Erwan Roussel

Romain Crec'hriou

Philippe Lenfant

Julien Mader

Serge Planes
email: planes@univ-perp.fr

Relative influences of space, time and environment on coastal ichthyoplankton assemblages along a temperate rocky shore

Keywords: ichthyoplankton, variation partitioning, environment, time, space, NW Mediterranean, nearshore ichthyoplankton, nearshore, variation partitioning, environment, time, space, NW Mediterranean

Fish egg and larval assemblages, and the factors that drive them in the nearshore environment remain largely unknown. In this study, two sampling methods were used to assess the relative influences of space, time and environment on ichthyoplantkon communities at nearshore stations, near the Cerbère-Banyuls Marine Protected Area (France), during spring and summer 2003. Resulting datasets were analyzed by variation partitioning, with redundancy analysis to estimate variance fractions based on adjusted R². A total of 42 environmental descriptors were considered for the analyses. The descriptors that best explained the variance of the dataset were selected to build models. Analyses of the relative influences show that the environmental conditions drive egg and larval density variations, specifically depth, currents and wind directions. However, time and space combined with environmental factors also contribute substantially to ichthyoplankton variability. The combined effect of space and environment is likely to be generated by the influence of the coast profile on ichthyoplankton from shallower water. At deeper stations, wind and current fluctuations result in a combined effect of time and environment in relation to eggs. These results strongly suggest that the nearshore area influence is between 25 and 30m depth and is separated from the inner continental shelf. We propose the hypothesis that the rocky shore ecosystem is favorable for coastal accumulation and/or retention of ichthyoplankton.

INTRODUCTION

Survival of fish offspring and their subsequent addition to existing populations is the result of a complex life history [START_REF] Sponaugle | Predicting selfrecruitment in marine populations: Biophysical correlates and mechanisms[END_REF]. Spawning marine fishes release their gametes and progeny into a naturally fluctuating environment. Therefore, survival depends on how the surrounding water mass characteristics meet their requirements for development and growth [START_REF] Cushing | The natural regulation of fish populations[END_REF]. In addition, fishes in their early stages are passive drifters, and hence the probability of them being placed in a favourable habitat is also linked to the local current circulation [START_REF] Cushing | Hydrographic containment of a spawning group of plaice in the Southern Bight of the North Sea[END_REF].

Favorable conditions for young fish development are defined by biological and physical factors. Biological factors that have been identified include predation [START_REF] Pepin | Early life history studies of prey-predator interactions: quantifying the stochastic individual responses to environmental variability[END_REF]) and food availability [START_REF] Fortier | Export production and the distribution of fish larvae and their prey in a coastal jet frontal region[END_REF][START_REF] Sclafani | Osmoregulation, nutritional effects and buoyancy of marine larval fish: a bioassay for assessing density changes during the earliest life-history stages[END_REF]. Several physical factors have also been reported as influencing ichthyoplankton abundance, such as temperature, salinity, winds and currents (e.g. [START_REF] Lee | Influence of Florida Current, gyres and wind-driven circulation on transport of larvae and recruitment in the Florida Keys coral reefs[END_REF][START_REF] Grothues | Larval fish assemblages and water mass history in a major faunal transition zone[END_REF][START_REF] Bergenius | Environmental influences on larval duration, growth and magnitude of settlement of a coral reef fish[END_REF][START_REF] Fossheim | Interactions between biological and environmental structures along the coast of northern Norway[END_REF][START_REF] Alemany | Influence of physical environmental factors on the composition and horizontal distribution of summer larval fish assemblages off Mallorca island (Balearic archipelago, western Mediterranean)[END_REF][START_REF] Knutsen | Egg distribution, bottom topography and small-scale cod population structure in a coastal marine system[END_REF]. These environmental factors also change according to the spatial and temporal scale considered [START_REF] Sanvicente-Añorve | Temporal and Spatial Scales of Ichthyoplankton Distribution in the Southern Gulf of Mexico[END_REF].

The surroundings in which ichthyoplankton evolve are the product of multiple influences of space, time and environment. Egg and larval densities change with the environment, and both ichthyoplankton and environmental factors change in time and in space. Space-time integration is the key to the understanding of many of the ecological processes driving population dynamics, since the underlying processes also vary in space and time [START_REF] Koenig | Spatial autocorrelation of ecological phenomena[END_REF]. Along rocky shores, one example of site-specific environmental characteristic changing with time is that of the topographically generated long-shore currents (hence spacedependant). These currents are also wind-driven and may vary with time. The dynamics of these currents has been shown to significantly alter the distribution of many planktonic organisms in coves, while they did not do so on an open coastline [START_REF] Shanks | Topographically generated fronts, very nearshore oceanography, and the distribution of chlorophyll, detritus, and selected diatom and dinoflagellate taxa[END_REF].

The coastal or nearshore area is generally defined as extending from the shore to the 20m isobath. At this depth, the surface and bottom Eckman layer are confounded [START_REF] Werner | The role of hydrodynamics in explaining variability in fish populations[END_REF]. These limits often correspond to the width of the long-shore current. In contrast to offshore areas such as the continental shelf or slope, ichthyoplankton in temperate nearshore areas has only been investigated more recently [START_REF] Bordehore | Composición y variabilidad del ictioplancton costero en la Reserva Marina de Tabarca, SE Ibérico[END_REF][START_REF] Sabatés | Larval fish communities in the Medes Islands Marine Reserve (North-west Mediterranean)[END_REF][START_REF] Koutrakis | Temporal patterns of larval fish distribution and abundance in a coastal area of northern Greece[END_REF][START_REF] Beldade | Depth distribution of nearshore temperate fish larval assemblages near rocky substrates[END_REF][START_REF] Borges | Horizontal spatial and temporal distribution patterns of nearshore larval fish assemblages at a temperate rocky shore[END_REF]. As a result, very little is known about the relationships between environmental factors and fish eggs and larval abundance [START_REF] Hernandez-Miranda | Larval fish assemblages in nearshore coastal waters off central Chile: temporal and spatial patterns[END_REF]Azeitero et al., 2006). The coastal habitat is thought to provide more suitable conditions for fish eggs and larval survival than the other open sea areas [START_REF] Myers | Recruitment variability and oceanographic stability[END_REF], because of higher water mass stability and higher food availability [START_REF] Laprise | Factors influencing the spatio-temporal occurrence of fish eggs and larvae in a northern, physically dynamic coastal environment[END_REF]. Published studies on eggs and larval distribution over the continental shelf that included the inner-shelf zone (above 20 or 30m isobath) have shown distinct ichthyoplankton assemblages in this latter region that are interpreted as a consequence of the reproductive behaviour of the adults, which is bottom type and depth related (Sabatés, 1990a;[START_REF] Sabatés | Unusual larval fish distribution pattern in a coastal zone of the western Mediterranean[END_REF][START_REF] Espinosa-Fuentes | Cross-shelf and vertical structure of ichthyoplankton assemblages in continental shelf waters of the Southern Gulf of Mexico[END_REF][START_REF] Munk | Assemblages of fish larvae and mesozooplankton across the continental shelf and shelf slope of the Andaman Sea (NE Indian Ocean)[END_REF][START_REF] Quattrini | Distribution of larval fishes among water masses in Onslow Bay, North Carolina: implications for cross-shelf exchange[END_REF], Lopez-sanz et al, 2009).

In this paper, we investigate the relationships between ichthyoplankton and the environmental factors in a rocky nearshore area of the north-western Mediterranean. We specifically addressed two questions: i) What are the relative influences of space, time and environment on ichthyoplankton structures? ii) Considering the large number of potential environmental factors, which are the ones probably driving egg and larval distributions in the near-shore area?

METHOD

Study area

The study site is located in the south of France (Fig. 1), in the vicinity of the Cerbère-Banyuls Marine Protected Area, orientated north-south, mainly straight, with some bays and capes.

Underwater slopes can be steep and fish habitats are diverse, including Posidonia meadows, coralligen, rocks and sand. Seasonality is well-marked with North-western winds blowing in January and July. South-eastern winds can be an important component in spring. The circulation is dominated by a southward long-shore current, which can reverse when strong south-eastern winds blow, limiting the cross-shelf transport [START_REF] Rouault | Etude dynamique des eaux du plateau continental dans la région de Banyuls/mer[END_REF]. Moreover, there is no upwelling and small-scale gyres can be observed in the bays that probably act as retention zones [START_REF] Guizien | Dispersal of Owenia fusiformis larvae by wind-driven currents: turbulence, swimming behaviour and mortality in a three-dimensional stochastic model[END_REF].

Sample collection

Sampling was conducted during spring and summer 2003. Two plankton sampling methods were used: Bongo nets and fixed nets, both mounted with 300 µ meshes and equipped with flowmeters (General Oceanics 2030R). The overall sampling framework consisted of 9 radial transects coupling Bongo and fixed net collection sites. For the Bongo net collections, a grid of 18 stations (Fig. 1a) divided in nine transects of two stations each from the coast (on the 20 m isobath) to offshore (on the 40 m isobath). This framework was surveyed 12 times from May 7 th to August 14 th . Bongo collections consisted of down and up oblique tows with a Bongo net, with a double 60 cm mouth opening, performed during daytime with the research vessel "NEREIS II" maintaining speed at 2 knots. The down tow was performed between the surface and a depth of 10m above the ocean floor (i.e., the "max depth") followrd by an up tow performed between this maximum depth and the surface. During this up tow, 3 horizontal tows of 5 minutes were performed at 20, 10 and 2 m depths, respectively, with the aim of targeting larvae of coastal fish species, which have been reported to be more abundant in the upper 20 m of the water column (Sabatès, 1990a, Sabatès et al., 2007). The GPS position of the vessel was recorded at the beginning and at the end of each tow, as well as at several intermediate points, in order to locate the exact position of the tow. Maximum depth of tows varied between 20m and 40 m within the sampling area. The catch of each tow (2 replicas) was sieved and fixed directly on board with 4% formalin-seawater leading to a total of 186 samples (one of the two replicas) analyzed from Bongo collections. The filtered volume was calculated by using flowmeters and the following formula:

( ) ( ) ( ) 999 . 999 . 4 14 . 3 2 const Rotor count Start count Arrival Diameter Net × - × ×
The mean volume filtered was 268 ± 70 m 3 (mean ± SD).

At the same time as the Bongo net collections, fixed plankton nets (300 µm mesh size and 60 cm mouth diameter) were deployed at 12 inshore stations regularly spaced along the coast (Fig. 1b). These nets, which are passive devices filtering and following ambient currents, were moored 10 to 20 m from the shore, on anchor lines fixed at depths ranging from 20 to 40 m, and maintained at 2 m depth in the water column with floats. This sampling technique, adapted from [START_REF] Bordehore | Composición y variabilidad del ictioplancton costero en la Reserva Marina de Tabarca, SE Ibérico[END_REF], is described in [START_REF] Crec'hriou | Fisheries replenishment of early life taxa: potential export of fish eggs and larvae from a temperate marine protected area[END_REF]. This method provided collection of fish eggs and larvae from very shallow waters in locations that could not be sampled with research vessels. Sampling with fixed nets was conducted twice a week from July, 22 nd to August, 20 th . This passive sampling was performed between dusk and dawn, as nets were deployed late in the afternoon and recovered the following morning with a total of 12-15 h of sampling daily. As currents were often low, nets were deployed with a low speed rotor on the flowmeters. During the collection of the samples, every morning, the plankton from each net was maintained alive, separately, in seawater in 5 L plastic containers.

These were sieved and fixed with 4% formalin once back at the harbor, leading to a total of 76 samples analyzed from Bongo collections. Before sieving, a random sub-sample was taken from the surface of the containers for live egg identification. Due to a technical limitation in the flowmeters' sensitivity to low currents, even with a low speed rotor, all samples with average nightly current speed lower than 2cm.s -1 were removed from further analysis. The mean volume filtered was 1185 ± 1392 m 3 . The filtered volume was very variable depending on the current speed at each location (min=199 m³, max=5984 m³).

Oceanographic data

Vertical profiles of temperature, conductivity, fluorescence and pressure from 2 m above the bottom to the surface were obtained with a SB19 CTD (Fig 1b). A moored ADCP (DCM 12, Teledyne RDI), located in the center of the area (Fig. 1b), recorded current strength and directions for the whole water column every 30 min. Wind data was kindly provided by Meteo-France. Strength and direction were recorded at 3-hour intervals at Cap Bear (Fig. 1).

Bathymetric data were collected at a 1x1m resolution using multi-beam sonar, along the French coast up to the 30m isobath. Complementary bathymetric data were extracted from a SHOM marine map (No 6843) which covers the study area.

Ichthyoplankton recovery

Fish larvae were sorted in the laboratory under a stereomicroscope and identified to the lowest taxonomic level possible (following [START_REF] Moser | Description of early stage of white Seabass, Atractoscion nobilis, with notes on distribution[END_REF]Sabatès, 1988;[START_REF] Alemany | Influence of physical environmental factors on the composition and horizontal distribution of summer larval fish assemblages off Mallorca island (Balearic archipelago, western Mediterranean)[END_REF][START_REF] Glamuzina | Early development of the hybrid Epinephelus costae ♀ X E. marginatus ♂[END_REF]. Fish eggs were sorted in the laboratory under a stereomicroscope and identified to the lowest taxonomic level possible [START_REF] Marinaro | Contribution à l'étude des oeufs et larves pelagiques de poissons mediterranéens. V-Oeufs pelagiques de la baie d'Alger. Pelagos[END_REF][START_REF] Jug-Dujakovic | Preliminary data on embryological and larval development of black scorpionfish Scorpaena porcus (Linnaeus, 1758)[END_REF][START_REF] Glamuzina | Egg and early larval development of laboratory reared dusky grouper, Epinephelus marginatus (Lowe, 1834) (Picies, Serranidae)[END_REF]. Based on this identification, eggs were classified into 12 categories (Table 1). When samples had less than 200 eggs, all eggs were identified. When eggs were more abundant, a sub-sample of at least 200 eggs was identified. Samples including more than 500 eggs were sub-sampled using a Motoda box.

Data analysis

Egg and larval abundances were divided by the volume filtered to obtain densities per 1000 m³. Rare species (i.e. present in less than 10% of the samples) were excluded. In addition, for the larvae a second selection by abundance sorting was performed to reduce the number of taxa [START_REF] Ibanez | Comparaison des evolutions a long terme (1977-1990) de deux peuplements macrobenthiques de la baie de Morlaix (Manche occidentale): relations avec les facteurs hydroclimatiques[END_REF]. This method uses an index mixing abundance and frequency of species to retain the frequent and the locally abundant taxa, and removes the others. In the first step, we used Multivariate Regression Tree (MRT; [START_REF] De'ath | Multivariate regression trees: a new technique for modeling species-environment relationships[END_REF]) at the community level to see if spatio-temporal variations are essential factors which explain an important part of the overall variability of the dataset. Results (Figure 2) show that variations between spring and summer lead to marked discontinuities in eggs and larvae. Both Bongo net datasets were split according to the season. The week has been also demonstrated to be the major temporal scale in density variations and was considered as the relevant time descriptor. As a result, six datasets were analyzed (Table 1 and2). For eggs, eight response variables (Taxa) were kept for spring for Bongo nets (n=84 samples), 11 for summer for Bongo (n=100 samples) and 10 for fixed nets (n=76 samples). A total of 14 larvae taxa were kept for Bongo nets for spring (n=70 samples), 20 for Bongo nets in summer (n=116 samples) and 13 for fixed nets (n=76 samples). Spatial distances were calculated as the metric distance given by the UTM coordinates and were centered on the origin to reduce collinearity between terms following [START_REF] Legendre | Numerical Ecology[END_REF]. Nine terms of a cubic surface trend analysis were included (X, Y, X², Y², XY, X 3 , Y 3 , X²Y and Y²X) [START_REF] Borcard | Partialling out the spatial component of ecological variation[END_REF].

To account for the environmental variation, 42 descriptors for Bongo nets and 38 for fixed nets were considered in the analyses (Table 3 andTable 4). These cover four categories:

1) Topography (Table 3): six descriptors were built for each station with the GIS (Map info Pro©) after Natural Neighbor interpolation of the bathymetric data:

-the distance to the coast and the depth were measured directly on the map.

-the average slope of the bottom, and the bottom complexity defined as the total length of the isobaths divided by the number of isobaths, to account for slope artifacts. Both derived from data taken in a 200 m radius circle from the station. This radius was found to yield a greater variability of highest coefficient of variation (CV around 0.30) of the three distances tried (100, 150 and 200 m) and found to be homogeneous between Bongo and Fixed nets.

-the coast profiles at small and large scale were used to characterize the topographic features of the coastline (bays, capes and straight lines). They were calculated as the percentage of land in a circle around the station, multiplied by the ratio shore length/circle perimeter to account for shore complexity artifacts. A 600 m and 2500 m radius circle was used for small and large scale respectively, centered on the perpendicular intersection between the shore orientation and the distance from the station to the coast. The small scale distance corresponded to the maximum distance from the nearshore stations to the coast, the large scale distance to the radius of the biggest topographic feature of the area (Banyuls Bay). 2) Hydrology (Table 4): Temperature, salinity, density, and fluorescence were measured with the CTD. For each parameter, six descriptors were considered: values at 1 m, 10 m and 20 m depth, the average of the whole water column, the average in the subsurface layer (0.5-2 m depth) and the average above the pycnocline. The latter was determined visually from the CTD profiles for each transects and each sampling date. A total of 25 descriptors were collected in this category.

3) Winds (Table 3) and4) Currents (Table 3): As wind and current directions could not be included in community analyses because of their circular nature, they have been transformed into five categories: NE for directions 10-90°, SE for directions 90-180°, SW for directions 180-270°, NW for directions 270-360° and variable. Two time scales were taken into account for each of the four descriptors of wind, current strength and direction: The first was the average on the day when sampling occurred. The second is the average over three days before and during the sampling date. Current strength was measured at 1 m depth for both Bongo and fixed nets. As the whole water column was sampled with Bongo nets, with a longer sampling duration in the upper layer, another descriptor was added for these datasets by compiling the mean of three depths (2 m, 3 m and 4 m). Subsequently there were four descriptors for wind, while there are four currents descriptors for fixed nets and eight for Bongo nets.

Redundancy analyses (RDA) were used to analyze the partitioning of variance between spatial, temporal and environmental components, following [START_REF] Anderson | Partitioning the variation among spatial, temporal and environmental components in a multivariate data set[END_REF]. This is an extension of [START_REF] Borcard | Partialling out the spatial component of ecological variation[END_REF] to three matrices or more. Before running the analyses, all spatial and environmental descriptors were submitted to several stepwise procedures known as forward selection, which adds environmental variables one at a time, until no other variables "significantly" explain residual variation in species composition. We added the constraint that no more than six explicative variables per source of variation (i.e. environment and space) were included in the models, and selected ones producing models explaining the higher total variation. Following [START_REF] Legendre | Ecologically meaningful transformations for ordination of species data[END_REF], a Hellinger transformation was applied to the species as it ensures the applicability of RDA in data containing zero results (long environmental gradient). Finally, the estimation and comparison of variance fractions was based on the adjusted R², since it is the only unbiased estimator of variance components in canonical analyses [START_REF] Peres-Neto | Variation partitioning of species data matrices: estimation and comparison of fractions[END_REF].

Analyses were performed using the software Brodgar® (Highland Statistics Ltd), GeoDa™ (Luc Anselin) and R software (R Development Core Team, 2007).

RESULTS

Environmental conditions

Topographic descriptors associated with each station are given in Table 5 for both sampling methods. Coast profiles (CP) quantitatively describes topographic features such as capes, bays and straight coastlines in front of nearshore stations. At the small scale, all coast profiles (except the northern most station) corresponded to capes (CP <0.30). At the large scale, coastal profiles indicate two capes (Bongo stations 4 and 19 in Fig. 1) and two bays (CP >0.60, Bongo stations 7 and 25). All other stations are located in front of straight coast profiles (0.30< CP <0.60). At the Bongo stations, slopes were steeper for the coastal stations (mean=6.85, SD=1.98) than for the shelf stations (mean=2.51, SD=1.62) with a maximum in the north (slope=10.83°). Results are very similar for the fixed nets stations. Bottom complexity values for the Bongo stations (mean=239, SD=71, min=147, max=388) and for the fixed net stations (mean=287, SD=86, min=148, max=406) showed that the bottom was more complex in the north and around Cape Cerbère (Bongo station 19), and that there was no difference between coastal and shelf stations.

During May, temperature, salinity and density were stable (T=15-17 °C, S=37.8 psu and σ t < 28.5) and homogenous in the water column with little subsurface variation (Fig. 3.I). In early June (Fig. 3.II), variations of temperature and salinity were marked and the upper layer (0-10m depth) less saline. The stratification appeared first in the north, as shown by the pycnocline at 5-15m depth. By late June, salinity variations decreased but temperature variations still persisted, and a second, deeper, pycnocline appeared at 20-25m depth (Fig.

3.III).

The upper layer (0-10m depth) was already homogenous. From July, the stratification was stable: the upper layer extended (0-20m depth) and was homogenous above the pycnocline. Temperature variations were notable above the pycnocline but salinity changes occurred only at the pycnocline depth. During summer, surface temperature reached 25°C and salinity was stable at 38.4 psu, while the pycnocline depth only exhibit noticeable variations below 25m depth in late July at the southern stations, rising to 5-15m depth in August.

Fluorescence levels were generally low. Few variations in time or space were recorded. However, from the establishment of the pycnocline and during the following 2-3 weeks (late June-early July) high values of fluorescence were observed in the deeper layer. The gradient began exactly at the pycnocline depth and increased toward the bottom for almost all stations.

Later in summer, this feature was observed again but much more sporadically.

Wind and current data during the study period are shown in Figure 4. Most of the time, the study area experienced northern winds (Fig. 4a), with greater strength in spring than in summer. Southerly wind events were much less frequent, localized and had less intensity.

Currents recorded at 3m depth generally followed the wind patterns (Fig. 4c). However, two differences were noted: northward current speeds were similar to those of southward currents, and northward events lasted longer for current than wind. In addition, transitional currents between northward and southward flows were almost always westward, i.e. in the direction of the shore. Subsurface currents (1m depth) were much more variable in direction (Fig. 4b). On average they were also 2.5 times stronger than recorded at 3m depth.

Eggs and larvae

Around 275,000 eggs were sorted, of which 42,000 were identified. Larvae were identified to the lowest possible taxa. Over 43,000 larvae were identified in Bongo net samples and over 23,000 in fixed net samples.

Egg and larval spatio-temporal assemblages are shown in Tables 1 and4 respectively.

The two most abundant egg categories are Coris julis and category 9 in both Bongo and fixed nets. Anchovies (Engraulis encrasicolus) and category 7 are also found in abundance in the Bongo nets. Dusky grouper (Epinephelus marginatus) and Scorpaena sp. were frequently caught in the fixed nets. The most abundant larvae for both sampling methods were Clupeiforms (dominated by anchovies) and Blennidae. Sparidae, Gobidae, Labridae and Gobiesocidae were frequent in the Bongo nets as well.

The season and the week were identified as the dominant temporal scales influencing egg and larval densities (Figure 2). Time had a greater influence than space for all datasets, although the influence of space was substantial, particularly in summer. The influence of space was also more obvious in fixed net datasets than in Bongo datasets. Moreover, models demonstrated the presence of spatio-temporal interactions.

Characteristic spatial homogenous clusters based on ichthyoplankton densities were defined for all datasets and closely matched topographic features. From these clusters three spatial structures were determined to characterize eggs and larval distributions (Table 1 and2): i) a north-south gradient, ii) a coast-shelf separation and iii) a zone with higher densities than its surroundings. Each larval taxon exhibited one, or in few cases a mix of two, of these spatial structures. Spatial structure presented no particular pattern. Globally, the main eggs spatial structure was a dense zone, particularly in the center of the study area, while the larval distributions were characterized by coast-shelf separation. In detail, this separation largely dominated in summer for both sampling methods and both developmental stages. For both sampling methods and both developmental stages, the gradient north-south appeared mostly in spring with very few cases in summer.

Relative influences of space, time and environment on ichthyoplankton

The relative contributions of the three explanatory matrices (space, time and environment) and their combined effects on the variability of eggs and larvae are shown in Table 6.

Negative variances estimated by adjusted R² were due to sampling error around a true population value of 0 (P. Peres-Neto, comm. pers.), and corresponded to a null contribution of the fraction to the overall variability.

According to RDA, the total explained variability ranged from 40.26% to 67.26% in the six datasets. On average, this total explained variability was substantially higher for the eggs (54.47%, SD=11.17) than for the larvae (41.43%, SD=1.11). However, there were no differences between Bongo nets and fixed nets, or between spring and summer. The environment contributed to most of the variability, either in its pure form (Bongo datasets) or in combination with space (fixed net datasets). The combined effect of time and environment also significantly influences both Bongo egg datasets. In total, the environmental contribution ranged between 33.57% and 61.95% of the ichthyoplankton variability. In contrast, there is no influence of the combined effect of the three matrices and the combined effect of space and time was always negligible. Pure time and space effects explained low fractions of the total variability as well (Table 6). However, because of their combined effect with the environment, time and space may have contributed to an important fraction of the variation in some datasets (from 3.45% to 32.81% and from 3.02% to 31.75%, respectively).

Table 7 shows that two environmental factors prevailed, both in term of explained variation and/or occurrences in the models: the depth and the current direction (mostly when measured at 1m depth averaged on the sampling day). Depth appears in all models, whereas current direction appeared in five out of six models and had the most explanatory power of all factors when used solely in the model. Current speed had little or no influence on ichthyoplankton densities. Fluorescence was also present in five out of six models, but had much less explanatory power. The best descriptor for this factor was the fluorescence averaged above the pycnocline. Density and temperature were the two other hydrological factors contributing to eggs and larval densities. Nevertheless, hydrological factors generally account for little of the explained variance. The contribution of winds is difficult to separate from that of currents, since many cases of collinearity between these two factors were detected in the RDAs. For all datasets, wind and current contributions were similar, but current explanatory power was Page 12 sur 31 generally slightly higher. This is why winds were less frequent in the models. The wind direction appeared to be more important than its speed. The combination of wind and current directions is characteristic of Bongo egg datasets. The coast profile at large scale influences both fixed net eggs and larvae highlighting the differences between the two sampling methods.

DISCUSSION

The purpose of this paper is to provide a synoptic snapshot to assess the relative influences of space, time and environment on ichthyoplankton abundance on a typical temperate coastal area, by collecting the broadest possible data. The temporal extent of the study covered the period when most species spawn (late spring -early summer : Sabatés, 1990b;[START_REF] Somarakis | Distribution and abundance of larval fish in the northern Aegean Sea -eastern Mediterranean -in relation to early summer oceanographic conditions[END_REF] and extended longer after this spawning peak to cover average larval duration (about 30 days, McPherson and Raventos, 2006). Similarly, the spatial limit (25 km) lay within the range of appropriate scales for realistic dispersal distance (10-100 km), crucial for population connectivity [START_REF] Cowen | Connectivity of marine populations: open or closed?[END_REF]. This work was limited to one year and undertaken at a site where inter-annual variability is known to be high. The differences between Bongo net and fixed net sampling lay in, i) the location of stations with respect to bathymetry which increases the spatial extent of the study to the coastline, ii) the sampling of the whole water column for Bongo nets or subsurface for fixed nets, which was expected to sample various potential ecological niches and catch various potential species and iii) passive vs. active filtering, which was expected to bias some developmental stages because of the avoidance effect of passive filtering. However, spatio-temporal variations of winds, currents and water masses were not taken into account and may still play an important role in structuring the assemblages of eggs and larvae.

With so many factors taken into account, the proportions of total variance explained obtained here for the six datasets may appear quite low. Estimates based on adjusted R² will always be lower than those based on non-adjusted R². The appropriate number of degrees of freedom is obtained by adjusting for the number of explanatory variables. The more variables used in the set of predictors, the more the adjusted R² will be lower than non-adjusted R². Estimates of total explained variation based on non-adjusted R² are: Bongo spring eggs (71.99%), Bongo summer eggs (53.11%), fixed net eggs (57.78%), Bongo spring larvae (51.63%), Bongo summer larvae (48.68%) and fixed net larvae (49.07%). The estimates of the total explained variation for the models are increased by 4.7-9.2% when non-adjusted R² are used rather than corresponding adjusted R². These non adjusted estimates are in the higher range of the total variation explained by environmental variables in RDA (25%-48% for [START_REF] Lee | Small-scale spatio-temporal variability in ichthyoplankton and zooplankton distribution in relation to a tidal-mixing front in the Irish Sea[END_REF] and the middle range of the total variation explained by environmental variables in CCA (83% for the four first axes in [START_REF] Grothues | Larval fish assemblages and water mass history in a major faunal transition zone[END_REF]; 25%-32% for the first axis in [START_REF] Alemany | Influence of physical environmental factors on the composition and horizontal distribution of summer larval fish assemblages off Mallorca island (Balearic archipelago, western Mediterranean)[END_REF], reported in the literature for the shelf areas. Nevertheless, the unexplained variation in the analyses remains important, and aside from sampling errors and unaccounted environmental variation, biological factors are likely to add a substantial influence to variability. Not surprisingly, the unexplained variation is more important in the case of larvae, for which unaccounted biological factors such as feeding and swimming ability add new sources of variation. The difficulties encountered in the taxonomic identification work can also explain the lack of relevance of space and time in explaining variability. In order to have a better interpretation of the results, the fact that species live in different habitats, with different biological behavior and can belong to the same family must be taken into account.. In this study, the temporal evolution of currents and winds were used as descriptors, since the spatial component of variation for these factors was not available. Therefore, their contribution to ichthyoplankton variability can only be assessed based on the temporal dimension. Similarly, the direct effects of topography on eggs and larval distribution are purely spatial. It has been shown that individual influences of time and space were very low, but their combined effect with the environment was substantial in some cases. By comparing Table 6 andTable 7, similarities and differences in the results can help to deduce two links between environmental factors and temporal and spatial variability. First, fixed net datasets are the only ones for which the combined space-environment component accounted for a greater degree of variability. They were also the only ones for which the coast profile at large scale is an influence. It seems straightforward that spatial structuring by the environment of eggs and larvae caught in fixed nets is dominant and due to topography. This supports the idea that the influence of the coast profile is limited to the nearshore ecosystem, since the location of stations is the only spatial difference between both sampling methods. Second, the combined time-environment component is only appreciable for Bongo nets eggs datasets, for which the simultaneous effect of winds and currents appeared in the models. Hence the temporal variation of eggs sampled with Bongo nets is very likely to be caused by temporal variations of winds and currents and also spawning season. However, the short time-scale of wind fluctuations and egg duration may explain why this is not the case for Bongo nets larvae. Explanations why this link is not present for the fixed net datasets, or why in the case of Bongo eggs there is no collinearity between current and wind directions remain unclear. Fluorescence is generally used as a proxy to estimate variations in phytoplankton concentration. Egg duration in the Mediterranean is generally very short (24-36h, Marinaro, J-Y, Perpignan, pers. comm.), and may reflect timing spawning to ensure optimum environmental conditions for coastal species [START_REF] Tremblay | The vertical and horizontal distribution of Sea Scallop (Placopecten magellanicus) larvae in the Bay of Fundy in 1984 and 1985[END_REF]. The strong discontinuity in ichthyoplantkon communities between both seasons (July, 3 rd for eggs and June, 23 rd for larvae) occurs when stratification of the water column has established and stabilized (Fig. 2). Stratification has been identified as a prevailing factor on the shelf [START_REF] Franco-Gordo | Larval fish assemblages in waters off the central Pacific coast of Mexico[END_REF][START_REF] Lee | Small-scale spatio-temporal variability in ichthyoplankton and zooplankton distribution in relation to a tidal-mixing front in the Irish Sea[END_REF], but [START_REF] Gray | Small-scale temporal variability in assemblages of larval fishes: implications for sampling[END_REF] found no effect of the thermocline on the vertical distribution of larvae. Here, density and temperature have been found to play a more important role than salinity. On the other hand, the best descriptor for the fluorescence factor is the average above the pycnocline. All these results can support the hypothesis that the pycnocline has a greater influence on ichthyoplankton horizontal distribution than the halocline or thermocline, as has been already shown by [START_REF] Munk | Assemblages of fish larvae and mesozooplankton across the continental shelf and shelf slope of the Andaman Sea (NE Indian Ocean)[END_REF]. However, the relatively poor influence of hydrological descriptors requires that this be treated with caution. This is possibly related to the position of the CTD casts in the middle of the transect instead of being placed at each station, or because of small scale temporal oscillation of the different parameters.

The results do however unequivocally demonstrate the influence of depth for all the datasets.

The influence of depth on ichthyoplankton assemblages has been widely documented on temperate continental shelves and slopes elsewhere (e.g. Sabatés, 1990b;[START_REF] Espinosa-Fuentes | Cross-shelf and vertical structure of ichthyoplankton assemblages in continental shelf waters of the Southern Gulf of Mexico[END_REF][START_REF] Auth | Distribution and community structure of ichthyoplankton off the coast of Oregon, USA, in 2000 and 2002[END_REF], but it has only been suggested as a factor in the coastal domain [START_REF] Koutrakis | Temporal patterns of larval fish distribution and abundance in a coastal area of northern Greece[END_REF]. In fact, the datasets cover the nearshore area as well as the edge of the continental shelf, and the "depth" factor primarily discriminates both oceanographic domains. Since this influence is also detected in the Bongo datasets (minimum sampling depth 20 m ), belonging to the nearshore area, the limit between both domains should be located around 25-30m depth. This result is consistent with numerical modeling results of [START_REF] Guizien | Dispersal of Owenia fusiformis larvae by wind-driven currents: turbulence, swimming behaviour and mortality in a three-dimensional stochastic model[END_REF] who, in the same location, found separated nearshore and offshore dispersals of the annelid polychaete Owenia fusiformis larvae due to a physical barrier located between 20m and 30m depth.

Other factors identified as influential by this study are the wind and current directions. The key element here is that the direction, much more than the speed of winds and/or currents, contributes to structure the ichthyoplankton community. Both wind (e.g. [START_REF] Dempster | Beyond hydrography: daily ichthyoplankton variability and short term oceanographic events on the Sydney continental shelf[END_REF][START_REF] Dalley | Atmospheric forcing, larval drift, and recruitment of capelin (Mallotus villosus)[END_REF] and current (e.g. [START_REF] Helbig | The effects of short space and time scale current variability on the predictability of passive ichthyoplankton distributions: an analysis based on HF radar observations[END_REF][START_REF] Sanchez-Velasco | Larval fish assemblages and geostrophic circulation in Bahia de La Paz and the surrounding southwestern region of the Gulf of California[END_REF] factors are widely reported to have a major influence on pelagic eggs and larval 7). However, in most investigations, only speed is taken into account, probably because the circular nature of direction data prevents them to be included in standard statistical analyses. In other studies, U and V components of velocity have been used as descriptors [START_REF] Dalley | Atmospheric forcing, larval drift, and recruitment of capelin (Mallotus villosus)[END_REF]. While they do take into account direction, they do not allow explicit discrimination of the relative influences between speed and direction. In the case of wind-driven current circulation which occurs in most coastal systems, the circulation is highly variable and this result has a strong implication for larval dispersal.

In conclusion, depth, wind and current directions as well as the topographic profiles of the coastline are among the factors most influential for ichthyoplankton abundance in this area of the Northwestern Mediterranean rocky shore. These results suggest that nearshore and continental shelf systems are separated, without being closed, and that alongshore transport of coastal eggs and larvae prevails. Since the direction of wind and/or current is dominant over their speed, the implications for dispersal of nearshore fishes in their early life are the following: If directions remain stable enough in comparison to pelagic life duration, there will be a coastal accumulation with advection in a direction parallel to the coast. If wind directions are unstable and change, changes in currents flowing toward the coast, eggs and larvae will be moved away and back, with a final result of retention near their spawning place. These outcomes can be enhanced or countered by the current speed: If the current speed is low when it's direction is stable, as is usually the case in summer in the Mediterranean, transport will still be limited. Therefore, we propose the hypothesis that the nearshore ecosystem of rocky shores can be favourable for coastal accumulation and/or retention of ichthyoplankton, at least for a certain period of the larval life. Table 6: Estimated percentages of variation in RDA explained by environmental (E), temporal (T) and spatial (S) fractions using adjusted R² for the six datasets. Explanations for negative variances are given in the text and correspond to a null contribution.

Table 7: Descriptors selected in RDA models with higher explanatory power for the six datasets according to each source of variation. Codes are given in Table 3 and4, X and Y correspond to longitude and latitude respectively. The "total explained variation" is the sum of all previous parcels.

  RDA models in this study have a current or wind direction as the second most explanatory environmental variable (Table

Figure 1 :

 1 Figure 1: Study area with Bongo net (a) and fixed net (b) stations. Stars indicate CTD sampling stations and the grey triangle is the position of the ADCP. Dotted line represent the MPA border.

Figure 2 :

 2 Figure 2: Multivariate Regression Trees with spatio-temporal factors of Bongo nets (a) and fixed nets (b). Values of factors splitting the trees are given near the corresponding node.Histograms represent the contribution of egg categories in each final leaf and n is the number of samples of these leaves.

Figure 3 :

 3 Figure 3: Vertical profiles for temperature (a), salinity (b), density (c) and fluorescence (d), collected near Station 4 of fixed nets in the middle of the study area, at four characteristic dates. Note: Turbidity not shown because of its homogeneity.

Figure 4 :

 4 Figure 4: Wind rose (a) and currents roses during the study period at 1m depth (b) and 3m depth (c). Direction follows wind and current direction. Currents at 3m depth are the mean of currents at 2, 3 and 4m depth.

  Abb.Descriptor Abb. Descriptor

Table 1 :

 1 Species and mean densities (± SD) of egg categories in number of egg per 1000 m³. Spatial structures of eggs have been identified with spatial models. Code: N north, S south, C center, N/S north-south gradient, Co/Sh coast-shelf structure. + zone of high density and ? unidentified structures. variable used in the dataset.

Table 2 :

 2 Frequent and locally abundant larval taxa selected for the two sampling methods.Densities (± SD) are in number of larvae per 1000 m³. Spatial structures of larvae have been identified with spatial models. Code: N north, S south, C center, N/S north-south gradient, Co/Sh the coast-shelf structure. + zone of high density and ? unidentified structures. variable used in the dataset.

Table 3 :

 3 Topography, wind and currents descriptors used in analyses and corresponding abbreviations.

Table 4 :

 4 Hydrology descriptors used in analyses and corresponding abbreviations

Table 5 :

 5 Topography descriptors associated to each station for both sampling methods determined by GIS. CP coast profile and is influential for nearshore stations.

Table 5 5

 5

	Sampling method	Station Depth (m)	Distance to the coast (m)	Slope degrees	Bottom complexity	CP Small scale	CP Large scale
		1	16	68	10,83	388	32,79	31,07
		2	33	808	0,51	334	-	-
		3	20	152	7,54	166	3,38	12,07
		4	35	497	3,59	194	-	-
		5	22	409	3,94	231	14,25	68,28
		6	39	1732	0,88	251	-	-
		7	23	270	6,08	200	20,15	36,80
		8	40	971	2,11	248	-	-
	Bongo nets	9 10	26 39	600 803	7,85 4,16	147 184	19,90 -	31,21 -
		11	25	286	5,31	163	10,44	45,50
		12	38	653	2,59	205	-	-
		13	27	189	7,98	173	14,18	25,02
		14	39	507	5,00	195	-	-
		15	16	148	5,83	328	16,65	46,02
		16	48	652	1,26	271	-	-
		17	20	168	6,25	335	18,37	77,93
		18	44	963	0,00	293	-	-
		1	6	24	10,72	400	32,79	31,07
		2	7	38	9,24	238	3,38	12,07
		3	8	120	4,86	149	14,25	68,28
		4	8	84	6,58	241	20,15	36,80
		5	7	73	6,10	232	19,90	31,21
	Fixed nets	6 7	7 8	49 47	7,73 10,88	174 406	10,44 14,18	45,50 25,02
		8	7	53	6,46	391	16,65	46,02
		9	9	78	6,94	350	18,37	77,93
		10	58	1434	6,78	272	-	-
		11	42	948	1,85	307	-	-
		12	51	1654	1,01	278	-	-

http://mc.manuscriptcentral.com/jplankt Journal of Plankton Research

ACKNOWLEDGEMENTS

We thank the European community during the Biomex Programme under contract QRTL-2001-0891 and the Cerbere-Banyuls MPA for funding. We also wish to thank the crew of the Research vessel "Nereis II", all the people who helped in field collection, sorting and identification. Météo-France kindly provided wind data. We are very grateful to Pedro Peres-Neto for his advice in interpreting fractions with negative variances and for his comments on the draft of this manuscript. We also thank Andrew L. Stewart, Clive D. Roberts, Vincent Zintzen and the 2 anonymous referees for language correction, advice and comments that enhanced this paper.


Vojtech Vlcek

Jakub Cizek

Jan Drahokoupil

Jan Valenta

Nobuyoshi Miyajima

Roman Skala

Vojtěch Vlček

Jakub Čížek

Roman Skála

Defects in CaF2 caused by long-time irradiation and their response to annealing

Keywords: defects, microstructure, photoluminescence, TEM, X-ray diffraction CaF2, fluorite, PAS CaF 2, fluorite, microstructure, defects, Positron Annihilation Spectroscopy, Photoluminescence Spectroscopy, Transmission Electron Microscopy, X-ray Diffraction

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

Introduction

Radiation-induced defects in fluorite (CaF 2 ) structure were investigated only in artificially irradiated samples in the recent studies (e.g., Refs. [1][2][START_REF] Watanabe | 16th International Microscopy Congress Abstracts[END_REF][START_REF] Xiang | [END_REF]). However, the response of the structure to a long-time irradiation (of the order of million years) is essential for understanding the processes of formation and the stability of defect centres. These recent studies showed that the radiation damage of fluorite should reach a saturation level and then there should be a dynamic balance of creation and Understanding how the fluorite structure responses to a long-term irradiation is important for its potential use under conditions of prolonged exposition to radiation in applications such as containment of radioactive waste (proposed in Ref. [2]), special optics or applications in electrotechnics (e.g. Ref. [5]). As a consequence, we chose the natural samples of fluorite to evaluate effect of the long-time irradiation on CaF 2 structure. The microstructure analysis from X-ray powder diffraction data, Positron Annihilation Spectroscopy (PAS), Photoluminescence Spectroscopy (PLS) and Transmission Electron Microscopy (TEM) were used to decipher the behaviour of fluorite under prolonged radiation.

Experimental methods and sample description

Samples

A natural CaF 2 sample from Kletno (Poland) was exposed to radiation emitted by surrounding uraninite (UO 2 ) for millions of years. It has a dark purple colour and dim surface. This sample was assumed to display the highest degree of irradiation damage. Fluorite from Vlastějovice (Czech Republic) was irradiated by allanite (Cesilicate). The activity of this mineral is several times lower in comparison to uraninite.

Hence, the sample from Vlastějovice was assumed to represent a low-irradiated CaF 2 .

A non-irradiated fluorite sample from the locality Jílové u Děčína (Czech Republic) and a synthetic standard (Suprapur, Merck) were used as reference materials.

X-ray diffraction

X-ray powder diffraction patterns were collected with a PANalytical X'Pert Pro diffractometer equipped with an X'Celerator position-sensitive detector and a secondary graphite monochromator (Institute of Physics, Academy of Sciences of the Czech Republic). Data were step-scanned over the range from 10° to 150° 2Θ with The diffraction peak parameters were fitted using Rietveld refinement procedure with Le-Bail fit as implemented in the HighScore software (PANalytical) .

The Williamson-Hall plot (described in Ref. [START_REF] Klug | X-Ray Diffraction Procedures[END_REF]) is used to visualize the difference between crystallite size and a micro-strain peak broadening.

PAS

A 22 Na 2 CO 3 positron source with activity of 1.5 MBq deposited on a 2 µm thick mylar foil was used in PAS measurements. The source was placed in the centre of a small cylindrical chamber with a diameter of 10 mm and height of 5 mm.

Subsequently, the chamber was completely filled with the sample powder and closed.

Dimensions of the chamber ensure that virtually all positrons are stopped inside the chamber and, thereby, annihilate in the studied powder.

Positron-lifetime measurements were performed on a digital spectrometer described in Refs. [START_REF] Bečvář | [END_REF]8]. The spectrometer is equipped with BaF 2 scintillators and fast photomultipliers Hamamatsu H3378. Detector pulses are directly digitized using a couple of 8-bit ultra-fast digitizers Acqiris DC 211 with sampling frequency of 4

GHz. Analysis of digitized pulses and construction of positron-lifetime spectrum is performed off-line using so called integral true constant fraction technique described in Ref. [9]. The spectrometer exhibits excellent time resolution of 145 ps (full width at half-maximum (FWHM) 22 Na). At least 10 7 positron annihilation events were Coincidence Doppler broadening (CDB) studies were carried out using a spectrometer [11] equipped with two high purity Ge detectors. The overall energy resolution of the CDB spectrometer is (1.02 ± 0.01) keV at 511 keV. At least 10 8

annihilation events were collected in each of two-dimensional γ-ray energy spectra, which were subsequently reduced into two one-dimensional cuts representing the resolution function of spectrometer and Doppler broadened annihilation profile. In this paper CDB results are presented as ratio curves with respect to a well annealed bulk Mg (99.99 %) reference specimen Theoretical calculations of positron parameters were performed from the first principles using an approach based on the density functional theory. Positron wave function was calculated within so-called conventional scheme employing the atomic superposition (ATSUP) method [12]. Electron-positron correlation was treated within local density approximation (LDA) using the scheme developed by Boronski and Nieminen [13] with the correction [14] for incomplete positron screening with high frequency dielectric constants ε ∞ = 6.8 [START_REF] Dickinson | Infrared laser windows materials property data for ZnSe, KCl, NaCl, CaF 2 , SrF 2[END_REF]. A cubic structure with lattice parameter a = 5.46305 Å [START_REF] Wyckoff | Crystal Structures[END_REF] was adopted for CaF The high momentum part (HMP) of momentum distribution of electrons that annihilated positrons was performed using ATSUP-based approach according to the scheme described in Refs. [START_REF] Alatalo | [END_REF]18]. Electron-positron correlation was treated using LDA approach [13,14] and also by generalized gradient approximation (GGA) scheme developed by Barbiellini et al. [19,20]. Only the contribution from positrons annihilated by localized core electrons were considered in the calculations. Hence, comparison of calculated HMP curves with experiment is meaningful only in the high momentum range, p > (10 × 10 -3 ) m 0 c, where contribution of positrons annihilated by core electrons dominates. The following orbitals were considered as core electrons and included in the calculations of HMP curves: Ca: 1s 2 ,2s 2 ,2p 6 ,3s 2 ,3p 6 , F: 5 , Mg: 1s 2 ,2s 2 ,2p 6 .

1s 2 ,2s 2 ,2p
The final one-dimensional HMP curve, which can be compared to the experimental CDB spectrum is obtained by summing up the contributions of the core states of all atoms in the system and integrating over the high-momentum tail. In order to compare the calculated HMP curves to experimental CDB spectra, they have to be properly normalized. The areas of the experimental CDB spectra were scaled to unity, while the areas below the theoretical HMP curves were set equal to λ core / λ, where λ core is the annihilation rate with all core electrons of the system, while λ is the total annihilation rate, i.e. the inverse of positron lifetime. In order to mimic the effect of the finite resolution of the experimental setup, the theoretical HMP curves were convoluted with a Gaussian with FWHM of (4.0 × 10 -3 ) m 0 c. were placed onto TEM copper grids coated with carbon holey films. Microscope used to study the samples was a Philips CM 20 FEG (at the Bayerisches Geoinstitut, Universität Bayreuth, Germany) operated at 200 kV voltage. The samples were imaged under bright field, dark field, and weak-beam dark-field conditions. Also, high-resolution TEM images were acquired. Selected area electron diffraction was used to define orientation of the samples. In order to investigate existence of some impurities, energy-dispersive X-ray spectra were also collected with 60 sec live time.

F

Results and discussion

X-ray diffraction

The diffraction peaks of the irradiated sample are broadened mainly due to micro-strain that is caused by defects and lattice deformations; the domain size broadening has negligible contribution. The diffraction patterns were collected during in-situ heating at different temperatures to obtain information about the structure The data plotted in Williamson-Hall graph (Fig. 1) shows that the main recovery process is started at temperatures higher than 300 °C. To determine possible slow kinetics at lower temperature the several measurements were done at 300 °C (total heating lasted 8 hours), however no change of micro-strain was observed.

The annealed sample (up to 450 °C) became colourless after the experiment, yet some micro-strains remained. We assume that some defects persist and are not affected by heating. It should be noted that the reference samples from Jílové and the synthetic CaF 2 showed also non-zero values of micro-strain. Nevertheless, these micro-strain values are substantially lower than those observed in the annealed and Xray irradiated samples.

Another interesting feature noted in the annealed samples is a colour change from colourless to purple upon irradiation by the X-ray beam during the XRD study.

The stability of colouration depends on the time of X-ray irradiation. After a short irradiation (about 1 hour) the colour dissipates in about three days; however after irradiation that took more than 500 hours the colour is stable. X-ray irradiation does not affect the microstructure characteristics of the sample (no peak-broadening was observable in diffraction pattern). This confirms the different character of the colour centers and the defects causing microdeformation.

PAS

Theoretical calculations

First principles calculations of positron characteristics were performed in order to identify defects in CaF 2 samples. for a perfect defect-free CaF 2 crystal is plotted in Fig. 2 A. Positron in a perfect CaF 2 crystal is delocalized in the lattice in the form of modulated Bloch-like wave.

Calculated bulk positron lifetime in a perfect CaF 2 crystal is 171.5 ps.

Figure 2 B shows calculated positron density in CaF 2 containing an Fvacancy. Although there is a slight enhancement of positron density in the vicinity of F-vacancy, there is still a significant probability to find positron elsewhere. Hence, Fvacancy is too shallow trap incapable to confine positron. This is confirmed by positron lifetime, which approaches the bulk positron lifetime in CaF 2 and also by a negligible positron binding energy to F-vacancy, see Table 1.

On the other hand, Ca-vacancy is a deep positron trap. Fig. 2 C shows that positron is completely localized in Ca-vacancy. Calculated lifetime of positron trapped in Ca-vacancy is 225.9 ps and positron binding energy to this defect is 1.68 eV.

Thus, theoretical calculations clearly demonstrated that F-vacancies as very shallow traps are "invisible" to positrons. On the other hand, Ca-vacancies as strong traps can be undoubtedly detected by PAS.

It is known that F-vacancies produced in CaF 2 by irradiation aggregate and form fluorine voids [START_REF] Johnson | [END_REF][23][24][25]. This process leads to formation of metallic Ca inclusions in CaF 2 where fluorine voids occur and only Ca atoms remain in their sites. Due to this reason, it is important to examine the possibility of positron trapping in aggregates of F-vacancies. Figure 3 shows results of the first principle calculations of positron parameters for F-vacancy aggregates of various sizes. One can see in Fig. 2 that positron lifetime and positron binding energy to an aggregate of F-vacancies increases with increasing number of F-vacancies (i.e., increasing size of fluorine void). The calculated positron density for a CaF 2 crystal containing F-divacancy is Even larger aggregates of F-vacancies are yet deeper traps characterized by a longer positron lifetime and higher positron binding energy, (Fig. 3). Figure 5 A shows calculated positron density for an agglomerate of 8 F-vacancies. One can see that positron is fully localized and lifetime of positrons trapped at this defect is comparable to that of positron trapped in Ca-vacancy (Fig. 3 A).

Calculated positron characteristics for a CaF 2 supercell with all F atoms removed represents an extreme case and simulates a very large fluorine void; it is plotted in Fig. 5 B. The figure illustrates that positron is delocalized inside the fluorine void and is located mostly in the empty sites in fluorine sub-lattice. Lifetime of positron delocalized in very large fluorine void is 301.9 ps and positron binding energy is 1.44 eV.

Positron lifetime spectroscopy

The reference non-irradiated CaF longer then lifetimes calculated for aggregates of F-vacancies (Fig. 3 A). It is even longer than the upper limit for F-vacancy aggregates, i.e., positron lifetime of 302 ps calculated for a large fluorine void. Hence, the longer component in positron lifetime spectrum of reference CaF 2 powder represents a contribution of positrons trapped at larger defects (voids) containing not only F-vacancies, but also Ca-vacancies.

In the frame of the two-state simple trapping model [START_REF] West | Positrons in Solids[END_REF] the quantity

τ f = I 1 τ 1 + I 2 τ 2       -1 (1)
equals to the bulk positron lifetime

τ f ≡ τ B
(2) Equations (1,2) are frequently used to check the consistency of spectrum decomposition with the two-state simple trapping model. For the reference CaF 2 powder we obtained τ f = (179 ± 8) ps, which is in a good agreement with the calculated bulk positron lifetime in a perfect CaF 2 crystal shown in Table 1. This confirms that assumptions of two-state simple trapping model (i.e., a single type of uniformly distributed defects) are fulfilled in the case of virgin CaF 2 powder. Note that positron annihilations studies of CaF 2 crystals were performed by angularcorrelation [START_REF] Brandt | [END_REF] but no positron lifetime investigations of CaF 2 crystals have been performed so far to our best knowledge.

The irradiated natural CaF 2 powder from Kletno exhibits two-component positron lifetime spectrum. Both lifetimes τ 1 , τ 2 of these components are longer than the bulk positron lifetime in CaF 2 . Thus, both these components represent a contribution of positrons trapped at defects. The longer component exhibits lifetime τ 2 = (335 ± 4) ps, which is comparable with the lifetime τ 2 measured on the reference powder. Hence, similarly to the reference powder, the longer component in the irradiated CaF 2 can be attributed to positrons trapped at larger voids containing both [START_REF] Johnson | [END_REF][23][24][25]. Indeed, the lifetime τ 1 corresponds to the calculated lifetime of positrons trapped at an agglomerate of 4 F-vacancies (Fig. 3 A).

The irradiated CaF 2 powder from Kletno was subsequently subjected to isochronal annealing. The mean positron lifetime is

τ mean = I i τ i i ∑ , (3)
where the centre of mass of positron-lifetime spectrum is a robust single parameter, which is not influenced by mutual correlations of fitted parameters. Figure 6 shows dependence of the mean positron lifetime on the annealing temperature for irradiated CaF 2 powder from Kletno. There is a strong increase of τ mean in the However, larger agglomerates containing at least 4 F-vacancies are capable of positron trapping and can be detected by PAS. Hence, agglomeration of isolated Fvacancies or very small F-vacancy clusters into larger agglomerates, which takes place at temperatures T ≥ 300 o C, enhances positron trapping to these defects, which is reflected by an increase of intensity I 1 . This is accompanied by a gradual increase of lifetime τ 1 of this component due to increasing average size of F-vacancy agglomerates. The lifetime τ 2 of the longer component increases after annealing at 300 o C. This could be due to F interstitials (H-centres) which become mobile at 300 o C and form fluorine bubble-like defects (described e.g. in Ref. [START_REF] Johnson | [END_REF]) in the sample.

Positrons trapped at these fluorine bubbles contribute to the longer component and causes an increase of lifetime τ 2 .

Coincidence Doppler Broadening

Figure 8 shows calculated HMP profiles for a perfect CaF 2 crystal and reference defect-free pure Mg. The experimental curves for a reference non-irradiated CaF 2 powder and a well annealed bulk Mg are plotted in the figure as well. It is clear that the curves calculated using GGA scheme are in better agreement with experiment than curves calculated using LDA approach. This is due to well known fact that LDA overestimates positron annihilations with core electrons [START_REF] Wojdyr | Fityk A curve fitting and data analysis program[END_REF]. Due to this reason only the curves calculated using GGA scheme will be considered in the further discussion.

As was explained in section 3. F electrons. This is not surprising because there is an attractive Coulomb interaction between positron and F anions. Thus, in a perfect CaF 2 crystal the overlap of positron density with F anions is significantly larger than with Ca cations, see Fig. 2 A. This effect can be seen also on the calculated HMP curves plotted in Fig. 11.

Clearly, the calculated ratio curves for positrons trapped at F-vacancy agglomerates are lower than the curve for a perfect CaF 2 crystal. This is due to reduced contribution of positrons annihilated by F-electrons. The ratio curve for F-vacancy agglomerate containing 8 F-vacancies is located below the curve for agglomerate containing 4

vacancies because the contribution of positrons annihilated by F-electrons decreases with increasing size of the agglomerate.

On the other hand, the calculated ratio curve for positrons trapped in Cavacancy is situated above the curve for a perfect CaF 2 because F-atoms occupy the nearest neighbour sites of Ca-vacancy. Hence, there is relatively high probability that it will be annihilated by F-electron, while the probability to be annihilated by Caelectron is negligible.

With increasing temperature the fraction of positrons annihilated by F-

PLS

The detected PL spectra revealed a distinct behaviour of irradiated and nonirradiated fluorites. Six different emission bands with peaks at about 431, 479, 514, 587, 644, and 720 nm were observed. They are labelled E 1 to E 6 , respectively, and they are listed in Table 3. However the natural reference fluorite sample from Jílové shows no emission bands, this confirms absence of impurities or luminescent defects.

The E 2 and E 5 bands are present in the synthetic reference sample and some irradiated samples and seem to be unaffected by heating or X-ray irradiation. Therefore these bands cannot be related to radiation-induced defects. We assigned the E 2 emission peak (corresponding to 2.59 eV) to oxygen centres (e.g. Ref. [28]).

For the irradiated samples the E 1 , E 3 and E 6 emission bands are characteristic (Fig. 12). The first one has the highest intensity and low FWHM (i.e., narrow energy distribution). It corresponds to energy of 2.88 eV and it is not affected by the annealing or further X-ray irradiation. The E 3 is a broad emission peak corresponding to energy of 2.41 eV. Its position is not affected by the annealing. The E 6 has a broad FWHM and its centre corresponds to energy of 1.72 eV. This emission is not present in the annealed samples which became colourless upon annealing but the E 6 emission reappears again in the samples irradiated by X-ray after being annealed.

The E 1 emission band can be assigned either to F-centres or their clusters or to the impurities, which cause emissions slightly shifted to lower wavelengths. This effect is discussed in previous studies for, e.g., Zn + , see [START_REF] Xiang | [END_REF], or Eu 2+ , see [29] Since impurities are common in all natural samples both impurities and F-centers can be expected to contribute to the E 1 emission band. Defect centres in natural samples could be bound to the foreign atoms in the structure. This binding makes the defects more stable and resistant to heating. However, the exact character of the substituents is difficult to identify as even very low concentration (ppm) can cause the luminescent effect and an additional study would be necessary to get the desired information. As the E 3 emission has behaviour similar to E 1 it probably represents the same type of luminescence centres. The interpretation of the E 6 emission band seems to be more complicated as it is influenced by heating and X-ray irradiation; it will be discussed later.

In the annealed samples the additional E 4 emission appears; corresponds to energy of 2.11 eV. However, it is placed in the region of a broad absorption band of F-or H-centres, see [START_REF] Xiang | [END_REF]. We suppose that the E 4 emission is present in irradiated sample before heating but it is absorbed within the sample. The small emission bands of different peak shape and very low FWHM visible on Figure 12 B are most likely emissions of impurities. As they should not be affected by heating, their presence only in the spectrum of annealed CaF 2 indicates that the (F and H-centers) absorption band disappeared.

The annealed samples of fluorite when X-ray irradiated exhibit the same PL spectra as untreated samples. As the XRD results showed that no new structural defects are formed (described in section 3.1) we assume that the E 6 emission is connected with some centres, which cannot be detected by XRD. The F-centers, which are known to be present in the irradiated CaF 2 samples, are considered as most probable candidates. Hence, one should take into account thermal stability of Fcentres. Most probably electron is released from F-centre during heating and the following X-ray irradiation causes the electron trapping again. It is in agreement with the observation that the reference non-irradiated material, which does not contain Fcentres, does not change its colour in X-ray beam. These processes (electron releasing and trapping) can also explain the E 6 emission band and its disappearance due to annealing. The TEM-EDS analysis showed no mutual intersample chemical differences within the instrument limits. Increasing defect concentration depending on radiation source activity was observed. The reference material showed no defects observable by TEM. However, in the low irradiated samples from Vlastějovice the dislocation loops are documented (Fig. 13 A). It is in a good agreement with results of previous studies [START_REF] Watanabe | 16th International Microscopy Congress Abstracts[END_REF]. The Kletno sample contains unexpectedly high density of defects as illustrated in the weak-beam dark-field image shown in Fig. 13 B. The dislocation density is so high in this case that it makes almost impossible to distinguish individual dislocations or dislocation-loops. The highresolution TEM image (Fig. 14) also confirms the presence of Ca inclusions, previously reported from irradiated samples, e.g., by [30]. These inclusions are produced by F-centres clustering and they represent stable void-superlattice.

However, the Ca inclusions are not present in the low-irradiated sample. This is probably due to different activities of radiation source.

Conclusions

The present study characterizes CaF 2 structure with a high density of radiation-induced defects created by long-time irradiation (in order of million of years) that causes significant lattice micro-strains whereas some previous studies (e.g.

[2]) expected only low lattice strains and consequently also suggested CaF 2 as a candidate for the containment of radioactive waste. These micro-strains decrease rapidly during heating to temperatures exceeding 300 °C. However the domain-size broadening was not observed. It was also shown that even after annealing some defects remain present in the structure (documented by non-zero strain observed by XRD or by PL spectra). The first principles PAS calculations showed that showed the presence of F-centre agglomerates and their clustering during heating as well as the H-centre clustering creating free fluorine bubbles in the structure. The knowledge of these processes on the atomistic scale could be necessary for using CaF 2 as a material for high-resolution electron beam litography or as an insulating layer for semiconductor technology as discussed in Ref. [5].

The defect-related emissions in PL spectra of irradiated CaF 2 were discussed in previous studies (e.g., [START_REF] Xiang | [END_REF]) without concrete assignment; as the results obtained from other methods revealed the true character of the defects we were able to make this assignment. The PL spectra also showed that the resistant defects are most probably stabilized by impurities; this kind of defects could then significantly influence the quality of optical devices mainly by causing decrease in transmittance.

Saturated positron trapping confirms a high-density of defects in irradiated CaF 2 , which was documented also by TEM observations.

  centres resulting in minimum strains within the lattice.

  step size and 300 s counting time per step. Cobalt tube was operated at 40 kV voltage and 30 mA current. The naturally irradiated fluorite sample from Kletno annealed up to 450 °C was subsequently X-ray irradiated on conventional X-ray source MIKROMETA (Faculty of Science, Charles University in Prague) with unfiltered radiation from Cu tube operated at 40 kV and 30mA.

  positron lifetime spectrum. Decomposition of positron-lifetime spectra into exponential components were performed using a maximum likelihood procedure described in Ref.[10]. The source contribution to positron-lifetime spectra consisted of two weak components with lifetimes of ~368 ps and ~1.5 ns and corresponding intensities of ~8 % and ~1 %. These components represent a contribution of positrons annihilated directly in Na 2 CO 3 source and the covering mylar foils.

  annealing. Subsequent peak-broadening analysis using Williamson-Hall method[START_REF] Klug | X-Ray Diffraction Procedures[END_REF] confirmed the expected decrease of micro-strain values.

  . 4 A. Similarly to F-vacancy also F-divacancy is too shallow trap to confine positron. This is demonstrated not only by absence of positron localization, but also by calculated positron lifetime, which is close the bulk positron lifetime in perfect CaF 2 and very small positron binding energy to F-divacancy.A remarkable increase of positron binding energy occurs for F-tetravacancy, see Fig.3 B. Calculated positron density for a CaF 2 crystal containing F-tetravacancy is plotted in Fig.4B and shows a significant increase of positron localization. Hence, F-tetravacancy becomes capable of positron trapping and can be detected by PAS.

  2 powder exhibits a two-component positron lifetime spectrum. The shorter component with lifetime τ 1 = (110 ± 10) ps and relative intensity I 1 = (41 ± 1) % can be attributed to free, delocalized positrons. The longer component with lifetime τ 2 = (322 ± 2) ps and relative intensity I 2 = (59 ± 1) % is a contribution of positrons trapped at defects. The lifetime τ 2 of this component is

F

  -vacancies and Ca-vacancies. On the other hand, the shorter component with lifetime τ 1 = (197 ± 1) ps represents a contribution of positrons trapped at new defects created by irradiation. It is well known that agglomerates of F-vacancies are formed in irradiated CaF 2

  temperature range from 200 to 300 o C indicating a change of defect structure. Finally, above 300 o C, the mean lifetime decreases. More information can be obtained from decomposition of positron lifetime spectra. At all annealing temperatures positron-lifetime spectra of irradiated CaF 2 are well fitted by two components. Lifetimes of these two components are plotted in Fig. 7 A as a function of annealing temperature whereas Fig. 7 B shows temperature dependence of the intensity I 2 of the longer component. Lifetime τ 1 of positrons trapped at F-vacancy agglomerates gradually increases with annealing temperature (inset in Fig. 7 A) indicating increasing size of the agglomerates. The intensity I 1 of positrons trapped at F-vacancy agglomerates plotted in Fig. 7 B increases remarkably after annealing above 300 o C. This behaviour indicates that agglomeration of irradiation-induced single F-vacancies or very small F-vacancy clusters occurs at temperatures T ≥ 300 o C. Theoretical calculations in 2.1 demonstrated that isolated F-vacancies or very small F-vacancy agglomerates containing less than 4 F-vacancies cannot be detected by PAS.

2 . 1 ,> 10 ×

 2110 only localized core electrons which retain their atomic character are considered in the calculations of HMP profiles. Low momentum valence electrons were not included in the calculations. Therefore, comparison of calculated curves with experiment is meaningful only in the high momentum range p 10 -3 m 0 c, where positron annihilations with localized core electrons dominate. Indeed, one can see in Fig. 8 that experimental curves for reference CaF 2 and Mg are well reproduced by theoretical calculations in the high momentum range p > 10 × 10 -3 m 0 c. The contributions of various electron orbitals to the calculated HMP profile for a perfect CaF 2 crystal are plotted in Fig. 9. From comparison of experimental profile with theoretical calculations, it is clear that positrons are annihilated mostly by

Figure 10 shows

 10 Figure10shows the ratio curve (related to Mg reference) for the reference

  Hence, an increase in positron trapping in F-vacancy aggregates causes a decrease in fraction of positrons annihilated by F-electrons.

  electrons firstly decreases due to increasing size of F-vacancy agglomerates (Fig.10B). The lowest contribution of the positrons annihilated by F-electrons was found after annealing at 100 o C. Annealing to temperatures above 200 o C leads to an increase of fraction of positrons annihilated by F-electrons because positrons become trapped at fluorine bubbles, i.e., the fraction of positrons annihilated by F-electrons increases. This enhancement of fraction of positrons annihilated by F-electrons agrees with increase of lifetime τ 2 observed by positron-lifetime spectroscopy (Fig.7 A) and explained by formation of fluorine bubbles.

  Samples of high-and low-irradiated fluorite and the reference sample of synthetic CaF 2 were investigated by TEM.

  of F-vacancies are detectable by PAS if they contain at least 4 Fvacancies. Lifetime of positrons trapped at F-vacancy agglomerates depends on size of the agglomerate and falls in the range from 190 to 302 ps. The presented positron lifetime spectroscopic study have not been performed so far and substantially helped to reveal the character of the defects and their behaviour. The detail measurements

Fig. 1

 1 Fig. 1 Williamson-Hall plot showing the data obtained through whole powder pattern

Fig. 2

 2 Fig. 2 Calculated positron density in (110) plane for (A) a perfect CaF 2 crystal, (B)

Fig. 3

 3 Fig. 3 Results of first principle calculations of positron parameters for F-vacancy

Fig. 4

 4 Fig. 4 Calculated positron density in (110) plane for a CaF 2 crystal containing (A) F-

Fig. 5 Fig. 6

 56 Fig. 5 Calculated positron density in (110) plane for a CaF 2 crystal containing (A) an

Fig. 7 Fig. 8

 78 Fig. 7 Temperature dependence of (A) lifetimes τ 1 , τ 2 of exponential components

Fig. 9

 9 Fig.9The calculated HMP curve for a perfect CaF 2 crystal with contributions of

Fig. 10 (Fig. 11

 1011 Fig. 10 (A) Experimental CDB ratio curves (related to pure Mg reference sample) for

Fig. 12

 12 Fig. 12 Photoluminescence spectra of long-time irradiated CaF 2 untreated (A) and

Fig. 13

 13 Fig. 13 Weak-beam dark-field TEM images with g = 022 of low-irradiated sample

Fig. 14

 14 Fig. 14 HRTEM images of high-irradiated sample from Kletno (left) and detail of

Table 1

 1

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

shows calculated positron lifetimes for various positron states in CaF 2 crystal. Calculated positron density in (110) plane

Table 1 .

 1 Results of the first principles calculations of positron parameters (positron lifetime τ and positron binding energy to defect E B ) for various positron states in

	5 Acknowledgement

Table 2 .

 2 Results of positron lifetime measurements of CaF 2 powders.

	Sample	τ 1 (ps)	I 1 (%)	τ 2 (ps)	I 2 (%)
	reference,	110 ± 10	41 ± 1	322 ± 2	59 ± 1
	non-irradiated
	irradiated, Kletno 197 ± 1	67 ± 1	335 ± 4	33 ± 1

Table 3 .

 3 Observed emission bands and their assignment.

	Emission	λ (nm)	Assignment
	E 1	431	F-centres bound to substituent
	E 2	479	non-radiation-induced defects
	E 3	514	F-centres bound to substituent
	E 4	587	F-/ H-centres
	E 5	644	non-radiation-induced defects
	E 6	720	electron-defect bound state

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This work was funded by the The Ministry of Education of The Czech Republic (projects MSM0021620855 and MS0021620834). One of the authors (JV) acknowledges the support through the Centre of nanotechnology and materials for nanoelectronics, LC510 (funded by the MSMT CR). RS thanks for the support through the research plan AV0Z30130516 of the Institute of Geology AS CR.