Stéphane Redon
email: stephane.redon@inria.fr

Abderrahmane Kheddar
email: kheddar@iup.univ-evry.fr

Sabine Coquillart
email: sabine.coquillart]@inria.fr

Hierarchical Back-Face Culling for Collision Detection

 suggested to apply a variant of back-face culling to speed-up collision detection between polyhedral objects. However, Vanecek's method is linear in the number of faces in the object, which is unpractical for large models. This paper suggests to add some geometrical information to hierarchies of bounding volumes, typically used in collision detection, and perform conservative back-face culling at the bounding-volume level in constant time. The method described in this paper can be applied to complement any kind of bounding-volumes hierarchy and allows a trade-off between memory and speed. Preliminary experimental results suggest that the method allows a significant speed-up, especially in close proximity situations.

Introduction

Collision detection (CD) is still a fundamental problem in numerous domains. Some typical examples are computer graphics (physically-based modeling, animation), robotics (path-planning, collision avoidance), industrial applications (virtual prototyping, assembly tests) and video games. Especially, haptics research has generated the need for algorithms able to achieve kilohertz rates.

A few years ago, Vanecek [START_REF] Vanecek | Back-Face Culling Applied to Collision Detection of Polyhedra[END_REF] suggested to apply a variant of back-face culling (BFC) to speed-up collision detection between polyhedral objects. The method consists in culling faces which are moving backwards, relatively to the other objects. Since it is insensitive to objects positions and orientations, the method is especially efficient in close-proximity configurations (a peg in a hole, for example). To our knowledge, this method is the only one offering such characteristics for general polyhedral objects1,2 .

Vanecek's method, however, performs back-face culling at the face level. Consequently, the algorithm is linear in the number of faces in the object, which is unpractical for large models. This paper suggests to add some geometrical information to hierarchies of bounding volumes (BVs), typically used in collision detection, and perform conservative back-face culling at the bounding-volume level. Precisely, this geometrical information is used to perform a constant-time culling test which detects most situations where every triangle associated to a bounding-volume is moving backwards, ie situations where the boundingvolume hierarchies need not be further descended, even when the BVs are overlapping.

The method described in this paper can be applied to complement any kind of bounding-volumes hierarchy, and doesn't require a separate hierarchy. It allows a trade-off between the memory overhead due to the addition of geometrical information in the bounding-volumes and the provided speed-up. Moreover, it can be applied to discrete and continuous collision detection.

Background

Back-face culling for collision detection

Let's briefly recall Vanecek's results. More details can be found in the original paper [START_REF] Vanecek | Back-Face Culling Applied to Collision Detection of Polyhedra[END_REF]. Let's consider a point p belonging to a rigid body. Let r denote the body's center of gravity and let ṙ and ω denote respectively the object's translational and rotational velocities at a given time. Then, the instantaneous velocity of p is ṗ = ṙ + ω ∧ (p -r). Now if i and j denote two objects, then the velocity of p from object i relatively to object j is:

ṗij = ṗi -ṗj = a ij + p ∧ (ω j -ω i ) (1)
where a ij = ṙiṙjω i ∧ r i + ω j ∧ r j . Relative velocities are linearly related. If p 1 ,. . . p t denote some motions to estimate lower bounds on time of impacts, they don't use the motion direction, as in Vanecek [START_REF] Vanecek | Back-Face Culling Applied to Collision Detection of Polyhedra[END_REF].

points from object i, then

p = t s=1 α s p s ⇒ ṗij = t s=1 α s ṗs ij (2)
for any (α 1 , ..., α t ) ∈ IR t . Now, if p denotes a point from face m in object i, and n m denotes the outward normal to the face, then p is moving backwards relatively to object j if and only if ṗij .n m < 0

Relation ( 2) and the linear property of the dot product leads to the following convex property:

( ṗs ij .n m < 0, 1 s t) ⇒ ( ṗij .n m < 0) (4)
for any point p in the convex hull of p 1 ,. . . p t . In Vanecek [START_REF] Vanecek | Back-Face Culling Applied to Collision Detection of Polyhedra[END_REF], this property is used to cull faces in two steps3 :

Compute extremal vertices' velocities

An enclosing convex polygon is associated to each face. The velocities of the vertices p 1 ,. . . p t of the enclosing polygon are computed from equation (1).

Perform culling tests

For each vertex p s of the enclosing convex polygon, a culling test is performed as in equation [START_REF] Cohen | I-COLLIDE: an interactive and exact collision detection system for largescale environments[END_REF]. If every vertex p s is culled, then the face is culled.

Bounding-Volumes Hierarchies

Using bounding-volumes hierarchies (BVH) is a common strategy in collision detection and other domains (rendering for example). Briefly, overlap tests between bounding-volumes are used to cull many irrelevant elementary tests between objects parts. Let's assume, for example, that each of the two objects currently processed by the CD algorithm is bounded by a sphere. If the spheres don't overlap, then there can't be any collision between the objects. If the spheres do overlap, however, then there may be a collision between the objects. In this case, the spheres are replaced by unions of smaller spheres and overlap tests between spheres are recursively performed. When spheres sizes are smaller than a pre-determined threshold, exact tests are performed between the object geometries (for example, triangle/triangle collision tests, in the case of triangle soups). For rigid objects, bounding-volumes hierarchies are usually computed offline. Some typical examples of BVs are spheres [START_REF] Hubbard | Collision detection for interactive graphics applications[END_REF], axis-aligned bouding boxes (AABBs), oriented bounding boxes [START_REF] Gottschalk | OBB-Tree: A Hierarchical Structure for Rapid Interference Detection[END_REF] (OBBs), and k-dops [START_REF] Klosowski | Efficient Collision Detection Using bounding-volume Hierarchies of k-DOPs[END_REF].

In order to include the backward-motion (BM) culling test in the BVHs traversal algorithm, this paper suggests to extend the BV/BV overlap test in the following way:

1. If one of the two BVs has already been BMculled (checked through a flag set in step 3), return, else go to 2.

2. Perform the BV/BV overlap test. If the BVs don't overlap, return, else go to 3.

Perform the BM culling test for each BV in turn.

If one BV is BM-culled, mark it and return.

For clarity, a simple definition will be useful in the remaining of the paper: in the following, the triangles associated to any particular node of a boundingvolumes hierarchy are the ones found in its descendent leaf-nodes.

Method Overview

In order to get a constant-time backward-motion culling test for a bounding-volume, we adapt both steps from Section 2.1. Precisely, whatever the number k of triangles associated to the bounding volume, the following algorithm is used:

Compute characteristic points' velocities

Instead of computing the velocities of the 3k vertices defining the k triangles, we compute the velocities of a fixed number of characteristic points c 1 , . . . c t whose convex hull contains the bounding-volume. For AABBs or OBBs, for example, the corners may by used (t = 8).

From the linear property (2) of relative velocities, the characteristic points' velocities approximate the triangles velocities. Since the number of characteristic points is fixed for a given bounding-volume type, the velocities computation is performed in constant-time, whatever the number of triangles associated to the bounding-volume.

Perform conservative culling tests

From the convex property (4), the characteristic points' velocities can be used to cull a triangle associated to a bounding-volume. However, culling all the triangles would still be linear in k.

BM v = r m=1 H(ñ m ) ⊂ k m=1 H(n m ) ( 5
)
where r is smaller than a user-defined constant r max . BM v is the polyhedral backward-motion cone (BMcone) added to the bounding-volume. Thus, the bounding-volume v is BM-culled when

ċs ij ∈ BM v , 1 s t (6)
r is the size of the BM-cone. Since t and r max are fixed, the bounding-volume culling test is performed in constant time.

Since constraint [START_REF] Hubbard | Collision detection for interactive graphics applications[END_REF] implies

ċs ij ∈ r m=1 H(ñ m ) ⇒ ċs ij ∈ k m=1 H(n m ) (7)
for 1 s t, all triangles associated to the bounding-volume are necessarily moving backwards when equation ( 6) culls the bounding-volume. Yet, this culling test is only conservative: it may fail even though every triangle associated to the boundingvolume is moving backwards.

The reasons for this should be clear. First, triangles velocities are approximated through those of a few characteristic points. And second, triangles normals are approximated through the backwardmotion cone. However, as the bounding-volumes hierarchy is being descended, the bounding volumes fit the object geometry better and better. Thus, these approximations are more and more precise and the backward-motion cone allows to cull more and more backward-moving triangles. Figure 1 depicts this phenomenon: as the hierarchy is descended, the BMculling tests allows to cull more and more bounding volumes (and thus more and more groups of associated triangles). 4 Building enhanced bounding-volumes hierarchies

Building hierarchies of BVs

Algorithms which compute bounding-volumes hierarchies can generally be split into two categories: top-down and bottom-up approaches. In the case of top-down approaches, a rule is used to split the triangles list for a given node into two sublists. Typical splitting rules include Min Sum, Min Max, Splatter and Longest Side [START_REF] Klosowski | Efficient Collision Detection Using bounding-volume Hierarchies of k-DOPs[END_REF]. Note that the choice of the splitting rule is generally independant of the choice of the bounding-volume.

In order to take advantage of BM-culling, a natural idea consists in deriving a splitting rule based upon the normals repartition. Thus, denoting n 1 , ... n k the triangles normals associated to the current bouding-volume, the normals mean µ = 1 k k i=1 n i is computed, as well as a covariance matrix C:

C lm = 1 k k i=1 (n i [l] -µ[l])(n i [m] -µ[m]) (8)
where 1 l, m 3, n i [l] and µ[l] denote vectors coordinates, and C lm denote the matrix components. This covariance matrix is diagonalized and the triangles are distributed into two sublists according to their normal projection along the greatest variance direction.

However, this idea misses the point of collision detection since the method is unable to compute tight bounding-volumes hierarchies. Instead, we suggest to use a traditional splitting rule (the MinMax rule for example). It turns out that, as the hierarchy is being descended, the local curvature is lower and lower and the normals vary less and less, enabling efficient BM-culling. While some future work include the search of a mixed splitting rule, which would use triangle normals and positions 4 , traditional splitting rules proved to be sufficient to yield significant speedups (see Section 7).

Adding BM-cones

Adding BM-cones in bounding-volumes is independent of the kind of approach used to build the bounding-volumes hierarchy, and the addition itself can be performed top-down or bottom-up. In the top-down case, the BM-cones are computed from the triangles normals n 1 , . . . n k associated to the bounding-volumes. In the bottom-up case, the BMcones are recursively computed from those of the bounding-volumes child-nodes according to the following rules:

1. The BM-cones of leaf bounding-volumes are computed from the triangles normals.

2. If (and only if) all child-nodes have a BM-cone, the BM-cones of internal nodes are computed from the BM-vectors in all child-nodes.

Note that using a bottom-up approach still provides conservative tests. If BM v1 , . . . BM vc denote the BM-cones in the bounding-volume's child-nodes, then

BM v ⊂ c i=1 BM vi (9)
Whereas the top-down approach yields more precise results (and, thus, bouding-volumes are more often BM-culled), the bottom-up approach is typically much faster and is preferably used for large models.

Building the backward-motion cone

In this section, we describe an algorithm able to build a bounding-volume's BM-cone from a set of vectors n 1 , . . . n k . From the previous section, these vectors are triangles normals or BM-vectors of all child-nodes.

Preliminaries

We need the following definitions:

Definition (Positive cone). The positive cone

P(v 1 , . . . , v k ) generated by k vectors v 1 , . . . v k in IR 3
is the set of positive linear combinations of these k vectors:

P(v 1 , . . . , v k ) = k m=1 λ m v m , λ m 0, 1 m k Definition (Minimal subset). Let v 1 , . . . v k be k vectors in IR 3 .
In this paper, a minimal subset of this vectors is a smallest set of s vectors v i1 , . . . v it of these k vectors such as

P(v i1 , . . . , v it ) = P(v 1 , . . . , v k ).
In other words, a minimal subset is a smallest subset of vectors which generate the same positive cone.

The vectors in a minimal subset are on the convex hull of the positive cone.

The constraint on the backward-motion cone is the inclusion property [START_REF] Hubbard | Collision detection for interactive graphics applications[END_REF]. Consequently, we are interested in building the BM-cone only when k m=1 H(n m ) is non-empty 5 . The following lemma indicates when the search for a BM-cone can be avoided:

Lemma 1. Assume P(n 1 , . . . , n k ) = IR 3 , then k m=1 H(n m ) is empty.
Proof. Assume there exists x ∈ IR 3 such as x.n m < 0, 1 m k (then x = 0). Since x ∈ P(n 1 , . . . , n k ), there exists k positive values λ 1 , . . . λ k such as x = k m=1 λ m n m . Since x = 0, at least one of these values is strictly positive. However, ||x|| 2 = x.x = k m=1 λ m x.n m < 0. This is impossible.

Note that this lemma only allows to avoid the construction of most unuseful (empty) BM-cones. Sometimes n 1 , . . . n k may not generate IR 3 while k m=1 H(n m ) is empty. This occurs for example when P(n 1 , . . . , n k ) contains a full line or a plane, but does not contain IR 3 . In these (rare) cases, our algorithm computes a set of r vectors ñ1 , . . . ñr . However, the resulting BM-cone is empty.

In order to practically determine when P(n 1 , . . . , n k ) = IR 3 , our algorithm uses the following lemma: Lemma 2. P(n 1 , . . . , n k ) = IR 3 if and only if (±1, 0, 0), (0, ±1, 0) and (0, 0, ±1) are in P(n 1 , . . . , n k ).

Proof. Let i = (1, 0, 0), j = (0, 1, 0) and k = (0, 0, 1). Assume ±i, ±j and ±k are in P(n 1 , . . . , n k ), and let x = x i i+x j j+x k k. Assume for example that x i 0, x j < 0 and x k 0. Then x = x i i + |x j |(-j) + x k k. Since i, -j and k are in P(n 1 , . . . , n k ), x is also a positive linear combination of n 1 , . . . n k . The seven other sign combinations are similar.

One final lemma is used by our algorithm to search for vectors ñ1 , . . . ñr satisfying condition (5):

Lemma 3. If n m ∈ P(ñ 1 , . . . , ñr ), 1 m k, then BM v ⊂ k m=1 H(n m ). Proof. Let x denote a point in BM v , then x.ñ m < 0, 1 m r.
For any 1 m k, since n m is a positive linear combination of ñ1 , . . . ñr , and since the dot product is bilinear, x.n m < 0. Since (n m ∈ P(ñ 1 , . . . , ñr ), 1 m k) ⇔ (P(n 1 , . . . , n r ) ⊂ P(ñ 1 , . . . , ñr )) [START_REF] Press | Numerical Recipes in C: The Art of Scientific Computing[END_REF] Lemma 3 indicates that a way to compute the BM-cone is to find a positive cone bounding P(n 1 , . . . , n r ). In order to BM-cull the boundingvolume as often as possible, the r vectors ñ1 , . . . ñr are chosen so as to minimize the difference between the BM-cone BM v and k m=1 H(n m ). Thus, the positive cone P(ñ 1 , . . . , ñr ) should be the tightest positive cone bounding P(n 1 , . . . , n k ).

The algorithm

The interest in using positive cones representations of vectors sets is that they provide a way to measure the difference between BM v and k m=1 H(n m ): in our algorithm, this difference is measured by computing BM-vectors' distances to P(n 1 , . . . , n k ).

Precisely, we use Wilhelmsen's algorithm [START_REF] Wilhelmsen | A Nearest Point Algorithm for Convex Polyhedral Cones and Applications to Positive Linear Approximations[END_REF] to compute the projections ñ * 1 = W(ñ 1 ), . . . ñ * r = W(ñ r ) of the BM-vectors on P(n 1 , . . . , n k ). The required distances are simply

d 1 = ||ñ 1 -ñ * 1 ||, . . . d r = ||ñ r -ñ * r ||.
Especially, Wilhelmsen's algorithm allows to know that a point belongs to a positive cone when the distance between the point and its projection is zero.

The algorithm building a BM-cone can now be described:

1. Preliminary test Compute W(±i), W(±j) and W(±k). If every point projects on himself, then return. No non-empty BM-cone can be built. Else, go to step 2.

Minimal subset computation

Use Wilhelmsen's algorithm to repeatedly remove vectors which are linearly dependent of the others and obtain a minimal subset v i1 , . . . v it6 . If t is smaller than r max , then return the minimal subset as the set of BM-vectors. Else, go to step 3.

BM-cone initialization

Compute the minimal vectors mean m = 1 t t j=1 v ij . Randomly pick up r max vectors ñ1 , . . . ñrmax from the minimal subset until m is in P(ñ 1 , . . . , ñrmax ) (r max should be greater than 3). Push the r max vectors outside P(v i1 , . . . , v it ) (ie in the directions ñi -m).

BM-cone refinement

Continuous culling

For now, the method only depends on relative velocities at a given instant. While this is valid for discrete collision detection methods, which detect objects interpenetrations at successive instants, this may not be suitable for continuous collision detection methods, which use the objects' motions between these instants to compute collision times (see for example [START_REF] Cameron | Collision detection by four-dimensional intersection testing[END_REF][START_REF] Canny | Collision detection for moving polyhedra[END_REF][START_REF] Redon | An Algebraic Solution to the Problem of Collision Detection for Rigid Polyhedral Objects[END_REF][START_REF] Snyder | Interval Methods for Multi-point Collisions between Time-Dependent Curved Surfaces[END_REF]). For these methods, the relative motion over a time interval may be general, and a triangle moving backwards at the beginning of the time interval may not do so during the whole time interval. However, the culling tests can be simply extended using interval arithmetic [START_REF] Snyder | Interval analysis for Computer Graphics[END_REF].

Essentially, interval arithmetic allows to bound functions ranges over intervals. Precisely, for any given function f : IR → IR, an inclusion function f : IIR → IIR is associated to f , such as:

t ∈ I ⇒ f (t) ∈ f (I) (11)
for any interval I. Thus, the dot products in the culling test (6) yield interval results:

ċs ij .ñ m ∈ [l s,m , u s,m ] (12)
and a bounding-volume is culled when u s,m < 0, 1 s t, 1 m r.

Results

The method has been implemented and added to CONTACT Toolkit, our simulation system [START_REF] Redon | An Algebraic Solution to the Problem of Collision Detection for Rigid Polyhedral Objects[END_REF][START_REF] Redon | Gauss' least constraint principle and rigid body simulations[END_REF][START_REF] Redon | Fast continuous collision detection between rigid bodies[END_REF]. Preliminary experiments have been conducted with industrial data (two instances of the door in Figure 1, 3530 triangles). One test constituted the hard-case for any collision detection method: a mobile object comes in close-proximity with a static object and goes through different contact configurations (transient and permanent contacts). The object's motions were recorded and replayed without and with BM-culling. For the tests, r max was set to 5 and the BM-cones were built using the bottomup method.

Conclusion

This paper has described a backward-motion culling test that allows to detect in constant-time situations where every triangle associated to a boundingvolume is moving backwards, and thus cull this bounding-volume during the BVHs traversal. This test is based upon the addition of some geometrical information in the bounding-volumes. An algorithm able to compute this geometrical information has been described. The method has been implemented and the conducted experiments suggest that the method allows to significantly speed up the collision detection, especially in close proximity situations.

Figure 1 :

 1 Figure 1: Hierarchical BM-culling of a moving door. Faces moving forwards are shown filled. The door is translating away from the viewer (snapshots a, b and c are taken at the same time, though). As the hierarchy is descended, the BMculling tests allows to cull more and more bounding volumes (and thus more and more groups of associated triangles). Levels of the BVH: a=7, b=9 and c=11.

  Precisely, each characteristic point c s is tested against each precomputed vector ñm as in equation[START_REF] Cohen | I-COLLIDE: an interactive and exact collision detection system for largescale environments[END_REF]. The bounding-volume is culled if all of the t × r tests are successful. IR 3 , x.n m < 0} the open half-space defined by n m , then p from i is moving backwards from j if and only if ṗij ∈ H(n m ). Using this notation, the constraint on the precomputed BM-vectors can be expressed simply: ñ1 , . . . ñr are chosen such as

	The precomputed vectors are chosen so as to pro-
	vide a constant-time conservative culling test. First,
	note that the elementary culling test (3) can be ex-
	pressed geometrically. Denoting H(n m ) = {x ∈

Thus, we use a bounded number of precomputed backward-motion vectors (BMvectors) ñ1 , . . . ñr which suitably approximate the set of triangle normals.

  Progressively refine the BM-cone thanks to a simulated annealing algorithm[START_REF] Press | Numerical Recipes in C: The Art of Scientific Computing[END_REF]. Briefly, BM-vectors are slightly modified step after step. Modifications are valid if the inclusion constraint (5) holds and if the increase in the distances d 1 , . . . d rmax ins't greater than a predetermined ratio. Wilhelmsen's algorithm is used to check the inclusion constraint (through Lemma 3) and to compute the distances.

Table 1 :

 1 Table 1 reports the resulting numbers of BV/BV overlap tests, edge/edge, vertex/face and face/vertex tests in each case7 , and shows that BMculling allows to reduce significantly the number of all kinds of tests, and results in an important speedup. BM-culling allows to significantly reduce the number of bounding-volume/bounding-volume (BV/BV), edge/edge (EE), vertex/face (VF) and face/vertex (FV) tests, which results in an important speed-up.

		Without BM-culling	With BM-culling
	BV/BV Tests	4.837.443	3.514.144
	E/E Tests	3.572.298	1.622.297
	V/F Tests	1.170.412	528.195
	F/V Tests	1.169.060	528.553
	Total time	15.46 sec.	11.85 sec.

For convex objects, however, separating plane algorithms are somewhat insensitive to the objects positions and orientations, even in close-proximity situations. Also, the incoming constraint in Snyder et al.[START_REF] Snyder | Interval Methods for Multi-point Collisions between Time-Dependent Curved Surfaces[END_REF] can be seen as back-face culling applied to collision detection between parametric or implicit surfaces.

[START_REF] Canny | Collision detection for moving polyhedra[END_REF] While some time-scheduling methods[START_REF] Mirtich | Impulse-based dynamic simulation of rigid body systems[END_REF] use the objects

Note that, actually, the velocities computations and the culling tests are interleaved in order to return earlier when a face is moving forwards. Hovever, all faces still have to be tested.

For example, Kumar et al.[START_REF] Kumar | Hierarchical back-face computation[END_REF] describe a method to perform hierarchical back-face culling for rendering which computes clusters from both faces normals and positions.

when k m=1 H(nm) is empty, at least one of the triangle associated to the bounding-volume is moving forwards, whatever the object's motion.

For a large-scale implementation, however, we suggest to adapt a convex hull algorithm.

Since our simulation system uses a continuous collision detection method, these are the only contact types that can occur.

Acknowledgments

The authors would like to thank Renault for providing the car model. The model parts are c Renault. Tangui Morvan, especially, has to be thanked for coding an inventor parser able to load the provided models. This research was funded by the French Ministry of Research through an AMX grant and the RNTL PERF-RV project.


Frederik Tielens

Dominique Bazin
email: dominique.bazin@upmc.fr

Operando Characterization and DFT Modeling of Nanospinels: Some Examples Showing the Relationship with Catalytic Activity

Keywords: XA, AWAX, DFT, Spinels, Zn, Co, Al

In this paper we have presented results on spinel nano-materials considering a collection of techniques, which is considered today a state-of the-art in the field of catalyst research (characterization and study of structure/reactivity relationship). Through a selected collection of techniques, experimental as well as theoretical, we illustrate this setup of techniques on the characterization of spinels (ZnAl 2 O 4 ) through XAS and by wide angle anomalous X-ray scattering (AWAXS). The effect of Al/Zn substitution was investigated as well and related Co/Al spinels were investigated on their catalytic properties using DFT. The catalytic properties towards NO, O 2 , and NH 3 are explored for the very first time on the Co/Al spinel surfaces, and possible reaction mechanisms proposed.

Introduction

As underlined by G. Ertl [1], it is after a report of J.W. Doebereiner regarding the reaction of hydrogen gas with oxygen on finely divided platinum powder that Berzelius defined this phenomenon as "catalysis", rather in order to introduce a classification than to offer a possible explanation. In fact, the definition of "catalysis" has been given by W.

Ostwald [2,3]: "A catalyst is a substance which affects the rate of a chemical reaction without being part of its end products". A significant breakthrough has been then performed by 1912 Nobel prize winner Paul Sabatier [START_REF] Sabatier | La catalyse en chimie organique[END_REF] when he suggested the presence of more or less stable reaction intermediates. J.C. Vedrine [START_REF] Vedrine | [END_REF]6] gives an elegant definition of the concept designated as "Sabatier principle". When a reactant is adsorbed on a catalyst surface, its energy of interaction should be strong enough for activation but not too strong to permit products to be desorbed (volcano curve of activity vs energy of adsorption). Such general explanation of catalytic phenomena based on the idea of the "temporary formation of unstable chemical compounds which, serving as intermediate steps in the reaction, determine its direction and increase its velocity".

Nowadays, many heterogeneous catalysts used in chemical industry consist of oxides.

As underlined by J.C. Vedrine et al. [START_REF] Vedrine | [END_REF]6], oxides are semiconductors or insulators and are used as active phases, as supports for active phases or even as both. Such catalysts exhibit redox properties (e.g. usually for transition metal ion oxides [START_REF] Millet | Role of water on the properties of FePO catalysts used for the oxidative dehydrogenation of isobutyric acid[END_REF]), or acid-base properties (e.g.

for MgO, SiO 2 -A1 2 O 3 , zeolites [START_REF] Vedrine | [END_REF]).

In order to describe catalytic reactions and active sites, a first step is given by a determination of the surface structure of the catalyst under reaction conditions. Such approach has to be completed by a fine description of the reaction mechanism, including the way the reactant molecules are adsorbed and activated. Numerous techniques, experimental and computational [START_REF] Che | Characterization of Solid Materials and Heterogeneous Catalysts: From Structure to Surface Reactivity[END_REF][START_REF] Tielens | [END_REF], have been developed to depict at the atomic scale the surface structure of catalysts. For example, spin-echo mapping technique is a powerful technique for determining the oxidation state of V through the chemical shift of 31 P NMR peak [11]. The complete set of data shows clearly the complexity of transformations in VPO materials during preparation, activation and reaction, and leads to meaningful structure-activity relationships [12].

In this contribution, we would like as a first example to assess operando characterization of oxides through synchrotron radiation related techniques. For that purpose, we consider the NO decomposition process on nanospinels ZnAl 2 O 4 . As underlined by F. Garin [13], research A c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 4 4 on such catalytic reaction starts in the 1960s and corresponds to the emergence of the notion of the environment quality. We start this contribution by recalling some basic notions regarding the emissions of CO, HC, NOx and particulates caused by traffic emissions, then we will present the different catalytic systems which have used different very strict legislation appeared, reduce the nitric oxide concentration in exhaust gas typically averages 600-1200 ppm, depending on the engine combustion conditions, diesel or gasoline, and on the driving conditions. In the second part we present complementary computational results. In our group DFT studies have been conducted on a broad set of systems such as MgO [14], SiO 2 [15][16][17][18][19][20],

TiO 2 [21][22][23], V 2 O 5 [24], CeO 2 [25], Al 2 O 3 [26], zeolites [27] etc. In this paper we present, results on spinels, on reactions related to the formation of nitric acid.

Generalities

Nowadays, significant characterization of catalysts made of nanoparticles is a reality [28][29][30][31][START_REF] Rodriguez | In-situ Characterization of Heterogeneous Catalysts[END_REF][START_REF] Bazin | [END_REF][34]. Among the different techniques which can be used such as high-resolution transmission electron microscopy [35][36][37] or X-ray photoelectron spectroscopy [38], X-ray absorption spectroscopy (XAS) [39,40] using either soft (K edge of light elements as well as L edge of 3d transition metals) [41,42] or hard X-rays (K edge of 4d transition metals as well as L edge of 5d transition metals) [43,44] play a pivotal role not only in catalysis [START_REF]X-ray Absorption Fine Structure for Catalysts and Surfaces[END_REF][START_REF] Guczi | [END_REF][47][48][49][50][51] but also in material science [52][53][54][55][56][57][58]. This is mainly due to the opportunity to combine at the very same time this technique specific to synchrotron radiation with other more classical spectroscopies such as Infrared [59,60], Raman [61,62], UV visible [63] spectroscopies or other techniques such as mass spectrometry with high time resolution [64]. Different breakthroughs have been also performed by combining XAS and X-Ray diffraction in heterogeneous catalysis [65][66][67][68][69][70][71][72][73][74][75][76][START_REF] Cai | Science China Chemistry in press[END_REF] and more precisely on spinel [START_REF] Beale | [END_REF]. Such approach allows the chemist to collect information on the catalytic reaction through the metal or the cations (through XAS) and through the molecules which interact at the surface of these nano-objects (through vibrational spectroscopies or through soft XAS [79]) at the very same time and on the very same catalyst. Note that such structural description is performed while the activity and selectivity of the reaction is measured [80,81]. Thanks to the different technological developments which have been performed on the optics and the detection, data acquisition can be done now at the milli [82,83] or at the microsecond [84,85] scale. Note that this technique has a major drawback, Exafs in unsensitiv to polydispersity [86,87]. From a fundamental point of view, some questions arise regarding the possibility to establish a significant relationship between the catalytic reaction (its activity and its selectivity) and the structural parameters which can be determined through XAS data.

Regarding the kinetic, F. Thibault-Starzyk et al. [88] have pointed out that an acquisition time of milliseconds may not be relevant to explain the catalytic behaviour of a catalyst. Moreover, we have to underline that numerical simulations of XAS data is not easy when nano-objects are taking into account. We have already discussed the case of nanometer scale metallic particles [89,90] and we will see in the next paragraph that the same difficulty exist for nanometer scale oxide particles. All these difficulties call for at the same time a critical discussion of the experimental data and a need to use theoretical tools. It is quite clear now that only such approach which combines experimental data coming from very different techniques collected while the chemical reaction occurs and theoretical simulations [91] using for example the DFT formalism will lead to a significant understanding of complex chemical reaction related to catalytic reactions.

Characterization of Nanomaterials through XAS

An elegant way to understand why special attention has to be paid to XAS data analysis of nanomaterials is given by the golden rule [START_REF] Park | Introduction to the quantum theory[END_REF]. From theoretical considerations, W, the probability per unit time for a transition from an initial state │i> to a final state │f> by the action of a perturbation (here, it is an X-ray photon) is equal to 2 πh│<i│H│f>│ 2 (E f ), where (E f ) is the density of final state. The fact that the density of state constitutes a physic parameter at the core of the peculiar properties of nanomaterial indicates clearly that special attention has to be paid on the data analysis procedure [START_REF] Friedel | Physics of Metals[END_REF][START_REF] Friedel | [END_REF].

In the case of nanometer scale metallic clusters [95][START_REF] Sarma | Nanotechnologies for the Life Sciences[END_REF][START_REF] Wang | [END_REF], we have already shown that a strong correlation exists between the shape of the absorption edge [98] and the size of the cluster through ab initio calculation [99,100]. Thus, to explain the variations of the shape of white line intensity present at the absorption edge, it is not necessary to assume a charge transfer. Such properties exist also with oxide materials, and numerical simulations have been showed significant differences between simulations obtained for CoO bulk and ones corresponding to the 13Co6O clusters [101].

The case of nanomaterials made of spinel such ZnAl 2 O 4 [102,103] is even more exciting. The starting point is given by a comparison between the Zn K and L III edge for the reference compound ZnAl 2 O 4 (figure 1). This compound is associated to Zn 2+ cations (3d 10 A c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 6 6 configuration). The strongest bonding effect in this 3d oxide is due to the overlap between the oxygen 2p band (filled) and the Zn 4s and 4p bands (empty) which forms the shape of the oxygen 2p valence band and also the Zn 4s and 4p conduction band. From an experimental point of view, the similarity observed between the K and the L edge leads to the fact that some overlap exists between the conduction band (zinc 4s and 4p with oxygen 2p) and the 3d band, creating very weak 3d character following the same shape as the 4p states.

The case of nanomaterials made of spinel such ZnAl 2 O 4 [104] is even more exciting.

The starting point is given by a comparison between the Zn K and L III edge for the reference compound ZnAl 2 O 4 (figure 1). This compound is associated to Zn 2+ cations (3d 10 configuration). The strongest bonding effect in this 3d oxide is due to the overlap between the oxygen 2p band (filled) and the Zn 4s and 4p bands (empty) which forms the shape of the oxygen 2p valence band and also the Zn 4s and 4p conduction band. From an experimental point of view, the similarity observed between the K and the L edge leads to the fact that some overlap exists between the conduction band (zinc 4s and 4p with oxygen 2p) and the 3d band, creating very weak 3d character following the same shape as the 4p states. A careful analysis of the X-ray absorption spectra indicates that significant differences exist between the reference compound and the nanomaterial. At the K edge, the amplitude of the first peak of the catalyst is clearly lower than the one associated with the reference compound. At the L edge (Figure 3), even if each feature present at the edge exists, the amplitudes are significantly different between the two compounds. Numerical simulations using the code FeFF8MPI [105,106] and a NERSC parallel machine with a cluster of 200 atoms were performed and quantitative agreements have been obtained. Such approach based on K and L edges have been also used in the case of Pd catalysts [107].

Regarding the literature dedicated to spinel compounds used as catalysts, numerous publications have been supported by XAS data [108][109][110][111][112][113][114]. Among them several are focused on Fischer-Tropsch synthesis for which the Co/Al 2 O 3 catalyst is the reference [115][116][117][118][119]. Indeed Co 3 O 4 is a spinel structure, with one-third of the Co 2+ occupying tetrahedral sites and two-thirds occupying octahedral sites and that CoAl 2 O 4 is a normal spinel with Co 2+ ions in tetrahedral sites. Improving the stability of such material constitutes an important challenge facing the commercial development of these catalysts for the conversion of coal, biomass, and natural gas to liquid fuels as alternative resources to crude oil. Recently, G. Jacobs et al. [120] have assessed the use of synchrotron radiation techniques to confront issues associated with cobalt [121][122][123][124][125] and iron catalysts. These authors underlined that there has been an important spike in publications in the area of Fischer-Tropsch synthesis regarding the application of synchrotron radiation techniques which appear as major tools in catalysis. Among the different breakthroughs which have been done, these authors quote the manner in which cobalt catalysts reduces (i.e., a two-step reduction process by way of Co 3 O 4 , CoO, and Co 0 ), the manner in which iron catalysts undergo carburization, the influence of promoters on cobalt reduction in hydrogen and iron oxide carburization and also the local atomic structure of common promoters in Co catalysts.

Opportunities offer by wide angle anomalous X-ray scattering (AWAXS)

Even for the ZnAl 2 O 4 spinel systems which can be considered quite simple because only the T d geometry has to be considered for Zn 2+ cations, different structural parameters have to be considered. For example, we have to assess the size and the morphology of these structural parameters can be difficult to assess through X-ray absorption spectroscopy due to the presence of multiple scattering processes of the photoelectron [126].

Different investigations have already been dedicated to heterogeneous catalysis [127][128][129][130], AWAXS experiments being a more easy way to consider such structural parameters [START_REF] Guinier | Théorie et technique de la radiocristallographie[END_REF][START_REF] Bazin | [END_REF][133][START_REF] Waseda | Novel Application of anomalous (resonance) X-ray scattering for Structural characterization of disordered material[END_REF][135][START_REF] Hodeau | Neutron and X-ray Spectroscopy[END_REF][START_REF] Shmakov | [END_REF][138]. This technique is based on the energy dependence of the atomic scattering factor, f(k,E), near an absorption edge. As a simplification, this parameter is expressed in electron

units as f(k,E)=f 0 (k) + f'(E) + if''(E)
where k (k = 4π sinθ/λ) bisects the angle between the incident and scattered directions and also defines the scattering plane. f 0 (k) (which has evaluated by Cromer and Mann [139]) is the energy independent part of f(k,E) the amplitude of the radiation coherently scattered by a single atom while f'(E) and f''(E) (which have been calculated by S. Sasaki [140]) are respectively the real and imaginary energy dependent correction. The success of the AWAXS technique [141][142][143] comes its ability to estimate the scattering intensity of nanometer scale clusters though the Debye equation [144]. Assuming a random (powder) arrangement of the structure with respect to the incoming X-ray beam, the intensity of coherently scattered X-rays is given by:

I(k,E) =ΣΣ ij f i (k,E) f j (k,E) sin(kR ij )/kR ij (1)
In this equation, I(k,E) is the intensity from coherent scattering, the sums over i and j are over all the atoms, R ij being the distance between the atom i and j and f i and f j being the

, and (111), the most stable one (100) has been chosen for the adsorption studies. For CoO (rock salt structure), the choice of the (100) face is obvious.

Computational details

Every geometry optimization (relaxation) and minimization of the total energy has been performed using the VASP code [147,148]. The energy calculated in VASP is the total energy, which is directly related to the thermodynamics, although at 0 K. In the periodic DFT framework used, the Kohn-Sham equations have been solved by means of the generalized gradient approximation (GGA-PW91) proposed by Perdew and Wang [149,150]. High level calculations: For the calculation of the bulk, surfaces, and single adsorptions the plane-wave expansion was truncated at a cut-off energy of 400 eV. For the Brillouin-zone integration a 6×6×6 Monkhorst-Pack special k-points grid has been used; the number of k-points has been We carefully checked the convergence of the energy with respect to the k-points. A spinunrestricted approach has been employed and the spin state has been optimized. A full optimization of atom positions, cell shape and volume has been performed via the action of a conjugate gradient optimization procedure.

A brief comparison of the two levels of calculation may be found looking at

Thermodynamics of adsorption and co-adsorption involving the NH x O y species

To our knowledge, the study of the surfaces and bulk of the Co/Al spinels has not been published before. However, some theoretical studies using periodic DFT have already been published on related topics: adsorption of CO on Co 3 O 4 spinel [151,22] and reactivity of Cu 2 AlO 4 towards ammonia [23].

Concerning the reaction paths, no studies on the adsorption of NH 3 on oxides were found in literature, in particular none on a Co/Al spinel type surface. An overview of the experimental and theoretical data when available can be found in [19].

The topology and electronic structure surfaces

For the bulk we have selected various spinels of different composition: (Co For all the spinels studied, the most stable surface was found to be the (100) surface (see Table 1, annex), confirmed by experimental findings [24]. In the following, we assume that the adsorption take place on the terraces of this surface.

From the point of view of reactivity, it is interesting to note that the cation T d site (see fig 5

The adsorption of reactants and products on the most stable surfaces

We have focused on the interaction/adsorption of NH The crystals where the adsorption is calculated to be strong are those expected to be poorly reactive from experiment [25]. Since NO adsorption is the strongest, it might decrease the reactivity. It has been suggested [19] that there is an optimal range (window) for the It is not obvious that strong adsorption is necessary. A weak adsorption might be more promising for reactivity. The rate determining step might differ from the adsorption process.

The effect of co-adsorption is studied in the next part. Finally, it should be recalled that for this study on the (100) surface, we have made the assumption that reactions occurred on terraces of the most stable surface. Steps, edges and other surfaces might be important favoring dissociation of adsorbates. In summary the adsorption mode of lowest energy correspond to the molecular adsorption (no dissociation). The adsorption trend: NO> O 2 > NH 3 can be observed on all the surfaces studied. Concerning the adsorbates, the adsorption strengths decreases as following:

CoAl 2 O 4 > Co 3 O 4 > Co 2 AlO 4 > CoO.
It is interesting to note that NH 3 does not dissociate on the surface (associative adsorption), and that the "surface oxygen" is poorly reactive, whereas the Co Td is the most reactive site.

Considering only the oxygen atom already present on the naked surface and excluding adsorbed oxygen, therefore we also call them lattice oxygen. From these results it is obvious that CoAl 2 O 4 and Co 3 O 4 have too high adsorption energies; NH x species will reside too much time on the surface and react to N 2 . Co 2 AlO 4 is expected to be the best catalyst, having intermediate adsorption energies for O 2 and weak for NO. The above mentioned spinels have the lowest O 2 affinities of the spinels considered, however having a relative high affinity for NH 3 . CoO spinel is found to have a too low affinity for O 2 and NH 3 . Concerning the adsorption, the behavior of the different spinels is expected to be comparable. Important here, is that the lattice oxygen does not participate in ammonia conversion and its oxidation to NO.

Finally, the search for the optimal catalytic behavior (in practice) could not simply be related to the heats of adsorption of individual molecules. Here we have to make the hypothesis of a compromise between sufficient NH 3 adsorption and relatively weak O 2 adsorption which is the case of Co 2 AlO 4 .

The co-adsorption of NH 3 and O over Co 2 AlO 4 ; formation of NO

The co-adsorption of O and NH The ammonia oxidation in the presence of adsorbed oxygen is expected to follow the resulting equations: 5). However, the effect is much more pronounced for the (100) Co 2 AlO 4 surface. The energy values in Table 5 are obtained by making the difference between the adsorption energies of the individual molecular adsorptions and the co-adsorption. If the values are negative, co-adsorption is predicted to be more favorable than isolated adsorption, when positive values are obtained the opposite is true. The favorable co-operative effect (negative values) is thus due to the favorable balance between intermolecular interactions and steric hindering originating from the competition between the most favorable adsorption sites on the surface, which have to be shared between both competing molecules. In summary, strong co-adsorption effects, cooperative effect being 0. The structure where the H atom is transferred to the O atom is 0.51 eV higher in energy. As for the O 2 co-adsorption, this structure would mark a progress toward the N 2 formation, with the formation of an N-N bond and the cleavage of the N-O bond. The high energy value that is calculated signifies that this path is unlikely.

The total gain of energy for the formation of N 2 is very pronounced after the first intermediate (see the rapidly descending curve in figure 10). It is governed by the thermodynamics of the N 2 formation that is strongly exothermic. Let us note however that the cooperative effect remains negative for the three first intermediates (the energies are above the reference line in figure 10). Only the last and final step represents a gain in energy relative to the simple adsorption (first intermediate);

A

  c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 2 A c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 3

A

  c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 5 5

Figure 1 .

 1 Figure 1. Comparison between the Zn K and L III edge for the reference compound ZnAl 2 O 4 .

A

  c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 7 ZnAl 2 O 4 /γ c -Al 2 O 3 for the K (figure2) and L edge (figure3). At first glance, regarding the shape as well as the position of the edge, a great similarity exists between the catalyst and the ZnAl 2 O 4 spinel above the edge.

Figure 2 .

 2 Figure 2. Near edge region at the Zn K edge of the model compound ZnAl 2 O 4 (line) compared with the near edge region associated with the catalyst (dots).

Figure 3 .

 3 Figure 3. Near edge region at the Zn L III edge of the model compound ZnAl 2 O 4 (line) compared with the near edge region associated with the catalyst (dots).

A

  c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 8 8

ZnAl 2 O

 2 4 cluster, the Al/Zn substitution (Zn 1-x Al x )T d (Al 2 )O h O 4 with x = 0 -0.9 as well as the spatial distribution of Zn 2+ cations inside the ZnAl 2 O 4 nanocluster. As already discussed, A c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 9 9

  atomic scattering factors. Such Debye equation leads to figure 4 on which we have reported the set of calculations which allows us to estimate the variation in scattered intensities in the case of a Al/Zn substitution.

10 Figure 4 .

 104 Figure 4. Numerical simulations based on a substitution Al/Zn of (Zn 1-x Al x )T d (Al 2 )O h O 4 with x = 0-0.9.

  A c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 11 Nitric Acid formation on CoAl spinels: a DFT study Nitric acid (HNO 3 ) is industrially produced by the stepwise catalytic oxidation of ammonia (NH 3 ) at high temperatures (800-950°C) and pressures (1-12 bar) on platinum metal group (PGM) alloys. NO is first formed by the oxidation of NH 3 . High NO selectivities are obtained, however this technology presents two major drawbacks: formation of N 2 O as a byproduct and noble metal losses. Oxide-based catalysts represent an attractive alternative to noble metal alloys, due to a lower catalyst cost, the absence of expensive metal loss, and low N 2 O production. Co-and Fe-based spinel and perovskite catalysts are the most promisingcatalysts identified so far[146]. However, the lower NO yield achieved (promising systems give 85-90% as compared to 95% over PGM catalysts) makes difficult its industrial implementation. A detailed understanding of the reaction mechanism of ammonia oxidation over oxide-based catalysts may serve as a rational basis for an improved catalyst design. It involves studying not only the successive elementary steps of reaction between NH 3 and O 2 , but also secondary processes, e.g. the interaction of unreacted NH 3 with produced NO. In this way, activity and selectivity can be coupled.We present results on the following points: Choice of bulk for the catalyst: Co/Al spinels (Co 3 O 4 , Co 2 AlO 4 , CoAl 2 O 4 and Al 3 O 4 ) and the rock salt structure CoO. Co 3 O 4 is ranked as one of the most selective catalysts. Co 2 AlO 4 has been chosen to represent the family of the spinels in the extensive investigation of the reaction (cation nature, oxidation state, and position). Choice of surfaces: after studying the stability of the low index surfaces: (100),

  A c c e p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 12 12 adjusted to the size of the supercell considered in order to keep the same number of k-points in the reciprocal space. Low level calculations: In the case of the coadsorption study the energy cut-off was lowered until 250 eV and the Brillouin zone was integrated on a single k-point. This enabled us to calculate at a relative low calculation cost the different adsorption geometries of the reaction intermediates. The low level calculations were introduced in order to accelerate the calculations, since a relative large number of geometries (different adsorption combinations of the N x H y O species on the different adsorption sites, different possibilities for NH bond breaking and for H-transfer) have to be relaxed to obtain a reaction path. The size of the unit cells for the different models is in general rather large, leading to time-consuming calculations when the best accuracy is demanded.

A c c e

  p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 13 13 the O sublattice, Co 2+ occupies the tetrahedral site while Co 3+ and Al 3+ are within the octahedral site. The different spinels considered were investigated on bulk and surface properties, allowing the study of the influence of the cations. The calculated lattice parameters are in agreement with known experimental determinations. The bulk of the most common mixed Co/Al spinel CoAl 2 O 4 was investigated in detail, geometrically as electronically.

and 6 )

 6 is pointing out of the (100) surface and is under coordinated (bridging 2 oxygen ions) while cation O h in the surface layer preserve a high coordination (five-fold). The surface oxygen is 4-fould coordinated.

Figure 5 :

 5 Figure 5: The (100) surface of the CoAl 2 O 4 spinel.

14 Figure 6 :

 146 Figure 6: The (100) surface of the Co 2 AlO 4 spinel.

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  3 has been studied by adding a single O atom to the unit cell; the adsorption is referred to ½ O 2 . The results for O 2 are presented in the next section they correspond to the undissociated form of O 2 . When the O atom is placed above a surface O atom (vertical), it moves without barrier to bind to the CoT d .

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  Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 2020 The co-adsorption energy of ½ O 2 and NH 3 is 2.41 eV while the sum of individual adsorption energies (table3) represents 2.03 eV. The gain due to the coadsorption is 0.38 eV. We have not found a thermodynamically favored dissociation of NH 3 . The mode of lower energy found so far is represented in figure7b. Both OH and NH 2 are adsorbed on the CoT d . It costs 0.27 eV relative to the undissociated form (figure7a). We expect that the ammonia dehydrogenation is the rate-determining step in ammonia oxidation over cobalt spinels, however only the study of the transition state could be a proof. The NH 3 -NO coadsorption was done over Co 2 Al 2 O 4 . From some preliminary tests we expect no significant differences if going to CoAlO 4 and Co 3 O 4 systems.

Figure 7 :Figure 8 :

 78 Figure 7: a. Best co-adsorption geometry found for the adsorption of atomic oxygen; the O atom is on the CoT d . b. Best co-adsorption geometry found with NH 3 cleavage.

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  figure9, the progression (from left hand-side to right hand-side) correspond to an increase of the number of N-H bonds cleaved. Note that this scheme presents the thermodynamics (no transition states were computed); energy barriers are to be passed to go from one intermediate to the other.

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  p t e d M a n u s c r i p t Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 23 23 In the next step involving an additional H transfer, another basic site has to be found. In the present model, there is no other OH group and the choice is between an intramolecular transfer (j) and a transfer to lattice oxygen (d). Both are not very favorable. The lattice oxygen atoms are indeed stabilized by the Madelung field and poorly reactive. An extra OH group would be necessary. This conclusion can also be reached independently from the consideration of the stoichiometry of the oxidation reaction. The reaction 5 O 2 + 4 NH 3 → 4 NO + 6 H 2 O may be simplified to OH + O 2 + NH 3 → NO + 2 H 2 O that respects the oxidation numbers. It is clear from this equation that an OH should be present, participating to the redox mechanism.

Figure 9 :

 9 Figure 9: Different intermediates in the NH 3 + O 2 reaction. The line of zero energy corresponds to the addition of the adsorption energies of NH 3 and O 2 (no co-adsorption effect).

  Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity" 2424

A c c e p t e d M a n u s c r i p t 25 Figure 10 :

 2510 Figure 10: Different intermediates in the NH 3 + NO reaction, compared to the NH 3 + O 2 reaction. The line of zero energy corresponds to the addition of the individual adsorption energies (no co-adsorption effect).

Table 2

 2

and 3. It shows that E ads (NH 3 ) on Co 2 AlO 4 is unaffected (-0.86 eV vs. -0.85 eV), while that of NO is E ads (NO) is slightly decreased (-2.12 eV vs. -2.56 eV). Their relative order is preserved.

  3 O 4 , Co 2 AlO 4 , CoAl 2 O 4 and Al 3 O 4 ) and rock salt CoO. The first set (spinels) allows following the influence of the composition while preserving the structure. Cations are Co 2+ , Co 3+ and Al 3+ . Relative to

Table 1 :

 1 Surface energies for the low index surfaces of CoAl 2 O 4 spinel. Surface energies were calculated for the non-relaxed, atom positions 2 layer-relaxed in fixed volume, and full relaxation of volume and 2 layer atom positions of a 4 layer slab. In order to keep the stoichiometry 2 different surfaces were obtained (non-symmetric slab, here called upper and lower surface). AlO 4 has the least accessible Co T d . In other words for CoAl 2 O 4 the Co T d is more accessible for adsorption (in comparison with the other spinels). Note that a too high heat of adsorption of O 2 (see Table 2) may also favor the conversion of NH 3 to N 2 and thus may have to be avoided. But to model the reaction NH 3 + O 2 or O and NH 3 + NO we selected Co 2 AlO 4 due to the unexpected lower activity toward O 2 (vide ultra).

	Surface Slab termination E surf (J/m²) E surf (J/m²)	E surf (J/m²)
			Non opt.	At. Pos. 2layers relax.	Vol. and at. pos. 2layers relax.
	100	1	6.01	4.39
		2	2.44	1.93	1.77 (upper surf.)
		2			1.65 (lower surf.)
	110	1	3.28	3.26
		2			3.12 (upper surf.)
		2	2.59	2.59	3.16( lower surf.)
	111	1	4.79	4.86
		2	3.34	4.11
		3	6.45	3.95
		4	2.24	2.18	1.89 (upper surf.)
		4			(lower surf.

)

From the surface geometries the following can be observed: a) for the (100) surface of CoAl 2 O 4 , the Co T d are pointing out of the surface; b) for the C(100) surface of Co 3 O 4 , the accessibility of the Co T d is intermediate relative to the two other spinels; and c) the (100) surface of Co 2

  At this stage we have chosen to investigate the former mechanism in which NH 3 , the reactant has to be adsorbed to react. The reaction is an oxidation and O 2 is necessary. NO is the product and should either desorb, further oxidize or be reduced by ammonia forming side products. On the spinel compounds, the most reactive site is the T d Co2+ . The adsorption on the surface oxygen atoms is weak or does not occur. The ordering is T d Co 2+ > O h Co 3+ > O h Al 3+ > O except for NH 3 that is more strongly bounded to Al 3+ . Coordination is the driving force explaining the adsorption at the T d Co 2+ site. NH 3 and NO do not dissociate. Preliminary study on the O 2 dissociation has been made; however this remains to be studied in more detail. The (100) surfaces have a higher affinity for NO than for O 2 and NH 3 . The molecules are more strongly bound on CoAl 2 O 4 than on Co 3 O 4 followed by Co 2 AlO 4 and CoO. The single adsorption of NH 3 , O 2 , and NO was calculated on a series of spinel-type oxides: Co 3 O 4 , Co 2 AlO 4 , and CoAl 2 O 4 , and the rock salt-type CoO. The order of adsorption strengths (CoAl 2 O 4 stronger Co 3 O 4 than, followed by Co 2 AlO 4 and CoO) is the same for all the adsorbates. The poor accessibility of the Co T d site for Co 2 AlO 4 explains that the heats of adsorption are weaker than for the other spinels. The electronegativity of the adjacent cations also contributes to explain this trend. The oxygen atoms bound to the Co 2+ are less stabilizing when they are also engaged in strong bonds with other cations (Al 3+ more than Co 3+ and much more than Co 2+ ).

	M a n u s c r i p t
	A c c e p t e d

3

, O 2 , and NO with the substrate, which should be present in the reaction. Different reaction mechanisms can be considered, considering co-adsorption of the reactants i.e. the so-called Langmuir Hinschelwood mechanism or the interaction of one of the reactants coming from the gas or liquid phase, so-Special Issue of the journal Applied Catalysis A "Nanocatalysis science: preparation, characterization and reactivity"

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16 called (Eley Rideal mechanism).

Table 2 :

 2 Calculated adsorption energies of NH 3 , O 2 and NO on the different spinels,

	considered. (Values in eV)
		NH 3				O 2				NO
		T d	O h	O h		T d	O h	O h		T d	O h	O h
		Co 2+ Co 3+ Al 3+ O 2-Co 2+ Co 3+ Al 3+ O 2-Co 2+ Co 3+ Al 3+ O 2-
	CoAl 2 O 4	-1.22 -	-1.26 -0.39 -1.30	-	-0.75 -	-3.02 -	-0.58 No
	(100)
	Co 3 O 4	-1.10 -0.81 -	-	-1.13	-1.17	-	-	-2.73 -1.71 -	No
	(100)
	Co 2 AlO 4	-0.85 -0.26 -0.58 -	-0.92* -0.86* -0.40 -	-2.56 -1.57 -0.13 No
	(100)
	CoO	-0.01 -	-	-	-0.37	-	-	-	-1.58 -	-	-
	(100)

* vertical adsorption (using lower level calculations, we have found other modes more stable; the values in this table are probably underestimated)

  adsorption strength of O 2 . It has been found that CoO is less selective for the production of NO. A too high heat of adsorption of O 2 (see table2) may favor the conversion of NH 3 to N 2 and thus should be avoided. The heat of adsorption of O 2 is found too small on CoO. The validity of the lower level of calculation was tested in the case of Co 2 AlO 4 ; the adsorption energies recalculated at a lower level where in qualitative agreement with those of high

quality, even if the absolute numbers are slightly different, trends are similar.

Table 3 :

 3 Calculated adsorption energies of NH 3 , O 2 and NO on Co 2 AlO 4 . (Values in eV)

		NH 3	O 2	(=1)	O 2 ( =1/2)	NO	N 2	H 2 O	H
			mol		diss
	Site	T d	T d -O h	T d	T d	T d	O h
		Co 2+	Co 2+ -Co 3+ Co 2+	Co 2+	Co 2+	Co 3+	O surf
	Co 2 AlO 4 -0.86	-1.91		-2.34	-2.12	-0.10	-0.73	-3.11
	From

Table 2

 2 one can conclude that NO and O 2 compete for the same adsorption site (CoT d ). The best surface should not adsorb O 2 too strongly, but should be reactive enough to sufficiently adsorb NH 3 . The clue of the reaction is to find the optimum in O 2 affinity with the catalyst surface.The spinel with the optimum O 2 heat of adsorption, due to the competition with NO, is expected to be Co 2 AlO 4 . NO is found to chemisorb too energetically to the substrate and act as a poison to the catalyst (See Table2). CoO is not appropriate since O 2 poorly adsorbs and NH 3 does not (or adsorbs very badly). Among the spinel structures, Co 2 AlO 4 represents the

O 2 seems to adsorb horizontally to the surface (side on), i.e. occupying both T d and O h Co sites on the surface whereas NO does not. This means that O 2 could easily saturate the surface before NO formation. Dissociation of O 2 should be more investigated. The value of the oxygen heat of adsorption matches experimental findings. The experimental heat of adsorption for O 2 on CoO is between -0.4 --1eV, and -1.7eV and -2.7eV on Co 3 O 4 T d and O h sites, respectively[19]. Co 3 O 4 is selective, maybe as a consequence of a more appropriate value for the O 2 adsorption. It is then important to carefully consider the heat of adsorption of O 2 on the oxide surface (coverage and co-adsorption effects). From literature (experiment) it is found that a weak O 2 binding makes the catalyst inactive, whereas a too strong O 2 binding favors N 2 production.

case of smallest heats of adsorption. This result is in agreement with experimental observations

[152]

.

  Thus, the study on the co-adsorption is a first step to consider a complete reactive system. Its thermodynamic evolution (not kinetics) was studied. Strong co-adsorption effects appear in our results, limited to Co 2 AlO 4 and some preliminary test on other spinels. In other words, NH 3 adsorbs better on an oxidized surface, in excess of O 2 . The adsorption site varies; NH 3 adsorbs on Al 3+ without oxygen; it is adsorbed on Co 2+ when co-adsorbed. Note however that the cooperative effect remains even for less favorable adsorption modes. The co-adsorption energy of O 2 and NH 3 is 3.57 eV while the sum of individual adsorption energies (table3) represents 2.77 eV. The gain due to the coadsorption, 0.80 eV, is very large (obtained using low level calculations). In the best adsorption mode (figure8) O 2 does not dissociate but forms a peroxo compound bridging a Co 2+ and an Al 3+ . The formation of peroxo that should be also expected to appear by atomic adsorption on stoichiometric surfaces was not found.

	4 O 2 + 2 NH 3 → 2 HNO 3 + 2 H 2 O
	Or
	5 O 2 + 4 NH 3 → 4 NO + 6 H 2 O	(2)
	The NH 3 does not spontaneously dissociate, even in the presence of O 2 . Products of co-
	adsorption are energy minima, and the N-H cleavage is weakly endothermic.

Table 4 :

 4 Co-adsorption energies and cooperative effect (Values in eV)

			NH 3 +1/2O 2	NH 3 + O 2	NH 3 + NO	NH 3 + H 2 O	NO+ H 2 O
				(=1) mol
	Site for first	Al 3+ O h	Co 2+ T d	Co 2+ T d	Co 2+ T d	Co 2+ T d
	adsorbate
	Site	for	Co 2+ T d	Co 2+ -Co 3+	Co 2+ T d	Co 3+ O h	Co 3+ O h
	second
	adsorbate
	Co 2 AlO 4		-2.41	-3.57	-2.02	-1.29	-2.51
	co-adsorp.	-0.31	-0.80	+0.96	+0.31	+0.34
	energy gain

Table 5 :

 5 cooperative effects for the co-adsorptions. (Values in eV)

	(100) Co 2 AlO 4 surface	(100) CoAl 2 O 4 surface
	NH 3 + O 2	-0.8	-0.4
	NH 3 + NO	+1.0	+0.7
	The first intermediates (b) and (e) (on figure 9) correspond to one N-H cleavage resulting
	from an H transfer. If the transfer is made on the closest O atom forming the peroxo-group
	(e), the cost is important. The transfer to the second one leads to a situation of much lower
	energy (b). It also marks a significant progress for the reaction; indeed, the peroxo cleaves and
	one NO bond is formed. The O-NH 2 -species is adsorbed by two bonds as already found on
	vanadium oxides (figure 6c in [153]).
	From this first intermediate (b), the postulated second intermediates can result either from an

intramolecular H transfer within the O-NH 2 -moiety (f) or by an H transfer to the OH group (c). The latter is the most reasonable.

adsorption of NH 3 and NO over Co 2 AlO 4 ; formation of N 2

  80 eV. A structure with NH 3 dissociation (NHO), is the lowest in energy (equivalent to N 2 O + H 2 O formation). Cooperative effects more favorable on the Co 2 AlO 4 surface than on the CoAl 2 O 4 surface. The comparison of the thermodynamics of NH 3 oxidation to N 2 is depicted in figure 10 by comparison with that for NH 3 oxidation to NO. The co-adsorption of NH 3 and NO is less favorable (by 0.95eV) than the sum of individual adsorptions. The NO does not bridge two cations, but remains attached to Co T d only. The N-N bond is made only after the breaking of the second N-H bond. The first intermediate is high in energy. Contrary to NO the NHO compound occupies a bridging situation by forming an O-Al bond; the H atom is then attached to the N that is the atom adjacent to the NH 2 group.

	The co-

Acknowledgements

This work was performed using HPC resources from the CCRE of Université Pierre et Marie Curie. F.T. acknowledges Prof. C. Minot and Dr. M. Calatayud for fruitful discussions.


A L Haj Omar

Peres Véronique

Serris Eric

Grosjean François

Kittel Jean

Ropital François

Cournil Michel

In situ high temperature oxidation analysis of Zircaloy-4 using acoustic emission coupled with thermogravimetry

Keywords: Thermogravimetric analysis (TGA), Acoustic Emission (AE), AE Burst, High temperature corrosion, Zircaloy-4 (Zircaloy-4)

Zircaloy-4 oxidation behavior at high temperature (900°C), which can be reached in case of severe accidental situations in nuclear pressurised water reactor, was studied using acoustic emission analysis coupled with thermogravimetry. Two different atmospheres were used to study the oxidation of Zircaloy-4: a-helium and pure oxygen, b-helium and oxygen combined with slight addition of air. The experiments with 20% of oxygen confirm the dependence on oxygen anions diffusion in the oxide scale Under a mixture of oxygen and air in helium, an acceleration of the corrosion was observed due to the detrimental effect of nitrogen. The kinetic rate increased significantly after a kinetic transition (breakaway). This acceleration was accompanied by an acoustic emission activity. Most of the acoustic emission bursts were recorded after the kinetic transition (post-transition) or during the cooling of the sample. The characteristic features of the acoustic emission signals appear to be correlated with the different populations of cracks and their occurrence in the ZrO 2 layer or in the α-Zr(O) layer.

Acoustic events were recorded during the isothermal dwell time at high temperature under air.

They were associated with large cracks in the zirconia porous layer. Acoustic events were also recorded during cooling after oxidation tests both under air or oxygen. For the latter, cracks were observed in the oxygen enriched zirconium metal phase and not in the dense zirconia layer after 5 hours of oxidation.

Introduction

Zirconium alloys are widely used as nuclear fuel cladding material, and several studies have investigated the behavior of these alloys in various high temperature oxidative atmospheres [1,2]. The oxidation of Zircaloy-4 at high temperature, is characterized by the growth of an inward ZrO 2 layer. Thermally grown zirconia oxide scale consists of an external monoclinic layer and of a thin tetragonal layer located close to the metal/oxide interface [3]. Some authors [1,2,3] have detected a variation of the kinetic rate, called breakaway, during the oxidation process of Zircaloy-4 samples under air. The growth of the ZrO 2 oxide scale leads to residual stresses, both in the metal and in particular in the oxide, due to the Pilling-Bedworth ratio of 1.56 for the volume difference between the metal and the oxide. Previous studies have proven the presence of different types of stresses during the oxidation of Zircaloy-4 [4,5]. These stresses have several consequences: ZrO 2 layer cracks, spalling of the thick scales, metal deformation, and stabilization of the cubic crystallographic phase of zirconia [START_REF] Schanz | Proceedings of 8th International Congress on Metallic Corrosion[END_REF]. Parise [4] attribute the breakaway to the oxide layer crack network which gives gases free access to the metal interface. Synchrotron X-ray diffraction (S-XRD) experiments [START_REF] Petigny | [END_REF][8][9][10] of samples oxidized in an autoclave have shown that oxides formed on zirconium alloys are strongly compressed. When the oxide layer thickness increases, there is a reduction in the compressive stress [START_REF] Barberis | Zircon. Nucl. Ind. 15th Int. Symp. ASTM STP[END_REF][START_REF] Chevalier | [END_REF]. Some combinations of mechanisms are relaxing the compressive stress as mechanical factors, oxidation-induced creep and strain, or crack formation in the oxide layer. But some questions still remain unresolved mainly at high temperature which is far from the operating conditions of the nuclear plants. As an example, it is not clear at which stages cracks occur during the oxidation process. Stress relaxation by cracks in the oxide layer may generate transient elastic waves which can be recorded and analyzed using the acoustic emission system (AE). This emission can be explained by abrupt variations in the stress field. When elastic energy relaxation occurs, it generates the high frequency elastic waves (10 kHz-1200 kHz) called acoustic emission (AE) [13]. Irreversible processes, such as local plastic deformations or cracks, produce AE signals during high temperature corrosion. One of the most important advantages of investigating acoustic emission is that the frequency of the signals is much higher than the frequency of the environment noise as machine vibrations or human interventions. Acoustic emission also represents an in-situ and a non-destructive monitoring method. It can be implemented on industrial equipment at a moderate cost, but it is important to adapt the AE devices to the industrial environmental conditions, particularly at high temperature under corrosive environments [START_REF] Ono | Acoustic emission, Encyclopedia of acoustics[END_REF].

In this study an innovative device was used, based on TGA analysis coupled with acoustic emission. Sample mass variation and AE signals were recorded during oxidation of a zirconium alloy, Zircaloy-4, at 900 °C. Simultaneous measurements of the two parameters, mass variation and AE burst, combined with post mortem characterization of oxidized samples, provided additional information on the Zircaloy-4 corrosion mechanism.

Experimental

The experiments were performed on Zircaloy-4 cut into coupons with dimensions of 4.8 x 4.6 x 0.5 mm 3 . The chemical composition can be found in Table 1. Samples were polished and cleaned with acetone and ethanol before the oxidation tests. Thermogravimetric analyses were carried out on a symmetric thermobalance (SETARAM TAG 24) with Pt-Rh 6%/ Pt-Rh 30% thermocouples (Figure 1), in order to measure sample mass changes during the oxidation tests with a precision of ± 0.001 mg. The oxidation test temperature was set at 900°C ± 0.1°C and the heating rate was 15°C/min in pure helium (Table 2). The isothermal dwell time was set at 5 hours. Once the desired temperature was reached (T = 900°C), pure helium was changed for a mixture of 75% He + 21% O 2 + 4% N 2 for the first series of oxidation tests. This first gas mixture was chosen to represent an air leak in an oxygen atmosphere. An oxidant gas (80% He + 20% O 2 ) was used for the second series of oxidation tests (Table 3). In both series, the oxidant gas was introduced by mass flow meters with a total gas flow rate of 50 ml/min at atmospheric pressure. The purge time is about 7 minutes when introducing the test gas. The cooling rate was 15°C/min under the same process gas mixture. A discontinuous acoustic emission analysis (burst analysis) is used in these tests. Burst analysis is based on acoustic emissions related to individual events occurring in a material. An AE burst starts when the signal amplitude exceeds the set threshold (this threshold may be fixed or self-adjusting to the noise level). Several parameters can be calculated from an AE burst. This study focused on the following parameters, the burst amplitude which is the maximum amplitude reached during an AE Burst (dB AE ), the count is the number of threshold crossings during an AE Burst, the average frequency which is obtained from Count divided by Duration; it determines an average frequency over one AE Burst (kHz).

Piezoelectric sensors enable AE signals to be recorded. They convert the mechanical waves generated during the irreversible processes into electric signals. When piezoelectric sensors are placed directly in contact with the materials, a low attenuation of the signal energy is observed [13,[START_REF] Ono | Acoustic emission, Encyclopedia of acoustics[END_REF]. When sensors cannot be placed directly on the sample, for example in a high temperature environment, a waveguide may be used in order to transmit the waves from sample to sensor [START_REF] Sikorska | [END_REF]. Different authors have mainly used alumina or platinum as waveguides [16,17]. These materials are characterized by a high propagation velocity, and they conserve the wave forms of the AE signals with a low attenuation of wave energy. Over the last few decades, several authors have used acoustic emission devices during studies of the high temperature corrosion behavior of metals and alloys, steel sulfidation [18], metal dusting inhibition [19], and alloy oxidation [20]. Since 1977 other authors have coupled acoustic emission with thermogravimetric analysis (TGA) in order to improve understanding of different high temperature corrosion phenomena [START_REF] Hochman | Proc. of the symp. On Properties of High Temperatures Alloys with Emphasis on Environnemental Effects[END_REF][START_REF] Bennett | [END_REF]23,24,25]. The sample mass variation and the AE signals are simultaneously recorded during these experiments.

A special acoustic device (wave guide) was developed to optimize the transmission of acoustic signals from samples (AE source) to the sensors (Figure 1). The waveguide was designed in alumina to meet the following criteria: i) chemical resistance to corrosive environments (oxygen or reductive atmospheres); ii) chemical inertness with regard to the alloy samples; iii) good transmission of the acoustic signals (low attenuation of the signal energy); and iv) optimization of the contact between the sample and the waveguide. The guide's dimensions were compatible with the internal diameter of the furnace (2 cm) and with the thermobalance maximum load (10 g). Coupons were placed on the wave guide while another wave guide without specimens was placed in the reference furnace of the thermobalance in order to minimize the baseline shift during experiments and to maintain symmetry between the two parts of the thermobalance (Figure 1).

AE piezoelectric sensors were linked to the waveguide via a metallic support, and then the sensors and the metallic support were placed inside the cold part of the thermobalance where the temperature does not exceed 150°C. The sensors were linked to an acquisition chain controlled by the AEwin TM software and results were analyzed using Noesis TM software provided by the Physical Acoustics Corporation Company. The characteristics of the acquisition chain are given in Table 4. The threshold is very low, set at 18 dB AE .

Table 4 Main characteristics of AE acquisition

Discontinuous acoustic emission analysis (AE burst) was used during this study. At ambient temperature, the normalized Hsu-Nielsen test [26] was carried out to verify the AE system. This test simulates an acoustic emission event by breaking a 0.5 mm pencil lead tip against the sample surface, generating an intense acoustic signal quite similar to a natural AE source that the sensors detect as a strong burst. Generally, the lead breaks should generate amplitudes of at least 80 dB AE for a reference voltage of 1 mV. The burst amplitude obtained Blank tests without any specimen at 900°C under air or oxygen were carried out to validate that the waveguide did not significantly react with the gas mixture. During the isothermal dwell time (Figure 2), the stability of the mass signal confirmed the chemical inertness of the waveguide and the symmetry of the experimental device.

Results

Oxidation tests under air

Thermogravimetry results

Specimen mass variations as a function of time for corrosion tests under a mixture of helium, oxygen and air (75% He + 21% O 2 + 4% N 2 ) are presented in Figure 3. Although the amount of air was low in the gas mixture, these tests are named "air tests" hereafter. Rates of mass gain are presented in Figure 4. Specimen mass was normalized compared to the sample surface. The sample weight was measured before and after the oxidation test with a precision balance Mettler AG204. The ex situ measurements always confirm the TGA's mass gains.

Time Average frequency

Weight Average frequency

There was no mass variation during the heating up under pure He, while air test results

show a significant increase of mass during the dwell time, with a gain of 42 mg/cm² after 5 hours of oxidation. Figure 4 shows no variations in the mass gain rate during heating up, while the kinetic rate fluctuates after the introduction of the gas mixture. At the end of the test, the sample mass gain is equal to 21 mg.

An acceleration of the kinetic rate was observed 2400 s (0.66 h) after the introduction of the oxidant gas mixture under air. This acceleration corresponds to the kinetic transition called breakaway. The breakaway is mainly explained by the appearance of cracks in the primary dense thin layer of ZrO 2, giving oxygen free access to the metal oxide interface [1][2][3][4][5][START_REF] Schanz | Proceedings of 8th International Congress on Metallic Corrosion[END_REF].

After the breakaway, the oxidation process is enhanced.

Acoustic emission results

Blank tests enabled the acoustic emission signals, which result from the instrumental noise (IN), to be distinguished. The characteristics of these AE signals are given in Table 5. They are characterized by a very short duration and a low number of counts, as 95% of the bursts are characterized by 1 count and a duration of 1 µs. They also have a high average frequency in the range of 200 kHz to 1000 kHz including the resonance frequency of the sensors (300 kHz). Burst absolute energy is very low and does not exceed 0.1 aJ/burst. These instrumental noise AE bursts were subtracted from the acoustic emission analysis for the rest of the study. (300 counts/burst on average). AE burst characteristics can be found in Table 5.

Sample characterization after cooling

The cross section of oxidized sample (Figure 7) obtained with scanning electron microscopy (JEOL 6500 F) indicates that cracks are located inside the inward zirconia layer.

Cracks are visible in the external dense zirconia layer (type 1), and well distributed thin convoluted cracks are observed parallel to the metal oxide interface (type 2) while big open cracks can be seen perpendicular to this interface, totally crossing the zirconia layer (type 3).

Based on the zirconium-oxygen binary diagram [START_REF] Abriata | The O-Zr (Oxygen-Zirconium) system[END_REF] and on Lassere and al. observations [1],

the sample core remains partially oxidized, forming an α-ZrO solid solution of oxygen in zirconium. Samples were also investigated using an in-situ Raman microscope (HORIBA JOBIN YVON -XPLORA) at 900°C under air (79% N 2 + 21% O 2 ). Real time observation of sample surface evolutions was possible, and therefore identification of when sample surface cracks (type 3) appeared (Figure 8) at between 3000s (0.83 h) and 4200s (1.12 h) of dwell time, i.e.

after the kinetic transition. Then the cracks grow, with micrometric thicknesses.

Oxidation tests under oxygen

Thermogravimetry results

In Figure 9, it can be observed that the mass gain for the oxygen tests (80% He + 20% O 2 ) is much lower than the mass variations observed for air tests. After 5 hours of oxidation the weight gain was about 8 mg/cm². The kinetic transition did not appear during the oxygen test, and the kinetic rate decreased or remained constant throughout the experiment (Figure 10). In order to confirm the absence of the kinetic transition under oxygen at 900°C, the dwell time was extended from 5 hours to 10 hours (Figure 10). Results obtained during the extended test (10 hours dwell time) also demonstrated the absence of kinetic transition during oxidation under oxygen. The apparent mass loss of the samples during the cooling is due the gravity effect.

Acoustic emission results

No AE signals (Figure 10) were observed during the dwell times. AE bursts recorded during short and extended tests under oxygen appeared only during the cooling step. The burst parameters of these tests are similar (Table 6). The AE bursts recorded during the cooling step are characterized by a high absolute energy (200 aJ/burst on average). Their count number is in the order of magnitude of hundreds of counts per burst, and their amplitude varied between 20 dB AE and 60 dB AE .

Sample characterization after cooling

The SEM cross section of a sample oxidized under oxygen for 5 hours at 900°C (Figure 1) The SEM cross section of a sample oxidized under oxygen for 10 hours at 900°C (Figure 12) shows cracks located in the α-Zr(O) phase perpendicular to the metal interface. Some of the cracks, longer ones, also cross the dense ZrO 2 layer. α -Zr

Discussion

In the following the isothermal oxidation and the cooling are discussed.

AE signals recorded during isothermal oxidation

The oxidation of Zircaloy-4 at high temperature has been intensively studied during the last few decades. The oxidation mechanism under air is still under discussion, but generally it has been assumed that there are three different stages during the oxidation process: the pretransition stage, the kinetic transition and post-transition stage. During the pre-transition stage the kinetic rate follows a parabolic law, and the diffusion of oxygen vacancies in the dense protective zirconia layer is the limiting step. Then the kinetic rate reaches a minimum, followed by an increase of mass gain rate corresponding to the kinetic transition. This breakaway has been associated with the first cracks in the dense oxide layer. In our study, the kinetic transition was observed 2400 seconds after the introduction of the gas mixture under air at 900°C. During the post-transition stage a major mass gain increase was observed.

Lasserre and al. [1] have conducted kinetic oxidation studies on Zircaloy-4 at high temperature in air. They have demonstrated the effect of the nitrogen partial pressure on the oxidation rate. They have proposed a mechanism where nitrogen acts as a catalyzer during the oxidation process under air. ZrN precipitates were formed at the metal oxide interface, and then these precipitates were oxidized with oxygen coming from the outside. Nitrogen atoms were released which were able to react with Zr metal at the internal interface, again creating

ZrN [1]. During the post-transition stage, it has been concluded that the presence of nitrogen in the atmosphere has an accelerated effect on the kinetic rate. Our results confirm the detrimental role of nitrogen which causes a rapid and a catastrophic oxidation of the Zircaloy-4 at high temperature.

In case of pure oxygen at 900°C the oxidation of Zircaloy-4 is less critical than the oxidation under air; the oxidation has not reached the breakaway stage. The weight gain of the sample remains moderate after 5 hours at high temperature. The dense zirconia layer remains protective even after 10 hours. The breakaway may appear after a longer dwell time.

As shown by the monitoring results, AE signals were recorded during the oxidation test dwell time under air. The first acoustic signals were recorded just after the kinetic transition.

Three different types of crack (Figure 7) are present in the zirconia layer and each of them will form via a different mechanism. The formation of type 2 lateral crack may be due to interface undulations [4]. Zirconia scale growth begins with the inward formation of a dense ZrO 2 layer at the metal-oxide interface. The Pilling-Bedworth ratio for the zirconia growth (ratio of the molar volume V(ZrO 2 )/V(Zr)) is equal to 1.56, which means that the transformation from metal Zr to oxide ZrO 2 induces a volume dilation. Stresses can thus be created in zirconia scale and in metal. The residual internal stresses increase in proportion to the zirconia scale thickness and once stresses exceed the fracture limit of zirconia, they can lead to cracks [5]. The mechanism for perpendicular crack formation (type 1 and 3) will be different. During oxidation after the breakaway, the perpendicular cracks in the oxide layer may be due to tensile stresses which appear at high temperature due to the elongation of the Zr metal submitted to creep.

The cracks can be associated with the AE signals recorded after the kinetic transition (Figure 13). The relationship between cracks and AE signals is confirmed by in-situ optical microscopy observations of oxidized samples under air. The cracks observed at the surface of the sample are in the scale of open cracks perpendicular to the metal oxide interface (type 3 in Figure 7). Some of the AE bursts can be attributed to these post-transition stage cracks. The number of type 2 convoluted lateral cracks parallel to the metal/oxide interface exceeds the amount of AE bursts which were recorded during the oxidation test. Thus even if the AE threshold is low (18 dB AE ), the energy of type 2 cracks seems to be too weak to generate recordable AE bursts. AE signals recorded during cooling under air and under oxygen correspond to energetic processes. The parameters of the acoustic events are summarized in Table 8. Figure 14 presents the evolution of the AE cumulative counts. For both tests, a phenomenon in common appeared at the beginning of the cooling, with high AE activity occurring as the temperature decreased from 750°C to 700°C. Then under air tests, AE activity remained stable during the rest of the cooling step while for oxygen tests, another major variation of AE activity appeared for temperatures lower than 400°C. The low level of acoustic signals observed during the cooling of the samples oxidized in air may be due to stress relaxation by cracks in the oxide layer during the oxidation dwell time. To further understand the cooling behavior of oxidized Zircaloy-4 samples from 900°C down to ambient temperature, short oxidation tests were made with differential scanning calorimetry (TGA/DSC 1 -Mettler Toledo). Heat flow variation measurements were carried out during the oxidation tests under air and under oxygen (Figure 16). The dwell time was reduced to 10 minutes in order to limit the zirconia scale thickness on the sample surface. The thermal conductivity of ZrO 2 is lower than that of Zircaloy-4, so it can impact the heat flow measurement coming from the whole sample. The deformation of the coupons at high temperature could also affect the measurement as they were not in direct contact with thermocouples in the DSC balance.

The curves indicate an exothermic peak around 820°C for both tests. Based on the Zr-O binary diagram, the transformation from pure β-Zr to α-Zr occurs at 863°C. The exothermic peak is under this reference value, it may be due to the presence of an oxide scale between the sample's metal core and the thermocouples.

Fig. 1 .

 1 Fig. 1. Symmetric thermobalance (TGA 24) coupled with acoustic emission devices (waveguide, sensors, preamplifier)

Fig. 2 .

 2 Fig. 2. Blank test without specimen at 900°C under air, mass gain (mg) and average frequency of the AE bursts as a function of time

Fig. 3 .

 3 Fig. 3. Mass gain (mg/cm²) as a function of time during Zircaloy-4 oxidation tests 1 and 2 under air

Fig. 5 .Figure 5

 55 Fig. 5. (▲)Burst average frequency variations as a function of time for a blank test, (•) burst average frequency for Zircaloy-4 oxidation under air, (─) Zircaloy-4 mass gain (mg/cm²)

Figure 6

 6 Figure6shows the burst amplitudes recorded during the oxidation tests in parallel with the kinetic rate variation as function of time. According to the kinetic rate curves, AE bursts were recorded just after the kinetic transition (breakaway) occurring 2400 s (0.66 h) after the introduction of the oxidant gas mixture. Each time, an intense AE activity appeared just after the breakaway. These bursts, called post-transition bursts, were recorded during the temperature dwell time and are characterized by mean amplitudes in the range of 18 to 40 dB AE . AE bursts possess a low average frequency varying between 1 kHz to 200 kHz with an absolute energy average of about 10 aJ/burst. AE signals were also recorded during sample cooling. The bursts recorded during this cooling step were more energetic (100 aJ/burst) and characterized by long duration (1000 µs/burst), and a high count number/burst

Fig. 6 .

 6 Fig. 6. Rate of mass gain and burst amplitude as a function of time during Zircaloy-4 oxidation tests under 75% He + 21% O 2 + 4% N 2

Fig. 7 .

 7 Fig. 7. SEM cross section of Zircaloy-4 oxidized under air at 900°C (X70)

Fig. 8 .

 8 Fig. 8. Optical microscopy observation during the oxidation of the Zircaloy-4 under air at 900°C: (a) 1800 seconds; (b) 3000 seconds; (c) 4200 seconds after the introduction of the oxidant gas

Fig. 9 .

 9 Fig. 9. Mass gain as a function of time during Zircaloy-4 oxidation tests 3 and 4 under oxygen

Fig. 10 .

 10 Fig.10. Rate of mass gain as a function of time and burst amplitude variations during Zircaloy-4 oxidation tests under oxygen (▲) [5 hours] -( ♦ ) [10 hours]

Fig. 11 .

 11 Fig. 11. SEM cross section of Zircaloy-4 oxidized 5 hours under oxygen at 900°C a-(X100); b-(X240)

Fig. 12 .

 12 Fig. 12. SEM cross section of Zircaloy-4 oxidized 10 hours under oxygen at 900°C (X80)Unfortunately it was not possible to realize an in-situ Raman microscope test under helium-oxygen mixture due to a leak of the high temperature cell.

Fig. 13 . 2 4

 132 Fig. 13. Rate of mass gain as a function of time and cumulated absolute energy variations during Zircaloy-4 oxidation tests under 75% He + 21% O 2 + 4% N 2

Fig. 14 .Fig. 15 .

 1415 Fig. 14. Cumulated count variations as a function of time during the cooling of the Zircaloy-4 for oxidation tests under air (---) and under oxygen (─) 5 hours

Fig. 16 .

 16 Fig. 16. Heat Flow variation as a function of temperature during cooling (T< 900°C) under air (─), and under oxygen (---)

Table 1 Chemical composition of Zircaloy-4 in weight% or ppm

 1

	Sn (wt%)	Fe (wt%)	O (wt%)	Cr (wt%)	C (wt ppm)	Nb (wt ppm)	H (wt ppm)	Zr
	1.32 -1.35	0.21	0.123 -0.129	0.11	125 -140	< 40	< 3	Bal.

Table 2 Impurity proportions (in ppm) present in He

 2

	O 2	H 2 O	THC (as CH 4 )	N 2
	< 1 ppm	< 2 ppm	< 0.5 ppm	< 5 ppm

Table 3 Data for the heating tests

 3

Test He (%) O 2 (%) N 2 (%) Temperature (°C) Dwell time (h) 1 and 2 75 21 4 900 5 3 and 4 80 20 900 5 5 80 20 900

Instrumentation Sensors Threshold (dB AE ) System filter (KHz) Model of the amplifier Sampling rate PDT -HDT -HLT Characteristics PICO 30 18 10 -1200 2/4/6 gain: 60 dB AE 0.25 µs (4MHz) 100 -200 -400 (µs) came

to 90 dB AE , confirming the satisfactory transmission of acoustic signals via the waveguide at ambient temperature (25°C).

Table 5 Parameters of acoustic bursts recorded during blank tests and oxidation tests under air Burst parameters 75% He + 21% O 2 + 4% N 2 Amplitude (dB AE / burst) Absolute energy (aJ/ burst) Duration (µs/burst) Count numbers/burst Average frequency (kHz/burst) Blank tests 18 -20 0 -0.01 1 -2 1 -2 200 -1000 Air test dwell time 18 -40 0.01 -100 2 -7 600 2 -500 1 -200 Air test cooling 18 -64 0.01 -1 000 2 -12 500 2 -1 500 1 -200

 5

Table 6 Parameters of acoustic bursts recorded during oxidation tests under oxygen Burst parameters Test 80% He + 20% O 2

 6

		Amplitude	Absolute	Duration	Count	Average
		(dB AE /	Energy	(µs/burst)	numbers/burst	frequency
		burst)	(aJ/ burst)			(kHz/burst)
	Cooling: 5 hours	18 -62	0.01 -10 000	2 -15 000	2 -2 200	1 -200
	Cooling: 10 hours	18 -52	0.01 -2 000	2 -15 000	2 -1 650	1 -200

Table 8 Parameters of acoustic bursts recorded during cooling for oxidation tests under air and oxygen Burst parameters Cooling Amplitude (dB AE / burst) Absolute Energy (aJ/ burst) Duration (µs/burst) Counts number/burst Air tests 18 -64 0.01 -1 000 2 -12 500 2 -1 500 Oxygen tests 18 -62 0.01 -10 000 2 -15 000 2 -2 200

 8

Acknowledgment

This work is part of the FUI program: IREINE (Innovation for REliability of INdustrial Equipment) dedicated to the development of devices and monitoring services to investigate the corrosion of industrial process equipment. The program is funded by the French Rhone Alpes Region.