Philippe Woloszyn
email: philippe.woloszyn@cerma.archi.fr

Aline Barlet
email: aline.barlet@bordeaux.archi.fr

Françoise Chartier
email: francoise.chartier@bordeaux.archi.fr

Hany Elsayed

Hossam Eldien

Perceptive Evaluation Procedures for Diffuse Reflexion Listening

Keywords: Diffuse reflection effect, Perception criteria, Free categorisation procedure, Acoustic immersion

Architectural morphology is an important factor for the prediction of soundscapes and noise propagation in urban areas. As in room acoustics, the sound field in a street is characterized by the building façades irregularities, in such a way that two similar streets (in size) can produce two different sound fields for two different building frontages. The main purpose of this paper is to investigate how the soundfield and urban soundscapes perception are influenced by building façades. This paper is a part of the national land transport research and innovation program (PREDIT) and is supported by the French ministry for ecology and sustainable development.

Introduction

Soundfield modelling in urban acoustics has attracted considerable attention in the last decades. Thus, many mathematical and numerical models have been derived to predict the soundfield in streets. However, many differences were observed between models and measurements in streets, suggesting that the part of multiple reflections, diffraction and diffusion of sound by building façades, could be more significant than expected and could account for these discrepancies. Moreover, as in room acoustics, one can also suppose that diffuse reflection effects can occur on urban soundscapes [START_REF] Kuttruff | A mathematical model for noise propagation between buildings[END_REF]. As the physical approach of the influence of the facade morphology on the acoustical diffusion in an urban street is an extensive subject for acoustics papers those last ten years, one can note that the perceptual aspect of this interaction has quasi-never been developed. This is why both CERMA and GRECAU-BX laboratories intend to proceed into this research topic within the "Bruit et Nuisances Sonores" Research Proposal Challenge, initiated by the Ecology & Sustainable Development Ministry, in collaboration with CSTB and LCPC laboratories [START_REF] Woloszyn | Procédures d'évaluation perceptive de la réflexion diffuse -Développements méthodologiques. 8 e Congrès Français d'Acoustique[END_REF]. One aim of this project was to evaluate the influence of these façade effects on the urban soundscapes in a street. The present paper is referring to this research program.

Evaluation procedure

This research aims to evaluate the influence of the urban facades morphology on a sound source perception (Coll. d'auteurs, 2006). Additionally, if this influence remains obvious, the experiment following will allow to define the exact nature of this effect. Therefore, we developed an evaluation procedure through spatial restitution of urban sonic objects, such as the tramway bells signals of Bordeaux. This will define the physical characterisation of the propagation space, with identifying the facade morphology as the varying parameter. Both recorded through a binaural technique and convoluted by a 4-channel B-Format Impulse Response (I.R.), those bell signals are then auralized through a restitution system that preserves their spatial components. Those auralization conditions depend on the recording techniques: headphone listening for the bells binaural recording, and immersive conditions in B-format acquisition [START_REF] Gerzon | Ambisonics in multichannel broadcasting and video[END_REF]. This experiment was proceeded within a canyon street in Bordeaux, Vital Carles street, in which six facades were selected for placement of the two following recording systems on the corresponding 6 points distributed into the length of the street:

-The binaural system used by the GRECAU-Bx consists into a stereophonic microphone based on the artificial head principle. Two electrets capsules are placed next to the sound recordist's ears so that they act as acoustic reflectors. This principle allows to register a stereophonic space very similar to the human hearing one. A digital audio tape (DAT) recorder connected to the system allows a 2 channel (stereo) recording under the PCM standard. While performing the sound recordings in Bordeaux, the binaural recording system was located over the same surface as the natural source and in front of the concerned façade.

-The B-format recording technique used by the CERMA provides a tridimensional Impulse Response (I.R.) of the street. This measurement technique for auralization of our urban sources has been applied at each recording point, the 4 information channels, called B-format signal, consists into acquiring the omnidirectional sound pressure signal (W), plus three first-order pressure gradient components, along the three Cartesian axes (X,Y,Z). The Soundfield 4-channel microphone used at this aim records the impulse responses with a sine sweep signal at every point of the street to be characterized. These B-format impulse responses are then convolved to the reference anechoic urban signal, which makes it possible to recreate the complete three-dimensional information of the street with the tramway bell for auralization. In order to enable the identification of relevant factors used for sonic objects subjective evaluation, immersion conditions for ambience restitution proceeded with a rigorous protocol, through exploiting a multichannel Ambisonic®6.2 sound reproduction system (6 channels and 2 subbass), lying under precise listener placement and controlled acoustic restitution [START_REF] Woloszyn | Virtual Reality as an Ambience Production Tool[END_REF].

Inquiry procedure involved listening tests, which were organized through an 8-sound sequences corpus, made from 6 selected points from the street, plus 2 "artificial pairs", strictly identical, in order to control the discrimination process. The two other pairs to discriminate are called "natural pairs", and correspond to the grouping of two recordings made in front of similar-styled facades (i.e. two windowed or two stone worked facades).

Counting about a hundred participants, two populations were concerned with the inquiry procedures: the experts group, composed with acousticians, musicians or soundscape research workers, and the students group, within the schools of architecture from Bordeaux and Nantes, including ECN students.

The presented recording techniques has produced 4 types of signals used for the pairs discrimination :

-Bell binaural signal (stereo), -3D convolved bell signal (B-Format), -Stereophonic convolved bell signal, -Pure Impulse Response (B-Format).

The three first signal types are based upon a common urban source from the city of Bordeaux, the tramway bell, permitting an easy association between signal and source, in order to facilitate the discrimination task itself. In the contrary, the last signal type does not reefer to a known urban source, as it is targeted to the experts group listening. Each of the 8-sound sequence corpus has been realised through emission of the 4 types of signals.

Listening tests were made within two towns: Bordeaux exploited both binaural and stereophonic convolved signals through a headphone diffusion for its students groups. Listening tests from Nantes involved four types of signal: pure Impulse Responses and B-Format convolved signals on one hand for its expert population, and B-Format convolved and binaural signals on the other hand for its students groups. A unique inquiry methodologyfree categorisation procedure-was applied for all experimental configurations in Nantes and Bordeaux.

Figure 1. Hearing tests experimental protocol

Free categorisation task involved two phases: first, subjects were asked to classify the sonic corpus elements into categories, without taking into account the number of categories nor the number of elements included in each category. A second task consists into a categorial construction through a free argumentation, leading to a class qualification. This method allow the analyse of the so-created categories, including the cluster criteria of the sonic elements.

First phase: Categories creation

Phase 1 first results shows 497 categories created that way by the 100 subjects. Independently from the subject status (expert or student) and the experimental conditions (towns, diffusion systems, auralized signal types), an average of five categories were created by every subject, with an individual variation from 2 to 11 created categories. Analysis of the inquiry results leads us to distinguish about three types of created categories including at least one pair, plus one category containing none:

-"exclusive" categories, composed uniquely from one of the proposed pairs, natural or artificial (22,13%), -"non exclusive" categories, composed from one of the proposed pairs and from other sequences (58,15%), -"double exclusive" categories, composed from the two proposed pairs, natural or artificial (2,01%), -"other" categories, composed uniquely from isolated sequences (no pairs) (38,23%).

The high percentile of the "non exclusive" categories can be explained by the multiple counting due to cumulative pair and isolated sequences, leading to a >100% percentile. This categories typology corresponds to a discrimination score of the sequences sound characterization: in the "other" categories case, nobody reconstitutes a pair, so that there is absolutely no discrimination. In contrary, when subjects isolate a pair in an "exclusive" category, discrimination is considered as "sharp". "Non exclusive" and "double exclusive" categories describe a more "relative" discrimination performance.

Global categorisation results referring to the whole population reveals a low "sharp" recognition level, for both natural and artificial pairs. In that way, "relative" discrimination performance and "no discrimination" are more important. Moreover, discrimination capacity depends on subjects groups, signal types, restitution modes and towns.

Both bell binaural (stereo) and Pure Impulse Response (B-Format) signals allow a better "sharp" identification of the natural and artificial pairs, for specific reasons. Indeed, as Pure Impulse Response (B-Format) has only been diffused to the expert group n°1, this last accuses a "sharp" discrimination performance of more than 22%, or till 72,9% with including "relative" discrimination performance (so including non-and double exclusive pairs). Bell binaural (stereo) signal is allowing a high "sharp" discrimination performance too, as the percentile of "exclusive" categories is the highest for the two groups who listened those signals (36,90% for students group n°1 -33% for students group n°4). Source knowledge appears to be a less significant variable for the recognition task, as the inquiry does not reveal a significant difference towards Bordeaux and Nantes sites (student group1 versus student group 4), the first of them necessary being familiar with the tramway bell. Influence of source recognition will being revealed through the qualification process, readable in the next part of the work.

Nevertheless, the two students groups 2 and 3 listening to the same signal with different restitution conditions, B-format signal (immersion room) for group 2, and binaural for group 3 (headphones), showed very different recognition levels concerning "sharp" (2.27% for group 2 and 18.87% for group 3) and "relative" (67% for group 2 and 88.68% for group 3) discrimination. This better performance of the group 3 confirms the advantage of the headphones restitution mode for discrimination process.

Those results lead us to the conclusion that restitution mode condition is clearly superior to source knowledge or recognition influence for pair identification task when using free categorisation method.

Second phase: Class qualification

Second phase of free categorisation task consists into description and argumentation of the created classification. This consists into identifying criterion relative to signal description, upon which were deduced categorisation criteria.

Whatever the discrimination level, "sharp", "relative", or "null", a 15 criterion items listing has been defined through the inquiry process, 8 items referring to the signal itself: A. "Source identification": the signal itself is identified and named as a source, B. "Reverberation": the presence or the absence of the reverberation effect is identified, C. "Temporality": describes the temporal evolution of the signal, D. "Description": qualities of the signal, E. "Spatialisation": perception effect of the signal in a particular space, F. "Sound level": sound volume perception, G. "Signal frequency": signal frequency perception, H. "Evaluation": positive or negative evaluation of the signal, 1 to the site evocation: I. "Site evocation", associating the heard sounds to a particular site, 6 to the background noise:

J. "Background source identification": background sources are identified and named, K. "Background noise description": qualities of the background noise, L. "Background noise level": sound volume perception, M. "Temporality": describes the temporal evolution of the background noise, N. "Background noise evaluation": positive or negative evaluation of the background noise, O. "Background noise frequency": background noise frequency perception.

Those 15 criteria listing is representative of the whole categorisation process, independently from the categories themselves. Influence of variables on the discrimination capacity is mainly the same as for the first phase (categories creation), that means depending on subjects groups, signal types, restitution modes and towns.

Influence of the signal type on its description is clearly established through the two criteria groups, referring to the signal itself or to the background noise: indeed, binaural signals were recorded and diffused with their corresponding background noise, leading to a "Source identification" (A) for signal and background noise, contrary to the convolved tram signal, which corresponding criteria are "Description" (D) and "Sound level" (F), and the pure impulse response, which is described through "Reverberation" (B) and "Sound level" (F) .

Influence of the recording / diffusion method on the signal perception modalities cannot be established yet, as the group student 2 provided a low recognition performance at 2.27%: this percentile does not allow sufficient statistical representation of the corresponding descriptors.

Influence of the sonic source knowledge on the signal evaluation appears clearly on the descriptors, which reefers to the background noise in Bordeaux, and to the signal itself in Nantes. We can note that those different descriptions does not interfere with the categorisation process (first phase), that provides the same recognition levels for Bordeaux and Nantes.

Conclusion

The three variables used in this research work -signal types, restitution modes and townshave a joint influence on sonic elements discrimination performance, and on perceived characteristics argumentation. The experimental condition that allows the most performing "sharp" discrimination corresponds to students group 1, which is composed with subjects familiarized with the diffused source (the tramway bell from Bordeaux), under headphones listening conditions (binaural signal). Nevertheless, the categorisation criteria used by this group are referring to background noise, without any relationship with the original signal characteristics. However, it is precisely the signal itself that carries the facades diffuse reflection effects.

On the contrary, the experimental immersive conditions diffusing Impulse Response signal to experts subjects implies a less performant sharp discrimination, but on the other hand, more referenced to the signal itself. In this framework, sole the expert group 1 who listened to pure Impulse Responses obtains a significant exclusive categories rate.

Final conclusion leads us to deduce that façade morphologies impacting on sound diffusion is only perceived in specific experimental conditions. So a particular trained listening like expert one (musicians, acousticians, sound engineers,…) and background noise absence constitute the minimal conditions for a performing discrimination of façade morphologies impact in soundscapes.

Figure 3 .

 3 Figure 3. Criteria used by the six groups

  Figure 2. Categories typology vs subjects groupsNevertheless, we have to keep in mind that, regarding to its acquisition process, binaural signal associates the tramway bell signal to its instantaneous urban background noise. Next part of the present work will tell us more about the background noise contribution in the recognition process.

	100%
	90%
	80%
	70%
	60%
	50%
	40%
	30%
	20%
	10%
	0%
	Expe r t s Gr oup 1	Expe r t s Gr oup 2	S t udent s Group 1 S t udent s Group 2 S t udent s Group 3 S t udent s Group 4
	Exc lusive c a t e gor ie s	Non e xc lusive c a t e gorie s	Double e xc lusive c a t e gorie s	Ot he r c a t e gorie s


Judicaël Picaut
email: judicael.picaut@lcpc.fr

Isabelle Schmich

Jérôme Defrance

Philippe Woloszyn

Aline Barlet

Françoise Chartier

EFFECTS OF DIFFUSE REFLECTION BY BUILDING FAÇADES ON THE SOUND PROPAGATION AND SOUNDSCAPES IN URBAN AREAS

Architectural morphology is an important factor for the prediction of soundscapes and noise propagation in urban areas. As in room acoustics, the sound field in a street is characterized by the building façades irregularities, in such a way that two similar streets (in size) can produce two different sound fields for two different building façades. However, most of the existing softwares and models take only the specular reflection into account implying a significant uncertainty in the sound prediction.

The main purpose of this paper is, first, to investigate how the sound field and urban soundscape perception are influenced by building façades, and secondly, to characterize several urban façade by typical reflection laws. Then, a coupling morphological and acoustical database will be built up and introduced in an urban acoustics simulation software, in order to be used by town planners and architects in urban projects.

This paper is a part of the national land transport research and innovation program (PREDIT) and is supported by the French ministry for ecology and sustainable development.

INTRODUCTION

Sound field modelling in urban acoustics has attracted considerable attention in the last decades. Thus, many mathematical and numerical models have been derived to predict the sound field in streets. However, many differences were observed between models and measurements in streets, suggesting that the part of multiple reflections, diffraction and diffusion of sound by building façades, could be more significant than expected and could account for these discrepancies. Moreover, as in room acoustics, one can also suppose that diffuse reflection effects can occur on urban soundscape perception.

In order to evaluate these effects, a research project within the "Bruit et Nuisances Sonores" Research Proposal Challenge, initiated by the French Ecology & Sustainable Development Ministry, was proposed. The first part of this project was to evaluate the influence of these façade effects on the sound propagation in a street and on the urban soundscape perception. Then, the main objective of the second part was to evaluate the reflection laws of real building façades, in order to include them in acoustic prediction software, thus to enhance acoustic predictions in urban areas.

DIFFUSE REFLECTION EFFECTS IN URBAN AREAS

Effects on sound propagation in a street

In order to evaluate the diffuse reflection effects on the sound propagation in urban areas, numerical simulations have been performed in a rectangular street used two different acoustic prediction methods. The first method was based on a sound particles tracing model in order to model diffuse reflections by arbitrary reflection laws, using a Monte-Carlo technique. Results, already published in Ref. [START_REF] Picaut | Effects of diffusion on the sound propagation in a street[END_REF], have shown important effects on the sound attenuation and the reverberation along the street. In some cases, these differences may reach 5 dB on the sound pressure level and 1 s on the reverberation time. These results were confirmed by numerical simulations using the MICADO boundary element method code [START_REF] Jean | A variational approach for the study of outdoor sound propagation and application to railway noise[END_REF], showing different sound pressure distributions in a street, for different building façade morphologies. As suggested in the paper introduction, these numerical results show that it is necessary to take the real reflection laws into account in acoustic prediction software, for accurate prediction in streets.

Effects on urban soundscape perception

A second part of this research project was to evaluate the influence of the urban façades morphology on the sound sources perception. Additionally, if this influence remains obvious, the experiment following will allow to define the exact nature of this effect. Therefore, we developed two evaluation procedures through spatial restitution of urban sonic objects, such as the tramway bells signals of Bordeaux. This will define the physical characterisation of the propagation space, with identifying the façade morphology as the varying parameter. Both recorded through a binaural technique and convoluted by a 4-channel B-Format impulse response, those bell signals are then auralised through a restitution system that preserves their spatial components. Those auralisation conditions depend on the recording techniques: headphone listening for the bells binaural recording, and immersive conditions in B-format acquisition. This experiment was proceeded within a canyon street in Bordeaux, Vital Carles street, in which six façades were selected for placement of both recording systems on the corresponding 6 points distributed into the length of the street.

The first recording system is a binaural system (SEB), consisting into a stereophonic microphone based on the artificial head principle, but using the sound recordist's ears so that they act as acoustic reflectors. This principle allows to register a stereophonic space very similar to the human hearing one. The SEB was located over the same surface as the natural source and in front of the concerned façade. The second system is based on a B-format recording technique providing a tridimensional impulse response of the street at each recording point. Impulse responses are then convolved to the reference anechoic urban signal, which makes it possible to recreate the complete three-dimensional information of the street with the tramway bell for auralization. In order to enable the identification of relevant factors used for urban ambience subjective evaluation, immersion conditions for ambience restitution proceeded with a rigorous protocol, through exploiting a multi-channel Ambisonic®6.2 sound reproduction system (6 channels and 2 subbass), lying under precise listener placement and controlled acoustic restitution [START_REF] Woloszyn | Procédures d'évaluation perceptive de la réflexion diffuse -Développements méthodologiques[END_REF]. Listening tests (Fig. 1) were organized through an 8-sound sequence corpus, made from 6 selected points from the street, plus 2 "artificial pairs", strictly identical, in order to control the discrimination process. Listening tests were made within two towns: Bordeaux exploited both binaural and stereophonic convolved signals through a headphone diffusion for its student population. Listening tests from Nantes involved four types of signal: pure Impulse Responses and B-Format convolved signals on one hand for its expert population, and B-Format convolved and binaural signals on the other hand for its student population. A unique inquiry methodology -free categorisation procedure-was applied for all experimental configurations in Nantes and Bordeaux. The free categorisation procedure consists into a classification of the sonic corpus elements, without taking into account the number of categories nor the number of elements included in each category. A second task consists into a categorical construction through a free argumentation, leading to a class qualification. This method allow the analyse of the so-created categories, including the cluster criteria of the sonic elements.

Phase 1 first results concerning the expert group n°1 investigation lead us to conclude on a quite good sample discrimination, through two emergent categorisation criteria: reverberation and sound level. SEB listening by group 1 students leads to quasi-exclusive background noise discrimination, using the following criteria: background noise source identification and description, temporal and energetic aspects of the background noise signal. As a first consequence, phase 2 results allow statements upon: (1) influence of the recording and diffusion method on the signal perception modalities, (2) influence of the sonic source recognition on the perceived signal evaluation.

Further results interpretations will help us to confirm and to define the diffuse reflection effect on urban sound sources perception.

CALCULATION OF REFLECTION LAWS

Method

Based on the room acoustic methods of diffuser characterisation, numerical simulation were performed to calculate the reflection laws of building façades in far field conditions [START_REF] Antonio | Acoustic Absorbers and Diffusers: Theory, Design and Application[END_REF]. This calculation treats the façade independently of the street in which it is located or any other environmental object so that a half-circle of receivers and a quarter-circle of sources can be placed around it in far field conditions. As a first approximation, the receivers and sources respectively are all at the same distance from the façade as show in Fig. 2.

The 2D calculations have been performed with the MICADO code [START_REF] Jean | A variational approach for the study of outdoor sound propagation and application to railway noise[END_REF], that is currently the only approach that is able to give exact calculation results for such an acoustic problem, and that can be used as a reference. The reflection laws have been calculated in terms of the Excess Attenuation of the reflected field relative to the free field, and corrected by the respective 2D geometrical divergence (cylindrical sources). For each source and each receiver this Excess Attenuation refl EA is given in dB by: where tot p is the total field sound pressure, lib p is the free field sound pressure,

refl SR d (
) is the distance from source to receiver trough the path reflected by the façade (see Fig. 2) and where ) (SR d is the direct distance between the source and receiver position. This method has been used to calculate the reflection laws for a real façade from Vital Carles street in Bordeaux (Fig. 2). To simplify the comparison, the calculations have also been carried out for a finite plane façade.

          - = ) ( * ) ( * ) ( log * 20 10 SR d p SR d p p EA lib refl lib tot refl , (1)

Results

Fig. 3 shows the results of the reflection laws of the real façade (in blue) and the plane façade (dotted red line) for source S5 (45°) at several frequencies from 31.5 to 1000 Hz. At very low frequencies no influence can be observed. The height of the façade is too small compared to the wavelength of the incident sound field. It is the lower limit of the calculations where the reflection law is valid. At low frequencies, the façade roughness has no influence on the reflection law. The façade acts as a plane façade. Only some negligible back-scattering on the plane façade edges can be observed. At medium frequencies, the reflection law of a real façade has its own shape noticeable different to that of a plane façade. At higher frequencies the reflection law is very different to that of a plane façade where specular reflection occurs. The reflection law of the real façade can be approximated by a uniform law for frequencies higher than the Rayleigh criterion, which is in the presented case around 200 Hz.

Introduction into an acoustic prediction software

The last step of the second part of this project is to show that such real reflection laws can be introduced in acoustic prediction software. In this study, the choice was done to use the ICARE code, based on a beam tracing method [START_REF] Deille | Real time acoustic rendering of complex environments including diffraction and curved surfaces[END_REF]. Instead of using the real geometry of the façade, a plane façade is used with the reflection law of the real façade. Because of the result of the weighted sum of reflection laws, is the reflection law itself, it can be applied at each point on the building façade. In this step, which is currently in progress, 3D reflection laws will be used. Since the calculations have been performed in 2D, an interpolation between the reflection laws of a horizontal and a vertical cross-section will be done. Contrary to classical prediction software which includes diffuse reflections, it is not necessary to separate the specular and the diffuse fields, since the reflection law already includes the specular part.

CONCLUSIONS

The main result of this work is that diffuse reflection must be included in acoustic prediction software, in order to give accurate predictions in urban areas. On the other hand, our results show that diffuse reflection effects is difficult to correlate with urban soundscape perception. The last part of this project is to validate these results by simulating a real street with real reflection laws, then by comparing the numerical results with experimental data.

Fig. 1 :

 1 Fig. 1: Hearing tests experimental protocol.

Fig. 2 :

 2 Fig. 2: Calculation set-up. Sources and receivers in far field conditions for a plane façade (left) and above a real building façade in Bordeaux (right).

Fig. 3 :

 3 Fig. 3: Reflection laws in terms of


Professor Etienne Sicard
email: etienne.sicard@insa-toulouse.fr

Introducing 14-nm FinFET technology in Microwind

This paper describes the implementation of a high performance FinFET-based 14-nm CMOS Technology in Microwind. New concepts related to the design of FinFET and design for manufacturing are also described. The performances of a ring oscillator layout and a 6-transistor RAM memory layout are also analyzed.

Technology Roadmap

Several companies and research centers have released details on the 14-nm CMOS technology, as a major step for improved integration and performances, with the target of 7-nm process by 2020. We recall in table 1 the main innovations over the past recent years.

Improved performances

The power, performance and area gains are an important metric for justifying a shift from older technology nodes to new ones. As compared to 20-nm technology node [Sicard2014], the 14-nm technology offers:

• 30 % less power consumption. This is a key feature for mobile industry for which the battery life is the top one problem. • 30 % increase in switching performance. This is equally important in server applications and smartphones, which use faster processors and higher resolution screens.

Page 2/25 etienne.sicard@insa-toulouse.fr 17/06/17

• 2 times higher density. This is a key advantage to produce the lightest and thinnest possible smartphones.

A comparison between 45nm, 32, 22, 14 and 10nm technologies in terms of density is proposed by [Brain2017] are reported in Fig. 1. The IC surface is shrunk by a factor of 5 between 45-nm and 14-nm nodes. The giant cost of fab and IC design in 14-nm

The consequences of the fab and chip design cost explosion is the drastic decrease of foundries. While more than 20 foundries existed for 130nm technology, only four major companies are providing the 14-nm process (Table 2). Within a same technology node, improvements are made over the years, such as Intel who improved on their original process "14nm" with the "14nm+" offering 12% higher drive current, followed 1 year later by "14nm++" process which allows for +25% higher drive current [Brain2017].

Company

Some examples of processors used in mobile phones, laptops and servers are reported in Fig. 3, with complexity approaching 10 Billion devices. A continuous increase in switching performance has been made possible thanks to several innovations, as shown in Figure 4. Starting 14-nm, the MosFET is replaced by the FinFET, for improved current capabilities.

Page 4/25 etienne.sicard@insa-toulouse.fr 17/06/17

Figure 4: most significant technology improvements over the past 15 years

14-nm Process variants

Within the same "14-nm" label, we may observe a wide variety of performances, depending whether the IC fabrication process is targeted to "high performance" (HP) devices (speed whatever the power consumption), "general purpose" (GP) or "Low Power" (LP) (lower speed but power-efficient), as summarized in Table 3. Significant differences may be observed in terms of Ion and Ioff currents, as illustrated in Figure 4. We implement in Microwind the general purpose 14-nm process.

Power supply operation

The supply voltage, both internal to the cores and the external I/O supply have been continuously

decreased due to the thinning of the gate oxide and faster switching rates thanks to reduced voltage swings. The 14-nm technology operates around 0.8V, while I/Os are supplied at 1.2, 1.5 or 1.8 V (Fig.

Page 5/25 etienne.sicard@insa-toulouse.fr 17/06/17

Key features of the 14-nm technology

Introducing the FinFET

The FinFET device has a different layout style than the MOS device. Instead of a continuous channel, the FinFET uses fins (Figure 6), which provide the same current at a smaller size. FinFET also provides a lower leakage current (Ioff) at the same (Ion) [Fischer2017]. Built on more than 15 years of FinFET research & development and solid foundation of high-K metal gate production experience, the 14-nm FinFET device reuses an important part of process elements from the previous 28-nm and 20-nm nodes, so that planar designs may be partially reused in 14-nm FinFET technology. However, the Fin design is a totally new feature which contrasts with the traditional MOS design. This leads to new screens and new acronyms such as "Fin Pitch", "Fin thickness", etc, as shown in Figures 7 and8.

Lambda

In Microwind, we use an integer unit for drawing, which is fixed to 8 nm for 14-nm CMOS process (Table 4).

• The drawn gate length is 2 λ that is 16 nm.

• The fin width is 1 λ that is 8 nm.

• The lower metal pitch is 48-nm.

Page 7/25 etienne.sicard@insa-toulouse.fr 17/06/17 Table 4: key parameters of the 14-nm processes used to configure Microwind rule file Cmos14n.RUL

Core MOS devices

Table 4 gives an overview of the key parameters for the 14-nm technological node concerning the Page 8/25 etienne.sicard@insa-toulouse.fr 17/06/17 Commercial 14-nm processes propose up to 3 threshold options, namely high-Vt (HVT), regular Vt (RVT), and low Vt (LVT).

• HVT -High Threshold Voltage causes less power consumption, but switching is slow. HVT are used in power critical functions. • LVT -Low Threshold Voltage causes more power consumption and switching timing is optimized. LVT are used in time critical functions.

• RVT -Regular Threshold Voltage (sometimes called Standard VT or SVT) offers trade-off between HVT and LVT i.e., moderate delay and moderate power consumption.

In Microwind, we only use 2 types of MOS devices for the core and reuse the same name as for previous nano-CMOS technologies:

• Low leakage MOS (LL), close to RVT

IO MOS devices

Table 5 gives an overview of the key parameters for the 14-nm technological concerning the Input/output MOS devices and associated supply voltage. In Microwind, we only consider 1.2V I/O supply and tune the "High-Voltage" (HV) MOS device on the median performances. Other standards usually supported in commercial 14-nm process include 1.2, 1.5 and 1.8V I/O supply.

Parameter

Transistor performances in 14-nm technology

Designing a 1µm-width FinFET

The evaluation of the equivalent FinFET channel width corresponds to the following formulation (Eq. 1). The evaluation of the current is usually expressed in mA/µm, meaning that a 1-µm equivalent width

FinFET design is needed to evaluate the current. In the proposed 14-nm technology, HFIN is 40nm, WFIN 8nm, so one fin has an equivalent width of 88 nm (Figure 10). An equivalent width of 1µm, as it would be designed using MosFET's, corresponds to around 12 fins in 14-nm technology. As seen in Fig. 11, the FinFET with a 1-µm width is smaller than a MosFET with the same width. We get the following I/V characteristics (Fig. 11) for n-channel FinFET and p-channel FinFET.

Page 10/25 etienne.sicard@insa-toulouse.fr 17/06/17 The drawback associated with this high current drive is the leakage current which rises from 1 nA/µm (low leakage NMOS) to 10 nA/µm (high speed NMOS), as seen in the Id/Vg curve at the X axis location corresponding to Vg= 0 V (Fig. 13). From a design view-point, the "option" menu in the MOS generator enables to switch from low leakage to high-speed. In terms of layout, the only difference is the option layer that contains the MOS option information (Fig. 14), which can be Low leakage (Regular Vt), High Speed (Low VT), or High Voltage.

Page 12/25 etienne.sicard@insa-toulouse.fr 17/06/17

P-channel MOS device characteristics

The p-FinFET drive current in 14-nm technology is quite similar to the n-FinFET thanks to the strain engineering for PMOS that nearly compensates the intrinsic mobility degradation of holes (P-channel) vs. electrons (N-channel). The leakage current is around 1 nA/µm for the low-leakage device and nearly 10 nA/µm for the high-speed device (Fig. 15). The effect of process variability on the MOS Ioff/Ion characteristics is plotted using the menu "Ioff vs.

Ion" under the "MOS I/V curve" menu (Fig. 17). It can be seen that the MOS devices have a wide variability in performances. The 3 MOS types (low leakage, high speed, high voltage) are situated in well-defined space in the Ioff/Ion domain. The low leakage is in the middle (medium Ion, low Ioff), the high speed on the upper right corner (high Ion, high Ioff), and the high voltage is at the lower left side of the graphics (low Ion, very low Ioff). Note that the exact locations of the dots will change for each MOS characteristics plotted because it is a random process.

Page 14/25 etienne.sicard@insa-toulouse.fr 17/06/17

Dummy gates

One solution to reduce MOS performance variability is to design in a regular way the MOS gates. An option exists in the device generator to add "dummy" gates around the active device (Fig. 18). The variability of lithography depending on the environment will significantly affect the dummy gate, but only little the central active gate.

Page 15/25 etienne.sicard@insa-toulouse.fr 17/06/17

Interconnects Metal Layers

As seen in figure 19, the original 14-nm technology from Intel [Brain2017, Natharajan2014, Fischer2015] comprises 10 to 12 layers depending on the option (here "High Performance" and "High Density"), the lower ones for short routing, the medium ones for long routing, and the upper ones for various purpose including supply network, Metal-Insulator-Metal (MIM) capacitance, and high quality embedded coil inductors thanks to a very thick upper layer (1µm). One innovation described by Layers metal5 and metal6 are a little thicker and wider, while layers metal7 and metal8 are significantly thicker and wider, to drive high currents for power supplies (Fig. 20).

Interconnect Resistance

The resistance and capacitance of interconnects are an important metric for evaluating the RC delay and consequently the switching speed of the signals. In figure 21, the spread of capacitance and resistance of Intel's 14-nm metal2 using a 52-nm pitch is reported [Fischer2015]. The order of magnitude is 43 ohm/µm and 0.3 fF/µm. Page 19/25 etienne.sicard@insa-toulouse.fr 17/06/17

We can see that the resistance is close to Intel's values at comparable pitch and length (Around 40 Ω/µm). However, the capacitance is underestimated: 0.15 fF instead of 0.3 fF. The main reason is the crosstalk capacitance that may be evaluated using the simulation parameter "Handle Lateral

Couplings", or "Simulate with Crosstalk". Consequently, the total node capacitance is close to 0.25fF/mm, a value close to [Fischer2015].

Page 20/25 etienne.sicard@insa-toulouse.fr 17/06/17

Double Patterning for M1-M2 Interconnects

The double patterning is required for metal layers as the pitch between tracks is smaller than 80nm.

Half the patterns go on the first patterning and half go on the second patterning, as illustrated in Fig.

24.

In order to ensure an easy selection of metal tracks for the first and second patterning, regular structures with straightforward orientation such as M1 east-west, and M2 south-north are requested.

The other solution is to relax the pitch constraints for an improved manufacturability, at the cost of an extended silicon area. M3-M8 with pitch of 80-nm and higher are still fabricated using simple patterning.

Simulation of Process Variations (PVT)

Considerable differences may be observed in terms of performances, depending on the process, voltage and temperature conditions. The usual temperature range is [-50°C..+125°C], the voltage variation VDD+/-10%, and the process may also vary +/-15% for some key parameters such as the threshold voltage and mobility. Microwind gives access to "Process-Voltage-Temperature" (PVT) simulation through the command Simulate → Simulation Parameters → Process Variations. Direct access from the simulation waveform window is also possible using the button "Process Variations".

The most usual simulation consists of simulating extreme situations (Min and Max), as compared to typical conditions (Table 7).

•

In Min situation, VT is high and the mobility U0 is low. The supply is minimum and the temperature is maximum. The ring oscillating is around 100 GHz. Another type of simulation consists in choosing a set of random variables and produce several iterations. Figure 28 shows the oscillation frequency variation with 100 random samples. The variation is much less as the random variation is of normal distribution around the typical values.

6-transistor static RAM

One of the most representative designs for comparing technology nodes is the static RAM cell designed using 6 transistors (6T-SRAM). The size reduction from 22 to 14-nm process is illustrated in Fig. 29 with Intel's implementation of the 6T-SRAM, with a surface divided nearly by 2. In our implementation in Microwind (see Fig. 30), the layout size is 328 x 129 nm, with a surface area of 0.043 µm 2 , close to

Conclusions

This application note has illustrated the trends in CMOS technology and introduced the 14-nm technology generation, based on technology information available from manufacturers. The key features of the 14-nm CMOS technology have been illustrated, including the FinFET, design for manufacturing and double patterning. A 3-stage ring, FinFETs wih 1-µm equivalent width as well as interconnects with 1-µm length have been used for comparison purpose.

Figure 1 :

 1 Figure 1: The evolution of silicon area with the technology nodes as presented by Intel [Brain2017]

Figure 2 :

 2 Figure2: The extraordinary increase of the fab cost: more than 6 billion $ for a 14-nm process, and associated chip design cost: 176 M$, more than 10 times the cost of a 130nm IC design.

Figure 3 :

 3 Figure 3: Examples of multi-giga-transistor processors used in mobiles, laptops and servers from various companies.

Figure 5 :

 5 Figure 5: The core supply voltage in 14-nm technology is 0.8 V, with typical IO voltage of 1.2 V

Figure 6 :Figure 7 :

 67 Figure 6: Introducing the FinFET in 14-nm technology: the same current switching capabilities in a smaller area. Fins cross the gate.

  internal MOS devices and layers. High performance NMOS/PMOS drive currents of 1.3/1.2 mA/um, respectively, have been achieved at 0.7 V and 100 nA/um off-state leakage in early versions of the Intel's 14-nm technology [Liu2015]. Drive currents near 2 mA/µm have been announced by [Fischer2017] for the 2 nd iteration of process improvement called 14++nm (Figure 9). Such performances are in phase advance with the roadmap of Figure 3.

Figure 9 :

 9 Figure 9: 3 versions of 14-nm technology by Intel, showing increased current drive with lower leakage current [Fischer2017].

Figure 10 :

 10 Figure 10: The equivalent width of a multi-fin FET

Figure 11 :

 11 Figure 11: The multi-fin FET with an equivalent width of 1 µm is almost twice more compact than the MosFET traditional design

Figure 14 :

 14 Figure 14: Changing the option of the device from low-leakage to high-speed using the option layer. Double-click in one corner of the option layer to change its properties

Figure 15 :

 15 Figure 15: Id/Vg characteristics of the low leakage and high-speed p-FinFET devices

Figure 17 :

 17 Figure 17: Ioff/Ion calculated on 100 samples of n-FinFET with random distribution of VT, U0, and LINT with a Gaussian distribution around the nominal value

Figure 18 :

 18 Figure 18: The layout generation includes the dummy gate option at any side (or all sides) of the active device to reduce variability and increase manufacturability

Figure 20 :

 20 Figure 20: The 8 metal layers proposed in 14-nm technology

Figure 21 :

 21 Figure 21: C and R per µm for metal 2 with 52-nm pitch, (Intel's 14-nm technology [Fischer2015])

Figure 24 :Figure 25 :

 2425 Figure 24: Single, double and quadruple patterning as a function of interconnect pitch [Brain2017]

Figure 27 :

 27 Figure 27: Modify VDD to extract the minimum operating voltage of the ring oscillator.

Figure 28 :

 28 Figure 28: Monte-carlo simulation with 100 random sets of technology parameters

[

  Song2015]. The layout obeys the basic design rules. Most contacts are shared with neighboring cells: the VSS, VDD contacts, the Select and Data lines. It is usual to find more aggressive layout design rules in RAM cell designs, in order to further decrease the cell area.

Figure 29 :

 29 Figure 29: Reduction of the 6T-SRAM memory from 22-nm to 14-nm process of Intel[Natharajan2014, Fischer2015]

Table 1 :

 1 Most significant technology nodes over the past 15 years

	Technology node	Year of	Key Innovations	Application note
		introduction
	180nm	2000	Cu interconnect, MOS options, 6 metal
			layers
	130nm	2002	Low-k dielectric, 8 metal layers
	90nm	2003	SOI substrate	[Sicard2005]
	65nm	2004	Strain silicon	[Sicard2006]
	45nm	2008	2nd generation strain, 10 metal layers	[Sicard2008]
	32/28nm	2010	High-K metal gate	[Sicard2010]
	20nm	2013	Replacement metal gate, Double	[Sicard2014]
			patterning, 12 metal layers
	14nm	2015	FinFET	This application note

Table 2 :

 2

4 major players in the 14-nm chip manufacturing Page 3/25 etienne.sicard@insa-toulouse.fr 17/06/17

14-nm Technology variant Pros Cons Target application Typical Ion/Ioff General purpose

		Medium speed	Medium	Laptops	1.3 mA/µm
			consumption		10 nA/µm
	High performance Fast speed	High	Servers	1.7 mA/µm
			consumption		100nA/µm
	Low power	Low speed	Low	Smartphones	1.0 mA/µm
			consumption		1 nA/µm
	Table 3: technology variants within the same node

Table 5 :

 5

	High Voltage (HV) MOS in
	Microwind

Key features of the I/O devices proposed in the 14-nm technology and corresponding values in Microwind

Page 9/25 etienne.sicard@insa-toulouse.fr 17/06/17

  Max situation, VT is low, mobility U0 is high and the channel is short (LINT<0). The supply is maximum and the temperature is minimum. The ring oscillation is around 250 GHz.

	Parameter	Parameter	Symbol	Unit	Min	Typ	Max
	class		(BSIM4)		(14-nm)	(14-nm)	(14-nm)
	Process	Threshold	VT	V	0.36	0.31	0.27
		Voltage
		Mobility	U0	m2/V.s	0.030	0.035	0.040
	Voltage	Supply	VDD	V	0.68	0.8	0.92
	Temperature	Temperature	TEMP	°C	125	25	-50
	Oscillating				100	196	250
	frequency

•

In

Table 7 :

 7 Variation of process parameters: the oscillating frequency ranges from 100 to 250 GHz

Acknowledgements

The adaptation of Microwind to 14-nm FinFET technology and the development of an e-learning course on nano-CMOS cell design have been made possible thanks to the financial support of the ERASMUS+ program Knowledge Alliance "Micro-Electronics Cloud Alliance" 562206-EPP-1-2015-1-BG-EPPKA2-KA.


Michele Catti

Mohammad Reza Ghaani

Ilya Pinus

Overpressure Role in Isothermal Kinetics of H2 Desorption-Absorption: the 2LiBH4-Mg2FeH6 System

Keywords: hydrogen storage, solid-gas reactions, thermodynamic driving force, dehydrogenation, Arrhenius law

come

INTRODUCTION

Combined dehydrogenation of assemblages of hydrides was suggested some years ago [START_REF] Vajo | Hydrogen Storage in Destabilized Chemical Systems[END_REF] as a way of reducing the temperature of H2 yield, with respect to those of separate compounds. This would solve one of the most serious operational drawbacks of materials for hydrogen storage, i.e. the significant amount of energy to be consumed at the stage of H2 retrieval. [START_REF] David | Effective Hydrogen Storage: a Strategic Chemistry Challenge[END_REF] The method was claimed to work when some of the products of the dehydrogenation reaction have large (negative) formation enthalpies, so that the (positive) reaction enthalpy decreases substantially. Several studies have shown that this is indeed the case for the LiBH4-MgH2 assemblage, because of the great stability of the MgB2 product of the reaction; [START_REF] Vajo | Reversible Storage of Hydrogen in Destabilized LiBH4[END_REF][START_REF] Bösenberg | Hydrogen Sorption Properties of MgH2-LiBH4 Composites[END_REF][START_REF] Pinkerton | Phase Boundaries and Reversibility of LiBH4/MgH2 Hydrogen Storage Material[END_REF][START_REF] Zhang | Hydrogen De/Resorption Properties of the LiBH4-MgH2-Al System[END_REF] further, first-principles calculations indicate that quite a number of other systems should share the same property. [START_REF] Siegel | Thermodynamic Guidelines for the Prediction of Hydrogen Storage Reactions and their Application to Destabilized Hydride Mixtures[END_REF] Along this line of research, we recently investigated the dehydrogenation reactions of the 2LiBH4-Mg2FeH6 assemblage from the thermodynamic point of view. [START_REF] Ghaani | Thermodynamics of Dehydrogenation of the 2LiBH4-Mg2FeH6 Composite[END_REF] This system is quite interesting, as it couples the very high gravimetric H2 density of lithium borohydride (13.9%) [START_REF] Züttel | Hydrogen Storage Properties of LiBH4[END_REF] to the very high volumetric hydrogen density of Mg2FeH6 (150 kg m -3 ). [START_REF] Bogdanovic | Thermodynamics and Dynamics of the Mg-Fe-H System and its Potential for Thermochemical Thermal Energy Storage[END_REF] Other studies on similar assemblages of these compounds have been recently reported. [START_REF] Langmi | Mg2FeH6-LiBH4 and Mg2FeH6-LiNH2 Composite Materials for Hydrogen Storage[END_REF][START_REF] Deng | L Hydrogen Storage Performance of 5LiBH4+Mg2FeH6 Composite System[END_REF] The main finding of our previous work [START_REF] Ghaani | Thermodynamics of Dehydrogenation of the 2LiBH4-Mg2FeH6 Composite[END_REF] is that dehydrogenation occurs in three subsequent steps, either on decreasing pressure isothermally, or increasing temperature isobarically:

(A) 2LiBH4 + 2Mg2FeH6  2LiH +4MgH2 + 2FeB + 5H2, (B) MgH2  Mg + H2, (C) 2LiBH4 + Mg  2LiH + MgB2 + 3H2.

Step A is irreversible, at least for p not exceeding 100 bar, whereas both B and C reactions are reversible. The van't Hoff line of reaction A is located at higher pressure and lower temperature with respect to those of both pure hydrides, proving that they are indeed destabilized by the joint decomposition reaction. However, this occurs by an increase of the reaction entropy rather than by decrease of reaction enthalpy, as found for the LiBH4-MgH2 system.

The first, yet minor, aim of the present investigation is to complete the thermodynamic study of this system by determining the van't Hoff plots of the B and C hydrogenation reactions. The major object is, on the other hand, to characterize the kinetic aspects of all processes of H2 exchange occurring with the 2LiBH4-Mg2FeH6 assemblage. For this purpose, the isothermal method [START_REF] Lozano | Empirical Kinetic Model of Sodium Alanate Reacting System (I). Hydrogen Absorption[END_REF][START_REF] Lozano | Empirical Kinetic Model of Sodium Alanate Reacting System (II). Hydrogen Desorption[END_REF] has been chosen rather than the more usual temperature-ramp method with constant heating rate. [START_REF] Sabitu | Kinetics and Modeling Study of Magnesium Hydride with Various Additives at Constant Pressure Thermodynamic Driving Forces[END_REF][START_REF] Evard | Kinetics of Hydrogen Evolution from MgH2: Experimental Studies, Mechanism and Modelling[END_REF] In facts the selected approach, though requiring much longer measurements, gives fully time-resolved results which allow a rigorous and straightforward kinetic interpretation; the dynamic method, instead, is known to suffer some ambiguities in the separation of temperature and time dependences of the reaction progress (cf. the case of Kissinger's method [START_REF] Blaine | Homer Kissinger and the Kissinger Equation[END_REF] ).

A peculiar objective of this work is also to investigate the role and kinetic importance of an additional physical parameter, the overpressure: this is defined as p/p = (p-pe)/pe, where pe(T) is the equilibrium H2 pressure calculated according to the van't Hoff equation. Overpressure is usually negative (underpressure) for dehydrogenation and positive for hydrogenation reactions. Further, it has a fundamental kinetic significance, as it is the source of the thermodynamic driving force G for chemical reactions involving production or consumption of a gaseous phase. [START_REF] Bradley | The Energetics and Statistical Mechanics of the Kinetics of Solid-Solid Reactions[END_REF][START_REF] Pokol | The Thermodynamic Driving Force in the Kinetic Evaluation of Thermoanalytical Curves[END_REF] We thus here want to explore the empirical dependence of reaction rate constants on both T and p/p, attempting to introduce the kinetic contribution of the driving force into the usual Arrhenius formalism.

EXPERIMENTAL

Mg2FeH6 was synthesized by reactive ball milling of MgH2 and Fe in stoichiometric ratio, and subsequent hydrogenation in a Sievert-type equipment. [START_REF] Zhang | The Synthesis and Hydrogen Storage Properties of Pure Nanostructured Mg2FeH6[END_REF][START_REF] Polanski | Dynamic Synthesis of Ternary Mg2FeH6[END_REF] A Retsch planetary mill with stainless steel vial and balls was used, with the same conditions as in previous work (Ar atmosphere, 30 h at 400 rounds min -1 , ball-to-powder weight ratio = 30). Then the ball milled sample was loaded in an automatic Sievert-type apparatus (Advanced Materials Corporation), brought to p(H2) =100 bar and then heated at 400 °C for 9 days. The final sample obtained proved to contain pure Mg2FeH6 and a small quantity of unreacted Fe, with no traces of MgH2, according to X-ray powder diffractometry results (Bruker D8 Advance equipment, CuK radiation). Samples of the 2LiBH4-Mg2FeH6 composite were prepared by grinding synthesized Mg2FeH6 powder with commercial LiBH4 (Sigma-Aldrich) in a glove box filled with recirculated argon atmosphere. All subsequent handling of such samples took place in the glove box.

All thermodynamic and kinetic measurements of the hydrogenation/dehydrogenation reactions were done by the Sievert-type equipment. The PCI (Pressure-Composition-Isotherm) experiments on hydrogenation were carried out with the same conditions reported previously. [START_REF] Ghaani | Thermodynamics of Dehydrogenation of the 2LiBH4-Mg2FeH6 Composite[END_REF] In kinetic isothermal-isobaric experiments of dehydrogenation, a 0.2 g amount of the composite was loaded into the 5 cm 3 sample holder, and after evacuation hydrogen gas of high purity (99.9995%) was introduced at room temperature (RT) and high pressure (100 bar). The sample was heated to the set temperature, then pressure was decreased isothermally to the set value, and the kinetic measurement began. The amount of evolved H2 gas vs. time was determined by recording pressure increments at short intervals of 1 min; these were immediately compensated by the system so as to keep p(H2) constant at the set value throughout the whole reaction. At the end, p was anyway slightly higher than its initial value by about 2-3%, with larger relative increase at lower pressures.

In the case of hydrogenation reactions, the sample was brought to the required temperature just after evacuation, and then p(H2) was increased to the wanted value isothermally, before starting the kinetic measurements. Each sample underwent the following cycles of measurements: at first, the irreversible A dehydrogenation; then three-four cycles of C dehydrogenation -C rehydrogenations steps. Tests on the reproducibility of kinetic results with respect to cycling were quite satisfactory.

RESULTS AND DISCUSSION

Van't Hoff plot for hydrogenation of 2LiH + MgB2.

In Figure 1, the van't Hoff plots ln(pe/bar) = rS/R -rH/RT of the A, B and C dehydrogenation reactions obtained from PCI measurements in the previous work [START_REF] Ghaani | Thermodynamics of Dehydrogenation of the 2LiBH4-Mg2FeH6 Composite[END_REF] are shown as full lines. In the same paper some preliminary data on C re-hydrogenation were reported, showing that that reaction is reversible at variance with the irreversibility of reaction A. In the present work more PCI results were obtained, so as to build up van't Hoff plots also for C and B hydrogenation reactions, which are shown in Figure 1 as dashed lines. The B line is nearly coincident with the corresponding one for dehydrogenation, confirming the well known good reversibility of B reaction. On the other hand, a strong hysteresis increasing with decreasing temperature is observed in the C case. Further, a peculiar feature appears immediately: the C hydrogenation line crosses the B one at about 370 °C, so that above that temperature the reaction occurs as 2LiH + MgB2 + 3H2  2LiBH4 + Mg, whereas below 370 °C the slightly different path 2LiH + MgB2 + 4H2  2LiBH4 + MgH2 is observed. In the latter case, the B process Mg + H2  MgH2 occurring at lower pressure consumes the Mg excess coming from Mg2FeH6 decomposition. The two variants of C hydrogenation reaction share approximately the same van't Hoff plot with rH = -27(2) kJ mol(H2) -1 and rS = -64(2) J K -1 mol(H2) -1 ; cf. the values for C dehydrogenation 8 rH = 48(2) kJ mol(H2) -1 and rS = 87(2) J K -1 mol(H2) -1 . The much smaller slope of the hydrogenation line makes the hysteresis gap to widen significantly at lower temperatures, consistently with what expected as reversibility is favoured by higher T values.

Isothermal kinetic curves.

Kinetic measurements in isothermal-isobaric mode were performed on the A and C dehydrogenation reactions at several T and p values, which were selected taking into account the corresponding thermodynamic van't Hoff plots. Some preliminary results were obtained also for C hydrogenation. For a given reaction, the equilibrium H2 pressure pe(T) is calculated on the basis of the reaction enthalpies and entropies reported in Table 1 of Ref. 8 (and given above in the C hydrogenation case). For each temperature, measurements were repeated at different values of overpressure p/p = (p-pe)/pe. Although this is usually negative for dehydrogenation and positive for hydrogenation, non zero reaction rates were observed also for small p/p values with the 'wrong' sign, as will be discussed below. Results of kinetic measurements are reported as curves of the normalized degree of reaction advancement  (vs. a total of 3.2 and 2.0 wt%(H2) for the A and C cases, respectively) against time t. As examples, the curves obtained for dehydrogenation A at 358 °C and p/p = -0.233, -0.067, 0.088 are shown in All kinetic curves for the C reaction have a clear sigmoidal shape, so as to immediately suggest use of the Avrami (or Johnson-Mehl-Avrami-Kolmogorov (JMAK)) equation [START_REF] Avrami | Kinetics of Phase Change. I. General Theory[END_REF][START_REF] Avrami | Kinetics of Phase Change. II. Transformation-Time Relations for Random Distribution of Nuclei[END_REF][START_REF] Avrami | Granulation, phase change and microstructure. Kinetics of phase change[END_REF][START_REF] Jena | Phase Transformations in Materials[END_REF][START_REF] Cahn | Transformation Kinetics during Continuous Cooling[END_REF][START_REF] Galway | Kinetic Background to Thermal Analysis and Calorimetry in Handbook of Thermal Analysis and Calorimetry[END_REF]

(t) = 1 -exp[- (kt) n ]
for fitting data and derive the rate constant k. In the A case, where the reaction kinetics is clearly much slower (compare Figures 2 and3), the shape of curves rather resembles that of firstorder kinetics. However, the JMAK formula is able to include also that as a particular case, so that the fitting was performed by the same equation for all A and C data. In each case the calculation was carried out both on relaxing the n exponent, and on fixing it at the closest integer value. The fitted rate constant k did not change significantly, proving to be rather independent of minor exponent variations. For the A reaction, the relaxed n exponent ranged between 1 and 2, whereas in the C case values between 2.5 and 3.5 were obtained. The quality of the fitting was always very good, with an average R 2 index value of 99.5% (cf. Figures 2 and3). However, we also tried different kinetic models, like the 'contracting volume' or 'moving boundary' equation, [START_REF] Galway | Kinetic Background to Thermal Analysis and Calorimetry in Handbook of Thermal Analysis and Calorimetry[END_REF] [START_REF] Vajo | Reversible Storage of Hydrogen in Destabilized LiBH4[END_REF] . In all cases the fit was definitely much worse than with the JMAK formula. Taking into account the physical basis underlying the Avrami model, and the fitted n exponent values, we can conclude that the C reaction kinetics is controlled by the slow step of growth of nuclei with n dimensions in cases with the lower n exponents, with a contribution of the nucleation step when n > 3. For the slower A reaction, a pure growth mechanism with low grain dimensionality seems to be appropriate.

(t) = 1-(1- kt) 3 , and the diffusion-controlled one, 27 (t) = 1-[1-(kt) 1/2 ]
A preliminary kinetic study was also carried out on the C hydrogenation reaction, by performing a limited number of measurements. In [START_REF] Lozano | Empirical Kinetic Model of Sodium Alanate Reacting System (I). Hydrogen Absorption[END_REF] we assume that this functional dependence can be factorized into the product

k = k0(T)k1(p/p), ( 1
)
where k0 is defined as the rate constant at vanishing overpressure (i.e. for p = pe), so that the condition k1(p/p=0)=1 must be fulfilled. More generally, the second factor k1 should be written as k1(T,p/p), in order to include a possible coupling of its thermal and pressure dependences.

At constant T, we tried to fit the k(p/p) empirical function at first by the power law lnk = aln(p/p+1) + b, obtaining satisfactory results but with quite large values of the -a exponent (between 5 and 6). This would indicate a stronger kinetic effect of overpressure than in the study of sodium alanate, [START_REF] Lozano | Empirical Kinetic Model of Sodium Alanate Reacting System (I). Hydrogen Absorption[END_REF][START_REF] Lozano | Empirical Kinetic Model of Sodium Alanate Reacting System (II). Hydrogen Desorption[END_REF] where a linear or parabolic dependence of the rate constant on overpressure was observed. Then an exponential law was tested, according to lnk = a(p/p) + b; (2) this linear relationship between lnk and overpressure proved to be always well obeyed, and thus the exponential empirical law was adopted for treatment of all data. Indeed this formula is easily integrated into a kinetic theoretical frame, as will be discussed below, at variance with the power law with large variable exponent. An example of two experimental straight lines of lnk vs. p/p for the C dehydrogenation is shown in Figure 5. The fitted a and b linear coefficients for all measured data of the A and C reactions are reported in Table 1.

__________________________________________

The zero-order coefficient in (2) can be written as b = lnk0, according to Eqn. ( 1) and the definition of k0. Eqn. (2) can then be restated as:

k = k0 (T)exp[a(p/p)], (3)
so that k1= exp[a(p/p)] is obtained with the a coefficient including a possible thermal dependence.

The Arrhenius-like dependence on temperature can be reasonably assumed for k0(T):

k0 = f exp(-∆ /RT) = f exp(∆ /R)exp(-/RT) = A0exp(-/RT), ( 4
)
where f is an effective vibrational frequency (or a dimensional coefficient time 1, a decreasing trend of a with increasing temperature appears clearly for both reactions; this can be simply modelled according to a = a0 + a1/T, with a0 < 0 and a1 > 0. This means that the higher the temperature, the more effective is overpressure to increase the reaction rate. On substitution into the k expression, one obtains:

k = k0exp[(a0 + a1/T)(p/p)] = f exp[∆ /R+a0(p/p)]exp[-( -Ra1(p/p))/RT] = Aexp(-Ea/RT). (5)
Eqn ( 5) can be interpreted by stating that (negative) overpressure has a twofold effect: it increases both the activation entropy and the activation energy. The second effect is due to the thermal dependence of the a coefficient with positive a1 parameter, and it reduces the increase of reaction rate k due to the first one:

Sa = ∆ + Ra0(p/p); Ea = -Ra1(p/p). ( 6
)
The thermal dependence of the rate constant was analyzed by plotting b = lnk0 against 1/T from data of Table 1 for each of the A and C dehydrogenation reactions. According to the Arrhenius relation ( 4): lnk0 = -Ea/RT + lnA0, so that by a linear fit of lnk0 vs. 1/T the activation energy and the pre-exponential factor A0 at p/p=0 can be obtained. The procedure was then repeated for nonvanishing overpressure values, by plotting lnk calculated by eqn. (2), instead of lnk0, vs. 1/T. In this way the Arrhenius parameters were obtained as functions of p/p, according to the dependence appearing in eqn. (5). The results are reported in Table 2 for each reaction and for different overpressure values.

-0.10 130

-0.20 139(

-0.30 149( The coefficients of the a = a0 + a1/T expression turn out to be for A: a0 = -34, a1 = 18 x 10 3 K; for C: a0 = -34, a1 = 19 x 10 3 K. Such coefficients could have been obtained also by direct fitting of the a values reported in Table 1 against 1/T, where the scatter of data shows that they are affected by a significant uncertainty. However, the overall trend is well defined, with not only the activation energies and entropies at p/p=0, but also their overpressure coefficients very similar for both dehydrogenation reactions. This suggests that the temperature/overpressure effects on the rate constant are controlled by physical features of the solid phases present (surface state and extension, defect distribution, interface energy, etc.), which are similar in the A and C cases, rather than by their chemical specificities.

For results of C hydrogenation, the rate constant k vs. p/p was again fitted by eqn. (2). The a and b coefficients obtained are reported in Table 1 for only two T values, so that the Arrhenius-like analysis of results could not be done because of insufficient data. However, one can notice that the a values are over 50% bigger than the corresponding ones for dehydrogenation, indicating a significantly larger effect of overpressure in accelerating hydrogenation (p/p>0) with respect to dehydrogenation (p/p<0) for the C reaction. Of course, the sign of a changes with reversion of the reaction direction. we obtain:

k = k0exp(aG/RT) = f exp[-(∆ aG)/RT]. (7)
This relationship connects the action of the thermodynamic driving force to the Arrhenius formalism, based on the activated state concept. It resembles somehow the Tafel equation of electrochemical kinetics, [START_REF] Bard | Electrochemical Methods. Fundamentals and Applications[END_REF] where the driving force G is proportional to overvoltage rather than to overpressure. However, there is a fundamental difference, because in Tafel equation a is replaced by the transfer coefficient 1  0; here, on the other hand, a is an empirical parameter with absolute value larger than 1. This means that, in the present instance, the overpressure driving force has a stronger action in increasing the rate constant: in addition to the maximum 'transfer' effect (=1), there is a further direct reduction of the activation barrier ∆ by a (a-1)G amount.

In cases where the dehydrogenation reaction is irreversible (A), or where it is reversible but with a large hysteresis (C), the Tafel (or Butler-Volmer) approach [START_REF] Bard | Electrochemical Methods. Fundamentals and Applications[END_REF] of electrochemical kinetics should be modified. In fact, it is not possible any more to use the same kinetic diagram of G free energy along the reaction coordinate in both directions of the transformation. One is forced either to consider only one of the two directions (A dehydrogenation), or to consider two different G diagrams specific for each direction (C dehydrogenation and hydrogenation). In particular, in the latter case two 'equilibrium' pressures are defined at each temperature: pe1(T) for dehydrogenation and pe2(T)

for hydrogenation, with pe1(T) < pe2(T): see the two experimental van't Hoff lines in Figure 1. In this instance 'equilibrium' means simply that both phase assemblages (cf. 2LiH + MgB2 + 3H2 and 2LiBH4 + Mg) may coexist together at either pe1(T) or pe2(T), but the direction of transformation is unique and different in each case. Therefore, using pe1 and pe2 as reference pressures for defining overpressures (as we did to analyze kinetic data in Table 1) may not be the only possible choice, particularly in the region pe1 < p < pe2(T), where overpressure ranges with 'wrong' signs (positive for dehydrogenation, negative for hydrogenation) are observed. An empirical alternative to remove this feature could be to use the average (pe1 + pe2)/2 as single reference pressure for both reactions.

Further investigations on that are planned in our future work.

CONCLUSIONS

The kinetic properties of H2 desorption-sorption reactions of the 2LiBH4-Mg2FeH6 assemblage were determined by isothermal-isobaric experiments, with a particular focus on the role of overpressure and its coupling with temperature. By extending measurements to conditions close to equilibrium, where reactions are very slow, a convenient range of overpressures could be covered. This allowed us to explore the kinetic effect of p/p in a proper way, and to interpreted the data on the basis of an exponential dependence of the reaction rate constants on overpressure.

Such a result fits naturally with the conventional Arrhenius formalism, suggesting simple linear relations of activation energy and entropy with overpressure. As p/p is straightforwardly connected to the thermodynamic driving force G, the empirical results found can be accounted for by a consistent theoretical frame related to that used in electrochemical kinetics. This analysis can have a broader interest for application to kinetic properties of a large class of solid-gas reactions, provided that their rates are compatible with measurable overpressure effects. However, irreversibility and/or hysteresis conditions specific of these processes require to extend and generalize the approach here proposed, and further research is planned in that direction.

Figure 1 .

 1 Figure 1. Van't Hoff plots of the A (stars), B (squares), and C (triangles) dehydrogenation

Figure 2 ,

 2 Figure 2, and those for C at 375 °C and p/p = -0.255, -0.149, -0.021, 0.064 are shown in Figure 3.

Figure 2 .

 2 Figure 2. Isothermal kinetic plots for the A reaction (2Mg2FeH6 + 2LiBH4  2LiH +4MgH2 +

Figure 3 .

 3 Figure 3. Isothermal kinetic plots for the C dehydrogenation (2LiBH4 + Mg  2LiH + MgB2 +

Figure 4

 4 examples of isotherms for a single temperature and different overpressure values (0.105, 0.133, 0.319) are shown. Such curves resemble more those of dehydrogenation A than C, as they lack the sigmoidal shape of the latter. The Avrami equation proved yet to be quite adequate to fit data, with a n exponent slightly smaller than 1.

Figure 4 . 3 . 3 .

 433 Figure 4. Isothermal kinetic plots for the C hydrogenation (2LiH + MgB2 + 3H2  2LiBH4 + Mg)

Figure 5 .

 5 Figure 5. Logarithm of the rate constant k (min -1 ) for the C dehydrogenation plotted against

_____________________________________________ In Figures 6 and 7 the

 7 Arrhenius plots are shown in the A and C cases, respectively, for p/p= 0 and -0.30. The corresponding linear relationships (6) are as follows: Ea = -151(p/p) + 118 kJ mol -1 , ln(A/min -1 ) = -34(p/p) + 16, for reaction A; Ea = -160(p/p) + 110 kJ mol -1 , ln(A/min -1 ) = -34(p/p) + 15, for reaction C.

Figure 6 .

 6 Figure 6. Arrhenius plots for the A dehydrogenation reaction at two different values of the

Figure 7 .

 7 Figure 7. Arrhenius plots for the C dehydrogenation reaction at two different values of the

3. 4 .

 4 Thermodynamic driving force and irreversibility. More insight into the fundamental kinetic meaning of the previous analysis can be obtained by relating overpressure p/p to the thermodynamic driving force G. According to basic thermodynamics, G = RT ln(p/p+1), with positive and negative signs for dehydrogenation and hydrogenation directions, respectively; for p/p smaller enough than 1, G  RT(p/p), so that by substitution of p/p in eqns. (3) and(4)

Table 1 .

 1 Coefficients

	T (°C)	a	b
	A dehydrogenation
	324	-3.3	-7.78
	343	-4.2	-6.92
	358	-5.8	-6.75
	363	-5.3	-6.25
	376	-5.4	-5.80
	C dehydrogenation

of the lnk = a(p/p) + b empirical relation between reaction rate constant k (min -1 ) and overpressure p/p, fitted to isothermal kinetic measurement data.

Table 2 .

 2 Arrhenius parameters (activation energy and logarithm of the pre-exponential factor) from kinetic measurements on dehydrogenation reactions A and C at different overpressures p/p. The e.s.d.'s are given in parentheses.

	p/p	Ea (kJ mol -1 ) ln(A/min -1 )
	A dehydrogenation
	0	118(13)	16(2)
	-0.10	132(10)	19(2)
	-0.20	148(7)	23(1)
	-0.30	163(6)	26

AUTHOR INFORMATION

Corresponding Author * E-mail: catti@mater.unimib.it; tel. +390264485139