François De

La Bourdonnaye

Céline Teulière

Jochen Triesch

Thierry Chateau

Learning to touch objects through stage-wise deep reinforcement learning

Learning complex behaviors through reinforcement learning is particularly challenging when reward is only available upon successful completion of the full behavior. In manipulation robotics, so-called shaping rewards are often used to overcome this problem. However, these usually require human engineering or (partial) world models describing, e.g., the kinematics of the robot or high-level modules for perception.

Here we propose an alternative method to learn an object palm-touching task through a weakly-supervised and stagewise learning of simpler tasks. First, the robot learns to fixate the object with its cameras. Second, the robot learns eye-hand coordination by learning to fixate its end effector. Third, using the previously acquired skills an informative shaping reward can be computed which facilitates efficient learning of the object palm-touching task. We demonstrate in simulation that learning the full task with this shaping reward is comparable to learning with an informative supervised reward.

I. INTRODUCTION

In recent years, deep reinforcement learning (RL) algorithms have allowed the learning of complex behaviors directly mapping pixels to actions without using hand-crafted features [START_REF] Finn | Deep spatial autoencoders for visuomotor learning[END_REF], [START_REF] Levine | End-to-end Training of Deep Visuomotor Policies[END_REF]. However, learning can be prohibitively slow when reward is only available when the full task has been completed successfully. This problem of sparse rewards is frequently addressed by specifying more informative reward functions that rely on additional forms of supervision. Indeed, informative shaping rewards have long been applied *This work is sponsored by the French government research program "Investissements d'avenir" through the IMobS3 Laboratory of Excellence (ANR-10-LABX-16-01), by the European Union through the program Regional competitiveness and employment (ERDF Auvergne region), and by the Auvergne region. J.Triesch acknowledges support from the Quandt foundation and the European Union's Horizon 2020 Research and Innovation Programme under grant agreement no. 713010 (GOAL-Robots Goalbased Open-ended Autonomous Learning Robots).

1 F. de La Bourdonnaye, C.Teulière and T. Chateau are with the university of Clermont Auvergne, the Pascal Institute CNRS, UMR6602, Aubière, France 2 J.Triesch is with the Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany in manipulation robotics [START_REF] Ghadirzadeh | Deep predictive policy training using reinforcement learning[END_REF], [START_REF] Chebotar | Combining Model-Based and Model-Free Updates for Trajectory-Centric Reinforcement Learning[END_REF], because they help to discriminate values of close states. For instance, [START_REF] Ghadirzadeh | Deep predictive policy training using reinforcement learning[END_REF], [START_REF] Chebotar | Combining Model-Based and Model-Free Updates for Trajectory-Centric Reinforcement Learning[END_REF], [START_REF] Deisenroth | Learning to Control a Low-Cost Manipulator using Data-Efficient Reinforcement Learning[END_REF], [START_REF] Gu | Deep reinforcement learning for robotic manipulation with asynchronous off-policy updates[END_REF] and [START_REF] Tsurumine | Deep dynamic policy programming for robot control with raw images[END_REF] use a distance measure between the current pose and a target pose to design an informative reward in manipulation tasks such as block stacking, reaching and door pushing or pulling. These rewards require knowledge of robot kinematics and target pose. Similarly, for tasks such as placing wooden rings or screwing bottle caps onto bottles [START_REF] Levine | End-to-end Training of Deep Visuomotor Policies[END_REF] and [START_REF] Levine | Learning contact-rich manipulation skills with guided policy search[END_REF] use an informative reward based on the distance between actual positions of end-effector or target object and their target positions. Tracking these points requires knowledge of the kinematics or non-trivial vision modules. For the same kind of task, [START_REF] Finn | Deep spatial autoencoders for visuomotor learning[END_REF] designs a reward based on a distance between visual features produced by an autoencoder and target features. This requires to place the robot in a target position and extract the target visual features each time the target location changes.

In contrast to these previous works, the aim of this paper is a robot that learns an object palm-touching task with only weak human intervention or supervision i.e. without kinematic models, hand-crafted features, or calibration parameters. More precisely, the task consists of reaching with the end-effector palm an object put on a table. This behavior can be seen as a natural predecessor to grasping. To learn this task with little supervision, we propose a stage-wise learning strategy inspired by infant development [START_REF] Hoffmann | Learning visuomotor transformations for gaze-control and grasping[END_REF], [START_REF] Carey | Magnetic Misreaching[END_REF], [START_REF] Fischer | A Theory of Cognitive Development: The Control and Construction of Hierarchies of Skills[END_REF]. The central idea is that an informative reward is constructed from knowledge that has been acquired during the learning of simpler predecessor tasks. Specifically, our robot first learns to fixate an object or its own end-effector using deep RL. Based on the knowledge acquired during these tasks an informative reward function is constructed that allows the robot to efficiently learn the object palm-touching task. Our results demonstrate that learning this task based on the learned informative reward signal works about as well as learning with a fully supervised reward, while naively learning from only a sparse reward signal fails completely in the same setting.

II. RELATED WORK

Our approach resembles developmental robotics methods [START_REF] Hoffmann | Learning visuomotor transformations for gaze-control and grasping[END_REF], [START_REF] Nori | Autonomous learning of 3D reaching in a humanoid robot[END_REF], [START_REF] Law | From Saccades to Grasping: A Model of Coordinated Reaching Through Simulated Development on a Humanoid Robot[END_REF], [START_REF] Chinellato | Implicit Sensorimotor Mapping of the Peripersonal Space by Gazing and Reaching[END_REF] which learn to reach using a hand-eye coordination function and object fixation. However, they are usually paired with supervision for the object and/or endeffector fixations [START_REF] Nori | Autonomous learning of 3D reaching in a humanoid robot[END_REF], [START_REF] Law | From Saccades to Grasping: A Model of Coordinated Reaching Through Simulated Development on a Humanoid Robot[END_REF], [START_REF] Chinellato | Implicit Sensorimotor Mapping of the Peripersonal Space by Gazing and Reaching[END_REF] or computation of action primitives [START_REF] Hoffmann | Learning visuomotor transformations for gaze-control and grasping[END_REF].

Our work is also related to methods which use sparseonly rewards in the sense that our sparse term fully defines the task. Though hardly using any supervision, sparse-only rewards generally require some strategies to increase the probability of getting a sparse reward. This can be done by increasing the number of agents learning the task [START_REF] Levine | Learning hand-eye coordination for robotic grasping with deep learning and large-scale data collection[END_REF] or by simplifying the action space using hand-crafted preprocessing [START_REF] Boularias | Learning to Manipulate Unknown Objects in Clutter by Reinforcement[END_REF]. Besides, if the agent has access to one of its goal states, a mechanism of learning from easy missions [START_REF] Asada | Purposive Behavior Acquisition for a Real Robot by Vision-Based Reinforcement Learning[END_REF] can be implemented to learn very precise robotic manipulation tasks [START_REF] Florensa | Reverse Curriculum Generation for Reinforcement Learning[END_REF]. We propose to increase the touching probabilities by building a weakly-supervised reward shaping term from learned skills without using action space simplification, several agents or the indication of a goal state.

III. METHODS

A. Background

An RL algorithm is usually based on Markov decision processes < S, A, R, T > where S is the set of states, A the set of actions, T the transition model (T : S × A → S) and R the reward function (R :

S × A × S → R).
The goal of the agent is to maximize the sum of discounted future rewards: J = ∞ k=0 r k γ k , where γ ∈ [0, 1] is a discount factor and r k the reward value at step k.

To optimize the criterion, we train a deterministic policy π : S → A. In the paper, we also estimate the state-action value function:

Q π (s, a) = E π ∞ k=0 r k γ k s, a , (s, a) ∈ S × A. (1)
Both the policy and the Q function are approximated by a neural network. Specifically, we use the DDPG algorithm [START_REF] Lillicrap | Continuous control with deep reinforcement learning[END_REF] which combines the deterministic policy gradient algorithm [START_REF] Silver | Deterministic Policy Gradient Algorithms[END_REF] and the DQN [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF]. DDPG is an "actor-critic" algorithm updating the critic Q φ with parameters φ and the deterministic policy π θ with parameters θ as follows. At each time-step, we choose N b transitions from a large memory buffer using a uniform distribution:

< s i , a i , r i , s i > i∈{1,...,N b } ∈ S × A × R × S.
The targets of the Q φ neural network are computed using a TD(0) update (with a learning rate equal to 1):

∀i ∈ {1, ..., N b }, y i = r i + γQ φ s i , π θ (s i ) . (2)
φ and θ are the parameters of the target networks updated using a rate parameter τ (t denotes a time-step):

φ t+1 = τ φ t + (1 -τ )φ t , θ t+1 = τ θ t + (1 -τ )θ t , (3)
The Q φ network updates its weights by minimizing the squared error

1 2N b N b i=1 (y i -Q φ (s i , a i )) 2 .
Using the Q φ network and the fact that the policy is deterministic, the following policy gradient is derived:

∂Q φ ∂θ 1 N b N b i=1 ∂Q φ (s i , π θ (s i )) ∂a ∂π θ (s i ) ∂θ . (4)
This update makes the policy select the actions that maximize the Q function at the batch states. In addition to this algorithm, we use the inverting gradient procedure of [START_REF] Hausknecht | Deep Reinforcement Learning in Parameterized Action Space[END_REF] to bound the actions. This method downscales the gradient when the action computed by the policy approaches its limit. When it exceeds its limit, the gradient is inverted. This mechanism prevents the actions from becoming too large.

B. Overview

We describe here the stage-wise learning process (see Figures 1 and2 for a schematic view). The task consists of touching the object with the palm. In the following, we use the notations:

• I = (I left , I right ) represents the images from the left and right cameras. • q = (q camera , q robot ) represents the 3 camera joint angles (one common tilt angle and two independent pan angles) and 7 joint arm joint angles. Our stage-wise learning framework involves three successive tasks:

First, the robot learns from raw pixels to fixate the object with a two-camera system. For this, we use [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF] to learn to fixate an object with weak supervision. At the end of the fixation, the camera system coordinates q camera fix implicitly encode the object position in 3D space.

Second, the robot learns a hand-eye coordination function f η which maps robot joint coordinates to virtual camera coordinates:

q camera virt = f η (q robot ). (5)
These virtual camera coordinates correspond to the camera coordinates which would make the camera system look at the end-effector. Finally, a reward signal using q camera fix and q camera virt to make the end-effector close to the object is computed and combined with a sparse reward, indicating if there is palm-touching or not. In the following, we describe each of the three steps.

C. Learning binocular object fixations

Fixating an object means bringing the object at the center of I left and I right by moving the cameras. To learn it, we build on our prior work [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF].

The task is learned with the DDPG algorithm [START_REF] Lillicrap | Continuous control with deep reinforcement learning[END_REF] using I and q camera as states, and ∆q camera as actions. The reward function is the sum of left and right camera components: r obj = r left obj + r right obj . For each camera c = left or right, the reward function is an affine decreasing function of the distance between the image center P i and the estimated object position P c o (computed below):

r c obj = 2 1 2 d max -||P i -P c o || 2 d max ∈ [-1, 1], (6)
with d max being the maximal distance between the image center and the object pixellic position. An episodic set-up is used. For each episode, a random object is put at a random location above the table. The episode ends when a given number of transitions has been reached.

The object detection mechanism involves a convolutional autoencoder training step in which images of the environment without object are encoded. Then, when an object appears in the environment, it is detected as an anomaly and localized in the images I left and I right . More precisely, we apply a kernel density estimator on the autoencoder reconstruction error images respectively |I left -Îleft | and |I right -Îright |. After that, the estimated object pixellic positions, respectively P left o and P right o are at the maximal probabilities as described in [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF]. This object detection principle only requires an autoencoder pre-training step without object and the assumption that there is an object in the scene subsequently.

D. Learning a hand-eye coordination function f η

To build f η , we need to have a database D of input-output pairs (q robot , q camera ) where q camera makes the camera look at the end-effector. To produce such samples, we learn how to fixate the end-effector the same way [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF] learns to fixate an object. We use the DDPG algorithm and a reward requiring weak supervision. The Markov Decision Process is the same as for the object fixation with the exception of the reward function. The latter involves the end-effector detection P c e (computed below) instead of P c o :

r c eff = 2 1 2 d max -||P i -P c e || 2 d max ∈ [-1, 1]. (7)
The set-up is also episodic. For each episode, random robot joint coordinates are generated using uniform distribution with fixed limits. They are empirically set to provide a large variety of reachable arm configurations.

During learning, training pairs (q robot , q camera ) are added to D when the reward is above a fixed threshold. When the number of samples in D is higher than the batch size N bf , we train f η on random batches of D as soon as a new sample is added to D.

We describe here how we detect the end-effector in the image. Unlike [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF] which uses an autoencoder to detect the object as an anomaly, the end-effector image position is computed using the difference in the image before and after pre-defined end-effector finger moves. This end-effector detection method inspired by [START_REF] Metta | Early Integration of Vision and Manipulation[END_REF] only requires to specify finger moves. Figure 3 presents the different steps of the end-effector detection:

• The image before the end-effector I c b is saved. • The end-effector fingers make pre-defined moves and the image I c a is saved • The difference of images is calculated and the endeffector position P c E is computed using a kernel density estimator the same way P c O is calculated from the autoencoder reconstruction error image.

E. Learning to touch

The goal of the robot is to touch with the end-effector palm the object above the table from a large set of initial arm positions.

It is defined by a sparse reward term r sparse which indicates if there is palm-touching or not:

r sparse = 1, if palm-touching, 0, otherwise. (8)
As the object is kept at the same position, the state space S is composed of the arm and camera coordinates, q. Indeed, for this task, we do not need to add images in the state space since the right arm movements can be decided from the robot joint angles only. The actions consist of the variations of the robot joint angles: a = ∆q robot which are seven real-valued scalars.

The object binocular fixation task and the hand-eye coordination function are used to compute the touching reward function.

After the execution of an object fixation step (using the object fixation policy π ψ ), we get the fixation camera angles q camera fix which localize the object. After that, using equation 5 at each time-step, the hand-eye coordination function f η gives us q camera virt which localizes the end-effector. Then, a reward shaping term r shaping can be computed:

r shaping = c cam ||q camera fix -q camera virt || 2 , (9)
with c cam < 0. r shaping represents an informative term which depends on the distance between the virtual camera coordinates and the camera coordinates which make the camera system fixate the object. It can be seen as an openloop term which constrains the 3 translational degrees of freedom of the end-effector. It takes negative values to ensure quick trajectories are learned. Furthermore, the slope c cam is chosen to ensure shaping rewards are small compared with the non-zero sparse reward. Finally, the reward function is the sum of the two terms:

r cam = r shaping + r sparse . (10)
IV. EXPERIMENTS

In this section, we describe the experimental protocol. The experimental objective is two-fold. First, we want to evaluate performances of our weakly-supervised reward in a palmtouching task. Second, we wish to compare our reward with an informative reward requiring external information.

A. Experiment environment

The experiments are carried out using the Gazebo simulator jointly with the ROS [START_REF] Quigley | ROS: an open-source Robot Operating System[END_REF] middleware. A two-camera system is mounted on a bi-arm robotic platform (see Figure 1). Only one arm is used for the experiments and a Barrett hand is attached to this arm. A table from the Gazebo object database is placed below the cameras and in front of the biarm platform. Note that this table is not present when we learn the hand-eye coordination function. Our method does not depend on a specific object model because the robot learned to look at any object in [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF]. In our experiments, we use a blue ball.

B. Different reward functions

In this paragraph, we present the reward functions which will be used in our experiments:

• r cam = r shaping + r sparse . This is the proposed reward function (described in Section III-E).

• r sparsePen = 1, if success, -0.0125, otherwise. This rewards the robot only when the palm touches the object. Besides, it penalizes each unsuccessful movement to encourage the robot to quickly touch the object.

• r cart = c cart ||X -X target || 2 +r sparse , with c cart < 0. To build this reward, we give a 3-dimensional end-effector target pose X target for the shaping part and we add a sparse reward. This reward is the closest to the proposed r cam but its shaping term requires forward kinematics and 3D object pose information. Finally, the slope c cart is chosen to make the shaping term take about the same values as r shaping .

We choose not to compare our reward function with one which would constrain both the end-effector position and orientation. Indeed, for such a reward function, a success would be to touch with the palm from a specific orientation and position. In our case, a success can be to touch with the palm from any position. The tasks are then too different to be compared in terms of touching improvement.

C. Experimental protocol

We describe how we compare the reward functions for the touching task. The protocol contains a training and a test phase.

1) Training phase:

For training, we use the DDPG algorithm [START_REF] Lillicrap | Continuous control with deep reinforcement learning[END_REF] and the previously defined reward functions. Learning happens on N tot fixed-length episodes of size N eps . Each episode has an initial arm position and an object position. The object position is kept fixed. For the initial arm position, we use two different settings. The first (P 1) one uses a single initial arm position for learning as in [START_REF] Tsurumine | Deep dynamic policy programming for robot control with raw images[END_REF]. This position is made well oriented for a palm-touching purpose. This means that the robot has to move its end-effector mainly in translation to touch the object. The second (P 2) uses random robot joint angles generated from uniform distributions. The goal of this setting is to check if we can learn to touch the object with our reward signal including initial positions with a badly oriented end-effector. In such a position, the robot has to substantially modify its end-effector orientation to touch the object. Furthermore, it is known that learning from different initial states allows to learn policies that are more robust to perturbations [START_REF] Rajeswaran | Towards Generalization and Simplicity in Continuous Control[END_REF].

We use constant zero-mean Gaussian noises trans and rot for the exploration. The variances of the noise are higher for joints which strongly influence the end-effector orientation ( rot ). Indeed, more exploration is required for wrist angles because "touching" orientations are only rewarded by the sparse reward.

To accelerate learning, we handle the times when the robot reaches "unsuccessful" contact areas where its movement is blocked. Indeed, in the training phase, the robot often touches the object without a palm contact though it is close to being successful. To make exploration easier in these areas, we record contact-less positions through a short-sized circular buffer. In case of contact, we pick the oldest position in the buffer, compute the action to go to this position, and apply it. This allows to more correctly discriminate actions in the contact areas.

Through the training experiments, we wish to compare our reward requiring weak supervision with other ones. Consequently, for all the reward signals, in order to monitor the learning progress, we specifically plot the touching frequency f type t over the episodes, type referring to a specific reward function. We average three experiments per setting with the exception of the sparse reward setting. The latter is done once.

2) Test phase: The goal of test experiments is to evaluate final reaching performances. We test the learned policies without any exploration noise on N tot random episodes. At the end, we compute the touching frequency f type test . Note that we do not apply the trick used in the training phase to deal with blocked situations. Instead, when the robot is blocked, it just computes its next action with the policy. Like in the training phase, the results are averaged over three experiments per setting.

D. Implementation details

For all the neural network algorithms, we use the caffe library [START_REF] Jia | Caffe: Convolutional Architecture for Fast Feature Embedding[END_REF]. A GPU (nvidia GeForce GTX Titan X) is used for the experiments.

We use the same neural network structures as in [START_REF] De La Bourdonnaye | Learning of binocular fixations using anomaly detection with deep reinforcement learning[END_REF] for the end-effector and object fixation tasks. The hyperparameter values are also the same with the exception of the number of iterations: 200000. The hand-eye coordination function is a neural network with 2 fully connected hidden layers of 10 and 5 neurons and a batch size N bf of 32 is used to learn it. For the episode initialization of the end-effector fixation task, the seven arm joint angle distribution amplitudes are 11, 46, 69, 92, 92, 86 and 0 • if we consider the ascending order in the kinematic chain i.e. from the base link to the end-effector.

For the touching task, the Q network has 3 fully connected layers with 250, 200 and 1 neural units. The policy network involves 3 fully connected layers with 200, 150 and 7 neural units. The weights are updated using the Adam [START_REF] Kingma | Adam: A Method for Stochastic Optimization[END_REF] solver. Table I and II provide values for the parameters used in the experiments. For the Q update, the discount factor γ is equal to 0.99. For the episode initialization of the P 2 problem, the distribution limits are the same as in the handeye coordination learning with the exception of the last joint (end-effector spin angle) for which the amplitude is 11

V. RESULTS AND DISCUSSION

We present here the results in the two previously defined settings which are used in the experiments.

A. P 1

Figure 4 shows the touching rates. First, we observe that f sparsePen t is zero almost everywhere. In the experiment, it touches one time and is never able to further improve. This is because transitions with high TD values are not trained enough through DDPG. Second, we have similarly good performance of over 90% for the proposed reward r cam and the reward function r cart , which requires forward kinematics and 3D object pose information. For this task, this shows that a shaping term which requires forward kinematics and precise 3D target information can be replaced without loss of performance by a weakly-supervised shaping reward resulting from learning simpler predecessor tasks. The reason is that the objective of the task is defined by the terminal sparse reward. The shaping term is used only to get closer to good touching postures. When the terminal rewards are back-propagated through the Q function to all the trajectory states, the shaping term becomes small compared to the Q values and therefore less important. The results from policy exploitation show that we reach the object with 100 % of successes for both policies for 300 test experiments. This shows that the residual errors at the end of learning were only due to the exploration noise applied to the policy.

B. P 2

Figure 5 shows the results of training experiments for the P 2 problem. We still observe that, with our setting, sparse rewards do not allow to efficiently learn a touching policy. Furthermore, we observe again that our weaklysupervised reward and its supervised counterpart give similar performances. It means that with very different initial positions including those with difficult end-effector orientations, the robot can learn to correctly orientate its end-effector given a long-delayed sparse reward. In the test phase, we Fig. 5. Learning curves for the P 2 problem observe 94,9 % and 95.4 % of success for the policy learned with, respectively, r cam and r cart , which represent good and comparable results. This shows that our reward signal with very little supervision allows to learn a complex touching task from different initial positions.

VI. CONCLUSION

For a complex palm-touching task, we have designed a stage-wise learning procedure which does not require any kinematic models, hand-crafted features, calibration parameters and needs minimal human supervision. Inspired by developmental robotics, our approach involves three steps. First, a binocular vision system learns to fixate an object. This implicitly encodes the position of the object in the 3D camera angle space, while requiring only an autoencoder pretraining step. Second, by learning to fixate the end-effector from its finger moves, the robot learns a hand-eye coordination function which maps robot joint angles to camera angles. In a nutshell, from a given arm configuration, this function allows to localize the end-effector in the 3D camera angle space. Third, we compute the reward signal for the palmtouching task by summing an informative shaping reward computed with the previous steps and a sparse terminal reward indicating the true objective of the task. This shaping term encourages the end-effector to be close to the object in the 3D camera angle space.

The experiments show that our reward signal allows to learn complex touching policies, notably from various initial positions. In addition, policies learned with our reward and with a supervised counterpart reward give similar performances. This shows that for this complex task, our reward based on weak supervision can replace a reward based on forward kinematics and object tracking.

One advantage of our framework is that it is suitable for other types of manipulation tasks with different terminal rewards such as object grasping or pushing. Indeed, our shaping term is used to bring the robot closer to terminal rewards. Thus, switching to another task just requires to change the terminal sparse reward.

Even though our reward computation framework is based on weak supervision, it still has a limitation regarding autonomy. Indeed, even if the object fixation method hardly requires external information, it cannot cope with environment changes in an online way. If the environment varies, the autoencoder has to be trained again. In future work, we wish to implement an object detection method which would adapt to variations. Finally, we wish to learn the same task in a real world setting.

Fig. 1 .

 1 Fig. 1. Palm-touching learning process: (a) Object fixation, (b) End-effector fixation and hand-eye coordination, (c) Palm-touching

Fig. 2 .

 2 Fig. 2. Overall scheme of the touching task learning procedure

Fig. 3 .

 3 Fig. 3. End-effector computation scheme

Fig. 4 .

 4 Fig. 4. Learning curves for the P 1 problem


Thomas Gheno

Gerald H Meier

Brian Gleeson

High temperature reaction of MCrAlY coating compositions with CaO deposits

Keywords: MCrAlY alloys, Multi-layer scales, Al 2 O 3 growth kinetics, CaO deposits

The reactivity of β-NiAl + γ-Ni-based NiCoCrAlY alloys with and without CaO deposits was studied by means of isothermal exposures in air.

Reaction with CaO at 1100 • C produced multi-layer scales of Al 2 O 3 and calcium aluminates, and a mixture of liquid calcium chromate and nickel-cobalt oxide particles. Calcium chromate formation was a rapid, transient process, and the transition to a steady-state of slower Al 2 O 3 growth was favored by increasing the alloy β fraction. The thermally-growing Al 2 O 3 reacted with the deposit to form calcium aluminates in a solid-state diffusion process, which led to an increased oxidation rate. The analysis of Al 2 O 3 growth kinetics in the production-destruction regime was used to account for the increased flux of aluminum entering the multi-layer scale. The effect of temperature on the ability to kinetically sustain an Al 2 O 3 scale was then evaluated on the basis of Wagner's criterion. Predicted results were consistent with the experimentally observed absence of passivation at 900 • C.

Introduction

Materials used in aero, marine and land-based gas turbines need to withstand significant thermo-mechanical loads, while maintaining good environmental stability. Coatings applied to structural alloys for corrosion resistance are mainly Pt-modified nickel aluminides β-(Ni,Pt)Al, or MCrAlY (M=Ni or Co or both) based on β and the γ-Ni solid solution. Reviews of the development, processing and performance of these materials can be found in Refs. [START_REF] Goward | Progress in coatings for gas turbine airfoils[END_REF][START_REF] Nicholls | Designing oxidation-resistant coatings[END_REF]. Thermal barrier coatings (TBCs) are used on components exposed to the highest temperatures, and possess a ceramic topcoat of yttria-stabilized zirconia (YSZ) that provides thermal insulation [START_REF] Evans | Mechanisms controlling the durability of thermal barrier coatings[END_REF][START_REF] Gleeson | Thermal barrier coatings for aeroengine applications[END_REF][START_REF] Evans | The influence of oxides on the performance of advanced gas turbines[END_REF][START_REF] Clarke | Thermal-barrier coatings for more efficient gas-turbine engines[END_REF][START_REF] Darolia | Thermal barrier coatings technology: critical review, progress update, remaining challenges and prospects[END_REF]. In addition to the chemically aggressive combustion atmosphere, the first stage of the high-pressure turbine is subject to deposit-induced modes of degradation, due to the ingestion of impurities from the air intake and combustion process. Calciummagnesium alumino-silicates (CMAS) have been identified as a major source of concern for TBC systems [START_REF] Smialek | Turbine airfoil degradation in the persian gulf war[END_REF][START_REF] Borom | Role of environmental deposits and operating surface temperature in spallation of air plasma sprayed thermal barrier coatings[END_REF][START_REF] Mercer | A delamination mechanism for thermal barrier coatings subject to calcium-magnesium-aluminosilicate (CMAS) infiltration[END_REF][START_REF] Kramer | Thermochemical interaction of thermal barrier coatings with molten CaO-MgO-Al 2 O 3 -SiO 2 (CMAS) deposits[END_REF][START_REF] Levi | Environmental degradation of thermal-barrier coatings by molten deposits[END_REF]. When the topcoat surface reaches temperatures of 1150-1250 • C, CMAS form glassy melts which can penetrate the openings and pores needed for strain tolerance of the TBC, and, depending on their composition, dissolve the YSZ [START_REF] Smialek | Turbine airfoil degradation in the persian gulf war[END_REF][START_REF] Borom | Role of environmental deposits and operating surface temperature in spallation of air plasma sprayed thermal barrier coatings[END_REF][START_REF] Mercer | A delamination mechanism for thermal barrier coatings subject to calcium-magnesium-aluminosilicate (CMAS) infiltration[END_REF][START_REF] Kramer | Thermochemical interaction of thermal barrier coatings with molten CaO-MgO-Al 2 O 3 -SiO 2 (CMAS) deposits[END_REF][START_REF] Levi | Environmental degradation of thermal-barrier coatings by molten deposits[END_REF]. Little is known about the reactivity of bondcoat materials with oxide or silicate deposits at intermediate temperatures, below their melting point.

Deposits relevant to aero and land-based turbines have the common characteristic that their compositions vary widely depending on the fuel used and on the geographic location where the turbine is in service. Combustion of bituminous and anthracite coal, for example, tends to produce fly-ash rich in SiO 2 and Al 2 O 3 , while fly-ash from subbituminous and lignite coals contains higher levels of CaO [START_REF]Clean Coal Technology Topical Report Number[END_REF]. The corrosion of Ni-and Fe-base alloys by deposits rich in CaO and CaSO 4 has been studied in the context of fluidized-bed combustion of coal. Results by Nagarajan et al. [START_REF] Nagarajan | Influence of solid-state CaS-CaO-CaSO 4 deposits on corrosion of high-temperature alloys in simulated FBC environments[END_REF] indicated that corrosion with CaO-CaSO 4 deposits at 900 • C was associated with an oxidation-sulfidation process. Jung et al. [START_REF] Jung | The effect of Ca-rich deposits on the high temperature degradation of coated and uncoated superalloys[END_REF] observed enhanced degradation in the presence of CaO during thermal cycling at 950 • C due to the formation of poorly adherent calcium aluminates, while Chiang et al. [START_REF] Chiang | The effects of deposits of CaO, CaSO 4 , and MgO on the oxidation of several Cr 2 O 3 -forming and Al 2 O 3forming alloys[END_REF] reported an extremely severe type of attack due to liquid calcium chromate formation at temperatures above 1000 • C. In the case of aero turbines, recent examination of the TBC degradation on an in-service airfoil [START_REF] Braue | Environmental stability of the YSZ layer and the YSZ/TGO interface of an in-service EB-PVD coated high-pressure turbine blade[END_REF][START_REF] Braue | Recession of an EB-PVD YSZ coated turbine blade by CaSO 4 and Fe, Ti-rich CMAS-type deposits[END_REF] showed that the YSZ topcoat had reacted with a CaO-rich CMAS, and was fully infiltrated by CaSO 4 .

The work reported here is part of a larger study on the reactivity of MCrAlY coatings with fly ash relevant to integrated gasification combined cycle (IGCC) systems [START_REF] Wright | Recent developments in gas turbine materials and technology and their implications for syngas firing[END_REF][START_REF] Sridhar | Materials challenges for advanced combustion and gasification fossil energy systems[END_REF][START_REF] Pint | High-temperature corrosion in fossil fuel power generation: Present and future[END_REF][START_REF] Sahraei | A survey on current advanced IGCC power plant technologies, sensors and control systems[END_REF]. A typical bondcoat composition, Ni-20Co-16Cr-23Al-0.1Y (at. %), and a γ-rich, high Cr developmental composition, Ni-30Co-33Cr-12Al-0.1Y, were selected for testing with the following individual oxides at 1100 • C: CaO, MgO, Al 2 O 3 , SiO 2 , Fe 2 O 3 . Only the relatively basic CaO and MgO had a significant impact, as their reaction with the thermally-grown Al 2 O 3 produced calcium and magnesium aluminates, respectively. This paper addresses the case of reaction with CaO. The reaction mechanism and the effects of alloy composition on the extent of degradation are first discussed. Emphasis is then placed on the kinetics of the solid-state reaction between Al 2 O 3 and CaO, and on the consequences this reaction has on the consumption of aluminum.

Materials and experimental methods

Ingots of nominal compositions (at. %) Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y were made by argon-arc melting, followed by drop casting into 10 mm diameter rods which were then homogenized in vacuum for 6 h at 1200 • C plus another 48 h at 1150 • C. All processing was conducted at the Materials Preparation Center of the Ames Laboratory [23]. Specimens approximately 1 mm thick were cut from the heat-treated rods, ground using SiC paper to a P1200-grit finish, then degreased with detergent and ultrasonically cleaned in ethanol before exposure.

Micrographs of the alloys after 50 h annealing in dry air at 1100 • C and air cooling are shown in Fig. 1. Both alloys exhibit a primarily β-γ microstructure at this temperature. In addition, the γ-rich Ni-30Co-33Cr-12Al-0.1Y formed 1 vol. % σ, while the β-rich Ni-20Co-16Cr-23Al-0.1Y contained a small amount (∼ 0.1 vol. %) of yttrium-rich intermetallics. An even smaller amount of yttrides were present in the γ-rich alloy, reflecting the higher solubility of Y in γ. Phase compositions measured by SEM-EDS and phase fractions obtained by image analysis using the ImageJ software [START_REF] Schneider | NIH image to ImageJ: 25 years of image analysis[END_REF] are given in Table 1. Overall compositions calculated from these experimental results are within 0.5 at. % of the nominal compositions.

Isothermal corrosion experiments were conducted at 900 and 1100 • C in flow- ing dry air, using an horizontal tube furnace. Linear gas flow rates were set to about 1 mm s -1 at reaction temperature, with a total pressure slightly over 1 atm. Deposits were prepared by mixing laboratory grade reagents in ethanol, and then applying the resulting slurry to one face of a given specimen using a dropper. The procedure was adjusted to produce approximately uniform 35 ± 5 mg cm -2 deposits after evaporation of the ethanol. In addition to time-lapse experiments, reaction kinetics were studied by thermogravimetric analysis (TGA) using a Setaram TAG thermobalance. A relatively high heating rate, 99 K/min, was chosen to reduce time spent at intermediate temperatures and hence resemble the time-lapse experiments in which the furnace was heated prior to inserting the specimens. For TGA experiments, a hole was drilled in the Ni-20Co-16Cr-23Al-0.1Y specimen, which was then dipped into the CaO slurry, and suspended in the thermobalance using Pt wire -both specimen faces were coated. As will be shown later, reaction of Ni-30Co-33Cr-12Al-0.1Y with CaO produced significant amounts of liquid. For this reason CaO was applied on one face only, and the specimen laid flat on an Al 2 O 3 crucible, also suspended in the thermobalance using Pt wire. In this case the weight gain corresponding to the oxidation of the uncoated regions was subtracted from the TGA signal, on the basis of data obtained for the same alloy with no deposit. A blank test was conducted using a sample of dense Al 2 O 3 coated with CaO, which confirmed that CaO did not evaporate significantly. Mounted cross-sections were prepared using conventional metallographic techniques, and observed by SEM with a JEOL JSM 6510 instrument, equipped with an Oxford X-Max SDD EDS detector and INCA analysis software. Oxides were examined by photo-stimulated luminescence spectroscopy (PSLS), which allows γ, θ and α polymorphs of Al 2 O 3 to be distinguished [START_REF] Tolpygo | Microstructural study of the theta-alpha transformation in alumina scales formed on nickel-aluminides[END_REF], using a 633 nm HeNe laser in a Renishaw inVia Raman microscope.

Results

The Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y alloys were reacted in dry air at 1100 • C, with and without CaO deposits, for durations ranging between 5 and 250 h. In the absence of a deposit, both alloys formed adherent Al 2 O 3 scales, with no or very little oxides of Ni, Co or Cr. Scales obtained after 250 h oxidation, shown in Fig. 2, were thick enough for reliable chemical analysis by SEM-EDS. The outer part was thus found to contain 0.5-1 at. % Cr in Al 2 O 3 .

In the presence of CaO deposits, the resulting scales comprised several layers of calcium aluminates (xCaO-yAl 2 O 3 , denoted C x A y ). Micrographs obtained after 50 h reaction, shown in Fig. 3, are representative of the reaction morphologies developed for all exposure durations. The layer sequence was Al-rich CA 2 nearest to the substrate, followed by equimolar CA, and occasionally the Ca-rich C 12 A 7 and C 3 A toward the CaO deposit. These were identified by matching compositions measured by SEM-EDS to the intermediate compounds known to exist in the CaO-Al 2 O 3 system (see Fig. 4a). A thin and continuous Al-rich oxide layer, identified as α-Al 2 O 3 by PSLS, was always present between the metal and the first aluminate layer. In addition, the γ-rich alloy produced a thick outer layer of calcium chromate, with (Ni,Co)O particles embedded throughout (Fig. 3b). These were occasionally found in small amounts on the β-rich alloy. It is noted that spallation of the reaction products occurred on a significant fraction of the surfaces of both alloys.

Calcium oxide is known [START_REF] Chiang | The effects of deposits of CaO, CaSO 4 , and MgO on the oxidation of several Cr 2 O 3 -forming and Al 2 O 3forming alloys[END_REF] to react with the chromium contained in MCrAlY alloys to form a low-melting calcium chromate, denoted here as L CaCrO , which is liquid at 1100 • C (T eutectic = 1061 • C, see Fig. 4b). The thickness of this layer was not uniform, which made measurements difficult. Qualitatively, the calcium chromate was found to develop rapidly on the γ-rich Ni-30Co-33Cr-12Al-0.1Y within 5 h exposure, and to not significantly thicken thereafter. The (Ni,Co)O particles did, however, grow to an appreciable extent, from an average diameter of 0.6 ± 0.2 µm after 5 h to 2.1 ± 0.7 µm after 250 h. The thickness of the β dissolution, C x A y and Al 2 O 3 regions are plotted against the square-root of time, t 1/2 , in Fig. 5, and compared with the relevant values obtained without deposit. All variables are seen to follow approximately parabolic kinetics, as expected for diffusion-controlled processes. The extent of β dissolution is much greater in Ni-30Co-33Cr-12Al-0.1Y than in Ni-20Co-16Cr-23Al-0.1Y, due to the lower starting β fraction in the former, 18 versus 57 vol. %. Alumina and C x A y thicknesses, however, are comparable. For both alloys, reaction with CaO yielded a thinner Al 2 O 3 layer but deeper β dissolution, i.e. more extensive Al consumption, than reaction with no deposit. This will be discussed in more detail later in this paper.

The observations discussed above suggest that calcium chromate formed only during an initial transient stage. In order to test this hypothesis, Ni-20Co-16Cr- 23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y were oxidized with no deposit in dry air for 10 h at 1100 • C, growing a continuous Al 2 O 3 scale. Upon subsequent exposure to CaO for 40 h in the same conditions, the Al 2 O 3 reacted to yield calcium aluminates, but no calcium chromate was formed, confirming the transient nature of the latter.

The weight gains recorded by TGA at 1100 • C, Fig. 6a, reflect the successive stages of the reaction process. Plots of m = f (t 1/2 ) yielded straight lines after a sufficient time was reached (not shown here). This indicates that steady-state kinetics were parabolic for both alloys, with and without CaO deposits. Reaction kinetics were further studied on the basis of the local fitting procedure described in Ref. [START_REF] Monceau | Determination of parabolic rate constants from a local analysis of mass-gain curves[END_REF]. The instantaneous parabolic constant k p was calculated in a translating time-mass window according to

t = a + b m + c m 2 , ( 1
)
where m is the weight gain per unit area, and a, b and c are constants, with c = 1 2kp . This procedure allows the reaction stages to be distinguished based on the time evolution of k p , Fig. metastable alumina polymorphs, was followed by a steady-state corresponding to α-Al 2 O 3 growth. Parabolic constants calculated by fitting Eq. ( 1) to TGA data over a 2-25 h window were found to be 3.7 ×10 -7 and 4.5 ×10 -7 mg 2 cm -4 s -1 for Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y, respectively, in good agreement with previously reported values for the growth of α-Al 2 O 3 at this temperature [START_REF] Hindam | Microstructure, adhesion and growth kinetics of protective scales on metals and alloys[END_REF][START_REF] Rybicki | Effect of the θ-α-Al 2 O 3 transformation on the oxidation behavior of β-NiAl+Zr[END_REF][START_REF] Brumm | The oxidation behavior of NiAl. 1. Phasetransformations in the alumina scale during oxidation of NiAl and NiAl-Cr alloys[END_REF]. In the presence of a CaO deposit, the rates of both transient and steady-state stages increased, and the transition was delayed. The effect of CaO was particularly marked in the case of Ni-30Co-33Cr-12Al-0.1Y, which exhibited a relatively large weight gain in the beginning of the reaction. Since a thick L CaCrO + (Ni,Co)O layer formed on this alloy within 5 h exposure, and only small amounts were found on Ni-20Co-16Cr-3Al-0.1Y, the elevated reaction rate is attributed to L CaCrO and (Ni,Co)O formation. As Fig. 6b indicates, this accelerated process was particularly short-lived (< 1 h). Until about 9 h exposure, both alloys maintained a relatively high reaction rate. The rate-limiting process associated with this period is not readily ascertained, as a continuous α-Al 2 O 3 layer was identified by PSLS at the base of the scale for both alloys after 5 h reaction. Nevertheless, both alloys did passivate, and the k p 's eventually reached lower, approximately stable values.

An additional experiment was conducted with a Ni-33Co-35Cr-7Al-0.1Y alloy, which is single-phase γ at 1100 • C, and has a composition similar to that of the γ in Ni-30Co-33Cr-12Al-0.1Y at this temperature (see Table 1). After 50 h exposure to CaO, the 100 % γ alloy developed a reaction morphology similar to that on Ni-30Co-33Cr-12Al-0.1Y. However, the amount of L CaCrO and (Ni,Co)O formed before passivation was much greater, and the ∼ 150 µm thick calcium chromate had also embedded C x A y particles (Fig. 7a). Furthermore, local regions were found on which passivation had not yet occurred, as no layer of C x A y or Al 2 O 3 was present (Fig. 7b). In these regions, calcium chromate or aluminate was not directly in contact with the metal, but instead the reaction front consisted of oxides: Another γ-rich alloy, Ni-30Co-27Cr-12Al-0.1Y, was used in a series of experiments with Al 2 O 3 -40 wt. % CaO deposits at 900 and 1100 • C. At 1100 • C, the alloy formed an Al 2 O 3 and C x A y layers, but no calcium chromate. This is attributed to the alloy Cr content, lower than that of the γ-rich alloys studied previously, and to the presence of Al 2 O 3 in the deposit itself. The latter partially neutralized CaO by forming calcium aluminates in the deposit, which was detected by SEM-EDS after exposure. At 900 • C, a mixed calcium aluminate-chromate and a continuous Al 2 O 3 sublayer formed on a small fraction of the alloy surface. Passivation was only local, however, and most regions were subject to internal oxidation and nitridation, as shown in Fig. 8. Close examination of the reaction morphology indicates the presence of Al 2 O 3 in the form of both internal oxide particles and a discontinuous layer located below a Cr-rich, mixed-oxide scale. This sequence suggests that the alloy initially formed an external Al 2 O 3 scale, but subsequently failed to sustain its growth, on most of its surface. Figure 8 also shows that an outer calcium chromate layer had formed, with mixed (Co,Ni)O particles embedded. Exposure to a CO 2 -20H 2 O-1.6O 2 gas mixture with the Al 2 O 3 -40 wt. % CaO deposit at 900 • C yielded a similar reaction morphology to that observed in air but with no nitrides, indicating that nitridation in air was not a cause of Al 2 O 3 failure, but rather a consequence.

(Ni,Co)O, Al 2 O 3 , Cr 2 O 3 , CoCr 2 O 4 ,
In the absence of a deposit, oxidation of this alloy at 1100 Al 2 O 3 intrusions were locally seen to grow into the alloy. Furthermore, the θ → α transformation was not complete after 50 h at 900 • C. Surface PSLS characterization showed that while most of the surface consisted of α-Al 2 O 3 , a significant fraction was still predominantly θ (Fig. 9).

Discussion

Influence of alloy composition

The case of pure CaO deposits at 1100 Aluminum and chromium strongly partition to the β and γ phases, respectively, as seen in Table 1. Thus γ will favor L CaCrO formation, while β will tend to form Al 2 O 3 and C x A y . As suggested by Chiang et al. [START_REF] Chiang | The effects of deposits of CaO, CaSO 4 , and MgO on the oxidation of several Cr 2 O 3 -forming and Al 2 O 3forming alloys[END_REF], calcium chromate is formed by reaction of CaO with transient chromium oxide. A remarkable finding is that, as mentioned in Section 3, the extent of transient Cr oxidation on the alloys studied here in the absence of a CaO deposit was very small. Thus, the reaction of CaO with chromium must be particularly rapid, which is confirmed by the TGA measurements for Ni-30Co-33Cr-12Al-0.1Y (Fig. 6). The fact that the (Ni,Co)O particles embedded in the chromate grew significantly with reaction time indicates that they did not precipitate on cooling, but instead developed at temperature. This is due to the fact that L CaCrO dissolves very little (< 1 at. %) nickel or cobalt oxide: as the reaction front advances into the γ-phase, Ni and Co are rejected from the liquid and precipitate as oxide particles. Similarly, the solubility of Al 2 O 3 in the chromate was measured by SEM-EDS to be quite low (1-2 at. %), as also reported by Kaiser et al. [START_REF] Kaiser | The system CaO-CaCr 2 O 4 -CaAl 2 O 4 in air and under mildly reducing conditions[END_REF]. This led to an Al:Cr elemental ratio of about 1:5, similar to that in the original γ phase in Ni-30Co-33Cr-12Al-0.1Y and Ni-33Co-35Cr-7Al-0.1Y. The conservation of this Al:Cr ratio indicates that the γ phase was consumed in situ by the rapidly advancing reaction front. However, some change in the boundary conditions, such as a decelerating reaction front and associated accumulation of Al in the alloy at the metal/oxide interface, must occur to allow for the eventual establishment of an Al 2 O 3 layer. The Cr-rich oxides observed at the reaction front in the non-passivated zones of the 100 % γ alloy (Fig. 7) likely represent an intermediate stage between rapid liquid formation and the establishment of an Al 2 O 3 layer.

Exactly how the alloy passivates remains unclear at this stage. Nevertheless, the implications of this reaction process are readily understood, in terms of alloy resistance to the severe degradation associated with liquid calcium chromate: metal loss should be minimized with a lower chromium content or a higher fraction of β. In particular, considerable resistance can be obtained by having a β fraction sufficiently high for the β phase to be continuous, as opposed to forming a dispersion in a γ matrix, as schematically represented in Fig. 10. The β-rich Ni-20Co-16Cr-23Al-0.1Y did form a very small amount of L CaCrO and (Ni,Co)O (Fig. 3a); the large β fraction (57 %) simply allowed the progression of the liquid phase to be undercut by an Al 2 O 3 layer sooner than in the γ-rich alloys. are considered in the following. Quite different from evaporation, destruction of the oxide in the present case occurred via a solid-state, diffusion-controlled process.

The case of Ni-20Co-16Cr-23Al-0.1Y, where very little L CaCrO formed and the outermost C x A y layer was in contact with the CaO deposit, is considered first. Figure 11 shows a schematic of the reaction process. Calcium aluminate growth is known to be controlled by Ca 2+ diffusion in the solid state [START_REF] Weisweiler | Kinetik der Festkörperreaktionen im System CaO-Al 2 O 3[END_REF][START_REF] Gülgün | Chemical synthesis and characterization of calcium aluminate powders[END_REF][START_REF] Mohamed | Kinetics and mechanism of formation of monocalcium aluminate, CaAl 2 2O 4[END_REF][START_REF] Ghoroi | Solid-solid reaction kinetics: Formation of tricalcium aluminate[END_REF]; its formation is therefore described to occur at the Al 2 O 3 /C x A y interface by the reaction

xCa 2+ + xO 2-+ yAl 2 O 3 = C x A y . (2)
The oxygen and calcium necessary for this reaction are provided by the decomposition of CaO at the CaO/C x A y interface:

CaO = Ca 2+ + O 2-. (3)
Two processes contribute to net Al 2 O 3 growth: (i) its destruction to form C x A y according to Eq. ( 2) at the Al 2 O 3 /C x A y interface, and (ii) its production by oxidation of aluminum contained in the metal substrate,

2Al 3+ + 3O 2-= Al 2 O 3 . (4)
For the sake of simplicity, Al 2 O 3 production is described to occur at the metal/oxide interface, with O 2-assumed to diffuse faster than Al 3+ . The choice of a mixed or predominantly outward growth mechanism would not change the resulting kinetics. As illustrated in Fig. 11, the oxygen necessary for Al 2 O 3 growth is supplied by solid-state diffusion through C x A y . This oxygen ultimately originates from the gas atmosphere. It is further assumed that the oxygen provided by decomposition of CaO is entirely consumed to form C x A y . This prevents the accumulation of calcium or oxygen in C x A y , and is realistic insofar as all known calcium aluminates are intermediate xCaO-yAl 2 O 3 compounds (Fig. 4a), in which the degree of oxidation of Ca and Al is not different from that in CaO and Al 2 O 3 , respectively. In the case of the γ-rich Ni-30Co-33Cr-12Al-0.1Y alloy, the C x A y layers are surmounted by liquid calcium chromate; it is assumed that the latter can rapidly provide the oxygen and calcium required for C x A y and Al 2 O 3 growth, and that this step is therefore not rate-limiting.

NiCoCrAlY Al 2 O 3 CaO O 2- Kinetics Transport Reaction 2Al 3+ + 3O 2-= Al 2 O 3 Ca 2+ , O 2- CaO = Ca 2+ + O 2- O 2- Al 2 O 3 production C x A y growth d𝑋 p d𝑡 = 𝑝 𝑋 d𝑌 d𝑡 = 𝑞′ 𝑌 = - 𝑉 C x A y 𝑦𝑉 Al 2 O 3 d𝑋 d d𝑡 Al Y X Al 2 O 3 destruction xCa 2+ + xO 2-+ yAl 2 O 3 = C x A y C x A y = N 2 -O 2 (g)
Several investigators have studied the growth kinetics of oxide scales that consist of multiple layers growing by diffusion of the same cation, taking into account the partitioning of the cation flux between the successive layers [START_REF] Wagner | The evaluation of data obtained with diffusion couples of binary single-phase and multiphase systems[END_REF][START_REF] Yurek | The formation of two-phase layered scales on pure metals[END_REF][START_REF] Gesmundo | The formation of multilayer scales in the parabolic oxidation of pure metals-I. relationships between the different rate constants[END_REF][START_REF] Viani | The relationships between the different rate constants and the diffusion properties of the oxides in the parabolic oxidation of a metal or a lower oxide to multilayer scales: application to the oxidation of iron[END_REF][START_REF] Hsu | The formation of multilayer scales on pure metals[END_REF][START_REF] Wang | Phenomenological treatment of multilayer growth[END_REF]. The present situation is slightly different in that it involves two types of cations, but it is equivalent if one considers the diffusion of oxygen instead. Provided that the degree of oxidation of aluminum and calcium does not change upon forming any of the aluminates from CaO and Al 2 O 3 , the present situation is a particular, simple case of the general formalism introduced by Yurek et al. [START_REF] Yurek | The formation of two-phase layered scales on pure metals[END_REF] for two-layer structures. That treatment provided a relationship between the thickening constant measured for each layer in the multi-layer scale and the "intrinsic" constants that would be observed if a single-layer of each individual oxide had formed.

Published studies of calcium aluminate growth mostly concern powders, and the reported rate constants tend to vary significantly depending on the starting materials and the method used to assess the results. In the absence of consistent data in the literature, the present analysis will rely on experimental data obtained here. The following considers the relationship between the constants measured for Al 2 O 3 and C x A y in the multi-layer structure and the constant for individual Al 2 O 3 growth, measured in the absence of a deposit. Since the stoichiometry and relative thicknesses of the aluminates do not affect the flux of oxygen used for the oxidation reaction, the aluminate layers are gathered into a single layer of average stoichiometry C x A y . Its thickening kinetics are described in accordance with the parabolic rate law,

dY dt = q Y , ( 5
)
where Y is the thickness of C x A y in the Al 2 O 3 -C x A y scale, and q is the associated parabolic constant. Since Y (t = 0) = 0, Eq. ( 5) yields

Y 2 = 2q t. (6)
Considering the mass balance underlying Eq. ( 2), the destruction of Al

2 O 3 is written (dX) d dt = - yV Al 2 O 3 V CxAy dY dt , (7)
where V i is the molar volume of phase i. Using the TGA data of Fig. 6, it can be shown that in the steady-state regime established in the absence of a deposit, Al 2 O 3 grows according to parabolic kinetics. Previous findings discussed in Ref. [START_REF] Heuer | Alumina scale formation: A new perspective[END_REF] show that the rate-limiting step for Al 2 O 3 -scale thickening is grain-boundary diffusion of O 2-and Al 3+ . This still holds when there is concurrent C x A y formation, so long as the alloy can provide sufficient Al to sustain Al 2 O 3 growth. Inasmuch as the constitution and predominant structure of Al 2 O 3 grain boundaries remain unchanged, the instantaneous growth rate in a situation of production-destruction is inversely proportional to the oxide thickness, with the same constant as in the absence of a deposit. Thus the production term is written

(dX) p dt = p X , ( 8
)
where X is the thickness of Al 2 O 3 in the Al 2 3 -C x A y scale and p is the parabolic constant for exclusive oxidation.

The net Al 2 O 3 growth is obtained by adding the two contributions, i.e., Eqs. ( 7) and ( 8):

dX dt = (dX) p dt + (dX) d dt = p X - yV Al 2 O 3 V CxAy dY dt (9)
or, using Eqs. ( 5) and ( 6),

dX dt = p X -α q √ 2q t , (10)
where

α = yV Al 2 O 3 V CxAy . This equation is solved to yield    X 2 = 2p t p = 1 2 2p + α 2 q -α q (4p + α 2 q ) . (11)
The form of Eq. ( 10) allows for another solution p = 1 2 2p + α 2 q + α q (4p + α 2 q ) , with p < p < p . Since Al 2 O 3 is being consumed by the reaction with the aluminate, p is the appropriate solution. Noting that the valence of aluminum is the same in Al 2 O 3 and C x A y , the same expression for p can be obtained from the general equations given by Yurek et al. [START_REF] Yurek | The formation of two-phase layered scales on pure metals[END_REF]. Based on that treatment, the relationships between the constants measured in the Al 2 O 3 -C x A y scale and the constants for individual Al 2 O 3 and C x A y growth are with the ratio of layer thicknesses in the multi-layer structure given by

p = p 1 + α Y X (12) q = q 1 + 1 α X Y (13)
Y X = α q p . ( 14
)
The analysis is now applied to the reactions of Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y. For each alloy, the intrinsic oxidation rate p is arrived at by fitting the TGA data measured with no CaO (Fig. 6), while q is determined from C x A y thickness measurements (Fig. 5). The ratio α = yV Al 2 O 3 /V CxAy is calculated as the average of values obtained for CA and CA 2 , which were found by SEM-EDS to constitute most of the C x A y . Values of p calculated with Eq. ( 11) are shown in Table 2, together with constants obtained from direct measurement of Al 2 O 3 thickness in Al 2 O 3 -C x A y scales (Fig. 5). The latter are seen to be within an order of magnitude but significantly smaller than those obtained indirectly via Eq. ( 11), especially for the β-rich alloy. This will be discussed subsequently.

After evaluating reaction kinetics based on direct thickness measurements, p is now calculated using TGA data (Fig. 6), which also reflect the rate at which the Al 2 O 3 layer thickens. According to the description adopted here and represented in Fig. 11, the weight gain per unit of surface area recorded during reaction with CaO corresponds to the oxygen uptake necessary for Al 2 O 3 production:

dm dt = dm O dt = (dm O ) p dt . ( 15
)
No net weight gain arises from C x A y growth, as the calcium and oxygen forming the x CaO units come from the CaO deposit, and the aluminum and oxygen forming the y Al 2 O 3 units come from the existing Al 2 O 3 . The net oxygen uptake is related to the quantity of Al 2 O 3 that is produced through the mass balance underlying Eq. ( 4):

1 M O (dm O ) p = (dn O ) p = 3(dn Al 2 O 3 ) p , (16)
where M O is the atomic weight of oxygen. Combining Eqs. ( 15) and ( 16), and converting the quantity of Al 2 O 3 into an equivalent thickness, one obtains

dm dt = 3M O V Al 2 O 3 (dX) p dt . ( 17
)
Using the TGA data of Fig. 6, one can show that at steady-state, weight gains of both Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y in the presence of CaO obey a parabolic law

m 2 = 2s t, ( 18
)
where s is the gravimetric constant. It follows from Eq. ( 17) that Al 2 O 3 production also obeys parabolic kinetics, which is written

(dX) p dt = r √ 2r t , (19)
where

r = s (V Al 2 O 3 /3M O ) 2
is the parabolic constant related to the rate at which Al 2 O 3 thickens by oxidation of the alloy in the Al 2 O 3 -C x A y structure. This production rate is inversely proportional to the layer thickness, Eq. ( 8), which yields

p X = r √ 2r t . (20)
Considering that X(t = 0) = 0, Eq. ( 20) is solved to provide

   X 2 = 2p t p = p 2 r . (21)
Thus p can be calculated from r and p, which are obtained by fitting TGA data recorded with and without CaO deposit, respectively. The results are seen in Table 2 to be in reasonable agreement with the values obtained with Eq. ( 11), although slightly higher.

Two observations should be made from the p values presented in Table 2. First, for a given alloy, a significant discrepancy exists between the values obtained with the three methods used. This is particularly the case for the β-rich alloy, where the value corresponding to direct thickness measurements is much lower than the calculated values. The difference is beyond possible experimental errors, and must instead reflect the incomplete satisfaction of the limiting assumptions made here. First, analysis by SEM-EDS showed small amounts (1-2 at. %) of chromium in the C x A y , and of aluminum in the L CaCrO . This slightly affects the mass balance underlying Eq. ( 11) and the interpretation of the TGA data, via Eq. ( 16). Furthermore, some aspects of the complexities associated with Al 2 O 3 growth were not accounted for in the present analysis. For instance, one aspect is related to the choice of boundary conditions: the oxygen activity at the Al 2 O 3 surface was assumed to be the same whether calcium aluminates form or not, although some p O 2 gradient probably exists across the layers in the Al 2 O 3 -C x A y scale. This arguably does not affect p significantly, inasmuch as Al 2 O 3 predominantly exhibits n-type behavior, and its growth rate is little affected by the external p O 2 [START_REF] Heuer | Alumina scale formation: A new perspective[END_REF]. Further, oxidation both with and without CaO involves a transient stage, as shown by the TGA data in Fig. 6, which possibly comprises the formation of metastable Al 2 O 3 polymorphs, base-metal oxides or L CaCrO prior to the establishment of α-Al 2 O 3 and C x A y layers. One can show that the extent of these processes does not directly affect the thickening rate achieved during steady-state. (Specifically, using equations of the form (x

-x i ) 2 = 2k (t -t i ) or x 2 -x 2 i = 2k (t -t i ) to describe Al 2 O 3 or C
x A y growth does not change the expression giving p in Eq. ( 11) for sufficiently long reaction times.) However, in accordance with the analysis of Brumm and Grabke [START_REF] Brumm | The oxidation behavior of NiAl. 1. Phasetransformations in the alumina scale during oxidation of NiAl and NiAl-Cr alloys[END_REF], aspects of transient oxidation such as the time needed for the θ → α transformation do have an influence on the microstructure of Al 2 O 3 , in particular its grain size, and therefore affect growth rates observed on the longer term. In this respect, because of the p-type nature of θ-Al 2 O 3 [START_REF] Doychak | Transient oxidation of singlecrystal β-NiAl[END_REF][START_REF] Jedlinski | On the oxidation mechanism of alumina formers[END_REF][START_REF] Pint | The oxidation mechanism of θ-Al 2 O 3 scales[END_REF], a reduced p O 2 at the oxide surface in the presence of C x A y could have an indirect effect on the α-Al 2 O 3 eventually established, by slowing the growth of the metastable polymorph. Due to its high reactivity, the presence of CaO certainly had an impact on the transient stage of the reaction, as evident in Fig. 6, although potential effects on Al 2 O 3 microstructure were beyond the scope of this investigation.

A second observation arising from the data gathered in Table 2 is that a significant difference exists between the p values obtained for the two alloys, which is not accounted for in the present analysis. This is most evident when considering p from direct Al 2 O 3 thickness measurements. Similarly, the C x A y -to-Al 2 O 3 thickness ratio, while approximately constant with time for each alloy as expected for diffusion-controlled growth processes, was found to be quite different for the two alloys: 12.8 ± 0.8 for Ni-20Co-16Cr-23Al-0.1Y, versus 6.2 ± 0.2 for Ni-30Co-33Cr-12Al-0.1Y. This could possibly be due to a difference in the constitution of the C x A y scale, as varying relative thicknesses would affect the average scale stoichiometry. This could not be assessed with sufficient accuracy because of the non-uniform, locally rumpled morphology of the reaction product. Another potential effect is related to the presence of liquid calcium chromate. In the case of the γ-rich alloy, the calcium and oxygen required for C x A y and Al 2 O 3 growth must be provided by the L CaCrO which forms a thick and continuous layer. If ionic transport in the liquid is not sufficiently rapid, it could limit the rate of C x A y growth, and allow a relatively thicker Al 2 O 3 to persist. Furthermore, a slow transport would also involve a local chromium enrichment in the liquid, and, since the latter occupies a small composition range at 1100 • C (Fig. 4b), this could result in the precipitation of CaCr 2 O 4 . The phase transformation would involve a partial reduction of chromium (the liquid contains a mixture of Cr III and Cr VI, while CaCr 2 O 4 contains only Cr III), which would affect oxygen both in the mass balance underlying Eq. [START_REF] Kramer | Thermochemical interaction of thermal barrier coatings with molten CaO-MgO-Al 2 O 3 -SiO 2 (CMAS) deposits[END_REF] and in the interpretation of the TGA data, via Eq. [START_REF] Jung | The effect of Ca-rich deposits on the high temperature degradation of coated and uncoated superalloys[END_REF]. Again the constitution of the L CaCrO could not be characterized with the degree of accuracy required because of experimental limitations.

Overall, the present results indicate that beyond a reduction in thickness, the growth mechanism of Al 2 O 3 is affected by the reaction with CaO. The details of the associated processes, as well as the role played by alloy composition, are outside the scope of the present paper and deserve further investigation. Yet, the present analysis is useful in that it provides a semi-quantitative evaluation of the effect of CaO on the rate of Al consumption. In essence, as Al 2 O 3 reacts to form C x A y , its thickness is reduced, and so is its ability to act as a diffusion barrier: the instantaneous oxidation rate p/X increases. This rate is expressed as (dX) p / dt = p/ √ 2p t, and since p < p, it is indeed larger than its CaO-free counterpart, p/ √ 2pt. Another metric that can be used to characterize Al consumption is the rate of β dissolution. Due to the larger oxidation rate, β is dissolved at a greater rate in the presence of CaO, as seen in Fig. 5.

Effect of temperature on Al consumption in the presence of CaO

We now consider the effect of the reaction with CaO on the ability of a given alloy to maintain an Al 2 O 3 layer, using Wagner's [START_REF] Wagner | Theoretical analysis of the diffusion processes determining the oxidation rate of alloys[END_REF] criterion for sustained external scaling. Briefly, this is based on the principle that external Al 2 O 3 growth can be maintained if the outward Al flux in the metal at the interface with the oxide matches the flux required for the oxide to grow. A maximum flux is obtained in the alloy when the interfacial Al content is set to zero, which in turn defines a minimum bulk concentration, N * Al . Since the flux of Al consumed by scale growth is related to the instantaneous oxide production rate, the above analysis suggests that taking into account the reaction with CaO will amount to replacing the oxidation constant p by the ratio p 2 /p in calculating N * Al . Under the assumptions of parabolic oxidation kinetics and of a constant Al diffusion coefficient in the alloy (D Al ) in the composition range of interest, N * Al is given by [START_REF] Wagner | Theoretical analysis of the diffusion processes determining the oxidation rate of alloys[END_REF]

N * Al = F 1 2 k c D Al ( 22
)
where F is the auxiliary function defined by F (u) = √ πu(1 -erf u) exp u 2 and k c the parabolic constant for metal recession, defined by d 2 = 2k c t with d the depth of the metal/oxide interface relative to the original alloy surface. In a situation of individual Al 2 O 3 growth, the mass balance on the aluminum contained in the oxide scale is written 2X

V Al 2 O 3 = d V a (23)
with V a the molar volume of the alloy, which yields a simple relationship between k c and p

k c = 2V a V Al 2 O 3 2 p. ( 24
)
This is now introduced in Eq. ( 22) to give

N * Al = F 2V a V Al 2 O 3 p 2D Al . (25)
When Al 2 O 3 reacts with CaO to form calcium aluminates, the mass balance of Eq. ( 23) becomes 2X

V Al 2 O 3 + 2yY V CxAy = d V a . (26)
Using Eqs. ( 6) and ( 11), Y can be given as

Y = V CxAy yV Al 2 O 3 2 p p t -X (27)
and the relationship giving k c from measurable constants becomes

k c = 2V a V Al 2 O 3 2 p 2 p ( 28
)
which finally yields

N * Al = F   2V a V Al 2 O 3 p 2 /p 2D Al   . (29)
A comparison between Eqs. ( 24) and ( 28) confirms that changing from an individual Al 2 O 3 scale to a multi-layer Al 2 O 3 -C x A y scale amounts to replacing p by p 2 /p when considering the flux of Al incorporated in the reaction product.

This analysis is now used to study the effect of a varying temperature on the reaction of Ni-30Co-27Cr-12Al-0.1Y with Al 2 O 3 -CaO deposits. No measured value of p or p is available for this alloy; instead, N * Al is evaluated as follows. The constant p is taken from data by Brumm and Grabke [START_REF] Brumm | The oxidation behavior of NiAl. 1. Phasetransformations in the alumina scale during oxidation of NiAl and NiAl-Cr alloys[END_REF] for α and θ-Al 2 O 3 growth on NiAl-Cr alloys, using activation energies of 350 and 231 kJ/mol, respectively. In the absence of direct data, q is first calculated at 1100 • C from Eqs. ( 13) and ( 14) using q measured here for Ni-30Co-33Cr-12Al-0.1Y (Table 2) and p for α-Al 2 O 3 in Ref. [START_REF] Brumm | The oxidation behavior of NiAl. 1. Phasetransformations in the alumina scale during oxidation of NiAl and NiAl-Cr alloys[END_REF]. Activation energies reported in the literature for the growth of calcium aluminates vary widely [START_REF] Gülgün | Chemical synthesis and characterization of calcium aluminate powders[END_REF], with most values in the 150-250 kJ/mol range [START_REF] Ghoroi | Solid-solid reaction kinetics: Formation of tricalcium aluminate[END_REF]; the median 200 kJ/mol is used here, in good agreement with results reported in Refs. [START_REF] Weisweiler | Kinetik der Festkörperreaktionen im System CaO-Al 2 O 3[END_REF][START_REF] Mohamed | Kinetics and mechanism of formation of monocalcium aluminate, CaAl 2 2O 4[END_REF]. Values of q at varying temperatures are then calculated from q at 1100 • C, based on the Arrhenius equation. Constants p and q are then obtained for each of α and θ-Al 2 O 3 using Eqs. [START_REF] Levi | Environmental degradation of thermal-barrier coatings by molten deposits[END_REF][START_REF]Clean Coal Technology Topical Report Number[END_REF][START_REF] Nagarajan | Influence of solid-state CaS-CaO-CaSO 4 deposits on corrosion of high-temperature alloys in simulated FBC environments[END_REF] and the constants for individual Al 2 O 3 (p) and C x A y (q) growth. Interdiffusion in a 5-component, 2-phase alloy system is complex. Since β is quite rapidly depleted from the subsurface of the γ-rich alloys, only diffusion in γ is considered. Nesbitt and Heckel [START_REF] Nesbitt | Interdiffusion in Ni-rich, Ni-Cr-Al alloys at 1100 • C and 1200 • C. II. Diffusion-coefficients and predicted concentration profiles[END_REF] published experimental interdiffusion data for the ternary Ni-Cr-Al system, including a regression equation allowing interdiffusion coefficients to be calculated as a function of alloy composition. Chromium concentration gradients were seen to have little effect on Al diffusion, such that the main term DNi Al,Al was prevalent. At 1100 Al,Al = 3.4 ×10 -10 cm 2 s -1 for the nominal composition (27Cr, 12Al), and DNi

Al,Al = 1.1 ×10 -10 cm 2 s -1 for an alloy fully depleted of its Al. Equation ( 29) is based on a constant diffusion coefficient; the average value DNi Al,Al = 2 × 10 -10 cm 2 s -1 is chosen as an approximation. This value is consistent with other experimental and calculated values for dilute NiCrAl alloys at 1100 • C gathered in Ref. [START_REF] Campbell | Development of a diffusion mobility database for Ni-base superalloys[END_REF]. The activation energy for DNi Al,Al , 288 kJ/mol, is taken from Ref. [START_REF] Nesbitt | Interdiffusion in Ni-rich, Ni-Cr-Al alloys at 1100 • C and 1200 • C. II. Diffusion-coefficients and predicted concentration profiles[END_REF].

Minimum Al concentrations calculated using Eq. ( 29) are plotted as a function of temperature in Fig. 12 for both α and θ-Al 2 O 3 growth, with and without CaO reaction. All predicted N * Al values are below the alloy nominal Al content (12 at. %). Considering α-Al 2 O 3 at 1100 • C, the reaction with CaO leads to a relatively small increase of N * Al , from 1.2 at. % with no deposit to 2.8 at. % with CaO. This is consistent with the observed ability of Ni-30Co-27Cr-12Al-0.1Y to maintain an external Al 2 O 3 layer at this temperature. For α-Al 2 O 3 reaction with CaO, the 900 • C value of N * Al , 4.9 at. %, is higher than the 1100 • C value, but still relatively low. This indicates that the decrease in the alloy diffusion rate is partly compensated by the slowing of diffusion in Al 2 O 3 and C x A y . However, PSLS measurements (Fig. 9) showed that θ-Al 2 O 3 was still present in significant amounts after 50 h at 900 • C, which suggests that the metastable polymorph controlled the oxidation rate for an extended period at this temperature. Indeed, several investigators [30, 31, Uncertainties in the activation energies and the limiting assumptions used here are such that predicted N * Al values should be regarded as rough estimates. Nevertheless, the trends are valid and indicate that reaction with CaO will be significantly more severe in terms of Al consumption, relative to its availability at the metal/oxide interface, at 900 • C than at 1100 • C. This is mainly due to the persistence of θ-Al 2 O 3 at the lower temperature. These observations are consistent with the observed failure of Ni-30Co-27Cr-12Al-0.1Y to passivate in the presence of CaO at 900 • C.

The above analysis neglects the multi-phase nature of the alloys studied here. Compositional changes in oxidizing multi-phase alloys have been studied in the past [START_REF] Gesmundo | Oxidation of multicomponent two-phase alloys[END_REF][START_REF] Carter | Calculation of precipitate dissolution zone kinetics in oxidising binary two-phase alloys[END_REF][START_REF] Nijdam | Modelling of composition and phase changes in multiphase alloys due to growth of an oxide layer[END_REF]. Applying a diffusional analysis to β-γ alloys shows that for a given bulk composition, the interfacial aluminum flux in steady-state conditions is greater when γ contains more Al and the volume fraction of β is correspondingly smaller. This is particularly evident using the analytical method of Ref. [START_REF] Gesmundo | Oxidation of multicomponent two-phase alloys[END_REF], as the minimum bulk concentration to maintain Al 2 O 3 scaling according to Wagner's criterion, i.e., N * Al in Eq. ( 22), is to be replaced by the expression

N γ Al N γ Al + 2f β N β Al -N γ

Al

, where

N i
Al is the Al mole fraction in phase i and f β is the volume fraction of β. In the case of the Ni-30Co-27Cr-12Al-0.1Y alloy, as the temperature decreases, f β increases, which is compensated by a decrease in N γ Al , from 9.7 at. % at 1100 • C to 7.3 at. % at 900 • C (measured by SEM-EDS). This results in a reduced interfacial Al flux, and further weighs against the alloy ability to sustain Al 2 O 3 growth at the lower temperature.

Conclusions

Two-phase β-γ MCrAlY alloys exposed to CaO at 1100 • C were found to suffer significantly more degradation than in the absence of a deposit. The reaction with CaO proceeded according to two distinct mechanisms. During the initial stage, formation of a liquid calcium chromate led to the rapid consumption of the Cr-rich γ-phase. The extent of degradation was particularly important for a single-phase γ composition, and was significantly reduced by increasing the alloy β fraction. In a subsequent stage, a continuous Al 2 O 3 layer established at the base of the scale, which led to a much lower oxidation rate. However, the protective oxide reacted with CaO to form calcium aluminates, and as its thickness was reduced, the instantaneous oxidation rate was higher than in the absence of a deposit.

Analysis of the reaction kinetics of this steady-state regime, where Al 2 O 3 is simultaneously produced by oxidation of the alloy and destructed by solid-state reaction with CaO, allowed growth rates obtained by thickness-measurement and gravimetric methods to be compared. The agreement was generally good, although some discrepancy existed, which was discussed in terms of possible changes to Al 2 O 3 growth mechanism due to the reaction with CaO. The analysis also led to evaluate the effect of CaO reaction on the flux of aluminum required to sustain external Al 2 O 3 growth. The temperature evolution of aluminum consumption was studied by considering the activation energies for Al diffusion in the alloy, and Al 2 O 3 and calcium aluminate growth. A temperature decrease to 900 • C was found to be detrimental to the kinetic stability of the protective oxide, mainly due to the longer persistence of the metastable and faster growing θ-Al 2 O 3 . Failure to maintain an external Al 2 O 3 scale resulted for an Al-lean alloy in internal oxidation of Al, and formation of a Cr-rich oxide scale. This did not have as severe consequences as at 1100 • C since 900 • C is below the calcium chromate eutectic.

Figure 1 :

 1 Figure 1: Micrographs of (a) Ni-20Co-16Cr-23Al-0.1Y and (b) Ni-30Co-33Cr-12Al-0.1Y after 50 h heat treatment in dry air at 1100 • C.

Figure 2 :

 2 Figure 2: Alumina scales formed after 250 h oxidation of (a) Ni-20Co-16Cr-23Al-0.1Y and (b) Ni-30Co-33Cr-12Al-0.1Y in dry air at 1100 • C.

Figure 3 :

 3 Figure 3: Reaction morphology observed after 50 h exposure of (a) Ni-20Co-16Cr-23Al-0.1Y and (b) Ni-30Co-33Cr-12Al-0.1Y in dry air with CaO at 1100 • C.

Figure 4 :

 4 Figure 4: Pseudo-binary phase diagrams. (a) CaO-Al 2 O 3 system, adapted from Ref. [26]; (b) CaO-Cr 2 O 3 system, adapted from Ref. [27].

Figure 5 :

 5 Figure 5: Thickness of reaction layers measured after exposure of (a) Ni-20Co-16Cr-23Al-0.1Y and (b) Ni-30Co-33Cr-12Al-0.1Y in dry air with and without CaO at 1100 • C.

Figure 6 :

 6 Figure 6: Reaction kinetics of Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y in dry air at 1100 • C, with and without CaO. (a) Weight gains recorded by TGA. (b) Local parabolic constants, determined after method in Ref. [28].

Figure 7 :

 7 Figure 7: Reaction morphology observed after 50 h exposure of 100 % γ alloy Ni-33Co-35Cr-7Al-0.1Y in dry air with CaO at 1100 • C. (a) overview; (b) metal/oxide interface in a zone where no continuous Al 2 O 3 layer is present at the base of the scale.

  or Cr-rich oxide containing varying amounts of Ca, Cr or Co, with the Al 2 O 3 and Cr 2 O 3 sometimes present as large internal particles. These reaction products were identified based on chemical analysis by SEM-EDS.

Figure 8 :

 8 Figure 8: Reaction morphology observed after 50 h exposure of the γ-rich Ni-30Co-27Cr-12Al-0.1Y (at. %) to Al 2 O 3 -40 wt. % CaO in dry air at 900 • C.

3 Figure 9 :

 39 Figure 9: PSLS spectra recorded after 50 h exposure of the γ-rich Ni-30Co-27Cr-12Al-0.1Y in dry air at 900 • C, with no deposit, showing regions of α and θ-Al 2 O 3 . Since θ-Al 2 O 3 luminescence is 10-12 times weaker than that of α-Al 2 O 3 [25], the top spectrum denotes regions primarily consisting of θ-Al 2 O 3 .

4. 2 Figure 10 :

 210 Figure 10: Schematics showing how the susceptibility for transient attack by CaO is determined by the distribution of the Cr-rich γ phase in the alloy.

Figure 11 :

 11 Figure 11: Schematic representation of the reactions and transport processes associated with the formation of calcium aluminate from CaO and thermally grown Al 2 O 3 . Variables are defined in text.

Figure 12 :

 12 Figure 12: Minimum bulk Al content to maintain external Al 2 O 3 growth with and without CaO reaction as a function of temperature. Calculated from Eqs. (25, 29), and parameters described in text.

Table 1 :

 1 Bulk phase compositions (SEM-EDS) and phase fractions (image analysis) of alloys Ni-20Co-16Cr-23Al-0.1Y and Ni-30Co-33Cr-12Al-0.1Y measured after 50 h heat treatment in dry air at 1100 • C. Ni-20Co-16Cr-23Al-0.1Y also contains 0.1 vol. % yttrides.

		vol. %			1.0
	σ	at. %	Ni Co Cr Al		10.8 27.8 58.1 3.3
		vol. %		56.9	18.2
	β	at. %	Ni Co Cr Al	43.6 14.3 8.8 33.4	34.3 18.8 13.6 33.3
		vol. %		42.9	80.8
	Nominal composition γ	(at. %) at. %	Ni Co Cr Al	Ni-20Co-16Cr-23Al-0.1Y 33.1 27.5 29.5 9.9	Ni-30Co-33Cr-12Al-0.1Y 22.3 32.0 37.5 8.2

  • C led to external Al 2 O 3 scaling with very little transient oxides, while at 900 • C, the Al 2 O 3 scale was surmounted by a layer of mixed Cr-Co-Ni oxide, and shallow (∼ 1 µm deep)

  CaCrO and (Ni,Co)O was seen to vary quite significantly with alloy composition and, in turn, alloy microstructure. The β-rich Ni-20Co-16Cr-23Al-0.1Y rapidly established continuous Al 2 O 3 and C x A y layers, which prevented the oxidation of Cr, Ni or Co; whereas, the 100 % γ Ni-33Co-35Cr-7Al-0.1Y sustained extensive degradation before it could passivate, and the γ-rich Ni-30Co-33Cr-12Al-0.1Y had an intermediate behavior.

• C is considered first. As noted in the introduction, Chiang et al.

[START_REF] Chiang | The effects of deposits of CaO, CaSO 4 , and MgO on the oxidation of several Cr 2 O 3 -forming and Al 2 O 3forming alloys[END_REF]

studied the reaction of nominally Al 2 O 3 -forming NiCrAl and CoCrAl alloys with CaO, and found that the formation of liquid calcium chromate led to very rapid alloy destruction. In the present study, the extent of metal loss due to L

Table 2 :

 2 Parabolic constants (10 -14 cm 2 s -1 ) for Al 2 O 3 and C x A y growth in Al 2 O 3 -C x A y scales, and for exclusive Al 2 O 3 growth, obtained from various methods (see text for details).

			Ni-20Co-16Cr-23Al-0.1Y Ni-30Co-33Cr-12Al-0.1Y
	Al 2 O 3 thickness	p	0.41	1.9
	TGA (no deposit)	p	11	13
	C x A y thickness	q	83	80
	Equation (11)	p	2.7	3.7
	TGA (with deposit) r	25	24
	Equation (21)	p	4.5	6.9

Acknowledgements

This work was supported by the Department of Energy through the University Turbine Systems Research (UTSR) Program run by the National Energy Technology Laboratory, Award Number DE-FE0007271, Seth Lawson, Project Manager. The authors thank Wei Zhao and Juan Manuel Alvarado Orozco for useful discussions on some aspects of this work.