Orcun Yildiz
email: orcun.yildiz@inria.fr

Matthieu Dorier
email: matthieu.dorier@irisa.fr

Shadi Ibrahim
email: shadi.ibrahim@inria.fr

Gabriel Antoniu
email: gabriel.antoniu@inria.fr

A Performance and Energy Analysis of I/O Management Approaches for Exascale Systems

Keywords: C.4 [Performance of System]: Performance ; D.4.8 [Operating System]: Performance-Measurement Measurement, Performance Exascale, I/O, Energy, Time partitioning, Dedicated Cores, Dedicated Nodes, Damaris

The advent of fast, unprecedentedly scalable, yet energyhungry exascale supercomputers poses a major challenge consisting in sustaining a high performance per watt ratio. While much recent work has explored new approaches to I/O management, aiming to reduce the I/O performance bottleneck exhibited by HPC applications (and hence to improve application performance), there is comparatively little work investigating the impact of I/O management approaches on energy consumption.

In this work, we explore how much energy a supercomputer consumes while running scientific simulations when adopting various I/O management approaches. We closely examine three radically different I/O schemes including time partitioning, dedicated cores, and dedicated nodes. We implement the three approaches within the Damaris I/O middleware and perform extensive experiments with one of the target HPC applications of the Blue Waters sustained-petaflop/s supercomputer project: the CM1 atmospheric model. Our experimental results obtained on the French Grid'5000 platform highlight the differences between these three approaches and illustrate in which way various configurations of the application and of the system can impact performance and energy consumption.

INTRODUCTION

Power has become an essential issue in the design of modern computing systems. Power bills become a substantial part of the total cost of ownership (TCO) of supercomputers: a typical supercomputer of thousands of cores consumes several megawatt of power [START_REF] Patel | Energy aware grid: Global workload placement based on energy efficiency[END_REF] which in turn presents almost 40% of the total cost [START_REF] Hamilton | Cost of Power in Large-Scale Data Centers[END_REF]. Performance has long been the major focus of the HPC community, today's supercomputers are therefore equipped with millions of processing cores that run parallel programs and consume a large amount of energy. For example, Tianhe-2, No.1 in the top 500 supercomputers list, is a 3,120,000 processor supercomputer with a Linpack performance of 33.8 petaflop/s,1 but with a 17 megawatt of power consumption. 2 This amount of energy will even increase as we reach the era of exascale systems.

Scientific simulations running on these machines have been traditionally designed to write their data in the form of many files stored in a parallel file system. Yet, the increasing computational power of new supercomputers largely overcomes the performance of storage systems, which substantially impacts the performance of these simulations. The traditional approach of periodically checkpointing the simulation's data into files and processing it offline to retrieve scientific results does not scale anymore. Therefore, a number of new approaches to large-scale data management have been proposed that make use of dedicated resources such as dedicated cores [START_REF] Dorier | Damaris: How to Efficiently Leverage Multicore Parallelism to Achieve Scalable, Jitter-free I/O[END_REF], dedicated nodes [START_REF] Zheng | PreDatA -Preparatory Data Analytics on Peta-Scale Machines[END_REF], accelerators (such as GPUs) or SSDs to process data as it is being generated by the simulation. As energy is becoming an increasingly important concern for large-scale systems, a major challenge of exascale computing is how to sustain a high performance per watt ratio. While most studies have been focusing on profiling and characterizing power usage in supercomputers, modeling and exploring data-related energy/performance tradeoffs [START_REF] Gamell | Exploring power behaviors and trade-offs of in-situ data analytics[END_REF], and exploiting dynamic voltage frequency scaling (DVFS) techniques to reduce power consumption [START_REF] Laros | Energy based performance tuning for large scale high performance computing systems[END_REF], there is comparatively little work on investigating the impact of I/O management on energy consumption (i.e., how much energy a supercomputer consumes while running a scientific simulation when adopting different data management approaches).

We implement three different approaches to I/O management (that is, (1) periodically stopping the simulation to write data, (2) using dedicated I/O cores and (3) using dedicated I/O nodes) within the Damaris middleware [START_REF] Dorier | Damaris: How to Efficiently Leverage Multicore Parallelism to Achieve Scalable, Jitter-free I/O[END_REF] and perform extensive experiments that involve one of the target HPC applications for the Blue Waters petascale supercomputer project -the CM1 atmospheric model-on Grid'5000 [START_REF] Bolze | Grid'5000: a large scale and highly reconfigurable experimental grid testbed[END_REF]. Our experimental results bring out the differences between these three approaches and show that they are only sub-optimal for different configurations of the application and of the system: the energy consumption under Specifically, we show evidence that a shorter execution time doesn't always imply better energy consumption, especially when comparing dedicated cores against dedicated nodes. Furthermore, there is a linearity between the output frequency and energy consumption regardless of which data management approach is employed.

The primary contributions of this paper are as follows:

1. It experimentally demonstrates that HPC applications experience variations in performance and power consumption under different I/O management approaches and provides a deep analysis to explain this variation and its cause.

2. It illustrates in practice how the different system's architecture influence the execution of HPC applications and how they shape the energy consumption of the entire system.

The proposed work aims at providing a clearer understanding of the interplay between current data management approaches in exascale supercomputers and energy consumption, and offers a preliminary insight into designing energy-efficient approaches for exascale supercomputers. Paper Organization. The rest of this paper is organized as follows: Section 2 briefly presents the three I/O management approaches considered in our study: time partitioning, dedicated cores and dedicated nodes. Section 3 describes an overview of our methodology, followed by the experimental results in Section 4. Finally, we conclude the paper and propose our future work in Section 5.

APPROACHES TO I/O MANAGEMENT IN HPC APPLICATIONS

As we approach the exascale era in HPC, mismatch between computation and I/O performance have become a limiting factor for the performance and scalability of HPC applications. The traditional approach to I/O requires the simulation to periodically stop and output data for checkpointing, visualization or analysis purpose [START_REF] Hoisie | Extreme-Scale Computing -Where 'Just More of the Same' Does Not Work[END_REF]. This results in a large number of processes competing for the access to the file system. Therefore, alternative approaches for performing I/O have been investigated recently by the HPC community [START_REF] Dorier | Damaris: How to Efficiently Leverage Multicore Parallelism to Achieve Scalable, Jitter-free I/O[END_REF][START_REF] Zheng | PreDatA -Preparatory Data Analytics on Peta-Scale Machines[END_REF]. These approaches perform I/O while the simulation keeps running, in an asynchronous manner, taking advantage of dedicated resources such as cores or nodes. These approaches eliminate the additional machine time needed for performing I/O by overlapping I/O with the simulation, but also require more resources. In this section, we present three different data management approaches which can be used for performing I/O tasks in HPC applications.

Time Partitioning

Time partitioning is the traditional approach to I/O in HPC applications. In this approach, I/O operations are performed in a synchronous manner: the simulation stops periodically, performs I/O operations and continues its computation where it left it off. This I/O activity is presented in Figure 1(a). While this approach takes advantage of direct access to simulation data, it impacts the simulation run time since it stops the simulation periodically to perform I/O. Besides, the time partitioning approach also increases the run time variability [START_REF] Skinner | Understanding the Causes of Performance Variability in HPC Workloads[END_REF][START_REF] Lofstead | Managing Variability in the IO Performance of Petascale Storage Systems[END_REF][START_REF] Dorier | Leveraging Multicore Parallelism to Mask I/O Jitter[END_REF]. In the following sections, we will present other approaches which use dedicated resources for performing I/O to minimize the I/O impact on the simulation.

Dedicated Cores

This approach takes advantage of the hierarchical nature of HPC systems and in particular the increasing use of multicore nodes, where many cores share a common memory. It dedicates one or multiple cores in each SMP nodes for performing I/O asynchronously while the simulation runs [START_REF] Dorier | Damaris: How to Efficiently Leverage Multicore Parallelism to Achieve Scalable, Jitter-free I/O[END_REF]. Since dedicated cores share the same resources as the cores which run the simulation, they can leverage the already available simulation data in the shared memory. By assigning asynchronous I/O tasks to dedicated cores, one can hide the I/O costs. Figure 1(b) presents this approach. In this approach, if I/O tasks do not scale with the simulation, they can start to impact the overall performance. What is more, memory space is limited and there is a need for buffer management coordination between simulation and dedicated cores.

Dedicated Nodes

With this approach, separate nodes are used for performing I/O operations while the simulation is running [START_REF] Zheng | PreDatA -Preparatory Data Analytics on Peta-Scale Machines[END_REF]. Data is transmitted from computing nodes to dedicated nodes through the network. Once the data transfer is completed, dedicated nodes interact with the file system to write the output files. This approach is demonstrated in Figure 1(c).

One of the challenges with this approach is the memory management on dedicated nodes. As we come closer to exascale, memory per core tends to shrink. When applying a dedicated nodes approach, one should be aware of the limited space in the dedicated nodes. While computing nodes send simulation data to dedicated nodes, they are not aware of the available space. Therefore, dedicated nodes should handle the incoming transfers according to their memory availability. The ratio between dedicated nodes and computing nodes is thus an important factor. A mismatch between capacity of dedicated nodes and computing nodes can lead to inefficiency. Another drawback of this approach is the requirement for data transfer through the network, less efficient than a transfer through shared memory. However, asynchronous data transfers can have less impact on the running simulation if one can overlap the cost of the data movement with the simulation.

Discussion

These three approaches have inherent advantages and disadvantages. While the traditional time partitioning approach can still be viable for some non-data-intensive applications, scientists would not be able to tolerate its large impact on the simulation running time for applications that output massive amounts of data. On the other hand, the other two approaches minimize this impact by performing I/O in an asynchronous manner while they differ in the location where the actual I/O tasks are actually performed. Dedicated cores approach use the same resources as the simulation and thus may impact the simulation more than an approach based on dedicated nodes that opts for the cost of data network transfers rather than taking the risk of impacting the simulation.

METHODOLOGY OVERVIEW

We a series of experiments in order to assess the impact of the three data management approaches on both energy consumption and application performance. We further describe the experimental environment: the platform, the HPC application, the tools used, and the deployment setup.

Platform

The experiments were carried out on the Grid'5000 [START_REF] Bolze | Grid'5000: a large scale and highly reconfigurable experimental grid testbed[END_REF] testbed, more specifically we employed nodes belonging to its Nancy and Rennes sites: On the Nancy site: each node is a 4-core Intel 2.53 GHz CPU with 16 GB of RAM. Intra-cluster communication is done through a 1G Ethernet network. On the Rennes site: each node is a 24-core AMD 1.7 GHz CPU with 48 GB of RAM. The nodes communicate through a 1G Ethernet network. 40 nodes of the Nancy site (the same on Rennes site) are equipped with power monitoring hardware consisting of 2 Power Distribution Units (PDUs) (4 PDUs on Rennes site), each hosting 20 outlets (10 outlets per PDU on Rennes site). Since each node is mapped to a specific outlet, we are able to acquire coarse and fine-grained power monitoring information using the Simple Network Management Protocol (SNMP). Grid'5000 allows us to create an isolated environment in order to have full control over the experiments and the obtained results.

Application use case

For our analysis, we chose one of the target HPC applications of the Blue Waters petascale supercomputer project [START_REF]BlueWaters project[END_REF]: the CM1 atmospheric model [START_REF] Bryan | A benchmark simulation for moist nonhydrostatic numerical models[END_REF]. CM1 is used for atmospheric research to model small-scale atmosphere phenomena such as tornadoes. It alternates computation phases and I/O phases. The simulated domain is a fixed 3D array. The number of points along the x, y and z axes is given by the parameters nx, ny and nz. Each point in this domain is characterized by a set of variables such as local temperature or wind speed. Parallelization is done using MPI, by splitting the 3D array along a 2D grid. Each process simulates a nsx × nsy × nz point subdomain. The I/O phase uses HDF5 to write one file per process at every output.

Metrics

In addition to the energy monitoring tools, described in section 3.1, we gathered information about the CPU usage, which is a crucial metric for many applications. These information are gathered using Dstat. Therefore, minimizing the effects of the monitoring system on our resource measurements. In each run we monitor the CPU usage for each node per second and we also measure the energy consumption with a resolution of one second.

Implementation of Data management approaches in Damaris

Damaris [START_REF] Dorier | Damaris: How to Efficiently Leverage Multicore Parallelism to Achieve Scalable, Jitter-free I/O[END_REF] is a middleware for I/O and data management (including data processing and in situ visualization). Initially developed to provide data management capabilities through dedicated I/O cores on multicore nodes, it has later been extended to support the more classical time partitioning approach. We further extended it to support dedicated nodes. Communications between the nodes running the simulation and dedicated nodes are performed using MPI (blocking send from clients, asynchronous receive posted by dedicated nodes to react to data management requests from clients). Although this preliminary implementation is potentially less efficient than other approaches using dedicated nodes along with RDMA technologies [START_REF] Zheng | PreDatA -Preparatory Data Analytics on Peta-Scale Machines[END_REF], it allows us to compare the three I/O approaches on a fair ground of a common implementation. In addition to dedicated nodes, we implemented in Damaris the capability to use more than one dedicated core per node.

Experimental deployment

We use 14 nodes (56 cores) to run CM1 on the Nancy site, 2 additional nodes are used by a PVFS [START_REF] Carns | PVFS: a parallel file system for linux clusters[END_REF] file system. These PVFS nodes are accessed by computation nodes through a 20G Infiniband network. On the Rennes site, we run CM1 on 12 nodes (288 cores) and 2 nodes are used by PVFS, also accessed from compute nodes through a 20G InfiniBand network. In addition, in both sites, we configure CM1 to complete 2400 time steps and vary the frequency of output, using 5, 10 or 20 time steps between outputs. Damaris is configured to run with CM1 in five different scenarios which cover the three I/O approaches: time partitioning (i.e., TP), dedicating core(s) employing one core per node (i.e., DC(ONE)) and employing two cores per node (i.e., DC(TWO)), and dedicating node(s) employing one node (i.e., DN(ONE)) and employing two nodes (i.e., DN(TWO)).

In our first experiment, the I/O output frequency is performed at every 5 time steps. In order to understand the impact of the output (i.e., checkpoints) frequency in the second set of experiments (Section 4.1), we vary the output frequency, using 5, 10 and 20 time steps between outputs. Finally, to illustrate the impacts of system's architectures, we complement the first set of experiments (i.e., Nancy site) by running CM1 simulation on Rennes site. Here, we fixed the number of I/O output frequency to every 5 time steps.

KEY RESULTS

In this section, we provide an analysis of the experimental results we obtained. Our goal is to study the impact of various I/O approaches on the energy and completion time of CM1.

In terms of performance, Figure 2 shows that the time partitioning approach largely impacts the simulation. This behavior results from the fact that it performs I/O from all processes and by stopping the simulation periodically. On the other hand, approaches that perform I/O asynchronously and from a reduced number of writers obtained a much better run time. Among these approaches, dedicating two nodes outperforms the other configurations. We can argue that the approach based on dedicated cores can have a larger impact on the simulation because there are only four cores per node, i.e., dedicating even one core already removes 25% of the computation resources that could have been used by the simulation. Additionally, it is worthwhile to note the importance of the ratio between dedicated and compute nodes in the dedicated nodes approach. As we mentioned before, mismatch between capacity of dedicated and computing nodes can result in inefficient simulation runs. Dedicating only one node for thirteen compute nodes appeared not to be an optimal choice under high I/O frequency where large outputs are produced every 5 time steps.

In terms of energy consumption, Figure 2 shows a strong correlation between completion time and energy consumption. However, we can also see that although dedicating one node (i.e., DN(ONE)) finishes the simulation earlier than with two dedicated cores (i.e., DC(TWO)), the former consumes more energy than the latter. This implies that short execution times do not always lead to less energy consumption. Table 1 confirms our observation since in the dedicated nodes approach all cores only perform computation tasks whereas in the dedicated cores approach we employed one or two cores to perform I/O, which leads to less CPU usage on average. Additionally, we can see the decrease of average CPU usage when we dedicate two cores instead of one. Since the average CPU utilization affects the completion time, we observe longer execution times for lower CPU utilizations. However, this can lead to less energy consumption as we described for the DC(TWO) approach, at the expense of performance compared to DN(ONE). This energy/performance trade-off can be favored according to the users' priority and, of course, largely depends on the application considered. Figure 3 shows the completion time and resulting energy consumption of the different data management approaches under different output frequencies (i.e., different number of iterations between each output). These results show that there is a linear relation between the output frequency and the energy consumption regardless of which data management approach is employed. Decreasing the output frequency leads to lower energy consumption which stems from shorter completion times. For example, by dividing the output frequency by half the resulting energy consumption is reduced by almost 60% for each configuration.

Impact of the output frequency

Impact of the system architecture

Figure 4 shows the energy consumption of each I/O approach and Figure 5 depicts the throughput and average power usage during the simulation using different system architectures. The results indicate that the comparative behavior of the different approaches with respect to performance and energy efficiency depends on the system on which they run. With a larger number of cores per node, dedicating one core outperforms the other configurations while the dedicated nodes approach was the optimal choice with a smaller number of cores per node. The different behaviors in dedicated cores approaches stem from reducing the number of cores that could otherwise be used by the simulation. Since CM1 is computation-intensive, dedicating cores for performing I/O tasks reduces the computing resources dramatically in an architecture with a small number of cores per node. However, with a larger number of cores per node, dedicating cores removes only a small amount of computing resources (e.g., 4% when dedicating one core out of 24 cores) and therefore its impact on the simulation stays minimal. Additionally, the power usage of the dedicated cores approaches changes drastically with one or two cores. Dedicating one more core per node reduces the power usage by 10% with 4 cores per node, while in the latter system this reduction is 1%. This observation also complies with our reasoning that the impact of dedicating cores on a system with a larger number of cores per node is minimal compared to a system with a smaller number of cores per node.

DISCUSSION AND FUTURE WORK

Power consumption has started to severely constrain the design and the way HPC systems are operated. As HPC systems and HPC application's data size rise, their power efficiency calls for empirical evaluations and technical innovations. In this study, we investigated the performance and energy efficiency of three I/O approaches in HPC systems: time partitioning, dedicated cores, and dedicated nodes. We implemented the three approaches within the Damaris I/O middleware and performed extensive experiments using the CM1 atmospheric model on the French Grid'5000 platform.

Our detailed study reveals a significant variation in the performance of CM1 and the energy consumption of the HPC system. Three factors at least contribute to such variations. First, the adopted I/O approach. Second, the output frequency (number of iterations between each output). Third, the architecture of the system on which we run the HPC application. As a future work, we plan to investigate an energy model based on the I/O management approach, HPC application's characteristics and the HPC system's architecture and use this model to pre-select an optimal I/O management approach prior to running the simulation, including the proper number of dedicated cores or nodes. In addition, within each I/O management approach, we plan to discuss the tradeoffs between reducing the CPU frequency of the resources that are dedicated to I/O (to reduce the overall energy consumption) and fully utilizing these dedicated resources (e.g., performing compression) and therefore reducing the I/O time and storage space. As a longer-term agenda, we are going to investigate the feasibility of building a hybrid I/O approach that not only incorporates all the aforementioned approaches but also adaptively selects the optimal approach at run time.

ACKNOWLEDGMENTS

This work is supported by the ANR MapReduce grant (ANR-10-SEGI-001), the Héméra INRIA Large Wingspan-Project (see http://www.grid5000.fr/mediawiki/index.php/Hemera) and the Data@Exascale Associate Team between the KerData team from IN-RIA Rennes -Bretagne Atlantique, Argonne National Laboratory (ANL) and the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana Champaign (UIUC).

The experiments presented in this paper were carried out using the Grid'5000/ALADDIN-G5K experimental testbed, an initiative from the French Ministry of Research through the ACI GRID incentive ac-

Figure 1 :

 1 Figure 1: Approaches to I/O management in HPC applications

Figure 2 :

 2 Figure 2: Energy vs completion time

Figure 3 :

 3 Figure 3: Measured energy Consumption under different approaches to I/O management in HPC applications with different output frequencies: different number of iterations between each output

Figure 4 :

 4 Figure 4: Energy consumption under different I/O management approaches and system architectures These different behaviors highlight the need for an energy efficient framework which can select the best I/O approach in terms of energy efficiency by considering different parameters such as the system's architecture or the output size and frequency.

Figure 5 :

 5 Figure 5: Average Power consumption and Throughput under different I/O management approaches and system architectures tion, INRIA, CNRS and RENATER and other contributing partners (see http://www.grid5000.fr/ for details).

Table 1 :

 1 Average CPU Usage (percentage) for the different I/O management approaches

	Iterations be-	TP	DC	DC	DN	DN
	tween outputs		(ONE)	(TWO)	(ONE)	(TWO)
	5	27.6	71.7	55.9	82.5	80.8
	10	40	72	62	84	83
	20	55.4	84.3	79.3	84.9	84.8

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ZnAl 2 O 4 as potential sensor : variation of luminescence with thermal history

ZnAl 2 O 4 spinel powders were prepared using the Pechini or co-precipitation synthetic route and were then treated at different temperatures (600-1350 °C). These powders were characterised by X-ray diffraction, scanning electron microscopy (SEM), diffuse reflectance and luminescence measurements. SEM investigations and the X-ray patterns showed that the spinel crystallite size was dependent on the synthetic route and the treatment temperature. In addition, the structural evolution was investigated by Rietveld refinements. The inversion rate decrease was correlated with the temperature, leading to a direct spinel phase for the sample treated at high temperature. Furthermore, luminescence measurements showed various emissions linked to the presence of defects in the matrix structure. The two main emissions observed were attributed to oxygen vacancy and Zn in the interstitial positions (as revealed by differential Fourier maps). The luminescence spectra exhibited strong differences between 1200 °C and 1350 °C. At the higher temperature, the characteristic emission spectra can be attributed to the direct spinel phase. The indirectdirect spinel transformation can be monitored through the change in the optical properties and correlated to the thermal history of the sample.

Introduction

ZnAl 2 O 4 spinel compounds have been widely studied: the keyword search "ZnAl 2 O 4 " in the Scopus database produces 460 hits. This material is useful in catalysis for automobiles (either as an active material 1,2 or mainly as a catalytic support 3,4 ), as a transparent conductive oxide, 5 as a sintering aid reagent for alumina ceramic 6 and for its dielectric properties. 7,8 Pure ZnAl 2 O 4 and Ag-doped ZnAl 2 O 4 are of interest for their photo-catalytic properties. 9,10 Doping with rare earth (RE 3+ ) elements leads to photophysical properties that have potential applications in up-conversion lasers. 11 Cobalt-doped ZnAl 2 O 4 is widely used as a blue pigment in glass or ceramic, 4,[12][13][14][START_REF] Fernández-Osorio | Nanotechnology 2010: Advanced Materials, CNTs, Particles, Films and Composites -Technical Proceedings of the 2010 NSTI Nanotechnology Conference and Expo[END_REF] and the nickel-doped analogue is used as a green-blue pigment, depending on the nickel concentration. [START_REF] Lorenzi | [END_REF]17 ZnAl 2 O 4 is a wide band gap (3.8 eV) semi-conductor; 18 as such, this material does not absorb at wavelengths higher than 325 nm. This compound is thus an appropriate white host matrix for doping with phosphor cations for photo-emission applications. Consequently, one of the most extensively studied properties of doped ZnAl 2 O 4 compounds is their photoluminescence. Cr 3+ -doped ZnAl 2 O 4 luminescence is widely known, [18][19][20] as is Mn 2+ luminescence 21 or RE 3+ luminescence in such spinel matrices; doping with Eu 3+ , 22 Er 3+ /Yb 3+ (ref. 23) or Tb 3+ (ref. 24) can also be found. Unfortunately, it is apparent from recent investigations that to consider the ZnAl 2 O 4 matrix as a "white material" is erroneous. The pure ZnAl 2 O 4 matrix (without any doping) was shown to exhibit luminescence properties when synthesised as small particles; 25 in addition, the absorption properties of ZnAl 2 O 4 in the UV-visible range and the opto-mechanical effects have been discussed in the literature. 5 Three families of spinel compounds can be distinguished based on the oxidation states of the metals. The "II-III" family corresponds to oxidation states of A(II) and B(III), and the "IV-II" and "I-VI" families also exist. 26 ZnAl 2 O 4 belongs to the "II-III" family and is also called gahnite. The ZnAl 2 O 4 spinel structure is crystalline and belongs to the Fd m space group with a cubic symmetry. Each unit cell is composed of eight AB 2 O 4 patterns. The unit cell contains 32 oxygen atoms, which form 64 tetrahedral sites and 32 octahedral sites. In the direct spinel structure, only 8 of the tetrahedral sites (Wyckoff positions 8a (1/8, 1/8, 1/8)) and 16 of the octahedral sites (Wyckoff positions 16d (1/2, 1/2, 1/2)) are respectively occupied by A and B cations. The oxygen atoms fully occupy the 32e positions. 27 Nevertheless, in the composition of ZnAl 2 O 4 , non-negligible equal proportions of A (Zn 2+ ) in the 16d Wyckoff position and B (Al 3+ ) in the 8d position can be reached. The proportion of A in the octahedral site is named the inversion rate δ, and describes the cation distribution in the structure. The general formula of the spinel structure can be written as

(A 1-δ B δ )[B 2-δ A δ ]O 4 .
Within the literature, ZnAl 2 O 4 compounds have been characterised with inversion rates of 0 < δ < 0.05. [28][29][30] It was previously shown that the synthesis temperature can modify the cation distribution (the inversion rate δ) in ZnAl 2 O 4 spinel structures. 31 Hence, it is very interesting to gauge the effect of different synthetic processes on the cationic distribution. Many synthetic routes to pure ZnAl 2 O 4 of various particle size have been reported in the literature, such as solid-state reactions, [32][33][34] tartaric complex formation as the oxide precursor, 35 microwave-assisted hydrothermal processes, 36 autocombustion using glycine/urea fuels, 37,38 sol-gel methods 27 and the Pechini route. [START_REF] Pechini | Ceramic Dielectric Materials[END_REF][START_REF] Gaudon | [END_REF] In this paper, the co-precipitation technique and the Pechini route with various final thermal treatments are compared, and the correlation of the luminescence properties of ZnAl 2 O 4 to its structure (inversion rate, presence of defects) is investigated.

Experimental 1-Synthesis of compounds

Two synthetic processes are compared: the Pechini route and co-precipitation. These two processes are illustrated in Fig. 1. For samples synthesised by the co-precipitation method, stoichiometric amounts of zinc nitrate hexahydrate (Alfa-Aesar, Puratronic 99.998% (metal basis)) and aluminum nitrate nonahydrate (Alfa-Aesar, low mercury, Puratronic 99.999% (metal basis)) were dissolved in aqueous solution to achieve a zinc concentration of 0.8 mol L -1 . Aqueous ammonia was then added until a pH of 8.45 was reached. The solution was centrifuged, and the precipitate was dried in an oven at 100 °C for 5 h. In the second step, various thermal treatments were performed between 600 °C and 1200 °C under an air atmosphere.

For the co-precipitation process, the aim is to obtain an amorphous nanoscale precipitate of zinc oxide and aluminum hydroxide. With this method, the difficulty is in producing a simultaneous and complete co-precipitation of both the Zn 2+ and Al 3+ cations, which are introduced into solution as a result of the increased pH. ZnO and Al(OH) 3 are known to exhibit amphoteric character. Consequently, the adequate pH window for the co-precipitation is very narrow. Indeed, as shown in Fig. 2, an optimal pH of 8.4 was determined, which allows the complete precipitation of both cations.

For the Pechini route, the same metal reagents were used and dissolved in aqueous solution at the same concentrations as in the co-precipitation process. This cationic solution was added to a second aqueous solution of polymeric precursors (citric acid (CA) and ethylene glycol (EG)). This Pechini solution contained a molar ratio of 1 : 4 : 4 salts : CA : EG. This solution enables the polyesterification of EG and CA and the formation of a viscous brown resin by heating to remove excess solvent. A highly viscous mixture was thus obtained, and while a gel was being formed, it was treated at 400 °C under air for 5 hours to lead to a black amorphous powder. In the second step, various thermal treatments of this black residue were performed between 600 °C and 1350 °C under an air atmosphere. In contrast to the co-precipitation process, the Zn : Al target ratio can be set at 1 : 2 in the final spinel structure because there is no possibility of changing the stoichiometry from the starting solution to the final product.

X-ray diffraction analysis

Powder X-ray diffraction patterns were collected on a Philips X'Pert MPD X-ray diffractometer with a Bragg-Brentano geometry using Cu Kα 1,2 radiation (10 < 2θ < 130°, step 0.02° and counting time of 30 s). The diffractograms were refined using the Rietveld method with the conventional reliability factors (Fullprof program package). Unit cell parameters, atomic positions, occupancies and Debye-Waller factors were refined on the basis of the Fd m space group corresponding to the spinel structure (and for coprecipitation compounds the ZnO phase was added). Fullprof peak profile function No. 7 was used, and the crystallite size was directly obtained.

SEM analysis

SEM micrographs were recorded with a HITACHI 4500-I apparatus equipped with a field-emission gun (SEM-FEG) working at 3.0 kV. Such equipment allowed a high spatial resolution (approximately 5 nm) while operating at low accelerating voltages.

Photoluminescence analysis

Excitation spectra were recorded with the spectrofluorimeter SPEX FL212 (450 W, xenon lamp) and corrected for the variation of the incident flux. Emission spectra were corrected for the transmission of the monochromator and the response of the photomultiplier. This equipment was also used to record the diffuse reflectance spectra. A black reference (B: blacktoner) and a white reference (W: Magnesia MgO) were scanned under identical conditions and the measurement from the sample (S) was corrected with the following relation, in order to obtain the desired data (D): D = (S -B)/(W -B).

Results and discussion 1 Structural characterization

The X-ray analysis of the green product (raw precipitate), obtained by co-precipitation synthesis, shows the presence of NH 4 NO 3 , which can be removed by washing. The amorphous behaviour of the raw precipitate is a clear indication of the homogeneity of the mixture between zinc oxide and aluminum hydroxide, which avoids separate crystallisation.

The amorphous precipitate transforms into the ZnAl 2 O 4 spinel phase after thermal treatment under air at temperatures between 600 °C and 1200 °C. Rietveld refinements allowed the determination of numerous parameters such as the cell parameter, the inversion rate and the crystallite size, depending on the thermal treatment temperature. These results and the reliability factors of the refinement are reported in Table 1. The experimental, calculated and difference spectra are shown in Fig. 3 for the two synthesis temperatures of 600 °C and 1200 °C. It should be noted that ZnO was detected as an impurity in the X-ray diffractogram of the sample prepared at the highest synthesis temperature. These impurity peaks are evident in the inset of Fig. 3. The presence of traces of zinc oxide results from the difficulty in adjusting the Zn/Al stoichiometry inside the precipitate due to the amphoteric behaviour of the zinc oxide and the aluminum hydroxide in aqueous solution. Hence, this process unfortunately cannot guarantee a pure spinel form. Even if the ZnO impurity could be selectively dissolved by post-washing with a slightly acidic aqueous solution, the Zn : Al stoichiometry inside the spinel lattice may deviate from the target 1 : 2 ratio due to the initial excess of zinc in the starting amorphous precipitate. However, this process offers the possibility of varying the crystallite size of the spinel compound over a very large range: from 5 nm to more than 100 nm via control of the final treatment temperature.

Using the Pechini process, a pure spinel phase can be obtained over the same range of temperatures as with co-precipitation, starting from 600 °C. The same parameters describing the structural and morphological properties were analysed by X-ray diffraction; the results are reported in Table 2. For illustration, Rietveld refinements of the 600 °C and 1200 °C samples are reported in Fig. 4.

The crystallite size determined from the peak profile refinements varies over a narrower range than from the co-precipitation process (from 20 nm to 120 nm). Crystallites smaller than 10 nm in diameter cannot be obtained by the Pechini synthesis. Nevertheless, no trace of impurity is observed in the X-ray patterns of samples obtained, regardless of the synthesis temperature.

The SEM images provided a direct illustration of the morphology of the powder samples as a function of the synthesis temperature and are shown for both processes in Fig. 5. It can be clearly seen from the SEM photographs that the crystallite size of the low synthesis temperature (600 °C) products varies between the two synthetic routes. At 1200 °C, the crystallite sizes are equal whatever the synthetic route chosen ( 120 nm for both synthesis temperatures), due to the advanced degree of sintering that occurs at such high temperatures. Moreover, the presence of two phases for the 1200 °C sample obtained from the co-precipitation process is clearly observed: besides the large crystallites of the main phase of ZnAl 2 O 4 , crystallites of approximately 100 nm of diameter are observed, attributed to the zinc oxide.

Hence, the co-precipitation process has the advantage of greater control of the spinel crystallite size obtained (to our knowledge, 5 nm ZnAl 2 O 4 crystals cannot be found in the literature), but the perfect stoichiometry of the Zn/Al ratio is not necessarily maintained, as observed with the occurrence of ZnO impurities. The Pechini route also allows control of the crystallite size, and adds the advantage of recovering pure ZnAl 2 O 4 no matter the synthesis temperature used.

Cation distribution and its correlation to the synthetic procedure

At this stage, it is interesting to correlate the inversion rate and/or the morphology of the spinel to the synthesis temperature for both synthetic routes. An asymptotic decrease of the inversion rate versus the synthesis temperature is observed for both processes (Fig. 6). That means that the key parameter which governs the value of δ is not expressly the crystallite size but the synthesis temperature. In fact, equal inversion rates are obtained for a 5 nm sample and a 23 nm sample prepared by the co-precipitation and Pechini routes, respectively. In this comparison, the smallest crystallite is obtained at the lowest temperature. The asymptotic decrease of the inversion rate versus the synthesis temperature is in good agreement with previous results reported in the literature on ZnAl 2 O 4 (ref. 40) and the analogous CoAl 2 O 4 spinel compounds. 8,[41][42][43][44][45][46][47] A final point is the observation of a second type of structural defect in the pure spinel compounds obtained from the Pechini route. Significant electron density residues are observed at the empty positions, extracted from differential Fourier cartographies between calculated and experimental signals (Fig. 7). The main electron density residues are located at the 16c Wyckoff position with (0, 0, 0) coordinates. This Wyckoff position corresponds to the empty octahedral sites of the spinel matrix. The six oxygen ligands are located at this position centre at 2.1441(8) Å. A simulated valence calculation from Brown and Altermatt 48 on this position for Zn 2+ and Al 3+ indicates without ambiguity that Zn 2+ is the cation occupying this interstitial position. New refinement iterations were performed taking into account these supplementary zinc cations in the (0, 0, 0) position, with a variable occupation rate to refine occupancy. The refinement results, which are reported in Table 3, show a direct correlation between the site occupancy and the synthesis temperature. An asymptotic decrease of the occupancy can be positively correlated to the inversion rate and/or the synthesis temperature.

Thus, variation of the synthesis temperature is linked to the crystallite size of the ZnAl 2 O 4 compounds and enables control over the inversion rate of the Zn 2+ and Al 3+ cations inside the spinel crystallographic network, as previously shown in the literature. [START_REF] Gaudon | [END_REF] Furthermore, the accurate comparison of the results obtained from the two "chimie douce" processes has shown that the inversion rate is actually controlled by the synthesis temperature rather than the crystallite size. Finally, the pure spinel phase obtained via the Pechini route over a large range of synthesis temperatures leads to high quality X-ray diffraction pattern refinements and Fourier differential maps. In addition to the cationic inversion phenomenon between the 8a and 16d sites, these analyses have shown that the synthesis at low temperatures generates a significant presence of Zn 2+ ions in interstitial positions as defects.

It is interesting to note that the last refinement series can be made without considering any inversion rate. Indeed, it can be proposed that the inversion rate is actually an artefact resulting from the lack of consideration of vacancies that are mainly located at the tetrahedral sites of the structure. This is an extreme point of view, but the vacancies should at least have some effect on the inversion rate. The formula Zn 1-3x [Zn 2x Al 2-2x ]O 4-4x was envisaged on the basis of the chemical composition, complete filling of the octahedral sites and the oxide electroneutrality. A partial occupation of the octahedral sites by Zn 2+ must be considered. There is the same number of adjustment parameters in the latter case as for the inversion rate model: the x variable directly replaces the inversion rate. The refinement results performed considering a tetrahedral vacancy rate of 3x are reported in Table 4. The correlation factors are on the same order as in previous models. Hence, the consideration of vacancies segregated inside the tetrahedral positions leads to the same results as those obtained with the partial inversion rate of Zn 2+ ions. The occurrence of both cationic and anionic vacancies cannot be rejected and should also be considered.

Luminescence characterisation and thermal probe behavior

The optical properties of the spinel matrix obtained through the Pechini synthetic route were studied as a function of the heat treatment of the materials. As the results obtained from both synthetic routes are equivalent, we limit the discussion of the optical properties to the Pechini prepared samples. The diffuse reflectance spectra are shown in Fig. 8. The increase of the heat treatment temperature from 600 °C to 1200 °C leads to a strong reduction of the absorption band between 300 nm and 360 nm. This band in the 1350 °C heat treated sample is very weak, which indicates that this absorption is related to the existence of Zn Al or Al Zn antisite defects (six-fold coordinated Zn 2+ and four-fold coordinated Al 3+ ) in the indirect spinel lattice.

The spectral distributions of the excitation and emission bands were examined at high (254-270 K) and low temperatures (10 K). Fig. 9a-d show the results obtained for two specific samples. The spectral distribution of the 1200 °C heat treated material corresponds to the indirect spinel structure. The 1350 °C heat treatment stabilised the nearly direct spinel, as demonstrated previously. The strongest variation of the optical properties is obtained for these two thermal treatment temperatures.

For the 1200 °C heat treated sample, there is a strong emission band at 610 nm (Fig. 9a) upon excitation at 370 nm. This emission is partially quenched at room temperature and shifted to higher energy at higher temperatures (580 nm for T > 250 K). Groups of lines can also be distinguished at approximately 688 nm. This red photoluminescence is due to the E g -4 A 2g R-, N-zero phonon lines of trivalent chromium at the octahedral site of the aluminium ions 49 (Fig. 10). The emission spectra also contain satellite lines distributed around the main peak, which can be identified as vibronic (phonon assisted transitions) sideband transitions of Cr 3+ ions. The presence of chromium impurities in aluminium compounds is often observed due to trace impurities in the precursor materials. For excitation at higher energy (λ ex = 235 nm), an additional band is detected at approximately 460 nm (Fig. 9c andd). This band is also affected by the temperature. Two thin lines can be distinguished at 368 nm and 372 nm. The first one can be attributed to a direct electron-hole pair recombination, or excitonic emission. The corresponding energy (3.3 eV) is slightly lower than that of the band gap value of ZnAl 2 O 4 (3.8 eV). 50 This indicates the existence of an intermediary energy level (level 1) below the conduction band in which the electron is trapped before radiative recombination with a hole in the valence band or in a shallow level above the valence band (level 2) (see Fig. 11). As the energy difference between the two lines is weak (0.03 eV or 492 cm -1 ), the second line may be due to another self-trapped exciton recombination or may be a phonon replica emission of the first self-trapped excitonic line. This electron-phonon coupling is commonly observed at low temperatures in ZnO wurtzite type structures. 51,52 The intensities of the 460 nm and 610 nm bands collapse after the 1350 °C heat treatment. Indeed, the second one cannot be detected anymore upon excitation at 235 nm. As discussed previously, one of the interesting properties of the spinel compound is the possibility to obtain and to control a high degree of disorder in the cation sub-lattice (the inversion rate). The reciprocal exchange of Zn 2+ ions and Al 3+ ions between octahedral and tetrahedral positions creates the existence of Zn Al or Al Zn antisite defects. This leads to the stabilisation within the lattice of local defects which are responsible for the spectroscopic features of this material. Many studies have reported on the intrinsic emission of spinel (natural mineral gahnite or a synthetic single crystal, ceramics) under ionising radiation and X-ray excitation. [53][54][55][56] In the indirect spinel, Zn 2+ ions are located at the octahedral lattice sites and form centres with excess negative charge. During high irradiation, the capture of a free hole by this site neutralises the defect. A complementary process is observed by the capture of a free electron by the excess positive charge of an Al 3+ ion. A neutral centre can be obtained as given by the following equation:

Because of the low electron affinity of Al 3+ ions, the captured electron may leave its trap and finally recombine with a nearby trapped hole. 55 These processes result in a radiative emission at approximately 255 nm. F-centres can also be responsible for emission bands at approximately 360 nm. 55,56 In the present study, the excitation energy is not sufficient to observe such emissions, which correspond to energy larger than the bandgap. Moreover, the two visible bands are strongly dependent on the inversion rate of the spinel lattice. Their origin is then related to the existence of antisite defects and all the processes that occur under irradiation to stabilise the system. Other defects may also cause radiative emission in the visible range. On the one hand, an oxygen vacancy in the vicinity of the octahedral antisite of Zn 2+ ions might favor a hole trapping process, contributing to the neutralisation of the negatively charged site. This could generate the existence of a shallow level located below the conduction band (level 1′). On the other hand, a hole centre may be created by capturing another hole at the oxygen vacancy site according to the following equation:

This will constitute a deep hole trapped level within the gap of the material (level 2′). One can imagine that a photogenerated electron in the conduction band or level 1′ can recombine with the deep hole trapped level 2′, giving rise to the 585 nm emission. We propose here a parallel between the reported visible emission of the as-synthesised spinel material and that of ZnO. Visible emission has been intensively studied in ZnO wurtzite type structures prepared by sol gel techniques, organometallic methods or other soft chemistry synthetic routes. [57][58][59] In this compound, Zn 2+ ions are located in a tetrahedral environment. ZnO is a direct semiconductor whose gap is comparable to that of spinel (3.37 eV and 3.8 eV, respectively). A yellow-green emission ranging from 500 nm to 600 nm has been reported by D. Hahn et al. 60 An explanation of this process was given by A. Van Dijken et al., 61 as being due to the recombination of a shallowly trapped electron with a deeply trapped hole. In this process, surface defects such as nonbridging O 2-/O -trapped the photogenerated hole, which then migrated to a vacancy positioned deeper in the particle. The resulting deep hole trapped level is then located in the band gap of the semiconductor, above the valence band. The photogenerated hole trapped in the deep oxygen vacancy level recombines with the photogenerated electron trapped in the shallow level located below the conduction band, giving rise to the yellow-green luminescence. We propose the assignation of the 610 nm band to a radiative process involving an oxygen vacancy (1′-2′ radiative recombination route) (Fig. 11). This radiative process is complex and probably linked to the existence of two energy levels 1′a and 1′b below the conduction band. At low temperatures, the 1′a-2′ electronic transition occurs, but an increase in the temperature results in a thermal equilibrium between 1′a and 1′b. The emission is then due to the 1′b-2′ electron transition, leading to a blueshift of the band. Because similar emission is seen with ZnO, 62 the origin of the blue emission (460 nm) may be related to the interstitial zinc ions in the spinel lattice. Blue luminescent centres have also been reported in ZnO, 63 and investigated by full-potential linear Muffin-tin orbital calculation published by P.S. Xu et al. 64 The authors positioned the interstitial zinc defect energy level 2.9 eV above the valence band, making it a shallow level below the conduction band. The corresponding energy is of the same order of magnitude as the radiative de-excitation observed in Fig. 9. Considering the structural refinement described previously and the high probability of interstitial zinc ions in the spinel lattice, the blue luminescence may reflect the contribution of these defects to the radiative processes (1′′-2′′ radiative recombination route). Radiative recombination pathways are depicted in Fig. 11. Note the existence of the N-line of trivalent chromium that seems to confirm (according to W. Zang et al.) the contribution of Cr 3+ ions to nearby interstitial zinc ions (results observed for ZnGa 2 O 4 spinel nano-sized phosphors 65 ).

Conclusion

We have demonstrated that the main factor governing the inversion rate of ZnAl 2 O 4 is not the crystallite size but the thermal history of the sample. The co-precipitation synthesis led to a larger crystallite size distribution, but with heat treatments above 800 °C, equivalent inversion rates are obtained for both the Pechini and co-precipitation syntheses.

For samples treated at low synthesis temperatures, the optical properties point to three types of defects responsible for the radiative emission bands: Zn Al antisites (linked to the partial inversion rate), oxygen vacancies and Zn 2+ ions in interstitial positions. Drastic decreases of the associated emission intensities between the 1200 °C and the 1350 °C heat-treated samples confirm that these emissions are caused by various defects. From the X-ray diffraction results and from previous studies on the ZnO wurtzite phase, the two groups of emission bands located at 460 nm and 610 nm were attributed to Zn 2+ ions in interstitial positions and oxygen vacancies resulting from the existence of Zn Al antisites, respectively. Finally, we successfully correlated the optical properties and the structural evolution (disappearance of antisites and nonstoichiometric defects) to the synthesis temperature of the as-prepared ZnAl 2 O 4 spinels, making ZnAl 2 O 4 a good candidate for an optical thermal history sensor.

Fig. 9

 9 Fig. 9 Luminescence spectra of ZnAl 2 O 4 prepared by the Pechini synthetic route: (a and c) 1200 o C heat treated sample; (b and d) 1350 o C heat treated sample.

Fig. 11

 11 Fig. 11 Energy levels in the band gap.

Acknowledgements

Lucile Cornu is the holder of the doctoral fellowship supported by the Bordeaux 1 University. The authors thank CNRS, the Aquitaine région and the ANR (ANR-2010-BLANC-0820) for financial support.


Sylvie Patron

"NARRATIVE KNOWS…": SOME REFLECTIONS ON THE THEORETICAL STYLE OF ANN BANFIELD

Introduction: the two styles of Ann Banfield

With Unspeakable Sentences: Narration and Representation in the Language of Fiction, Ann Banfield produced one of the most interesting works on the linguistics of literature in the 1980s. The theory aims to meet the requirements formulated by Noam Chomsky for linguistics as a scientific discipline (it could also be said that, for Banfield, Chomskyan linguistics represents the prototype of a science, or at least a "human science", which she attempts to make her theory comply with 1 ). She defined its goal and its principles. She produced a theoretical model of the interaction between systems (the relationships between the language of fictional narrative and language in general). She developed her concept of literary competence, included in linguistic competence. 2 While it is a product of generative grammar, it is nevertheless not an applied linguistics, and even less a mechanical transposition of linguistic concepts to another field, like the structuralist poetics she is directly opposed to. 3 This theory is thus accompanied by a particular type of idealisation or reduction of the literary phenomenon as an object, which defines its style. Certain notation and terminological conventions and a formalised and axiomatic-style presentation, which appear for example in the formulation of the 1 E/1 SOI and Priority of SPEAKER principles:

We revise 1 E/1 I accordingly:

(48) (a) 1 E/1 SELF. For every node E, there is at most one referent, called the "subject of consciousness" or SELF, to whom all expressive elements are attributed. That is, all realizations of SELF in an E are coreferential. (b) Priority of SPEAKER. If there is an I, I is coreferential with the SELF. In the absence of an I, a third person pronoun may be interpreted as SELF. 4 Use of goodness-of-fit tests:

We can test this prediction if we alter sentences otherwise interpreted with a third person SELF by the addition of a first person. Indeed, in (48) we find that the sentences without the parenthetical are read as expressions of the SPEAKER; in them, the syntactic past tense has its normal interpretation as past. When the parentheticals are added, making the attribution of point of view to a third person explicit, the sentences become anomalous.

(49) Oh how extraordinarily nice I i was! (*she j thought.) […] Where were my i paints? (*she wondered j .) […] 5 1 See Banfield 1979;1982: 1-21;1983;[START_REF]L'Écriture et le Non-Dit[END_REF]1995. 2 See in particular Banfield 1983. 3 See in particular Banfield 1979; 1982: 1-21. 4 Banfield 1982: 93. In Banfield's theory, E (for Expression) replaces S (for Sentence) as the initial symbol of the structure of the sentence. E is distinguished by the fact that it isn't recursive, which is to say it can't be subordinated to another . For the discovery of E, see Banfield 1973. See also Milner, J., 1973; Milner and Milner 1975; Milner 1978; Nique 1978: 88-102; Milner 1986. 5 Banfield 1982: 94.

S

If we make the assumption of the dual voice theory explicit and add a first person to the sentences of (1), no part of them can any longer be attributed to a third person SELF; this is true for the revised form (1b and c) in (15) (15) Je sais qu'elle aimait la brebis malade, le sacré coeur percé de flèches aiguës, ou le pauvre Jésus qui tombe en marchant sur sa croix.

[I know that she loved the sick lamb, the sacred heart pierced by sharp thorns, or poor Jesus falling as he carries his cross.] I said that she liked Miss Overmore better than she liked papa. 6 This style can also be considered as a non-style, as the adoption of a neutrality that appears to eliminate style. It can be seen in other authors. One example, among many others, is the formulation of the A/A principle in the dialogues between Chomsky and Mitsou Ronat: This condition hypothesizes that a constituent of the category A cannot be extracted from within another constituent of the same category A. This prevented, for example, the complement of a noun contained within a direct object from being chosen as the NP displaced by the passive transformation: But there is a second theoretical style in Ann Banfield. It is especially apparent in the conclusion -"the moment of closure", as Jean-Claude Milner puts it, who associates it with the inscription of the linguist's presence/jouissance. 8 There is no more formal notation, axiomatic presentation, clarification or tests. On the contrary we find, on almost every page, obscure and often condensed claims, with plays on words, which would seem to require, in order to be comprehensible and a fortiori accepted, clarifications, connections and justifications, which are generally absent. Here are a few examples:

By separating SELF from SPEAKER, this style reveals the essential fictionality of any representation of consciousness, of any approximation of word to thought, even of our own. Through it, language represents what can exist without it, yet which can scarcely be externalized except through language, but it does it without bringing this externalization to the level of speech. 9

The language of narrative, in particular, knows that events simply occur to be recounted or that things exist in themselves, because they can be so described. 10 By purely and simply recounting events, language is transformed into an externalized, objective knowledge; by simply representing consciousness, language renders its subjective aspects opaque. Just as it is narration which knows what happened, so it is the language of represented consciousness which knows as its subject knows. 11 In language, this knowledge remains unknown as long as it remains spoken -that is, in man. Its existence can be seized and subjected to a self-conscious, objective scrutiny only when it is separated from its human author and incarnated in a text. 12 Just as the clock embodies the fact that time passes and is inherently (re)countable, so the lens is witness to the fact that representation, even a representation of the mind, need not imply a representing mind. It may be true that the lens captures in its relation to what it focuses on the stance or point of view of any subject looking through it, but the image on its glass is nevertheless independent of the mind behind it, registering this image and representing it to itself. 13 6 Ibid.: 195. 7 Chomsky 1979: 182 (Mitsou Ronat's note). 8 "It would be relevant to make a survey of the figures of evidence and to set up a typology of the moments of closure: for Troubetzkoy, complementarity, by which two entities are to be identified by having no common predicate; for Benveniste, the pure difference which separates, from the point of view of a system of relations, two entities all of whose empirical predicates are the same; for Jakobson, the laying out in terms of symmetry and asymmetry of the disjoint elements; for Chomsky, the deduction of the most erratic series starting from a few minimal writings. Are not the great linguists thus those who succeed in making generally accepted a new figure of evidence -that is to say at one and the same instant an unprecedented trace of their thrill, their jouissance" (Milner 1990: 142, n. 2). " [E]ach great linguist meets with his truth as a subject in the singular structure of a moment of closure […]" (Milner 2002: 132; my translation, M. M.). 9 Banfield 1982: 260. 10 Ibid.: 270. 11 Ibid.: 271. 12 Ibid.: 273. 13 Ibid.: 273-274.

In his review of Unspeakable Sentences, Brian McHale points out this tendency to make extrapolations from ambiguous words (such as "fiction" or, here, "(re)countable"). 14 Gérard Genette was ironical about certain over-hasty logical shortcuts. 15 For my part I would like, with no intention of ridiculing of or depreciating Banfield's theses in any way, to examine two stylistic features which seem to me to be characteristic of her singular mode of closure: firstly, the turn of phrase "Narrative knows…"; secondly, the analogy made between the unspeakable sentences of fictional narrative and machines or scientific instruments.

"Narrative knows…"

2.1. We should firstly mention that this is a recurring stylistic feature of Banfield's work. It can be described as the association of an "inanimate" nominal group (which is to say, one that refers to an inanimate object) with an "animate" verbal group (which is to say, one that refers to an activity generally attributed to a living human being). Here are a few examples:

The language of narrative, in particular, knows that events simply occur to be recounted or that things exist in themselves, because they can be so described. 16 Just as it is narration which knows what happened, so it is the language of represented consciousness which knows as its subject knows. 17

For the writer, however, language has already solved the technical problem of silencing the speaker and his authority. 18 The linguistic evidence suggests that in some sense language cannot count; it can only distinguish between singular and a quantifiable plurality. 19 The specific innovation of novelistic style is to have suppressed the first person and, in the process, to have discovered in the linguistic repertoire a third person pronoun which is not an anaphor but what I have called an "E-level deictic". 20

2.2.

In the examples containing the verb "to know", we can try to get closer to the specificity of Banfield's statements by opposing them to much more banal statements that concern, for example, the ability of narrative, fictional narrative in particular, to transmit and legitimise forms of knowledge that may not be accessible via other mediums (for example, "Narrative is a privileged instrument for the transmission of knowledge", "Every fictional narrative is didactic"). In Banfield, knowledge is not the knowledge of such or such a category of individuals who use narrative, it is the knowledge of narrative itself (more precisely the language of narrative or of fictional narrative). It is possessed by the narrative and not simply mediated by it. On the other hand, it is not a knowledge about the world, external or internal, but rather a knowledge about narrative, or fictional narrative. Or else a knowledge without a specific object, but characterised by its mode, whether objective or subjective. We can note that in Mieke Bal's commentary on one of the cited examples, this specificity is denied and reduced to the more banal problem of how different knowledges are expressed and conveyed.

When [Banfield] writes toward the end of Unspeakable Sentences about two conceptions of knowledge, The language of narrative, in particular, knows that events simply occur to be recounted or that things exist in themselves, because they can be so described. In the other mode, nothing is known without the mediation of the mind (1982: 270) she points to a bond between language and the kind of knowledge it serves to construct and convey. 21 14 See McHale 1983: 40. We can also mention the appropriation of the words "narration" and "representation". 15 See Genette 1988: 100: "'It is, no doubt, not accidental that it was the period in intellectual history sometimes called 'cartesian' which saw the emergence in France of the sentence with an unspoken historical tense and, at the same time, in the Fables of La Fontaine, the sentence of represented speech and thought and that it was this same period in which the pendulum clock and the telescope were invented' (p. 273). It is, no doubt, not accidental". We find the construction, "It is no accident that..." again p. 270, as well as variations of this construction p. 319, n. 13 and 14. 16 Banfield 1982: 270. 17 Ibid.: 271. 18 Ibid.: 274. 19 Banfield 1985a: 394. The sentence is accompanied by the following note, which I will only cite the beginning of: "There is some evidence that language can count up to two. Many languages, including Old English, know a dual number". 20 Banfield 2002 (para. 8). 21 Bal 2008: 28-29.

The question that arises here is: are we dealing with a metaphor, simply a way of conveying or expressing a phenomenon? Or has the metaphor become interiorised (as Gaston Bachelard writes, "more here than just description by a word: there is explanation by a thought"22 )? In other words, is the phenomenon considered as the sign of a substantial property? 2.3. We can first of all note that statements such as "The language of narrative […] knows that events simply occur to be recounted or that things exist in themselves, because they can be so described" or "Just as it is narration which knows what happened, so it is the language of represented consciousness which knows as its subject knows" can be paraphrased in a literal way, which is to say without animating inanimate objects. For the first statement, I suggest the following paraphrase:

The language of narrative (it being understood that we are referring specifically to fictional narrative here) contains narrative sentences proper and descriptive sentences that share the same syntactical properties. The first narrate fictional events; the second describe fictional objects (places, characters). Events only exist in the fictional world because there are sentences of narration per se that narrate them, and the objects (places, characters) only exist in the fictional world because there are sentences of description that describe them. This paraphrase also eliminates certain obscure elements, or even contradictions, in Banfield's statement, for example the purpose phrase "to be recounted" and the causal clause "because they can be so described", placed on the same level in the sentence. My guess is they are both connected to a quote from Käte Hamburger given a few pages earlier, which contrasts the mode of existence of real objects and that of fictional objects: "[…] whereas a real identity is because it is, a fictive reality 'is' only by virtue of its being narrated […]". 23 For the second statement, I suggest the following paraphrase, shorter than the first:

The sentence of narration per se articulates or expresses a knowledge of events, which is an objective knowledge, without a subject; the sentence that represents consciousness articulates a subjective knowledge, a knowledge that is mediated by a subject. In Banfield's statement, it seems to me that the parallelism between "narration knows" and "the language of represented consciousness knows" attenuates rather than accentuates the animation of inanimate objects, by emphasising the process. This parallelism also allows us to understand that "knows what happened" refers to the possession of an objective knowledge, just as "knows as its subject knows" refers, in a much more explicit way, to the possession of a subjective knowledge.

These paraphrases, relatively far removed from the original statements, come close on the other hand to other statements of Banfield's; for example: Narration divides the knowledge which its language articulates between the objective and the subjective. 24 […] narrative fiction is formed by the dialectic of objective and subjective, of the sentence appropriate also for the recording of real events divorced from all subjectivity and the sentence whose syntax stimulates the movements of the mind and arrests them in its eternal NOW. 25 [N]arration […] provides the context within which the sentences which articulate these two aspects of knowledge are brought face to face. 26 The sentence of narration bears witness to the possibility of an objective knowledge -statements without the intervention of a knowing subject. 27 It is narrative which offers the evidence of statements without subjective coloring, because, in narration, as Benveniste says, no one speaks. And against this objective statement, narrative sets a sentence whose structure cannot escape the knowing subject's presence. 28 We could also translate these paraphrases into what I call Banfield's first theoretical style, by saying that the sentence that represents consciousness is generated under E and not under

(it has all of its syntactical properties, in particular that of never being subordinate to another E; it contains some characteristic elements and constructions). As for the sentence of narration per se (or the sentence of description sharing the same syntactical properties), it is generated under , outside of any E (it can be subordinated and is characterised by the absence of elements and constructions connected with E). We find equivalent or similar statements in Unspeakable Sentences, for example:

In indirect speech, the quoted clause is an , in direct speech, it is an E. Thus, in indirect speech, as in all embedded clauses, the elements which can occur only in the expansions of E permitted by ( 29) and ( 33) and not in those of , are excluded. 29 The distinction between an E and introduced there provides the formalism for differentiating represented speech and thought from indirect speech, for the E of represented speech and thought allows the elements and constructions expressive of subjectivity or point of view to appear. 30 It remains that these paraphrases are, by definition, different from Banfield's original statements. It is one thing, in effect, to say that the unspeakable sentences of fictional narrative articulate or express two types of knowledge of the fictional world: an objective knowledge, without a subject, and a subjective knowledge that is mediated by one (or several) subject(s). This proposition can be illustrated by examples; the following two are taken from Banfield:

Then her mother died, her sisters went their separate ways, a farmer took her in, and employed her, little as she was, to tend the cows in the fields.

[Puis sa mère mourut, ses soeurs se dispersèrent, un fermier la recueillit et l'employa toute petite à garder les vaches dans la campagne.] 31 It was turning into a man! He could not watch it happen! It was horrible, terrible to see a dog become a man! 32 It can even be validated on the scale of a whole narrative. 33 But it is something else to say that fictional narrative possesses a knowledge that I will call "meta", bearing on the status of sentences of narration per se (or sentences of description sharing the same syntactical properties). Such an astonishing argumentative leap would require a detailed justification. But there is no justification in the immediate context of Banfield's statements.

2.4.

More than a simple metaphor, it seems we are dealing here with a substantialisation of the qualities that are attributed more or less metaphorically to the unspeakable sentences of fictional narrative ("more or less metaphorically" because we could discuss at length the metaphorical or non-metaphorical nature of the terms "knowledge", "objective", "subjective" used in reference to the unspeakable sentences of fictional narrative). It is accompanied by a strong valorisation of the language of fictional narrative, within language in general, and we could easily contrast the markers of the valorisation of the language of fictional narrative and the markers of the devalorisation of the language of discourse or communication. I will give just one example that strikes me as representative:

These two kinds of knowledge exist also, before narration, in the language of discourse. There, however, they are not recognizable as such, because they are subsumed under the intention to communicate: to narrate in speech is to tell someone something which happened; to represent subjectivity is to express it -subjectivity is "pressed out", betrayed, made public, i.e. conveyed to another. 34 This observation calls for a few qualifications, however. In the first place, we should stress that there is nothing intuitive or immediate about the qualities that Banfield attributes to the unspeakable sentences of fictional narrative. On the contrary, they are the result of an elaborate construction that combines linguistic arguments, more specifically syntactical ones, and material from literary history. Any immediacy, if such exists, would rather be on the side of the competing theory, namely the communicational theory of fictional narrative, 29 Ibid.: 41. 30 Ibid.: 75. 31 G. Flaubert, "Un coeur simple", quoted in Banfield 1982: 266. 32 V. Woolf, Mrs Dalloway, quoted in Banfield 1982: 262. 33 See Patron 2013 (on a novella by M. Benedetti, "Cinco años de vida", studied in Spanish and English). 34 Banfield 1982: 271. according to which there is always a speaker in all fictional narrative and every sentence of fictional narrative, and we can agree with Banfield when she says that [t]his assumption is treated as axiomatic and not as subject to empirical verification, 35 or that:

[the] appearance [of represented speech and thought] could not be predicted either from an a priori assumption that language is equivalent to linguistic communication or from the facts of the spoken language alone. 36 In the second place, we need to remind ourselves that the statements in question appear in the conclusion of Unspeakable Sentences. In other words, they occur at the end and not at the beginning of the process of scientific investigation. They thus have no impact on this process and in particular they don't expose it to the danger Bachelard refers to of "[going] off on the wrong track, where false problems will give rise to worthless experiments whose negative results will even fail to act as a warning because the first, naive image is so dazzling, so blinding, and its attribution to a substance so decisive". 37 In the third place, we have to realise that while this conception of the language of fictional narrative in animated human form could, absolutely speaking, be interpreted in purely animistic and anthropomorphic terms and in terms that aren't necessarily anthropomorphic, in the context of Banfield's theory, only a non-anthropomorphic or even anti-anthropomorphic interpretation is possible. In other words, when Banfield refers to the knowledge of language, or of the language of fictional narrative within language in general, she means something that is not about projecting human qualities, but rather about dissociating from any idea of person or human being. As a result, we mustn't make the mistake of opposing the ideas contained in these statements to the following idea, taken from a slightly later article:

Écriture thus is the name for the coming to language of a knowledge, whether objective or subjective, which is not personal. 38 The are, on the contrary, equivalent.

The analogy with scientific instruments

3.1. The conclusion of Unspeakable Sentences is entitled "Narration and representation: the knowledge of the clock and the lens" 39 . It's a mysterious title, whose explanation is deferred until the penultimate page:

We might, in fact, take as emblems of these two kinds of knowledge -one subjective and the other objective, but both objectivized -two mechanisms or machines -Huygens's clock and Huygens's lens. One, like narration, "tells time", counts its discrete units and assigns them an order and like narration, "incarnates the passage of time" (Lacan 1978: 94). The other captures and externalizes the gaze behind which is always placed the silent mind, the means by which the world is represented to the mind, the lens which focuses an image of the world as seen. 40 This passage contains an elliptical reference to Lacan (The Seminar, book II). In effect, in the sixth session of the seminar, on "Freud, Hegel and the machine", Lacan mentions Huygens' pendulum clock as an example of what a machine is, "this thing which […] pursues a human hypothesis, whether man be there or not". 41 It is probably this idea, even more than the fact that the clock "embodie[s] […] the measure of time", to use Lacan's exact words, 42 that caught Banfield's attention. A few pages later, Banfield also quotes Frege, who uses the analogy of a telescope to explain the difference between "sense", "reference" and "idea". The moon corresponds to the reference, "the real image projected by the object glass in the interior of the telescope" corresponds to the sense, and "the retinal image of the observer" corresponds to the individual idea. The image in the telescope can be considered objective to the extent that it is determined by the laws of optics. Two observers using the same 35 Ibid.: 7. 36 Ibid.: 234. See also McHale 1983: 21;Yamaguchi 1989: 495. 37 Bachelard 2002: 109. 38 Banfield 1985b: 13. 39 Banfield 1982: 257. 40 Ibid.: 273. 41 Lacan 1978: 73. 42 Ibid.: 74. Lacan contrasts here clocks worked by weights which "nonetheless embodied the measure of time" and Huygens' pendulum clock which represented a qualitative leap in terms of precision. telescope would witness the same optical image: "At any rate it could be arranged for several to use it simultaneously. But each one would have his own retinal image". 43 3.2. Banfield indicates quite precisely the points on which these two categories of phenomena are comparable with each other. The pendulum clock corresponds to objective knowledge, associated with the (sentence of) narration per se. It "'tells time', counts its discrete units and assigns them an order"; it "embodies the fact that time passes and is inherently (re)countable". 44 Huygens' lens corresponds to subjective knowledge, associated with the (sentence of) represented consciousness., in a way that's a little less obvious. We need to understand that the image in the lens of the telescope is subjective insofar as it depends on the position of the observer, but also objective in so far as it is determined by the laws of optics and does not depend on a individual observer. As Banfield writes in a more recent article:

The power of the instrument to reveal increasingly more of the world is thus a function of the elimination of the person of the observer […]. 45 In the same way, the (sentence of) represented consciousness is subjective (it reflects the point of view or subjectivity of the subject of consciousness), but at the same time it is objective in so far as it is determined by laws that, according to Banfield, exist in language, independently of the speaker, or rather the writer, who applies them without necessarily being aware of knowing them.

We can nevertheless observe some displacements and ellipses. In other passages, it is the passé simple (or "aorist"), the characteristic tense of the sentence of narration per se in French, which is supposed to "count discrete units and assign them an order" and so on; in short, which shows an affinity with number:

A sequence of French sentences in the aorist […] establishes by tense alone no other relation than one where the events follow one another in time. The normal reading of a sequence of sentences in the aorist interprets the events referred to or enumerated by their verbs as occurring one after the other. 46 Moreover, in the series of events signaled by the narrative tenses no one moment is privileged over the others, just as no number is privileged with respect to the others in the system of either cardinal or ordinal numbers. To be fifth, as opposed to first or fourth, is only to be earlier or later than. 47 The essential characteristic of the passé simple is to recount, to give an account, to tell a tale, in other words, to count, to tally, to sum up. It "tells time", establishing for events a linear order, that of the integers. For this reason, there is no privileged moment, no NOW with respect to which other moments are placed. Its role is objectivizing -enumerating discrete entities which are past events. 48 If we see the passé simple as a tense that counts, so to speak, the oscillations of the pendulum, we can explain why, among the following examples from Flaubert, the sentences in the passé simple, […] are normally interpreted as the representation of a series of events that take place one after the other, "the passé simple indicating the succession of events", as Sensine says […]. 49 […] in the sentence containing a narrative past tense, the moment referred to by the verb is not deictically anchored, but calculated solely in terms of before-and-after, in a chronological order which is that of the integers. 50 In the case of sentences of Narration, those appearing in French in the passé simple, there is no subjective temporal and spatial center whatsoever. Such sentences recount the past by placing discrete entities that are past events in a linear order. But there is no privileged moment to which the others are referred; the order of time is that of history, outside of any experience. One recognizes in this account the conception of time that Bergson, in L'essai sur les données immédiates de la conscience, defines by contrast to la durée; it is "le temps que l'astronome introduit dans ses formules, le temps que nos horloges divisent en parcelles égales" (80). This explains why the French narrative past, as Benveniste has pointed out, tolerates no deictics. 51 The 1985 article reinforces this analysis by accompanying it with a series of distributional tests:

This schema, which treats the narrative past as that tense which counts past events, points the direction for investigation. It suggests the co-occurrence of this past and the temporal adverbs specifying "the number of time" an event has occurred, such as the numerals themselves. Indeed, one finds sentences like those in (4). […] (4) Je revis, du reste, sa femme cinq fois.

[Moreover, I saw his wife five more times.] Mais une fois, au moment où je remontais par l'ascenseur, le lift me dit que […] (À la recherche du temps perdu, Pléiade II, p. 1025) [But once, at the precise moment I was taking the elevator up, the operator said to me that […]] [START_REF] Banfield | The co-occurrence of the passé simple + "une fois", "deux fois", etc. is then opposed to the non-cooccurrence of the imparfait + "une fois", "deux fois[END_REF] On the other hand, there is an ambiguity concerning what I will call, following Banfield, the "elimination of the person of the observer". It occurs in two ways, or for two reasons, in the (sentence of) represented consciousness. In the first place because linguistic laws (of which the laws of the representation of consciousness are a part, according to Banfield) are prior to and independent of the person of the speaker, or rather the writer, who applies them without necessarily being aware of knowing them. In the second place because, in accordance with the principles of 1 E/1 SOI and priority of the speaker, the speaker, or rather the writer, is obliged to efface him or herself as speaker, which is to say as an I, so that a third-person pronoun can be interpreted as the subject of consciousness of the sentence. This is the meaning of the final sentence of Unspeakable Sentences (which follows an evocation of Cocteau's Orpheus):

For the writer, however, language has already solved the technical problem of silencing the speaker and his authority. 53 3.3. We find other uses of the analogy with scientific instruments in Banfield's later monographs and articles, coinciding with a more in-depth reading or re-reading of G. E. Moore, Alfred North Whitehead and above all Bertrand Russell. Banfield writes for example in 1988:

In a certain, essential way, the instrument reflects both the world, under one of its aspects, and the conscious subject. For Russell, this reflection is close to sensory perception and sensation. We can thus speak of "instruments of sensation" or "sensitive" instruments. Russell considers that the function of the instrument is to give precision to the notion of sensation in a very particular direction. For him, it is the instrument that allows us to constantly detach ourselves from certain aspects of subjectivity in favour of a logical economy, such that only a residue of the logically necessary notion of subjectivity, "the core of pure sensation", can be "extracted" (The Analysis of Mind, p. 139). In this way, the instrument could occupy the place of the "ideal observer" of science, and offer guarantees of precision and rigour superior to what the human observer is capable of : "[…] the microscope and the telescope are better than the naked eye" (The Analysis of Matter, p. 224). This is true not only because an instrument is more precise and more powerful but because the power of observation is no longer the preserve of an individual subject and is securely entrusted to an impersonal instrument, not in order place sensation beyond the reach of thought, but in order to give thought access to a set of data that is less variable and more coherent because more impersonal.

54

The most interesting use is the one that appears in a 1987 article, often cited or reused afterwards. 55 This article establishes a link between the Russellian concept of sensibilia, "those objets which have the same metaphysical and physical status as sense-data, without necessarily being data to any mind", 56 and a type of sentence that is quite often encountered in the novels of Virginia Woolf and that Banfield suggests calling "the sentence that represents the unobserved". 57 For example:

Now the sun had sunk. Sea and sky were indistinguishable. 58 According to Banfield,

The literary sentence incorporating the sensitive instrument's knowledge is a descriptive sentence which gives grammatical representation of the appearance of things not necessarily observed, and it is the fact that it is a written sentence which makes possible its description of the unobserved. 59 We can ask ourselves whether this use of the analogy of the instrument calls into question the foundations of the analogy as it is presented in the conclusion of Unspeakable Sentences. Several arguments follow the same line, implying a form of continuity rather than a questioning. For example, the fact that sensibilia are a particular type of sense-data recorded by the instrument, just as the "unobserved", also called "impersonal subjectivity" or "subjectless subjectivity" by Banfield, 60 is a particular type of subjectivity represented by the literary sentence. Also the fact that the absence of any observer, authorised by the instrument, is a radicalisation of the objectivisation or elimination of the person of the observer, just as the absence of any subject, speaker or subject of consciousness, permitted by the sentence that represents consciousness, is a radicalisation of the objectivisation or elimination of the person of the speaker. Other arguments are more suggestive of a calling into question or global reinterpretation. We can note that in the analogy as it is presented in the conclusion of Unspeakable Sentences, the correlate of the observer is the speaker, or rather the writer, of the sentence that represents consciousness, whereas in the second use of the analogy, it is the subject of consciousness (to be precise, the speaker and the subject of consciousness, but the emphasis is above all placed on the absence of the subject of consciousness in the fictional world constructed by the text). In this second use, the theme of the elimination of the person of the observer is realised in a much more literal way.

Conclusion

Unspeakable Sentences is based on an objectivising approach, undertaken at the cost of a certain stylistic neutralisation. Its conclusion, on the other hand, is characterised by a certain number of figures or recourses, such as the recourse to analogy, where we can see, with Milner, the expression of the truth of the Banfieldsubject. It is interesting to note the paradoxical character of what is presented here as conclusive. It is disturbing, irritating for some, but also -this is any case the position I have tried to communicate -very intellectually stimulating.

Translated by Melissa McMahon

Bibliographical references

  (a) John saw ((Mary)'s brother) NP NP (b) Mary was seen brother by John. 7

[START_REF] Bachelard | The Formation of the Scientific Mind[END_REF] 103. Bachelard gives the following example, which, although it concerns a visual phenomenon, bears a certain resemblance to Banfield's statements: "a speck of dust sticks to an electrified surface and therefore electricity is a glue, a very sticky glue".

[START_REF] Hamburger | The Logic of Literature[END_REF]: 136, quoted in Banfield 1982: 263.

Banfield 1982: 180. The term "narration" means something different here to "narration" in "the sentence of narration" or "the sentence of narration per se". See infra "[N]arration […] provides the context…".

[START_REF] Banfield | The co-occurrence of the passé simple + "une fois", "deux fois", etc. is then opposed to the non-cooccurrence of the imparfait + "une fois", "deux fois[END_REF]

 26 Ibid.: 270.27 Ibid.: 270.28 Ibid.: 271.