Jean Marc Salotti

New conditioning model for robots

We present a neural network for the prediction of rewards in a conditioning model. It is based on two noisy-or and one noisy-and nodes and update rules inspired from BANNER technique. In specific cases, we show that the computation is similar to Rescorla-Wagner's equation, which inspired many computational models in the domain of conditioning.

Conditioning

The objective of this work is to define the behaviors of robots according to the theory of conditioning. Animal conditioning occurs when a stimulus is repeatedly presented before a reward or a punishment. Pavlov' experiments with dogs are well known and classical or operant conditioning have been studied for a long time [START_REF] Pavlov | Conditioned Reflexes: An Investigation of the Physiological Activity of the Cerebral Cortex (translated by G. V. Anrep)[END_REF]. However, despite several decades of works on conditioning models, it is still difficult to establish all the rules that govern the properties of conditioning. Most approaches are based on the original model proposed by Rescorla and Wagner [START_REF] Rescorla | A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement[END_REF] in which conditioning is characterized by associative strengths. Modification of the associative strength of a stimulus X after a new trial is given by equation [START_REF] Balkenius | Computational models of classical conditioning: a comparative study[END_REF]. The increase is proportional to the salience of X (parameter α) and the efficiency of conditioning (parameter β). λ is the maximum strength and V Total is the sum of all associative strength of the present stimuli.

) (

1 n Total X n X n X V V V - + = + λ β α (1)
The associative strength of a given stimulus can be interpreted as the degree to which a reward is predicted. Another important model has been proposed by Klopf with further considerations by Grossberg [START_REF] Balkenius | Computational models of classical conditioning: a comparative study[END_REF], [START_REF]Neural Network Models of Conditioning and Action[END_REF]. In these models, stimuli were represented by neurons and associative strengths were determined by synaptic weights. Other authors followed the same principles [START_REF] Balkenius | Computational models of classical conditioning: a comparative study[END_REF], [START_REF] Rescorla | A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement[END_REF], [START_REF] Salotti | Noisy-Or nodes for conditioning models[END_REF]. Sutton and Barto also proposed a model of classical conditioning based on well known reinforcement learning techniques (TD model, 1987 and1990 [7]). Despite all these works, all models suffer from specific drawbacks. We propose in this paper a new prediction system for conditioning and its application in robotics. It is based on a specific neural network architecture corresponding to the nodes of a Bayesian network. The method is explained in Section 2. Some results are then presented in Section 3. In Section 4, we describe a simple application of our model with robots. We finally conclude with the perspectives of this work.

Proposed model

Description of the network

Stimuli are defined as perceptual events in the representation of robots. In a simplified world, there is only one reward (or only one unconditioned stimulus, which predicts the reward with probability 1) and the objective is to determine if one or several observed stimuli predict the reward event in the next few seconds or eventually if they inhibit it. Our neural network is defined by three levels (see Fig. 1). In the first level, the output of the neurons corresponds to the observation of the different stimuli. In the second level, the output of the neurons correspond to the probability of obtaining a true value for a hidden Boolean variable. There are two hidden variables. Each of them corresponds to a Noisy-Or node of the conditional probabilities of the first level (see next section). The first one can be considered as the probability of triggering the real but hidden cause of the reward event and the second one corresponds to the probability of triggering a hidden inhibitory mechanism that prevents the action of the cause and the observation of the reward. That second variable is necessary to allow inhibitory conditioning [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF]. Inhibitory conditioning indeed occurs if the conditioned response is always observed after the detection of a given stimulus X (reward expected) but is never observed if Y is present at the same time. If a single noisy-or node had been used, the reward would have been expected if one of the causal mechanisms had been present. That specific problem has already been identified in previous work [START_REF] Salotti | Noisy-Or nodes for conditioning models[END_REF]. The neuronal output of the third level corresponds to the probability of observing another event. It is defined as the probability of presence of the cause with absence of the inhibitory mechanism. Inhibitory conditioning is thus easily integrated in the model. In general, the last event is the reward, but not necessarily.

Neural computation

Pearl proposed the Noisy-Or to simplify the problem of updating many conditional probabilities in a Bayesian network [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF]. We propose to implement his method as follows. First of all, we define P(H 1 |X) as the conditional probability of obtaining H 1 =true during a limited period of time (for instance 5 seconds) following the observation of event X. In the neural network, synaptic weights correspond to conditional probabilities. For instance the conditional probability P(H 1 |X) is the synaptic weight between node P(X) and P(H 1 ). If X 1 ..X n are possible stimuli events predicting H 1 =true, in a Noisy-Or node it is sufficient to have an estimate of all P(Y|X i ) to compute P(Y|X 1 ..X n ) [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF]. For the second level, the output of the neuron is therefore determined by the output of the neurons of the first level and their associative weights according to equation ( 2).

∏ - - = i i i X P X H P H P )) ( ) ( 1 ( 1 ) ( 1 1 (2)
A similar equation holds for the computation of P(H 2 ). The difference only appears during the updates of the synaptic weights (e.g. the conditional probabilities). At the last level of the network, P(Reward) is computed according to equation (3).

)

) ( 1 )( ( ) (Re 2 1 H P H P ward P - = (3)

Update rules

As it is suggested in the BANNER method proposed by Ramachandran, the update of the conditional probabilities can be performed according to a rule that minimizes the mean square error [START_REF] Ramachandran | Theory Renement of Bayesian Networks with Hidden Variables[END_REF]. However, since we do not want to stop the robot during learning, we propose to take into account each error and to update the probabilities in an incremental way. Let us consider the error for a given trial. There are two cases. If the reward is observed after a given set of stimuli, the global error is 1-P(Reward) and if no reward is observed the global error is P(Reward). Since the computation of P(Reward) involves a multiplication between P(H 1 ) and P(H 2 ), the propagation of the error to the second level is trivial. If X k is an observed stimulus, the update of the conditional probabilities P(H 1 |X k ) and P(H 2 |X k ) can be easily performed using a gradient descent technique, which is very similar to the one proposed in BANNER, see equations ( 4) and (5).

) ( ) ( )) ( ( 1 1 1 H P H P H P Err corr - = (4
) P corr (H 1 ) is the correct value of P(H 1 ) considering only the current observations. It is equal to 1 if the reward has been observed and 0 otherwise.

        ∂ ∂ - + = + ) ( ) ( ( ) ( ) ( 1 1 1 1 1 H P H P Err X H P X H P t t k t k t α ∏ ≠ + - - + = k i i i t k t k t X Vu X H P X H P X H P )) ( ) ( 1 ( ) ( ) ( 1 1 1 1 α ( 5
)
where t is the time according to a given discretization, α is a learning rate smaller than 1, Vu(X i ) is a logical variable equal to 1 if X i has been observed and 0 otherwise. There is an increment or a decrement of the probability according to the sign of the error. A similar equation holds for P(H 2 |X k ) with a symmetric error. The problem is that we are dealing with probabilities and even though the update rule takes into account the partial derivative of the error and evoluates in the appropriate slope there is no guarantee that the probability would remain in the range [0..1] depending on the value of the learning parameter. We therefore propose taking into account the maximum modification of the probability. If the update rule increases the probability, the maximum local error is 1-P(H 1 |X k ) and if it is decreasing, it is equal to P(H 1 |X k ). We propose to multiply the right term by this maximum local error so that the update is always a fraction of the maximum allowed modification. The new equations are therefore (6)( 7) and (8)(9), respectively, when the reward is observed and when it is not.

∏ - + = + i i i t k t k t X Vu X H P X H P X H P )) ( ) ( 1 ( ) ( ) ( 1 1 1 1 1 α (6) ∏ ≠ + - - = k i i i t k t k t k t X Vu X H P X H P X H P X H P )) ( ) ( 1 ( ) ( ) ( ) ( 2 2 2 2 2 1 α (7) ∏ ≠ + - - = k i i i t k t k t k t X Vu X H P X H P X H P X H P )) ( ) ( 1 ( ) ( ) ( ) ( 1 1 3 1 1 1 α (8) ∏ - + = + i i i t k t k t X Vu X H P X H P X H P )) ( ) ( 1 ( ) ( ) ( 2 4 2 2 1 α (9)
Note that in equations ( 6) and ( 9) the new term does not explicitly appear because it is now included in the product. Remark: We suggested that a predicted reward event would be expected during a fixed period of time after a stimulus event. We therefore have to memorize all events during that period. However, if a reward is observed at a given time t, the traces of the stimulus and the reward events might still be present at time t+1, t+2 and so on depending on time discretization. If this is the case, we have to apply equations ( 6) and ( 7) at every step. This is in fact an interesting property because the increase of the conditional probability is inversely proportional to the interval between the stimulus and the reward and that property has been observed in the domain of animal conditioning. Conversely, if the reward event is absent during all the fixed period, equations ( 8) and (9) are applied only once and the trace of the stimulus event is forgotten. and after 3 seconds a reward is presented. The probability of reward after that stimulus is equal to P(H1). Then during the next 60 trials, the stimulus is still presented but not the reward. The probability of reward after that stimulus decreases below 0.5. There is extinction of conditioning. Finally, during the last 60 trials, the stimulus and the reward are presented (reacquisition of conditioning).

Results

Some results are presented Fig. 2. The following parameters have been used: α1=α2=0.002, α3=α4=0.008, time discretization: 0.2s, fixed period: 5s. It is important to note that similar curves would be obtained with different parameters. If we consider that conditioning is acquired if the probability of the reward exceeds 0.5, our experiment illustrates a conditioning followed by its extinction and finally its reacquisition at a faster rate. Other conditioning experiments are correctly described with the proposed model. Let us consider the blocking effect. Conditioning with a given stimulus Y is blocked or takes a long time if Y always follows a stimulus X and X is already a stimulus that predicts the reward. In equation ( 6), P(H 1 /Y) does not increase much because P(H 1 /X) is close to 1 and the product is proportional to 1-P(H 1 /X). Latent inhibition is characterized by an inhibition of conditioning if the stimulus has already been observed without the reward. In our model latent inhibition is observed because P(H 2 ) increases before P(H 1 ). Our model can account for many conditioning properties. More importantly, the main advantage of our model is that it is not necessary to reset the parameters before a new experiment. The conditioning with a given stimulus can be extinguished, reacquired, combined with another stimulus at all time. The model can therefore be used in robotics in real time.

Application in robotics

We implemented our model in Java for Lego Mindstorms robots. The robot is a simple rover equipped with ultrasonic sensors for measuring distance to an obstacle and a RFID sensor. There are three action modes. In the normal mode, the robot randomly chooses an action among several ones, such as "go forward 20 cm", "turn 45° east", "turn 45° west". If an obstacle is detected at a distance less than 20 cm, the robot switch on a red light and enters a reactive mode. It waits 2 seconds, then makes a 180° turn and return to the normal mode. The obstacle plays the role of an unconditioned stimulus. In the real world, stimuli are typically sounds or visual features and the problem of stimulus recognition is known to be hard. A RFID sensor has been used to simplify interactions with the robot. If an emitter is presented in front of the sensor, its radio frequency is immediately identified with 100% certainty.

In our experiments stimuli are different emitters. Each time a stimulus is detected (and identified), its trace is memorized during 5 seconds. Meanwhile, if an obstacle is detected, the conditional probability of observing an obstacle after the detection of that stimulus is updated according to our model. We adapted the learning rates such that conditioning is functional after 3 similar situations. As a consequence, the fourth time the same stimulus is detected, the robot enters a conditioning mode, switch on a red light and goes foward during 5 seconds waiting for the detection of the obstacle. If it is detected before the end of the 5 seconds, it enters a reactive mode. If the obstacle is not detected it returns to the normal mode. Experiments have also been conducted with several stimuli. Extinction, reacquisition, latent inhibition, blocking and inhibitory conditioning (obstacle never expected after a given stimulus) have been successfully observed.

Conclusion

Our model has been briefly described. There are many other interesting results that could be discussed. The application of our model to the real world of robots is currently investigated. A promising perspective is the use of the model for the training of robots like the training of animals to do simple tasks such as sit down, jump, go and take an objet and so on. This is possible if the model is used for operant conditioning. Since conditional probabilities can take into account any event, it is easy to consider the actions of the robots as possible events that would predict rewards or punishments.

Fig. 1 :

 1 Fig. 1: Neural network model.

Fig. 2 :

 2 Fig. 2: Conditioning experiment: during the first 60 trials a stimulus event occursand after 3 seconds a reward is presented. The probability of reward after that stimulus is equal to P(H1). Then during the next 60 trials, the stimulus is still presented but not the reward. The probability of reward after that stimulus


Clement Antoine

Laurens Stéphane

Girard Stéphane

A Novel Damage Sensitive Feature Based on State-Space Representation 1

Damage detection in civil structure is a challenging task, mainly because of the strong environmental variations and the variable and unknown excitation. There is still a lack of a robust damage detection process. Taking advantage of the development of the nonlinear dynamical systems theory which represents times series in a reconstructed state-space, a novel damage sensitive feature vector is proposed. Statistical modelling using extreme value theory is conducted to classify measurement as damaged or undamaged. The whole approach is tested on two case studies. The first one is a simple 4dof mass/spring numerical model, damaged by stiffness reduction. The second one is a concrete beam subjected to temperature variations to simulate realistic conditions. Damage is introduced buy loading cycles.

From 30% of stiffness reduction, damage is correctly detected with a monotonic trend. In the more realistic case, only few true detection are observed before macro-cracking whereas all points are well classified after. Furthermore, the method is robust against strong temperature variations.

INTRODUCTION

For few years, vibration-based Structural Health Monitoring (SHM) process is presented in terms of statistical pattern recognition [START_REF] Farrar | An introduction to structural health monitoring[END_REF]. The extraction of Damage Sensitive Feature (DSF), in which high dimensional vibration data are compressed into low dimensional vectors, takes a central place in this process. The main challenge is to preserve information about structure condition. For this purpose, the paradigm of nonlinear dynamical systems offers some promising abilities [START_REF] Nichols | Using state space predictive modeling with chaotic interrogation in detecting joint preload loss in a frame structure experiment[END_REF][START_REF] Todd | Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio[END_REF][START_REF] Nichols | Structural health monitoring of offshore structures using ambient excitation[END_REF][START_REF] Olson | Sensitivity and computational comparison of state-space methods for structural health monitoring[END_REF]. The information contained in time-series is extracted using reconstructed state-space representation [START_REF] Takens | Detecting strange attractors in turbulence[END_REF]. Among the numerous candidate features, the Lyapunov Exponents (LE) have been particularly studied [START_REF] Ghafari | Effect of localized faults on chaotic vibration of rolling element bearings[END_REF][START_REF] Livingston | Application of nonlinear dynamics analysis to damage detection and health monitoring of highway structures[END_REF][START_REF] Casciati | Structural health monitoring by lyapunov exponents of non-linear time series[END_REF]. They are related to the long term predictability of dynamical system. To be more precise, two trajectories initially close in the state space will diverge as time evolves with an exponential rate proportional to LE. But two remarks can be formulated on their use as damage sensitive feature. First, the practical calculation of LE is very time consuming as trajectories need to be followed for several thousand of time steps [START_REF] Brown | Computing the lyapunov spectrum of a dynamical system from an observed time series[END_REF]. Then, since damage manifests itself as local irregularities in the signal (due to opening and closing of cracks or loosened assembly) it should be more visible if short evolutions of trajectories are considered. This leads to the proposition of a new damage sensitive feature referred to as Jacobian Feature Vector (JFV) [START_REF] Clément | An alternative to the lyapunov exponent as a damage sensitive feature[END_REF]. It is formed by the components of the Jacobian matrix of the dynamic estimated in the reconstructed state-space.

Once DSF are extracted from measurement, each new DSF has to be classified as damaged or undamaged (when the aim is limited to damage detection). In civil structures, since only data from the undamaged state are available, damage is detected by comparison with the undamaged database. The statistical classification is carried out in two steps. First, the Mahalanobis distance of the new DSF vector from the undamaged database is calculated to provide a scalar value. Then, exceedances statistical model is used to set classification threshold for control charts. This modelling is related to extreme value theory which is more accurate in determining control limits when dealing with tails of an unknown distribution.

The proposed approach is tested on two case studies. The first one is a 4 dof mass/spring/damper numerical model, and the second one is a concrete beam subjected to temperature variations.

The first section of the paper details the theoretical background of the new DSF and the statistical modelling. Then the case studies are presented before discussing the results in the third section.

THEORETICAL BACKGROUND State-Space Damage Sensitive Feature

The evolution of any dynamical system can be represented as a trajectory in it statespace where each dimension is a degree of freedom. When it is impossible to measure all dof, as in instrumented civil structures, one can reconstruct qualitatively the statespace based on the measurement of only one scalar time series by using the delayed coordinates method [START_REF] Takens | Detecting strange attractors in turbulence[END_REF].

The scalar time series ( ) ( ) ( )

1 , , x x x N = … is transformed into a collection of n-dimensional vectors: ( ) ( ) ( ) ( ) ( ) { } , , , 1 X k x k x k x k n τ τ = + + - … . ( 1
)
The first minimum of the autocorrelation function or the first zero of the mutual information function of (x) provides an estimate of τ [START_REF] Fraser | Independent coordinates for strange attractors from mutual information[END_REF]. Then the best embedding dimension, n, is estimated with the false nearest neighbors method [START_REF] Kennel | Determining embedding dimension for space-phase reconstruction using a geometrical construction[END_REF]. More details on the reconstruction procedure can be found in [START_REF] Henry | The analysis of observed chaotic data in physical systems[END_REF].

In the reconstructed state-space, the dynamical system can be represented by the evolution operator F, which links one point to the next one, in a trajectory:

( ) ( ) ( ) 1 X k F X k + = . ( 2
) If ( ) Y k is a close neighbour of ( ) X k , and noting ( ) ( ) i X X k i Y k i δ = + - + , the
first order Taylor expansion of F introduces the Jacobian matrix calculated at the point ( )

X k , i.e.
( )

J X k     : ( ) ( ) ( ) 1 0 0 2 0 0 , 1 . X J X k X X X J X k J X k X X δ δ ο δ δ δ ο δ   = +       = + +     (3)
To evaluate the Jacobian matrix with experimental data, the first steps of the method used to estimate the Lyapunov exponents are employed [START_REF] Brown | Computing the lyapunov spectrum of a dynamical system from an observed time series[END_REF]. The algorithm presented hereafter is illustrated in Figure 1.

A fiducial point ( )

X k is chosen in the reconstructed state space, and its r nearest neighbors, noted ( )

i nn Y k , 1 i r = … , are selected to form a neighborhood. The difference vectors are constructed as follows ( ) ( ) { } ( ) 1, , i nn nn X k X k Y k i r δ = - = … . ( 4
)
The least-square method is used to evaluate the Jacobian matrix as the best linear mapping between the neighborhoods k and k+1 (Eq.4 and Eq.5).

( ) ( ) (

) ( )

1 2 1 2 1 . nn nn nn nn X k J X k X k J X k δ δ δ δ   + =     + = +   (5)
A previous study [START_REF] Clément | An alternative to the lyapunov exponent as a damage sensitive feature[END_REF] has shown that the sensitivity to damage is improved if the mapping does not include the initial neighborhood. Hence, the components of J 2 (Eq.5) are used to form a feature vector which will be referred to as the Jacobian Feature Vector (JFV). (6) This process is repeated for 100 fiducial points across the state-space. The number of neighbors, r, is set to twice the number of parameters to be estimated in the Jacobian matrix.

Novelty Detection

In order to compare a point from a set of points, the calculation of the Mahalanobis distance (MD) is common. Unlike Euclidian distance, it takes into account the correlations between coordinates (Figure 2). Its use is widely spread in outlier analysis or novelty detection [START_REF] Worden | Damage detection using outlier analysis[END_REF]. It converts a multivariate DSF to a scalar value which is easier to analyse with statistical modelling.

If the reference baseline is characterized by a mean vector JFV and a covariance matrix JVF C , the square MD of the i th JFV vector is:

( ) ( ) ( ) 1 2 T i i JFV i D JFV JFV C JFV JFV - = - - . ( 7
)

Statistical Modelling

The use of control charts implies the setting of control limit. Using the normal hypothesis to set the limit can lead to wrong value since extreme events reside in the tails which are poorly modelled when the nature of the distribution in unknown. To overcome this problem, it is possible to consider the variable Y, which represents the exceedances of D over a threshold u. Regardless the distribution of D, if u is in the tail of D, the distribution of Y will follow a Generalized Pareto Distribution (GPD) [START_REF] Castillo | Extreme value and related models with applications in engineering and science[END_REF]. This is an equivalent of the central limit theorem for extreme values. A special case of GPD is the exponential distribution which is easy to fit. Thus, for d u ≥ :

( ) ( ) ( ) :

1 1 ( ) exp u x F d P D d F u σ -   = ≤ ≈ --     (8
( ) 1 1 k m k u d k m and F u m = < = -+ . ( 9
)
The parameter σ is estimated using maximum loglikehood method [START_REF] Castillo | Extreme value and related models with applications in engineering and science[END_REF].

: 1

1 k i m i d k σ = = ∑ . (10)
Finally, since only data from the undamaged state are available, the classification of a new sample d as damaged or undamaged is done with a hypothesis test. To improve the robustness of control charts, it is common to consider a run of p measurements instead of each measurement individually [START_REF] Zapico-Valle | Experimental validation of a new statistical process control feature for damage detection[END_REF]. Thereby, the null hypothesis (undamaged state) is rejected if p consecutives values of d exceed the control limit:

0 1 : , : 1 i i H d CL H d CL i p ≤ > = … . (11)
The control limit is fixed with respect to a probability α of type I error. So, with the verified assumption that d i are independent, α is the probability that p successive values exceed the control limit when the state is undamaged.

( ) ( ) ( ) 1 1 1 p p p P D CL F CL F CL α α   = > = - ⇒ = -   . ( 12
)
CL is calculated using Eq.12 and inversing Eq.8.

Database repartition

When a learning process is involved in pattern recognition, data are usually split in three parts to control the quality of the training.

• The reference baseline is composed of half of the undamaged database. It is used as reference for Mahalanobis distance calculation. • The classification base is composed of a quarter of the undamaged database. It is used to estimate the parameters of the statistical model and fixes the control limit. • The test base is composed of a quarter of the undamaged database and all damaged base. It is used to test the damage detection method.

CASE STUDIES Case study 1

The first case study (CS1) is a 4 dof mass/spring/damper numerical model, excited by a white noise. The system is solved by a fourth order Runge-Kutta method sampled at 30Hz. Damage is introduced by reducing the stiffness in traction of the spring k 1 to simulate opening and closing of a crack (Figure 3). The database is composed of 120 times series of 8192 values at the undamaged state, and 90 damaged one with a reduction of stiffness by 10% every 10 measurements. This case is a first test for the damage detection algorithm, with very clean data and no external variations.

Case study 2

To test the robustness of the approach, it has to be tested on more realistic data. In civil engineering structures, environmental variations cause large fluctuations of damage indexes making damage detection very difficult.

This second case study is a 200x12x10cm fibre reinforced concrete beam ( Figure 4). To simulate environmental variations, 4 infra-red lights are used to heat the beam on one face, up to 50°C. Damage is introduced by four points flexion cycles with an increasing load. While temperature fluctuates, vibration measurements are recorded through 4 uniaxial accelerometers placed on the top. Accelerometers will be referred as #1 to #4 from the right to the left of the beam. The excitation is an 800Hz band-limited noise and is produced by an electrodynamic shaker. For each measurement sequence, 5 times series are recorded. Each time series counts 8192 points at 2048Hz. The undamaged and the damaged databases are composed of 210 times series each (42 sequences).

RESULTS AND DISCUSSION

The reconstruction procedure suggests that the optimal delays are 6 and 3 for respectively CS1 and CS2, and reconstruction dimension of 7 for both. This leads to JFV formed by 49 components. To determine the control limit, the probability of type I error is set to 0.01 and between 15 exceedances are used to calibrate the statistical models. The quality of the model can be assessed by the quantile and probability plot (Figure 5 and Figure 6). As most of the points lay on the central line for accelerometer #2 (CS2), the fit is acceptable. Similar results are obtained for other models.

The Figure 7 presents the Mahalanobis distance as function of the percentage of stiffness decrease. The filled markers indicates that the null hypothesis is rejected (three consecutive points exceed the control limit). Only one false alarm is detected. From 30% of stiffness reduction, all measurements are correctly classified (except one point). Furthermore, the MD presents a monotonic trend as damage increase; this could lead to a quantification of the degree of degradation. This simple case, with very clean data, proves that the proposed DSF offers some promising abilities. The task is more complicated in more realistic conditions. Figure 8 shows the control charts for each accelerometer. There are almost no differences between sensors, it is not possible to locate the damage. This means that it affects the global behavior of the beam significantly.

All the undamaged points in the test base are correctly classified since no false alarms are detected. On the other hand, between measurement sequences 44 and 60 only few points are classified as damaged (1 for accelerometer #1 to 7 for accelerometer #2). This indicates that the damage induced by the first cycles of loading does not affect significantly the dynamic of the beam. It is likely that only micro-cracking is developing during the early loadings. However, the few true detections alert that a slight change occurs in the beam. Beyond the 60 th sequence, all points are detected as damaged and the change is strong between 60 and 61. It is related to the apparition of the first macro-crack which modifies considerably the behavior of the beam.

Once the macro-cracking appears, the MD presents variations which are not related to the severity of damage but more likely to the temperature fluctuations. Since it is not present before the sequence 60, the cracking somehow amplifies the sensitivity to environmental variations. In spite of this increased variability, the damage detection algorithm keeps correctly classifying the measurements.

CONCLUSION

A damage detection strategy is proposed. It is formed by a new damage sensitive feature based on state-space embedding of time series. More precisely, the damage sensitive feature is formed by the evaluation of the Jacobian matrix of the evolution of trajectories in the state space. Then, the Mahalanobis distance compares a new vector to a reference database, converting the multidimensional vector information into a unique scalar value. The classification is finally carried out through control charts, in which the control limit is set using extreme value statistics modeling.

The global approach is tested successfully on a simple 4 dof mass/spring numerical model. It is able to detect damage from 30% of stiffness reduction, with no false alarms. When tested on a concrete beam subjected to loading cycles, as well as temperature variations, only few true detections are observed during the microcracking. As soon as macro-cracking occurs, all points are classified as damaged in spite of a greater dispersion due to temperature fluctuations.

To enhance the method, further investigations on the statistical modeling are needed. Indeed, it appears that in spite of the small type I error probability selected, some false alarms can occur depending on the repartition of measurements in the three bases (train, classification and test). It is important to work on the selection of these bases and on their minimum size required to achieve good statistical modeling.

The robustness of the algorithm has to be confirmed on different case studies and compared to other damage sensitive features like time series models (AR) or modal analysis.

  2 (:) JFV J= .

Figure 1 .

 1 Figure 1. Illustration of the JFV calculation algorithm Figure 2. Mahalanobis vs Euclidian distance

F

  ) with σ, the scale parameter.The calibration of the model starts by the determination of the threshold, u. It is done by choosing a number of exceedances k, among a sample of size m taken from the undamaged database { } u is associated with the k order statistics : u is estimated by the empirical distribution of D.

Figure 3 .

 3 Figure 3. CS1 : Numerical model Figure 4. CS2 : Concrete beam dimensions [cm]

Figure 5 . P-P plot for accelerometer 2 Figure 6 .

 526 Figure 5. P-P plot for accelerometer 2 Figure 6. Q-Q plot for accelerometer 2

Figure 7 .

 7 Figure 7. CS1 : Mahalanobis distance as function of the percentage of stiffness reduction

Figure 8 .

 8 Figure 8. From top right, to bottom left : Accelerometer #1 to #4 ; Mahalanobis distance for each sequence of measurement


J A Barrat
email: barrat@univ-brest.fr.

B Zanda

F Moynier

C Bollinger

C Liorzou

G Bayon

Geochemistry of CI chondrites: Major and trace elements, and Cu and Zn Isotopes. By

In order to check the heterogeneity of the CI chondrites and determine the average composition of this group of meteorites, we analyzed a series of 6 large chips (weighing between 0.6 and 1.2 g) of Orgueil prepared from 5 different stones. In addition, one sample from each of Ivuna and Alais were analyzed. Although the sizes of the chips used in this study were "large", our results show evidence for minor chemical heterogeneity in Orgueil, particularly for alkali elements and U. After removal of one outlier sample, the spread of the results is considerably reduced. For most of the 46 elements analyzed in this study, the average composition calculated for Orgueil is in very good agreement with previous CI estimates. This average, obtained with a "large" mass of samples, is analytically homogeneous and is suitable for normalization purposes.

Finally, the Cu and Zn isotopic ratios are homogeneously distributed within the CI parent body with a spread of less than 100 ppm per atomic mass unit (amu).

"What is pride*? A whizzing rocket that would emulate a star.

Introduction

Carbonaceous chondrites are rare types of meteorites that comprise less than 5 % of the meteorite falls. These rocks display a wide range of petrographical, chemical and Oisotopic features, and are classified in 8 main groups (CI, CM, CO, CV, CK, CR, CH and CB) derived from very diverse asteroids. The CI chondrite group is small: it comprises only 5 falls (Alais (6 kg), Ivuna (0.7 kg), Orgueil (14 kg), Revelstoke (1 g), Tonk (10 g)) and possibly a few finds from Antarctica (Yamato (Y) 86029 (11.8 g), Y-86737 (2.81 g), Y-980115 (772 g), 980134 (12.2 g)). Unlike other chondrites, these rocks are essentially devoid of chondrules and other high temperature components. They have undergone the highest degree of aqueous alteration of all the meteorite classes [START_REF] Scott | Chondrites and their components[END_REF]. Despite the scarcity of such chondrites, they have been the center of a large number of studies. They are generally considered to be among the most primitive rock types in the Solar System from a chemical point of view. Indeed, their bulk compositions are similar to that of the solar photosphere excepted for volatiles such as H, C, N and O. Thus, because they mirror the composition of the Sun, their compositions are widely used to estimate the abundances of almost all the elements in the Solar System (e.g., [START_REF] Cameron | Elemental and nuctidic abundances in the solar system[END_REF][START_REF] Anders | Solar-system abundances of the elements[END_REF][START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF][START_REF] Lodders | Abundances of the elements in the solar system[END_REF].

Over the years, a huge amount of chemical data has been obtained on CI chondrites (e.g., [START_REF] Lodders | Abundances of the elements in the solar system[END_REF]. Taken as whole, the results show noticeable spreads for many elements including the refractory ones (i.e., the REEs). Determining an average composition is not straightforward. First, these rocks are extremely rare, and samples from only two of them (i.e., Orgueil and Ivuna) can be usually obtained from institutional collections. Therefore, the great majority of the chemical and isotopic data available for CI chondrites was obtained from the analysis of Orgueil, the largest one, and to a lesser extent of Ivuna [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF]. Second, chemical analyses have been performed generally on small samples by different analysts, using different analytical procedures, different calibration strategies, different standards, and finally, with different accuracy and analytical precision. Hence, part of the spread of the results is most probably explained by analytical biases or artifacts.

Moreover, some CI-chondrite analyses are based on samples < 100 mg, which [START_REF] Morlok | Brecciation and chemical heterogeneities of CI chondrites Geochim[END_REF] showed to be mineralogically and chemically heterogeneous. An additional part of the spread of the results could hence be explained by the possible lack of representativeness of these small samples. To overcome these problems, the database for CI chondrites was filtered with the aim of eliminating any anomalous data prior to calculating average compositions (e.g., see [START_REF] Lodders | Abundances of the elements in the solar system[END_REF] for the details of the calculations). Although it is widely accepted that the average CI composition is at present reasonably well constrained for most of the elements, adjustments or improvements are possible for some elements.

In this study, we present new major, trace element, and Cu and Zn isotopic compositions obtained on six "large" chips (from 0.6 to 1.2 g each) prepared from five different stones of Orgueil. Our aim was to evaluate the chemical heterogeneity of Orgueil at this scale of sampling. In addition, we analyzed samples of Alais and Ivuna. These data will be used to calculate and discuss an improved average for the chemical composition of CI chondrites.

Samples and Analytical Procedures

Samples

Six chips of Orgueil prepared from five different stones, and one chip of Alais and Ivuna were provided by the Muséum National d'Histoire Naturelle, Paris (Table 1). CI are extremely friable and most samples are partly or totally disintegrated into chips within the clear polystyrene boxes or glass jars in which they are stored. Fusion-crust free chips of the appropriate sizes were selected under a binocular microscope with the help of plastic tweezers.

Bulk rock compositions

Chips were totally powdered using a boron carbide mortar and pestle. Typically 120 mg of the powder were dissolved in closed screw-top teflon vessels (Savillex) at about 130 °C for three days using 5 ml of concentrated HF, and 2 ml of concentrated HNO 3 . The vessels were then opened. After evaporation to dryness of the acid mixture, approximately 2 ml of HNO 3 was added, and the vessels were capped and placed back on the hot plate and left overnight.

The samples were then dried again, and taken up in about 20 g of 6 M HCl ("mother solutions"). No residual grains were observed in the mother solutions excepted in a couple of Orgueil solutions which contained some "fine black dust" (insoluble carbon?) with apparently no impact on the results. Only reagents double-distilled in quartz or teflon sub-boilers were used. Abundances of both major and trace elements were analyzed using aliquots of the same mother solutions for all samples at the Institut Universitaire Européen de la Mer (IUEM), Plouzané.

The concentrations of Ti, Al, Cr, Fe, Mn, Mg, Ca, Na, P, Co and Ni were determined by ICP-AES (inductively coupled plasma-atomic emission spectrometry) using a Horiba Jobin Yvon Ultima 2 spectrometer following the procedure of [START_REF] Cotten | Origin of anomalous Rare-Earth Element and Yttrium enrichments in subaerially exposed basalts-evidence from French-Polynesia[END_REF]. Aliquots of mother solutions containing the equivalent of 50 mg of samples were used for the determination of the concentrations of these elements.

The concentrations of trace elements were determined by ICP-SFMS (inductively coupled plasma-sector field mass spectrometry) using a Thermo Element 2 spectrometer following the procedures described by [START_REF] Barrat | The Stannern trend eucrites: Contamination of Main-Group eucritic magmas by crustal partial melts[END_REF][START_REF] Barrat | Geochemistry of diogenites : Still more diversity in their parental melts[END_REF]. Two aliquots of each mother solutions containing the equivalent of 15 mg of sample were weighted in dry screw-top Teflon vessels.

One was spiked with a solution of pure Tm, and the other not. After evaporation to dryness, the residues were taken up at 130°C with 5 drops of conc HNO 3 , and subsequently diluted with 15 ml of ultrapure water containing traces of HF, to ensure the stability in solution of high field strength elements (especially Nb and Ta). The solutions were transferred to vials and analyzed at least twice. The concentrations were determined using the unspiked solutions (determination of the Tm/Yb and Tm/Er ratios in order to calculate the Tm abundances) and the spiked solutions (all the other elements), following calculations adapted from [START_REF] Barrat | Determination of rare earth elements in sixteen silicate reference samples by ICP-MS using a Tm addition and an ion exchange chromatography procedure[END_REF]. Notice that the results obtained with the unspiked solutions were used to control the quality of the reported analyzes but were not averaged with the final results. Two procedural blanks were processed in parallel in each series of analyses. The contributions of the blanks were insignificant for all the elements.

The precision and the accuracy of the results were estimated using well characterized standards and sample duplicates. The results obtained for a series of standards (WS-E, JB2, BIR1) and for the Allende chondrite (USNM 3529, [START_REF] Jarosewich | The Allende Meteorite Reference Sample[END_REF] are reported in Tables 2 to 4. For ICP-AES results, the accuracy is better than 7 % for Na and P, and probably much better than 3 % for the other elements.

The trace element concentrations obtained by ICP-SFMS are given relative to our revised working values for the USGS basalt BHVO-2 (Table 3), which are based on our own measurements and values from the literature (see Table 3). These working values are identical to those given by [START_REF] Barrat | The Stannern trend eucrites: Contamination of Main-Group eucritic magmas by crustal partial melts[END_REF], excepted for a few elements. Our previous working value for Cs is not correct, because it generates results which are systematically about 15 % higher than the recommended values for all the well-characterized rock standards, and thus has been corrected accordingly. For Zr, Hf, Nb, and Ta, we have adopted the values obtained by [START_REF] Pfänder | Nb/Ta and Zr/Hf in ocean island basalts -Implications for crustmantle differentiation and the fate of Niobium[END_REF] which are among the most accurate available at present for this group of elements. Finally, we have redetermined the W abundance in BHVO2 and our new results were significantly lower than our previous estimation by a factor of about 23 %, and indistinguishable of the W abundance determined in BHVO2g (a glass standard prepared with the BHVO2 powder) by isotope dilution [START_REF] König | Mobility of tungsten in subduction zones[END_REF]. In the event of future change to these BHVO-2 values, the data need only to be corrected by the ratio of the new and old values. Moreover, these working values can be used to evaluate possible interlaboratory bias.

A correction can be made accordingly if necessary.

The trace element concentrations obtained for the basalts BIR-1, JB2 and WS-E are reported in Table 3. The concentration reproducibility is generally much better than 5 %. The results are in very good to excellent agreement with various literature values (see the GEOREM database (http://georem.mpch-mainz.gwdg.de) for a more extensive compilation of literature values). One of the most significant differences is for Y in the JB2 basalt, for which the concentration measured by [START_REF] Makishima | Determination of major, minor and trace elements in silicate samples by ICP-QMS and ICP-SF-MS applying isotope dilution-internal standardisation (ID-IS) and multi-stage internal standardisation[END_REF] is not correct (as suggested by the non-chondritic Y/Ho (=23) they have obtained for this standard). In order to validate our procedure for chondrites, we obtained 3 splits of the Allende powder standard USNM 3529 from the Smithsonian Institution (14/2, 14/22, and 15/3). Each split was analyzed twice and 125 to 162 mg were used per analysis. The results are given in Table 4. The relative standard deviations (RSD) for the six analyses are 9 % for W, 4 % for Pb and much less than 3 % for all the other elements. Again, the concentrations are in excellent agreement with literature data. This Allende powder is known to be heterogeneous for lead and the concentrations we obtained are in the range of the reported values [START_REF] Jarosewich | The Allende Meteorite Reference Sample[END_REF].

The good reproducibility of our analyses is illustrated by the results obtained on the rare earth elements (REE). The Allende powder USNM 3529 displays an unusual REE pattern displaying a prominent Tm positive anomaly, and small negative Ce and Eu anomalies (Fig. 1). These unusual features are certainly inherited from some Ca, Al-rich inclusions which are frequent in Allende and display the same anomalies (e.g., McPherson, 2004). Notice that the spread of our results is more restricted than the spread of the literature data (e.g., [START_REF] Jarosewich | The Allende Meteorite Reference Sample[END_REF][START_REF] Pourmand | A novel extraction chromatography and MC-ICPMS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite abundances and Post-Archean Australian Shale (PAAS)[END_REF]. The powder could be slightly heterogeneous for the refractory elements. The fact that we dissolved more powder than most other analysts could explain the good reproducibility we achieved for the REEs.

Cu and Zn isotopes

The Zn and Cu isotopic composition were analyzed following the procedure described in [START_REF] Maréchal | Precise analysis of copper and zinc isotopic compositions by plasmasource spectrometry[END_REF] and Moynier et al. (2010a and b). Zn was first purified on AG1X8 anion-exchange resin in HBr/HNO 3 . Cu was further purified on AGMP-1 anion-exchange resin in HCl. For both Zn and Cu chemical purifications, the yield was found to be better than 99 % and the blanks of <10 ng for Zn and <5 ng for Cu are negligible (<0.05%) with respect to the total amounts of Zn and Cu in the samples, which are >20 µg. Isotopic ratios of Zn and Cu in all samples were analyzed with the MC-ICP-MS Thermo-Finnigan Neptune Plus at Washington University in St Louis as described in [START_REF] Herzog | Isotopic and elemental abundances of copper and zinc in lunar samples, Zagami, Pele's hairs, and a terrestrial basalt[END_REF]. Isotope ratios are expressed as permil relative deviations from the standards NIST 976 for Cu (δ 65/63 Cu), and JMC-Lyon for Zn (δ 66/64 Zn. δ 67/64 Zn and δ 68/64 Zn). Replicate analyses of the same samples carried out during different analytical sessions define an external reproducibility of ± 0.09 ‰ for δ 66 Zn, ± 0.26 ‰ for δ 67 Zn, ± 0.27 ‰ for δ 68 Zn and ± 0.10 ‰ for δ 65 Cu (see [START_REF] Herzog | Isotopic and elemental abundances of copper and zinc in lunar samples, Zagami, Pele's hairs, and a terrestrial basalt[END_REF] for extensive discussion of our analytical precision).

Results

Major and trace elements

Orgueil At first glance, the six samples of Orgueil display a limited range of abundances for most major and trace elements (Tables 5 and6). This is well shown by the relative standard deviations (RSD), which are around or below 5 % for most elements. Only four elements exhibit RSD > 10 %: Na (22 %), K (20 %), Rb (13 %), U (13 %). These variations are much larger than the analytical reproducibility, and can be explained by the heterogeneity of the meteorite at the 0.6-1 g scale. Indeed, Na and K concentrations, respectively determined by ICP-AES and ICP-SFMS, are strongly correlated (r = 0.990), and it can be noticed that our six samples display very similar Na/K ratios close to 8.6. In the case of Rb and U, the high RSD are due by sample ORG6, which displays Rb and U abundances significantly lower and higher respectively than the five other samples.

Elements displaying lower RSD, display ranges that could still reflect a real, although limited, heterogeneity of the meteorite. For example, Mn and P abundances range respectively from 0.178 to 0.210 wt% and from 0.094 to 0.108 wt% as determined by ICP-AES. These ranges were nicely confirmed by the ICP-SFMS analyses. Interestingly, the sample ORG6 is again significantly distinct from the other samples, and shows the lowest Zn abundance, and somewhat unusual REE abundances (slight LREE enrichment compared to the 5 other samples, Fig. 2). Similar light REE enrichments were recently observed in a few other Orgueil fragments much smaller in size by [START_REF] Pourmand | A novel extraction chromatography and MC-ICPMS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite abundances and Post-Archean Australian Shale (PAAS)[END_REF]. In agreement with these authors, such a feature is more likely explained by a local redistribution of the REEs from phosphates (merrillite or apatite) by aqueous fluids on the CI-parent body. We thus consider the sample ORG6 as an outlier, and we have excluded it in the Orgueil average that we discuss in this paper. We will use this average composition for normalization purposes. It is in agreement with literature results for most elements (e.g., [START_REF] Kallemeyn | The compositional classification of chondrites -1. The carbonaceous chondrite groups[END_REF][START_REF] Anders | Solar-system abundances of the elements[END_REF][START_REF] Beer | Neutron capture cross sections and solar abundances of 160,161 Dy, 170,171 Yb, 175,176 Lu, and 176,177 Hf for the s-process analysis of the radionuclide 176 Lu[END_REF][START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF]Lodders et al., 1989), and differences will be extensively described later.

Alais and Ivuna

Previous analyses obtained on these two chondrites have shown that their compositions are close to that of Orgueil (e.g., [START_REF] Kallemeyn | The compositional classification of chondrites -1. The carbonaceous chondrite groups[END_REF][START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: Implications for the terrestrial and solar-system Th/U ratios[END_REF][START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF]. The results obtained here on Ivuna are in agreement with literature data, and are in the range defined by our five "normal" Orgueil samples for most elements, with the exception of K (Tables 5 and6). The fragment of Alais analyzed here was small (327 mg), and probably not representative of the meteorite. Indeed, its composition deviates slightly from the other CIs, as shown by its unusual convex REE pattern (Fig. 2). The Cu and Zn isotopic compositions of Orgueil and Ivuna have been previously determined by [START_REF] Luck | Coupled 63 Cu and 16 O excesses in chondrites[END_REF][START_REF] Luck | Zn and Cu isotopic variations in chondrites and iron meteorites: early solar nebula reservoirs and parent-body processes[END_REF]. Because the sample of Orgueil used by these authors was an aliquot of the powder made with the anomalous chip ORG6 (see above), we analyzed our 8 samples of CI chondrites in order to refine the Zn and Cu isotopic composition of CI and detect possible heterogeneities. The results are in agreement with the previous studies (Table 7). The samples display narrow ranges of Cu and Zn isotopic compositions, including the Alais and ORG6, the two anomalous chips. These ranges are of the same order as the external reproducibility of the analyses for Zn isotopic compositions, and twice the external reproducibility for the δ 65 Cu values. Thus, all these data can be used to define an average CI composition (Table 7).

Cu and Zn isotopes

Discussion

How heterogeneous is Orgueil really?

The heterogeneity of the CI-chondrites is well known for the major elements at the mm scale (e.g., [START_REF] Morlok | Brecciation and chemical heterogeneities of CI chondrites Geochim[END_REF]. Furthermore, trace element analyses made on samples smaller than 200 mg give results that can deviate substantially from canonical CIcompositions (e.g., [START_REF] Evensen | Rare-earth abundances in chondritic meteorites[END_REF][START_REF] Ebihara | Are C1 chondrites chemically fractionated? A trace element study[END_REF][START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: Implications for the terrestrial and solar-system Th/U ratios[END_REF][START_REF] Mittlefehldt | Geochemistry of the ungrouped carbonaceous chondrite Tagish Lake, the anomalous CM chondrite Bells, and comparison with CI and CM chondrites[END_REF][START_REF] Pourmand | A novel extraction chromatography and MC-ICPMS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite abundances and Post-Archean Australian Shale (PAAS)[END_REF]. Although the ranges of major and trace element abundances observed in this study are relatively narrow for most elements, the spread of concentrations displayed by some of them suggests that heterogeneity is still detectable using a series of ~ 0.5 -1g size samples prepared from different stones. Alternatively, it can be argued that the chips used in this study were all lower than the threshold mass for chemical heterogeneity of Orgueil. We are confident that the ranges obtained reflect a real heterogeneity among the different stones collected. If the limited spread shown by our data were explained solely by the size of the samples, we should observe variations for a number of elements whatever their geochemical behaviors (e.g., [START_REF] Mittlefehldt | Geochemistry of the ungrouped carbonaceous chondrite Tagish Lake, the anomalous CM chondrite Bells, and comparison with CI and CM chondrites[END_REF]. In fact, the elements exhibiting the highest relative standard deviations (Na, K, Rb, Cs, U) are notoriously known for their mobility with aqueous fluids. Thus, these ranges are more likely the result of the complex aqueous alteration suffered by the Orgueil parent body. Although some chemical variations can be detected in Orgueil, these heterogeneities are not strong and should not be overemphasized. Indeed, as pointed out by [START_REF] Lodders | Abundances of the elements in the solar system[END_REF], the secondary processes that this meteorite has suffered, must have been essentially isochemical on a cm-scale, otherwise its chemical composition, and certainly its Zn isotopic composition, which can be modified by aqueous alteration [START_REF] Cloquet | Zn mobility during oceanic crust alteration inferred by its isotopic composition[END_REF], would be much more heterogeneous.

Cu and Zn isotopic compositions of CI chondrites

The lack of isotopic anomalies (i.e. δ 68/64 Zn/2~δ 67/64 Zn/1.5~δ 66/64 Zn) confirms the conclusions from [START_REF] Luck | Zn and Cu isotopic variations in chondrites and iron meteorites: early solar nebula reservoirs and parent-body processes[END_REF] and [START_REF] Moynier | Search for 70 Zn anomalies in meteorites[END_REF] that despite different nucleosynthetic origins Zn isotopes were well mixed in the solar nebula. By combining our data with those of [START_REF] Luck | Coupled 63 Cu and 16 O excesses in chondrites[END_REF][START_REF] Luck | Zn and Cu isotopic variations in chondrites and iron meteorites: early solar nebula reservoirs and parent-body processes[END_REF], we calculate an average of δ 66/64 Zn =0.46±0.08 and δ 65/63 Cu =0.05±0.16 for CI chondrites. These results show that Zn and Cu isotopes are homogenized within the CI chondrite group and represent the best estimate for the Cu and Zn isotopic composition of solar system so far. Other groups of chondrites are isotopically distinct from CI for both Cu and Zn (see Figure 3). These variations have been suggested to represent a mixing between two or more sources of Zn in the early solar system [START_REF] Luck | Coupled 63 Cu and 16 O excesses in chondrites[END_REF][START_REF] Luck | Zn and Cu isotopic variations in chondrites and iron meteorites: early solar nebula reservoirs and parent-body processes[END_REF]. The isotopic composition of terrestrial mantle rocks overlap within error with the average reported in this study (see [START_REF] Albarède | The stable isotope geochemistry of copper and zinc[END_REF][START_REF] Ben Othman | Cu-Zn isotopic variations in the Earth's mantle[END_REF], [START_REF] Cloquet | Variation in the isotopic composition of zinc in the natural environment and the use of zinc isotopes in biogeosciences: a review[END_REF] for average composition of terrestrial igneous rocks) and suggest that the bulk silicate Earth is CI-chondritic for Cu and Zn isotopes (see Figure 3).

Using a different technique (double spike-TIMS), [START_REF] Ghidan | Isotope fractionation and concentration measurements of Zn in meteorites determined by the double spike, IDMS-TIMS techniques[END_REF] analyzed the Zn isotopic composition of Orgueil. Our results are similar to theirs within analytical uncertainty, but with a much smaller analytical uncertainty (±0.30 on δ 66/64 Zn in Ghidan and Loss vs. ±0.10 in the present study).

Orgueil and the CI average composition

The vast majority of the chemical data available at present on CI chondrites were determined on Orgueil (e.g., [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF][START_REF] Lodders | Abundances of the elements in the solar system[END_REF]. In view of the available masses of the 5 CI falls in the institutional collections, the situation will undoubtedly not change in the near future, unless a new large fall of this type is recovered. The average composition of the CI-chondrites has been calculated using a weighted average of all the CIchondrites (e.g., [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF] or using only Orgueil (e.g., [START_REF] Palme | Abundances of the elements in the solar system[END_REF]. Because the compositional differences among CI-chondrites are probably limited (e.g., [START_REF] Kallemeyn | The compositional classification of chondrites -1. The carbonaceous chondrite groups[END_REF][START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF], and because Orgueil is by far the most analyzed one, the two approaches converge to very similar results. Here, we will consider the average composition of Orgueil using the major and trace element abundances obtained on the five "regular" chips (ORG1 to ORG5). We will compare it with the CI-chondrite average calculated by [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF], one of the most used CI-chondrite averages, and with the values calculated by [START_REF] Lodders | Abundances of the elements in the solar system[END_REF], this time the most recently updated Orgueil composition (Table 8). The convergence of our average composition with both of these compositions is excellent, with differences less than ± 5 % for most of the elements (Fig. 4). Thus, only a limited number of elements need to be discussed here.

Beryllium: This element has been rarely determined in CI chondrites [START_REF] Vilcsek | Bestimmung von Beryllium in extraterrestrischer Materie mit Hilfe der Flammenlosen Atomabsorbtiontspektroskopie[END_REF][START_REF] Makishima | Determination of major, minor and trace elements in silicate samples by ICP-QMS and ICP-SF-MS applying isotope dilution-internal standardisation (ID-IS) and multi-stage internal standardisation[END_REF]. Our new analyses for Orgueil are in agreement with the literature data. Note that our average value is very similar to the results obtained for Alais and Ivuna. Our data confirm the good agreement between the photospheric [START_REF] Grevesse | The composition of the Sun[END_REF] and meteoritic Be abundances, suggesting that the destruction of this element has not occurred over the Sun's lifetime contrary to most solar Li which has been burned [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF][START_REF] Lodders | Abundances of the elements in the solar system[END_REF].

Sodium and potassium:

The ranges displayed by the Na and K abundances in Orgueil are significant and reflect a real heterogeneity of the samples. The average reported in Table 5 has been calculated without an outlier (ORG6) that displays low K and Na abundances. It can be emphasized that the results are very close to those calculated by [START_REF] Lodders | Abundances of the elements in the solar system[END_REF] based on a large compilation of literature data (n=20 for Na, n=17 for K). Although we believe these average compositions to be correct, it is possible that the results were slightly biased by the filtering of the data.

Aluminum and calcium: our Al and Ca concentrations are about 10 % lower than those obtained by [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF] and [START_REF] Lodders | Abundances of the elements in the solar system[END_REF]. We suspect a slight underestimation of the Al and Ca abundances during the course of our study. However, these differences are not highly significant.

Phosphorus:

The average abundance obtained for P is 1010 µg/g. It is in agreement with the XRF data of [START_REF] Wolf | The solar system abundances of phosphorus and titanium and the nebular volatility of phosphorus[END_REF], and the ICP-MS data of [START_REF] Makishima | Determination of major, minor and trace elements in silicate samples by ICP-QMS and ICP-SF-MS applying isotope dilution-internal standardisation (ID-IS) and multi-stage internal standardisation[END_REF]. The P abundance in CI chondrites given by [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF] is overestimated (1220 µg/g) and should not be used in future studies.

Zirconium and hafnium:

The range of Hf abundances obtained here for Orgueil is tight (0.104-0.109 µg/g), and consequently the average concentration is well determined. The concentrations measured for Ivuna and Alais are identical to the Orgueil average value. Unsurprisingly, our new Hf average is in good agreement with the [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF] and [START_REF] Lodders | Abundances of the elements in the solar system[END_REF] values. Furthermore, our Zr concentration (3.52 µg/g) confirms the value calculated by [START_REF] Lodders | Abundances of the elements in the solar system[END_REF] (3.62 µg/g), and suggests that of [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF], 3.94 µg/g, is overestimated. The Zr/Hf ratio we have obtained (32.8) is only 2 % lower than the CI-chondrite average (33.4) obtained by [START_REF] Lu | Coprecipitation of Ti, Mo, Sn and Sb with fluorides and application to determination of B, Ti, Zr, Nb, Mo, Sn, Sb, Hf and Ta by ICP-MS[END_REF], and 4 % lower than the chondritic value (34.3) proposed by [START_REF] Münker | Evolution of planetary cores and the Earth-Moon system from Nb/Ta systematics[END_REF], both obtained by isotope dilution. These differences are small and should not be overemphasized.

Niobium and tantalum: Nb and particularly Ta are notoriously difficult to determine accurately in carbonaceous chondrites. Our Orgueil average displays a Nb abundance markedly higher than the estimation made by [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF], and similar to the average proposed by [START_REF] Lodders | Abundances of the elements in the solar system[END_REF] (Fig. 2 andTable 5), which are based on a limited number of analyses (e.g., [START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: Implications for the terrestrial and solar-system Th/U ratios[END_REF][START_REF] Jochum | Niobium and tantalum in carbonaceous chondrites : constraints on the Solar System and primitive mantle niobium/tantalum, zirconium/niobium, and niobium/uranium ratios[END_REF][START_REF] Münker | Evolution of planetary cores and the Earth-Moon system from Nb/Ta systematics[END_REF][START_REF] Lu | Coprecipitation of Ti, Mo, Sn and Sb with fluorides and application to determination of B, Ti, Zr, Nb, Mo, Sn, Sb, Hf and Ta by ICP-MS[END_REF], or have been inferred from the Zr/Nb ratios of carbonaceous chondrites. The Nb/Ta ratios we obtained for Orgueil (Nb/Ta=19.4) are similar to the chondritic value (Nb/Ta=19.9) obtained by [START_REF] Münker | Evolution of planetary cores and the Earth-Moon system from Nb/Ta systematics[END_REF] using an accurate isotope dilution procedure. (Notice that the Nb and Ta abundances that we have previously reported [START_REF] Bollinger | How heterogeneous is Orgueil really?[END_REF] were systematically overestimated due to a loss of these elements in one of our standard solutions).

Rare earth elements: These elements received considerable attention during the last forty years, and the REE abundances in chondrites have been determined not only for cosmochemical purposes, but also for the normalization and presentation of geochemical data.

Many sets of chondritic values have been proposed, some of which became very popular in the geochemical literature. It is beyond the scope of our work to review and compare each reference chondrite and discuss how the concentrations have been measured and/or calculated. Here, we selected some of them [START_REF] Evensen | Rare-earth abundances in chondritic meteorites[END_REF][START_REF] Beer | Neutron capture cross sections and solar abundances of 160,161 Dy, 170,171 Yb, 175,176 Lu, and 176,177 Hf for the s-process analysis of the radionuclide 176 Lu[END_REF][START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF][START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF][START_REF] Mcdonough | The composition of the Earth[END_REF][START_REF] Lodders | Abundances of the elements in the solar system[END_REF][START_REF] Pourmand | A novel extraction chromatography and MC-ICPMS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite abundances and Post-Archean Australian Shale (PAAS)[END_REF], and compare them with our Orgueil average in Figure 5. The patterns show that the new Orgueil average is in good agreement with all these reference values. Interestingly, our average is analytically undistinguishable from the results obtained by isotope dilution on a "large" sample (> 3 g) of Orgueil [START_REF] Beer | Neutron capture cross sections and solar abundances of 160,161 Dy, 170,171 Yb, 175,176 Lu, and 176,177 Hf for the s-process analysis of the radionuclide 176 Lu[END_REF]. The other chondrites (except for the values given by [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF], which are largely derived from the previous analysis) appear somewhat slightly more light REE enriched, but this is at most marginally significant. More importantly, some scatter is apparent for monoisotopic REEs, which is explained by the fact that their concentrations are in most cases, an assemblage of results obtained by different methods, often on different samples. In any case, the use of each of these reference chondrites produces a REE pattern with a very similar shape, and the differences are subtle especially when a logarithmic scale is used.

Nevertheless, the use of the [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF] values should be made with caution when Tm is determined and when Yb anomalies are discussed. We suggest that our Orgueil values are among the best currently obtained, especially when REE are compared with other lithophile refractory elements, in order to avoid the use of reference concentrations obtained on different samples.

Yttrium: The Y/Ho ratio of Orgueil is well constrained and close to 27.6 (Table 6). This value is undistinguishable from that obtained in the course of our study on CM-chondrites (Y/Ho=27.5, RSD=0.9%, n=6), and on the terrestrial standards BIR-1 and BHVO-2 (respectively 27.8 and 27.6). These analyses confirm that terrestrial basalts and carbonaceous chondrites exhibit similar Y/Ho ratios (Pack et al., 2007). Although the difference is small, our CI-value is slightly higher than the result reported by Pack et al. (2007), who obtained a ratio close to 25.9 for the carbonaceous chondrites. This slight discrepancy is probably explained by a calibration effect, as shown by the results obtained by these authors on the BCR2-G standard (Y/Ho=26.3). Our results on BCR2 (the powder used to made BCR2-G) is consistently slightly different (Y/Ho=29.03, RSD=1.2 %, n=30) and identical to the well known BCR1 standard (Y/Ho=29.18 , RSD=1.1 %, n=6) from the same quarry.

Tungsten: W has not often been measured on Orgueil. Recent analyses reported in the literature display a significant range (e.g., 0.078 to 0.117 µg/g, [START_REF] Friedrich | Comparison of the trace element composition of Tagish Lake with other primitive carbonaceous chondrites[END_REF][START_REF] Kleine | 182 Hf-182 W isotope systematics of chondrites, eucrites, and martian meteorites: Chronology of core formation and early mantle differentiation in Vesta and Mars[END_REF]Babechuk et al., 2007). The W abundances obtained here on CI-chondrites (including Alais and Ivuna) are between 0.10 and 0.12 µg/g (Table 3). Thus, the W abundance in Orgueil is well determined here (0.11 µg/g), a value about 15 % higher than those reported in the compilations made by [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF] and [START_REF] Lodders | Abundances of the elements in the solar system[END_REF]. Our values (W abundance, and W/Hf ratio) are in perfect agreement with the results obtained by [START_REF] Kleine | 182 Hf-182 W isotope systematics of chondrites, eucrites, and martian meteorites: Chronology of core formation and early mantle differentiation in Vesta and Mars[END_REF] by isotope dilution using a 400 mg chip.

Thorium and uranium: our average concentrations for these two elements are slightly lower than the values reported by [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF] and [START_REF] Lodders | Abundances of the elements in the solar system[END_REF]. [START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: Implications for the terrestrial and solar-system Th/U ratios[END_REF] have shown that U and Th are heterogeneously distributed in CIs at a low scale, and that some small samples display a noticeable U enrichment. This enrichment could be explained by a local redistribution of U from phosphates by aqueous fluids. Although the databases used for the estimations of the abundances of U and Th were filtered to avoid the anomalous samples, the results could be slightly hampered by this redistribution. Nevertheless, the differences between our Orgueil average composition and the literature ones are very limited for both elements and should not be considered very significant.

Conclusions

(1)

It is well known from previous studies that Orgueil and other CI-chondrites are significantly heterogeneous at a scale of 100 mg [START_REF] Morlok | Brecciation and chemical heterogeneities of CI chondrites Geochim[END_REF]. In this study, we show that significant heterogeneity can occasionally be detected using chips ranging in mass from 0.6 to 1.2 g, particularly for elements mobile during aqueous alteration (alkali elements and U). This result is important because it is generally believed that Orgueil is rather homogeneous at this level of sampling. Thus, a single chip, even if its mass is in the order of 1 g, is not necessarily representative of this famous fall, nor of the CI-chondrite group.

(2) In our sampling, a 1 g chip was chemically distinct for many elements, including some refractory ones such the REEs. Despite this anomalous sample, no significant heterogeneity has been detected for Cu and Zn isotopes. Our results obtained on Orgueil and on two other falls give a definitive characterization of the CI-chondritic reservoir for these isotopes.

(3) The average chemical composition calculated with the "regular" Orgueil samples is very close to the previous estimates, which were calculated from a compilation of literature results. Although the agreement is excellent for most elements, our results show that only measured concentrations for W depart significantly from compiled values. We strongly recommend the use of our average composition for normalization purposes, because 1) it has been calculated using results obtained on "large" samples, and 2) the concentrations have been determined using the same sample digestions. Makishima andNakamura (1999, 2006) and [START_REF] Makishima | Determination of chromium, nickel, copper and zinc in milligram samples of geological materials using isotope dilution high resolution inductively coupled plasma-mass spectrometry[END_REF]). Because of the use of a Tm-spike, we did not determine the abundances of this element in these standards. [START_REF] Nakamura | Determination of REE, Ba, Fe, Mg, Na and K in carbonaceous and ordinary chondrites[END_REF], [START_REF] Shinotsuka | Detailed abundances of rare earth elements, thorium and uranium in chondritic meteorites : an ICP-MS study[END_REF], Makishima and[START_REF] Makishima | Determination of major, minor and trace elements in silicate samples by ICP-QMS and ICP-SF-MS applying isotope dilution-internal standardisation (ID-IS) and multi-stage internal standardisation[END_REF][START_REF] Pourmand | A novel extraction chromatography and MC-ICPMS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite abundances and Post-Archean Australian Shale (PAAS)[END_REF]).

BHVO2

La Ce Pr Nd

Sm Eu Gd Tb Dy Ho Er Tm Yb Lu [START_REF] Luck | Coupled 63 Cu and 16 O excesses in chondrites[END_REF][START_REF] Luck | Zn and Cu isotopic variations in chondrites and iron meteorites: early solar nebula reservoirs and parent-body processes[END_REF], and this study). [START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF][START_REF] Lodders | Abundances of the elements in the solar system[END_REF] normalized to the average Orgueil composition calculated in this study (Table 8).

La Ce Pr Nd SmEu Gd Tb Dy Ho Er TmYb Lu Anders and Grevesse (1989) [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF] McDonough and [START_REF] Mcdonough | The composition of the Earth[END_REF] CI/CI (this study) [START_REF] Evensen | Rare-earth abundances in chondritic meteorites[END_REF]) Pourmand et al. (2011[START_REF] Beer | Neutron capture cross sections and solar abundances of 160,161 Dy, 170,171 Yb, 175,176 Lu, and 176,177 Hf for the s-process analysis of the radionuclide 176 Lu[END_REF] Figure 5. Selected CI chondrite reference compositions normalized to the average Orgueil composition calculated in this study (Table 8)

.

Figure 2 .Figure 3 .

 23 Figure 2. REE patterns of the chips of CI chondrites normalized to the average Orgueil composition calculated in this study

Figure 4 .

 4 Figure 4. Average compositions of CI chondrites[START_REF] Anders | Abundances of the elements: Meteoritic and solar[END_REF][START_REF] Lodders | Abundances of the elements in the solar system[END_REF] normalized to the average Orgueil composition calculated in this study (Table8).

Table 1 .

 1 Details of samples studied

		MNHN n°	mass (g)
	Orgueil
	ORG1	219239	1.00
	ORG2	222	0.62
	ORG3	222	0.61
	ORG4	234	0.84
	ORG5	250	0.86
	ORG6	237	1.02
	Ivuna	3578	0.71
	Alais	24	0.33

Table 2 .

 2 Major element, Cr, Ni and Co abundances in the BIR1 and JB2 basalts and in the Allende standard determined by ICP-AES and compared with literature values (a: GEOREM preferred values, b: Gavindaraju (1994), and c: Jarosewich et al. (1987)).

			BIR 1 RSD% reference a	JB2	RSD% reference b	USN3529 RSD% reference c
	n		5			4			3
	TiO 2	wt%	0.91	1	0.97	1.10	1	1.19	0.13	6	0.15
	Al 2 O 3	wt%	15.25	1	15.4	14.36	0.4	14.67	3.52	1	3.28
	Fe 2 O 3	wt%	11.83	1	11.3	14.84	0.3	14.34	33.40	0.3	33.7
	MnO	wt%	0.17	1	0.176	0.22	1	0.22	0.18	8	0.19
	MgO	wt%	9.76	0.5	9.70	4.77	1	4.66	24.09	0	24.59
	CaO	wt%	13.16	1	13.4	9.68	1	9.89	2.62	0	2.58
	Na 2 O	wt%	1.85	6	1.81	2.07	6	2.03	0.48	2	0.45
	K 2 O	wt%	< 0.05		0.03	0.38	2	0.42	< 0.05		0.04
	P 2 O 5	wt%	0.07	4	0.027	0.13	7	0.12	0.26	2	0.24
	Cr	µg/g	409	2	391	16	11	27	3623	0.2	3630
	Co	µg/g	54	4	52	38	5	33	659	1	600
	Ni	µg/g	190	1	166	12	18	17	14758	1	14200

Table 3 .

 3 Trace element abundances (in µg/g) selected for the international standard BHVO2 (B : our lab, P :[START_REF] Pfänder | Nb/Ta and Zr/Hf in ocean island basalts -Implications for crustmantle differentiation and the fate of Niobium[END_REF], R : Raczek et al. (2001), T : Tomascak et al. (2008) ; U : US geological survey, certificate of analysis ;), and results obtained by ICP-SFMS for BIR1, JB2 and WD-E compared with reference values (G : GEOREM preferred values; L: Lu et al. (2007); M:

Table 4 .

 4 Trace element abundances (in µg/g) obtained by ICP-SFMS for the Allende powder USNM 3529 and compared with literature values (1 : Jarosevich et al.(1987), 2 :[START_REF] Makishima | Determination of major, minor and trace elements in silicate samples by ICP-QMS and ICP-SF-MS applying isotope dilution-internal standardisation (ID-IS) and multi-stage internal standardisation[END_REF]), 3 : Lu et al. (2007), 4 : Dauphas et al. (2011) for U, Th , Hf and[START_REF] Pourmand | A novel extraction chromatography and MC-ICPMS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite abundances and Post-Archean Australian Shale (PAAS)[END_REF] for the other elements, 5 :[START_REF] Shinotsuka | Detailed abundances of rare earth elements, thorium and uranium in chondritic meteorites : an ICP-MS study[END_REF] 6 : Nakamura (1974).

		Split 14/2	Split 14/22	Split 15/3	average RSD%	1	2	3	4	5	6
		A	B	A	B	A	B
	mass (g) 0.16228 0.15083 0.1325 0.13535 0.12532 0.15975
	Li	1.89	1.82	1.79	1.83	1.73	1.79	1.81	3		1.48
	Be	0.0461	0.0429	0.0461	0.0451	0.0436	0.0465	0.0450	3	0.03	0.0445
	P	1181	1169	1154	1153	1175	1205	1173	2	1047	1163
	K	274	276	273	277	282	279	277	1	330	295
	Sc	10.57	11.50	11.49	11.12	11.54	11.47	11.28	3	11	11.35		11.33
	Ti	866	873	878	863	889	897	878	1	899		896
	V	93.9	94.2	95.1	92.7	96.5	98.6	95.2	2	92	99.5
	Mn	1422	1408	1407	1393	1426	1464	1420	2	1471	1506
	Co	623	622	609	605	616	623	616	1	600	717
	Cu	99.7	100	96.8	96.6	99.1	101.4	99.0	2	119	118
	Zn	116	118	118	119	120	122	119	2	110	139
	Ga	5.71	5.70	5.57	5.52	5.72	5.85	5.68	2	6	6.79
	Rb	1.18	1.17	1.15	1.17	1.19	1.20	1.18	1	1.2	1.29
	Sr	14.75	14.56	14.67	14.46	14.84	15.05	14.72	1	12	16.1
	Y	2.84	2.86	2.86	2.82	2.95	2.93	2.88	2	3	2.83		2.70	2.47
	Zr	6.48	6.57	6.56	6.51	6.80	6.76	6.61	2	9		6.60
	Nb	0.559	0.579	0.570	0.565	0.576	0.591	0.573	2			0.561
	Cs	0.0890	0.0885	0.0872	0.0861	0.0877	0.0903	0.0881	2		0.0911

Table 4 (

 4 continue)

		Split 14/2	Split 14/22	Split 15/3	average RSD%	1	2	3	4	5	6
		A	B	A	B	A	B
	Ba	4.55	4.50	4.54	4.47	4.53	4.59	4.53	1	4	4.51				4.85
	La	0.516	0.517	0.517	0.503	0.518	0.525	0.516	1	0.52	0.534		0.548	0.503	0.507
	Ce	1.28	1.27	1.29	1.26	1.31	1.31	1.29	2	1.33	1.32		1.37	1.26	1.33
	Pr	0.200	0.200	0.202	0.197	0.203	0.204	0.201	1	0.21	0.206		0.212	0.197
	Nd	1.02	1.03	1.03	1.00	1.03	1.04	1.02	1	0.99	1.06		1.09	0.968	1.004
	Sm	0.327	0.328	0.330	0.324	0.332	0.334	0.329	1	0.34	0.338		0.346	0.323	0.330
	Eu	0.113	0.114	0.114	0.112	0.115	0.116	0.114	1	0.11	0.111		0.118	0.104	0.113
	Gd	0.427	0.421	0.422	0.404	0.419	0.410	0.417	2	0.42	0.411		0.447	0.393	0.414
	Tb	0.0776	0.0760	0.0774	0.0746	0.0768	0.0750	0.0762	2	0.081	0.0735		0.0807	0.069
	Dy	0.510	0.507	0.516	0.496	0.511	0.508	0.508	1	0.42	0.491		0.544	0.466	0.504
	Ho	0.107	0.108	0.108	0.104	0.108	0.107	0.107	1	0.1	0.106		0.109	0.0954
	Er	0.309	0.314	0.310	0.303	0.313	0.310	0.310	1	0.29	0.284		0.317	0.288	0.303
	Tm	0.0554	0.0562	0.0563	0.0552	0.0565	0.0556	0.0559	1	0.055	0.0518		0.0551	0.0496
	Yb	0.322	0.323	0.325	0.323	0.328	0.330	0.325	1	0.3	0.317		0.328	0.311	0.315
	Lu	0.0455	0.0461	0.0457	0.0454	0.0468	0.0459	0.0459	1	0.052	0.0451		0.0460	0.0456	0.0465
	Hf	0.197	0.202	0.201	0.199	0.206	0.205	0.202	2	0.21		0.201	0.1939
	Ta	0.0347	0.0352	0.0343	0.0338	0.0334	0.0340	0.0342	2			0.0314
	W	0.206	0.232	0.192	0.204	0.186	0.184	0.200	9	0.2
	Pb	1.26	1.33	1.34	1.21	1.23	1.22	1.27	4	1.39	1.09
	Th	0.0587	0.0593	0.0607	0.0582	0.0599	0.0597	0.0594	2		0.0551		0.05864	0.061
	U	0.0149	0.0152	0.0151	0.0148	0.0156	0.0156	0.0152	2		0.0154		0.01554 0.0154

Table 5 .

 5 Major and minor element abundances in Alais, Ivuna and Orgueil obtained by ICP-AES.

			Alais Ivuna						Orgueil
					ORG1 ORG2 ORG3 ORG4 ORG5 ORG6	av. 1-6 RSD(%) av. 1-5 RSD(%)
	mass mg 120.62 133.40	119.60 111.33 124.76 118.62 104.50 106.60
	Ti	wt% 0.043 0.043	0.044 0.043 0.042 0.045 0.044 0.042	0.043	2.6	0.044	2.3
	Al	wt% 0.776 0.784	0.778 0.798 0.789 0.806 0.788 0.760	0.786	2.0	0.792	1.3
	Fe	wt% 18.64 18.88	18.97 19.15 20.92 19.36 19.19 18.73	19.39	4.0	19.52	4.1
	Mn	wt% 0.218 0.202	0.186 0.194 0.209 0.188 0.210 0.178	0.194	6.5	0.197	5.7
	Mg	wt% 9.41	9.55	9.17	9.38	9.55	9.48	9.52	9.03	9.36	2.3	9.42	1.6
	Ca	wt% 0.860 0.921	0.782 0.808 0.964 0.778 0.890 0.810	0.839	8.8	0.844	9.5
	Na	wt% 0.422 0.490	0.485 0.423 0.442 0.453 0.596 0.291	0.448	22.0	0.480	14.3
	P	wt% 0.101 0.102	0.094 0.098 0.104 0.104 0.108 0.096	0.101	5.6	0.102	5.6
	Cr	wt% 0.263 0.257	0.257 0.264 0.263 0.268 0.262 0.257	0.262	1.6	0.263	1.5
	Ni	wt% 1.08	1.20	1.23	1.12	1.08	1.12	1.12	1.15	1.14	4.7	1.13	5.2
	Co	µg/g	494	531	535	519	502	529	510	520	519	2.3	519	2.6

Table 6 .

 6 Trace and minor element abundances in Alais, Ivuna and Orgueil obtained by ICP-SFMS (in µg/g).

	Alais	Ivuna

Table 7 .

 7 Isotopic compositions of Cu and Zn in CI chondrites. The isotopic compositions are represented using the δ notation (parts per 1000 deviation from terrestrial Cu standard NIST 976 or Zn standard JMC-Lyon respectively).

		δ 65 Cu	δ 66 Zn	δ 67 Zn	δ 68 Zn
	Alais	0.02	0.46	0.61	0.85
	Ivuna	0.00	0.54	0.83	1.06
	Luck et al. (2005):
	Chunk 1		0.49	0.60	0.92
	Chunk 2		0.46	0.48	0.86
	Orgueil
	ORG1	0.13	0.42	0.60	0.79
	ORG2	-0.01	0.45	0.68	0.88
	ORG3	-0.03	0.43	0.57	0.79
	ORG4	0.19	0.43	0.60	0.80
	ORG5	0.11	0.51	0.75	1.02
	ORG6	0.04	0.45	0.60	0.87
	Luck et al. (2003, 2005):
	Chunk 1 (ORG6)	-0.09	0.46	0.71	0.90
	Chunk 2		0.52	0.75	1.01
	Mean CI (this work)	0.05	0.46	0.66	0.88
	2 σ σ σ σ	0.16	0.08	0.18	0.21

Table 8 .

 8 Abundances in CI-chondrites based on the Orgueil meteorite. (*Si has been estimated using the same Si/Mg ratio as Lodders et al. (2009)).Figure 1. REE patterns of the Allende standard normalized to the average Orgueil composition calculated in this study (literature results from

	Element	unit	this	RSD	Lodders	Anders and	atoms per
			work	%	et al. (2009)	Grevesse	10	6 Si atoms
						(1989)	(this work)
	3 Li	µg/g	1.44	3	1.47	1.5		55.5
	4 Be	µg/g	0.0226	5	0.021	0.0249		0.671
	Na	wt%	0.480	14	0.499	0.5		55700
	Mg	wt%	9.42	2	9.58	9.89	1.03 10	6
	Al	wt%	0.79	1	0.85	0.868		78340
	Si	wt%	10.52*		10.7	10.64		10	6
	P	µg/g	1010	5	967	1220		8710
	K	µg/g	550	14	544	558		3760
	Ca	wt%	0.84	10	0.922	0.928		56240
	Sc	µg/g	5.85	2	5.9	5.82		34.7
	Ti	µg/g	449	3	451	436		2502
	V	µg/g	52.4	2	54.3	56.5		275
	Cr	µg/g	2627	2	2650	2660		13490
	Mn	µg/g	1910	6	1930	1990		9280
	Fe	wt%	19.52	4	18.5	19.04	9.33 10	5
	Co	µg/g	519	3	506	502		2350
	Ni	wt%	1.13	5	1.08	1.1		51560
	Cu	µg/g	127	6	131	126		534
	Zn	µg/g	303	2	323	312		1236
	Ga	µg/g	9.48	2	9.71	10		36.3
	Rb	µg/g	2.33	6	2.31	2.3		7.29
	Sr	µg/g	7.73	7	7.81	7.8		23.6
	Y	µg/g	1.56	5	1.53	1.56		4.68
	Zr	µg/g	3.52	2	3.62	3.94		10.3
	Nb	µg/g	0.289	6	0.279	0.246		0.83
	Cs	µg/g	0.189	5	0.188	0.187		0.38
	Ba	µg/g	2.46	5	2.41	2.34		4.79
	La	µg/g	0.235	3	0.242	0.2347		0.452
	Ce	µg/g	0.600	3	0.622	0.6032		1.142
	Pr	µg/g	0.0910	3	0.0946	0.0891		0.173
	Nd	µg/g	0.464	3	0.471	0.4524		0.859
	Sm	µg/g	0.153	4	0.152	0.1471		0.272
	Eu	µg/g	0.0586	4	0.0578	0.056		0.103
	Gd	µg/g	0.206	3	0.205	0.1966		0.350
	Tb	µg/g	0.0375	4	0.0384	0.0363		0.0630
	Dy	µg/g	0.254	3	0.255	0.2427		0.418
	Ho	µg/g	0.0566	4	0.0572	0.0556		0.0916
	Er	µg/g	0.166	4	0.163	0.1589		0.266
	Tm	µg/g	0.0262	4	0.0261	0.0242		0.042
	Yb	µg/g	0.168	4	0.169	0.1625		0.259
	Lu	µg/g	0.0246	4	0.0253	0.0243		0.0376
	Hf	µg/g	0.107	2	0.106	0.104		0.160
	Ta	µg/g	0.0148	6	0.0145	0.0142		0.0218
	W	µg/g	0.11	10	0.096	0.0926		0.15
	Pb	µg/g	2.69	6	2.63	2.47		3.47
	Th	µg/g	0.0283	2	0.031	0.0294		0.0325
	U	µg/g	0.0077	5	0.0081	0.00893		0.00866

Acknowledgements

Samples were kindly provided by the Muséum National d'Histoire Naturelle de Paris (Orgueil, Alais and Ivuna), and by the Smithsonian Institution (Allende powder USNM 3529). We thank A. Krot for the editorial handling, H. Palme, M. Humayun and J. Wasson for their constructive comments, and Pascale Barrat for her help. Discussions on REE in chondrites with Nicolas Dauphas have been highly appreciated. We gratefully acknowledge R.H. Hewins for his careful reading of the manuscript, and the Programme National de Planétologie (INSU) for financial support. This research has made use of NASA's Astrophysics Data System Abstract Service.