Saskia Jancke
email: saskia.jancke@googlemail.com

Peter Giere
email: peter.giere@mfn-berlin.de

Patterns of otter

Keywords: Road kill, Habitat connectivity, Mitigation measures, Uckermark County, Germany

come

Introduction

Eurasian otters Lutra lutra suffered a widespread decline in Central Europe over the last century due to persecution, habitat loss and pollution of watercourses with pesticides [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Macdonald | Otter distribution in Europe[END_REF][START_REF] Strachan | Otter survey of England 1991-94[END_REF].

The otter is listed in Appendix II of the Council of Europe Convention on the Conservation of European Wildlife and Natural Habitats (Council of Europe 1996) and in Appendix I of CITES (International Union for Conservation of Nature 2009). Otters are further protected under European law, being listed in Annex IIa and IVa of EC Directive 92/43, Conservation of Natural Habitats and Wild Fauna and Flora (the "Habitats Directive"). In the Red List of Germany, Eurasian otters are listed as an endangered species [START_REF] Binot | Rote Liste gefährdeter Tiere Deutschlands[END_REF].

Road mortality replaced drowning and trapping [START_REF] Stubbe | Der Fischotter Lutra lutra in der DDR[END_REF][START_REF] Stubbe | Der Fischotter Lutra lutra (L., 1758) in den mittleren Bezirken der DDR[END_REF] as the predominant cause of otter deaths recorded in Europe [START_REF] Green | Otter survey of Scotland 1991-1994[END_REF][START_REF] Hauer | Mortality patterns of otters (Lutra lutra) from Eastern Germany[END_REF][START_REF] Körbel | Vermeidung der durch den Straßenverkehr bedingten Verluste von Fischottern (Lutra lutra)[END_REF][START_REF] Sommer | Daten zur Populationsökologie des Fischotters Lutra lutra (Linnaeus, 1758) in Mecklenburg-Vorpommern[END_REF][START_REF] Stubbe | Tiere im Konflikt 1, Monitoring Fischotter 1985-1991[END_REF][START_REF] Wölfel | Ein kohärentes Netz von Schutzgebieten für den Fischotter in Mecklenburg-Vorpommern[END_REF][START_REF] Zinke | Fischotterverluste in der Westlausitz und angrenzenden Gebieten in den Jahren 1985 bis 1995[END_REF], and the numbers of otters killed on roads are increasing [START_REF] Green | The impact of hunting, poaching and accidents on otter survival and measures to protect individual animals[END_REF][START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Zinke | Die Todesursachen der im Museum der Westlausitz Kamenz von 1985-1991 eingelieferten Fischotter Lutra lutra (L., 1758)[END_REF][START_REF] Zinke | Fischotterverluste in der Westlausitz und angrenzenden Gebieten in den Jahren 1985 bis 1995[END_REF]. Despite the likelihood of being better recorded than other forms of mortality, road mortality is expected to have a strong impact on populations [START_REF] Philcox | Patterns of otter Lutra lutra road mortality in Britain[END_REF]. Furthermore, traffic collisions with otters may pose a risk to motorists. Consequently, a methodology for predicting potential accident sites involving wildlife is increasingly important.

In many other regions, otter road accidents mainly occur where roads cross watercourses [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Körbel | Vermeidung der durch den Straßenverkehr bedingten Verluste von Fischottern (Lutra lutra)[END_REF][START_REF] Philcox | Patterns of otter Lutra lutra road mortality in Britain[END_REF]) because otters avoid swimming underneath bridges but instead often leave the watercourse to cross the road. So far, different explanations for this behaviour have been brought forward [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Körbel | Vermeidung der durch den Straßenverkehr bedingten Verluste von Fischottern (Lutra lutra)[END_REF][START_REF] Madsen | Otter Lutra lutra mortality in relation to traffic, and experience with newly established fauna passages at existing road bridges[END_REF]. In the Uckermark County, however, the abundance of lakes creates a potentially different situation regarding accident sites.

Strongholds of otters are nowadays found in Ireland and Britain. Some parts of Central Europe (e.g., Germany and Austria) appear to support fragmented populations, while otters are extinct in Switzerland [START_REF] Kranz | Zum Potential der natürlichen Wiederbesiedlung der Schweiz durch den Fischotter Lutra lutra[END_REF]) and the Netherlands, where reintroduction attempts took place (de Jongh 1999; [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Weber | Fischotter (Lutra lutra) im Schwarzwasser-Sense-Gebiet: Dokumentation eines gescheiterten Wiedereinbürgerungsversuchs[END_REF].

The state of Brandenburg is one of the few regions in Germany with stable populations of otters [START_REF] Teubner | Die aktuelle Verbreitung des Fischotters Lutra lutra (L., 1758) im Land Brandenburg[END_REF]. Their existence in Germany is mainly threatened by habitat fragmentation and an increasing volume of road traffic [START_REF] Ansorge | Zur Situation des Eurasischen Fischotters Lutra lutra Linné, 1758 im Raum Oberlausitz-Sachsen[END_REF][START_REF] Dolch | Haupttodesursachen des Fischotters-Lutra lutra (L., 1758) im Land Brandenburg in der Zeit von 1990 bis 1994[END_REF][START_REF] Uthleb | Zur Populationsstruktur des Fischotters Lutra lutra (L. 1758) im östlichen Deutschland[END_REF][START_REF] Wölfel | Ein kohärentes Netz von Schutzgebieten für den Fischotter in Mecklenburg-Vorpommern[END_REF][START_REF] Zinke | Fischotterverluste in der Westlausitz und angrenzenden Gebieten in den Jahren 1985 bis 1995[END_REF]).

The aims of our research were to find characteristics of typical otter road accident sites in the lake-dominated landscape of the Uckermark County, predict potential accident sites using geographic information system (GIS) tools and, ultimately, to find adequate mitigation measures to reduce otter road mortality.

Materials and methods

Study area

The study area comprises the entire Uckermark County, which is located in the northeast of the state of Brandenburg in Northeast Germany. Covering an area of 3,058 km², it is the largest county of Germany with a relatively low population density of 47 residents per square kilometre. The Uckermark County has 600 lakes larger than 1 ha and 2,800 km of watercourses (Fig. 1). The landscape comprises dry grassland, heathland and forest. About 60% of the area is intensively used for agriculture, while around 50% is designated for nature conservation.

Due to the abundance of water bodies and the relatively low human population density, the Uckermark County offers good conditions for the otters, which are distributed all over the area [START_REF] Teubner | Die aktuelle Verbreitung des Fischotters Lutra lutra (L., 1758) im Land Brandenburg[END_REF]. Otter populations in the Uckermark County are connected with those in the state of Mecklenburg-Western Pomerania and in Poland by watercourses such as the rivers Oder and Untere Havel [START_REF] Dolch | Der Fischotter im Land Brandenburg[END_REF].

Data collection and causes of mortality

All otters found dead in the Uckermark have routinely been recorded by the Naturschutzstation Zippelsförde des Landesumweltamtes Brandenburg (Brandenburg State Office for Environment) since 1990. The records provide information about the cause of death, date and location of the finding (marked on a 1:25,000 map) and, in some cases, details about the finder as well as about the specimen found (size, weight, sex, age and nutritional condition).

For the present study, accident sites from the years 1990-2003 (Fig. 1) were characterised with features of traffic and road patterns, otter habitat suitability, as well as watercourse crossings modified from Ebersbach and Hauer (1998, unpublished report: Untersuchungen zur Lebensraumgestaltung und Biotopvernetzung für den Fischotter-Erkennen von Gefahren, Aufzeigen von Lösungen und Maßnahmen. Abschlußbericht zum Fischotterprojekt im Spree-Neiße-Kreis im Auftrag des NABU-Landesverbandes Brandenburg e.V). Road patterns were examined to assess the influence of speed limit on the risk potential. Habitat features such as the surrounding vegetation, landscape, distance to the next watercourse, situation within a network of watercourses, size and characteristics of the water body were included in the survey to find out whether otters prefer certain habitat features or passage ways. All variables are listed and described in Table 1. River crossings are an important feature concerning the investigation of otter road mortality. Therefore, the presence and type of river crossings, as well as the presence and size of ledges or banks, were recorded to describe otter road accident sites.

Statistical analysis

For the distance between road and watercourse, as well as the number of casualties relating to speed limit, correlation coefficients of determination were calculated using parametric (for speed limit-Pearson's r) and nonparametric (distance between watercourse and road, Kendall's tau) tests of correlation.

Using SPSS 12.0, the main features of water bodies at the accident site, the occurrence and structure of a bridge, distance to the nearest body of water, vegetation at the accident site, flow velocity and the situation within a network of watercourses (all ordinal data) of the otter road accident sites were combined to two components using a principal component analysis (PCA). A preliminary analysis was accomplished to test the included variables for multicollinearity. An initial PCA was conducted to obtain the eigenvalues and to conclude the number of components.

Using these two components, the accident sites were plotted in a two-dimensional illustration. In this scatterplot, different groups of accident sites were identified. These groups were tested using a discriminant analysis in SPSS, which examines the significant difference of these groups. The features describing these groups were tested for significance (χ²-test).

Geographic information system

ArcView GIS 3.2 was used to identify potential accident sites. ATKIS layers depicting the water distribution and road networks of the Uckermark as well as the topograph-ical grid map of the area were provided by the Environment State Office of Brandenburg.

All roads on the road network layer were split into 100m fragments, while features within a significant distance to water bodies were selected by theme. The selected road

Variable Features

Width of watercourse (m) <1, 1-2, >2-5, >5-10, >10-20, >20 Depth of watercourse (m) <0.5, 0.5-1, 1-2, 2, >2 Network of watercourses Linear watercourse without major tributary, single branching watercourse on one side, small individual watercourses on either side, several branching watercourses on either side, network of ponds, network of lakes Flow velocity Dry/stagnant water (<0.1 m/s), slow (0.1-1.5 m/s), fast (>1.5 m/s), turbulent (with rapids) Bridge span (m) <0.5, 0.5-0.8, >0.8-1, >1-1.2, >1.2-1.5, >1.5-1.8, >1.8-2, >2-3, >3-5, >5 Bridge clearance (m) <0.5, 0.5-1, >1-1.5, >1.5-2, >2-2.5, >2.5-3, >3 Width of ledge (cm) <20, 20-50, >50-100, >100-200, >200

Road at otter accident site Crosses watercourse, parallel to watercourse, between ponds, parallel water bodies on either side, no water body present Distance to the nearest water body (m) <50, 50-100, >100-250, >250-500, >500-1000, >1000 Width of road (m) <5, 5-6, >6-7, >7-8, >8-10, >10-20, >20 segments present potential accident sites, and locations thus identified were plotted on a topographical map.

Results

Spatial patterns and characteristics of otter road accident sites

Of the 88 otter road accident sites investigated, 68% were within 200 m of the nearest water body (Kendall's tau, R²=1.00, n=88, p<0.05; Fig. 2). Sixteen percent of all accidents occurred at a distance of more than 500 m from a water body. The minority of otter road accidents were recorded where a linear watercourse (drainage ditch 11%; streams, rivers and channels 11%) intersected a road and therefore where a river crossing was present (16% at culverts; 6% at bridges; Fig. 3). This finding is also represented by the low number of otter casualties found per kilometre around a bridge or culvert (which is defined as a 400-m stretch of road having a bridge or culvert in the centre). Only 4.8 otters per 100 km of bridge or culvert were found as opposed to 9.57 otter casualties per 100 km of roads in the Uckermark County (calculation based on unpublished data obtained from Brandenburg Road Administration). The number of casualties and the speed limit at the accident site were significantly positively correlated (R²=0.9623, n=88, p<.01; Fig. 4).

A PCA was conducted on 12 variables with orthogonal rotation matrix (varimax). The Kaiser-Meyer-Olkin (KMO) measure verified the sampling adequacy for the analysis, KMO=0.628 [START_REF] Field | Discovering statistics using SPSS[END_REF], and the Bartlett's test indicated that correlations between variables were large enough for PCA, χ²=821.23, df=66, p<0.001 [START_REF] Field | Discovering statistics using SPSS[END_REF]). An initial analysis was carried out in which the inflexion of the scree plot justified retaining either five components or two. Two components were obtained in the final analysis. Table 2 shows the factor loadings after rotation. Component 1 refers to the presence of a water crossing, while component 2 represents the type of water body.

The two-dimensional illustration of all accident sites using the two components showed three groups of accident sites (Fig. 5). Grouping the sites and testing the groups with a discriminant analysis showed that 98% were correctly classified. The discriminant analysis revealed two discriminant functions. The first explained 91.5% of the variance, R²=0.987. As apparent in Tables 3 and4, both discriminant functions differentiate the groups significantly.

The investigation of the features describing these groups resulted in the following: Group 1 The largest number of all accident sites (n 1 =39; 44.5%) were characterised by a lake located adjacent to a road (χ²=14.308, α<0.005, df=2). There was no bridge at the accident site (χ²=31.41, α<0.001, df=1), and the characteristic speed limit was at 100 km/h (χ²= 19.564, α<0.001, df=3). The second largest group (n 2 =31; 35%) consisted of accident sites where no body of water was present within 200-m distance (χ²=45.355, α<0.001, df=2). These accident sites were located in a network of water bodies in the surrounding area (χ²=12.065, α<0.05, df=4), where the speed limit was 100 km/h (χ²=31.839, α< 0.001, df=3). Group 3 Fewest accident sites (n 3 =18; 20.5%) were located where a road crosses a watercourse (χ²=8.000, α= 0.05, df=1). Significant features describing the members of this group were a water depth of less than 0.5 m (χ²= 10.889, α<0.05, df=1) and the presence of a culvert as watercourse crossing (χ²=9.000, α<0.05, df=2). Speed limit was not a significant feature of this group (χ²= 1.333, α>0.05, df=2).

Prediction of potential accident sites using ArcView GIS Using ArcView® GIS 3.2, 226 potential accident sites on roads within a distance of 200 m to one or more lakes were identified in the Uckermark County (cf. Fig. 6 for details). Thirty-three of these locations were identical with sites where 52 accidents involving otters had already been recorded. After assessing the respective speed limits in the field, 138 of the predicted accident sites were categorised as especially dangerous, as the speed limit was 100 km/h or more. By extending the examined range to 500 m from the nearest body of water, 545 potential accident sites throughout the Uckermark County were found (cf. Fig. 6 for details).

Discussion

This paper makes two major contributions: firstly, we described a methodology for identifying key environmental factors associated with wildlife collisions where data are limited, and secondly, the analysis of our novel empirical data indicates that the situation in the Uckermark County is unexpectedly exceptional (compared with previously studied habitats)-highlighting the risk associated with extrapolating non-local data.

According to unpublished data of the Naturschutzstation Zippelsförde des Landesumweltamtes Brandenburg, road mortality is the most commonly recorded cause of death for otters in the Uckermark County, a fact that was also found in other regions of Germany [START_REF] Körbel | Vermeidung der durch den Straßenverkehr bedingten Verluste von Fischottern (Lutra lutra)[END_REF][START_REF] Sommer | Daten zur Populationsökologie des Fischotters Lutra lutra (Linnaeus, 1758) in Mecklenburg-Vorpommern[END_REF][START_REF] Wölfel | Ein kohärentes Netz von Schutzgebieten für den Fischotter in Mecklenburg-Vorpommern[END_REF][START_REF] Zinke | Die Todesursachen der im Museum der Westlausitz Kamenz von 1985-1991 eingelieferten Fischotter Lutra lutra (L., 1758)[END_REF][START_REF] Zinke | Fischotterverluste in der Westlausitz und angrenzenden Gebieten in den Jahren 1985 bis 1995[END_REF]. In the Uckermark County, the volume of traffic has significantly increased between the years 1993 and 2000 (unpublished data of the Brandenburg Road Administration), while the number of otter casualties recorded has increased between 1990 and 2001 (unpublished data of the Naturschutzstation Zippelsförde des Landesumweltamtes Brandenburg). Similar results were found in Great Britain The extraction method used was PCA, and rotation method was varimax with Kaiser normalisation. Factor loadings over 0.40 are in boldface [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Philcox | Patterns of otter Lutra lutra road mortality in Britain[END_REF]. One simple explanation for this correlation could be the increased risk of otter road kills due to increasing traffic volumes. However, in a study involving parallel roads with considerable differences in traffic volume, [START_REF] Clevenger | Spatial pattern and factors influencing small vertebrate fauna road-kill aggregations[END_REF] found lower numbers of mammal road kills in the road with higher traffic. For otters in Eastern Germany, this finding is supported by [START_REF] Hertweck | Raumnutzung und Migration des Fischotters Lutra lutra (L., 1758) in der Oberlausitzer Teichlandschaft[END_REF] in an unpublished report from the Umweltforschungszentrum Leipzig (Raumnutzung und Migration des Fischotters Lutra lutra (L., 1758) in der Oberlausitzer Teichlandschaft. UZLAR Teilprojekt 3.1) who argue that on road sections with lower volumes of traffic, a higher frequency of road crossing otters should be expected. Another possible explanation for the rise of recorded road kills is an increase in the otter population during the time of investigation. A higher number of otters would in turn increase the number of otter casualties. Unfortunately, no population data for otters in the Uckermark County are available. Most otter casualties in the Uckermark County were recorded at road sections with a speed limit of 100 km/ h (Fig. 4), which could be explained by a reduced reaction time of the driver.

Research in other regions shows that accident sites are typically located where a road crosses a watercourse as in group 3 of this study [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Körbel | Vermeidung der durch den Straßenverkehr bedingten Verluste von Fischottern (Lutra lutra)[END_REF][START_REF] Philcox | Patterns of otter Lutra lutra road mortality in Britain[END_REF]. In contrast to this, fewest accidents in the Uckermark County occur where a bridge or culvert was present at the accident site (Fig. 3). Furthermore, the relation between otter casualties per kilometre of bridges and culverts is only half of that of otter casualties per kilometre of road in the special topography of the Uckermark County. Besides representing low casualty numbers compared to other-albeit multi-species-studies on road mortality such as [START_REF] Grilo | Spatial-temporal patterns in Mediterranean carnivore road casualties: consequences for mitigation[END_REF] or [START_REF] Malo | Can we mitigate animal-vehicle accidents using predictive models?[END_REF], these results on the single species studied can be explained by the abundance of lakes in the Uckermark, whereas linear watercourses are less common than in other study areas. They also corroborate the results of other studies that find otters travelling overland for various purposes, e.g. to get from one body of water to the next [START_REF] Vincent | A radio-tracking survey of otters Lutra lutra on a Perthshire river system[END_REF]. Finally, every kind of water body in close proximity to a road creates a potential accident site since otters occur in a very wide range of aquatic habitats including both marine and freshwater systems [START_REF] Kruuk | Wild otter: predation and populations[END_REF][START_REF] Prauser | Habitat destruction and otters-suggestions towards a more systematic approach[END_REF].

The high number of otter casualties parallel to a water body leads to the conclusion that in landscapes abundant in lakes such as the Uckermark County, it is not sufficient to focus mitigation measures exclusively on bridges but also to create wildlife passages where a body of water occurs in close proximity to a road.

To identify potential accident sites, the investigation of a possible combination of features describing an accident site is essential. Therefore, the number of features describing an accident site had to be limited to significant characteristics by using a PCA.

The PCA yielded three groups of accident sites which were mainly characterised by the presence of a water body within a certain distance (group 1: lake within 200 m; group 2: water body within a distance of more than 200 m) and speed limit or, as in group 3, the presence of a culvert. These findings were then used to identify potential accident sites using GIS. This tool has successfully been used to create models of otter distribution [START_REF] Janssens | The recovery of the otter in the Cevennes (France): a GIS-based model[END_REF], for genetic and habitat caused distribution barriers [START_REF] Hobbs | Landscape genetics applied to a recovering otter (Lutra lutra) population in the UK: preliminary results and potential methodologies[END_REF], as well as to investigate distribution patterns of otters [START_REF] Prigioni | Otter Lutra lutra movements assessed by genotyped spraints in Southern Italy[END_REF]. In order to identify potential accident sites for group 1, road sections within 200 m of a lake were assessed with GIS and 226 sites were successfully identified (cf. Fig. 6 for details). Since speed limit is currently not available as GIS data for the Uckermark County, this variable could not been taken into account in the GIS analysis. This variable, however, should be included in future analyses of potential accident sites wherever this dataset is available. Nevertheless, since a strong correlation was found between speed limit (as assessed in the field) and number of otter road casualties in our study (Fig. 4), the potential accident sites within 200 m of a lake identified in the analysis were examined in the field. Out of these 226 identified potential accident sites, 138 were classified as especially dangerous since the speed limit at these locations was 100 km/h or more. Particularly interesting is group 2, where no watercourse was present within a distance of 200 m. This result is in stark contrast to what was expected at the outset of the study and to the situation encountered in other regions [START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF][START_REF] Körbel | Vermeidung der durch den Straßenverkehr bedingten Verluste von Fischottern (Lutra lutra)[END_REF][START_REF] Philcox | Patterns of otter Lutra lutra road mortality in Britain[END_REF]. A characteristic feature for this group was its location within a network of watercourses, which nevertheless is a characteristic feature for the entire Uckermark County. Therefore, it would be important to concentrate on finding important corridors used by otters between two utilised but distant habitats. This could be achieved through telemetry (cf. Zimmermann and Breitenmoser 2007;[START_REF] Drygala | Habitat use of the raccoon dog (Nyctereutes procyonides) in northeastern Germany[END_REF]. Due to the strong correlation between distance and number of otter casualties (Fig. 2), ArcView GIS was also used to identify sites which lie within 500 m of water bodies. The 545 sites found that refer to group 2 represent a unique approach to assessing potential road hazards for otters, since otter road kills have so far predominantly been recorded close to river crossings, and distant accident sites have been neglected. However, the practical aspects of this result for mitigation measures will be limited to special cases due to the sheer number of identified potential accident sites.

In order to reduce otter road mortality, it is important to improve habitat connectivity. Because of the abundance of lakes in the Uckermark County, otters move across areas of dry land to get from one lake to another. Therefore, it is essential to provide passageways for wildlife such as underpasses or green bridges at the most important potential accident sites. The use of vegetation and fences to guide otters and other wildlife towards these tunnels and banks may improve the acceptance of these measures (Körbel 1995a(Körbel , b, 2001)). Tests on the Island of Skye, Scotland show that otter road mortality can also be significantly reduced by installing wildlife-deterring reflectors at dangerous sites [START_REF] Yoxon | Alleviating otter (Lutra lutra) road deaths by using wildlife-warning reflectors, on the Isle of Skye. International Otter Survival Fund, Broadford Zimmermann F, Breitenmoser U[END_REF].

Since a speed limit of 100 km/h was a significant feature at the accident sites, an otter traffic sign in conjunction with a lower speed limit can also be used to reduce otter deaths at problem sites, an option which is already being used in other regions (e.g. Mecklenburg-Western Pomerania, Northeast Germany). This method can be implemented instead of, or in conjunction with, the structural mitigation measures described above.

To improve the situation regarding group 3, the conditions found at bridges and culverts must be considered. Different theories attempt to explain why some otters avoid swimming through culverts or under bridges. Reasons discussed are the increased water velocity under bridges, a "tunnel effect" or the lack of natural banks or even ledges [START_REF] Madsen | Otter Lutra lutra mortality in relation to traffic, and experience with newly established fauna passages at existing road bridges[END_REF][START_REF] Grogan | Nature conservation and roads: Advice in relation to otters[END_REF]. If there is no natural bank, ledges on either side of the watercourse above the high water mark should be created for the use of otters and other wildlife as a mitigation measure. Since otters get killed at river crossings regardless of the existing speed limit, a reduction of the speed limit at these sites seems to have little influence on the improvement of the situation.

The mitigation measures described here may contribute to the reduction in the number of otter road casualties in the Uckermark County and elsewhere.

Conclusions

Our results show that most accidents happen where a road runs within 200 m of a lake. However, accidents in the Uckermark County also occur further away from water bodies. Because of the abundance of lakes, otters move longer distances over dry land between attractive habitat patches. Therefore, besides adequate bridges with ledges or natural banks, the construc-Fig. 6 Example section of map with potential otter accident sites in the Uckermark County, Germany tion of wildlife underpasses is essential to reduce otter road mortality both in the study site and in general.

The GIS was shown to be an effective and useful tool for the prediction of potential accident sites for otters and could be similarly used for other wildlife species if the features of habitat fragmentation are known.

Fig. 1

 1 Fig. 1 Study area Uckermark County (Brandenburg, Germany) and sites of otter road accidents (n=88). Boxed area delineates region covered in Fig. 6

Fig. 4 Fig. 3 Fig. 2

 432 Fig. 4 Relation between the number of casualties and speed limit (kilometre per hour; n=88)

Fig. 5

 5 Fig. 5 Combined groups' plot of the canonical discriminant function

Table 2

 2 Summary of the PCA results for the characteristics of otter road accident sites in the Uckermark County

	Variables	Rotated factor loadings
		Component 1	Component 2
	Width of waterbody	0.097	0.964
	Depth of waterbody	0.075	0.944
	Width of bridge	0.927	-0.178
	Height of bridge	0.953	-0.177
	Width of ledge	0.780	-0.188
	Distance to next watercourse	0.015	-0.262
	Width of road	-0.112	-0.004
	Vegetation at accident site	0.032	-0.363
	Speed limit	-0.208	-0.166
	Network of watercourses	0.021	-0.093
	Flow velocity of watercourse	0.631	0.663
	Type of watercourse within 200 m	0.815	0.373

Acknowledgements We are indebted to Jens Teubner and staff members (Brandenburg State Office for Environment) and Katja Glante and Heidrun Kaiser as well as to the staff members of the Brandenburg Road Administration for providing data as well as logistic support. Hermann Ansorge (Staatliches Museum für Naturkunde Görlitz) is acknowledged for his advice and useful discussions of the topic. Henning Scholz (Museum für Naturkunde, Berlin), Christel Richter (Humboldt Universität zu Berlin) and Edith Braun (Freie Universität Berlin) provided valuable advice in our statistical analyses. We thank Siegfried Ostermaier (Forstamt Templin) and John Dye (Moy, Scotland) for supporting our GIS analyses, Lars Möller (Museum für Naturkunde, Berlin) for assistance with the data analysis, Eva Wochnik (Berlin) for her contribution to Fig. 1 and Ulrich Zeller (Humboldt Universität zu Berlin) for the formal supervision of the thesis of S. Jancke. Both Nicole Ulbrich (Galway, Ireland) and David Hetherington (Grantown-on-Spey, Scotland) are acknowledged for their linguistic advice. Two anonymous reviewers are acknowledged for useful suggestions and improvements of the manuscript.


Daniel ; Goran

Paul Verlaine-Metz

Toth
email: toth@univ-metz.fr

J J Fundenberger

E Bouzy

W Skrotzki

S Suwas

T Grosdidier

L S Tóth

Local texture and microstructure in cube oriented Nickel single crystal deformed by equal channel angular extrusion

Keywords: plastic deformation, shear bands, nickel user supplied): Single crystal, ECAE, Microstructure Single crystal, ECAE, Texture, Microstructure, Heterogeneity

Local texture and microstructure have been investigated in order to study the deformation mechanisms during equal channel angular extrusion of a high purity nickel single crystal of cube initial orientation. A detailed texture and microstructure analysis by various diffraction techniques reveals the complexity of the deformation patterns in different locations of the billet. A modeling approach, taking into account the slip system activity, is used to interpret the development of this heterogeneous deformation.

Introduction

The processing of metals and alloys through equal channel angular extrusion (ECAE) [1,2] has attracted much attention within the last decade primarily because this technique has shown the potential to achieve very large strains leading to ultrafine grain microstructures (≤ 300 nm) in bulk polycrystalline materials [3]. The process involves passing a billet through two channels of equal area of cross-section generally inclined at an angle of 90°. This imparts large deformation to the material in one pass itself and the process can be repeated to refine the grain size down to a value characteristic of the material.

The mechanisms of grain refinement through ECAE are, however, not uniquely agreed. The key phenomenon is the development of dislocation structures and their transformation into high angle boundaries. The principal difficulty is to find out the response of individual grains to such a deformation in terms of evolution of dislocation structure. The evolution mechanisms of dislocation structures during straining were examined, for example, by Hansen and co-workers [4][5][6]. It is, however, difficult to propose a unified description of the dislocation mechanisms governing both microstructure and texture evolution during large strain deformation. Correlations between dislocation structures and processing characteristics can be examined experimentally [7][8][9] or by statistical modeling [10][11][12]. For metals with medium to high stacking fault energy, the main feature of the dislocation structure development is the transformation of tangles into three-dimensional structures of dislocation cells or subgrains [4]. For higher strains, as applied in ECAE, the deformation microstructure is characterized by larger structural heterogeneities, e.g. deformation and shear bands. The formation of such deformation heterogeneities is a very important feature of ECAE and requires a systematic and rigorous analysis in order to improve the understanding of the 3 microstructural refinement process and provide a realistic input to deformation texture models that generally are limited to homogeneous grain deformation modes. Although, it is well documented that microstructure and texture after ECAE processing can be quite heterogeneous [13][14][15][16][17][18], the origin of such heterogeneities has not been sufficiently investigated from the viewpoint of microstructural development. When the deformation heterogeneities are to be addressed experimentally, single crystals are preferred instead of polycrystals as they can provide a simplified and deeper insight into the complex phenomenon of plastic deformation. Only a few studies have been carried out in this direction on copper [19][20][21], aluminum [22,23] and nickel [24][25][26] as well as Nb [27] single crystals. On the other hand, different types of microstructures and textures were observed in these ECAE deformed single crystals, which were attributed to the formation of local deformation heterogeneities such as deformation and/or shear bands. It is therefore important to investigate the effect of the nature of such heterogeneities on the development of the texture and the microstructure during ECAE processing. With this goal, most of the studies on deformation structures in ECAE carried out so far have concentrated on the central area of the extruded billet whichbeing far from the walls where friction intervenes -was expected to be more representative of the response corresponding to the imposed deformation geometry. However, significant variations in texture and microstructure were also observed in ECAE deformed single crystals along the billet height [14,24]. In addition, the recent analysis of a cube-oriented nickel single crystal extruded through a squared section die has also revealed strong differences in deformation pattern along the transverse direction of the extruded material [26]. These changes in deformation mechanisms resulted in significant macroscopic deformation heterogeneities on the overall cross-section of the sample even when a single crystal was used [26]. To this end, the crystallographic orientations are determined globally by neutron diffraction and locally by texture measurements carried out using X-ray and electron diffraction. These analyses are completed by a modeling of the slip system activities that helps to explain the development of the associated heterogeneity. cross-section (ED-plane) and the right-side section (TD-plane), were analyzed with all the techniques mentioned above. The analysis on the TD-plane was made at approximately 1.5 mm depth from the side face, in order to avoid the friction effects on the microstructure and texture. OM was carried out using a Zeiss Axiophot optical microscope after mechanical polishing and subsequent chemical etching with a solution of nitric acid (25.7 vol.%), glacial acetic acid (67.5 vol.%) and distilled water (6.8 vol.%). Texture measurements were carried out on a texture goniometer using Schultz reflection geometry with Co (λ = 0.1789 nm) radiation. Local X-ray texture measurements were made at different locations on both sections (see Fig. 2) using a pure (99.9%) annealed molybdenum mask, 100 µm thick and containing an aperture of 3 mm in diameter. Necessary corrections were applied to the raw experimental data in order to reduce the effects induced by the mask. Four pole figures, namely (111), ( 220), ( 200) and (311), were measured and from these data the orientation distribution function (ODF) was calculated with the TexEval software developed by LETAM (University of Metz) based on the series expansion method of Bunge [START_REF] Bunge | Texture Analysis in Materials Science, Mathematical Methods[END_REF]. No sample symmetry restriction was imposed for the calculation of the ODF, that is, the ODFs were calculated using triclinic sample symmetry.

Material and experimental procedures

Global texture measurements were done by neutron diffraction at TEX-2 (GKSS Research Centre, Geesthacht, Germany) on a cube of (10 mm × 10 mm × 10 mm) taken from the middle section of the ECAE deformed bar (sample 2 in Fig. 1c). Complete (200), (220) and (111) pole figures were measured. The orientation distribution function was calculated from these pole figures in the same way as above.

Although the majority of the measurements were made on the ED-plane, the reference system x, y, z for the Euler angles of the ODFs is kept as it is defined in Fig. 1b. Because all the major components of the texture that develop in the cube oriented Ni single crystal could be observed in the section ϕ 2 =0° of the ODFs, only this section has been displayed for each set of results. All the ODFs in this paper are in the full range (0-360°) of ϕ 1 due to the fact that apparently there is no monoclinic symmetry around the z-axis (TD), which represents the ideal case for simple shear [START_REF] Tóth | [END_REF].

EBSD analysis was carried out using a Jeol JSM 6500F microscope equipped with a field emission gun and an electron back-scattering diffraction (EBSD) detector. The specimen surfaces for EBSD investigation were mechanically polished with grit paper and diamond suspension solution up to 0.25 µm and subsequently electropolished in a solution of 70% glacial acetic acid and 30% perchloric acid 60%. The EBSD patterns were processed and analyzed with the CHANNEL 5 software (HKL Technology, Denmark). The colors in the EBSD maps relate to the color key expressed in the standard stereographic triangle while the characteristic fcc crystal direction is registered along the normal direction ND. When needed, a good resolution (0.1 µm step size) was used in the acquisition process. No noise reduction was applied, thus the maps represent the raw EBSD results (non-indexed points are shown in black).

For TEM bright-field analysis, thin foils were prepared from the ED-plane using the polishing solution mentioned above. The TEM examination was done in a Philips CM 200 operated at 200 kV. planes. The cross-section is characterized by a heterogeneous banded microstructure. As already depicted in [26], excluding the two layers experiencing the direct effect of the friction on the lower and upper die walls (they were 800 and 500 µm thick, respectively), the rest of the billet section can be divided into different zones characterized by different aspects of the deformation patterns.

Results

Optical microscopy

The upper part of the section, zone I, depicts a very complex banded microstructure. A major feature in this area is the presence of very broad inclined bands. These bands are roughly inclined along two distinct directions. Comparatively, the microstructure in the lower part of the sample (zone III) is characterized by long parallel thin bands almost parallel to TD. These thin bands can also be seen on the TD-section extending over several millimeters along ED.

The two lateral zones of the extruded billet are mirror like images (labeled II L and II R , respectively). They are essentially characterized by more or less featureless domains located next to the lateral wall from which very large parallel bands appear to originate and extend towards the centre of the sample. It is interesting to note that the central part of the sample (labeled II in Fig. 2) -which, being far from the die, is generally considered to be the most homogeneous and representative one -is in fact characterized by the most complicated deformation pattern. The microstructure here consists of an intermixed of different features such as thin bands parallel to TD and larger inclined ones. These sets of bands are also visible on the longitudinal section (TD-section) in the area labeled II RS of Fig. 2. They clearly extend all through the billet length and are slightly inclined to ED. The local X-ray texture measurements have shown that the components found by neutron diffraction are not homogeneously distributed within the ECAP billet but are located in a systematic manner to a certain extent within its cross-section. Similar results have been obtained by more localized texture measurements with high energy synchrotron radiation in the central section along ND of the same ECAP processed single crystal [30].

Global and local texture

EBSD analysis

The main objectives of the EBSD analyss were to validate the OM and XRD texture results as well as finding the links between the microstructural features and the different texture components observed in the local X-ray texture results. Trace analyses were carried out to characterize the crystallographic alignment of the different types of bands.

Figure 4 shows the EBSD map obtained from the upper part of the sample (zone I) and the corresponding ϕ 2 =0° ODF section. The map depicts a quite complex banded microstructure with different types of bands intersecting each other. These bands belong to the cube component rotated by different angles around TD and extending somewhat towards the ideal C and A 1 components (Fig. 4b).

The very broad bands at the centre of the cross-section, as revealed by OM, were analyzed in detail by EBSD. The EBSD map (Fig. 5a) shows the typical microstructure of the right side of zone II with a very broad band (colored in green) inside the matrix (colored in blue). The corresponding ϕ 2 =0° ODF section given in Fig. 5(b) shows that the orientation of the matrix is C 2 , while that of the broad band except of a slight φ rotation is a TD-rotated cube component. The border to the matrix does not have any crystallographic alignment. Also, fine This indicates that they are related to the crystallographic shear planes and therefore may be called microbands or crystallographic shear bands (CSBs). The broad green band may be interpreted as deformation band (DB). The CSBs are deviated at the boundary between the matrix and deformation band giving rise to a kink-type configuration. The texture component given by the CSBs, as represented in reddish-pink color, is in a -∆ϕ 1 TD-rotated position from the matrix and deformation band orientation. This is clearly seen in the ODF sections (Figs. 5c,d) belonging to selected areas within matrix and DB. Thus, the CSBs are just shear zones leading to heterogeneous overall straining or strain partitioning. A similar observation is made on the left side of zone II by analyzing a DB of a TD-rotated cube component (with a slight -∆ϕ 1 rotation in the same manner as observed in the right side of zone II) in a matrix of C 1 (Fig. 6). Although the DBs described have mirror symmetry the CSBs have the same shear sense (compare ODF sections of Figs. 5c, d and6c, d).

The results of EBSD measurements at the centre of zone II SR of Fig. 2 are presented in Fig. 7a. The microstructure is characterized by thin parallel CSBs (colored in red) inside the matrix of component C 2 colored in blue. These CSBs are the same as those found in the matrix in the ED-sections of Figs. 5 and6.

Similar microstructural features as depicted in Figs. 567were reported by Basson and Driver [31] after plane strain compression of a cube oriented Ni single crystal up to a strain of 1.5.

The authors described the features inside the large deformation bands as being micro-shear bands associated with TD (φ 1 ) and some RD (Φ) rotations which is exactly the case in the present work. The EBSD map shown in Fig. 8 is characteristic of the microstructure in the lower part of the sample (zone III in Fig. 2). In this zone the microstructure is as complex as in the upper zone and possesses very high spreads in orientation. The characteristic features of this part of the sample are large horizontal bands either composed of a sequence of smaller bands colored in green and reddish-yellow or of a fine-grained structure, which according to a misorientation analysis contains a high frequency of high angle grain boundaries. The horizontal fine-grained bands are shear bands of non-crystallographic character. They produce the same shear as the ECAE process, however, leading to +∆ϕ 1 rotation, i.e. higher shear. In terms of texture, the major component is the rotated cube component (red colored) that spreads about ED

High resolution EBSD and TEM analysis

To investigate the nature of the CSBs inside the matrix in more detail, high spatial resolution EBSD maps have been acquired with an ultra fine step size of 50 nm. The boundaries map corresponding to the scanned area is shown in Fig. 9a overlapped with the band contrast (BC) map. Boundaries with misorientations smaller than 15º degrees are shown in white while the high angle boundaries i.e. >15 º are indicated by black lines. As can be clearly seen in Fig. 9a, compared with the matrix, the CSBs contain a higher density of both high and low angle grain/subgrain boundaries, thus, indicating a higher shear strain. This correlates with the microstructural features revealed by TEM analysis (Fig. 9b). The grain and/or cell size in the CSB shown in Fig. 9b. is significantly smaller than in the matrix.

Discussion

Deleted: OIM

Deleted: Transmission electron microscopy

Deleted: 50 nm Deleted: To show the nature of the CSBs in the matrix in more detail, first of all the misorientation distribution has been mapped and superposed with the Kikuchi band contrast which is a qualitative measure of the degree of deformation (Fig. 9a). As can be clearly seen, compared to the matrix, the CSBs show a higher band contrast and contain a higher density of high angle grain boundaries, thus, indicating a higher shear strain. This correlates with the microstructure revealed by TEM (Fig. 9b). The grain and/or cell size in the CSB is significantly smaller than in the matrix. ¶ The microstructure in ECAE deformation of a cube oriented Ni single crystal is quite heterogeneous at the macro-, meso-and microscale. The heterogeneity of deformation in ECAE is well documented for single and polycrystals [13-27, 29, 30], with some studies focusing on texture heterogeneities [13][14][15][16]30] and others dealing with the deformed microstructures [19,22,23] without making a detailed study on both. To the best of our knowledge, all the literature published in this area mention the heterogeneity of ECAE deformation on polycrystals only along the height of the sample, i.e. along ND [13][14][15][16]30], and therefore, the corresponding theoretical formulations are based on this. However, in the present work, heterogeneities in texture and microstructure were also observed along the transverse direction, indicating that phenomena taking place along all directions should be addressed in order to have a clearer view of the complex plastic deformation in the ECAE process. In the following, an attempt is made to interpret the formation of the macro-, mesoand microscale heterogeneities observed in the microstructure of the one pass ECAE deformed Ni single crystal and their effect on the texture development.

Heterogeneous deformation of materials may be of various different origins. In the present case, the heterogeneities observed are related to the die geometry of the ECAE process and the single crystal orientation. In the following subsections, these aspects will be discussed in more detail. First of all, the slip activity in the cube component subjected to simple shear is analyzed. Then, based on the peculiarities found, the origin of the heterogeneities with respect to texture and microstructure in normal and transverse direction of the billet is discussed.

Finally, a comparison is made with ECAE of cube textured polycrystalline aggregates. Because of its highly symmetrical nature, the cube is one of the most studied orientations. It is generally accepted that the cube orientation is metastable during plastic deformation at room temperature and exhibits heterogeneous deformation as well as splitting into strongly misoriented microstructural features, e.g. shear bands and deformation bands [6,31]. In order to get a clearer understanding of the stability of cube orientation, slip system activity calculations were made for the exact cube and rotated cube orientations subjected to simple shear deformation. To do this, the full constraints viscoplastic crystal plasticity model [START_REF] Tóth | [END_REF]32] was employed on the initially cube oriented crystal using the {111}<110> slip systems (see Table 1). The ideal simple shear model was used with a shear rate of

Slip system activity in the cube orientation during simple shear

1 1.0s γ - = - & applied in
the 45° intersection plane of the ECAE die, i.e. in the x'-y'-z reference system, see Fig. 1. The corresponding velocity gradient -when expressed in the x-y-z frame -is given by [START_REF] Tóth | [END_REF]:

1 1 0 1 1 0 2 0 0 0 L γ -     = - -       & .
This strain mode was used in the simulations in small strain increments up to a total shear of γ= -2.0. The obtained slip rates are depicted in Fig. 10 for a strain rate sensitivity index of m=0.05. It is to be mentioned here that when smaller m values are used, the slip distribution remains nearly the same.

The lattice rotation rate for the initially cube orientation was found to be equal to the applied rigid body spin, meaning that only the ϕ 1 angle changes with a rate of

2 / 1 γ ϕ & & = . Moreover, 1 ϕ &
remains constant for any rotated position of the cube. This result is in agreement with the analysis of Tóth and Jonas [33]. Consequently, the total rotation of the ideal cube component is 57.3° in the ϕ 1 angle while the other two Euler angles remain unchanged, see Fig. It can be seen from Fig. 10 and Table 1 that the average slip vector remains always in the x-y plane. A consequence of this is that the stress state remains also plane stress state (like the strain state in the x-y plane) for any rotated position of the cube. This is an important finding for the discussion of the possible effects exerted by the walls of the channel on the crystal.

One of the consequences is that lateral walls (with normal TD) do not have to exert forces on the crystal during its plastic deformation.

Influence of the ECAE process on the stability of the cube orientation

The stability of the cube orientation has already been discussed by Dillamore and Katoh [35] for rolling deformation and by Akef and Driver [36] for plane strain compression (strains in the range of 0.25-1.5). From their theoretical considerations, it follows that small deviations from the exact cube orientation lead to rotations in different directions, as has been observed in this investigation where the single crystal not only rotates about ϕ 1 (as seen above and as predicted by the Taylor theory for the exact cube orientation) but also about φ . This means that the small deviations (2 -3°) from the exact cube orientation existing in the undeformed sample may already lead to texture components spreading towards the C orientation. and Hatherly [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF], one of the origins of deformation banding is the ambiguity associated with the selection of the operative slip systems. In many cases the imposed strain can be accommodated by more than one set of slip systems and the different sets of slip systems lead to different lattice rotations. Another origin is given by inhomogeneous straining, i.e. different regions of a grain may experience different strains if the work done within the bands is less than that required for homogeneous deformation and if the bands can be arranged so that the net strain matches the overall deformation. These deformation bands are separated by geometrically necessary boundaries (GNBs). In addition, boundaries are formed by statistical trapping of dislocations forming so-called incidental dislocation boundaries (IDBs). In general, the misorientation of both types of boundaries increases with strain [START_REF] Hansen | [END_REF] the rate being larger for GNBs, i.e. GNBs accumulate dislocations at a higher rate than IDBs. Besides, the spacing of both types of boundaries decreases with increasing deformation indicating that grain subdivision continues to refine with increasing strain. With increasing misorientation this process leads to the formation of new high angle grain boundaries the percentage of which increases with strain. Grain fragmentation depends on grain orientation. Because of the symmetry of special orientations, one choice of slip systems leads to an opposite lattice rotation from the other choice. The orientation changes due to grain fragmentation lead to the destabilization of the cube component and support the formation of orientations close to C

The formation of the split C component has been successfully simulated with Tóth's flow line model by applying the viscoplastic self consistent polycrystal code on a cube texture represented by 1000 grains which were selected to represent a 6° Gaussian distribution around the cube position [30]. To explain the heterogeneous texture and microstructure observed in normal and transverse direction in the billet it is necessary to take into account the geometry of the ECAE process.

In the present case a die has been used with an ingoing channel moving with the billet except the x-wall, thus reducing friction within this channel and reducing the pressing force. On the other hand, friction on the walls of the outgoing channel has been increased by narrowing this channel on each side by 0.1 mm and on the top by 0.2 mm in order to compensate for elastic rebound of the billet after extrusion [39]. Otherwise machining of the billet to the original size is necessary before performing another pass. As a consequence, friction at the side walls leads to shear processes producing rotations around the TD-rotated crystal x-axis, i.e. φ-rotations.

Such rotations during shearing lead to orientation motion towards C. Indeed, the split C component in mirror symmetry is found on the left and right side of the billet in zones II L and II R . In contrast, high friction at the top and bottom wall leads to a TD-rotation, i.e. ϕ 1 -rotation of the cube component. Friction on the top wall produces a shear sense coinciding with that of the ECAE process, while that on the bottom wall is opposite. Thus, cube rotations on the top are enlarged while on the bottom they are diminished.

As seen in Figs. 3, 4 and8, as well as shown by [30], the rotation of the cube component progressively increases up to 90° from top to bottom. The theoretical simulated rotations show much less dependence on the position, see Fig. 10. Actually, they are limited to 57.3° which is the rotation value corresponding to the simple shear model. This theoretical rotation agrees with the rotation that can be obtained from only rigid body spin without any plastic spin in the lattice rotation. Such a behavior of the cube component for fcc crystals was already predicted by Tóth and Jonas [33] for simple shear. The 90° rotation in the bottom part, however, is more than the theoretical limit. This can be explained with the effect of friction which works against the plastic deformation process by reducing the plastic strain drastically. It is seen in finite element simulations [16] that in the bottom part there is practically no plastic strain. The material, however, is forced to flow, and an initial cube-shaped material element must rotate by 90° in rigid rotation. Thus, this rotation is not a rigid body rotation originating from plastic strain; it is just a kinematical rotation during which there is no shape change in the material element during flow. The relative weakness of the rotated cube in the experiment may be due to that process.

The shear bands passing through the entire sample change their character from the top to the bottom of the billet. In zones I and II they are more or less crystallographically oriented while in zone III they lie on the ND-plane disregarding deformation banding. The change in the character may be due to the high constraints given by the friction at the bottom wall.

Crystallographic shear banding may be caused by the instability of the "homogeneous" deformation structure due to changes in the slip activity. As seen in Fig. 10 for the cube component the initially active slip systems (no. 3, 6, 9, 12) with Burgers vector in shear direction become less active after rotation from the ideal cube orientation. However, rotations in the -∆ϕ 1 direction -as taking place in the CSBs -favor those slip systems which have shears without conflict with the side walls.

Comparison with ECAE of cube textured polycrystals

Various polycrystal simulations based on the simple shear model [2] or even the flow-line model [START_REF] Tóth | [END_REF] predict the formation of the C component for high to medium stacking fault energy materials. Suwas et al. [32] have reported that a strongly cube textured polycrystal of 18 copper -when subjected to ECAE -gives rise to a texture having a predominant C component while in weakly textured copper the texture evolves towards A 1 and C. In the aluminum alloy AA 5109, the pronounced cube component rotates about 65° and its intensity drastically decreases from about 13 to 3 mrd [15]. Simultaneously, all the typical shear components develop with low intensities (<4 mrd). Interestingly, the C component is split similar as here (∆ϕ 1 ≈ 5°, ∆φ ≈ 20°). However, in contrast, some other components also appear. This is due to a larger spread of the initial cube component compared to the present case, where the material is perfect cube oriented single crystal. The result of these differences is that grains rotate and fragment at the same time, leading to the formation of other shear components.

While the texture heterogeneity in the normal (ND) direction of ECAE deformed polycrystals is well proven, there are no studies known so far in the transverse (TD) direction. However, compared to single crystals, the influence of friction at the side walls, which strongly depends on the die geometry, should extend less into the interior of the billet in case of polycrystals.

Conclusions

In order to find the origin of deformation inhomogeneities in a cube oriented pure Ni single crystal deformed by ECAE at room temperature, a thorough analysis of microstructure and texture at macro-, meso-and microscale has been carried out using different complementary techniques. From the results obtained, the following conclusions can be drawn: 2) The continuous change in the activity of the {111}<110> slip systems as well as the simultaneous activity of eight slip systems were found to be the principal reasons of the multistage heterogeneous deformation characterized by deformation and shear bands.

3) The deformation heterogeneity across the billet in the TD direction is due to friction of the sample with the side walls.

4) The microstructure and texture in the lower part of the billet evolved in a different way compared to the rest of the sample due to strong friction with the bottom wall.

( 1 1 -1) [ 0 1 1] 2 ( 1 1 -1) [ 1 0 1] 3 ( 1 1 -1) [ 1 -1 0] 4 ( 1 -1 -1) [ 0 1 -1] 5 ( 1 -1 -1) [ 1 0 1] 6 ( 1 -1 -1) [ 1 1 0] 7 ( 1 -1 1) [ 0 1 1] 8 ( 1 -1 1) [ 1 0 -1] 9 ( 1 -1 1) [ 1 1 0] 10 ( 1 1 1) [ 0 1 -1] 11 ( 1 1 1) [ 1 0 -1] 12 ( 1

  examines in detail the microstructure at different locations of an extruded Nickel single crystal in order to improve our understanding of the local deformation patterns.

AFormatted

  bar of dimensions 40 mm × 10 mm × 10 mm was cut by spark erosion technique from a Ni single crystal (4N purity) grown by the Bridgman technique in the cube orientation. EBSD measurements were carried out to verify the crystal quality by precise orientation measurements at 18 locations on the polished {100} surfaces, revealing non-systematic deviations from the perfect cube orientation with maximum deviations of 4.5° and a mean value of 2°. Although only one sample was studied because of the complexity obtaining a Ni single crystal in cube orientation, the obtained results are expected to be representative for this orientation as the sample had relatively large dimensions and in general, the reproducibility of the testing by ECAE is very good.The ECAE experiment was carried out at room temperature using a Zwick 200 kN screw driven machine and a die set with rectangular intersection of the square extrusion channels, without any rounding of the corner region. A sketch of the ECAE setup with the coordinate systems is presented in Fig.1a. Two specimens were cut from the middle of the billet length (Fig.1c), one for optical microscopy (OM), EBSD analysis and local texture measurements by XRD and the other for global texture measurements by neutron diffraction. Two faces, the

7 Figure 2

 72 Figure 2 represents a 3D view of the specimen obtained by OM mapping on the ED-and TD-

8 Figure

 8 Figure3ashows the results obtained from the global texture measurement using neutron diffraction. ECAE textures for cubic materials were analyzed before and the location of ideal orientations was reported by Tóth et al.[START_REF] Tóth | [END_REF]; a representative key figure is given in Fig.3gonly for the ϕ 2 = 0° ODF sections. With respect to this figure the global texture in Fig.3ais characterized by a partial fibre about the shear plane normal (SPN) having a strong texture component: the split C ideal orientation with components C 1 and C 2 . Another texture component identified is the TD-rotated cube orientation (here with a rotation of about 60° around the z-axis).

  in the matrix as well as in the broad bands. Trace analysis shows that there is a preferred alignment of these bands along the traces of two {111} planes on the ED-plane.

Formatted

10

 10

1 = 22 .

 122 . The operating slip systems, however, change completely during this large strain rotation of the Four slip systems are active in the exact cube component as well as in the ϕ 5° position; however, in general, eight systems are active. Actually, a large number of active slip systems are necessary to produce zero plastic spin, which is the condition to have the lattice spin to be equal to the rigid body spin. It has been shown in Tóth et al.[34] that the minimum number of active slips systems for zero plastic spin actually is four.

  the exact cube orientation develops during shear due to deformation banding favored by the operation of a large number of slip systems. According to Humphreys

  heterogeneous evolution of microstructure and texture was found to be the effect of both the initial cube orientation of the Ni single crystal and the geometry of the ECAE process.

Figure 1 :

 1 Figure captions

Figure 2 :

 2 Figure 2: 3D view of the extruded billet showing the highly heterogeneous microstructure observed by optical microscopy on the TD and ED-plane. Different zones from top to bottom (I, II, III) and from left (II L ) to right (II R ) and right side (II RS ) are indicated. The circles match the approximate areas used for XRD local texture measurements while the white rectangles represent the approximate areas used for EBSD analysis.

Figure 3 :

 3 Figure 3: ϕ 2 =0° ODF sections: (a) global textures measured by neutron diffraction, (b -f) local textures measured by XRD at different locations (zones indicated in Fig.2) on the ED-and TD-plane. (b) zone I, (c) zone II, (d) zone II L , (e) zone II RS and (f) zone III. The key figure with the ideal shear components and the initial cube orientation with a 6° spread are given in (g) and (h), respectively.

Figure 4 :

 4 Figure 4: (a) Orientations distribution map (0.3 µm step size) with (b) the corresponding φ 2 =0° ODF section obtained on the top part of the cross-section (zone I); the colors indicate the ND direction in the standard stereographic triangle (isolines in mrd: 1, 2, 4, 8, 16, 32).

Figure 5 :

 5 Figure 5: (a) Orientations distribution map (0.25 µm step size) of the right side of zone II (center of the cross section) with the corresponding φ 2 =0° ODF sections: (b) whole image, (c) subsets 1 and 2; the colors indicate the ND direction in the standard stereographic triangle (isolines in mrd: 1, 2, 4, 8, 16, 32). Dashed lines in (a) mark the approximate traces of the {111} planes on the ED-plane for the corresponding C (blue) and rotated cube (green) components.

Figure 6 :

 6 Figure 6: (a) Orientations distribution map (0.3 µm step size) of the left side of zone II (center of the cross section) with the corresponding φ 2 =0° ODF sections: (b) whole

Figure 7 :

 7 Figure 7: (a) Orientations distribution map (0.2µm step size) of zone II RS (middle part on TD-plane) with (b) the corresponding φ 2 =0° ODF section, the colors indicate the ND direction in the standard stereographic triangle (isolines in mrd: 1, 2, 4, 8, 16, 32, 64). Dashed line in (a) marks the approximate trace of the {111} plane on the TD-plane for the C (blue) component.

Figure 8 :

 8 Figure 8: (a) Orientations distribution map (0.15µm step size) of the lower part of the crosssection (zone III) with the corresponding φ 2 =0° ODF sections: (b) whole image, (c) subsets 1 and 2); the colors indicate the ND direction in the standard stereographic triangle (isovalues 1, 2, 4, 8, 16, 32).

Figure 9 :

 9 Figure 9: (a) Boundaries map superimposed on a band contrast map (gray scale representation of the quality of Kikuchi patterns) given by EBSD (0.05 µm step size) on the central area, (b) TEM micrograph of the same area showing the boundary between matrix and shear band.

Figure 10 :

 10 Figure 10: Slip activity in the rotated cube orientation calculated with the viscoplastic fullconstraints Taylor model for an applied macroscopic shear rate of -1/s in the 45° intersection plane of the ECAE die up to a total shear of 2.0. Numbers indicate the slip systems as defined in Table1.

FiguresFigure 1 :

 1 Figures

Figure 2 :Figure 3 :

 23 Figure 2: 3D view of the extruded billet showing the highly heterogeneous microstructure observed by optical microscopy on the TD and ED-plane. Different zones from top to bottom (I, II, III) and from left (II L ) to right (II R ) and right side (II RS ) are indicated. The circles match the approximate areas used for XRD local texture measurements while the white rectangles represent the approximate areas used for OIM EBSD analysis.

Figure 4 :Figure 5 : 2 Figure 6 :Figure 7 :Figure 8 :

 452678 Figure 4: (a) Orientations distribution map (0.3 µm step size) with (b) the corresponding φ 2 =0° ODF section obtained on the top part of the cross-section (zone I); the colors indicate the ND direction in the standard stereographic triangle (isolines in mrd: 1, 2, 4, 8, 16, 32).

Figure 9 :Figure 10 :

 910 Figure 9: (a) Boundaries map superimposed on a band contrast map (gray scale representation of the quality of Kikuchi patterns) given by EBSD (0.05 µm step size) on the central area, (b) TEM micrograph of the same area showing the boundary between matrix and shear band.

Table 1 :

 1 1/s in the 45° intersection plane of the ECAE die up to a total shear of 2.0. Numbers indicate the slip systems as defined in Table 1. Slip system identification Index slip plane slip direction 1

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	23

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Acknowledgements

The authors acknowledge Prof. A. Eberhardt (Metz, France) his help during the ECAE experiments. The neutron texture measurements were carried out by Prof. H.-G. Brokmeier (GKSS Geesthacht, Germany). D.G. acknowledges the doctoral scholarship accorded by the Conseil Régional de Lorraine, France.