Alexandre Mettey

Dr Anne-Marie Bouvier
email: anne-marie.bouvier@u-bourgogne.fr

Valerie Jooste
email: vjooste@u-bourgogne.fr

Yves Boucher
email: yves.boucher@univ-paris-diderot.fr

Patrick Quercia
email: doc.quercia@gmail.com

Mettey Alexandre1

Bouvier Anne-Marie1

Jooste Valérie1

Boucher Yves2

Are changes in the stomatognatic system able to modify the eye balance in dyslexia?

Keywords: Dental occlusion, oral sensory innervation, vertical heterophoria, dyslexia, postural control, eye balance

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction.

Developmental dyslexia is a specific learning difficulty that primarily affects the skills involved in accurate and fluent reading and spelling. It is generally considered to be the result of specific impairments relative to phonological representation. It is characterized by difficulties with processing speed, working memory and rapid naming, and is not influenced by exogenous factors such as lack of intelligence or educational access.

Dyslexia affects around 10% of the population and is categorized into three distinct clinical types 1 : i) Surface: difficulty in recognizing the visual form of written words, especially if they are irregular, ii) Phonological: a specific inability to handle speech sounds and the grapheme-phoneme conversion, iii) Mixed: the most frequent type, combining surface and phonological anomalies.

Previous studies have emphasized that children with dyslexia may have multi-deficit disorders including deficits in the auditory, visual and motor system 2 . Among dyslexics, abnormal motor skills can be expressed by anomalies in body tone and posture [START_REF] Kapoula | Postural control in dyslexic and non-dyslexic children[END_REF][START_REF] Pozzo | Static postural control in children with developmental dyslexia[END_REF] . Other peculiarities can affect the fine motor skills, especially the ocular and oral muscles [START_REF] Gouleme | Vertical disconjugacy during reading in dyslexic and non-dyslexic children[END_REF][START_REF] Montgomery | Do dyslexics have difficulty accessing articulatory information[END_REF] .

Reading is a complex oculomotor and cognitive activity whose exact mechanisms are still poorly understood. Eye movements must be very precise to allow the visual capture of written words by fixing the center of both retinas (fovea) at a particular location within the word designated as the center of gravity of the word [START_REF] Peterson | Developmental dyslexia[END_REF] . Concerning muscular function, this position is coded from the efferent oculomotor control information and from the afferent proprioceptive information originating in the eye muscles, although the relative importance of each of these two elements remains unknown [START_REF] Ventre-Dominey | Extraocular proprioception is required for spatial localization in man[END_REF] . Ocular proprioception, which depends on the trigeminal nerve, is primarily used for error correction and to modulate visual attention [START_REF] Balslev | Eye proprioception used for visual localization only if in conflict with the oculomotor plan[END_REF] . Abnormal ocular muscle function could be responsible of binocular dyscoordination during reading [START_REF] Seassau | Binocular saccade coordination in reading and visual search: a developmental study in typical reader and dyslexic children[END_REF] . In dyslexia, coordination disorders affect horizontal but also oblique and vertical eye movements [START_REF] Seassau | Binocular saccade coordination in reading and visual search: a developmental study in typical reader and dyslexic children[END_REF] .

Fine oral articulatory movements are crucial for the appropriate production of sounds when reading aloud. Beyond their local motor action, they also have an important role in the perception of sound units [START_REF] D'ausilio | The role of the motor system in discriminating normal and degraded speech sounds[END_REF] . That is why, according to the motor theory of speech perception proposed by Liberman, abnormal oral muscle function could play a role in phonological dysfunction which is one of the main characteristic of dyslexia [START_REF] Liberman | The motor theory of speech perception revised[END_REF] .

This idea is at the origin of the motor-articulatory feedback hypothesis of developmental dyslexia which suggests that phonological awareness may be linked to an abnormal production of intended oral articulatory gestures [START_REF] Heilman | Developmental dyslexia: a motorarticulatory feedback hypothesis[END_REF] . We thus attempted to clarify the link between eye muscle function and oral information, using two indicators: heterophoria, taken as a measure of coupling of the eyes during a visual task and dental information as a trigeminal mechanical input.

The purpose of this exploratory study was to compare a group of dyslexic readers (DR) to a group of normal readers (NR) in order to answer the following questions:

1. Is it possible to modify visual perception by modifying oral sensory information? 2. Do these changes vary for DR and NR? 3. Is there a difference in response when the stimuli is sensory or mechanical? 4. Is there a relationship between the lability of the visual axes and changes in oral, spinal or podal positions? 5. Could the mouth be a link between the ocular and phonological signs of dyslexia? Subjects and Methods.

Participants.

Children were recruited during pediatric ophthalmological consultation. Exclusion criteria were: a history of neurological, psychiatric or genetic disease, delayed or abnormal psychomotor development, IQ below 85, orthodontic treatment in progress, children under psychotropic treatment (especially drugs from the phenylethylamine group or anti-epileptics). After consent was obtained from the children and their parents, they were tested within the guidelines of the declaration of Helsinki. Children with a visual acuity of 20/20 in both eyes with no refractive error and no organic abnormalities of the anterior or posterior segments were retained. Children with the following visual features were excluded: strabismus with or without surgery, orthoptic rehabilitation in progress, re-educated amblyopia, stereopsis> 100 sec. The inclusion criteria for the dyslexic children were a documented diagnosis of dyslexia and a score of at least 24 months of reading delay on the WWIT/TIME 3 test (Written Word Identification Test) [START_REF] Ecalle | Evaluation in reading: preliminary study for the development of a new word recognition test[END_REF] . This test identifies the decoding skills and the comprehension and spelling of 40 words for children aged 7 to 15. In the group of dyslexic children only, the use of the Odedys Battery helped classify the type of dyslexia 14 .

Children were recruited from consecutive consultations. A total of 35 children fulfilled the inclusion criteria: 21 DR children (11 males and 10 females) participated in the study and were compared with a group of 14 NR children (9 males and 5 females). The average delay in reading months was 11 ± 9 months in the DR group. Odedys tests found mixed dyslexia for all the dyslexic children.

Experimental Procedure.

To sensitize the action of oral stimulation on the ocular muscles, the parallelism of the visual axes is weakened by manipulating the fusion of the two retinal images. The coordinated position of the two eyes is indeed linked to a coupling between the control of the ocular motricity (efference copy and muscle proprioception) and the retinal fusion.

When the latter is impaired, the eye axes tend to deviate slightly. This deviation is called heterophoria. The parallelism of the ocular axes is almost perfect in the vertical plane (0.12 ° of deviation) and the natural compensation possibilities are very low. This is why we studied vertical heterophoria (HV) while the oral information changed, either by sensorimotor variations in the tongue or lips, or by mechanical variations of the dental occlusion. As the eyes and the mouth are established sensors influencing the postural regulation, we also investigated the influence of four different bodily positions on lability [START_REF] Khan | Neuromuscular dentistry: Occlusal diseases and posture[END_REF][START_REF] Guerraz | Ocular versus extraocular control of posture and equilibrium[END_REF] .

Vertical Heterophoria Measurement

Changes in vertical heterophoria were observed using a Maddox Rod Test which has been used for more than a century in ophthalmology [START_REF] Guerraz | Ocular versus extraocular control of posture and equilibrium[END_REF] . It is performed with a red Maddox rod, consisting of 17 bi-convex cylinders that have enough convergence to transform the image of a point of white light into a red line perpendicular to the cylinder axis (Movie 1). When the cylinders are vertical, the patient sees two dissociated images from the same light source: a red horizontal line through the Maddox rod and a colorless spot of light in direct vision. The light is placed four meters from the subject (the Frankfurt plane being horizontal) at eye level. It is important that the light be very small (diameter = 1-2 mm) so that the red line caused by the Maddox rod is as thin as possible.

The test is performed for each of the two eyes starting with either the right or left and leaving a time of one second between each eye so as to provide a moment of binocular fusion. The child must reply, without changing the position of the tongue, by directing the thumb horizontally, up or down indicating that the red line has been seen respectively in the exact center, above or below the light (Figure 1). The test procedure is very easy for the clinician and the child. Clinically, it is an inexpensive and effective way to detect very small variations in the vertical stability of both eyes when retinal fusion is changed.

Its effectiveness is comparable to other, more invasive methods [START_REF] Casillas | Comparison of subjective heterophoria testing with a phoropter and trial frame[END_REF] . The Maddox rod test is a conventional tool to dissociate binocular vision by modifying retinal fusion. Indeed this test forces the brain to perceive two different images even though the visual input has the same temporal and spatial characteristics (one single light spot located in one single place). In this situation, both eyes tend to dissociate and lose their parallelism with appearance of a heterophoria. Depending on the position of the red screen, it is possible to break the parallelism of the visual axes in the horizontal or vertical direction or even in torsion in the frontal plane. We chose to study vertical deviation because ocular motor compensation is very weak in this plane.

Oral modifications

The test was performed using five well-defined oral conditions (Movie 1).

-Three conditions that do not affect dental occlusion:

-the tip of the tongue firmly touching the central retro-incisor papillae -the lips tightly closed -the tip of the tongue planted against the lower incisors -Two conditions that modify dental occlusion:

-dental rolls between the molars -use of a dental splint.

Postural modifications

The five oral modifications described were done in four different postures:

-child sitting in a spontaneous and natural position without plantar support -sitting straight up without plantar support -standing in a natural position to add the information from the plantar sole with the mouth also in a natural position -standing with a foam insole between the foot and the ground to decrease exteroceptive plantar information At the end of the test, in each postural condition, an index of lability was created. It matches the number of times, as a result of a modification, that the VH changed when compared with the previous situation (see example Table 1). For each postural condition the index is thus between 0 and 5:

-0 corresponds to no modification of the position of the red line, -5 corresponds to a modification of position of the red line in front of the right eye and / or the left eye for each of the oral stimulations, the result being compared to the position just before. Whether the line is above, below, or in the center of the light is not taken into account.

Statistical Analysis

All studied parameters were collected for the 35 children. Univariate analyses that compared the characteristics of DR and NR children were done with i) Chi2 test for qualitative variables, ii) Student's T test for quantitative variables after validation of homoscedasticity using Bartlett's test. The normality of distribution was assessed with Shapiro-Wilk test. The Spearman correlation coefficient was used to assess whether reading delay was correlated with lability index. P <0.05 was considered statistically significant. All statistical analyses were performed with Stata Statistical Software V.1.5.

Results

The proportion of DR and NR children did not significantly vary with sex (55% DR in boys vs 67% in girls, p=0.486). Mean age was 125.0 months (SE +/-7.1) for normal readers and 134.6 months (SE +/-4.8) for dyslexics (p=0.258).

Overall, 69% of children presented at least one change in visual perception using the Maddox Rod Test when the oral information was modified, whatever the stimulation. This proportion was 50% in NR and 81% in DR (p=0.053). Considering the whole population, the index of lability varied significantly with the group of children: it was on We tested the relation between reading delay and index of lability: in DR, the Spearman correlation coefficient was 0.483 (p=0.026). Among DR, the less reading delay they had, the higher their index of lability. In NR, there was no statistical correlation between literacy level and index of lability.

The proportion of children whose results on the Maddox Rod Test changed was significantly higher in the DR group than in the NR group after the introduction of sensory stimuli: tongue normally held in the mouth (p=0.002), tongue firmly touching the central retro-incisor papillae (p<0.001), and lips tightly closed (p=0.005). The tip of the tongue pushing against the lower incisors had no significant effect (p=0.091) (Table 2). The results were similar after the introduction of mechanical stimuli: dental occlusion modified by dental rolls between the molars (p=0.009) or using a dental splint (p=0.004).

The response to the Maddox Rod Test similarly varied whether the stimuli were sensory or mechanical. For the three tests, the mean lability index was 1.35 (95% CI: [0.38-2.33]) in normal readers and 4.19 (95% CI: [3.01-5.36] in dyslexics, (p=0.001). For mechanical stimuli, the mean was 0.71 (95% CI: [0.01-1.44]) for NR, and 2.61 (95% CI:

[1.70-3.53] for DR, (p=0.003). The index of lability was thus 2 to 3 times higher in dyslexic children whatever the type of stimuli.

The lability caused by changes in the spinal and podal sensors differed for a given oral condition.The proportion of DR presenting at least 1 modification of VH with the Maddox test was significantly higher than for NR when the oral modifications were performed in patients sitting in natural position (p=0.005), sitting straight up (p=0.036), or standing in a natural position with the mouth also in a natural position (p=0.035) (Table 3). Standing with a foam insole between the foot and the ground had no significant influence. Conversely, the lability caused by changes in the oral sensor differed for a given spinal or podal condition.

Discussion.

The main results of this study strongly suggest that manipulation of oral conditions modify visual perception and that changes affect differentially dyslexic children than normal readers.

Global effect of oral stimulations on the visual axis:

Using the Maddox rod test, which weakens the binocular balance, we demonstrated for the first time that it is possible to modify visual perception by changing the oral sensory information for 69% of dyslexic and non-dyslexic children. Changes were significantly more frequent in the dyslexic population, and the variation (lability) was drastically higher in dyslexics. The mechanism of the variation of the ocular axes remains unclear. The quality of the images was not changed during the oral manipulation. However, it should be noted that the quality of the binocular balance depends not only on the fusing of the retinal images of both eyes but also on maintaining the tone of the ocular muscles. This tone is regulated by the internal monitoring of the innervations sent to the muscles (efference copy) with the afferent proprioceptive discharge [START_REF] Mon-Williams | A framework for considering the role of afference and efference in the control and perception of ocular position[END_REF] . The role of eye proprioception discharge is enhanced for visual localization when there is a conflict with the oculomotor plan perception, as was the case in our study [START_REF] Balslev | Eye proprioception used for visual localization only if in conflict with the oculomotor plan[END_REF] . Because proprioceptive information from the eye muscles is carried by the upper branch of the trigeminal nerve, it is therefore not so surprising that oral changes may interfere when ocular balance is unstable because of changes in retinal fusion.

Specific effects of oral stimulations on visual axis: each of the oral stimuli led to a huge difference between normal readers and dyslexics, except for inferior incisor stimuli.

Three of the oral modifications were located exclusively in the anterior part of the mouth and were chosen because their effect is supposed to be more sensory than mechanical:

1) the tip of the tongue firmly touching the central retro-incisor papillae stimulates recovery of a corporal postural reflex related to contact with the lingual and palatine mucosa [START_REF] Marino | Vers une orthodontie neuro-sensorielle[END_REF] , 2) the stimulation of the facial nerve with lips tightly closed has an antagonistic action on the trigeminal nerve (Bratzlavsky reflex) [START_REF] Bratzlavsky | Reflexes with intraoral afferents in human lip musculature[END_REF] , 3) the tip of the tongue planted against the lower incisors mechanically stimulates the periodontal ligaments that may be involved in one aspect of the feeling of body ownership [START_REF] Trulsson | Brain activations in response to vibrotactile tooth stimulation: a psychophysical and fMRI study[END_REF] .

Compared to stimuli involving the tongue and the lips, the action of the other stimuli was located further back between the molars (dental rolls) or the entire dental arch (splint).

They are supposed to have a stronger action on the temporo-mandibular joint and its proprioceptive sensors, and modify occlusion intensely. Their action is obviously more mechanical, and the stimulation of the periodontal ligaments is more global and less precise. However, in our study, the effect on the visual axis was not different. This suggests that any action in the mouth is likely to have an impact on visual perception when the binocular balance is unstable.

Oral stimulations and posture regulation: the lability of the ocular effect depends on changes on spinal and podal sensation. This dependence was significantly more marked for dyslexic children and higher after oral stimulation. These results suggest the existence of links between eye stability, trigeminal information and postural regulation. They also suggest that these links could be more unstable in dyslexia. Postural adjustments use feed-back and feed-forward mechanisms. Feed-back information includes several types of afferent inputs: exteroceptive (skin sensitivity in the feet), proprioceptive (especially from the cervical, hip, ankle, and knee joints), vestibular (utriculus, sacculus, semicircular canals), and visual (retinal and muscle proprioception). For visual inputs, retinal flow, efference copy and extraocular muscle afferent information consecutive to eye movements operate congruently [START_REF] Guerraz | Ocular versus extraocular control of posture and equilibrium[END_REF] . Interestingly, the presence of small vertical eye deviation like VH can alter postural balance in young healthy adults and VH correction improves postural stability [START_REF] Matheron | Vertical phoria and postural control in upright stance in healthy young subjects[END_REF] . Thus the appearance of a small vertical deviation of ocular axes during oral changes could be one of the mechanisms connecting the mouth modifications and postural imbalances. This phenomenon could be explained by the narrow relationship between the muscles of the eye and mouth in the trigeminal nerve nucleus. Indeed, the sensory neurons of extraocular muscles are present as along with the primary afferent neurons associated with muscles for chewing, tooth pulp, and periodontal ligaments [START_REF] Buisseret-Delmas | Central projections of extraocular muscle afferents in cat[END_REF] . There are also direct links between the trigeminal nucleus and the superior colliculus which receives visual, somesthetic, and proprioceptive afferent fibers and is involved in posture control and gaze movements [START_REF] Hikosaka | Role of the basal ganglia in the control of purposive saccadic eye movements[END_REF] .

The link between VH and sensory oral modification is interesting because in the scientific literature, the relationship between the stomatognathic system and posture regulation is mainly centered on the responsibility of malocclusion or temporomandibular joint pathology, that is to say mechanical dysfunction [START_REF] Cuccia | The relationship between the stomatognathic system and body posture[END_REF] . The stomatognathic system, which is composed of muscle and ligament structures linked to the cervical region, is considered a functional complex known as the "cranio-cervico-mandibular system" [START_REF] Milani | Relationship between dental occlusion and posture[END_REF] . A change in the position of the mandible may affect the center of foot pressure (COP) position and gait stability [START_REF] Bracco | Effects of different jaw relations on postural stability in human subjects[END_REF] . In this case, proprioceptive and periodontal afference is sometimes said to be responsible, but mostly the mechanism is thought to be predominantly mechanical though it has been shown that anesthesia of the lower branch of the trigeminal nerve causes postural imbalance [START_REF] Gangloff | Dental occlusion modifies gaze and posture stabilization in human subjects[END_REF] . Nevertheless, the importance of mechanical stomatognathic factors is not always recognized because some studies do not find any relationship between posture, asymmetrical malocclusion or different dental positions, and temporomandibular disorders [START_REF] Michelotti | Postural stability and unilateral posterior crossbite: is there a relationship?[END_REF] . We showed that a change in posture modifies the behavior of the eyes during oral stimulation, suggesting more complex interferences between posture, mouth and eyes. They exist even if the stimulation modifies the occlusion or the position of the temporomandibular joint only slightly. Our results suggest that sensory stimuli are as active as the mechanical disturbances. It would be interesting to simultaneously compare the effect of sensory and mechanical stimuli on the posterior and the anterior arches.

We found that the effect of changes in oral stimuli on vision was greater in the group of dyslexic children than in the group of normal readers. The difference increased between the two groups of children when proprioception was modified in the back. Using a global approach, some clinical studies reinforce the possibility of a link between posture deficits and dyslexia [START_REF] Quercia | Ocular proprioception and developmental dyslexia. Sixty clinical observations[END_REF] , but co-occurrence of postural deficits and dyslexia do not prove their interdependency, and postural regulation of dyslexic children has been the subject of several studies with somewhat contradictory findings. Indeed, many studies have demonstrated impaired automatization of balance control in dyslexic children and adults [START_REF] Stoodley | Impaired balancing ability in dyslexic children[END_REF] , but others have failed to replicate this result [START_REF] Ramus | Developmental dyslexia: specific phonological deficit or general sensorimotor dysfunction?[END_REF] . Despite such discrepancies, there is a consensus that motor difficulties are frequent in the dyslexic population. This postural instability could indicate that such children lack the ability to assimilate multiple sensorimotor inputs. Interestingly, postural control can be improved by the use of very low-power oblique prisms (0.5°) to correct VH [START_REF] Vieira | Cognitive demands impair postural control in developmental dyslexia: a negative effect that can be compensated[END_REF] . Our study suggests that this improvement could also be obtained with guided oral stimuli. It also suggests that therapeutic adjustments in the mouth could have a damaging effect on ocular stability and on postural regulation. These results reinforce the importance of inter-professional cooperation, especially in the care of children with specific learning disabilities.

Oral stimuli, VH and dyslexia: the majority of dyslexic children have both visual and phonological disorders. Imprecise eye movements, difficulty with visual recognition, and phonological disturbances are usually considered to have a neurodevelopmental origin 1 .

Heilman has proposed that the mouth could play a role in the emergence of the phonological problems of dyslexic children who are unaware of the position of their articulators during speech [START_REF] Heilman | Developmental dyslexia: a motorarticulatory feedback hypothesis[END_REF] . The inability to associate the position of their articulators with speech sounds may impair the development of phonological awareness and the ability to convert graphemes to phonemes. The high level of oculomotor lability found in our study when the position of the tongue is changed might help to understand the presence of both visual and phonological disorders in dyslexia. It could also explain why some dyslexics have more difficulty reading aloud [START_REF] Alves | Prosody and reading in dyslexic children[END_REF] . On the other hand, there is no association between the position lability of the ocular axes during oral stimulation and the level of delayed reading in dyslexics. This lability must be considered above all as a clue depending on the stability of general proprioceptive information. It does not intervene directly in the ability to read as it was demonstrated in a previous study [START_REF] Quercia | The distinctive vertical heterophoria of dyslexics[END_REF] .

This study has highlighted the interdependence of the position of the visual axes and the trigeminal information that comes from the mouth when the fusion of the retinal images is manipulated. This is more marked for dyslexic children than for normal-reader children. This phenomenon varies according to posture. Our study opens a new field of research on the relations between oral sensory perception, visual perception and postural regulation.

average 9 .

 9 76 (95% CI: [7.04 -12.47) in DR and 4.21 (95% CI: [1.33 -4.97]) in NR (p=0.007).

Figure 1 .

 1 Figure 1. How to indicate the position of the red line without changing information

Table 1 . Example of calculating the index of lability (postural condition = sitting in natural position without oral modification).Table 2 . Comparison between normal readers and dyslexics readers for changes in vertical heterophoria measured using a Maddox Rod Test according to oral conditionsTable 3 . Comparison between normal readers and dyslexic readers for changes in vertical heterophoria measured with the Maddox Rod Test according to spinal and podal then oral sensors.

 123

Acknowledgments

The authors thank the parents and children for their kind participation.

Funding: This work was partially supported by a grant of the 3Dys French Association

Disclosure

The authors report no conflicts of interest in this work.

All authors have approved the final article.

Condition:

Sitting

Index of lability

H H H O H O H h H H H H

Points for lability index

Note: Each time that the type of VH changes as a result of the stimulation of one sensor (when compared to the previous stimulation) gives 1 point.

Abbreviations: O, line in the middle of the light; h, line over the light; H, line under the light.


Pierre Anschutz
email: pierre.anschutz@u-bordeaux.fr

Sylvain Bouchet

Gwenaël Abril

Romain Bridou

Emmanuel Tessier

David Amouroux

Abril Gwenaël

) David

In vitro simulation of oscillatory redox conditions in intertidal sediments: N, Mn, Fe, and P coupling

Keywords: benthic biogeochemistry, redox oscillation, nutrients, coastal sediments, iron oxide, manganese oxide

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

1.Introduction

The successive use of electron acceptors that yield the highest amount of free energy in the terminal step of bacterial oxidation of organic matter partly explains the vertical stratification of redox compound distribution below the sediment water interface [START_REF] Froelich | Early oxidation of organic matter in pelagic sediments of the eastern equatorial Atlantic: suboxic diagenesis[END_REF]. However, the steady state hypothesis implying that a parcel of sediment deposited under oxic conditions moves to suboxic conditions, and then definitively to anoxic conditions through burial below the oxygen penetration depth is unwarranted in most aquatic environments. Indeed, sediments are subjected to redox oscillations due to advective transport of particles and solutes, migration of the redox front, or a combination of both processes.

Consequently, considerable effort has been devoted to understanding diagenetic processes under transient redox conditions [START_REF] Sundby | Transient state diagenesis in continental margin mud[END_REF].

Redox oscillations due to advection of sediment particles have been described in several cases, such as fluid mud mobilization and bioturbation. Mobile fluid muds, which can be found in the Amazon deltaic plume and in the turbidity maximum zone of estuaries, experience oxygenation during resuspension of particles [START_REF] Aller | Mobile deltaic and continental shelf muds as suboxic, fluidized bed reactors[END_REF][START_REF] Abril | Transient, tidal time-scale, nitrogen transformation in an estuarine turbidity maximumfluid mud system (the Gironde, south-west France)[END_REF].

Oxygen inputs allow a new stock of nitrate and reactive iron and manganese oxides to be regularly built, which eventually enhances the mineralisation of organic matter [START_REF] Sun | Laboratory studies and anoxic degradation of chlorophyll-a in Long Island Sound sediments[END_REF][START_REF] Aller | Bioturbation and remineralization of sedimentary organic matter: effects of redox oscillation[END_REF][START_REF] Abril | In vitro simulation of oxic/suboxic diagenesis in an estuarine fluid mud subjected to redox oscillations[END_REF]. Bioturbation due to the mixing activity of infaunal macrobenthos [START_REF] Rhoads | Organism-sediment relations on the muddy sea floor[END_REF][START_REF] Aller | The effects of macrobenthos on chemical properties of marine sediment and overlying water[END_REF] significantly affects the distribution of biogeochemical species inside the sediment as well as their fluxes at the sediment-water interface (e.g. [START_REF] Yingst | The role of bioturbation in the enhancement of microbial turnover rates in marine sediments[END_REF][START_REF] Aller | The effects of macrobenthos on chemical properties of marine sediment and overlying water[END_REF][START_REF] Blackburn | Benthic mineralization and bacterial production[END_REF][START_REF] Meysman | Bioirrigation in permeable sediments: Advective pore-water transport induced by burrow ventilation[END_REF]. Organic material and electron acceptors are thus redistributed in the sediment column, generating redox oscillation of sediment parcels. [START_REF] Aller | Bioturbation and remineralization of sedimentary organic matter: effects of redox oscillation[END_REF][START_REF] Sun | Effects of oxygen and redox oscillation on degradation of cell-associated lipids in surficial marine sediments[END_REF][START_REF] Gilbert | The influence of macrofaunal burrow spacing and diffusive scaling on sedimentary nitrification and denitrification: An experimental simulation and model approach[END_REF][START_REF] Volkenborn | Oscillatory porewater bioadvection in marine sediments induced by hydraulic activities of Arenicola marina[END_REF].

In coastal environments, excursion of redox fronts below the sediment-water interface occurs at different time scales. The oxygen penetration depth can change everyday due to photosynthetic and respiration activity of biofilms or macrophytes at the surface of sediments [START_REF] Pringault | Irradiance regulation of photosynthesis and respiration in modern microbialites built by benthic cyanobacteria in a tropical lagoon (New Caledonia)[END_REF][START_REF] Sundby | Redox chemistry in the root zone of a salt marsh sediment in the Tagus Estuary, Portugal[END_REF][START_REF] Frederiksen | Oxygen dynamics in the rhizosphere of Zostera marina: a two-dimensional planar optode study[END_REF]. It may also migrate toward the sediment surface after pulses of labile organic matter supply (e.g., [START_REF] Gobeil | Diagenetic separation of cadmium and manganese in suboxic continental margin sediments[END_REF][START_REF] Katsev | Modelling vertical migration of the redox boundary in sediments: application to deep basins of the Arctic Ocean[END_REF]Glud, 2008 and references therein). In permeable sediments, redox conditions also vary according to wave action, tidal pumping, and bottom topography [START_REF] Ziebis | Impact of biogenic sediment topography on oxygen fluxes in permeable seabeds[END_REF][START_REF] Precht | Oxygen dynamics in permeable sediments with a wave-driven pore water exchange[END_REF][START_REF] De Beer | Transport and mineralization rates in North Sea sandy intertidal sediments, Sylt-Rømø Basin, Wadden Sea[END_REF][START_REF] Cook | Benthic solute exchange and carbon mineralization in two shallow subtidal sandy sediments: impact of advective porewater exchange[END_REF]Deborde et al., 2008a). In such sediments, oxygen can be advected deep into the sediment while outwelling may also force anoxic porewater right to the sediment surface [START_REF] Huettel | Advective Transport Affecting Metal and Nutrient Distributions and Interfacial Fluxes in Permeable Sediments[END_REF]Ibanhez and Rocha, 2016).

Examples cited above suggest that in almost all the modern sediments, particulate redox-sensitive phases are in contact with either oxic or reduced reactive dissolved species.

Among redox-sensitive phases, particulate reactive Mn-and Fe-(oxyhydr)oxides (Mn-ox and Fe-ox) play a central role in sedimentary biogeochemical reactions, because they are involved in the benthic cycle of major nutrients such as N and P. Among the many possible redox reactions, there is the oxidation of ammonia to di-nitrogen by Mn-ox in the presence of oxygen [START_REF] Luther | Interactions of manganese with the nitrogen cycle: alternative pathways for dinitrogen formation[END_REF], the oxidation of sulphide to sulphate and ammonia to nitrate by Mn-ox in the absence of oxygen [START_REF] Aller | Complete oxidation of solid phase sulfides by manganese and bacteria in anoxic marine sediments[END_REF][START_REF] Hulth | Coupled anoxic nitrification/manganese reduction in marine sediments[END_REF][START_REF] Anschutz | Interactions between metal oxides and species of nitrogen and iodine in bioturbated marine sediments[END_REF]2005;[START_REF] Mortimer | Anoxic nitrification in marine sediments[END_REF], and the oxidation of Fe(II) to Fe-ox by nitrate [START_REF] Hyacinthe | Early diagenetic processes in the muddy sediments of the Bay of Biscay[END_REF] or by Mn-ox [START_REF] Hartmann | Atlantis II deep geothermal brine system. Chemical processes between hydrothermal brines and Red Sea deep water[END_REF][START_REF] Anschutz | Chemical mass balances in metalliferous deposits from the Atlantis II Deep (Red Sea)[END_REF][START_REF] Dellwig | A new particulate Mn-Fe-P-shuttle at the redoxcline of anoxic basins[END_REF].

Iron plays an important role in the cycle of phosphorus since dissolved phosphate can be strongly sorbed or co-precipitated with Fe-ox and be removed from sediment pore water (e.g. [START_REF] Krom | Adsorption of phosphate in anoxic marine sediments[END_REF], while Fe-ox reductive dissolution releases stored phosphate (e.g., [START_REF] Sundby | The phosphorus cycle in coastal marine sediments[END_REF]. Therefore, redox oscillations may result in a complex sequence of reactions that make the predictive modelling of N and P behaviour difficult [START_REF] Katsev | Modelling vertical migration of the redox boundary in sediments: application to deep basins of the Arctic Ocean[END_REF].

Redox oscillations have been studied mostly in order to assess their impact on organic carbon and nitrogen mineralization efficiency (e.g. [START_REF] Aller | Bioturbation and remineralization of sedimentary organic matter: effects of redox oscillation[END_REF][START_REF] Aller | Mobile deltaic and continental shelf muds as suboxic, fluidized bed reactors[END_REF][START_REF] Abril | Oxic/anoxic oscillations and organic carbon mineralization in an estuarine maximum turbidity zone (The Gironde, France)[END_REF], 2010;;[START_REF] Gilbert | Redox oscillation and benthic nitrogen mineralization within burrowed sediments: An experimental simulation at low frequency[END_REF]. Their impact on the links between Fe/Mn cycles and N/P cycles has been largely overlooked. Microcosm experiments are useful to unravel environmental mechanisms that are hardly discriminated during in situ experiments and to assess the processes occurring under oscillating conditions [START_REF] Abril | In vitro simulation of oxic/suboxic diagenesis in an estuarine fluid mud subjected to redox oscillations[END_REF]). Here we present in detail the evolution of redox species concentrations observed in two independent experiments carried out in a specifically designed reactor. Sediment slurries with different Fe-ox and Mnox content were subjected to changing redox conditions under controlled conditions. The objective of this study was to compare the various diagenetic reactions occurring in these two sediments under short (days) redox oscillations with respect to their Mn and Fe contents, and especially their influence on the N and P behaviour.

Methods

Sediment sampling and slurries preparation

The sampling conditions and preparation of the slurries have been previously described in detail [START_REF] Bouchet | An experimental approach to investigate mercury species transformations under redox oscillations in coastal sediments[END_REF][START_REF] Bouchet | Investigations into the differential reactivity of endogenous and exogenous mercury species in coastal sediments[END_REF]. Briefly, bulk superficial sediments (~5 kg, 1-3 cm depth) and overlying waters (20 L) were sampled from the two sites using protocols adapted for trace metals. Material preparation included successive cleaning with a specific detergent, 10% HNO 3 (Baker Analysed, JT Baker) (twice) and 10 % HCl (Baker Analysed, JT Baker) baths, rinsed with ultrapure MQ water (Quantum EX, Millipore), dried under laminar flow hood and stored in double sealed polyethylene bags until use. For the Arcachon bay, the sediment was sampled on an intertidal mudflat exposed to the atmosphere for a minimum of 12 h/day. The salinity of the overlying water sampled during high tide was 32, which is in the 22-34 salinity range observed during the year at the sampling location (Deborde et al., 2008a).

For the Adour estuary, the sediment was collected on a tidal mud flat and the salinity of the overlying water was at 8. Sediment and water samples were kept at 4 °C before processing. These two sites were chosen since they are naturally subjected to redox oscillations due to bioturbation and resuspension and exhibit different contents of Mn-ox in surface sediment and different salinities. The fine fraction (<63 µm) represented more than 80% for both sediments, the organic carbon content was 4.2 and 3.2 %, and the sulphur content was 1.7 and 0.2%, in the lagoon and the estuarine sediment, respectively (Table 1). The day following sampling, sediments were homogenized and sieved to 2 mm and then to 300 µm, mixed with an appropriate volume of overlying water to reach a final volume of 20 L and introduced in the reactor (Fig. 1). The resulting slurry contained 93 ± 6 and 70 ± 4 g L -1 suspended particle for the Arcachon bay and the Adour estuary, respectively. Suspensions were kept between 3 and 5 days under continuous stirring and N 2 conditions to allow the re-equilibration of the system before the beginning of the experiment.

Experimental setup and operating conditions

The sediment slurries were incubated in the dark at room temperature in a custom-made set-up designed to simulate redox oscillations by maintaining them in oxic or anoxic homogeneous conditions for a determined period [START_REF] Abril | In vitro simulation of oxic/suboxic diagenesis in an estuarine fluid mud subjected to redox oscillations[END_REF][START_REF] Bouchet | An experimental approach to investigate mercury species transformations under redox oscillations in coastal sediments[END_REF].

The main component of the set-up is a 25-L gas-tight reactor made of Pyrex set on a magnetic stirrer [START_REF] Gilbert | Redox oscillation and benthic nitrogen mineralization within burrowed sediments: An experimental simulation at low frequency[END_REF], which allow flushing the slurries to either air or O 2 free gas through an immersed glass frit bubbler (Fig. 1). Gas flushing of the whole slurry prevented CO 2 accumulation and drastic pH changes. The slurry was continuously stirred by a central Teflon-coated magnetic stirring bar. This design prevented the sedimentation of particles, which would have created an anoxic sedimentary environment in periods when oxic conditions were sought.

Probes for pH/temperature (Metrohm 713 pH-meter) and a polarographic oxygen electrode (YSI 5000, calibrated in water-saturated air) were located in the lower part of the reactor. An outlet pipe equipped with a Teflon lined glass valve also allowed discrete samples to be collected at high frequency using gas tight syringes to avoid any alteration from the ambient air.

For each sample, about 60 mL slurry was removed from the reactor, immediately transferred to a polypropylene tube flushed with N 2 and centrifuged (under N 2 or ambient atmosphere according to the period) for 15 min at 2280 g. Supernatant fluids were filtered through 0.2 µm acetate cellulose syringe filter, split into several aliquots and acidified with a 1% equivalent volume of ultrapure concentrated HCl for dissolved Fe, Mn and inorganic phosphorus determinations. These subsamples were kept refrigerated in the dark until analysis. Samples for ammonium, nitrate, and nitrite analysis were transferred to polyethylene vials and frozen immediately. The residue was immediately frozen at -20°C for solid-phase composition analyses.

Oxic or anoxic conditions were obtained by occasionally purging the gas and water phases with either air or N 2 . Both experiments started with anoxic conditions. For the Adour estuary sediment, stable anoxic conditions were maintained for 4 days. This period was followed by 6 days of oxic conditions with a mean oxygen saturation of 40% (111 µM). The sediment was anoxic again between day 10 and day 12. For the Arcachon lagoon sediments, the initial anoxic period was of 11 days, but a leak occurred on day 4 so that the slurry became accidentally oxic for a few hours. At day 11, the slurry was purged with air and it was maintained oxic for one week, except at day 14, when the slurry became temporarily anoxic because of a magnetic stirred failure. Although it was difficult to maintain stable oxic conditions because of the numerous redox reactions, most of the measured oxygen concentrations were between 30 and 150 µM. From day 18, the slurry was kept anoxic for one week. Despite these unfortunate accidental oxidation events and the differences between incubation treatments for the two sediments, significant insight into redox cycling was obtained, as outlined in the results and discussion.

Samples were collected every 20 (± 5) hours. The sampling time step was shortened during non-accidental redox transitions in order to assess the rates of transformations. The pH was influenced by gas flushing, but the values remained between 7.1 and 7.7 in the Arcachon slurry, and between 6.9 and 7.5 in the Adour slurry. Low values were measured during oxic periods These 2-and 4-weeks experiments were not replicated, because we had only one 25-L reactor, and in the dynamic intertidal environments studied we would have had difficulties to find exactly the same sediment for duplicating experiments with the same sediment. All data were integrated into Microsoft Excel® software for further analyses of all experimental results. Rates of reactions were determined using the slope of linear regression of concentration evolution with time [START_REF] Abril | In vitro simulation of oxic/suboxic diagenesis in an estuarine fluid mud subjected to redox oscillations[END_REF]. Error margin were calculated with the standard deviation of the slope.

Analyses

The freeze-dried solid fraction was homogenised. Particulate organic carbon (POC) was measured on freeze-dried samples by infrared spectroscopy (LECO 200 C-S analyzer) after removal of carbonates with 2M HCl from 50 mg powdered sample [START_REF] Etcheber | Distribution and quality of sedimentary organic matter on the Aquitanian margin (Bay of Biscay)[END_REF]). An ascorbate reagent (50 g NaHCO 3 , 50 g Na-citrate, 20 g ascorbic acid for 1L solution, buffered at pH 8) was used to obtained the Mn-ox content [START_REF] Anschutz | Solid speciation, oxidation state, and reactivity of manganese in marine sediments[END_REF] and the most reactive Fe(III) fraction (Fe-asc) [START_REF] Kostka | Partitioning and speciation of solid phase iron in saltmarsh sediments[END_REF] and the associated phosphorus (P-asc) [START_REF] Anschutz | Burial efficiency of phosphorus and the geochemistry of iron in continental margin sediments[END_REF]. About 100 mg dried sample was leached with 10 mL solution for 24h while shaking continuously at ambient temperature. The supernatant was diluted with 0.2N HCl. After each extraction, the Fe and P contents of the supernatant were determined by colorimetric procedures in a mixture of reagents adapted for each sample matrix [START_REF] Anschutz | Spectrophotometric determination of phosphate in matrices from sequential leaching of sediments[END_REF]. Extracted Mn concentration was measured by atomic absorption spectrometry with external standard prepared in the same matrix.

Nitrate and nitrite were measured by flow injection analysis (FIA) according to [START_REF] Anderson | Simultaneous spectrophotometric determination of nitrite and nitrate by flow injection analysis[END_REF]. Ammonium was analysed with the FIA method described by [START_REF] Hall | Rapid, small volume, flow injection analysis for SCO 2 and NH 4 + in marine and freshwaters[END_REF]. Sulphate was measured with a nephelometric method adapted from [START_REF] Rodier | L'analyse de l'eau, eaux naturelles, eaux résiduaires[END_REF] and Fe 2+ with the colorimetric method using ferrozine [START_REF] Stookey | Ferrozine-A new spectrophotometric reagent for iron[END_REF]. Dissolved sulphide was measured by a methylene blue method adapted from [START_REF] Cline | Spectrophotometric determination of hydrogen sulphide in natural waters[END_REF]. Phosphate was measured by a colorimetric method according to [START_REF] Murphy | A modified single solution method for determination of phosphate in natural waters[END_REF]. Dissolved Mn 2+ was determined by atomic absorption spectrometry. The precision of these procedures was ± 5%.

Detection limit (DL) was 1 µM, 0.05 µM, 0.02 µM, and 0.3 µM for NO 3 -, NO 2 -, phosphate, and dissolved Fe(II), respectively. Ammonium and sulphate DL was 10 µM.

Results

Concentrations in the solid phases

Concentrations measured in the solid fraction did not change significantly during both incubations. The mean value of particulate organic carbon was 3.2 and 4.2 wt% in the Adour estuary and Arcachon lagoon sediments, respectively. The mean value of iron extracted with ascorbate was 180 µmol g -1 in the Arcachon lagoon. Phosphorus content associated with this fraction was at 11 µmol g -1 . The respective values for the Adour estuary sediment were 47 and 9.8 µmol g -1 . The manganese oxide content differed greatly between the two sediments, its concentration was 9.8 µmol g -1 in the Adour estuary sample and 1.4 µmol g -1 in the Arcachon lagoon sample (Table 1).

Dissolved Fe and P behaviour

Dissolved reduced solutes were initially present in both dissolved fraction (Fig. 2) but lagoon sediments were much more concentrated in dissolved iron (II) and ammonium than estuarine sediments. The concentration of dissolved Fe 2+ was close to 400 µmol L -1 (µM) in the lagoon slurry and at about 50 µM in the estuarine slurry. As soon as the slurries became oxic, dissolved iron concentrations collapsed to values close to zero at a rate above 2000 µM day -1 . In the Arcachon slurry, Fe 2+ concentration then remained below 20 µM during the oxic period while it remained below 3 µM in the Adour slurry. Low and variable concentration of dissolved iron was observed during the accidental oxidation that occurred between days 4 and 7. When anoxic conditions were recovered at the end of the experiments dissolved Fe increased regularly at a slow rate of 29 ± 1 µM day -1 after the day 22 in the lagoon sediment whereas it remained low in the estuarine sediment. Initial dissolved inorganic phosphorus (DIP) concentrations were of the same magnitude in both slurries (12 -16 µM). DIP dropped to a value close to 0 (0.2 µM) in the lagoon sediment when dissolved oxygen was introduced in the reactor, and increased again when reduced conditions were recovered, but still remained below 2 µM. The concentration was increasing at a rate of 0.7 ± 0.1 µM day -1 during the first 2 days and then 0.1 µM day -1 . DIP also decreased right after oxygen input in the estuarine sediment, but the concentration remained at about 1 µM. After day 6, DIP concentrations remained between 2 and 3 µM, even after the anoxic-oxic redox transition.

Dissolved nitrogen species cycling

In the Arcachon lagoon sediments, ammonium concentration was 684 µM at the beginning of the experiment (Fig. 2). It increased at a rate of 22 ± 1.5 µM day -1 from day 0 to day 10, and at a relatively similar rate of 26 ± 1.4 µM day -1 between day 22 and day 25, during the well-established anoxic periods. During the 8 days of oxic conditions, it remained constant at a value around 1000 µM but then its production peaked at a rate of 52 ± 14 µM day -1 during the subsequent 3.5 days. The mean ammonium production rate was thus 23 µM day -1 over the entire incubation period. In the estuarine slurry, the initial ammonium concentration was 250 µM, and it increased at a rate of 12 ± 1.4 µM day -1 until oxic conditions started. Then, it dropped at a rate of 200 ±1 0 µM day -1 to values below 10 µM and remained so until the beginning of the next anoxic period (day 10), when it increased again at a rate of 34 ± 4 µM day -1 to a value that remains constant at 50 µM after day 11.

During the initial and final anoxic periods, nitrate+nitrite (ΣNO 3 ) concentrations remained below the detection limit of 0.3 µM in the Arcachon lagoon sediment. During the oxic period, ΣNO 3 lately increased at a rate of 44 µM day -1 (nitrite accounting for 25 to 50 %) but it vanished very quickly at a rate of 89 ± 6 µM day -1 when the conditions became anoxic again. In the estuarine sediment experiment, ΣNO 3 concentrations ranged between 7 and 13 µM during the initial anoxic period. Shortly after the oxic period started, nitrate reached a value of 310 µM at a rate of 243 ± 22 µM day -1 and then remained constant at about 250 µM.

During the last anoxic period, nitrate concentrations did not collapse and oscillated between 216 and 470 µM.

Dissolved Mn

In the lagoon slurry, dissolved Mn evolved with little variation from an initial concentration of 62 µM to a final value of 50 µM. At the beginning of the oxic period, concentrations decreased rapidly at a rate of 27 ± 10 µM day -1 and then at a slower rate of 0.7 ± 0.2 µM day -1 to a minimal value of 36 µM. After the establishment of anoxic conditions at day 21, dissolved Mn increased again to reach 51 µM the day 24. The estuarine slurry showed a relatively constant concentration of dissolved Mn of 93 µM during the initial anoxic period.

At the onset of oxic conditions Mn concentration abruptly decreased by 10 µM and then reached a value below 1 µM in 4 days at a mean rate of 22 ± 2.5 µM day -1 . After the recovery of anoxic conditions, dissolved Mn concentration increased again at a rate of 10 ± 1 µM day -1 to reach a plateau at 8 µM after a few hours.

Dissolved sulphur species

Free sulphide was never detected under any conditions in both experiments (detection limit 2 µM). Mean sulphate concentration were 25 mM at the beginning of the Arcachon sediment experiment. It increased to a concentration of 27 mM as the slurry became oxic.

Adour estuary experiment showed the same pattern with an initial concentration of 6 mM and a value that reached rapidly a mean and a constant value of 6.9 mM after the oxygenation of the slurry.

Discussion

Similarities and differences in the initial solid composition of the two sediments

Both sediment contained high concentrations of organic carbon with measured values typical of the sampling location (Deborde et al., 2008b;[START_REF] Mouret | Spatial heterogeneity of benthic biogeochemistry in two contrasted marine environments (Arcachon bay and bay of Biscay, SW France)[END_REF][START_REF] Point | Reactivity, interactions and transport of trace elements, organic carbon and particulate material in a mountain range river system (Adour River, France)[END_REF]. The water/sediment ratio was in the same range for both experiments with a suspended particulate matter concentration of 93 ± 6 and 70 ± 4 g L -1 for the Arcachon lagoon and the Adour estuary, respectively. Differences occurred in the ascorbate extracted fractions; ascorbic acid buffered at pH 8 is known to extract selectively only the most reducible fraction of Fe-ox [START_REF] Kostka | Partitioning and speciation of solid phase iron in saltmarsh sediments[END_REF][START_REF] Hyacinthe | An authigenic iron phosphate phase in estuarine sediments : composition, formation and chemical reactivity[END_REF], that carries the major part of P associated with Fe(III) phases [START_REF] Anschutz | Burial efficiency of phosphorus and the geochemistry of iron in continental margin sediments[END_REF], but also dissolves almost all the Mn(III,IV) phases [START_REF] Anschutz | Solid speciation, oxidation state, and reactivity of manganese in marine sediments[END_REF][START_REF] Mouret | Benthic geochemistry of manganese in the Bay of Biscay, and the sediment accumulation rate[END_REF]. Both sediments contain high concentrations of Fe-asc, which is normal for the Arcachon lagoon because the watershed of the main river that feeds the lagoon consists of a Quaternary sandy soils enriched in iron oxides [START_REF] Buquet | Nutrient sequestration in Aquitaine lakes (S France) limits nutrient flux to the coastal zone[END_REF]. The phosphorus associated with the Fe-asc fraction showed a Fe-asc/P-asc mole ratio of 16.4 and 4.8 for the Arcachon sediment and the Adour sediment, respectively. The Arcachon value is within the ones previously published (Deborde et al., 2008b) while this is the first report for the Adour estuary sediment. The difference in Fe-asc/P-asc ratios is likely due to the size of the Fe(III) particles and the low Fe/P ratio of the Adour suggests the existence of a Fe-ox phase with very high adsorption capacity, i.e. a very large specific surface area due to colloidal size [START_REF] Waychunas | Surface chemistry of ferrihydrite: Part 1. EXAFS studies of the geometry of coprecipitated and adsorbed arsenate[END_REF]).

More Fe-ox, as in the sediments from the Arcachon lagoon, would imply larger authigenic particles or thicker coatings on other particles and therefore fewer surface adsorption sites per unit weight or volume. In turn this would lead to higher Fe/P ratios, as observed. Other factors may also play a role, for example competition with As and OM for binding sites (e.g. [START_REF] Manning | Modeling competitive adsorption of arsenate with phosphate and molybdate on oxide minerals[END_REF][START_REF] Hunt | Inhibition of phosphorus sorption to goethite, gibbsite, and kaolin by fresh and decomposed organic matter[END_REF].

The Mn-asc concentration in the Adour estuary sediments is close to the mean value of Mn-asc measured in particles from the turbidity maximum zone of the Gironde estuary that drains the same geological domain (Pyrenean belt). A similar mean value of 8 µmol g -1 is also reported for the suspended particles of the nearby Bay of Biscay [START_REF] Anschutz | Deposition and fate of reactive Fe, Mn, P and C in suspended particulate matter in the Bay of Biscay[END_REF]. On the contrary, the Mn-ox concentration of 1.4 µmol g -1 found in the Arcachon lagoon surface sediment is very low but can be explained by the fact that the portion of sampled sediment consisted mostly of anoxic sediment. Actually, the thickness of the oxic layer of these sediment does not exceed 3 mm depth below the sediment water interface [START_REF] Delgard | In situ study of short-term variations of redox species chemistry in intertidal permeable sediments of the Arcachon lagoon[END_REF], whereas we sampled a 3 cm thick sediment layer. Nevertheless, profiles of Mn-asc reported for Arcachon bay sediments indicate that the oxic layer does not contain more than 2 µmol g -1 (Deborde et al., 2008a;[START_REF] Mouret | Spatial heterogeneity of benthic biogeochemistry in two contrasted marine environments (Arcachon bay and bay of Biscay, SW France)[END_REF]. This low value is related to the nature of the soil of the watershed that is very poor in manganese. Therefore, one of the main difference between the Arcachon and Adour sediment is that the first is very poor in Mn-ox, whereas the second contains a more typical concentration for the region, and thereafter we attempt to relate the different reaction pathways to the initial composition of each sediment.

Organic matter mineralization.

The accumulation of dissolved inorganic nitrogen (DIN) during the experiments can be related to organic matter mineralization. The initial conditions were relatively comparable in the two slurries with high concentrations of ammonium but nitrate close to zero. Several experiments showed that for relatively refractory land-derived organic matter, aerobic respiration is almost always faster than anaerobic respiration [START_REF] Aller | Bioturbation and remineralization of sedimentary organic matter: effects of redox oscillation[END_REF][START_REF] Aller | Mobile deltaic and continental shelf muds as suboxic, fluidized bed reactors[END_REF][START_REF] Kristensen | Aerobic and anaerobic decomposition of organic matter in marine sediment: Which is the fastest?[END_REF][START_REF] Andersen | Fate of organic carbon added as diatom cells to oxic and anoxic marine sediment microcosms[END_REF][START_REF] Hulthe | Effect of oxygen on degradation rate of refractory and labile organic matter on continental margin sediments[END_REF]. During the lagoon sediment experiment, DIN accumulation occurred at a mean rate of 23 µM day -1 but slightly higher rates were observed during the oxic period (44 µM day -1 ) suggesting that a labile fraction was involved in anaerobic respiration processes, and possibly an additional less labile one in the presence of dissolved oxygen. In the estuarine sediment experiment, DIN also accumulated during the first anoxic period but at a slower rate (12 µM day -1 ) compared to the same conditions in Arcachon sediments. Measurements of the lability of particulate organic matter have been performed for Arcachon Lagoon sediments [START_REF] Relexans | Benthic respiratory potential with relation to sedimentary carbon quality in seagrass beds and oyster parks in the tidal flats of Arcachon Bay, France[END_REF][START_REF] Dubois | Origin and Composition of Sediment Organic Matter in a Coastal Semi-Enclosed Ecosystem: An Elemental and Isotopic Study at the Ecosystem Space Scale[END_REF], but not for the Adour estuary. Lower rate of DIN production is probably due to the higher proportion of less reactive continental organic matter in estuarine particles. During the oxic period, DIN concentrations did not increase significantly. The highest DIN rise occurred during the oxic-anoxic transition, suggesting that labile organic matter became suddenly available during this transition. The recycling of bacteria biomass accumulated during the oxic period that died because of the redox transition could be at the origin of this new DIN [START_REF] Aller | Mobile deltaic and continental shelf muds as suboxic, fluidized bed reactors[END_REF].

Potential redox reactions during the experiments

Several reactions involving Mn, Fe, N, and P species may occur in these experiments and can explain our observations. Table 2 shows the common half-redox reactions of electron acceptor reduction and associated equilibrium constant for one electron transfer at standard conditions for major species involved during early diagenesis. The standard condition for concentration is 1 M, including H + . The stoichiometry of these half reactions shows that the proton activity has a significant effect on LogK and the variation of logK (∆logK) can be represented as a function of pH (e.g. [START_REF] Luther | Interactions of manganese with the nitrogen cycle: alternative pathways for dinitrogen formation[END_REF][START_REF] Bethke | The thermodynamic ladder in geomicrobiology[END_REF] in order to get the equilibrium value at the pH of our incubations experiment. The pH was generally lower during oxic periods than during anoxic periods, but it remained at 7.3±0.4. The half reaction stoichiometry shows that the activity of N or S species does not influence markedly the equilibrium constant, because of the small values of the stoichiometric coefficient. However, the concentrations of Mn and Fe significantly influence the equilibrium of half reaction of Mn-ox and Fe-ox reduction. At standard conditions Mn-oxides or oxihydroxides cannot oxidize ammonium to nitrate, but as a concentration of Mn 2+ of 100 µM (rigorously, an activity of 10 -4 ) or less is considered, ammonium oxidation to nitrate by Mn(III) and Mn(IV) species gains the thermodynamic advantage (Fig. 3). It has been pointed out by several authors that the reduction of Mn-ox by diffusing ammonia could be an important process of di-nitrogen production (e.g. [START_REF] Hulth | Coupled anoxic nitrification/manganese reduction in marine sediments[END_REF][START_REF] Anschutz | Interactions between metal oxides and species of nitrogen and iodine in bioturbated marine sediments[END_REF]. Anaerobic nitrate production has been observed in several marine sediments [START_REF] Aller | Biogeochemical heterogeneity and suboxic diagenesis in hemipelagic sediments of the Panama Basin[END_REF][START_REF] Anschutz | Burial efficiency of phosphorus and the geochemistry of iron in continental margin sediments[END_REF][START_REF] Mortimer | Evidence for suboxic nitrification in recent marine sediments[END_REF][START_REF] Deflandre | Early diagenetic processes in coastal marine sediments disturbed by a catastrophic sedimentation event[END_REF][START_REF] Chaillou | Experimental study of transient diagenesis in modern turbidites[END_REF], due to oxidation of ammonia by Mn(III)-oxyhydroxides [START_REF] Hulth | Coupled anoxic nitrification/manganese reduction in marine sediments[END_REF][START_REF] Anschutz | Solid speciation, oxidation state, and reactivity of manganese in marine sediments[END_REF]. Dissolved Mn(II) could theoretically be oxidized by nitrate to give N 2 , as proposed in several studies [START_REF] Aller | Bioturbation and manganese cycling in hemipelagic sediments[END_REF][START_REF] Schulz | Early diagenetic processes, fluxes, and reaction rates in sediments of the South Atlantic[END_REF][START_REF] Murray | Oxidation-reduction environmentsthe suboxic zone in the Black Sea[END_REF][START_REF] Luther | Interactions of manganese with the nitrogen cycle: alternative pathways for dinitrogen formation[END_REF] and as shown by thermodynamic calculations (Fig. 3), but this reaction has not been directly observed in the field [START_REF] Thamdrup | The fate of ammonium in anoxic manganese oxide-rich marine sediment[END_REF]. Dissolved Mn(II) and nitrate generally co-exist below the oxygen penetration depth in sediment cores [START_REF] Mouret | Oxygen and organic carbon fluxes in sediments of the Bay of Biscay[END_REF], suggesting that the latter is not an efficient oxidant for the first.

Thermodynamic calculations show that nitrate is an oxidant for Fe 2+ at both standard or corrected dissolved iron concentrations. The penetration depth of nitrate below the sedimentwater interface generally fits with the upper boundary of dissolved Fe +2 detection (e.g., [START_REF] Hyacinthe | Early diagenetic processes in the muddy sediments of the Bay of Biscay[END_REF][START_REF] Mouret | Spatial heterogeneity of benthic biogeochemistry in two contrasted marine environments (Arcachon bay and bay of Biscay, SW France)[END_REF]. Evidence for anaerobic reduction of nitrate to N 2 with Fe 2+ has been found in many field investigations (e.g. [START_REF] Hauck | Ferrous iron oxidation by denitrifying bacteria in profundal sediments of a deep lake (Lake Constance)[END_REF][START_REF] Straub | Anaerobic, nitrate-dependant microbial oxidation of ferrous iron[END_REF]. Oxidation of Fe with MnO 2 is a thermodynamically feasible process. This process has been proposed by several authors to explain the removal of Fe 2+ and a part of the reductive dissolution of particulate Mn during early diagenesis [START_REF] Myers | Microbial reduction of manganese oxides : interactions with iron and sulfur[END_REF][START_REF] Postma | Concentration of Mn and separation from Fe in sediments. 1. Kinetics and stoichiometry of the reaction between birnessite and dissolved Fe(II) at 10-degrees-C[END_REF][START_REF] Hyacinthe | Early diagenetic processes in the muddy sediments of the Bay of Biscay[END_REF] or in stratified waters [START_REF] Davison | Iron and manganese in lakes[END_REF][START_REF] Anschutz | Chemical mass balances in metalliferous deposits from the Atlantis II Deep (Red Sea)[END_REF][START_REF] Crowe | The biogeochemistry of tropical lakes: A case study from Lake Matano, Indonesia[END_REF].

Succession of reactions during the redox oscillations.

4.4.1. Fe reactivity with oxygen, sulphur and nitrate. The collapse of dissolved iron during the aeration periods suggests that dissolved Fe(II) was rapidly oxidized to a Fe(III) non soluble species. In the Arcachon experiment, an accidental oxygenation occurred between day 4 and day 7 and about 420 µmol L -1 of iron precipitated. As the concentration of particles was 93 g L -1 , this new Fe(III) phase represented an addition of 4.5 µmol g -1 of Fe-asc to the solid fraction. Given the analytical precision, this change was undetectable compared to the initial concentration of 180 µmol g -1 of Fe-asc. However, this accidentally removed fraction was rapidly recovered once the conditions became anoxic again, since the concentration of dissolved iron reached 417 µM on day 10. This suggests that the freshly precipitated Fe(III) phase, but not the initial Fe-asc fraction, was very reducible with a fast kinetic of reduction [START_REF] Bonneville | Microbial reduction of iron(III) oxyhydroxides: effects of mineral solubility availability[END_REF]. The fast recovery of dissolved iron did not match with a simultaneous increase in dissolved ammonium, which suggests that the electron donor for iron reduction was not in organic matter assuming that organic matter mineralization would have logically produced ammonium. The Fe(III) may have been reduced by FeS because even if dissolved sulphide was not detected, some FeS may have remained in the slurry after the oxidation accident, as the oxidation rate of this species with O 2 is about three orders of magnitude lower than the oxidation of Fe 2+ with O 2 [START_REF] Millero | The oxidation kinetics of Fe( II) in seawater[END_REF]Wang and VanCappellen 1996). After several days of oxic conditions, dissolved Fe 2+ appeared again during the last anoxic cycle in the Arcachon lagoon slurry but its increase was slower than after the accidental oxidation event, which suggests that the rate of Fe(III) phase reduction depended on the time of exposure to dissolved oxygen. In the Adour sediment, the 40 µM of dissolved Fe 2+ dropped immediately to zero as conditions became oxic. However, because nitrate accumulated in pore waters, dissolved reduced iron could not be recovered when the conditions became again oxygen-free.

P availability constrained by

Fe. Dissolved inorganic P collapsed down to zero in the Arcachon lagoon sediment during the first accidental oxidation event and did not reach its initial value, despite the reduction of Fe-ox when the conditions became anoxic again. On the contrary in the estuarine slurry, DIP did not drop to zero during the oxic period. The scavenging of P by Fe-ox is a well known process (e.g., [START_REF] Lijklema | Interaction of orthophosphate with iron(III) and aluminum hydroxides[END_REF][START_REF] Sundby | The phosphorus cycle in coastal marine sediments[END_REF].

The molar ratio between oxidized Fe and scavenged P was much higher in the Arcachon slurry (423/10.7 = 39.5) than in the Adour slurry (45/9 = 5), indicating that the capacity of fresh Fe-ox to sequester P was much higher than available P in the Arcachon sediments.

Therefore, P liberated from the reduction of a part of fresh Fe(III) and from organic matter mineralization was probably directly trapped on remaining Fe(III) phases. In the Adour slurry, newly formed adsorption site of precipitated Fe-ox were probably saturated with phosphate because of the low Fe/P ratio. This most likely explains why DIP was not titrated during oxic periods.

4.4.3. Mn reactivity constrained by oxygen and Fe. Dissolved Mn concentrations decreased slowly during oxic periods, due to the slow kinetics of Mn 2+ oxidation at the pH of the slurries [START_REF] Morgan | Manganese in natural waters and Earth's crust: its availability to organisms[END_REF] even if the presence of Mn-ox catalyses the rate of Mn(II) oxidation [START_REF] Davies | Manganese(II) oxidation kinetics on metal oxide surfaces[END_REF]. Mn-ox content was very low in the Arcachon lagoon slurry, which may explain the very low decrease in dissolved Mn during the oxic period.

Nevertheless, we observed a fast decrease at the beginning of this oxic period, when dissolved Fe collapsed, suggesting that the Fe(III) phase that precipitated trapped dissolved P, and probably a fraction of dissolved Mn too. Similarly, in subsurface anoxic sediments, the Mn(II) that is produced by reductive dissolution of manganese oxides can be in part adsorbed onto sediment particles and released to the porewater ( [START_REF] Van Der Zee | Absorbed Mn 2+ and Mn redox cycling in Iberian continental margin sediments (northeast Atlantic Ocean)[END_REF][START_REF] Sundby | Transient state diagenesis in continental margin mud[END_REF].

Adsorption occurs more rapidly than oxidation and allows a fraction of dissolved manganese to be trapped [START_REF] Richard | Kinetics of manganese adsorption, desorption, and oxidation in coastal marine sediments[END_REF]. In the Adour sediments, dissolved Mn was quantitatively removed during the oxic period, and then it was partly recovered after the day 12. The initial high concentration of Mn-asc probably accelerated the rate of Mn 2+ oxidation, which may explain the difference in Mn 2+ decrease between both slurries.

In Arcachon sediments ammonium accumulated in waters during anoxic periods. It did not decrease during oxic conditions. Nitrate appeared after a few days of oxic conditions probably from particulate organic nitrogen oxidation, not from nitrification of ammonium, which seemed to be inhibited. Nitrate was reduced rapidly under anoxic conditions. The increase in the slope of ammonium concentration while nitrate decreased suggests that dissimilative reduction of nitrate to ammonium (DRNA) occurred. The slight decrease in DIN concentration between day 19 and day 20 also suggests that denitrification or anammox process occurred at the beginning of the second anoxic period. In the Adour estuary slurry ammonia was quantitatively oxidized to nitrate in the presence of O 2 . Under anoxic conditions after day 10 nitrate remained in solution and even increased. This suggests that anoxic nitrification occurred. Thermodynamic calculation indicates that in absence of dissolved oxygen, anoxic nitrification only is possible in the presence of Mn-ox, which is the case for the Adour estuary slurry experiment. [START_REF] Javanaud | Anaerobic ammonium oxidation mediated by Mn-oxides: from sediment to strain level[END_REF] showed that the bacteria strain M4AY14 only expressed anaerobic nitrification when Mn-ox were present at ranges equal to or higher than those of nitrate. Nitrate is supposed to be ultimately denitrified, but denitrification was not complete in the Adour experiment, because it was most likely limited by labile organic matter availability.

Summary

To recap, the differences in the succession of redox processes between the two incubation experiments was probably partly explained by the nature of organic matter as an electron donor, but it was also explained by the coupling between transition metal redox cycle and nutrient cycle. In one case water accumulated ammonium when Mn-ox was lacking and in the other case waters accumulated nitrate in the presence of Mn-ox. In Mn-ox depleted sediment, we can propose that there is no anaerobic oxidation of NH Marine sediments generally contain manganese oxides in the oxic layer and their advection to the suboxic zone is ubiquitous in the coastal zone, because bioturbation takes place across the redox boundary or the oxygen penetration depth oscillates daily or seasonally. It also occurs frequently in deep sea sediments (e.g. [START_REF] Gobeil | Diagenetic separation of cadmium and manganese in suboxic continental margin sediments[END_REF]. Several studies reported that the concentration of nitrate was not actually at zero below the layer of denitrification. Our investigation shows with an amplified experimental approach that anoxic nitrate production is linked to the presence of Mn-oxides. Because of this suboxic nitrate production, the oxidation of Fe(II) coupled to nitrate reduction occurs efficiently in the suboxic layer of a sediment and inorganic phosphorus is consequently trapped on authigenic Fe(III) particles. Sediments depleted in Mn-oxides are atypical, but can be found in some coastal environments like the Arcachon lagoon and sandy beach sediments. In such sediment, ammonium may accumulate preferentially in the oscillating or the bioturbated layer and dissolved iron can accumulate as well in the absence of oxygen as anaerobic nitrate production does not occur. DIP is not trapped under suboxic conditions but when shifted toward oxic conditions, such sediment then represents an effective trap of DIP powered by rapid and substantial Fe-ox authigenesis.

Conclusions

Oscillating redox experiments allowed us to examine changes in water compositions that match with thermodynamic calculations. The Mn-N-Fe coupling outlined here, and deserving further investigations, is an apparent indirect oxidation of Fe(II) by Mn-ox through anaerobic nitrification (with Mn-ox) and denitrification (with Fe-ox). The presence or absence of reactive manganese oxide represents a major variable of the evolution of a redox oscillating sediment, because Mn-oxides intervene in the N cycle, which plays a part in the Fe cycle. The redox Fe cycle ultimately determine the DIP availability. Therefore the initial content of Mnoxide, or the input of new Mn-oxide in an oscillating environment may partly determine the speciation and the availability of nutrient in natural pore waters.

Table 1. Averages (±SD) of the biogeochemical parameters measured in the solid fraction of the Adour and the Arcachon sediments used for the incubations. Adour estuary slurry Arcachon lagoon slurry Organic carbon (dry weight %) 3.2 ± 0.1 4.2 ± 0.1 Mn-asc (µmol g -1 ) 9.8 ± 1.0 1.4 ± 0.2 Fe-asc (µmol g -1 ) 47.0 ± 5 180.0 ± 20 P-asc (µmol g -1 ) 9.8 ± 1.5 11.0 ± 2.0 [START_REF] Robie | Thermodynamic properties of minerals and related substances at 298.15°K and 1 Bar (10 5 Pascals) pressure and at higher temperatures[END_REF] and [START_REF] Stumm | Aquatic Chemistry[END_REF] 2. The grey area shows the range of pH during the redox oscillation experiments. All these reactions may be associated in pairs. The energy yield is favourable when the oxidant species of a redox reaction is that of the half reaction that has the highest logK, and the electron donor species is that of the half reaction with the lowest logK.

Figure caption

The total free energy of pairs of half-redox is proportional to the vertical distance between the two lines (∆G°r = -∆(∆log K) × (RT ln10))

Figure 1 :

 1 Figure 1 : Experimental set-up for incubation of the slurries in oxic or anoxic conditions.

Figure 2 :

 2 Figure 2 : Evolution with time of concentration of redox-sensitive species in the Arcachon

Figure 3 :

 3 Figure 3: Variation of log K (∆log K) with pH and an activity of 10 -4 for Fe 2+ and Mn 2+ for

Table 2 .

 2 Half-redox reactions written with one electron transfer with the electron on the left side of the reaction and equilibrium constant (p° or LogK) at standard state condition (1M in all species)

	Half redox reaction			p° (LogK)
	1/4 CO 2 + H + + e -	1/4 CH 2 O+ 1/4 H 2 O	-0.20
	1/4 O 2 + H + + e -	1/2 H 2 O		20.78
	1/5 NO 3	-+ 6/5 H + + e -	1/10 N 2 + 3/5 H 2 O	21.03
	1/3 NO 2	-+ 4/3 H + + e -	1/6 N 2 + 2/3 H 2 O	25.54
	1/8 NO 3	-+ 5/4 H + + e -	1/8 NH 4 + + 3/8 H 2 O	14.88
	1/2 MnO 2 + 2 H + + e -	1/2 Mn 2+ + H 2 O	20.78
	MnO(OH) + 3 H + + e -	Mn 2+ + 2 H 2 O	25.34
	Fe(OH) 3 + 3 H + + e -	Fe 2+ + 3 H 2 O	18.28
	FeO(OH) + 3 H + + e -	Fe 2+ + 2 H 2 O	13.60
	1/8 SO 4 2-+ 5/4 H + + e -	1/8 H 2 S + 1/2 H 2 O	5.08
	1/8 CO 2 + H + + e -	1/8 CH 4 + 1/4 H 2 O	2.86
	1/6 N 2 + 4/3 H + + e -	1/3 NH 4 +	4.64
	1/6 NO 2	-+ 4/3 H + + e -	1/6 NH 4 + + 1/3 H 2 O	15.09
	1/2 NO 3	-+ H + + e -	1/2 NO 2	-+1/2 H 2 O	14.27
	LogK derived from

Acknowledgements

Dominique Poirier and Marion Falco are warmly acknowledged for help in the analyses. This research was supported by the Aquitaine region and the MERCIS project supported by the French national program "Ecosphere Continentale" (INSU-ECCO, ACI/ANR). S.B. acknowledge the French Minister of Education and Research for PhD fellowships.


H Maiz

Hadj Ahmed

H Benaissa

A Zaoui
email: azaoui@polytech-lille.fr

M Ferhat

Exploring new insights in BAlN from evolutionary algorithms ab initio computations

Keywords: B x Al 1-x N alloys, evolutionary algorithm, density functional theory (DFT), mechanical, dynamical and optical properties, optical band gap bowing parameter

BN-AlN alloys are potential candidates to achieve wide band gap material for ultraviolet device applications. By combing density functional theory and evolutionary structure predictions, we systematically explore the thermodynamic, mechanical, dynamical and optical properties of B x Al 1-x N alloys. Through structure search, three compounds (cubic (BAl 3 N 4 , and B 3 AlN 4 , space group P-43m), and tetragonal (BAlN 2 , space group P-42m)) have been predicted. The calculated relative large formation enthalpies suggest that large miscibility gap exists in BAlN alloys. In addition, computed elastic constants and phonon show that these structures are mechanically and dynamically stable. From the state of the art LDA-1/2 we show that the direct band gap of BN-AlN evinces strong deviation from a linear dependence on B composition. We found -in particular-giant direct band gap bowing parameter of b∼11.6eV for the entire range of composition, where b parameter is found to be sensitive to composition x. From a detailed analysis of the physical origin of the optical gap bowing b, we found that structural and chemical contributions play the most significant effects behind the huge optical band gap bowing parameter of BAlN alloys.

Introduction

InGaN and AlGaN ternary III-V alloys based on wurtzite AlN, GaN and InN have recently revolutionized lighting industry and paved the way for efficient visible and ultra-violet light emitting diodes (LEDs). This was awarded the 2014 Nobel price of Physics.

Compared to the well-studied III-V-N (AlGaN, InGaN, AlInN) alloys, the research involving common-anion nitride based ternary alloys such as B x Al 1-x N is still at its early stage. Recently wurtzite BAlN alloys have been the subject of several experimental [1][2][3][4] and theoretical [5][6] studies.

A fundamental property while designing optoelectronic devices of semiconductors alloys is the variation of the fundamental direct energy gap E g (x) with composition x, which is a prerequisite for band gap engineering in order to fulfill devices applications. Unfortunately the variation of E g (x) differs from the simplest Vegard's linear 'law', but has a quadratic form, i.e., it exhibits bowing parameter b. Traditionally to model such alloys, two methods are currently used: (i) virtual crystal approximation (VCA), and (ii) supercells methods. Methods such as VCA are disqualified for any serious study of semiconductors alloys [7]; whereas by means of methods such as (ii) accurate results can -in principle-be obtained with large supercells. Nevertheless, such an approach requires very large supercells [8][9][10][11][12][13] to adequately reproduce the statistics of random alloys.

In the present study, we opted for a novel strategy to describe accurately the band gap dependence on B composition of B x Ga 1-x N alloys. We use an evolutionary algorithm within the density functional theory (DFT) to find all possible stable phases in the BAlN alloys at ambient conditions. We also analyse the band gaps and the optical band gap bowing parameter of BAlN alloys. In addition, the mechanical and dynamical properties of BAlN alloys will be also discussed.

Computational details

Using the evolutionary algorithm approach as implemented in Material project database [14][15] we explore all possible state phases of BAlN alloys. In the framework of density functional theory (DFT) [16] using a plane-wave basis set. The underlying total-energy calculations were carried out by the Quantum ESPRESSO Package code [17]. The exchangecorrelation term was approximated by the linearized density approximation (LDA) [18]. The interaction between the ions and the electrons are described by the projector-augmented wave pseudopotential scheme (PAW) [19]. We used a plane-wave energy cut-off of 65 Ry, and an energy cut-off of 600 Ry was included for the charge density. The Brillouin zone integrations was sampled at a higher level of accuracy using a finer Monkhorst-Pack [MP] [20] mesh of 10×10×8 for BAlN 2 and 12×12×12 for BAl 3 N 4 and B 3 AlN 4 . The phonon properties are calculated using the density functional perturbation theory (DFTP) [21]. A 4 × 4 × 3, 2 × 2 × 2, and 2 × 2 × 2 q-points MP mesh has been used to perform inverse Fourier transformation for BAlN 2 , BAl 3 N 4 , and B 3 AlN 4 respectively. The atomic positions, lattice parameters and cell volume were fully relaxed until the forces on each atom were less than 1meVÅ -1 . The total energy was converged to within 1meV/cell.

Results and Discussion

The analysis of the evolutionary algorithm gives a list of three candidate phases of B x Al 1-x N alloys: BAl 3 N 4 (x = 0.25, cubic phase, space group P-43m), BAlN 2 (x = 0.5, tetragonal phase, space group P-4m2), and B 3 AlN 4 (x = 0.75, cubic phase, space group P-43m). For all the predicted structures shown in Figure 1, the corresponding structural information is listed in Table I.

The calculated lattice constant a, and c/a ratio of wurtzite (WZ) BN and AlN are in good agreement with experimental measurements. Figure 2 displays the variation of the lattice parameter a and the lattice constant ratio c/a versus the composition x. Small deviations from Vegard-like law is found. The calculated bowing for a and c/a are ∼0.11Å and ∼0.60 respectively.

Thermodynamic stability of BAlN alloys is quantified by determining the alloy mixing enthalpy defined as:

∆H = E(x) -(1-x) E(AlN)-x E(BN)
Where E(x) is the total energy of the alloy at composition x, and E(AlN) and E(BN) are the total energy of WZ AlN and BN respectively. Figure 3 shows the alloy formation enthalpy ∆H. The positive sign of ∆H indicates that the ground state of these alloys at T = 0 corresponds to a tendency to phase separation into pure WZ constituents BN and AlN.

Moreover, the magnitude of ∆H is relatively strong (i.e., for x = 0.5, ∆H = 170meV) suggesting that large miscibility gap can exist in this system.

The mechanical properties of BN-AlN alloys were further studied. The calculated elastic constants C ij of wurtzite BN and AlN compounds and BAlN alloys are presented in Table II.

The WZ phase of BN and AlN, which have a stable phase at room temperature, meet the mechanical stability criteria. Furthermore, the calculated elastic constants of BAl 3 N 4 , BAlN 2 , and B 3 AlN 4 compounds satisfy also the Born stability criteria.

The bulk modulus B 0 (calculated from the elastic constants), shear moduls (G), Young's modulus (E) and Poisson's ratio (ν) are given in Table III. Figure 4 manifests the change of E, B 0 and G with composition x. The composition dependence of B 0 is sublinear; whereas G, and more precisely E, shows significant superliner dependence on composition (i.e., strong deviation from VCA). Moreover, the Poisson's ratio ν is found rather relatively indifferent with respect to composition x. In order to evaluate the ductility of the material, the B 0 /G values were calculated and are listed in Table III. Higher B 0 /G values greater than 1.75 corresponds to a ductile material; while values less than 1.75 correspond to a brittle material.

As shown in Table III, except AlN which indicate that this compound is a borderline material, for all other phases B 0 /G values are less than 1.75, which reflects a brittle characteristic of those compounds.

The dynamical stability of cubic (BAl 3 N 4 , and B 3 AlN 4 ) and tetragonal (BAlN 2 ) phases of BAlN alloys was tested from the calculation of the phonon dispersion curves along the highsymmetry lines (Figure 5). All frequencies are real, i.e., no imaginary phonon frequencies are found in the whole Brillouin zone for all phases, indicating the dynamical stability of BAl 3 N 4 , BAlN 2 and B 3 AlN 4 ordered structures of BN-AlN systems.

Here we discuss the band gap dependence of B x Al 1-x N on B composition. It is well known that DFT underestimates severely the band gap by 50%-100%, that's why we used the LDA-1/2 method [28]. This approach competes well with more advanced method such as GW quasiparticle approach [29]. We obtain a direct band gap of 6.16eV (Γ→Γ) for WZ AlN that is within the range of experimentally measured gaps (6.19eV [30], 6.23eV [22]). For WZ BN, we obtain a direct Γ→Γ (indirect, Γ→K) band gap of 10eV (7.18eV). No experimental data are available so far. However, our calculated indirect band gap is close to GW calculations of 6.86eV [31] and scissor operator method of 6.8eV [5].

Figure 6 shows the resulting calculated change of direct band gap energy E g (Γ→Γ) for B x Al 1-

x N alloys as function of composition x. The band gap bowing representing the deviation from a linear interpolation of the component band gaps of BN and AlN was calculated according to:

E g (x) = (1-x) E g (AlN)-x E g (BN)-b x (1-x)
The values of E g (x) deviates from the linear behavior (i.e., the Vegard's law) and is characterized by the bowing parameter b. The band gap bowing parameter for the direct band gap is found giant (b = 11.62eV) for the entire range of composition. The calculated b is similar to other III-V-N mixed anion semiconductors (e.g., GaAsN, InAsN… [7,22]). This is in contrast to common III-V semiconductors (e.g., GaAlAs), where it is relatively weak and composition-independent. Our results are consistent with the calculated bowing parameter of 8.55eV [6].

To understand the physical origins of b (i.e., having structural and electronic components), we determine the three physically distinct contributions of b [8]: volume deformation (VD), charge exchange (CE) and structural relaxation (SR). The VD term represents relative response of (AlN)BN to hydrostatic pressure from their equilibrium volume V GaN (V BN ) to the alloy V(x). The CE term is related to a charge transfer in bringing AlN and BN at V=V(x), and the SR term describes the change of the gap upon passing from the unrelaxed to the relaxed alloy, i.e., V(x)→V eq . The total optical band gap bowing is b=b VD +b CE +b SR . At x = 0.

Conclusion

In summary, a systematic search for stable compounds in BN-AlN alloys has been carried out using ab initio evolutionary algorithm. We have uncovered three structures, cubic BAl 3 N 4 (space group P-43m) and B 3 AlN 4 (space group P-43m) and tetragonal BAlN 2 (space group P-4m2). All those phases are thermodynamically unstable but mechanically and dynamically stable. State-of-the-art LDA-1/2 approach was used to determine the direct band gap of B x Al 1- x N alloys. We found an extreme optical band gap bowing parameter of b∼11.6eV over the entire range of composition. Furthermore b is found composition-dependent. Our analysis evidences that b parameter for x = 0.5 mainly arises from structural and chemical effects. b Ref. [23]. b Ref. [START_REF] Kim | [END_REF].

Table Captions

Table II

  5, we found b VD = 4.88eV, b CE = 3.64eV, and b SR = -0.01eV yielding a total bowing parameter of 8.51eV. The volume deformation contribution b VD is giant and can be correlated to the large mismatch of the lattice constants a of BN and AlN (∼20%). The chemical electronegativity term b CE is strong and scale with the strong electronegativity mismatch between B and Al atoms. Using Pauling"s electronegativities of 2.04 and 1.5 for B and Al atoms respectively, we have an electronegativity mismatch of 0.54 for B-Al. The bowing contribution due to the structural relaxation term b SR is negligible. As found previously, b SR gives weak contribution to mixed cation alloys [8]. According to our calculated total optical band gap bowing parameter at x = 0.5 (b = 8.51eV) and b∼11.6eV for the entire range of composition, we can expect that b depends strongly on composition x.

Figure 1 :

 1 Figure 1: Crystal structures of B x Al 1-x N alloys: a) WZ-AlN, b) BAl 3 N 4 , c) BAlN 2 , d) B 3 AlN 4

Figure 2 :

 2 Figure 2: Calculated lattice constant a, lattice ratio c/a of B x Al 1-x N alloys as function of B

Figure 3 :

 3 Figure 3: Calculated formation enthalpy of B x Al 1-x N alloys.

Figure 4 :

 4 Figure 4: Calculated bulk modulus B 0 (GPa), Young's modulus E (GPa), and shear modulus

Figure 5 :

 5 Figure 5: Phonon band structure and phonon density of states (PDOS) of a) BAl 3 N 4 , b)

Figure 6 :

 6 Figure 6: Band gap dependence of B x Al 1-x N on B composition.

2 Figure 3 Figure 4

 234 Figure 1

Figure 6

 6 Figure 6

Table I :

 I Calculated equilibrium structural parameters, for AlN, BAl 3 N 4 , BAlN 2 , B 3 AlN 4 and BN.

Table II :

 II Calculated elastic constants (in GPa) of AlN, BAl 3 N 4 , BAlN 2 , B 3 AlN 4 and BN.

Table III :

 III Calculated bulk modulus B 0 (in GPa), Young's modulus E (GPa), shear modulus G (in GPa), Poisson's ratio ν (GPa) and B 0 /G.

Table I

 I

	Phase	a(Å)	c/a	Space group
	AlN	3.088	1.600	P6 3 mc
		3.112 a	1.601 a
	BAl 3 N 4	4.162		P-43m
	BAlN 2	2.774 1.475	P-4m2
	B 3 AlN 4	3.791		P-43m
	BN	2.525	1.653	P6 3 mc
		2.553 b	1.656 b

a Ref.

[22]

.

Table III

 III

		B 0	E	G	ν	B 0 /G
	AlN	212(208 a ) 311	124	0.25	1.71
	BAl 3 N 4	246	380	153	0.24	1.61
	BAlN 2	282	460	187	0.23	1.51
	B 3 AlN 4	332	612	257	0.19	1.29
	BN	402(410 b ) 908	404	0.12	0.99

a Ref.

[26]

.

b Ref.

[27]

.