly linked to the reached local temperature distribution obtained. Besides, the SLS manufacturing technique, involving compulsory and significant thermal variations that cause stresses, is therefore subject to many limitations. Especially, for ceramic materials, the rapid heating of the laser-irradiated area at very high temperatures (ceramics characterized by typically very high melting points) combined with low thermal conductivity (ceramic and thermal insulating materials) result in very high local temperature gradient within the ceramic [START_REF] Kruth | Selective laser melting of iron-based powder[END_REF]. Besides, ceramics are known as brittle materials, not elastic materials. The laser process can result in detrimental mechanical constraints if process parameters are not well selected. Hence, selective laser sintering has been extensively studied on polymers (PVC, , etc.) or metallic materials [START_REF] Yadroitsev | Parametric analysis of the selective laser melting process[END_REF][START_REF] Shirazi | A review on powder-based additive manufacturing for tissue engineering: selective laser sintering and inkjet 3D printing[END_REF][START_REF] Stansbury | 3D printing with polymers: challenges among expanding options and opportunities[END_REF]. In the case of ceramics, although the laser beam can induce a temperature high enough to ensure the densification of ceramics due to advanced sintering, it is difficult to achieve the local densification of ceramic powders [START_REF] Chen | 3D printing of ceramics: A review[END_REF][START_REF] Kruth | Binding mechanisms in selective laser sintering and selective laser melting[END_REF], and ceramics are much more prone to constrains induced by the temperature gradient mentioned above causing large cracks formation. Nowadays, the use of an organic binder to perform "indirect selective laser sintering" is largely predominant in literature for ceramic preparation resulting from additive manufacturing [START_REF] Tang | Slurry-based selective laser sintering of polymercoated ceramic powders to fabricate high strength alumina parts[END_REF][START_REF] Friedel | Fabrication of polymer derived ceramic parts by selective laser curing[END_REF][START_REF] Tan | Scaffold development using selective laser sintering of polyetheretherketone-hydroxyapatite biocomposite blends[END_REF][START_REF] Gao | Enhanced sintering ability of biphasic calcium phosphate by polymers used for bone scaffold fabrication[END_REF]. Furthermore, as another drawback for the direct SLS process, it has been observed that samples irradiated with the same laser energy density but from distinct laser power / lasing writing speed pairs have a different microstructure affecting the density and final mechanical properties of the sample [START_REF] Juste | Shaping of ceramic parts by selective laser melting of powder bed[END_REF][START_REF] Prashanth | Is the energy density a reliable parameter for materials synthesis by selective laser melting?[END_REF][START_REF] Shahzad | Additive manufacturing of zirconia parts by indirect selective laser sintering[END_REF]. So, the local temperature control is complex for ceramic powder. The energy applied to a line on the powder bed is directly related to the power composition, powder bed density and powder particle size distribution, and to the scanning speed of the laser such as the applied linear energy is proportional to the power of the laser and inversely proportional to the scanning speed.

But different temperature gradients, leading to various widths for the irradiated zone line, the occurrence or not of the balling effect, are produced from same laser energy depending on the laser power / laser speed couple [START_REF] Das | Physical Aspects of Process Control in Selective Laser Sintering of Metals[END_REF][START_REF] Hao | Selective laser sintering of hydroxyapatite reinforced polyethylene composites for bioactive implants and tissue scaffold development[END_REF][START_REF] Tolochko | Balling processes during selective laser treatment of powders[END_REF]. A priori, the thermal profiles according to the width of the lased line respond to characteristic profiles of the Gaussian beams, by means both the Gaussian dispersion of laser radiation intensities according to this axis, but also the thermal conductivity profiles within the material. But, as far as we know, the thermal profile of the lased track produced on the ceramic powder layers during the SLS process is not experimentally measured and clearly reported in literature. Nonetheless, the accurate control of the temperature gradients is the key parameter to achieve the final 3D piece with optimized microstructure: surface roughness, density, absence of defects (cracks, pores), high relative density and so good mechanical properties as shown in the rare reports of a successful use of direct SLS for small ceramic pieces production [START_REF] Ferrage | Dense yttria-stabilized zirconia obtained by direct selective laser sintering[END_REF].

On the other hand, additive manufacturing of phosphate materials and especially biophosphate materials is of great interest, and at the same time, Mn 2+ -doped Zn 3 (PO 4 ) 2 phosphate exhibits a rich thermal history with numerous events [START_REF] Salek | Mn 2+ doped Zn 3 (PO 4 ) 2 phosphors: irreversible thermochromic materials useful as thermal sensors[END_REF]. For such compound, various allotropic forms can be stabilized with irreversible transitions for a 600°C up to 1000°C temperature range. The Mn 2+ transition metal can occupy distorted tetrahedral or octahedral sites depending on the low or high temperature form. Hence, versus the thermal history of the samples, different types of emission spectra can be obtained. By increasing the annealing temperature, the green emission associated with Mn 2+ in a tetrahedral environment progressively disappears in favour of the red one that corresponds to Mn 2+ stabilized in five-and six-fold coordination sites. The chromaticity of Mn 2+doped Zn 3 (PO 4 ) 2 strongly changes in the 600°C -1000°C range, and one can consider this phosphate as an interesting thermal sensor. The additive manufacturing of aluminium based oxide is also extensively proposed in literature. Mn 2+ -doped ZnAl 2 . 2 O 4+ phosphors get in the same way a large change of emission spectra after annealing treatment from 600 °C up to 1400 °C [START_REF] Cornu | Luminescence switch of Mn-Doped ZnAl 2 O 4 powder with temperature[END_REF]. As the annealing temperature increases, the global inversion rate, which characterizes the cation distribution in both A and B sites of the spinel structure, decreases leading to a more direct matrix. So, the red luminescence related to the presence of Mn 2+ in octahedral sites fades away to be replaced by a new green emission due to Mn 2+ ions located in tetrahedral sites within the spinel structure. Such properties lead to consider the Mn-doped zinc-aluminium spinel as a potential candidate for developing stable and highly sensitive thermal sensors.

In this article, we propose to use the two thermal sensors Mn 2+ -doped Zn 3 (PO 4 ) 2 and Mn 2+doped ZnAl 2 . 2 O 4+ as material for SLS process temperature probe. Laser tracks are realized on 2D films of these two ceramic compositions previously prepared by Dr Blade process. Then micro-luminescence using confocal microscope is utilized to analyse post mortem the temperature gradient reached during laser process. The study aims to show that such thermochromoluminescent materials, able to change their emission spectra with temperature, could be the solution to optimize the control of the laser-matter interaction during the SLS process of metallic or ceramic materials.

Materials and methods

Samples preparation

The Mn 2+ -doped Zn 3 (PO 4 ) 2 compound was synthetized by aqueous co-precipitation method: stoichiometric amounts of ZnCl 2 ,6H 2 O and MnCl 2 ,6H 2 O were previously dissolved in aqueous medium and added dropwise in an equimolar solution of (NH 4 ) 2 HPO 4 . The reaction was performed under vigorous stirring at room temperature with three hours of ripening. Then, the as-prepared precipitate was allowed to dry at ambient temperature.

The Zn 0.95 Mn 0.05 Al 2.2 O 4+ sample was synthetized by the Pechini route. Stoichiometric amounts of zinc nitrate hexahydrate, aluminium nitrate nonahydrate and manganese nitrate hydrate were dissolved in mineral water. Then, citric acid (CA) and ethylene glycol (EG), used as polyesterification precursors, were added to the solution (salt:CA:EG molar ratios 1:4:4) and water was slowly evaporated by heating on a hot plate. The highly viscous mixture formed after polyesterification was annealed at 400 °C for 5 hours under air. A dark brown powder was then obtained. Thereafter, various thermal post-treatments were performed at 500 °C under air atmosphere during 10 hours.

The SLS experiments have conducted using a laser system equipped with a IPG Photonics ytterbium fiber laser (YLM-400-AC*Y11) delivering a power up to 400 Watt at a monochromatic wavelength of 1.07 µm, and a galvanometric mirrors scanner (ScanLab -Hurry scan 20).

Characterization techniques

X-ray diffraction patterns were recorded on a Philips X'Pert MPD apparatus equipped with a copper K α1 anticathode (40 kV, 40 mA). Diffraction patterns were collected from 8 to 80° in 2θ with a 0.017° step scan and a counting time of 5 s.

The morphology of the as-prepared particles was observed thanks to a Leica DMI 3000 M inverted microscope using a Leica SFL 100 diode enabling an excitation at 365 nm and the fluorescence collection recorded with a Leica MC 120 HD camera. Microscope objective N PLAN EPI 10×, NA 0.25 was used. For microstructural analyses, SEM investigations were performed using a TESCAN Vega II SBH microscope or JEOL JSM-6700F. The film thickness was measured by the Dektak 150 Surface Profiler (Veeco), fitted with a stylus which had a radius of 12.5 μm and a resolution of 0.8 μm.

The photoluminescent properties were analysed using a spectrofluorimeter SPEX FL212 equipped with a 450 W Xenon lamp. The excitation spectra were corrected for the variation of the incident flux as well as emission spectra for the transmission of the monochromator and the response of the photomultiplier. This equipment was also used to record diffuse reflectance spectra.

In this case, the emission and the excitation monochromator were set in a synchronous mode, in order to collect all the diffuse reflection of the xenon lamp without catching any fluorescence photon. A black reference (B: black toner) and a white reference (W: Magnesia MgO) were scanned in the same conditions and the measurement from the sample (S) was corrected to obtain the desired data (D) following the relation: D = (S-B) / (W-B). The x and y chromatic coordinates were directly determined from the emission spectra.

Finally, the micro-luminescence was carried out with a Labram 800-HR spectrophotometer (Horiba Jobin-Yvon) equipped with an Olympus microscope objective (10x), a CW laser diode excitation at 405 nm (100 mW) and a thermoelectric cooled CCD camera (Synapse Model 354308).

Results and discussion

Powder sample properties

Two thermal sensors were chosen for their ability to mark temperatures variation induced by the laser -matter interaction during the SLS process across the irradiated zone. The choice takes benefit in both cases of the capacity of Mn 2+ luminescent cation in inorganic oxides to get an emission colour which can drastically vary from red to green while the coordination site of the cations is, irreversibly, modified when a thermal treatment is applied to the Mn-doped oxide compound.

The first material is the manganese doped zinc phosphate phosphors. First the hopeite hydrated form (Zn 2.94 Mn 0.06 (PO 4 ) 2 ,4H 2 O) is obtained by co-precipitation and then this compound is pre-annealed at 500°C to prepare the anhydrous compound (Mn-doped Zn 3 (PO 4 ) 2 ) in the monoclinic form [START_REF] Salek | Mn 2+ doped Zn 3 (PO 4 ) 2 phosphors: irreversible thermochromic materials useful as thermal sensors[END_REF][START_REF] Robertson | Structural transformation and thermochromic behavior of Co 2+ -doped Zn 3 (PO 4 ) 2 •4H 2 O hopeites[END_REF][START_REF] Pawlig | Synthesis and characterization of α-hopeite[END_REF][START_REF] Stephens | Crystal structure of β-Zn 3 (PO 4 ) 2[END_REF][START_REF] Wang | Synthesis, photoluminescence and thermostimulatedluminescence properties of novel red long-lasting phosphorescent materials beta-Zn 3 (PO 4 ) 2 :Mn 2+ ,M 3+ (M ~ Al and Ga)[END_REF]. In the -form as the starting material, the Mn 2+ ions are located in two non-equivalent distorted tetrahedral sites (Figure 1a). The β and γ phases are the two hightemperature forms. In these forms, the Mn 2+ ions are located in distorted octahedral and five-fold coordination sites (Figure 1a) [START_REF] Salek | Mn 2+ doped Zn 3 (PO 4 ) 2 phosphors: irreversible thermochromic materials useful as thermal sensors[END_REF][START_REF] Stephens | Crystal structure of β-Zn 3 (PO 4 ) 2[END_REF]. Mn 2+ ions possess d 5 electronic configuration; the main phenomenon of this luminescent dopant corresponds to a 4 T 1  6 A 1 transition, which is strongly dependent on the ligand field and so the coordination number. Hence, the phase transition from the α-form to the γ-or β-form results in a strong modification of the ligand field around the Mn 2+ ions with an increase in the coordination number. A decrease of the crystal field strength around the Mn 2+ ions leads to a shift in the Mn 2+ luminescence emission from green to red [START_REF] Salek | Mn 2+ doped Zn 3 (PO 4 ) 2 phosphors: irreversible thermochromic materials useful as thermal sensors[END_REF][START_REF] Smith | Luminescence of Three Forms of Zinc Orthophosphate:Mn[END_REF]. Phase transition phenomena from the -form to the high polymorphs take progressively place for thermal treatments in the temperature range from 700 to 1000°C.

The second material which is going to be used as thermal-history sensor is manganese-doped zinc aluminate spinel. The optical properties of Mn-doped ZnAl 2 O 4 were shown to depend on the location of Mn 2+ ions within the spinel network. Spinel structure is a multisite matrix including both octahedral and tetrahedral sites as potential cationic sites for Mn 2+ ions [START_REF] Cornu | Luminescence switch of Mn-Doped ZnAl 2 O 4 powder with temperature[END_REF][START_REF] Cornu | ZnAl 2 O 4 as a potential sensor: variation of luminescence with thermal history[END_REF]. This luminescent ion substituted for Zn 2+ may occupy octahedral and/or tetrahedral sites depending on synthesis parameters, especially the annealing temperature (as evidenced above). From of Mn-doped ZnAl 2 O 4 sample prepared at relatively low temperature from Pechini process [31], a drastic change in the emission spectra was observed as temperature increases from 1000 °C to 1400 °C, which also dependent on the Zn/Al molar ratio. This emission property is changing versus the thermal posttreatment by a progressive migration of both manganese and zinc cations into the tetrahedral coordination polyhedral sites. In a previous paper [START_REF] Cornu | Luminescence switch of Mn-Doped ZnAl 2 O 4 powder with temperature[END_REF], for the 0.5% Mn-doped ZnAl 2.2 O 4+ sample, asprepared in this study, the luminescent properties were already shown to change, for temperature evolution from 800°C to 1400°C, from an emission spectrum with a double contribution in the green range (associated with Mn 2+ in tetrahedral coordination) and in the red part of the spectrum (associated with Mn 2+ in octahedral coordination) to an emission spectra with only the occurrence of the green emission band. Confirming our previous results with the temperature increase [START_REF] Cornu | Luminescence switch of Mn-Doped ZnAl 2 O 4 powder with temperature[END_REF], the structural variations were emphasized by X-ray diffraction studies (Figure 2a) for the anhydrous Zn 2.94 Mn 0.06 (PO 4 ) 2 compound. The annealing time was fixed to 10 min and followed by an air quenching. When the temperature is increased from 600 to 900°C, the intensities of the diffraction peaks assigned to the γ phase increase whereas the α peak intensities decrease, indicating a phase transition phenomenon.

At higher temperatures, between 900°C and 1000°C, an additional phase transition corresponding to the yβ form is observed. It can be noticed that an annealing treatment at 1100°C followed by a rapid quenching produced the melting of the compound.

With the same post-treatments, for the Zn 0.95 Mn 0.05 Al 2.2 O 4+ samples, as shown by the X-ray spectra, a pure spinel form is obtained (Figure 2b). The crystallite size, from Debye-Scherrer equation based on diffraction peak width, varies from less than 20 nm for an annealing temperature of 600°C up to 55 nm for thermal treatment at 1400°C. Regarding our previous work [START_REF] Robertson | Structural transformation and thermochromic behavior of Co 2+ -doped Zn 3 (PO 4 ) 2 •4H 2 O hopeites[END_REF], the increase of the crystallite size should be associated with a change in the cationic distribution, especially with a decrease of the manganese ions amount located into the octahedral sites while the average particle size is enlarged. The evolution of the luminescence spectral distribution as a function of the annealing temperature for the phosphate compound is plotted in Figure 3a. For an excitation at 405 nm, two contributions of manganese luminescence for an annealing treatment at temperatures lower than 850°C are clearly visible. A first band is centred at approximately 530 nm and a second one is located at 640 nm (i.e. lower energy). They correspond respectively to the 4 T 1  6 A 1 transitions of Mn 2+ in tetrahedral and in octahedral polyhedra. The green emission is then correlated to manganese location in a low coordination site (four-fold coordination site) of the low-temperature form (form). The red -orange contribution is issued from Mn 2+ ions in five-and six-fold coordination sites in the appearing y phase with the annealing treatment temperature increase. For the low annealing temperature range (up to 800°C), we have observed experimentally that the green luminescence intensity increases versus temperature. The increase of the luminescence efficiency is commonly due to the increase of the crystallite size. But, the target here is to sense the temperature not from a change of efficiency but from a change of the chromaticity of the luminescence (the luminescence intensity is difficult to extract in a robust way and to correlate with the thermal history since the luminescence intensity depends on many extrinsic parameters as the powder bed thickness, the spectrometer efficiency, the filters used, the excitation wavelength, etc. [START_REF] Rabhiou | Phosphorescent thermal history sensors[END_REF]). By increasing the annealing treatment (T>900°C), the green emission is drastically quenched in favour of the red one, which clearly indicates the disappearance of the  allotropic form of the zinc phosphate phase. The evolution of the emission properties as a function of temperature can be summed up by the plot of the x and y coordinates (of the x,y,z trichromatic color space) (Figure 3b) of the Mn-doped zinc phosphate sample versus the thermal treatment temperature. The chromaticity path following the heat-treatment temperature shows that an accurate characterization of the annealing temperature can be efficiently extracted from the sample emission properties for annealing temperatures varying between 700°C and 1000°C; especially the sample is a very sensitive sensor able to mark a change of temperature between 800 and 850°C, a large optical contrast taking place between the two samples obtained at these temperatures.

(double column width)

The evolution of the luminescence spectral distribution and the X, Y colorimetric parameters as a function of the annealing temperature for the Zn 0.95 Mn 0.05 Al 2.2 O 4+ spinel powder compound are plotted in Figures 4a and4b, respectively. As for the previous sample, for an excitation at 405 nm, two contributions of manganese luminescence for an annealing treatment at temperatures lower than 900°C, with a first band centred at approximately 560 nm and a second one located at a lower energy at 700 nm can be observed. Once again, they correspond respectively to the 4 T 1  6 A 1 transitions of Mn 2+ ions in tetrahedral and octahedral environment, respectively. For treatment temperatures between 600°C and 1000°C, and especially between 800°C and 1000°C, the green contribution intensity increases to the detriment of the red emission intensity. Thus, a reverse chromaticity modification, in regard of the previous zinc phosphate compound, is observed for the spinel sample. Then, for treatment temperatures higher than 1000°C, another phenomenon is detected with a new contribution, constituted by a discrete series of fine peaks in the red region. This series of discrete peaks, based on our previous works devoted to the luminescence of un-doped ZnAl 2 O 4 compound, is compatible with the spectral signature of a d 3 element. Considering the synthesis route and the composition, these lines should be attributed to Cr 3+ or Mn 4+ . We cannot discard the presence of chromium impurities in precursor materials as this element is often detected due to trace impurities in the aluminium. The lines peaking in the red range are in a good agreement with the E g -4 A 2g R-, N-zero phonon lines of trivalent chromium in the octahedral site of the aluminium ions [START_REF] Cornu | ZnAl 2 O 4 as a potential sensor: variation of luminescence with thermal history[END_REF][START_REF] Mikenda | N-lines in the luminescence spectra of Cr 3+ -doped spinels (I) indentification of N-lines[END_REF]. The emission spectra also contain satellite lines distributed around the main peak, which can be identified as vibronic (phonon assisted transitions) sideband transitions of Cr 3+ ions. We can suppose that the Cr 3+ luminescence is quenched by the structural defects present in smallest crystallites; only a very high annealing temperature treatment reveals the chromium presence. A stabilization of Mn 4+ is also possible because of the heat-treatment at high temperature performed in air atmosphere. This will also be consistent with the decrease of the green emission between 1000°C and 1200°C. Thus the evolution of the spinel compound's emission properties as a function of temperature can trace the temperature within the 800°C to 1000°C range from the change of the green / red emission band ratio of the Mn 2+ phosphor. Furthermore, the brutal appearance of the specific luminescence lines associated to the Cr 3+ impurities and/or Mn 4+ ions allow the clear indication of a reached temperature of 1200°C at least.

Film preparation and properties

The two as-prepared thermal sensors are then deposited on silica glass substrates for film preparation using Dr. Blading as film coating process (illustrated in Figure 5a). In a first step, the powder is dispersed in ethanol (30-35 wt%) and ultra-sonication is used to improve the dispersion quality. A viscous suspension thanks to the high powder concentration that can be coated in a facile way with the blade apparatus is so obtained. Thickness was adjusted thanks to razor blade to about 40 m -50 m as shown by the film profile obtained by interferential profilometry taking 0 height at the glass substrate surface (Figure 5f), i.e. a thickness which can be considered inferior to the penetration depth of the laser ensuring a quite homogeneous energy along the cross section. After the coating, the films are dried in an oven at 100°C for 2 hours, and a pre-annealing treatment at 500°C during 10 min was performed. The as-prepared films, for both the phosphate and the spinel samples, are white, with homogeneous surface, as illustrated by the optical microscope pictures for the phosphate sample in Figure 5b, 5c. SEM micrographs reveal that the starting films are highly porous with porosity about 50%. Both can be described as a powder bed constituted as a pack of micron-size aggregates. The two SEM pictures with different magnification reported in Figures 5d and5e illustrates the high porosity rate. However thanks to the annealing pre-treatment, the films are easily handled; however the films can be removed by fingers scratches.

SLS process was firstly applied to the Mn-doped Zn 3 PO 4 film, varying the power of the laser and/or the laser scanning speed. Thanks to the quick SLS processing to write laser tracks, different sets of parameters have been tested. The aim is not to optimize here the SLS parameters but to detect if post mortem, the material luminescence modification could indicate the reached temperature. Hereafter, we have chosen to illustrate our work on a Mn 2+ -doped Zn(PO 4 ) 2 film after the application of the laser as horizontal lines with various laser scanning speeds and laser powers, with high energy for the laser (low speed and/or high power) (Figure 6). Most of the lines reflect a too high deposited energy and the film is clearly melted because the lines appear with glassy and transparent aspect under white light. This transparent aspect can be evidenced by photographs of the film deposited (or coated) on its glass substrate on a black support as illustrated in Figure 6a. The access to the melting point is evidenced by the presence of air bubbles embedded in the glassy lines as shown in the insert of the Figure 6b showing the laser strikes obtained for the largest dose deposition. Surprisingly, a luminescence halo with high intensity is detected around these lines. This is not a green to red chromaticity evolution with the proximity of the glassy part, but, on the contrary, a homogeneous bright greenish chromaticity. Hence, the red emission corresponding here to the presence of the high temperature forms seems by-passed. May some film parts have transited through the high temperature form, but in any case, the high temperature form is nowhere stabilized. Indeed, a brutal modification from a low green luminescence attesting the presence of low temperature forms far from the lased lines (at least with Mn 2+ remaining inside a tetrahedral coordination) to a halo around the glassy lines with green luminescence is observed. Because of the high intensity of the green-emissive halo around the glassy lines, it is difficult to observe the luminescence of the glassy parts, even using confocal microscope. The green luminescence halo is, by the way, fully compatible with the beginning of ceramic to glass transformation, Mn 2+ in low concentration in glass systems showing green luminescence [START_REF] Félix-Quintero | RGB emission of Mn 2+ doped zinc phosphate glass[END_REF]. (double column width)

The next experiments are focused on the very small defects observed for the lowest dose deposition of the previous Figure 6b (punctual defects marked with a star). Concentrating our attention on those punctual defects, few balls formed under the laser excitation are shown by SEM (Figure 7a). Accurate analyses of the variation of the luminescence variation of the sample film around the formed balls are performed using confocal microscopy (Figure 7 b). Emission spectra are recorded on the micrometric analysis zones which are marked from 1 to 7 (Figure 8a), X, Y color parameters are reported in Figure 8b. As it can be seen in Figure 7a, the laser irradiation follows a line of about 300 m width.

Apart from the formation of few balls, as punctual defects, the laser seems to have no sintering activity, based on the morphology of the particles constituting the powder film. Using the confocal microscope, the analysed points are along a straight line which crosses the largest ball formed by the

 300 m (a) (b) (d)
laser interaction. The luminescence spectrum suddenly changes in the ball location from green to red. Outside this region, the film even after the laser irradiation still exhibits a main green emission band (about 525 nm) coupled with as low contribution, a minor intensity red band (around 600 nm, Figure 8a). Hence, while the laser is applied with this intermediate scanning speed and low power value (29 mm.s -1 , 16 W), the transferred energy is not sufficient to produce the phase transition from the Mn 2+ -doped Zn 3 (PO 4 ) 2 low temperature form (within tetrahedral sites) to the high temperature form (within octahedral sites). Thus, basing on the emission powder properties reported in Figure 3, the laser allows a priori, the maximal temperature level is remaining below 800°C for the points 1,2,6 and 7 whereas temperature seems to be between 800°C and 900°C for the points 3 to 5 (Figure 3). Nonetheless, the formed ball offers an emission spectrum showing a red luminescence band as main band, coupled with, as minor band, the green emission one. According to the perfect spherical shape of the ball, one can assume that this zone well corresponds to a punctual hot spot with a local heating close to the vicinity of the melting point. Additionally, the structural feature of the ball is not similar to the rest part of the film, with Mn 2+ ions located into octahedral sites, as in the zinc phosphate high temperature form. As conclusion on the possibility of using the Mn-doped zinc phosphate, severe restrictions need to be expressed. Although the change from the low to the high temperature form should occur significantly below the phase transition occurs on the range from 700 to 900°C (the melting point takes place between 1000 and 1100°C). One can suspect that the working temperature range is here too narrow or with too low kinetic in regard of the absorption at the laser wavelength too high and the temperature diffusion too slow. The differences observed between the set of powder samples, annealed 10 min in a furnace, and the film submitted to the laser irradiations, take place without any doubt on the very different kinetic conditions between these sample sets. With a speed of 29 mm.s -1 and laser track of 1.5 cm length, the irradiation time to plot a full line is about half a second. The powder absorbing do not diffuse the temperature fast enough to avoid the melting. Apparently, the change of structural form, i.e. the phase transition between the low and high crystallographic forms which is not detected, has no time to efficiently occur before the sample melting. A sensor based on such a phosphate structural phase transition seems not well adapted to extract temperature cartographies in a fast heating process.

SLS process was secondly operated on the Mn-doped ZnAl 2 O 4 film, with the same procedure (varying again the power of the laser and/or the laser scanning speed). Briefly and focusing straight on the best results, one can concentrate on a lased tracks using a scanning speed: laser power parameters: 50 mm.s -1 and 72 W. It can be noted that the spinel absorption at 1 µm is lower than the phosphate phase absorption. Significantly higher laser power must be used for heating.

Macroscopically and microscopically, no clear effect that the melting or an advanced sintering is observed on the irradiated area. Accurate analyses of the variation of the luminescence variation of the sample film across the lased line, extracted from optical microscope (top picture) and from confocal microscopy (bottom picture), are shown in Figure 9 (8 analysis points). Clearly, on the picture depicted from the confocal microscopy, the centre of the line is associated with a greenish luminescence whereas the un-lased part of the film is associated with reddish luminescence. The emission spectra corresponding to the eight analysis points are reported in Figure 10a; corresponding x, y chromatic parameters calculated from each spectrum are plotted in Figure 10b. A clear gradual evolution from the outside to the centre of the lased line can be observed. A progressive switch from emission spectra dominated by the red range band (centred at 700 nm) to emission spectra dominated by the green range band (at 520 nm) is evidenced. In regard of the powder reference samples annealed 10 min, the temperature gained during the irradiation progressively increases up to 1000°C from far to the centre of the area impacted by the laser. Kinetic aspects are herein, on the contrary to what it has been noted for the phase transition of the zinc phosphate compounds, not a drastic limitation of the analysis. This aspect may be related to the lower absorption of the aluminate as compared to the phosphate phase which favour diffuse 500 m 500 m reflectance and more homogeneous absorption and heating and/or the kinetic of the mechanism at the origin of the thermochromism in these two phases. Indeed, the change of the luminescence originates from the cationic reorganization in the spinel multisite matrix (with both octahedral and tetrahedral sites). No energy barrier has to be crossed, and the cation distribution has to be directly linked to the thermal history, whatever the duration of the heating time.

(single column width)

From the emission spectra (Figure 11, bottom), it can be concluded that the scratched defects are well associated with hot spots. Indeed, these areas get a strong emission linked to the Cr 3+ impurities or Mn 4+ ions, which was shown to be revealed only by very high temperature treatments over 1200°C (Figure 4b). Manganese-doped spinel material as temperature sensor gets not only the capacity to mark temperature transition from 800°C to 1000°C from the red to green luminescence variation but it is also adequate, from the sudden appearance of the discrete red emission lines, to mark the raise of temperatures over 1200°C during thermal history, thanks to the presence of the series of discrete and fine peaks in the red region.

Conclusion

In this article, based on our previous studies, two home-prepared compounds: Mn 2+ -doped Zn 3 (PO 4 ) 2 and Mn 2+ -doped ZnAl 2 . 2 O 4+ were used as thermal sensors, thanks to their thermochromoluminescence properties, as SLS process probe. Our work may be particularly useful for printing of mixed materials such as in situ alloying and composites rather than a single material, using then, for illustration, the spinel compound mixed as minor rate to record the thermal history of an alloy as main compound (composite matrix). Composite materials, in this way, have been recently shaped from SLM additive manufacturing [START_REF] Martinez | In situ alloying of elemental Al-Cu12 feedstock using selective laser melting[END_REF][START_REF] Yu | Particle-reinforced metal matrix nanocomposites fabricated by selective laser melting: A state of the art review[END_REF]. The target of the study was to be able to extract from the emission spectra of the materials a real idea of the temperatures that are reached during the laser -matter interaction. In a first part, the luminescent chromaticity of both the as-prepared compounds versus the annealing temperature (for 10 min. annealing treatments) was plotted, as abacus curves. The changes of the emission spectra were a priori well-adapted to mark temperature in the range 600-1200°C, for a temperature gradient of 500°C versus no more than 100 microns about. Chen Bo et al. studies [START_REF] Cheng | Infrared thermal imaging for melt pool analysis in SLM: a feasibility investigation[END_REF] on SLM have shown that it is possible to estimate on alloys the melt pool dimension (about 0.36 mm × 0.21 mm) based on appropriate thermal imager setting (thermography), but with difficulties to extract the true temperatures. This comparison with alternative processes in order to record thermal history shows that both thermal resolution and spatial resolution proposed herein are competitive. For the Mn-doped zinc phosphate, large differences were observed between the abacus curve from the annealed powders and the change of the optical properties observed on doctor bladed film submitted to the laser irradiations. This can be interpreted as a consequence of a local absorption which is too high in the phosphate compound and/or the different kinetic condition between these two studied compounds; avoiding the phase transition at the origin of the thermochromoluminescence in the case of the "ultra-rapid' heating using laser irradiation. On the contrary, for the spinel compound, the change of the luminescence originates from the cationic reorganization in the spinel multisite matrix and the comparison between the abacus curves obtained on annealed powders and laser-irradiated films have shown that for both cases, the emission spectra are directly linked in a same way to the maximal temperature gained during the thermal history, whatever the duration of the heating time. This material can so be used as thermal sensor for SLS process.

Figure 1 .

 1 Figure 1. Representation of the various cationic sites (a) in the different α, γ, and β allotropic forms

Figure 2 .

 2 Figure 2. X-ray diffraction patterns of (a) Zn 2.94 Mn 0.06 (PO 4 ) 2 and (b) Zn 0.95 Mn 0.05 Al 2.2 O 4+ obtained by annealing 10 min.at different temperatures and followed by air quenching ( means average crystallite size).

Figure 3 .

 3 Figure 3. (a) Luminescence spectra and (b) chromatic x and y parameters of the Zn 2.94 Mn 0.06 (PO 4 ) 2 sample heated from 600°C to 1000°C during 10 min and then quenched.

Figure 4 .

 4 Figure 4. Luminescence spectra of the Zn 0.95 Mn 0.05 Al 2.2 O 4+ sample heated from 600°C to 1000°C (a) from 1000 °C to 1400 °C during 10 min and then air quenched.(double column width)

Figure 5 .

 5 Figure 5. (a) Schematic drawing of the "Dr. Blade deposit process to obtain the ceramic film. Illustration of the microstructure obtained for the Mn 2+ -doped Zn(PO 4 ) 2 film : (b) & (c) macroscopic view and optical microscope images and (d) & (e) SEM images of the film, (f) Thickness of the fiml estimated form the optical profilometer.(single column width)

Figure 6 (

 6 Figure 6 (a) Photograph under white light source of Mn 2+ -doped Zn 3 (PO 4 ) 2 film on a black support after the application of the laser as horizontal lines with various laser scanning speeds and laser powers, (b) Photograph under UV-light monochromatic source of the same Mn 2+ -doped Zn(PO 4 ) 2 film (the inserted photographs are taken with the confocal microscope (l = 405 nm).

Figure 7 .

 7 Figure 7. (a) SEM image of the Zn 2.94 Mn 0.06 (PO 4 ) 2 film with "ball effect" on the lased area and (b) corresponding luminescence cartography from confocal microscopy (single column width)

Figure 8 .

 8 Figure 8. (a) Luminescence spectra of the Zn 2.94 Mn 0.06 (PO 4 ) 2 film recorded on the 7 analysis points and (b) the corresponding chromatic x and y parameters (plot in same scale than for Figure 3b.) (double column width)

Figure 9 .

 9 Figure 9. (top) Optical microscope image on the Zn 0.95 Mn 0.05 Al 2.2 O 4+ film (focus on a lased area) and (bottom) corresponding luminescence cartography from confocal microscopy

Figure 10 .

 10 Figure 10. (a) Luminescence spectra of Zn 0.95 Mn 0.05 Al 2.2 O 4+ film recorded on the 8 analysis points and (b) the corresponding chromatic x and y parameters.(double column width)

Figure 11 .

 11 Figure 11. (top) Optical microscope image on the Zn 0.95 Mn 0.05 Al 2.[START_REF] Ferrage | Dense yttria-stabilized zirconia obtained by direct selective laser sintering[END_REF] O 4 film (focus on a lased path line) and (bottom) the corresponding luminescence spectra of recorded on the three analysis points.

  Figure 11