Céline Clauzel
email: celine.clauzel@univ-fcomte.fr

PhD Xavier Girardet
email: xavier.girardet@univ-fcomte.fr

Impact assessment of a

Keywords: Environmental assessment, Transport infrastructures, Landscape graphs, Connectivity, Species distribution model, Hyla arborea

come

Introduction

The extension of linear infrastructures is thought to be a major threat to biodiversity, much like other anthropogenic phenomena such as more intensive farming and urban sprawl [START_REF] Forman | Roads and Their Major Ecological Effects[END_REF]. The construction of transport infrastructures causes a direct loss of ecological habitats and road traffic generates wildlife-vehicle collisions [START_REF] Coffin | From roadkill to road ecology: A review of the ecological effects of roads[END_REF][START_REF] Fahrig | Effect of road traffic on amphibian density[END_REF][START_REF] Forman | Roads and Their Major Ecological Effects[END_REF][START_REF] Geneletti | Some common shortcomings in the treatment of impacts of linear infrastructures on natural habitat[END_REF][START_REF] Trombulak | Review of Ecological Effects of Roads on Terrestrial and Aquatic Communities[END_REF]. Apart from these direct effects, linear infrastructures cause the loss of landscape connectivity [START_REF] Forman | Roads and Their Major Ecological Effects[END_REF][START_REF] Geneletti | Using spatial indicators and value functions to assess ecosystem fragmentation caused by linear infrastructures[END_REF], which is recognized as a key functional factor for the viability of species and their genetic diversity [START_REF] Fahrig | Effect of road traffic on amphibian density[END_REF]. Major infrastructures such as motorways or high-speed railway lines act as barriers to the movement of animals through collisions and infrastructure avoidance because of traffic noise and isolate organisms in small subpopulations which become more sensitive to the risk of extinction [START_REF] Forman | Roads and Their Major Ecological Effects[END_REF]. This is especially the case for populations of amphibians whose daily movements and seasonal migrations mean they regularly cross the landscape matrix [START_REF] Alford | Global Amphibian Declines: A Problem in Applied Ecology[END_REF][START_REF] Allentoft | Global Amphibian Declines, Loss of Genetic Diversity and Fitness: A Review[END_REF][START_REF] Cushman | Effects of habitat loss and fragmentation on amphibians: A review and prospectus[END_REF][START_REF] Eigenbrod | Quantifying the road effect zone: threshold effects of a motorway on anuran populations in Ontario, Canada[END_REF][START_REF] Fahrig | Effect of road traffic on amphibian density[END_REF][START_REF] Lengagne | Traffic noise affects communication behaviour in a breeding anuran, Hyla arborea[END_REF][START_REF] Scherer | The importance of local and landscape-scale processes to the occupancy of wetlands by pond-breeding amphibians[END_REF].

Several case studies have contributed to identifying and quantifying the effects of linear infrastructures on species distribution in many regions of the world, using various methods. Authors have related data describing species (e.g. abundance, road mortality) to proximity of infrastructures [START_REF] Brotons | Reduced bird occurrence in pine forest fragments associated with road proximity in a Mediterranean agricultural area[END_REF][START_REF] Fahrig | Effect of road traffic on amphibian density[END_REF][START_REF] Huijser | The effect of roads and traffic on hedgehog (Erinaceus europaeus) populations[END_REF][START_REF] Kaczensky | The impact of high speed, high volume traffic axes on brown bears in Slovenia[END_REF][START_REF] Li | Ground-dwelling birds near the Qinghai-Tibet highway and railway[END_REF] and to the degree of habitat fragmentation [START_REF] Fu | Characterizing the "fragmentation-barrier" effect of road networks on landscape connectivity: A case study in Xishuangbanna, Southwest China[END_REF][START_REF] Serrano | Landscape fragmentation caused by the transport network in Navarra (Spain)[END_REF][START_REF] Vos | Effects of habitat fragmentation and road density on the distribution pattern of the moor frog Rana arvalis[END_REF]. These studies measure the real impact of the infrastructure using species data collected after its construction. However, before the construction phase, an impact prediction stage is also necessary to compare alternative infrastructure routes [START_REF] Fernandes | Landscape ecology and conservation management-Evaluation of alternatives in a highway EIA process[END_REF][START_REF] Geneletti | Using spatial indicators and value functions to assess ecosystem fragmentation caused by linear infrastructures[END_REF][START_REF] Vasas | Graph theory in action: evaluating planned highway tracks based on connectivity measures[END_REF] or to guide the mitigation measures from the beginning of the project [START_REF] Mörtberg | Landscape ecological assessment: A tool for integrating biodiversity issues in strategic environmental assessment and planning[END_REF][START_REF] Noble | Environmental assessment framework for identifying and mitigating the effects of linear development to wetlands[END_REF].

Reviews by [START_REF] Geneletti | Some common shortcomings in the treatment of impacts of linear infrastructures on natural habitat[END_REF] and [START_REF] Gontier | Biodiversity in environmental assessment-current practice and tools for prediction[END_REF] show that the effects of landscape fragmentation are more difficult to predict than the direct loss of habitat. According to these authors, current assessment methods are often restricted to protected areas or to a narrow strip on either side of the infrastructure. However, landscape fragmentation may have consequences on a far broader scale [START_REF] Forman | Estimate of the Area Affected Ecologically by the Road System in the United States[END_REF].

To assess the long-distance effect of linear infrastructures on species distribution, models must include connectivity metrics that take into account both structural (arrangement of habitat patches) and functional (behaviour of the organisms) aspects. With this aim in mind, the development of methods based on graph theory is promising [START_REF] Dale | From graphs to spatial graphs[END_REF][START_REF] Urban | Graph models of habitat mosaics[END_REF]. Graph theory, which originated in mathematics and the social sciences, is being used increasingly in landscape modelling [START_REF] Galpern | Patch-based graphs of landscape connectivity: A guide to construction, analysis and application for conservation[END_REF]. Landscape graphs provide a simplified representation of ecological networks and require relatively few species data [START_REF] Urban | Graph models of habitat mosaics[END_REF]. This approach is considered an interesting trade-off between information content and data requirements [START_REF] Canty | A comparison-shopper's guide to connectivity metrics[END_REF]. It is used to quantify landscape connectivity for focal species [START_REF] Ricotta | Quantifying the network connectivity of landscape mosaics: a graph-theoretical approach[END_REF][START_REF] Urban | Landscape connectivity: a graph-theoretic perspective[END_REF], select corridors between habitat patches [START_REF] Alagador | Linking like with like: optimising connectivity between environmentally-similar habitats[END_REF] and identify the key landscape features to be conserved in order to maintain connectivity [START_REF] Bodin | Ranking individual habitat patches as connectivity providers: Integrating network analysis and patch removal experiments[END_REF][START_REF] Saura | A new habitat availability index to integrate connectivity in landscape conservation planning: Comparison with existing indices and application to a case study[END_REF]. More recently graph-based connectivity metrics have been integrated as predictors into species distribution models [START_REF] Awade | Using binary and probabilistic habitat availability indices derived from graph theory to model bird occurrence in fragmented forests[END_REF][START_REF] Decout | Integrative approach for landscape-based graph connectivity analysis: a case study with the common frog (Rana temporaria) in human-dominated landscapes[END_REF]Foltête et al., 2012a;[START_REF] Pereira | Using spatial network structure in landscape management and planning: A case study with pond turtles[END_REF].

In this paper, we propose to assess and to map the long-distance effect of a high-speed railway (HSR) line on the distribution of the European tree frog (Hyla arborea) in the Franche-Comté region (eastern France). This study is based on a predictive modelling approach that estimates the potential impact of the HSR but does not measure the real impact. This approach is therefore put in place before the construction of the infrastructure and allows areas potentially affected by isolation to be mapped.

The choice of the European tree frog is justified by the recent decline in populations of this species in western Europe. This decline has several causes: climate change, increased UV-radiation [START_REF] Alford | Global Amphibian Declines: A Problem in Applied Ecology[END_REF], predation or competition, pollution and eutrophication of ponds [START_REF] Borgula | Causes of the decline in Hyla arborea[END_REF], road-kill [START_REF] Elzanowski | Amphibian road mortality in Europe: a meta-analysis with new data from Poland[END_REF], and in particular the destruction and fragmentation of the tree frog's habitat [START_REF] Andersen | Habitat fragmentation causes bottlenecks and inbreeding in the European tree frog (Hyla arborea)[END_REF][START_REF] Cushman | Effects of habitat loss and fragmentation on amphibians: A review and prospectus[END_REF][START_REF] Vos | Comparison of habitat-isolation parameters in relation to fragmented distribution patterns in the tree frog (Hyla arborea)[END_REF]. In the region under study, the development of the HSR and consecutive changes in connectivity may therefore impact the viability of tree frog populations. As the potential effect of the HSR is assumed to occur up to a long distance from the line, and not only in its direct vicinity, we used the methodological framework of [START_REF] Girardet | Designing a graph-based approach in the landscape ecological assessment of linear infrastructures[END_REF] and Foltête et al. (2012a) to integrate graph-based connectivity factors in the impact assessment. This method allowed us (1) to integrate connectivity metrics in a distribution model of the European tree frog defined at an initial state before the presence of the infrastructure, (2) to extrapolate the model after the construction of the infrastructure and (3) to compute the rate of change between the two probability maps from which to make a spatial assessment of the impact of the HSR.

Materials and methods

Data preparation

Study area

The study was carried out in the Ognon valley, a zone of 4600 km² in the Franche-Comté region of eastern France (Fig. 1). In this zone, where altitude ranges from 184 to 768 m, the landscape mosaic is dominated by forests (42% of total area), arable land (27%) and meadows (20%). The Ognon valley is strategic for environmental conservation because it contains many threatened species of birds (such as the little bustard, Tetrax tetrax), mammals (lesser horseshoe bat, Rhinolophus hipposideros), reptiles (European pond turtle, Emys orbicularis) and amphibians (European tree frog, Hyla arborea) [START_REF] Paul | Liste rouge des vertébrés terrestres de Franche-Comté[END_REF].

In December 2011, a high-speed railway line came into service in the Franche-Comté region after four years of construction. It is part of a larger project which will improve connections for eastern France with both Paris and the south of France. This infrastructure is 140 km long and 30 m wide on average and crosses the study area from west to east following the Ognon valley. The line includes a total 1300 m of viaducts and 2000 m of tunnels. In this study, this infrastructure is considered as impassable either because it forms a physical barrier or because traffic noise can disrupt the animal behaviour [START_REF] Eigenbrod | Quantifying the road effect zone: threshold effects of a motorway on anuran populations in Ontario, Canada[END_REF][START_REF] Lengagne | Traffic noise affects communication behaviour in a breeding anuran, Hyla arborea[END_REF] even when the infrastructure is on a viaduct. This simplified representation of reality is used to better predict the potential impact of the infrastructure on landscape connectivity and by repercussion on tree frog populations.

Study species

The tree frog is widely distributed in Europe from Spain to western Russia, but its populations have declined in north-western Europe over the last 50 years [START_REF] Corbett | Conservation of European reptiles and amphibians[END_REF]. The species is classified as endangered and is on the IUCN Regional Red List of Threatened Species for Franche-Comté where it is mainly present in the Ognon valley (Fig. 1) [START_REF] Pinston | Amphibiens et Reptiles de Franche-Comté. Atlas commenté de répartition[END_REF].

The tree frog occupies both an aquatic habitat for breeding and its larval period and a terrestrial habitat after breeding and during hibernation. The breeding pond consists in shallow and sunny ponds, marshlands, gravel-pits or river pools. Pond size does not appear decisive and ranges from 1 m² to 4000 m² [START_REF] Grosse | Migration in the tree frog Hyla arborea[END_REF]. Although its breeding pond is essential for reproduction, the tree frog spends most of its time on land. Its terrestrial habitat is composed of dense vegetation (trees, shrubs, bushes) which is well exposed to the sun [START_REF] Stumpel | The terrestrial habitat of Hyla arborea[END_REF]. The species often prefers edge habitats in agricultural environments: banks, ditches, edges of fields or of forests [START_REF] Pellet | Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland[END_REF]. The seasonal migrations between this terrestrial habitat from the breeding pond range from 250 m to 1000 m [START_REF] Stumpel | The terrestrial habitat of Hyla arborea[END_REF]. [START_REF] Vos | Comparison of habitat-isolation parameters in relation to fragmented distribution patterns in the tree frog (Hyla arborea)[END_REF] report that its presence in a pond is correlated with the amount of terrestrial habitat surrounding the pond.

Dispersal events are very important in the tree frog's life cycle. Juveniles disperse from the breeding pond into the surrounding landscape to join other ponds. Despite the fidelity of the tree frog to its breeding ground, some adults may disperse and change ponds [START_REF] Fog | Migration in the tree frog Hyla arborea[END_REF]. These dispersal events allow individuals to colonize new ponds or to recolonize sites where the species is nearing extinction [START_REF] Vos | A frog's-eye view of the landscape: quantifying connectivity for fragmented amphibian populations[END_REF]. Observed dispersal distances are generally less than 2000 m but may reach up to 4000 m [START_REF] Vos | Comparison of habitat-isolation parameters in relation to fragmented distribution patterns in the tree frog (Hyla arborea)[END_REF]. In this study, 2500 m was arbitrarily considered as the maximum dispersal distance.

Species data

Species presence was identified by listening for the calling males during the breeding period (April to July) and recorded between 1997 and 2010 by field specialists of a wildlife association (LPO Franche-Comté). Listening was done from sunset to midnight on warm, wet nights. Surveys were conducted near ponds known to be occupied by the tree frog and near other potentially favourable ponds. Each site was visited several times during the breeding period to ensure maximum probability of detection. Field specialists considered that a pond was occupied if at least one calling male was heard. In this study, the presence points corresponded to breeding ponds that were occupied at least one year from 1997 to 2010.

These surveys identified 87 geo-located presence points in the study area. These presence points were sampled using a rule of a minimum distance of 500 m between points to remove redundant points, such as the same point at different times, or points too close together. In this way 57 points were selected in all. From the surveys, individuals were mostly observed in ponds ( 22), marshlands (15) and river pools (13). The remaining 7 individuals were found in grasslands and forest edges. Half of the presence points were located within a 2500 m-wide strip on either side of the HSR line.

Because absence data for the tree frog were unavailable, the study used pseudo-absences instead of real absences [START_REF] Pearce | Modelling distribution and abundance with presence-only data[END_REF]. Starting from a grid of 5000 m-sized cells corresponding to twice the dispersal distance, a set of pseudo-absence data was generated by randomly sampling one point within each cell without a presence point. In this sampling procedure, a rule of inter-point distance of 2500 m was applied to avoid having two points close together. The resulting set of 119 pseudo-absence points and 57 presence points was considered as the target variable likely to be modelled from landscape predictors.

Landscape data

The study required the creation of two landscape maps, the first one describing the initial state before construction of the HSR line, the second map including the linear infrastructure. Except for the HSR line, the land use was identical on both maps so only the impact of the infrastructure would be estimated. Different data sources were combined using ArcGis 10 (ESRI, 2011). The 1 m-accuracy vectorial landscape databases provided by French cartographic services (DREAL Franche-Comté, BD Topo IGN) were used to represent wetlands, hedgerows, forests, buildings, roads, railways and rivers. In agricultural areas, remotely sensed data (IRS PAN+LISS-III, 7 m spatial resolution) were used to separate grassland and bare ground. A morphological spatial pattern analysis (MSPA) [START_REF] Vogt | Mapping spatial patterns with morphological image processing[END_REF] was also applied to the forest category to identify forest edges. All these data elements were combined into a single raster layer with a resolution of 10 m. In this raster layer, the HSR line was represented by a 3-pixel wide line to reflect its actual size. It also avoided potential discontinuities induced by the conversion of linear elements in a raster format [START_REF] Adriaensen | The application of "least-cost" modelling as a functional landscape model[END_REF][START_REF] Gurrutxaga | Key connectors in protected forest area networks and the impact of highways: A transnational case study from the Cantabrian Range to the Western Alps (SW Europe)[END_REF]. Altogether, thirteen landscape categories were obtained (Table 1).

Definition of cost values

As the ability of the tree frog to disperse depends greatly on the surrounding matrix, it is expected that cost distances should be more relevant than Euclidean distances. The ecological literature and expert opinions were thus used to classify each landscape category according to its resistance to movement (Table 1). Radio tracking experiments [START_REF] Pellet | Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland[END_REF][START_REF] Vos | Comparison of habitat-isolation parameters in relation to fragmented distribution patterns in the tree frog (Hyla arborea)[END_REF] have concluded that wooded grasslands and linear elements like hedgerows or forest edges facilitate movement and often provided the species' terrestrial habitat. Rivers and wetlands are less favourable because their permeability depends on the density of vegetation. Conversely, grasslands, roads and railways tend to constrain movement. Finally, the cores of forest patches, bare ground, buildings and motorways are considered highly impassable and are mostly avoided by the tree frog.

Given the difficulty in assigning cost values to landscape categories from the ecological literature [START_REF] Rayfield | The sensitivity of least-cost habitat graphs to relative cost surface values[END_REF], several resistance sets (Table 1) were tested in order to assess the sensitivity of the model to these cost values [START_REF] Pereira | Using spatial network structure in landscape management and planning: A case study with pond turtles[END_REF][START_REF] Verbeylen | Does matrix resistance influence Red squirrel (Sciurus vulgaris L. 1758) distribution in an urban landscape?[END_REF]. In the uniform resistance set, all landscape categories had a resistance value of 1, meaning that the landscape matrix was considered as homogeneous and Euclidean distance alone mattered. The equidistant set included values from 1 to 100 in increments of 25. The compressed set included values from 1 to 40 in increments of 10. The contrasting set included values close to either the minimum (1) or the maximum (100) values. The highly contrasting set was similar to the contrasting set with high cost values for the 'barrier' category.

Landscape graph analysis

Landscape graph construction

The nodes of the graphs corresponding to the habitat patches were defined as being the aquatic habitat units (breeding ponds) adjacent to an area of potential terrestrial habitat. From the resistance sets (Table 1), five sets of links characterized by a complete topology were defined to connect all the patches [START_REF] Galpern | Patch-based graphs of landscape connectivity: A guide to construction, analysis and application for conservation[END_REF]. Each link contained both the recording of its Euclidean distance and its cumulative cost distance. As least-cost distances were used, the maximum dispersal distance of 2500 m was converted to a value expressed in cost units, using a regression analysis where the Euclidean distance of all the links was considered as a linear function of the cost distance. Given the maximum dispersal distances thus obtained, five thresholded graphs were built by removing the links whose cumulative cost was higher than the maximum dispersal distance. As the HSR line on the second landscape map was considered to be an absolute barrier, its cost value was chosen so as to remove any links crossing the infrastructure when the graph was thresholded.

Computation of patch-level metrics

Many connectivity metrics have been developed in the literature [START_REF] Galpern | Patch-based graphs of landscape connectivity: A guide to construction, analysis and application for conservation[END_REF][START_REF] Rayfield | Connectivity for conservation: a framework to classify network measures[END_REF]. They may be calculated at different levels of the graph structure (global, by component, local) but in this study, only the patch-based level is relevant for providing predictive variables in a distribution model. From the works of [START_REF] Bunn | Landscape connectivity: A conservation application of graph theory[END_REF], Foltête et al. (2012a) and [START_REF] Urban | Landscape connectivity: a graph-theoretic perspective[END_REF], three metrics were defined representing the way in which a habitat patch can contribute to population dynamics.

(1) For a given patch i, recruitment R i represents the demographic potential which is intrinsic to the patch and independent of the graph. This metric may be quantified by patch size or the area of available resources within a given perimeter a i such that:

R i = a i (equation 1)
In this study, the potential recruitment of a patch corresponds to the amount of terrestrial habitat within a 500 m radius around the ponds, following [START_REF] Vos | Comparison of habitat-isolation parameters in relation to fragmented distribution patterns in the tree frog (Hyla arborea)[END_REF] and [START_REF] Pellet | Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland[END_REF] who emphasize the greater importance of such habitat over pond size.

(2) The weighted dispersal flux (F) represents the capacity of a patch to disperse individuals to surrounding patches independently of its own potential recruitment. This metric depends on the patches connected to the focal patch, weighted by both their recruitment and a decreasing function of the distance that separates them from the focal patch:

Fi=Σ n j=1 R j exp(-αd ij ) (equation 2)
where R j is the recruitment of patch j, d ij is the distance between patches i and j and α is a parameter representing the intensity of the distance effect.

(3) The betweenness centrality of long distances (BCl) represents the potential for a patch to be crossed by a path linking other patches, by giving more weight to the longer paths (Foltête et al., 2012a). This metric was used to access the potential role of long-distance paths for re-colonization of habitat patches after an extinction [START_REF] Urban | Graph models of habitat mosaics[END_REF]. Each path is weighted both by the recruitment of the two end patches and by the probability of occurrence of the path to improve its ecological significance, in the same way as the adaptation of the BC index proposed by [START_REF] Bodin | Ranking individual habitat patches as connectivity providers: Integrating network analysis and patch removal experiments[END_REF]. For a patch i, this index is given by:

BCl i = Σ n j Σ n k a j a k (1-p* jk ) j,k∈{1.
.n},k< j, i∈ P jk (equation 3)

with a j and a k being the potential recruitment of the patches j and k, p* jk the maximum product probability between patches j and k and P jk the set of patches crossed by the least-cost path between patches j and k.

F and BCl were adjusted using the same threshold distance of the graphs as a reference value corresponding to a movement probability of 0.05. In order to test the sensitivity of the model to the distance used both to threshold the graph and to adjust the metrics, four other threshold values were tested, in accordance with the movement abilities of the tree frog: 1000 m and 4000 m for the dispersal distance, 250 m and 750 m for the terrestrial habitat around ponds. Graphab 1.0 software (Foltête et al., 2012b) was used to construct the landscape graph and compute the patch-level metrics.

2.3. Species distribution modelling and diachronic analysis 2.3.1. Integration of patch-based metrics in a species distribution model (SDM)

An SDM was developed consisting in modelling the presence/absence variable from predictors representing functional connectivity. Following Foltête et al. (2012a), the patch-based metrics computed from the graphs were generalized to any point of the study area to provide predictive factors that could be integrated into this SDM. As the data points were not necessarily located within a patch, they were connected to the nearest patches according to the maximum dispersal distance and were associated with the mean of the local values of R, F and BCl. As individuals have a decreasing probability of dispersion with distance away from the patches, the values are weighted by a decreasing function of the distance from the edge of the patch such that w=exp(-αd).

The statistical analysis was performed using Microsoft® Excel 2010/XLSTAT©-Pro (Version 2012.6.02, 2003, Addinsoft, Inc., Brooklyn, NY, USA). In order to reduce multicollinearity, the correlation coefficients between each pairwise combination of explanatory variables were calculated using a Spearman rank correlation at a 5% confidence level. If pairs were highly correlated (>0.70), the less significant variable in relation to presence of the tree frog was eliminated. The relationship between the presence and absence of the species and predictive variables was analysed using a generalized linear model [START_REF] Mccullagh | Generalized Linear Models[END_REF] with binomial distribution and a logit link function [START_REF] Hosmer | Applied Logistic Regression[END_REF]. Several logistic regression models were computed by testing the dependent variable against all possible combinations of variables. The model that better explained the presence of the tree frog was selected based on the minimization of the Akaike information criterion (AIC) value. Models with AIC differences (ΔAIC) of less than 2 with the best model (i.e. the one with the smallest AIC) were considered as competing models [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF].

McFadden R-square values were calculated for the final model to give a measure of model fit by quantifying the amount of variability in the dependent variable explained by predictors. The assessment of the final model's accuracy was based on the measures derived from the confusion matrix: sensitivity, i.e. the proportion of observed presences correctly predicted; specificity, i.e. the proportion of observed absences correctly predicted; Cohen's kappa and the area under the ROC curve (AUC) [START_REF] Fielding | A review of methods for the assessment of prediction errors in conservation presence/absence models[END_REF]. Spatial autocorrelation of the residuals of the best-fitting model was checked by using a Moran's I correlogram to test assumptions of constant variance. As the data set was too small to be split into separate data sets, the final model was evaluated by the bootstrap resampling technique, i.e. using a random sampling with replacement from the original dataset, following [START_REF] Efron | An introduction to the Bootstrap[END_REF]. If the statistical model is globally validated, the SDM can be extrapolated to the entire study area with a spatial resolution of 50 m providing a continuous map of the probability of presence before the construction of the HSR line (time t 0 ).

Species distribution assessment

The landscape map was then modified by including the infrastructure (time t 1 ); a new graph was built with the same parameters as for time t 0 and the patch-based metric values were computed. From these data describing the state at t 1 , the model was again extrapolated to map the probability of tree frog presence after the construction of the HSR line. Diachronic data were thus produced describing the species distribution models before and after the construction of the infrastructure.

The rate of change in the probability of presence was calculated for each cell from the formula: Δp=(pt1-pt0)/pt0. This rate represents the local variation in probability of tree frog presence according to the model. The mapping of Δp in ArcGis 10 (ESRI, 2011) was used to visualize the impact of the HSR line and to identify areas likely to be most affected by the infrastructure. To investigate the relationships between the level of disturbance and the distance from the route, a regular grid with a 100 m spatial resolution was generated over the entire study area. A point was sampled at each node of this grid and contained both the rate of change in the probability of presence and the distance to the HSR line. Since this procedure is irrelevant if the species was absent before the construction of the infrastructure, only points with a presence probability of more than 0.5 before the HSR line was constructed were selected. The average and maximum rate of change was plotted against the distance from the infrastructure grouped into class intervals of 500 m. The two curves provide information about the spatial structure of the impact and the maximum distance of disturbance.

Results

On the landscape map for before the HSR line was built, 1464 habitat patches were identified varying from 0.01 to 86 ha (mean 0.6 ha). The resistance sets proposed in Table 1 were used to generate five graphs. For each graph, the metrics R, F and BCl were computed and analysed as predictive variables for tree frog presence. The correlation analysis (Table 2) showed that the R and F metrics were closely correlated. Of the two metrics, F was removed because it is the least significant variable and the more closely correlated with BCl. The model's sensitivity to the cost values was analysed by comparing the global results of the logistic regressions (Table 3). For each resistance set, the best model was always the one with R and BCl metrics. The highly contrasting resistance set was the most relevant with the smallest AIC value (124.68). The other four resistance sets were less relevant with AIC differences > 10. From the highly contrasting resistance set, the metrics R and BCl were calculated for several threshold distances to assess the model's sensitivity. For each threshold distance, the best model was still the one which included both the R and BCl metrics. For dispersal distances, the best model was the one with the lowest values (0> Δ AIC<2 for 1000 m and 2500 m) whatever the terrestrial habitat distance used. Conversely, models using the dispersal distance of 4000 m were less relevant with Δ AIC value > 10. According to the graph thresholded at 1000 m, the mapping of the links shows that the habitat network is highly fragmented in the Ognon valley (Fig. 2). Conversely, the network is more connected and joins that of the Doubs valley to the south with the graph thresholded at 4000 m. For terrestrial habitat distance, models using shorter distances (250 m or 500 m) are better whatever the dispersal distance (Table 4).

Table 4. Comparison of the best selected models using a logistic regression under each of the threshold distances to predict the occurrence of the tree frog. The dispersal distance was used to threshold the graph and to set the BCl metric. The terrestrial habitat distance was used to set the R metric. All of the best selected models listed in the table used both R and BCl metrics. Models were ranked according to Δ AIC. Fit statistics included the Akaike weight (ωi) and the area under the receiver operating characteristic curve (AUC). Given the results of the logistic regression (Table 3), four models (1, 2, 4 and 5) were considered as competitors for predicting the presence of the tree frog. As all of these models used two variables, the final model was selected based on the highest AUC value. So, the analysis used model 2 with the dispersal distance of 2500 m and the terrestrial habitat distance of 250 m.

Model

The two variables in this model explained 44% of the variance of the response variable (Table 5). The addition of altitude to the metrics R and BCl increased the model's explanatory power, which provided an AIC of 107.56 and explained 52% of the variance. Results of the regression analysis indicate that all variables are significant (p-value<0.01) and that BCl, followed by R, are positively correlated with the presence of the tree frog. Conversely, altitude has a negative effect on the species. This model has good discriminating power with an AUC value of 0.943 and a high correct classification rate with a Cohen's kappa of 0.69. However, absence is predicted better than presence (93% correctly classified against 74%). No significant spatial autocorrelation of the residuals was detected.

Table 5. Results of logistic regression modelling for the presence of the tree frog using a dispersal distance of 2500 m and a terrestrial habitat distance of 250 m (model 2). The limits of the 95% interval resulted from 10 000 bootstrap samples. From the two landscape maps, extrapolation of this model to all cells in the study area provided two probability maps of tree frog occurrence, before and after construction of the infrastructure (Fig. 3).

Variables

The highest values of presence probabilities are located in the Saone valley in the north, the Ognon valley in the centre and the Doubs valley in the south. The diachronic analysis shows that the impact of the HSR line is not uniform across the study area (Fig. 4). In the east, the probability values decrease sharply (from -60% to -99%) over a distance of several kilometres from the infrastructure. In the west, the impact is more focused on its route with values ranging from -20% to -70%. In the central part, the probabilities of presence seem to remain stable near the infrastructure but decrease slightly between 3 and 5 km. The superimposition of these results on the landscape map shows that the areas impacted by the HSR line correspond to the favourable landscape categories for the tree frog.

The curves of the average and maximum rate of change (Fig. 5) confirm that the impact decreases with distance from the HSR line. The largest disturbances (from -60% to -80%) occur within the first 500 m. Between 500 m and 3500 m, the HSR line generates a moderate disturbance with 90% of the points having a value of less than -50%. Beyond 3500 m the average disturbance is less than -10%. The 9th decile curve shows an increase of disturbance around 7 km with maximum values close to -25%. These points correspond to the impact estimated by the model in the north-east of the study area on the south side of the HSR line (Fig. 4). This area is occupied by several wetlands connected by a narrow corridor to the Ognon valley and could be potentially affected by the infrastructure despite its distance.

Discussion

This study was designed to prospectively assess the impact of the construction of an HSR line on the distribution of the tree frog in a study area located in the region of Franche-Comté. The combination of graphs and species distribution modelling is relevant in this study as it improves the ecological significance of models and makes a diachronic analysis feasible.

In terms of modelling of the species distribution, the final model is significant with only two graphbased metrics and altitude as predictors. These results confirm the role of the pond network (BCl) and the area of terrestrial habitat (R) as mentioned in [START_REF] Pellet | Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland[END_REF] and [START_REF] Vos | Comparison of habitat-isolation parameters in relation to fragmented distribution patterns in the tree frog (Hyla arborea)[END_REF].

Given that BCl proves to be the most significant predictor, the results of the modelling suggest that long-distance migrations play an important role in the distribution of the tree frog. Such findings are consistent with earlier studies showing that this species is characterized by a metapopulation structure [START_REF] Arens | Microsatellite variation and population structure of a recovering Tree frog (Hyla arborea L.) metapopulation[END_REF][START_REF] Pellet | Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland[END_REF][START_REF] Vos | A frog's-eye view of the landscape: quantifying connectivity for fragmented amphibian populations[END_REF]. However, this result could be partly related to the extent of the study area and to the landscape configuration. Linear-shaped valleys result in elongated subgraphs which increase potential patch crossings by a path linking other patches. As these valleys contain many presence points, the role of long-distance paths may explain the significant contribution of the metric BCl.

The analysis of sensitivity to cost values suggests that highly contrasting values between favourable and unfavourable landscape categories are especially relevant. Increasing the maximum cost value in the highly contrasting set significantly improved the model. It is essential therefore to take into account the effects of the landscape matrix, in particular barriers, when predicting the occurrence of the tree frog. Variability in the relevance of the model confirms the need to test several resistance sets as mentioned by [START_REF] Sawyer | Placing linkages among fragmented habitats: do least-cost models reflect how animals use landscapes[END_REF] and [START_REF] Spear | Use of resistance surfaces for landscape genetic studies: considerations for parameterization and analysis[END_REF]. The model was also tested with several threshold distances because of the many dispersal distances of the tree frog mentioned in the literature [START_REF] Fog | Migration in the tree frog Hyla arborea[END_REF][START_REF] Pellet | Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland[END_REF][START_REF] Vos | A frog's-eye view of the landscape: quantifying connectivity for fragmented amphibian populations[END_REF]. The shorter dispersal distances (1000 m and 2500 m) are the more relevant, which is consistent with the analysis conducted over the entire region of Franche-Comté (Foltête et al., 2012a). For the terrestrial habitat, the shorter distance (250 m or 500 m) is also more relevant, which suggests that the presence of the tree frog is related to the proximity of this habitat around ponds.

The diachronic analysis of the presence probability values shows that the potential impact of the HSR line declines with distance from this infrastructure. The impact ranges from a few metres to several kilometres, the largest decreases in the presence probability being close to the HSR line. However, in some sections, the impact is not necessarily located along the route and may occur 3 km from the HSR line. This variability is related to the landscape configuration and the initial state of the connectivity of habitat patches in the study area. Indeed, the extent of disturbance depends on the size of the subgraphs in the network, with a large subgraph increasing the distance of the impact as in the north-east of the study area. The maximum rate of change plotted against the distance from the infrastructure shows that the disturbance occurs at a distance greater than the maximum dispersal distance of the tree frog, thus confirming the assumption of the long-distance effect of the infrastructure.

This graph-based approach provides an approximation of the potential impact based on the model but not a hard and fast measurement of the true impact. The extent of the perturbation may be overestimated here by the species distribution sampling points. In order to validate our approach, these findings could be confirmed by field observations in the coming years to test whether the real impact of the infrastructure is similar to that predicted by the model. These surveys will also identify the causes of extinction of breeding populations. Several environmental factors may lie behind the extinction process and compound to the long-distance effect of the infrastructure.

The methodological approach used appears to be a handy tool for planners in assessing the impact of linear infrastructures on different spatial scales including the regional level, which is recognized as a gap in current methods [START_REF] Fernandes | Landscape ecology and conservation management-Evaluation of alternatives in a highway EIA process[END_REF][START_REF] Geneletti | Some common shortcomings in the treatment of impacts of linear infrastructures on natural habitat[END_REF][START_REF] Mörtberg | Landscape ecological assessment: A tool for integrating biodiversity issues in strategic environmental assessment and planning[END_REF].

The variation in the presence of the species can help to optimize the location of new protection areas or mitigation measures such as wildlife crossing structures, by identifying the areas most affected by the infrastructure. The results also provide information about the maximum distance of the impact, which is often difficult to assess. In the case of the HSR line in the Franche-Comté region, the environmental assessment studies focused only on a strip of 800 m on either side of the HSR line, which allowed the creation of new ponds to replace those destroyed by the construction of the infrastructure.

This study takes a species-oriented approach, which provides for a more realistic ecological analysis by considering the behaviour of a focal species. The species distribution model can also be validated using presence/absence data. This approach is particularly relevant to the conservation of threatened species. Nevertheless, given the diversity of wildlife, the impact assessment of an infrastructure cannot be limited to a single species. In this case, the habitat-oriented approach may seem more relevant by focussing on certain landscape categories such as forests or wetlands [START_REF] Gurrutxaga | Key connectors in protected forest area networks and the impact of highways: A transnational case study from the Cantabrian Range to the Western Alps (SW Europe)[END_REF][START_REF] Quintana | A model for assessing habitat fragmentation caused by new infrastructures in extensive territories -Evaluation of the impact of the Spanish strategic infrastructure and transport plan[END_REF][START_REF] Tannier | Assessing the capacity of different urban forms to preserve the connectivity of ecological habitats[END_REF]. But these habitat models raise the difficulty of the validation needed in an impact assessment process. Furthermore, the same habitat category may contain several species that have different behaviours and dispersal abilities and will not be affected in the same way by infrastructure. The habitat-oriented approach does not allow us to assess these different impacts. For a generic approach when species presence data are missing, the virtual species approach developed by [START_REF] Hirzel | Assessing habitat-suitability models with a virtual species[END_REF] to model the distribution of several species might be one way to quantify the impact in habitat patches and in their vicinities [START_REF] Girardet | Designing a graph-based approach in the landscape ecological assessment of linear infrastructures[END_REF].

Conclusion

The combination of landscape graphs and SDM seems a relevant way to improve methods for assessing the impact of linear infrastructure on the distribution of a given species. The species distribution assessment provides spatial indicators about the magnitude of the impact. The analysis carried out in the Franche-Comté region shows that probabilities of tree frog presence decrease by -90% in some areas. The extent of the impact is often greater than the maximum dispersal distance of the species. Used in a predictive approach, this method can assess several scenarios of linear infrastructure routes in order to select the one that generates the least impact on species distribution. After the construction of the infrastructure, the results may guide land planners in identifying the areas most affected with a view to conservation.

Fig. 1 .

 1 Fig. 1. Location of the study area in the Franche-Comté region. The land-use map was merged into four landscape categories to improve its readability.

Fig. 2 .

 2 Fig. 2. Complete graphs thresholded at different dispersal distances: a. 1000 m ; b. 2500 m and c. 4000 m.

Fig. 3 .

 3 Fig. 3. Probability of tree frog occurrence before (a) and after (b) the construction of the HSR line. These probabilities result from the SDM using model 2 including R, BCl and altitude as predictors.

Fig. 4 .

 4 Fig. 4. Estimated impact of the construction of the HSR line on the probability of tree frog presence, according to the species distribution assessment.

Fig. 5 .

 5 Fig. 5. Average and maximum variation in the probability of tree frog presence with distance from the HSR line grouped into class intervals of 500 m.

Table 1 .

 1 Sets of resistance values for each of the 13 landscape categories.

	Landscape categories	Function	Uniform Equidistant Compressed Contrasting	Highly contrasting
	Ponds	Aquatic habitat	1	1	1	1	1
	Hedgerows	Terrestrial habitat 1	25	10	5	5
	Forest edges	Terrestrial habitat 1	25	10	5	5
	Rivers	Suitable	1	50	20	10	10
	Wetlands	Suitable	1	50	20	10	10
	Wooded grasslands Suitable	1	50	20	10	10
	Grasslands	Unfavourable	1	75	30	95	95
	Roads	Unfavourable	1	75	30	95	95
	Railways	Unfavourable	1	75	30	95	95
	Bare ground	Barrier	1	100	40	100	1000
	Forests	Barrier	1	100	40	100	1000
	Buildings	Barrier	1	100	40	100	1000
	Motorway (A36)	Barrier	1	100	40	100	1000

Table 2 .

 2 Spearman correlation coefficients among study variables with a significance level of 5%

	Variables	R	F	BCl
	R
	F	0.835
	BCl	0.516	0.659

Table 3 .

 3 Comparison of the best selected models using a logistic regression under each of the five resistance sets to predict the occurrence of the tree frog. All of the best selected models listed in the table used both R and BCl metrics. Models were ranked using the change in the Akaike Information Criterion (Δ AIC). Fit statistics included the Akaike weight (ω i ) and the area under the receiver operating characteristic curve(AUC)

	Resistance sets	AIC	Δ AIC	ω i	AUC
	Uniform	147.38	22.70	0.00	0.869
	Equidistant	145.35	20.67	0.00	0.875
	Compressed	145.63	20.95	0.00	0.879
	Contrasting	135.86	11.18	0.00	0.911
	Highly contrasting	124.68	0.00	1.00	0.941

Acknowledgements

The research has been funded by the French Ministry of Ecology, Energy, Sustainable Development and the Sea (ITTECOP Program). Field data about Hyla arborea were provided by LPO Franche-Comté. The graph analysis was conducted as part of the Graphab project managed by the USR 3124 MSHE 744 Ledoux. Computations were performed on the supercomputer facilities of the MSHE Ledoux.


J N Mei

J L Soubeyroux

J J Blandin

Structural relaxation of Ti-based bulk metallic glasses

Keywords: Bulk metallic glass, Titanium alloy, Structural relaxation, Glass forming ability, Thermal stability

The enthalpy relaxation behavior of Ti41.5Cu37.5Ni7.5Zr2.5Hf5Sn5Si1 bulk metallic glass (BMG) was investigated in this study. It is found that relaxation behavior follows the general characteristics for amorphous materials: the annealing time dependence of recovery enthalpy follows a stretched exponential function with the mean relaxation time obeying an Arrhenius law. In addition, the equilibrium recovery enthalpy H T eq , mean relaxation time and stretching exponent are annealing temperature dependent, and the higher the annealing temperature, the lower the values of eq T H , and higher of .

The activation energy for enthalpy relaxation is calculated to be 3.06 eV, suggesting that the governing mechanism for the enthalpy relaxation process of this alloy is the rearrangement involving the collective hopping mechanism for the small and medium size atoms. Two parameters, g and g, representing the stretching exponent and the mean structural relaxation time at the calorimetric glass transition temperature, respectively, have been introduced to construct the correlation with glass forming ability and thermal stability. The high value of g for Ti41.5Cu37.5Ni7.5Zr2.5Hf5Sn5Si1 BMG that is higher than 0.84 however lower than that of typical BMGs which approaches unity reveals its relatively good, however worse glass forming ability compared with typical BMGs; in addition, its high value of g indicates its comparable good thermal stability with typical BMGs.

Introduction

Since a glass can be described as an undercooled melt, such glassy structure is thermodynamically metastable compared with the ideal glassy state and tends to undergo structural rearrangement to reach the ideal glassy state (structural relaxation) [START_REF] Chen | Glassy metals[END_REF]2] or transform to an equilibrium crystalline structure through a series of continuous transformations (crystallization) once the external energies are supplied either thermally by heat treatments or mechanically by application of external stresses, leading to continuous changes in physical, chemical and mechanical properties of amorphous materials. Ti-based bulk metallic glasses (BMGs) have attracted more attention as potential structural materials due to their excellent properties (low density, high strength and high specific strength) [3][4][5][6][7][8][9]. Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG, as a typical Be-free Ti-based BMG, has been found to exhibit good glass forming ability (GFA), thermal stability as well as room-temperature mechanical properties [10]. In addition, our recent investigations have shown that its mechanical property changes were caused by structural transformations [11], and the crystallization behavior of this alloy has been presented in a previous report [12]. The aim of this study is thus to clarify the structural relaxation behavior of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG for further understanding the GFA and thermal stability of this alloy in addition to the mechanical response induced by structural relaxation.

Experiment

The ingots of master alloy with nominal composition of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 were prepared according to the process described in ref. [11]. Cylindrical samples (2 mm in diameter, 40 mm in length) were prepared for these experiments. The glass transition temperature (T g ) and the onset crystallization temperature (T x1 ) were determined to be 432 and 485 o C, respectively, by differential scanning calorimetry (DSC).

Structural relaxation was investigated through measuring the relaxation of the frozen-in enthalpy towards the equilibrium state as a function of time at a certain temperature by using DSC. The enthalpy reduction during an isothermal relaxation below the calorimetric glass transition is recovered as an "overshoot" in the glass transition region during a subsequent continuous heating DSC run. The detailed experimental program can be summarized as followed: to erase the thermal history of metallic glasses, each sample is heated from room temperature to the desired temperature (about 20 °C above T g ) at a heating rate of 20 K/min, then immediately cooled down to room temperature at a cooling rate of 50 K/min, and then reheated to the isothermal annealing temperature T (387, 397, 412 and 422 °C) at a heating rate of 30 K/min to be annealed for various time t (5 min-10 h); after each isothermal annealing, the sample was heated up to high temperature to complete the crystallization (700 °C) at a heating rate of 20 K/min for the following calculation of recovery enthalpy; finally, this heating process was repeated for the baseline correction.

Results

The enthalpy relaxation of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG was investigated according to the process described above. Fig. 1 shows the typical continuous heating DSC curves of the Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 sample isothermally annealed (relaxed) at 387 o C as well as the as-cast (unrelaxed) sample. The enthalpy of a glass at a certain temperature T (below T g ) may deviate from its equilibrium value eq T H , since some additional enthalpy can be trapped when the glass forms. Long-time annealing of the glass at that temperature will result in the loss of this additional enthalpy and the glass gradually relaxes into the equilibrium supercooled liquid state. The enthalpy of the glass that is lost during the isothermal annealing can be recovered by a subsequent DSC scan of the annealed sample (H T (t)), resulting in an overshoot in the DSC curve with respect to the unrelaxed sample, as it can be observed from Fig. 1 where an overshoot is located at the vicinity of glass transition region (marked with dashed rectangle) and the area of the overshoot increases with annealing time t. The reduction of the enthalpy during relaxation can be understood as the result of local rearrangements of the atoms causing the reduction of the free volume that has been frozen-in during cooling throughout the glass transition. The measured recovery enthalpies H T (t) as a function of annealing time t at various annealing temperatures T of 387, 397, 412 and 422 o C for Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG are shown in Fig. 2. It is clearly seen that the relaxation process is time and temperature dependent. The value of H T (t) increases rapidly with increase in t at the initial stage of relaxation, then changes to increase gradually, finally tends to saturate, indicating that the amorphous materials relax towards lower enthalpic state with increase in annealing time t and eventually approach to the equilibrium state after a long-time annealing. Further investigation reveals that the H T (t)-t relation does not follow a simple exponential relaxation function, which could be due to the microstructure heterogeneities of the sample, and suggests that the enthalpy relaxation of the Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 liquid does not involve a single Debye relaxation event, in accordance with the previously reported amorphous materials. The time dependence of H T (t) at a given temperature of amorphous materials can be generally fitted by a stretched exponential relaxation function [13][14][15]:

]} ) ( exp[ 1 { ) ( t H t H eq T T =
(1) where is the mean structural relaxation time, eq T H is the equilibrium value of H T (t) for t at the annealing temperature T, is the stretching exponent whose value is 0<1, reflecting the width of relaxation time distribution spectrum originating from the inhomogeneity of the supercooled liquid. The value of =1 corresponds to a single relaxation time with exponential behavior. The smaller the value of , the more the distribution of atomic motions deviates from a single exponential behavior. So, if the relaxation time distribution becomes broader, the value of will be reduced, and the enthalpy recovery curve will be spread out over a wider temperature range. Obviously, the experimental H T (t)-t relation for Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG can be well fitted with stretched exponential relaxation function. The obtained eq T H , and , at various annealing temperatures are summarized in Table 1.

H

, and are annealing temperature dependent, and the higher the annealing temperature, the lower the values of eq T H , and higher of , indicating that the enthalpy recovery is determined by the annealing temperatures. The increase in equilibrium recovery enthalpy eq T H as well as the prolongation of mean relaxation time with decrease in annealing temperature is attributed to the slowdown of the relaxation kinetics. The annealing temperature dependence of eq T H , and is mainly ascribed to the degree of the amorphous phase deviating from its equilibrium state at each annealing temperature. It should be pointed out that for Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG, the stretching exponent is not constant but slightly increases with annealing temperature. Such annealing temperature dependence of stretching exponent has been found in some BMGs, for example, Pd 43 Cu 27 Ni 10 P 20 [15] Zr 46.75 Ti 8.25 Cu 7.5 Ni 10 Be 27.5 [16], and Zr 58.5 Cu 15.6 Ni 12.8 Al 10.3 N b 2.8 [17] BMGs, implying a complex structural relaxation behavior of BMGs.

It is also found that the experimental annealing temperature dependence of the mean relaxation time for Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG can be well fitted with an Arrhenius plot, and yields a ' 0 of 2.9610 -20 s and an E a of 294 kJ/mol (3.06 eV), similar to Zr-based BMGs [17]. It should be pointed out that such Arrhenius behavior couldn't hold over a wide temperature range since that actually T 0 is not equal to 0 and approximately several tens of Kelvins below T g for glasses. However, the T 0 item in VFT equation can be ignored when considering the temperature dependence of in the experimental annealing temperature range. The mechanism of enthalpy relaxation is believed to be associated with the atomic rearrangement. It is known that the activation energies for diffusion of the small size atoms such as Ni, Cu are about 2 eV, whereas the medium size atoms such as Ti have activation energies of about 3 eV, however, the activation energies for diffusion of the large size atoms such as Zr are much larger with respect to the small and medium size atoms. In the case of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 alloy whose activation energy for enthalpy relaxation is 3.06 eV, although the rearrangements of the medium size atoms Ti as well as the small size atoms Cu, Ni and Si are sufficient to cause complete relaxation into the enthalpic state of the supercooled liquid without involving the motion of the large size atoms (Zr, Hf, Sn). The complete rearrangement of the backbone of the structure is necessary because that the medium size atoms Ti are considered to occupy the backbone position of the amorphous structure, so the rearrangement involving the collective hopping mechanism for the small and medium size atoms is the governing mechanism for the enthalpy relaxation process of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 alloy, as is in agreement with the case of Zr 46.75 Ti 8.25 Cu 7.5 Ni 10 Be 27.5 alloy [18].

Discussion

The characteristic parameters, stretching exponent and mean structural relaxation derived from the stretched exponential relaxation function, are essential for the analysis of enthalpy relaxation behavior, which are believed to be correlated with GFA and thermal stability of amorphous materials. However, their characteristic of temperature dependence brings about difficulties for constructing the correlations with GFA and thermal stability.

In this study, two parameters, g and g , representing the stretching exponent and the mean structural relaxation time at the calorimetric glass transition temperature T g , respectively, are proposed to be the indicators of enthalpy relaxation properties. The relation between g and GFA of bulk metallic glasses is constructed through fragility index m as a chain, since the stretching exponent has a correlation with the fragility index m which is an indicator of the fragility of supercooled liquid and a strong liquid (with small fragility index) is generally correlated with a good GFA. It is known that most of the bulk metallic glasses show strong liquid behavior and generally have a fragility index of less than 50 [16,19,20]. In addition, a reduced m=42/ relation can be derived from a relation between the fragility index m and stretching exponent based on the defect diffusion model proposed by Bendler et al. [21], and this expression has been confirmed to be suitable for describing the m-relation for polymeric, alcoholic and metallic glasses. Accordingly, the value of stretching exponent for the bulk metallic glasses who exhibit a good GFA empirically should be larger than 0.84. It is found that the value of g for Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG is higher than 0.84, implying its relatively strong liquid behavior and accordingly relatively good GFA; however, the fact that its g value is lower than other typical BMGs indicates its worse GFA compared with other typical BMGs.

The relation between g and thermal stability of metallic glasses was constructed on the simple idea that the long structural relaxation time corresponds to a good thermal stability. There exists a linear relationship between the logarithmic relaxation time ln and the difference between the glass transition temperature and annealing temperature T, namely, ln = ln g + AT. The g value for this alloy is 160 s, much higher than that of other Ti-based BMGs, suggesting that Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG need relatively long relaxation time to reach the internal equilibrium state, and indicating its comparable good thermal stability with other typical BMGs.

Conclusions

Structural relaxation behavior of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 bulk metallic glass was investigated through relaxation enthalpy recovery measurements; the main results are the followings.

(1) Its enthalpy relaxation behavior follows the general characteristics for amorphous materials. Namely, the annealing time dependence of recovery enthalpy follows a stretched exponential function with the mean relaxation time obeying an Arrhenius law. In addition, the equilibrium recovery enthalpy eq T H , mean relaxation time and stretching exponent are annealing temperature dependent, and the higher the annealing temperature, the lower the values of eq T H , and higher of .

(2) The activation energy for enthalpy relaxation of Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG is calculated to be 3.06 eV, suggesting that the rearrangement involving the collective hopping mechanism for the small and medium size atoms is the governing mechanism for the enthalpy relaxation process of this alloy.

(3) Two parameters, g and g , representing the stretching exponent and the mean structural relaxation time at the calorimetric glass transition temperature, respectively, have been introduced to construct the correlation with GFA and thermal stability, respectively. The high value of g for Ti 41.5 Cu 37.5 Ni 7.5 Zr 2.5 Hf 5 Sn 5 Si 1 BMG that is higher than 0.84 is however much lower than unity revealing its relatively good glass forming ability. However, presents a worse glass forming ability compared with typical bulk metallic glasses; while its high value of g indicates its comparable good thermal stability with typical bulk metallic glasses.

Figure 1 .

 1 Figure 1. Typical enthalpy recovery DSC curves of the Ti41.5Cu37.5Ni7.5 Zr2.5Hf5Sn5Si1 samples after isothermal relaxation at 387 o C for different times as well as the DSC curve for an unrelaxed sample.

Figure 2 .

 2 Figure 2. Experimental relaxation recovery enthalpy HT(t) as a function of annealing time t at various temperatures of 387-422 o C for Ti41.5Cu37.5 Ni7.5Zr2.5Hf5Sn5Si1 BMG, and fitted with stretched exponential function.

Table 1 . The values of eq T H , and at various temperatures for Ti41.5Cu37.5Ni7.5Zr2.5Hf5Sn5Si1 BMG determined from the HT(t) vs. t curves fitted with the stretched exponential relaxation function.

 1

	T (°C)	H	eq T	(J/g)	(s)
	387		9.4		5988	0.7537
	397		7.4		2753	0.7870
	412		4.7		800	0.7953
	422		3.4		361	0.8762
	It is found that the values of	eq T

Acknowledgements

National Natural Science Foundation of China (50601011), National Basic Research Program of China (2007CB607603), Fundamental Research Project of National Defense of China (A2720060295) and China Scholarship Council supported this work.


Sarah Petit

Sébastien Pairis

Melissa Mikolajczyk

Luc Ortega

Jean-Louis Soubeyroux
email: jean-louis.soubeyroux@grenoble.cnrs.fr

Philippe Odier

Effect of twins in Ni substrates on the microstructure of La 2 Zr 2 O 7 films for coated conductors

Keywords: epitaxy, film, microstructure, La 2 Zr 2 O 7

La 2 Zr 2 O 7 (LZO) films were deposited by chemical solution deposition on Ni 95 Wi 5 Rolling Assisted Bi-axially Textured substrates to be used in YBa 2 Cu 3 O 7 (YBCO) coated conductors.

These LZO films were proved of good qualities for YBCO deposition by Metal Organic Chemical Vapour Deposition that is an economic process. The mosaic of LZO films is only slightly degraded by the process of grain-to-grain epitaxial transfer (16% with respect to that of the substrate). The film is composed of small crystallites (20 -40 nm) and larger anomalous crystallites (100 -400 nm) found in great number in transferred twins from the substrate. The anomalous crystallites are poorly crystallised or amorphous and contain more C than areas with normal crystallites. High temperature in-situ X ray shows a sudden crystallisation at 860°C that does not seems to involve a solid state reaction. The anomalous crystallites are analysed to result from a locally enhanced barrier to nucleation and might reveal sor characteristics of the crystallization.

Introduction

Many examples of buffer layer made of La 2 Zr 2 O 7 oxide (LZO) have been studied by chemical solution deposition (CSD) on highly bi-axially textured Ni-5at %W (Ni 95 W 5 ) substrates [1][2][3][4][5][6] obtained by the so called Rolling Assisted Bi-axially Textured technique (RABIT). LZO acts as a barrier against diffusion of the Ni toward YBCO [7,8] and must limit the oxidation during the different steps of the synthesis process of the coated conductor [9,10]. This buffer layer is used as a template to grow epitaxially the superconducting layer made of YBa 2 Cu 3 O 7 (YBCO) and for example deposited by Metal Organic Chemical Vapour Deposition (MOCVD) [11][12][13][14][15][16]. We focus on a simplified architecture composed of only one substrate, one buffer layer in LZO and one YBCO superconducting layer. This choice is made with the perspective of making an economic process. Using the combination of CSD for the buffer and MOCVD for the YBCO, critical currents reaching or exceeding 1 MA/cm 2 (self field at 77 K) have been obtained on Ni RABIT substrates. In MOCVD deposited YBCO on Ion Beam assisted Deposition (IBAD) structures, although the process is being much more advanced, a limitation to the current flow has been recently analysed to be caused by a-axis growth [17]. We also have observed similar phenomenon on our MOCVD deposited YBCO samples made on a single LZO buffer layer, see fig. 1. It is interesting to notice that these a-axis growths are not restricted to YBCO MOCVD on IBAD substrates but are also observed when YBCO is deposited on RABIT substrates by reel-toreel pulsed laser deposition [18].

The development of coated conductors requires attention to these defects. Their origin is not clear but is frequently assigned to a too low YBCO processing temperature; however it should be questioned whether it could be issued from the buffer itself. It is then necessary to identify all possible sources of defects in the buffer that could induce such disoriented grains.

Compared to more complexes architectures generally used (involving up to 5 or 6 intermediate layers), line ending with defects in the buffer layer is expected to be more prominent. Rikel et al. [13] have shown the importance of the quality of the buffer layer in this case where one LZO buffer on Ni RABIT substrate is covered with YBCO deposited by MOCVD.

LZO (a cubic structure with a 7.7 % structural mismatch with Ni 95 W 5 ) grow by epitaxy on Ni 95 W 5 after a rotation of 45° of its unit cell for better matching the substrate lattice [19]. Due to this property, many papers show that LZO reproduces exactly the grain morphology of the substrate obtained by the RABIT process [20]. The microstructure of LZO is made of small rounded crystallites (20-50 nm) with nanovoids [7] originated from the released gases in the CSD process under Ar-5% H 2 [21], but the crystallization process made these voids cubic [8]. The grain boundaries of the Ni substrate are transferred to the LZO microstructure by the epitaxial process giving rise to the typical grain morphology mentioned above. Twins that are present in the substrates are also reproduced in the LZO microstructure and an example is shown in the following (see fig. 2 with a transferred twinned grain visible in the center of the image). Many authors have attempted to optimize composition and annealing procedure of their rolled substrate in order to maximize the cube texture content and to minimize the residual twins because twins are considered as defects expected to inhibit epitaxial growth. However, very few publications have verified this fact (see for example ref [22]).

The aim of this work is to investigate peculiarities of the microstructure of LZO buffer layers grown on Ni 95 W 5 by CSD. This paper focuses on grains transferred from twins in the substrate and observed by Secondary Electron Microscopy (SEM), Electron Backscattering Scanning Diffraction (EBSD) and Emission Dispersion X ray spectroscopy (EDX) techniques. It is discovered that these grains are composed of anomalous crystallites that are also detected, sometimes, inside grains where most of the LZO crystallites are normal. The occurrence of these anomalous crystallites is discussed considering the nucleation of LZO with the help of in-situ X ray diffraction at high temperature.

Experimental details

Ni 95 W 5 RABIT substrates were received from Evico's company (Dresden-Germany) and coated after cleaning in acetone and methanol for 15 min each in an ultrasonic bath. The substrates (typically 5 cm long) were covered with LZO according to a procedure where the propionic precursors of La and Zr are synthesized first separately [23], then mixed (1:1) at 60°C for 1 h with propionic acid to a concentration of 0.6 M. This solution was used to dip-coat the samples at a withdrawal speed of 66 mm/min. After drying and crystallization at 960°C in Ar-5%H 2 forming gas, the thickness of the film was ∼ 70 nm [10]. The film thickness was measured by optical means and controlled by microscopy on cross section obtained by ion milling.

Texture of both substrates and LZO films were obtained by X-ray diffraction (Cu K α ) with a Seifert MZ-VI in the Schultz geometry. The beam size (horizontal 0.8 mm x vertical 2 mm) is defined by an appropriate collimating multilayer optics from Xenocs (Grenoble-France) which provides a parallel beam (divergence of 0.06°). A graphite analyzer coupled to a point detector (NaI) collects the diffracted intensities with a very high signal/noise ratio (>10 5 ).

Measurement of the direct beam and careful sample alignments were performed before each measurement allowing valuable comparisons between samples.

In situ X-ray diffraction versus temperature (called further "in situ HT X-ray") was performed with a Brucker Advance D8 diffractometer working at the wavelength of CuKα and equipped with a heating stage protected with a graphite dome allowing measurements of asymmetric reflections. The furnace was flushed with He-5%H 2 and both (222) and (400) reflections of LZO were recorded quasi simultaneously versus temperature thanks to a fast Vantek positive sensitive detector. The heating temperature schedule (heating 300°C/h, dwell 60 min at 960°C) was selected to be as close as possible as the one used in the films' crystallization.

SEM images have been performed using a Field Emission Scanning Electron Microscope (FESEM) from Zeiss Ultra+ (Zeiss, Germany) equipped with an EBSD unit using "HKL" indexing software (Oxford Instruments) and an EDX spectrometer from Bruker. SEM images were taken at low operating voltage, 3kV, to have more sensitivity to the surface details. EDX spectra were obtained on a silicon drift detector Bruker 4010 (SDD) used with a thin window Moxtek AP3.3 (x-ray transmittance for carbon line of about 46%). The SDD detector has an energy resolution of 51eV for C-Ka, 57eV for O-Ka and 124eV for Mn-Ka.

The analyses were done with a 8mm working distance, a take-off angle of 35°, a measure time analysis of 100s (with a dead time less than 2%), at 5kV. Atomic Force Microscopy (AFM) images were acquired with a Veeco D3100 and a Nanoscope V controller, operating in a tapping mode with Si tip (radius 10 nm) at ambient conditions.

Thermal analysis was performed with a SETARAM (Lyon, France) TAG1600 flown with Ar and allowing measurements up to 1600°C with a high sensitivity (µg). The occurrence of two symmetrical furnaces allows avoiding gas density corrections. The TAG1600 is equipped with a differential thermal analysis modulus enabling to measure simultaneously weight variations and thermal analysis. It uses two crucibles made in alumina (150 µl), one is used as a reference and the other for the sample (a few mg).

II. Results

The deposited LZO films were crystallized according to a process close to the one described in ref [6]. This process involves a pyrolysis step under vacuum that allows an efficient elimination of organic solvents in the temperature range 350°C. It is composed of a ramp under vacuum up to 350°C (550°C/h) followed by a dwell of 60 min and then a crystallization step involving a ramp up to 960°C followed by a dwell of 30 min under Ar -5 %H 2 flow (5 l/min).

This treatment provides reproducible results concerning the texture. On a series of 35 samples, the average in-plane misorientation was Δφ = 7.0° ± 0.7° and out of plane misorientation was Δω = 6.3°±0.6° RD and Δω = 10.4°±1.5° TD respectively. Compared to Ni misorientation, the ratio (misorientation) LZO /(misorientation) Ni was constant and equal to 1.16, revealing only a small degradation of the texture transferred to the buffer by grain-to-grain epitaxy. Moreover, this process gives crystallized films up to their ultimate surface as probed by EBSD. Similar results were observed at Nexans Hürth [24]. Figure 32 shows the overall microstructure observed by SEM with well visible grains transferred from Ni substrate. Some grain boundaries are more marked than others. The different grey levels are related to variations of orientation of the different grains which are easily quantified by EBSD (not shown) and correspond to the out of plane and/or in-plane deviations also revealed by X-ray diffraction. Figure 23 shows a zoom of another sample of the same series with a twin transferred from the Ni substrate in the center of the image. Twins in substrates are originated from the recrystallisation process of the substrate [25].

To get information about the individual crystallites of LZO, zoomed pictures of the surface have been obtained by SEM and AFM, with the advantage in this case to get 3D information. The images of fig. 4 show typical features of LZO microstructure; in our case it is mainly composed of rounded crystallites (20-40 nm) with some additional larger crystallites, see fig. 4b and fig. 5. In the following we shall distinguish between grains transferred from substrate and crystallites of LZO developed during the crystallization of the film. The larger crystallites are in rather small number in this portion of the sample. Analysis of their surface, insert of fig. 5,

shows clearly that these large crystallites possess low surface roughness and are underdeveloped crystallites in comparison to normal crystallites (their surface is 3 nm below the mean surface of the normal grains). The overall roughness is in the range of 2 nm, i.e. smaller than the depth of the anomalous crystallites below the surface. These anomalous crystallites are 4-10 times larger than the normal crystallites, with sizes reaching 400 nm, they have not been discussed so far in literature, although some reports do show their finger print [7,26]. We have also observed these anomalous crystallites in LZO films produced at Nexans-Hürth (Germany) and more recently on LZO coated substrates from AMSNA. Curiously, it was observed that some grains do not contain any anomalous crystallites while, for unknown reasons, an adjacent grain could contain several or even many. Their aspect is also variable as is shown fig. 6 This suggests that a transformation between "amorphous like" to "crystallized like" exists within the time scale of the annealing, that is a rather slow kinetic.

Because these anomalous crystallites have rather small sizes, it was not easy to determine for sure their crystallization state by EBSD nor their chemical composition by EDX. Zones containing high concentration of such anomalous crystallites were then searched. where either no Kikuchi lines are discernible or cannot be indexed. In our case, the underlined area does not show visible Kikuchi lines (no diffraction) despite the fact that it is covered with the same thickness of LZO than elsewhere (this was deduced from the evolution of the EDX intensity of Zr and La peaks in a profile made across a twinned area). Note that adjacent grains show the typical Kikuchi lines of LZO crystallites. The loss of observable Kikuchi pattern in anomalous crystallites was then checked in grains containing isolated anomalous crystallites. It was confirmed that the Kikuchi lines disappears in many anomalous crystallites but not for all of them; some are crystallized but with different orientations with respect to the majority of crystallites.

To get some insight in the chemistry involved in the inhibition of the crystallization of anomalous crystallites, local chemical analyses were performed. It was not possible to get any difference between an anomalous crystallite and normal crystallites because of the spatial resolution of the EDX measurement. We then measured a twinned area containing many anomalous grains assuming it to be representative of the anomalous crystallites. A composition profile across a grain and an adjacent twin does not show any anomaly for Zr, La, O, Ni.

Investigation of the carbon content reveals some interesting differences. The C level is systematically higher, up to four times more, in the twinned area compared to the normal area, as shown in fig. 10. A comment concerning the carbon detection must be made here. Although, the voltage was limited to 5 kV (compared to 20 kV often used) to favor ionization of low energy lines and limit the contribution of the substrate, cracking of the residual atmosphere by the electron beam is a major phenomenon resulting in the deposition of carbon under the spot of the electron beam. It can be seen (points 19, 20 and others) on fig. 10. The kinetic of deposition is interesting to follow: it is composed of a first rapid step followed by a slow one. The first step is due to the carbon contained in the film while the slow step is due to the progressive carbon contamination from the residual atmosphere. In the twinned area, the contribution of film's contained carbon is much larger than elsewhere in normal crystallites areas. This observation was repeated several times on several twinned areas.

Finally, the crystallization of the film was investigated with the aim to get insight into the nucleation mechanism. The in-situ HT X-ray system allows to record (400) and (222) reflections from LZO versus temperature quasi simultaneously. On fig. 11, the diffracted intensity versus Bragg angle is represented in a 2D plot when the sample surface was set vertical (i.e. parallel to the X-ray diffusion vector). The temperature cycle is superimposed in red and refers to right and upward scales. The main contribution arises from Ni (200) reflection at 2θ = 51.5° which is insensitive to heating except small shifts due to thermal expansion. This is the position expected for Ni 95 W 5 (a = 3.541 Å). This reflection is accompanied by a reflection at 2θ ∼ 33° observed when the temperature is above T = 860°C, it is due to (400) Bragg planes of LZO growing parallel to the substrate. Weak reflections are due to AlN support and parasitic diffraction induced by the graphite dome. Fig. 11 shows a similar image but for the sample tilted at χ = 54.7° from vertical and then in position to make (222) LZO planes to diffract. As a consequence, fig. 11 is marked by a unique feature at 2θ ∼ 29° corresponding to (222) planes appearance. The exact angles are consistent with the unit cell parameter of LZO (a = 10.786 Å). The threshold for the onset of this diffraction is observed at the same temperature as for (400) planes. This confirms the epitaxial growth of LZO on Ni 95 W 5 substrate from in situ X ray at high temperature.

Although, this is not new, the high temperature (860°C) of crystallization and its sudden onset is surprising considering the early mineralisation of ZrO 2 observed at 450°C according to thermal studies on the decomposition of Zr propionates [23]. In our case, although Zr propionate was mixed with La propionate to form the precursor for LZO deposition, the thermal weight evolution measured previously [28] is consistent with the early formation of ZrO 2 [25]. As a consequence, LZO synthesis was expected to involve a solid state reaction between ZrO 2 and La 2 O 3 or more probably an oxycarbonate of this oxide. Effectively, the thermal decomposition of La acetylacetonate involves the intermediate formation of an oxycarbonate, and we have observed that the decomposition of La propionate also involves a step with oxycarbonate [29], see figure 12. According to this, the mixture ZrO 2 + oxycarbonate remain amorphous up to a rather unexpected high temperature (860°C). The very high under-cooling of such amorphous films may justify a high temperature of nucleation as observed here [30].

Discussion

The observation of locally amorphous crystallites or even amorphous areas in crystallized buffer layers is of importance since they are sources of defects in the YBCO layer to be deposited on top. This is even more important in the present case of a simple architecture composed of only one buffer layer. Because YBCO nucleates on the top surface of the buffer, amorphous areas will become zones where homogeneous nucleation or a axis nucleation will take place because they have lower energy barrier to nucleation. These non orientated c axis areas are non favorable orientations for super-current flow and source of current limitation. Unfortunately, we have presently no correlation with the a axis content and Jc, we just know that it limits the current flow [17]. This is also a big challenge to correlate a axis growth to defects of the buffer layer. We just know for the moment, from cross sections studies, that a axis growth can appear from the buffer and go across the entire YBCO layer (not shown).

The observation of areas where crystallization is absent is surprising considering the high temperature used for crystallization, i.e. 960°C, that is 100°C above the crystallization onset measured here and confirms previous measurements made with equipments measuring only symmetrical lines and not able to ascertain the epitaxial growth directly [31,32]. This proves that the energy barrier to nucleation was higher in these areas than elsewhere and has not been overcome with the temperature used. In confirmation, recent experiments show that heating at a higher temperature; i.e. 1000-1050°C, make these anomalous crystallites to disappear.

The anomalous grains, also amorphous, are underdeveloped grains which surface remains below the surface of normal crystallites. This gives an insight in the crystallization process. When the crystallization occurs, one can anticipate that a 3D grows starts with the creation of voids and a redistribution of the solid matter. In this viewpoint, voids observed by many persons in LZO film produced by CSD would have their origin in the crystallization mechanism more likely than in gas release. This is still an open question.

In twinned area (with frequent orientation (122)), due to crystallographic strains, the nucleation of (200) planes is highly improbable and the LZO remains amorphous on top or crystallized locally with a random orientation due to homogeneous nucleation. Patches of uncrystallized LZO on normal grains of Ni is more difficult to understand and suggests that some properties of the interface are in cause. More efforts have to be done in this direction in the future to make the buffer layer more reliable and exempt of deficient zone.

III. Conclusion

Amorphous crystallites have been found in LZO films processed by CSD technique.

These crystallites are due to a higher barrier for nucleation than for normal crystallites that is not overcome by the processing temperature used here. Amorphous crystallites are in high concentration on twin zone transferred from the substrate and found sporadically on normal grains transferred by grain-to-grain epitaxy from the substrate. Reducing the number of twins is an obvious conclusion already taken in charge by the substrates manufacturers. Moreover, identification of the reason for locally inhibited nucleation is important if one wants to decrease the processing temperature and take benefit of the large temperature range (100°C) that exists between the actual processing temperature and the crystallization temperature.

Figure Captions

Fig. 1 YBCO a-axis oriented grains have grown on a grain of Ni bi-axially textured covered by an epitaxial buffer layer of LZO. This is clear on the center of the figure. YBCO was deposited by MOCVD.

  by SEM. In this figure, different portions have been underlined to guide eyes. Portion denoted (a) appears "amorphous like" with no contrast inside the anomalous crystallite. Portion denoted (b) shows normal crystallites (typical size of 20-40 nm), grouped in colonies having an identical size and shape than the anomalous crystallites (a). Notice that the frontier between colonies disappears in grains where no anomalous crystallites are visible. Portion (c) denotes areas which are intermediate between (a) and (b).

  Anomalous crystallites are observed with a high concentration in of twins transferred grains, as shown in fig.7, part a. Part b of this figure shows a zoomed picture of such transferred twin. These anaomalous crystallites have the same typical morphological features than those detailed previously. Note that the adjacent grains, which are not twinned, do not contain anomalous crystallites. X-Ray diffraction has been acquired on these films, with the aim to identify, if possible, the crystallization state of transferred twin grains. Figure8compares the contribution of the substrate (pole figure of Ni(111) reflection, part a) to that of the LZO film (pole figure of LZO(222) reflection, part b) deposited on top of it. These pictures show raw data plotted in log scale with the same criterion: the intensity levels are separated with the same interval of intensity to give a similar representation. The substrate shows the typical behavior of a cube texture plus diffracted intensities for tilted angles in the range χ = 0-20° which is typical of contributions from twinned grains of the Ni matrix [27]. In comparison, LZO film's pole figure shows intense contribution at χ = 54.7° of the cube texture and small distributed contributions elsewhere. For LZO crystallized on the twinned area one expect spots in a crown around χ = 16°. No such spot are visible suggesting perhaps amorphous grains. A typical twinned area was then investigated by EBSD to provide information concerning the crystallization of the surface (10-20 nm in depth) and on its orientation. A SEM image of the area, tilted at 70° from the normal to the sample, is shown in part 1 of fig.9. It evidences the presence of a twinned area that is underlined by the dotted line. An EBSD image of this area is shown in part 2 of fig.9 where the different color encodes rotations around the normal of the grains with the Euler angles coordinates. Black encoding is for non-indexed parts, i.e. areas

Fig. 2 Fig. 3

 23 Fig.2 LZO on Ni 95 W 5 with a twin (at center) transferred from the substrate.

Fig. 4

 4 Fig.4 Microstructure of typical LZO grains by AFM.

Fig. 5

 5 Fig.5 An anomalous grain of fig.4a. Insert: height profile.

Fig. 6

 6 Fig.6 Aspect of different crystallites. Contour of colonies of grains has been highlighted by

Fig. 7

 7 Fig.7 Areas with twined grains showing high proportion of anomalous grains.

Fig. 8

 8 Fig.8 Pole figures for a LZO/ Ni 95 W 5 buffer.

Fig. 9

 9 Fig. 9 SEM (tilt = 70°) and EBSD of a twinned area with normal adjacent grains.

Fig. 11

 11 Fig.11 Crystallization of a LZO film on Ni 95 W 5 RABIT substrate followed by in-situ HT X-ray

Fig. 12

 12 Fig.12 Thermal weight analysis/Differential thermal analysis of La(prop) 3 showing the

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Acknowledgments

The authors wish to thank the Cluster MACODEV of Rhône-Alpes Region (France) for supporting equipment acquisition, FEDER European funds and AMSNA for supporting salaries for Dr S. Petit and M. Mikolajczyk and Nexans for supplying LZO films deposited on Ni 95 W 5 RABIT substrates. Dr O. Stadel from Percotech is acknowledged for MOCVD deposition on LZO buffered Ni RABIT substrates.