Somsack Inthasone

Nicolas Pasquier
email: pasquier@i3s.unice.fr

Andrea G B Tettamanzi

Célia Da Costa Pereira

The BioKET Biodiversity Data Warehouse: Data and Knowledge Integration and Extraction

Keywords: Biodiversity, Information Technology, Ontologies, Knowledge Integration, Data Mining

Biodiversity datasets are generally stored in different formats. This makes it difficult for biologists to combine and integrate them to retrieve useful information for the purpose of, for example, efficiently classify specimens. In this paper, we present BioKET, a data warehouse which is a consolidation of heterogeneous data sources stored in different formats. For the time being, the scopus of BioKET is botanical. We had, among others things, to list all the existing botanical ontologies and relate terms in BioKET with terms in these ontologies. We demonstrate the usefulness of such a resource by applying FIST, a combined biclustering and conceptual association rule extraction method on a dataset extracted from BioKET to analyze the risk status of plants endemic to Laos. Besides, BioKET may be interfaced with other resources, like GeoCAT, to provide a powerful analysis tool for biodiversity data.

Introduction

Biological diversity, or biodiversity, refers to the natural variety and diversity of living organisms [26]. Biodiversity is assessed by considering the diversity of ecosystems, species, populations and genes in their geographical locations and their evolution over time. Biodiversity is of paramount importance for a healthy environment and society, as it ensures the availability of natural resources and the sustainability of ecosystems [START_REF] Eldredge | Life on Earth: An Encyclopedia of Biodiversity, Ecology, and Evolution[END_REF][START_REF]Biological Diversity and Sustainable Resources Use[END_REF][START_REF] Institute | Ecosystems and human well-being: Biodiversity synthesis[END_REF][START_REF] Midgley | Biodiversity and ecosystem function[END_REF][START_REF] Shah | Why Is Biodiversity Important? Who Cares? Global Issues[END_REF][START_REF] Talent | Earth and Life: Global Biodiversity, Extinction Intervals and Biogeographic Perturbations Through Time. International Year of Planet Earth[END_REF]. The effects of biodiversity loss on the environment, caused by habitat loss and fragmentation, pollution, climate change, invasive alien species, human population, and over-exploitation can affect all life forms and lead to serious consequences [START_REF]Global biodiversity outlook 3[END_REF]. Understanding biodiversity is an essential prerequisite for sustainable development.

For many years, biodiversity datasets have been stored in different formats, ranging from highly structured (databases) to plain text files, containing plant descriptions (vocabularies and terms). Numerous data and knowledge repositories containing biodiversity and environmental information are available on the Internet as on-line and off-line resources nowadays. Data repositories store large amounts of information depicting facts on concrete objects related to a specific domain of application, e.g., results of environmental studies or inventories of species in a geographic location. This makes it difficult for botanists or zoologists to combine and integrate them to retrieve useful information for the purpose of identifying and describing new species.

The ever increasing availability of data relevant to biodiversity makes the idea of applying data mining techniques to the study of biodiversity tempting [START_REF] Hochachka | Data-mining discovery of pattern and process in ecological systems[END_REF].

Data mining, also known as knowledge discovery from data (KDD), is a set of concepts, methods and tools for the rapid and efficient discovery of previously unknown information, represented as knowledge patterns and models, hidden inside massive information repositories [START_REF] Han | Data Mining: Concepts and Techniques[END_REF].

One important obstacle to the application of data mining techniques to the study of biodiversity is that the data that might be used to this aim are somewhat scattered and heterogeneous [START_REF]Data Mining for Global Trends in Mountain Biodiversity[END_REF]. Different datasets cover different aspects of the problem or focus on some geographical areas only. None of them is complete and there is no standard format.

To overcome these limitation, we have designed and implemented BioKET, a data warehouse whose purpose is to consolidate a maximum of data sources on biodiversity in a logically organized, coherent, and comprehensive resource that can be used by the scientific community as a basis for data-intensive studies.

The main contribution of this paper is to provide a detailed account of how the BioKET data warehouse has been designed and populated, by consolidating and integrating multiple and heterogeneous sources of data. The reader should not underestimate the methodological challenges and the practical problems that had to be overcome in order to achieve that result. As all data mining practitioners agree, pre-processing, which includes data cleaning, integration, and transformation is the most time-consuming and critical phase of the data mining process [START_REF] Marbán | A data mining & knowledge discovery process model[END_REF][START_REF] Mariscal | A survey of data mining and knowledge discovery process models and methodologies[END_REF] illustrated in Figure 1. We demonstrate the use of such resource by applying FIST, a combined biclustering and conceptual association rule extraction method already described in the literature [START_REF] Mondal | A new approach for association rule mining and bi-clustering using formal concept analysis[END_REF], on a dataset extracted from it to analyze the risk status of plants endemic to Laos.

The BioKET Data Warehouse

The BioKET data warehouse is the consolidation of four main data sources:

-BIOTIK [START_REF]Biodiversity informatics and co-operation in taxonomy for interactive shared knowledge base (BIOTIK)[END_REF] (Western Ghats of India and National University of Laos), which contains 652 species records; -the herbarium from the BRAHMS repository [START_REF]Botanical research and herbarium management system (BRAHMS[END_REF] (National University of Laos, Faculty of Forestry), with 7548 species records; -the herbarium from the NAPIS repository [START_REF]Natural products information system (NAPIS)[END_REF] (Lao Ministry of Public Health, Institute of Traditional Medicine), with 747 species records; -the IUCN Red List Data [START_REF]The IUCN Red List of Threatened Species[END_REF], with 71570 species records. These data sources are stored in different formats: BIOTIK and IUCN Red List are in HTML, while the two others use, respectively, the dBase and Paradox file formats. Integrating such diverse data sources required performing the following tasks:

1. Listing all botanical and plant ontologies available on the Internet. 2. Selecting relevant information (phenotypic/plant traits/features/characteristics). 3. Relating terms in our database with terms in these ontologies. 4. Searching for thesauri/glossaries/taxonomies of terms for plants available on the Internet. 5. Relating terms in our database with terms in these thesauri. 6. Relating terms in Plant Ontology (PO) (which seems to be the most complete ontology in Botany) with terms/definitions (e.g., Latin terms) in these thesauri.

The first step was to extract data from sources and store them in a standard file format (such as an Excel spreadsheet), by using database management tools. Then, data cleaning was performed by using advanced Excel functions. The next step was to generate and link Google Maps Geocoding Service with the BIOTIK, BRAHMS, and NAPIS data by using VBA script (GoogleGeoLocation Function). The last step was to import the data thus obtained into the BioKET database, under MySQL.

A key factor for the integration and the enrichment of the data was the use of ontologies. Formal ontologies are a key for the semantic interoperability and integration of data and knowledge from different sources. An ontology may be regarded as "a kind of controlled vocabulary of well-defined terms with specified relationships between those terms, capable of interpretation by both humans and computers" [START_REF] Whetzel | What are ontologies?[END_REF]. From a practical point of view, an ontology defines a set of concepts and relations relevant to a domain of interest, along with axioms stating their properties. An ontology thus includes a taxonomy of concepts, a formally defined vocabulary (called a terminology), and other artifacts that help structure a knowledge base. A knowledge base that uses the terms defined in an ontology becomes usable by and interoperable with any other system that has access to that ontology and is equipped by a logic reasoner for it [START_REF] Obrst | Ontologies for semantically interoperable systems[END_REF].

It was thus important to construct a map among all the concepts in all the data sources and all the considered ontologies. It is worth noting that (i) some concepts are not equally represented in all the sources, (ii) some are represented in some sources and not in others and (iii) other concepts are not represent at all. The mapping process works as follows: the textual descriptors of plants are segmented into small chunks, which are then matched with the labels of concepts in the target ontology. For instance, from the descriptor "evergreen tree up to 8 m", we can in infer that "evergreen" is related to "shedability", "up to 8m" is related to "height" and "tree" is related to "plant type ". In the process, new concepts may be generated (e.g., from the textual descriptor "branches ascending or horizontal", where "branch", "branch ascending", and "branch horizontal" match concepts in the ontology, a new concept "branch ascending or horizontal", subsumed by "branch" and subsuming the latter two is generated). The plant record can thus be automatically enriched with a large number of "implicit" fields, inferred from the ontology. We have designed a relational data base of concepts that make it possible to relate concepts represented in different ways.

The result of this integration process -the BioKET data warehouse -is schematized in Figure 2. BioKET contains 77 relationship entities and a total of 80,517 records. As pointed out by many researchers (see, e.g., [START_REF] Benniamin | How to identify rare and endangered ferns and fern allies[END_REF]), to conserve organisms, whether plant or animal, one important step to take is to identify rare and endangered organisms in a given geographical area or country. The integration of geographical information from Geographical Information Systems (GIS) with species data, and its use in data mining studies is the object of the biodiversity informatics project of the W. P. Fraser Herbarium (SASK) [START_REF] Peters | Data mining and mapping of herbarium specimens using geographic information systems[END_REF]. The participants in such project developed an integrated bio-geography GIS model, using Google Maps API, based on data mining concepts to map and explore flora data. This allows data to be explored on a map and analyzed in several ways to reveal patterns showing relationships and trends that are not discernible in other representations of information.

The BioKET data warehouse integrates geographical information and 8,947 species out of the 80,517 total species have descriptions of specimen location and risk status that may differ depending on the area considered. This information is described at different levels of precision, from continent to specific places such as cities or villages. For example, Cratoxylum formosum grows up in Myanmar, South China, Thailand, Indochina, and Laos (Khammouan) [START_REF]Biodiversity informatics and co-operation in taxonomy for interactive shared knowledge base (BIOTIK)[END_REF]. This species is also reported in the Lower Risk/Least Concern category by IUCN Red List data [START_REF]The IUCN Red List of Threatened Species[END_REF]. The integration of geolocation information allows to explore species properties in different areas using the GeoCAT (Geospatial Conservation Assessment Tool) platform [START_REF]Geocat: Geospatial conservation assessment tool[END_REF]. GeoCAT is based on Google Maps to explore geographical information if coordinates, i.e., latitudes and longitudes, are provided. We already linked Google Maps with the terms of geographical information of each source (BIOTIK, BRAHMS, and NAPIS) and extracted their coordinates into BioKET database system. Google Maps does not support coordinates of directions (South, North, East, West, etc.) like "South China", but Google Bounding Box (BBox) coordinates are provided. We propose to improve this issue by calculating the coordinates for each direction (Figure 4) from Google BBox coordinates.

In the geolocation domain, the BBox of an area on Earth is defined by two points corresponding to the minimal and maximal longitudes and latitudes of the area [4]. Figure 4 shows the 13 partitions of an area: the 9 elementary partitions and the North, South, East and West partitions that result of merging the 3 corresponding elementary partitions, e.g., NW, NC and NE for North. This multilevel partitioning allows to represent location related properties of species, such as risk status or abundance for instance, at different area covering levels.

L = (M ax -X -M in -X) 3 , H = (M ax -Y -M in -Y ) 3 .
This computation of partitions can be applied to all objects defined by a geolocation bounding box, from continents to cities. For example, using the BBox of China, that is {73.4994137, 18.1535216, 134.7728100, 53.5609740}, the BBox of Southern China will be computed as {73.4994137, 18.1535216, 93.9238791, 53.5609740}.

BioKET Experimental Analysis

For experimental purpose, we constructed a dataset containing information on the 652 species extracted from the Biotik repository. This information is represented as 1834 binary attributes describing morphological and environmental properties (characteristics of part of the plant, size, habitat, exudation, etc.) and risk status of species. Extracting knowledge patterns can then provide support to relate increases and decreases in risk status to environmental factors impacting specific species (climate change, pollution, etc.). They can also help taxonomists to analyze the different types of species in an ecosystem, e.g., associating species

M in Y M in X M in Y + H M ax X North M in Y + 2H M in X M ax Y M ax X West M in Y M in X M ax Y M ax X + L East M in Y M in X + 2L M ax Y M ax X SW M in Y M in X M in Y + H M in X + L SC M in Y M in X + L M in Y + H M in X + 2L SE M in Y M in X + 2L M in Y + H M ax X CW M in Y + H M in X M in Y + 2H M in X + L Center M in Y + H M in X + L M in Y + 2H M in X + 2L CE M in Y + H M in X + 2L M in Y + 2H M ax X NW M in Y + 2H M in X M ax Y M in X + L NC M in Y + 2H M in X + L M ax Y M in X + 2L NC M in Y + 2H M in X + 2L M ax Y M ax X
with specific features and risk categories, and their viability, or growth rate, in some particular areas.

Conceptual Bicluster Extraction

This dataset was analyzed using the FIST approach which is based on the frequent closed itemsets framework. FIST extracts minimal covers of conceptual association rules and biclusters jointly. Conceptual biclusters of the form {I 1 V 1 } associate to a maximal set of instances I 1 , a maximal set of variable values V 1 that are common to all instances. In other words, a bicluster is a sub-matrix associating a subset of rows and a subset of columns such that all these rows have a similar value for each of these columns. Conceptual biclusters are partially ordered according to the inclusion relation and form a lattice. This hierarchical organization allows to explore groups of instances (species) and properties (characteristics) at different levels of abstraction: the highest biclusters in the lattice regroup a large number of properties shared by small groups of instances; the lowest biclusters regroup small set of properties that are common to large group of instances.

Conceptual association rules are rules with the form {V 1 -→ V 2 , I 1 , support, confidence, lift} where V 1 and V 2 are sets of variable values (properties) and I 1 is the set of instances (species) supporting the rule. Statistical measures computed for each rule are:

-support = P (V 1 ∪V 2 ) (or count(V 1 ∪V 2 ) = |I 1 | if given as an absolute number)
evaluates the scope, or weight, of the rule in the dataset. It corresponds to the proportion of instances containing V 1 and V 2 among all instances. -confidence = P (V1∪V2)

P (V1)
evaluates the precision of the rule. It corresponds to the proportion of instances containing V 2 among those containing V 1 . Rules with confidence = 1, that have no counter-example in the dataset, are called exact rules. Rules with confidence < 1 are called approximate rules.

lift = P (V1∪V2) P (V1)P (V2) corresponds to the correlation between occurrences of V 1 and V 2 :

• lift > 1 means there is positive correlation between V 1 and V 2 ,

• lift = 1 means V 1 and V 2 are independent,

• lift < 1 means there is a negative correlation between V 1 and V 2 .

Extraction parameters are the minsupport threshold, which corresponds to the minimal number of supporting instances required for a rule to be considered valid, and the minconfidence threshold, which corresponds to the minimal confidence required in order to consider a rule valid.

Experiments were conducted on a Dell PowerEdge R710 server with 2 Intel Xeon X5675 processors at 3.06 GHz, each possessing 6 cores, 12 MB cache memory, 24 GB of DDR3 RAM at 1333 MHz and 2 Hot Plug SAS hard disks of 600 GB at 15000 rounds/min with RAID 0 running under the 64 bits CentOS Linux operating system.

The numbers of patterns extracted, i.e., generators, biclusters, and rules, are shown in Figure 5. For this experiment, the minsupport threshold was varied between 50% (326 species) and 0.5% (3 species). The minconfidence threshold was varied between 50% and 1%. It should be noted that the vertical axes are on a logarithmic scale.

Generators, biclusters and exact rules

Approximate rules

Extracted Pattern Evaluation

In this section, we present some interesting conceptual association rules obtained from FIST. We would like to stress that these results mainly depend on the data collected within BioKET, which, as far as we know, is the only data warehouse consolidating different biodiversity information sources. These rules make it possible to estimate the risk status of a plant species according to IUCN RedList categories (Lower Risk, Endangered, Least Concern, Vulnerable, Critically Endangered, Rare, Data Deficient, Rare & Threatened, Possibly Extinct) with respect to their characteristics and vice-versa. For this experiment, the minsupport threshold was set to 1%, which corresponds to 6 species in the dataset, and the minconfidence threshold was set to 50%. One of the obtained rules with the highest lift (11.75) is INFL:pedicels up to 3 mm long, BBT:Twigs terete, INFL:axillary ⇒ RS:Lower Risk.

(1) According to this rule, of the six species with pedicels up to 3 mm long, twigs terete, and axillary inflorescence, 66,67% belong to the lower risk category. The identified species are Cratoxylum cochinchinense, Cratoxylum formosum, Engelhardtia serrata, Engelhardtia spicata, Irvingia malayana, and Knema globularia. This result is corroborated, for example, by information from Singapore flore. 1The following rule states, with 83.33% confidence, that a plant species classified as critically endangered has simple leaves: RS:Rare ⇒ LEAVES:Leaves simple.

(

) 2
This rule is corroborated, for example, by [START_REF] Fritsch | A new species of gaultheria (ericaceae) from mount kinabalu, borneo, malaysia[END_REF]

which identifies species Bentinckia condapanna, Drypetes malabarica, Glycosmis macrocarpa, Holigarna grahamii, Lasianthus jackianus, Pittosporum dasycaulon, and Vepris bilocularis, all found in the Western Ghats.

The following rule states, with 79.59% confidence, that a plant species classified as Vulnerable has simple leaves: RS:Vulnerable ⇒ LEAVES:Leaves simple.

(4)

This result is corroborated, for example, by [START_REF] So | The potential of local tree species to accelerate natural forest succession on marginal grasslands in southern vietnam[END_REF][START_REF] Wickneswari | Hopea odorata roxb[END_REF]. In [START_REF] So | The potential of local tree species to accelerate natural forest succession on marginal grasslands in southern vietnam[END_REF], the author discusses the applicability of the Accelerated Pioneer-Climax Series (APCS) method for restoring forests to degraded areas in Southern Vietnam using many local species such as Hopea odorata directly concernend by the above rule and which has been identified as vulnerable in the IUCN red list. Wickneswari [START_REF] Wickneswari | Hopea odorata roxb[END_REF], instead, proposes a document which can help the readers to understand the entire life cycle of Hopea odorata Roxb in Malaysia, Vietnam, Cambodia, and Thailand.

The following rule, whose lift is 1.189 and whose support is 4.14%, states, with 55.1% confidence, that a plant species classified as vulnerable has both glabrous and simple leaves: RS:Vulnerable ⇒ LEAVES:glabrous, LEAVES:Leaves simple.

(5)

Indeed, [START_REF] Rahangdale | Plant species composition on two rock outcrops from the northern western ghats, maharashtra, india[END_REF], proposing a deep and comprehensive botanical study of two rock outcrops in India, corroborates this rule.

Another interesting rule with a support of 3.37% and a lift of 1.07, states, with 59.46% confidence, that a plant species classified as having a lower risk has alternate leaves:

RS:Lower Risk ⇒ LEAVES:alternate.

This result is corroborated, for example, by results obtained by Craenel [START_REF] De Craenel | Floral development and anatomy of salvadoraceae[END_REF]. Species concerned include Aglaia elliptica, Aphanamixis polystachya, and Prunus arborea. As seen for Rule 3, the integration of geolocation information with multiple heterogeneous biological data can show common properties related to species with a specific risk status and/or in a specific area. For instance, the following rule with a lift of 4.26 states that 88.9% of species having a lower risk in the Indochina geographic region (i.e., 8 species) have leaves with entire margin: RS:Lower Risk, GEO:Indochina ⇒ LEAVES:Margin entire.

Another example of such rules is the following, showing that 88.2% of endangered species in Western Ghats have alternate leaves: RS:Endangered, GEO:Western Ghats ⇒ LEAVES:Alternate.

This rule, whose lift is

If we consider the Agasthyamalai area, lying at the extreme southern end of the Western Ghats mountain range along the western side of Southern India, we can see from the following rule that only 50% of endangered species in this area have alternate leaves, whereas the percentage is of 88.2% in the whole Western Ghats:

RS:Endangered, GEO:Agasthyamalai ⇒ LEAVES:Alternate.

This rule, which has a lift of 4.27, concerns 10 species.

All the above rules have been constructed from the consolidation of data from the four data sources presented above. Although some of the species are not yet included in the IUCN red list, combining information from the three other data sources allowed us to infer their risk status using the rules constructed by FIST. This is the case, e.g., for the species related to Rule 3, with the sole exception of Bentinckia condapanna, whose risk category is explicitly in IUCN. Indeed, Glycosmis macrocarpa's taxon has not yet been assessed for the IUCN Red List, but is listed in the Catalogue of Life as Glycosmis macrocarpa Wight. The same holds for Drypetes malabarica (in the Catalogue of Life as Drypetes malabarica (Bedd.) Airy Shaw ), Lasianthus jackianus (in the Catalogue of Life as Lasianthus jackianus Wight), Pittosporum dasycaulon (in the Catalogue of Life as Pittosporum dasycaulon Miq), and Vepris bilocularis (in the Catalogue of Life as Vepris bilocularis (Wight & Arn.) Engl.).

Conclusion

We presented BioKET, a data warehouse obtained by consolidation of a number of heterogeneous data sources on biodiversity. As far as we know, this is the first data warehouse containing that amount of heterogeneous data which can be used for conducting data-intensive studies about biodiversity. For the moment, the scopus of BioKET is botanical, but we plan to integrate other types of data.

We have demonstrated the usefulness of BioKET by applying FIST, an existing conceptual biclustering method, on a dataset extracted from BioKET to analyze the risk status of plants endemic to Laos. The evaluation of the extracted patterns against the botanical literature shows that meaningful knowledge can be infered from BioKET.

Fig. 1 :

 1 Fig. 1: Main phases of a data mining process

Fig. 2 :

 2 Fig. 2: An Overview of the BioKET Data Integration Process

Fig. 3 :

 3 Fig. 3: Overview of the BioKET Datawarehouse Entity-Relationship Model

Fig. 4 :

 4 Fig. 4: Thirteen partitions for an area on Earth

Fig. 5 :

 5 Fig. 5: Number of Patterns Generated by FIST.

Table 1 :

 1 Partition Bounding Box Computations

	Area Min Long Min Lat	Min Long Max Lat
	South

  , which describes Gaultheria paucinervia, a new species restricted to the eastern slopes of Mt. Kinabalu in Sabah State, Borneo, Malaysia, which has been confused with Gaultheria borneensis Stapf, but differs in its more erect habit and larger stature, longer nonappressed leaf trichomes, purple (vs. white) fruiting calyx, and lower elevation range, among other features. Gaultheria paucinervia has not yet been assessed for the IUCN Red List, (but is in the Catalogue of Life: Gaultheria paucinervia P.W. Fritsch & C.M. Bush apparently). Besides, by taking into account the features in the geographical data source, the FIST algorithm finds the rule RS:Rare, GEO:Western Ghats ⇒ LEAVES:Leaves simple,

  1.96, concerns 15 species. Such patterns can help comparisons between different geographical areas, at different levels of abstraction. For instance, considering the Malaysia geographic region, a part of Indochina, only 61.5% of species having a lower risk have leaves with entire margin as stated by the following rule, whose lift is 2.95 and which concerns 8 species:

RS:Lower Risk, GEO:Malaysia ⇒ LEAVES:Margin entire.

URL: http://florasingapura.com/Home.php. The aim of this site is to to bridge the gap between the terse technical descriptions of plants found in various botanical text books and what is observed in the Singapore forests.


J.-L Maurice
email: jean-luc.maurice@polytechnique.edu

Didier Pribat

Z He

Costel G Patriarche

Sorin Cojocaru

C S Cojocaru

Catalyst faceting during graphene layer crystallization in the course of carbon nanofiber growth

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

Introduction

Carbon nanofibers (CNFs) [START_REF] Melechko | Vertically aligned carbon nanofibers and related structures: Controlled synthesis and directed assembly[END_REF] or multiwall carbon nanotubes (CNTs, MWCNTs) obtained by catalytic crystallization on metallic particles at low temperature (450-700 °C), have numerous prospects in applications [START_REF] Teo | Microwave devices: Carbon nanotubes as cold cathodes[END_REF][START_REF] Bokobza | Multiwall carbon nanotube elastomeric composites: A review[END_REF][START_REF] Zhang | Nanomaterials in pollution trace detection and environmental improvement[END_REF][START_REF] Ren | Carbon nanotubes as adsorbents in environmental pollution management: A review[END_REF][START_REF] Haniu | Basic potential of carbon nanotubes in tissue engineering applications[END_REF][START_REF] Schnorr | Emerging applications of carbon nanotubes[END_REF] but still suffer from irregularand irreproduciblecrystalline structures. The purpose of the present work is to shed some light on the atomic mechanisms that are at work during the crystallization of graphene layers at the surface of iron-based catalysts, to finally propose routes for the low temperature controlled growth of CNTs/CNFs.

In the cases of Ni [START_REF] Helveg | Atomic-scale imaging of carbon nanofibre growth[END_REF][START_REF] Hofmann | In situ observations of catalyst dynamics during surface-bound carbon nanotube nucleation[END_REF][START_REF] Lin | Dynamical observation of bamboo-like carbon nanotube growth[END_REF] and Co [START_REF] Zhu | Atomic-resolution imaging of the nucleation points of single-walled carbon nanotubes[END_REF] catalyst nanoparticles, the nucleation and growth of graphene layers has been shown to rely upon the dynamics of surface steps. The growth of MWCNTs with iron-based catalysts has been studied in situ on different scales: in situ XRD experiments [START_REF] Cambedouzou | Anomalous thermal expansion of γ-iron nanocrystals inside multiwalled carbon nanotubes[END_REF][START_REF] Wirth | The phase of iron catalyst nanoparticles during carbon nanotube growth[END_REF] have for instance brought important results on the phase of the catalyst during growth. However, studies at the atomic scale have yet brought little data on the role of atomic stepsparticularly their dynamicsin the nucleation and growth of graphene.For instance, Rodriguez-Manzo and co-workers [START_REF] Rodriguez-Manzo | In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles[END_REF] have emphasized the role of steps in the nucleation of CNTs from Co, Fe and FeCo (1:1 alloy) nanoparticles using in situ high resolution transmission electron microscopy (HRTEM); however they did not study step flow on the catalysts' surface. Yoshida et al. [START_REF] Yoshida | Atomic-scale in-situ observation of carbon nanotube growth from solid state iron carbide nanoparticles[END_REF] have observed the growth of MWCNTs on cementite particles (Fe 3 C) in situ in HRTEM, but did not focus on atomic-scale nucleation of graphene layers. Begtrupet al. [START_REF] Begtrup | Facets of nanotube synthesis: High-resolution transmission electron microscopy study and density functional theory calculations[END_REF] have studied Fe faceting during CNT growth, but not in a geometry where step flow was active or visible. Pigoset al. have explained faceting of Ni catalysts, but during the unsticking of graphene layers rather than during their nucleation [START_REF] Pigos | Carbon nanotube nucleation driven by catalyst morphology dynamics[END_REF].

In their seminal paper, Helveget al. have studied Ni-catalyzed CNF growth using in situ environmental transmission electron microscopy (ETEM) [START_REF] Helveg | Atomic-scale imaging of carbon nanofibre growth[END_REF]. They were the first to clearly show graphene nucleation at step edges on the lateral walls of the catalyst particles.

Nucleation was followed by the receding of the metal steps towards the leading and trailing edges of the metal particle, leaving behind a graphene layer. Movements of metallic matter thus promoted graphene growth on the surface terraces of the catalyst and a concomitant elongation of the catalyst particle.

We focus here on the geometry and atomic complexity of those metal steps at the surface of iron-based nanoparticles. We show that, during CNT/CNF growth from Fe-based particles, the movement of these steps tend to create planar facets at the catalyst surface in contact with the graphene layer that is being crystallized. Moreover, we find that those steps travel along the curved or faceted surface of the catalyst. Thus, they can adapt themselves to the varying local surface orientation. At the end of their trip along the surface, they may eventually form bunches, which induce some characteristic and familiar shapes of catalysts observed after growth. Mastering this step bunching process could open up the way to a better structural control of CNTs and CNFs grown at low temperature.

Experimental

The present growth experiments were carried out in situ in the transmission electron microscope (TEM), on catalyst particles around which a nanofiber had already developed during a previous direct-current plasma-enhanced chemical vapor deposition (dc-PECVD) growth in a home-made reactor [START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF]. Transmission electron microscopy observations were done in a Topcon 002B microscope working at 160 kV (point resolution of 0.2 nm). Some in situ experiments were performed in a Philips CM30 instrument working at 300 kV (nominal resolution of 0.23 nm but ~0.4 nm in our high temperature observations), using a Gatan Model 652 heating sample holder. Finally, for the in situ HRTEM experiments, we used a Jeol 2200FS microscope working at 200 kV (0.19 nm resolution) equipped with a ProtochipsAduro heating sample holder.

In order to dispose of a source of carbon atoms inside the electron microscope, we either amorphized the existing nanotube by electron irradiation [START_REF] Krasheninnikov | Engineering of nanostructured carbon materials with electron or ion beams[END_REF] or used the carbon presentor injected [START_REF] Rodriguez-Manzo | In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles[END_REF] in iron carbide (Fe 3 C, cementite) catalysts. Similar experiments were performed by Rodriguez-Manzoet al. [START_REF] Rodriguez-Manzo | In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles[END_REF] for electron-beam assisted CNT growth inside the TEM, by Ichihashiet al. [START_REF] Ichihashi | In situ observation of carbon-nanopillar tubulization caused by liquidlike iron particles[END_REF] and Sinclair et al. [START_REF] Sinclair | In situ TEM studies of metal-carbon reactions[END_REF], for growth from an amorphous feedstock, and also by Sun et al. [START_REF] Sun | Carbon nanotubes as high-pressure cylinders and nanoextruders[END_REF], for growth from irradiated iron carbide. Quite interestingly, without prior amorphization, we obtained almost no change when annealing -Fe based nanotubes at 650°C, while we observed the large changes shown below with Fe 3 C, at the lower temperature of 550°C. We noticed that a part of the carbon atoms dissolved in the cementite catalyst came from the dissolution of graphene planes perpendicular to the catalyst surface (see supplemental material). We had previously observed this phenomenon with Ni catalysts but not with Fe ones [START_REF] Maurice | Different mechanisms of graphene wall nucleation on Fe and Ni particles[END_REF].

The in situ experimental protocol was actually the following: (i) 30-min irradiation with a focused 300-keV electron beam (-Fe only), (ii) 10-min annealing at 450°C, (iii) 10-min annealing at 550°C, (iv) annealing at 650°C (-Fe only).

We started the heat treatment with the relatively low temperature of 450°C because we had observed in another set of experiments using Ni catalysts that graphene readily crystallized at that temperature during a dcPECVD run [START_REF] Lee | Synthesis of conducting transparent few-layer graphene directly on glass at 450°C[END_REF].

In both cases --Fe and Fe 3 C, the electron irradiation at work during observation played a role in the growth process: we did observe changes of shape of the catalyst in reference nonirradiated nanotubes, but of significantly lower extent than in the examples presented below.

We focus here on multiwall carbon nanotubes or nanofibers that have a direct application in actual field emission devices [START_REF] Teo | Microwave devices: Carbon nanotubes as cold cathodes[END_REF]. Direct-current plasma-enhanced chemical vapor deposition allows one to obtain the verticality mandatory for field emission applications [START_REF] Melechko | Vertically aligned carbon nanofibers and related structures: Controlled synthesis and directed assembly[END_REF][START_REF] Chhowalla | Growth process conditions of vertically aligned carbon nanotubes using plasma enhanced chemical vapor deposition[END_REF]. The gas mixture we used for the first growth was made of isopropyl alcohol, water vapor and hydrogen; see details in ref. [START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF]. We study iron-based catalysts because iron allows one to play with three types of catalysts: -Fe, -Fe and iron carbides [START_REF] Wirth | The phase of iron catalyst nanoparticles during carbon nanotube growth[END_REF][START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF]. Also, compared to nickel, it appears to favor in certain conditions the growth of real MWCNTs (instead of nanofibers), where the graphene layers are parallel to the tube axis [START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF][START_REF] Maurice | Different mechanisms of graphene wall nucleation on Fe and Ni particles[END_REF].

We note that during such a dc-PECVD growth, the CNTs/CNFs have their catalyst particle on top, so that growth beneath the particle remains shielded from the bombardment of incoming plasma species. Moreover, the growth of each new graphene layer is protected from the outside atmosphere by the already formed layers beneath which it develops. Thus the nucleation and growth processes are quite characteristic of the catalyst surface rather than of the details of the gases or plasma conditions. Hence, reproducing a growth experiment in the TEM with no gas (as we do here) remains a valid approach for the general understanding of growth mechanisms, as long as one sticks to the atomic phenomena at work at the catalyst surface.

Results

Ex situ observations

When observed in the TEM, as-grown CNFs often exhibit features that look like the remnants of a growth by a step flow mechanism. In the CNF with a -Fe catalyst particle shown in Fig. 1, the start of a new graphene plane always corresponds to a step on the metal surface (blue arrows in Fig. 1b). There exists, moreover, an inversed shoulder beneath the head of the particle (Fig. 1d, yellow circle). The fact that the steps and the shoulder have the same orientationis an indication that the steps have been moving during growth, and that they have somehow gathered to form the inversed shoulder. We shall come back later on this inversed shoulder, leading to a "nail head" shape for the catalyst,which is a distinctive characteristic of PECVD-grown CNTs/CNFs. The height of the steps at the catalyst surface can hardly be measured directly. However, the disorientation angle  between the terraces and the average catalyst surface should be such that tan = d/D where d is the step height and D the terrace width. Here, the latter is worth ~ 10 nm and the disorientation angle is ~ 2°: this gives a step height of ~ 0.35 nm, i.e. to a good approximation, the interplanar spacing of graphite. It is quite remarkable that the present iron surface, a priori curved around the particle, offer precisely the atomic step height worth the thickness of one graphene layer. Looking in more detail, the local orientation of the present terraces is . The (33-4) interplanar spacing being 0.05 nm, these atomic planes have a geometrical existence but are not dense enough to have a real physical meaning. Given their height, the present steps include seven such planes. At high magnification (Fig. 1b'), the actual step presents itself like a nanofacet in (110) orientation. Thus the iron surface has arranged itself so as to create steps incommensurate with low-index real Fe atomic planes, but with local nanofacetsfrom which graphene layers appear to be extruded. The circle in d) highlights the inverse shoulder that forms due to step bunching.

Regarding now the step migration and bunching upon heat treatment, they are well known in surface studies: they may be the result of an equilibrium phase transition obtained through surface self-diffusion [START_REF] Williams | Surface faceting and the equilibrium crystal shape[END_REF] or they can be part of an irreversible mechanism associated with preferential sublimation at edges [START_REF] Wilson | Weak mismatch epitaxy and structural Feedback in graphene growth on copper foil[END_REF]; we shall see that the present mechanism is related to self-diffusion. Let us note for the moment that the catalyst steps present two remarkable and original features: (i) they are intimately related to the nucleation and growth of graphene layers, as shown in ref. [START_REF] Helveg | Atomic-scale imaging of carbon nanofibre growth[END_REF] for a Ni catalyst and (ii), they have non trivial atomic structure, as they are on a faceted conical surface [START_REF] He | Direct evidence for the existence of multiwalled carbon nanotubes with hexagonal cross-sections[END_REF] and their height,although it depends upon the metal atomic structure, fitsthe graphite interlayer spacing. This means that the catalyst surface layer that gives birth to a graphene layer by a step-receding mechanismmay include a variable number of catalyst crystallographic planes, depending on the local facet plane.

In situ nucleation and growth on an-iron catalyst

Figure 2 shows the in situ growth at 650°C of a proto-nanotube starting from amorphous carbon feedstock [START_REF] Maurice | Different mechanisms of graphene wall nucleation on Fe and Ni particles[END_REF]. The nanofiber has been amorphized at room temperature by irradiation with a focused 300 keV electron beam [START_REF] Krasheninnikov | Engineering of nanostructured carbon materials with electron or ion beams[END_REF][START_REF] Ichihashi | In situ observation of carbon-nanopillar tubulization caused by liquidlike iron particles[END_REF], during 30 min. Before being annealed at 650°C, it had firstly undergone in situ heating at 450°C and 550°C, each time for 10 min. A central part of the catalyst particle (which we call sub-nanoparticle in the following) serves as catalyst for the crystallization of the graphene layers of the proto-nanotube. While doing this, it adopts a faceted shape and its volume decreases (the iron atoms moving in the outer parts of the catalyst). Previous observations [START_REF] Rodriguez-Manzo | In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles[END_REF][START_REF] Begtrup | Facets of nanotube synthesis: High-resolution transmission electron microscopy study and density functional theory calculations[END_REF] had shown the volume change and the appearance of facets perpendicular to the graphene layers, but this is the first time to our knowledge that faceting parallel to the graphene layers is reported. The shrinking of the subnanoparticle is due to iron atoms migrating away, starting up a creep mechanism that presently leads to forming a sort of corona around the proto-nanotube (see Supplemental material, Fig. S2). It is remarkable that the re-organization of the Fe nanoparticle occurs within a volume that seems to be limited by the original outermost envelope. In particular, the overall diameter of the nanofiber's tip does not evolve during the process, even though there is a large movement of Fe atoms during the reshaping of the nanoparticle. It looks as if the Fe crystal were now advancing inside the amorphized carbon, incorporating carbon atoms at the Fe/C interface, so that this interface moves away from the tip of the nanofiber.

The outside shape of the catalyst stabilizes, once low index facets have fully developed on the side surface of the Fe nanoparticle (Supplemental material, Fig. S1). The carbon atoms from the amorphous feedstock are incorporated inside the metal (at the advancing Fe/C interface) by a ring-shaped surface of the catalyst's head, which progressively becomes the corona (Supplemental material, Figs. S1 &S2). They may travel to the surface schematized in Fig. 3d FIG. 2. (Color online) TEM images of a carbon nanofiber firstobtained with -Fe catalyst by dcPECVD at 650°C [START_REF] Maurice | Different mechanisms of graphene wall nucleation on Fe and Ni particles[END_REF]. The fiber has been amorphized at room temperature by irradiation with a focused 300 keV electron beam (see text), then annealed in situinside the TEM at 650°C during the time indicated. The arrows are positioned at the same place in all micrographs, to serve as markers. During annealing, the width of the sub-nanoparticle shrinks while the proto-nanotube thickens by its interior, as if Fe atoms in the -Fe lattice were being replaced by C atoms in the graphene lattice. After 12min, the shrinkage leads the subnanoparticle to unstick from the protonanotube, which stops the thickening of the latter (see also Supplemental material, Fig. S1).

either following a transport path along the sidewalls of the particle (at the interface with the encapsulating graphene layers) as described by Begtrup [START_REF] Begtrup | Facets of nanotube synthesis: High-resolution transmission electron microscopy study and density functional theory calculations[END_REF], or by direct bulk diffusion [START_REF] Rodriguez-Manzo | In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles[END_REF], the carbon diffusion coefficient in -Fe being very high at 650 °C [START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF] (See schematic of Cdiffusion in Suppl. material, Fig. S2). While some C atoms have to diffuse all the way up to the tip of the sub-nanoparticle, to feed the nucleation and development of new graphene layers (such as those schematized in Fig. 3d), most of them feed the growth of the already developed external walls of the protonanotube, at the bottom part of the sub-nanoparticle. At 12 min.

(Fig. 2), graphene layers start to unstick from the catalyst, which starts in turn to retract, leaving vacuum inside the new nanotube (14 min in Fig. 2). Faceting has disappeared from the tip of catalyst when it is abandoned by the graphene layers; its radius of curvature is 8 nm at this stage.

Let us now give some details on the structure of the protonanotube and its catalyst. The analysis of the selected-area electron diffraction patterns (EDPs) and their comparison with a real-space image in Fig. 3 indicate that the development of the first graphene layers has induced a {110} faceting of the Fe sub-nanoparticle. We note, however, that the two main facets (parallel to the protonanotube axis) are only vicinal to (-101) and (10-1), with a disorientation angle of about 10° with respect to the [111] zone axis. Given the step height of one {110} plane (0.203 nm), this represents a high density of surface steps: approximately one every nm. We also note, however, that the graphene layers are oriented parallel to the physical surface, and not to the {110} planes. Thus the number of steps active in the formation of graphene is probably low. These active steps may be of the type seen in the ex situ experiment (Fig. 1), adapted to the thickness of graphene. However, {110} planes in the bcc structureare physically quasi compact and their interplanar spacing is relatively large (0.203 nm), which makes it difficult to precisely provide a given step height. Moreover, the graphite interlayer spacing (0.341 nm) has no commensurability with the -Fe {110} spacing: one needs approximately five Fe {110} planes to accommodate three graphene layers. Thus those active steps might presently correspond to single {110} Fe planes andprovoke a disorientation in the graphitestructure like a regular array of partial edge dislocations, the Burgers vector of which would be the difference between the interplanarspacings of Fe and graphite, i.e. 0.14 nm. Hence, there would be an angle between graphite and Fe surface, due to the presence of these dislocations.

Taking a terrace width of about 10 nm as in Fig. 1, the active steps would provoke a disorientation of the graphene layers with respect to the surface of about 0.8 degrees, which is within the present measurement error. We note that the {110} facets have disappeared when the sub-nanoparticle further shrank (Fig. 2, 12 min and 13 min). This transient character would explain why the faceting of the catalyst surface in contact with graphene is often not visible in ex-situ grown samples [START_REF] He | Etchant-induced shaping of nanoparticle catalysts during chemical vapour growth of carbon nanofibres[END_REF][START_REF] He | Nickel catalyst faceting in plasma-enhanced direct current chemical vapor deposition of carbon nanofibers[END_REF].

Quite remarkably, the large shape evolution of the Fe catalyst implied neither phase change nor orientation shift (see electron diffraction patterns in Fig. 3 a-b). This is another indication that the change in shape is rather governed by surface motion of atoms/steps and not by bulk reorganization such as that observed with smaller catalysts [START_REF] Yoshida | Atomic-scale in-situ observation of carbon nanotube growth from solid state iron carbide nanoparticles[END_REF]. After 9 min of growth the protonanotube was thus also facetted, with facets parallel to Fe {110} facets. Figure 3d gives an example of how a graphene nucleation spot could initiate a step flow responsible for the thinning observed in Fig 2 .   In such a scheme of growth, the catalyst surface step and the graphitic plane that it "trails" have to cross facet edges, thus adapting their structure to each new facet orientation. It is important, in this respect to check whether the graphitic planes are indeed continuous across facet edges (see below).

Atomic scale observation of nucleation and growth on a cementite catalyst

In order to get more insights on the way steps and graphene layers cross facet edges, we carried out the annealing experiment in a high-resolution microscope, with carbon nanofibers also obtained by dcPECVD at 650 °C but this time with an iron carbide catalyst † . Figure 4 shows lattice-resolved images of the sequential formation of graphene layers at the surface of the cementite particle (for the phase determination, see suppl. material, Fig. S3.). This time, the nutrients for graphene growth are obtained from the catalyst itself, probably through electron-induced injection of carbon atoms [START_REF] Rodriguez-Manzo | In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles[END_REF][START_REF] Sun | Carbon nanotubes as high-pressure cylinders and nanoextruders[END_REF]. The nanofiber has firstly been annealed in situ for 10 min at 450°C. It has then been further annealed in situ for 4 min 10s at 550°C before the micrograph in Fig. 4a was recorded.

We note that, although cementite has a structure quite different from that of -Fe, the mechanism of graphene layer growth on Fe 3 C exhibits no apparent difference with that on iron: the active part of the catalyst shrinks and develops facets while it gives birth to successive graphene layers (see suppl. mater. Fig. S4). When focusing on a rounded part of the catalyst (rectangles in Fig. 4 a-a'), we observe that the graphene layers have developed following its curved surface. This would indicate that the catalyst steps at the origin of those layers have traveled across that curved area, following the purple arrow in Fig. 4d, indicating in turn that the Fe 3 C atomic steps at the origin of graphene layer growth would be of a versatile nature.

As in the case of -Fe, the catalyst appears to have faceted during graphene layer growth (see suppl. material, Fig. S4). At rounded parts of the catalyst as well as at edges between the facets, most of the graphene layers are continuous (Fig 4). Thus, graphene layers seem to be able to cross these edges during their growth. Such a conclusion is strengthened by the fact that there is no difference in graphene layer numberon either side of facet edges (see Fig. 4c&e). † The starting catalyst is a thin film of pure iron: upon dewetting, a part of it stays in the form of iron nanoparticles when exposed to isopropanol for CNT growth, whereas in the same growth run another part becomes carbide [START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF].

Again here, the faceting of the Fe-based particle evolves as graphene layers are generated, with the presence of steps in facets where graphene layers are "extruded" from the catalyst. In the present case as in that of -Fe, the step flow results in a net transport of catalyst matter, which strongly modifies facet surfaces and the catalyst shape in general(see also supplemental material, Fig. S4). Here again, it is quite remarkable that, during such a significant evolution, the catalyst mono-crystalline structure remains apparently unchanged. showing the most likely movement of the steps (purplearrows). The blurred contrast is due to an out-of-focus part of catalyst in the path of the electron beam (see Fig. 5 and supplemental material, Fig. S4, for a view at lower magnification).The blue arrows in (c) and (e) indicate garphene layer edges.

Step bunching and collective growth

As expected when analyzing Fig. 1, the catalyst steps migrate and end up by bunching. This is particularly clear in Fig. 2, where after 12 min at 650 °C, the protonanotube does not thicken anymore as growth now proceeds by feeding the alreadyexisting graphene layers: all the active steps have gathered at the bottom of the proto nanotube. There is thus a transition from onion-type growth (layer by layer growth by the interior of the nanofiber) to nanotube growth (collective growth of existing graphene layers) that corresponds to the blocking of individual step motion.In the case of our cementite example, step bunching is building up in Fig. 4b' and collective growth is takingplace on the other side of the catalyst during the observations in Fig. 4 (see Supplemental material, Fig. S4). Figure 5 shows a region of the graphite thus obtained in situ after 5 min 27 s at 550°C. The Fourier transform of the HRTEM image exhibits reflections resembling very much those of standard graphite (Bernal stacking). Thus collective growth has enabled the development of a nanoshell that locally has the graphite structure.

Figure 6 summarizes the two possible geometries of growth. In the present case, the system shifts from individual growth of single graphene layers (onion or nanofiber-type in fig. 6) to the collective growth of all the layers at the same time (nanotube in fig. 6). In the former case, the active interface between catalyst and graphite is parallel to graphene planes; in the latter, it mater. for more information.) is perpendicular (Fig. 6). In the former case, it is a low energy interface(but over a large surface), in the latter, a higher-energy one (but over a small surface) [START_REF] Begtrup | Facets of nanotube synthesis: High-resolution transmission electron microscopy study and density functional theory calculations[END_REF].

In standard conditions, the dcPECVD growth of nanofibers is essentially of the onion type (Fig. 6) [START_REF] He | Etchant-induced shaping of nanoparticle catalysts during chemical vapour growth of carbon nanofibres[END_REF]. One sees directly that the electrical current path from bottom to top, in such an object, crosses all the graphene layers. In the case of collective growth of all the layers at the same time on the contrary, the layers end up parallel to the tube axis to form a real multiwall carbon nanotube (Fig. 6). The resistivity of graphite is four orders of magnitude lower in the graphene planes than perpendicular to the planes. Hence, as far as field emission applications are concerned, one sees directly the advantage of being able to tune the growth conditions so as to promote MWCNT growth at the expense of CNF growth. collective growth can take place: no new graphene nucleation events are needed. In the case of onion-like growth (nanofiber, bottom), the step motion brings more matter to the top surface where the steps get "erased": new graphene layers are needed for growth to proceed.

Discussion: the origin of faceting

Although faceting of the catalyst has been discussed before [START_REF] Pigos | Carbon nanotube nucleation driven by catalyst morphology dynamics[END_REF][START_REF] He | Etchant-induced shaping of nanoparticle catalysts during chemical vapour growth of carbon nanofibres[END_REF][START_REF] He | Nickel catalyst faceting in plasma-enhanced direct current chemical vapor deposition of carbon nanofibers[END_REF][START_REF] Tessonnier | Recent progress on the growth mechanism of carbon nanotubes: A review[END_REF], we are aware of only few previous observations of its occurring during the nucleation of graphene layers [START_REF] Begtrup | Facets of nanotube synthesis: High-resolution transmission electron microscopy study and density functional theory calculations[END_REF][START_REF] Pigos | Carbon nanotube nucleation driven by catalyst morphology dynamics[END_REF] and of no previous mention of its occurring parallel to the graphene layers. Furthermore, the present observation of faceting on two quite different types of iron catalysts (-Fe and cementite) gives us a clue that this mechanism could be quite general.

We have seen thatcatalyst facets develop while the step flow mechanism,where their atomic planes are "replaced" by graphene layers, is at work. We first discuss whether or not epitaxial relationships between graphene layers and those facets could be a driving force for that development. We start from the (more simple) case of -Fe (Fig. 3). Quite generally, there is no real match between the periodicities of graphene and those of -Fe. However, the Fe (110) surface provides the less unfavorable epitaxial match between graphene and -iron, with the [START_REF] Lin | Dynamical observation of bamboo-like carbon nanotube growth[END_REF] direction of graphene parallel to the [001] of Fe, and the graphene [START_REF] Cambedouzou | Anomalous thermal expansion of γ-iron nanocrystals inside multiwalled carbon nanotubes[END_REF] direction parallel to Fe[1-10] (Fig. 7). Vinogradovet al. have studied thatgeometrical configuration [START_REF] Vinogradov | Formation and structure of graphene waves on Fe(110)[END_REF] and have found that, in their ultra-high vacuum and stabilized environment, this "epitaxial"relationship was energetically favored. However, several works have focused on the epitaxy of graphene on the a priori more favorable compact surfaces of Ni(111) and Co(001). Like Fe, Ni and Co are 3d transition metals with an incomplete d band, likely to offer carbon atoms a bonding similar to that offered by Fe. Those two respective surfaces fit the graphene lattice much better than Fe(110), with the six-fold symmetry of the graphenelayer and small mismatches of respectively 1.3 and 1.8%. Moreover, these metals are also used for carbon nanotube growth, with results quite similar to those obtained with Fe. In these two more favorable cases, there appears to be a gain in epitaxy, but small. FIG. 7. (Color online) The superimposed structures of graphene and -Fe (110).

In the case of Ni, Eizenberget al. [START_REF] Eizenberg | Carbon monolayer phase condensation on Ni(111)[END_REF][START_REF] Eizenberg | Carbon interaction with nickel surfaces: Monolayer formation and structural stability[END_REF] have noticed that there was "some rotational disorder" about the [111] axis for graphene precipitationon the (111) surface [START_REF] Eizenberg | Carbon monolayer phase condensation on Ni(111)[END_REF], and remarked that "the fact that monolayer condensation is observed on all surfaces studied [i.e. not only (111)] appears to suggest that the nature of the geometrical fit between the overlayer and substrate is of secondary importance". Their experiments were carried out at temperatures between 727 and 827 °C. On our side, we studied the growth of graphene on polycrystalline Ni after carbon ion implantation and annealing at 725 and 900°C: we actually found two mechanisms of growth, including the present step-flow one (which gave the best crystal quality) [START_REF] Baraton | On the mechanisms of precipitation of graphene on nickel thin films[END_REF], but could not evidence epitaxial relationships [START_REF] Baraton | Synthesis of few-layers graphene by ion implantation of carbon in nickel thin films[END_REF]. cobalt, the C-Co phase diagram is quite similar to that of C in Ni. Ago et al. have shown that graphene can be epitaxially grown by CVD onto Co (001) at 1000°C [START_REF] Ago | Epitaxial chemical vapor deposition growth of single-layer graphene over cobalt film crystallized on sapphire[END_REF].

However, these authors also showed that growth at a lower temperature of 900°C ended up in misaligned graphene, indicating again weak energy gain in the epitaxial relationship.

Thus epitaxy appears as a weak promoter of faceting: the origin of the laterduring graphene layer developmentprobably rests on other causes than simply providing epitaxial match.

A first other cause could be the tendency of any particle to reach its Wulff-polyhedron shape.

Having the highest density surface in -Fe, bare {110} facets have the lowest possible surface energy among the possible free surfaces. They remain the lowest energy facets when considering surfaces covered by one graphene layer [START_REF] Begtrup | Facets of nanotube synthesis: High-resolution transmission electron microscopy study and density functional theory calculations[END_REF]. The step flow at catalyst surface, during the development of a graphene layer, generates significant atomic movements in the whole catalyst (see fig. 2, and supplemental material, figs. S1 andS3). These movements are so significant that, if there wasno proof of crystallinity, they could be interpreted as an indication of liquid state. Those movements certainly help the surfaces to reach their lowest energy configuration. Thus areason for the development of low energy {110} facets lies in the fact that they become dynamically accessible.

A last cause that must be consideredis the atomic order needed for creating a stable graphene layer nucleus.Yang et al. have recently demonstrated, by producing 92% single wall carbon nanotubes having the same chirality on WCo catalysts, that a crystalline catalyst transmitsindeed a given structure to the growing graphene layer [START_REF] Yang | Chirality-specific growth of single-walled carbon nanotubes on solid alloy catalysts[END_REF]. Abild-Pedersen et al., based on their in situ observations of ref. [START_REF] Helveg | Atomic-scale imaging of carbon nanofibre growth[END_REF], have carried out a thorough theoretical investigation of the nucleation of graphene layers on nickel, using ab initio calculations [START_REF] Abild-Pedersen | Mechanisms for catalytic carbon nanofiber growth studied by ab initio density functional theory calculations[END_REF].

These calculations show that a monoatomic step on the compact Ni(111) surface is a preferred site for the nucleation of graphene. The energy of creating that step and bringing carbon atoms to develop a graphene nucleusappears as the cheapest way of precipitating a graphene layer. Thus in Ni, nucleationappears favored on the compact surface, even though that includes creating surface steps. A remarkable point is that the step height is the highest for compact surfaces, i.e. the closest to the space needed for the growth of a graphene layer.

The present large Fe-based catalysts are different from the small WCo catalyst of ref [START_REF] Yang | Chirality-specific growth of single-walled carbon nanotubes on solid alloy catalysts[END_REF]probably also by the atomic mobility inside the particle. The catalyst atomic "cradle" in the present case has to move with respect to the rest of the catalyst for the growth to occur: the surface steps glide along the surface plane. As any crystallographic surface can be described in terms of compact-plane nanofacets, it is clear that surfaces along compact planes will be the most appropriate to provide the right plane for that gliding.

Thus low-index facets appear favored nucleation sites for two reasons: i) they provide the atomic step that has the largest height, the closest to graphite interlayer spacing, and ii) they provide the easiest glide plane for that step.

Conclusions

The three examples given above are illustrations of the "knitting" of graphite crystal planes by the receding of metal surface steps thatleave behind theircarbon content in the form of graphene layers. The present observations uncover a remarkable property of that phenomenon, which is that it generates faceting of the catalyst, giving a clue that graphene layer nucleation is favored by a given facet step atomic order ..A recent study demonstrates the long-postulated link between catalyst structure and carbon nanotube chirality [START_REF] Yang | Chirality-specific growth of single-walled carbon nanotubes on solid alloy catalysts[END_REF]. The large catalysts used here for the growth of multiwall carbon nanotubes are chemically quite different from the smaller ones involved in ref. [START_REF] Yang | Chirality-specific growth of single-walled carbon nanotubes on solid alloy catalysts[END_REF] but the principle of catalyst atomic order transferred to growing graphene layers has a general nature. The present study shows that, for low temperature growth of MWCNTs, this transfer takes place through catalyst faceting.

FIG. 1 .

 1 FIG. 1. (Color online) TEM images of a carbon nanofiber obtained with a-Fe catalyst by dcPECVD at 700 °C. a) Low-magnification image; b) and d) high magnification images of respectively the tail and head part of the right-hand side of the catalyst. Blue arrows indicate steps in the catalyst surface that give birth to single graphene layers; b') enlargement of a step in b). (c) Diffraction pattern showing that the catalyst is -Fe in [1-10] zone axis.The (110) indications in (b), (b') and (d) show the tendency of the catalyst to create (110) facets.

FIG. 3 .

 3 FIG. 3. (Color online) Structure of the protonanotube and catalyst presented in Fig. 2. (a-b) Electron diffraction patterns (EDPs) recorded over an area of 300 nm around the catalyst: (a) at the beginning of the 650°C treatment; (b, b') after 9 min at that temperature (same EDP with different marks). The main reflections in the pattern show that the catalyst particle is a-Fe single crystal viewed in [111] zone axis. These reflections remain unchanged during the 9 min while the particle undergoes the significant change of shape visible in Fig. 2: creep of the particle does not affect its original phase and orientation. After 9 min at 650°C (b and b'), individual 002 graphite reflections become clearly visible (arrows in b), indicating the growth of graphite nanocrystals along preferred orientations: their (002) planes are approximately aligned with the {110} iron planes. Drawing these preferred orientations in (b') and reporting them in direct space (image in c), confirms that they correspond (i) to a vicinal {110} faceting of the Fe catalyst and (ii) to a concomitant faceting of the protonanotube. c, d) Image and corresponding schematic diagram of the protonanotube after 9 min of growth. The correlation between the faceting of the sub-nanoparticle and that of the protonanotube clearly appears. A possible step flow that would allow for the observed catalyst thinning (Fig. 2) is indicated by arrows in d).

FIG. 4 .

 4 FIG. 4. (Color online) HRTEM images of a carbon nanofiber first obtained with iron carbide catalyst by dcPECVD at 650 °C. In (a) the nanofiber has been annealed in situ for t 0 = 4 min 10s at 550°C. In (a'), after 30 additional seconds at 550°C, six graphene layers have developed at the expense of an equivalent volume of the carbide catalyst. (b-b' and c) Enlargements of the yellow rectangles in (a-a') showing the surface steps that give birth to the graphene layers; the yellow line in (b-b') is a guide to the eye that shows a same graphene layer before andafter the 30 more seconds. (d-d' and e) Schematic diagrams

FIG. 5 .

 5 FIG. 5. (Color online) (a) Low magnification image of the cementite catalyst after 5'27 in situ annealing at 550°C;the dotted square indicates where the images in Fig. 4 have been recorded (1 min before the present recordings); the catalyst has been extruded from its original place in the nanotube. (b) HRTEM of the yellow rectangle in (a) showing the graphite structure obtained after collective growth of the graphene layers. The Fourier transform in (c) indicates that the structure in the yellow square in (b) is essentially that of standard graphite.(See suppl.

FIG. 6 .

 6 FIG. 6. (Color online) Schematic diagrams showing the two geometries of growth. In the case of collective growth (nanotube, top), catalyst steps are blocked in their progression so that

Acknowledgements

JLM & CSC would like to acknowledge fruitful discussions with Dr P. Legagneux, Dr J-P.Mazellier and F. Andrianiazy (Thales R&T France) as well as with Dr I. Florea (LPICM). JLM & ZH thank Dr. G. Garry (Thales R&T France) for the use of the Topcon 002 microscope, as well as Dr . G. Rizza and Dr . P.-E. Coulon (Laboratoire des SolidesIrradie ś , Ecole Polytechnique, France), for the use of the CM 30 microscope. ZH and JLM thank Dr A.

Gohier (then at LPICM) for providing samples. JLM and GP thank B. Jacobs and S. Shannon (Protochips, inc.) for their help with the Aduro holder. This work has been partly supported by French ANR in the framework of the Equipex program TEMPOSNanoMAX.

A lastpoint, finally, is that of the end-destination of the catalyst steps. During dcPECVD growth, a "nail head" shape of the catalyst after growth is frequentlyobserved. There, the step migration all around the particle is probably blocked by the ion bombardment on the plasmaexposed surface, leading to step bunching which creates the shoulder (Figs. 1c and6top).

Note that in this situation, a first stage of growth must involve the step flow discussed here, which thins down the bottom part of the catalyst. In a second stage however, no new graphene layers are created, only those already existing continue to grow, eventually leading to the geometry of real MWCNT. In such a geometry, where graphene layers are parallel to the tube axis [START_REF] He | Iron catalyst for the growth of carbon nanofibers: Fe, Fe3C or both?[END_REF], all the graphite planes making up the nanotube now grow at the same time.

In the framework of applications involving electrical conductivity, like the field emission of interest here, that geometry should drastically decrease the nanotube resistance as conductivity along the planes in graphite is four orders of magnitude better than across the planes.