Keywords:

Objective 1: Develop a sustainable and scalable operating model for transnational life-science data management support by leveraging national capabilities (WP1, WP5) Key Result 1.1: Established European expert network of data stewards that connect national data centres and similar infrastructures and drive the development of interoperable solutions following international best practice, including national interpretations of the General Data Protection Regulation (GDPR) Yes Key Result 1. 2: Development of joint guidelines and common toolkit that are adopted into funder recommendations, with support available nationally and in local languages Yes Key Result 1.3: The catalogue of successful national business models incorporated into national strategies No Key Result 1.4: The developed "sustainable and scalable operating model for transnational life-science data management support" is adopted into national ELIXIR Node Yes Objective 2: Strengthen Europe's data management capacity through a comprehensive training programme delivered throughout the European Research Area (WP2, WP6) Key Result 2.1: A comprehensive ELIXIR Training and Capacity building programme in Data Management, directed at both data managers and ELIXIR users, and connected to the national training programmes in Data Management in the ELIXIR Nodes and prospective ELIXIR Member countries. No Key Result 2.2: Development of a collective group of trainers that support scalable deployment of Data Management training across ELIXIR Nodes. No Key Result 2.3: A substantial cohort of data managers, Node coordinators and researchers with specific data management skills, business planning and knowledge of transnational operations across the ELIXIR Nodes No Objective 3: Align national data management standards and services through a sustainable, scalable and cost-effective data management toolkit (WP2, WP3, WP5) Key Result 3.1: Assemble a full-stack harmonised common toolkit comprising all aspects of data management: from data capture, annotation, and sharing; to Yes

that, six demonstrator use-cases were created and they are described in the previous deliverable (D5.1) .

1 This deliverable includes a description of the main resources that can be used to assess researchers in the process of creating DMPs for at least two use-cases including a gap analysis. The DMPs are related to the demonstrator use-case #1 (Plant sciences) and #3 (Marine metagenomics). Moreover, specific aspects for use-cases #4 (Human data) and #6 (Biomolecular simulation) are also added.

The main activities described in this deliverable are related to the ELIXIR Research Data Management Kit (RDMkit) and the Data Stewardship Wizard (DSW) in connection with ELIXIR 2 3

Converge WP3 activities. For all use-cases except use-case 5 (Toxicology data), a 'Your domain' page in the RDMkit has been assembled with the information necessary to consider when managing research data in their corresponding domains. Also, a 'Tool assembly' page in the RDMkit for the plant sciences, marine metagenomics and human data use-cases have been added. Finally, the DSW has been used to perform the initial description of the first DMPs including a gap analysis.

Since ELIXIR Converge started, the work of WP5 has been centered in understanding the needs of the demonstrator use-cases to develop, if necessary, customized DMPs for each of them considering the domains they are part of. Also, once this characterization was done, several resources have been created to help users in the development of their DMPs. Indeed, these demonstrators are expected to serve as examples for researchers developing their own DMPs.

The domain and tool assemblies pages added in the RDMkit are ready to use internally in ELIXIR after the beta-release in February, 2021. They provide a valuable resource for researchers and data stewards in the life sciences to help them in their data management processes. The Knowledge Models (KMs), the central component of the DSW, are under periodic revision to incorporate outcomes from ELIXIR Converge including specific aspects identified by the use-cases in order to complete their content and release an official version of them.

The final objective is to provide refined DMP versions for the remaining 4 use-cases. This will allow us to cover a broad range of data-driven demonstrators, with its associated challenges, and assess how the general process scales up when applied to other communities served by ELIXIR. All these efforts will contribute to harden the work developed in other ELIXIR Converge WPs like the RDMkit and the DSW (WP3), the dedicated training materials and capacity building actions (WP2) as well as to provide reference information to the data management experts network (WP1) and external members to the project, e.g. Industry, in WP4.

Introduction

Data Management Plans (DMPs) are key for good research data management, as they describe how research data is handled before, during and after the end of the project. The overall goal of ELIXIR 4 Converge WP5 is to assess the capacity of ELIXIR and its national nodes to assist users' projects in implementing DMPs in their projects at a EU scale. A set of six very diverse demonstrator use-cases were selected and are addressed for this purpose:

1. Harmonised FAIR plant genotype & phenotype data management toolkit for Europe 2. Reproducible, comparable and FAIR Epitranscriptomics 3. Common Data management plans for the marine metagenomics Community 4. Federated access to human genomics data: GDPR 5. FAIR encoding and access to Toxicology data 6. FAIR organisation of biomolecular simulation information

In previous steps, in task 5.1, the different demonstrators use-cases were analysed in light of the process necessary to implement their DMPs and to propose a categorization based on users' needs.

During that effort, the needs in terms of DMP of the demonstrator use-cases were described, and a project categorization was presented (Deliverable D5.1 ). 5

Scope of Deliverable

This deliverable includes a description of the main resources that can be used to assess researchers in the process of creating DMPs for at least two of the use-cases in close collaboration with ELIXIR Converge WP3. In addition, This work is completed by a gap analysis. The DMPs are related to the demonstrator use-case #1 (Harmonised FAIR plant genotype & phenotype data management toolkit for Europe) and #3 (Common Data management plans for the marine metagenomics Community). Also, considering their broad reach, specific contributions for the demonstrator use-cases #4 (Federated access to human genomics data: GDPR) and #6 (FAIR organisation of biomolecular simulation information) are also included in this deliverable.

The main activities described in this deliverable are related to the ELIXIR Research Data Management Kit (RDMkit) and the Data Stewardship Wizard (DSW) . The RDMkit is a 6 7

website-based toolkit designed to guide life sciences scientists and data stewards in their efforts to better manage their research data while the DSW has been designed to assist their users to efficiently compose data management plans (DMPs) for their research projects.

• For all use-cases except use-case 5 (Toxicology data), a 'Your domain' page in the RDMkit has been assembled with the information necessary to consider when doing data management in their corresponding domains. • A 'Tool assembly' page in the RDMkit for the marine metagenomics and human data use-cases have been also added.

• The DSW has been used to perform the initial description of the first DMPs including a gap analysis.

These activities provide feedback to WP3 contributing to the development of processes to enrich and extend the RDMkit (Task 3.2). pages in the RDMkit for some of the demonstrator use-cases, as well as the marine metagenomics 'Tool assembly' page. • ELIXIR Converge WP4 members contributed in providing reference information to the external members to the project, e.g. Industry.

Relationship with other WPs

• ELIXIR Converge WP7 Federated EGA members helped in the design and gap analysis of the human data use-case.

Methodology

The methodology of work for this deliverable was developed with the representatives of the demonstrator use-cases mainly during the monthly meetings and side exchanges with some relevant ELIXIR communities (e.g. Plant Science), experts of DSW and ELIXIR Converge WP3 partners.

The tool assembly pages related to the demonstrators use-cases and the work on the DSW were developed through two complementary approaches:

1. 2. A working session with DSW experts on the adaptation of the DSW features in the context of the demonstrators use-cases.

Description of work accomplished

The different activities done for this deliverable are focused on creating resources for researchers of the different domains comprising the demonstrator use-cases. This effort will provide life sciences researchers and data stewards with reference DMPs, which can assist them in the process of creating their own DMPs. This includes the pages in the RDMkit and also adaptation of the general Knowledge Model (KM) of the DSW. Since most of the tasks described for this deliverable were done in close collaboration with ELIXIR Converge WP3, the description of work accomplished has shared many references with the work described in D3.2 . 10

RDMkit 'Your domain' pages

A page in the RDMkit was created for all the demonstrator use-cases except for Toxicology data, which is under construction. These pages are under 'Your domain' category on the RDMkit and they describe the needs and considerations that need to be considered to implement good data management practices depending on the domain which they belong to.

In the RDMkit 'Your Domain' pages, challenges specific to domains such as data types, species or areas are highlighted together with the main considerations and solutions that can be used to overcome them. The scope of the 'Your Domain' content varies depending on the context. For some domains it can be very large (e.g. Human Data) and for others it is narrower (e.g. Epitranscriptomics).

RDMkit 'Tool assembly' pages

In addition to the 'Your Domain' pages, two tool assemblies were also added in the RDMkit corresponding to three of the demonstrator use-cases: Plant Sciences, Marine Metagenomics and Human data. Tool Assemblies are examples of combining tools to provide data management across the stages of the research data management lifecycle or a subset of stages, and the distillation of assembly patterns (blueprints) to guide how tools can be combined.

In order to write these pages, members of WP5 participated in the contanthons organized by WP3 to extend the tool assemblies pages in the RDMkit. These contentathons happened in May and June 2021 and they had participants from WP1, WP2, WP3 and WP5.

D5.2 Report on the first two DMP processes

Data Stewardship Wizard Knowledge Models

For the generation of DMPs for this deliverable, the DSW was used as a tool that brings together data stewards and researchers to efficiently compose DMPs for their research projects. The DSW is built around a hierarchical KM that is used to lead data stewards through a decision tree to help them choose the right tools, resources and practices when making DMPs. Since the information relevant for the DMPs might vary between domains, these KMs can be customized for each of the use-cases.

To create these customized KMs, a DSW instance for the ELIXIR Converge project was created (URL).

Then, a specific session with DSW experts and representatives of the different use-cases was held, where the general KM for DMPs was analysed to detect areas that can be improved for each of the use-cases. During this session, four of the demonstrator use-cases were analysed (Plant Sciences, Marine Metagenomics, Human Data and Biomolecular Simulation) and a method was set up to enrich the DSW KMs.

This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075.

Results

RDMkit 'Your domain' pages

Use-case #1: Plant sciences

In this page , challenges specific to the plant sciences domain are highlighted together with the main 11 considerations and solutions that can be used to overcome them. In the plant sciences, the main challenge addressed is data integration that needs a standardized way to identify the heterogeneous ensemble used in various experiments comprising plant varieties, their accessions obtained from a genebank or a laboratory and all the samples derived from them. The description of the plant material at infra-specific levels (e.g. subspecies, variety, accession name) often lacks consensus. Recently, guidelines have been developed to solve this problem by the plant sciences community.

Another particularity of this domain is the absence of central deposition databases for certain important data types, in particular data coming from plant phenotyping experiments. Whereas datasets from plant omics experiments are typically deposited in global deposition databases for that type of experiment, those from phenotyping experiments remain in institutional or at best national repositories. Finding, accessing and interconnecting plant phenotyping data is therefore based on utilizing a common metadata standard and on following the FAIR principles to facilitate the emergence of federations of interoperable information systems.

Use-case #2: Epitranscriptome data

Epitranscriptome modifications are appearing as important factors to fine tune gene expression and regulation in a variety of organisms and experimental conditions. Thus the detection of RNA modifications requires bioinformatics pipelines and the use of computing intensive tools to handle the huge amount of available deep transcriptome sequencing experiments.

A fruitful organization of data and computational workflows is an important aspect for the data management of this domain. It has been decided to tackle those challenges by FAIRing those components as well as providing recommendations for this particular domain. In this page , 12 challenges that are characteristic to the epitranscriptome data domain are mentioned together with the main considerations and solutions that can be used as a solution for them.

Use-case #3: Marine metagenomics

The marine metagenomics domain has very specific challenges when considering research data 13 management. They have been listed in this entry for the RDMkit as well as different considerations and potential solutions for those challenges.

The marine metagenomics domain characterizes for using large datasets that require access to substantial storage and High-Performance Computing (HPC) for running complex and memory-intensive analysis pipelines, and therefore are difficult to handle for typical end-users and are beyond the resources available to many service providers. To enable research under those conditions, the community has put the focus on the use and re-use of metagenomics data. To be able to share and reuse metagenomics datasets, they have to be in compliance with the FAIR principles which relies entirely on recording rich metadata in all the data lifecycle steps from sampling to data analysis.

Use-case #4: Human data

There are additional challenges that need to be considered when doing research with data derived from human individuals. Those particular challenges associated with the fact of working with sensitive data are described in this RMDkit page. Much of the topics discussed on this page refer to the EU General Data Protection Regulation (GDPR) as it is a central piece of legislation that affects basically all research done on human subjects in the EU and on individuals residing in the EU. Also, much of the information on this page is of a general nature when it comes to working with human 14 data but an additional focus is on human genomic data and the sharing of such information for research purposes.

RDMkit 'Tool assembly' pages

Use-case #1: Plant sciences tool assembly

This page is created to help users from the plant sciences community in the management of 16 genomic data during the different steps of the data life-cycle. It has particular focus on ensuring traceability of the biological materials to enable interoperability with plant phenotyping data.

Use-case #3: Marine metagenomics tool assembly

This tool assembly aims to provide an example of combining tools for management of marine genomic research data throughout a project's data life cycle. In this case, the tool assembly is established at national level, especifically to the Norwegian node of ELIXIR.

Use-case #4: TransMed tool assembly for working with sensitive human data

The TransMed tool assembly is also a blueprint showing how a collection of tools can be combined 18 to support data life cycle management in clinical and translational projects. This is especially relevant for those projects handling sensitive data associated with phenotypic and genotypic patients.

The TransMed data and computing tool assembly is an infrastructure provided by ELIXIR Luxembourg for clinical and translational projects. TransMed assembly provides the tools for managing ongoing projects that often require the management of cohort recruitment, and processing of samples, data and metadata. This entails GDPR-compliant and secure data collection, storage, curation, standardisation integration and analysis of clinical data and associated molecular, imaging and sensor/mobile data and metadata.

Data Stewardship Wizard Knowledge Models

The KMs in DSW contain the knowledge about what should be asked and how to get the necessary information from users to generate a DMP. The KMs follow a tree-like structure and are organized into Chapters, Questions, Answers and additional resources. Therefore, the KMs are the cornerstone to generate the set of questions that a given user is present to.

In the Converge DSW instance, there are two KMs available for consideration (see figure 8). One of them is a more general one called "Common DSW Knowledge Model" and another specific for life sciences called "Life Sciences DSW Knowledge Model". For this deliverable, the Common DSW KM was used as a template to be evaluated, commented and refined by each of the use-cases. To initiate this work, a gap analysis was done to evaluate the missing aspects of the Common DSW KM in order to make it more specific for each of the use-cases' domains.

In figure 8, it is possible to see the projects that were created in the DSW for the documentation of this gap analysis. For the marine metagenomics use-case, the norwegain instance of the DSW was used and therefore it is not shown in the picture.

Use-case #1: Plant sciences

For the Plant science demonstrator use-case, the focus was on the most specific type of data: the data derived from plant phenotyping experiments.

• Reusing data: The first step is to gather existing passport data and identifiers associated with the plant material. This information can be obtained from genebanks if the material was obtained from a gene bank via their own catalog or via international catalogs of plant genetic resources (e.g. EURISCO for Europe and Genesys at the global level); advanced research plant material is also often generated by laboratories with internal identifiers and metadata sets.

For the moment, the catalogs of genetic resources are poorly connected to the scientific community, not referenced in FAIRsharing and therefore not available in the Common DSW KM.

• Creating and collecting data: the (meta)data created will correspond to data about the seed lots or samples generated for phenotyping experiments, data about the protocols of measurements and the phenotypic data themselves.

It is often difficult to understand at what level the questionnaire is and it would be useful to have a section summarizing the different data sets that will be described in the preserving and archiving sections and associated data and metadata.

The plant specific metadata standard MIAPPE, although in FAIRsharing it was not in the proposed list.

The section on the provenance of the data is very oriented towards human health applications and could be adapted in a template dedicated to plants.

• Processing data: this step was not the focus of the plant use-case.

• Interpreting data: the section on interoperability with other data is very relevant to the plant use-case but might have to be checked with researchers for the use cases of integrations that are proposed (are they the most frequents? Is the phrasing understandable?)

• Preserving data: the datasets are described here and the difference in terms of information with the "collecting data" section is to be clarified to avoid repetitions (e.g. in terms of ontologies). Again a section somewhere describing briefly the datasets and the metadata and data associated could help.

As a conclusion, the Common DSW KM could very well be used to generate a specific template dedicated to the plant science community by filtering out or re-phrasing some items, which are oriented towards human health data, into plant science specific questions as well as by adding some plant specific resources in the lists, e.g. MIAPPE.

This exercise also points out some improvements needed in the plant science community, in particular in terms of specific reference repositories around the plant material and the phenotyping data. The conclusion is clear, the community needs better cataloging strategies and start using such catalogues connected with their respective data repositories.

Use-case #3: Marine metagenomics

For the marine metagenomics use-case, the DMP model is based on the Life Sciences DSW Knowledge Model -ELIXIR Norway localization which is a customization of the Life Sciences DSW Knowledge Model. This KM is hosted in the Norwegian DSW instance but is publicly available from the Marine Metagenomics RDM tools assembly page. At present, this KM is established at national level to be compliant with several European DMP models, such as Science Europe and Horizon 2020. It also encompasses information required at the national level such as the NeLS storage request form. The model covers all the needs of norwegian users and partly that of other european users at the moment. An effort to develop a more general European version is ongoing with the objective to understand the process of dedifferentiation from a specific KM towards a general one. This result can provide feedback on the process of creating specific versions and/or branches of the Common KM.

The most important gaps to achieve this dedifferentiation mainly lie in the solutions for data storage, sharing and computation, which are built in connection with national services and infrastructure. Such services and infrastructures are delivered by ELIXIR Norway and are described in the Norwegian e-Infrastructure for Life Sciences (NeLS) tool assembly. Suggestions in the KM describing these solutions would not always be relevant or even accessible to non-norwegian users and will have to be reworked for pan-european users.

Of note users can select different tags to create their DMPs covering questions relevant for European projects, e.g. H2020 and HE. The KM also makes ubiquitous suggestions on existing workflows, databases, vocabularies, ontologies and file formats specifically directed towards marine metagenomics. These can be isolated into a marine metagenomics project DMP by selecting the Marine MMP tag.

In addition the KM includes a short section on data sensitivity and general ethical guidelines even though this aspect, in most cases, will be less important for marine metagenomics projects than for the human related ones.

The practical aspects around the implementation of a Marine Metagenomics -European KM are currently being explored. The main challenge is that there is no easy way to migrate the ELIXIR Norway location DSW back to the parent model. The selection of databases and tools specific to marine metagenomics will be expanded to include additional important resources such as MGnify and the Marine Microbial Gene Catalogue (MarCat) among others.

Use-case #4: Human data

To perform the gap analysis for the human data use-case, it was evaluated that the considerations mentioned in the RDMkit Human Data page were reflected in DSW. The main gaps that were found 19 in the DSW KM for this particular use-case are:

• There are no questions on Ethical Considerations, and Legal Considerations appear to come up serendipitously in "data processing" and onwards. Therefore, separate sections are needed, one that covers the ethical and another that covers the legal aspects that the project should consider during the data management planning phase, like general data protection aspects and their implementation through the Data Protection Impact Assessment (DPIA) .

20

• The DSW is trying to direct the user to making the data open by applying every method possible (aggregation or anonymisation). We think that controlled-access and registered-access should be brought forward and presented as valid legal options to share human-subject data.

• Under the "Giving access to data" section, the DSW touches upon a number of use restrictions that could be applicable to data. For the sake of completeness, it might be useful to point the user to the Global Alliance for Genomics and Health (GA4GH) Data Usage Ontology (DUO) codes and ask the researchers if there will be any further restrictions and/or data access scenarios not being contemplated in such ontology.

• GDPR and anonymisation/pseudonymisation is found under "data processing" within an information security related section "Is the risk of information loss, leaks and vandalism acceptably low?" We believe this is a bit late to introduce these concepts. Perhaps in the "Ethical and Legal Considerations" section or under "Creating and collecting data" researchers should be asked whether researcher will pseudonymise the data at source.

• In the question "Is the risk of information loss, leaks and vandalism acceptably low?", would be good to add a close by section, on whether national platforms for secure processing are known e.g. Ga4GH compatible clouds, GA4GH data security toolkit, ISO/IEC 27001.

When completing the questions of the KM, it makes the user understand that to have open data is always the best option. In the case of human data, most of the time it doesn't have to be open, it can be controlled access it wouldn't be a problem.

Use-case #6: Biomolecular simulation data

• Metadata: A choice between Dublin Core Metadata, DataCite Metadata or DDI Metadata is given. In the case of the Biomolecular simulation field, most of the time it is not needed to use any metadata standards and therefore people from this field might not know any of them.

• Checksums / Swaps: might be too specific to ask if checksums or check file swaps of the data are saved.

• Standard Operating Procedure (for file naming): giving such a complicated name to ask if standard nomenclature is used, makes it more difficult to understand what the actual question means.

• Provenance: It is possible to choose between lab notebooks, electronic lab notebooks, and "other". In computing, most of the time it will be "other". In this case, the documentation, or appropriate reference are missing to know what other provenance standards could be used.

• Saving data: Options are Object Store, Relational database (DB), Graph DB, and Triple Store.

Other options including noSQL and non-relational DBs are missing.

• Identifiers: In this case, options are Handle, DOI, ARK, URL and other. It is possible that identifiers for the entries in a dataset are not used. Entries in biomolecular simulation can be N files of a single molecular dynamics simulation, including path, topology, analysis, etc. In some projects an URL with a persistent identifier is included, but not for all of them.

• In general, a certain sense of repetition especially in regards to data types / formats when you get to step 5.

Conclusions

Since ELIXIR Converge started, the work of WP5 has been centered in understanding the needs of the demonstrator use-cases to develop customized DMPs for each of them considering the domains they are part of. Also, once this characterization was done, several resources have been created to help users in the development of their DMPs. This includes the "Your domain" and "Tool assembly" pages in the RDMkit and an evaluation towards personalized knowledge models for the DSW.

The exercise to build tool assemblies for the demonstrators use-cases was facilitated by the work achieved to deliver domain pages and adding questions about the national implementations of tool assemblies. Therefore, some of the resources needed along the data life-cycle, such as storage and computing resources, are provided at the institutional or country level. The Marine Metagenomic use case is an example on that aspect: a Norway-grounded tool assembly was delivered (NeLS) and the partners responsible of the demonstrator use-case are working on approaches to give a more generic tool assembly.

The DSW is overall a well received system and is very well suited to generate DMPs for all demonstrator use-cases but some important sections would be necessary (ethical and legal aspects) or helpful (overview of the data sets and data and metadata associated) to be added. To solve this, a modular approach could be considered. This can imply an additional chapter in the Common KM with pre-requisites, e.g. have you covered all ethical and legal considerations for the type of data you will managed along the project life cycle, or links to external complementary resources, e.g. DAISY for the ethical and legal issues management for human sensitive data. Some pre-listed resources or formats are missing in the DSW KM and could be added, together with cross links between the domain pages of the RDMkit and DSW.

The domain and tool assemblies pages added in the RDMkit are ready to use internally in ELIXIR after the beta-release in February, 2021. They provide a valuable resource for researchers and data stewards in the life sciences to help them in their data management processes. The KMs are under periodic revision to incorporate outcomes from ELIXIR Converge including specific aspects identified by the use-cases in order to complete their content and release an official version of them.

After a year and a half of work, the ELIXIR Converge WP5 has built a productive team that includes data management experts as well as representatives of all the 6 demonstrator use-cases. The division of the tasks among members and the participants on internal activities has been very successful. Even with the broad difference between use-cases, WP5 managed to develop common methods to work and produce great and valuable work in close collaborations with other WPs in the project.

Figure 1 .

 1 Figure 1. Plant science domain page in the RDMkit

Figure 2 .

 2 Figure 2. Epitranscriptome data domain page in the RDMkit

Figure 3 .

 3 Figure 3. Marine metagenomics domain page in the RDMkit

Figure 4 .

 4 Figure 4. Human data domain page in the RDMkit

Figure 5 .

 5 Figure 5. Biomolecular simulation page in the RDMkit

Figure 6 .

 6 Figure 6. Plant genomics tool assembly page in the RDMkit

  The toolkit, developed by students and researchers in Norway, contains resources and software tools for both data management (Planning, Processing, Storing and Sharing), data analysis and training. It is built on the Norwegian e-Infrastructure for Life Sciences (NeLS) tool assembly of ELIXIR Norway and the Marine Metagenomics Platform (MMP).

Figure 7 .

 7 Figure 7. Norwegian marine metagenomics tool assembly page in the RDMkit

Figure 8 .

 8 Figure 8. Luxemburg TransMed tool assembly page in the RDMkit

Figure 9 .

 9 Figure 9. Data Stewardship Wizard Knowledge Models.

Figure 10 .

 10 Figure 10. Data Stewardship Wizard projects

This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075.

https://ds-wizard.org/ 6 https://rdmkit.elixir-europe.org/ 5 10.5281/zenodo.4674490 4 https://ec.europa.eu/research/participants/docs/h2020-funding-guide/cross-cutting-issues/open-access-datamanagement/data-management_en.htm

https://zenodo.org/record/5139897#.YQAyoRNKj0o

This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075.1

https://ec.europa.eu/info/law/law-topic/data-protection/reform/rules-business-and-organisations/obligation s/when-data-protection-impact-assessment-dpia-required_en 19 https://rdmkit.elixir-europe.org/human_data.html This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075.2

This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075. D5.2 Report on the first two DMP processes 2. Contribution toward project objectives With this deliverable, the project has reached or the deliverable has contributed to the following objectives/key results: Objective no. / Key Result no. This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075. D5.on Membership (EU and international) or strategic partnerships (international countries) following ELIXIR-CONVERGE workshops. No This project has received funding from the European Union's Horizon 2020 Research and Innovation programme under grant agreement No 871075.

data publicly available according to international standards.

Impact

The activities associated with this deliverable have had a direct impact across different components of the projects, e.g. the RDMkit and the DSW. In the case of RDMkit, pages for the "Your domain" section have been added for all the demonstrator use-cases except one, which gives a lot of value to the toolkit. From now on, users from the domains of plant sciences, marine metagenomics, human data, biomolecular simulations and epitranscriptomics will be able to address their specific challenges when doing data management by just having a look at these pages. Also, the tools listed in the "Your domain" pages as solutions, have been flagged in bio.tools with the domain name. This categorization will allow researchers and data stewards that work in these particular domains to be able to find solutions to their data management problems in an easier and faster way.

Globally, the work achieved so far by WP5 has also given a push towards completing common catalogs with important resources in the context of each demonstrator use-cases. This effort has to be pursued, with a global vision, e.g. making sure that important resources not maintained by ELIXIR members are visible, to give more impact to the RDMkit.

In addition, the tools assemblies for plant sciences, marine metagenomics and human data give a very good insight on how national nodes use a combination of their tools for different steps of their data life-cycle, which can help other nodes to do the same.

Next Steps

The perspective of the work is:

1. Finish the RDMkit domain page for the Toxicology data use-cases. 2. Add a tool assembly page in the RDMkit for the rest of the use-cases. 3. Generate a knowledge model adjusted to each of the use-cases, and evaluate the best strategy to release it. Current strategies are two: incorporate use-case driven particularities as part of the branches of the common model or create adjusted KM per domain. 4. Continue the collaboration with the ELIXIR Converge WP2 on the definition of the training and capacity building activities.

Deviation from Description of Action

The Description of Action proposal included a description of the first two DMP processes. However, more work regarding the rest of the use-cases was done and therefore stated in this deliverable. All demonstrator use-cases except one have a page in the RDMkit and three of them a tool assembly. Also, a gap analysis of the KM in the DSW has been done for four of the use-cases already. Once these KMs are completed, they will serve as a template for the users to generate DMPs.


Hakim Amara
email: hakim.amara@onera.fr

Jaysen Nelayah

Jérôme Creuze

Adrian Chmielewski

Damien Alloyeau

Christian Ricolleau

Bernard Legrand

Is There Really a Size effect on the Surface Energy of Nanoparticles ?

Surface energy is a key quantity that controls many physical properties of materials, yet determining its value at the nanoscale remains challenging. By using N -body interatomic potentials and performing analytical calculations, we develop a robust approach to determine the surface energy of metallic nanoparticles as a function of particle size and temperature. A strong increase in the surface energy is obtained when the size of the nanoparticle decreases, both in the solid and liquid states. However, we show how the use of the classical spherical approximation to characterise the surface area of a nanoparticle leads to an almost constant surface energy with size as usually done to characterize the thermodynamic and kinetic properties of NPs in many works. We then propose a correction of the spherical approximation that is particularly useful for small size nanoparticles to improve the different models developed in the literature so far.

Surface energy (γ) is an important descriptor of metallic nanoparticles (NPs) as it drives, among others, their nucleation-growth mechanism, 3D morphology, reactivity in various environments, surface segregation,... [1]. To characterize these wide range of phenomena, the main theories developed in the literature are derived from models that involve surface energies of infinite systems [2]. In other words, γ is basically assumed to be size-independent. With this assumption, it is then possible to remarkably predict the equilibrium shape of free and supported crystallites based respectively on the Wulff and Wulff-Kaishew relations at the nanoscale [3][4][5]. Other examples illustrating the success of such a choice include understanding Ostwald's ripening during particle synthesis or annealing [6,7] and the reactivity of different metal facets to gas environments in catalytic processes [START_REF] Chmielewski | Reshaping dynamics of gold nanoparticles under H2 and O2 at atmospheric pressure[END_REF]. From a fundamental point of view, this is very surprising because it is well-known, both experimentally and theoretically, that many properties (thermodynamic, optical, mechanical, . . . ) of nanomaterials are strongly different from their bulk counterparts [START_REF] Ph | Size effect on the melting temperature of gold particles[END_REF][START_REF] Alloyeau | Size and shape effects on the order-disorder phase transition in CoPt nanoparticles[END_REF][START_REF] Delfour | Exotic behavior of the outer shell of bimetallic nanoalloys[END_REF][START_REF] Magnin | Size dependent phase diagrams of nickelcarbon nanoparticles[END_REF][START_REF] Rabouw | Excited-state dynamics in colloidal semiconductornanocrystals[END_REF][START_REF] Guo | Mechanical properties of nanoparticles: basics and applications[END_REF].

Despite the agreement of the different models employing the surface energy of the infinite system with the experimental observations, there is no direct evidence that the surface energy in case of NPs is indeed sizeindependent. This is a very complicated issue to be addressed since there is not any clear and straightforward answer to it at present. Experimentally, no systematic studies on measurement of surface energy as a function of size are presented due to the extreme difficulty to measure absolute surface energy of very small NPs [START_REF] Nanda | Higher Surface Energy of Free Nanoparticles[END_REF][START_REF] Chmielewski | Direct Measurement of the Surface Energy of Bimetallic Nanoparticles : Evidence of Vegard's Rulelike Dependence[END_REF]. Theoretically, the existing literature contains many conflicting and contradictory results concerning the variation of the surface energy of metallic NPs with size. Actually, a simple dimensional argument is often put forward in case of solid NPs [START_REF] Perini | Interfacial contribution to cluster free energy[END_REF][START_REF] Martin | Shell structure of clusters[END_REF]. According to this hypothe-sis, γ decreases with increasing size as the contribution of the different surface sites (vertices, edges), which are preponderant for small sizes, decreases at the expense of the facets. Although many studies agree with this trend [START_REF] Müller | The dependence of the surface energy of regular clusters and small crystallites on the particle size[END_REF][START_REF] Medasani | Theoretical study of the surface energy, stress, and lattice contraction of silver nanoparticles[END_REF], other suggest an opposite tendency [START_REF] Xiong | Modeling size effects on the surface free energy of metallic nanoparticles and nanocavities[END_REF][START_REF] Yao | Size effect of the sur-face energy density of nanoparticles[END_REF][START_REF] Jiang | Modeling the effects of size and surface broken bond on surface energy of nanocrystals[END_REF]. Indeed, the dimensional argument is not that simple since γ is commonly defined as an excess energy with respect to a reference energy normalised to a surface area related to the NP. All the discrepancies are mainly due to the difficulty to correctly define the reference state to characterize the excess energy resulting from the presence of a surface and in particular the definition of the considered surface area [START_REF] Molleman | Size and shape dependency of the surface energy of metallic nanoparticles: Unifying the atomic and thermodynamic approaches[END_REF]. In any scenario, it can be noted that there is no direct evidence that the surface energy remains constant with the size.

In this letter, we investigate the surface energy of solid and liquid Cu NPs as a function of particle size with the aim to provide a robust γ calculation applicable to characterize the thermodynamic and kinetic properties of NPs through experimental or theoretical data. We focus on cuboctahedral NPs where an analytical study is possible, which is an asset of incomparable richness to the understanding of the numerical results. With our approach, the correlation between the effective area considered for γ calculation and its dependence on size is clearly demonstrated. ical potential with the size of the NP making its use perfectly universal and adapted to characterize the thermodynamic and kinetic properties of NPs.

We perform calculations at the atomic level for Cu NPs by using a specific N -body interatomic potential derived from the second moment approximation of the tight-binding scheme (TB-SMA) [START_REF] Rosato | Thermodynamical and structural properties of f.c.c. transition metals using a simple tight-binding model[END_REF][START_REF] Creuze | Model of surface segregation driving forces and their coupling[END_REF][START_REF] Ducastelle | Module élastique des métaux de transition[END_REF]. More details of the TB model can de found in Sec. I of the Supplemental Material. Our TB framework gives direct access to the total energy of each atom. This possibility to easily analyze local energy distributions will be decisive in the following. The atomic interaction model is implemented in a Monte Carlo (MC) code in the canonical ensemble, based on the Metropolis algorithm, which allows to relax the structures at finite temperatures [START_REF] Frenkel | Understanding Molecular Simulation[END_REF]. We consider cuboctahedral solid NP bounded by six squares and eight equilateral triangles which structure is constructed on the face-centered cubic (fcc) lattice, leading to the presence of outer facets of {100} and {111} orientations, respectively. From this structure, it is possible to define analytically all the sites for a given cluster size with k shells [START_REF] Martin | Shell structure of clusters[END_REF]. Indeed, this cluster contains 12 vertices (v), 24(k-1) atoms in edges (e), 6(k-1) 2 and 4(k-2)(k-1) atoms on {100} and {111} facets (f ), respectively. Moreover, the total number of atoms N (k), the surface S(k) and the volume V (k) are given by the following equations :

N (k) = 10 3 k 3 + 5k 2 + 11 3 k + 1 (1) S(k) = 2(3 + √ 3)(kd) 2 (2)
V (k) = 5 √ 2 3 (kd) 3 (3)
where d corresponds to the equilibrium distance between first neighbors. To characterize the evolution of surface energy of solid and liquid states, calculations are done at two temperatures (T = 5 and 1500 K). Numerically, the so-called surface energy [START_REF] Ip | The equivalency of surface tension , surface energy and surface free energy[END_REF][START_REF] Müller | Elastic effects on surface physics[END_REF] resulting from the creation of a surface is defined as an excess internal energy (E exc ) normalised to a given surface area, A:

γ(R) = E exc A , ( 4
)
where

E exc = E N P (R) -E ref . E N P (R)
is the total energy of the NP of radius R where necessarily R and the number of k shells are linked. Lastly, E ref is a reference energy to be defined. The calculation of E N P (R) is not an issue since it is a straightforward output of the MC simulations. On the contrary, E ref and A are not well defined quantities. Typically the reference energy is commonly chosen as the energy of the bulk fcc in the solid state [START_REF] Ali | Sizedependent strain and surface energies of gold nanoclusters[END_REF][START_REF] Wei | Size-dependent surface energy density of spherical face-centered-cubic metallic nanoparticles[END_REF][START_REF] Holec | Surface energy of Au nanoparticles depending on their size and shape[END_REF]. Regarding the surface area, its choice is not unique [START_REF] Molleman | Size and shape dependency of the surface energy of metallic nanoparticles: Unifying the atomic and thermodynamic approaches[END_REF] and can strongly affect the results. To overcome this problem, we first consider the case of solid particles and then extend our approach to liquid systems.

We apply two complementary approaches to get an insightful analysis of our results. The first is to calculate the surface energy from MC simulations according to Eq. 4 where E N P (R) is obtained after relaxation at 5 K. The second one consists of developing an analytical model by assuming that all excess energy is ascribed to the surface sites [START_REF] Perini | Interfacial contribution to cluster free energy[END_REF][START_REF] Martin | Shell structure of clusters[END_REF]. This is made possible because all surface sites are perfectly identified. In both approaches, it is quite natural to consider A as the exact surface S(k) of the cuboctahedral shape (see Eq. 12). Furthermore, the identification of local energies within the NP turns out to be very precious to tackle the challenge of correctly defining E ref . More precisely, by analyzing the energy profile along the radius of the NPs, we can clearly identify two populations, i.e. the core and surface atoms (see Sec. II of the Supplemental Material). Consequently, E ref is simply the average energy of atoms identified in core position. In case of solid NP, E ref is equal to -3.50 eV/at which is exactly the total energy per atom of a face centered cubic bulk Cu in our TB model. This result confirms that defining E ref from the bulk system, as done in many works, is completely justified. At this stage, all the quantities required to determine γ(R) from MC simulations according to Eq. 4 are known. The calculated surface energies for the cuboctahedral Cu NP as a function of size are shown in Fig 1a . It can be seen that the surface energy decreases with particle size. More precisely, there is a significant variation for small particles (<20 Å), from 1.92 to 1.22 J/m 2 . For larger particles, the decrease of γ with the size becomes negligible to reach a constant value around 1.20 J/m 2 . We now consider an analytical model where the determination of γ(k) is simply reduced to the following equation :

γ cubo (k) = i n i γ i A , (5)
where γ i represents the local excess energy for each surface sites i (i = v, e, f ) defined as E i -E ref and n i being the number of sites of type i. In this approach, it is assumed that the excess energy is located only on the surface sites. As seen in Sec. II of the Supplemental Material, also subsurface atoms have still a slightly different energy than in bulk. We consider that they do not play a decisive role and that they can be neglected in γ calculations. In a first step, A is considered as the exact surface S(k) of the cuboctahedral NP (see Eq. 12), the related surface energy is noted γ exact cubo (k). Meanwhile, the local energies of all sites (E i ) are calculated from our TB-potential for clusters of various sizes (see Sec. III of the Supplemental Material). The resulting values of γ i are presented in Table I. From γ exact cubo (k), the analytically γv γe γ100 γ111 2γe -γ100 -γ111 2γe - calculated surface energy for the cuboctahedral Cu NPs as a function of size is shown in Fig. 1a. Similarly to results obtained from MC simulations, the surface energy decreases strongly with size. Moreover, results from the analytical model are in good agreement with the complete MC calculations, the small difference observed being due to the the subsurface contributions. To go deeper and analyse this tendency, the first-order Taylor expansion of γ exat cubo (k) turns out to be very precious (see details in Sec. IV of the Supplemental Material) :

γ exact cubo (k) ≈ γ exact ∞ + 6 [2γ e -γ 100 -γ 111 ] kd 2 (3 + √ 3) (6)
γ exact ∞ = 3γ 100 + 2γ 111 d 2 (3 + √ 3) ,
where γ exact ∞ corresponds to the plateau observed in Fig. 1 for large NPs (i.e. for k → ∞ in Eq. 14). In addition, the second term is necessarily positive according to the γ i hierarchy discussed above. As seen in Table I, this argument is valid for all noble metals. Consequently, the heterogeneity of the surface with different types of site explains the decrease in γ(R), as already argued in previous works with a simple dimensional argument [START_REF] Perini | Interfacial contribution to cluster free energy[END_REF][START_REF] Martin | Shell structure of clusters[END_REF].

On a purely theoretical point of view, it is quite natural to consider the true surface of the cuboctahedron S(k) as done so far. Experimentally, it is however not always possible to identify the exact shape of the NP (i.e. icosahedron, decahedron, cuboctaedron,...) and even less to determine the exact surface area of the observed NPs. In practice, a spherical approximation of the different NPs to be analysed is made. Typical examples from Transmission Electron Microscope (TEM) images are presented in Fig. 2a where a radius R can be assigned to each NPs in solid states (see Sec. V of the Supplemental Material for experimental details). Within this spherical approximation, determining A of a solid NP from MC simulations is also non-trivial. Actually, the effective surface is For the liquid cases, it is obvious that a snapshot is not so representative of the situation since the particle is strongly deformed during the simulation.

equal to 4πR 2 . To address the arising difficulty in MC simulations, R is determined from the atomic density, ρ ∞ = √ 2/d 3 , (see Sec. VI of the Supplemental Material) using the following relation : R 3 (k) = 3N (k)/4πρ ∞ . To highlight the relevance of such a choice, Fig. 2a shows the sphere obtained from ρ ∞ on snapshots of MC simulations from solid NPs, whose surface area is noted S sa (k). The comparison with the determination of the radius of the NPs from TEM images is clearly relevant. From Eq. 4, it is now possible to calculate the dependency with the size of the surface energy within the spherical approximation from MC simulations. As seen in Fig. 1b, the conclusion differs significantly from the exact calculation. Indeed, almost no variation is observed and γ remains rather constant around 1.23 J/m 2 . Consequently, the surface energy using the spherical approximation does not depend on the size of the system. In fact, the apparent discrepancy between the two approaches can be attributed to the different ways to calculate the surface area. Once the gap between both approaches becomes negligible, then an equivalent behaviour can be observed where the surface energy varies only slightly (see Fig. 3). Obviously, this happens for sufficiently large particles where the spherical approximation is all the more adapted. To better

!" !# !$ !% ! & ' ( ) ( & * + , " # $ % &-./012&34&567&89&*:, FIG. 3.
Relative difference between the surface area calculated according to the spherical approximation and the exact one of the cuboctahedron as a function of size. understand these differences with the strong decrease observed for γ exact cubo (k), a first-order Taylor expansion of γ(k) within the spherical approximation (sa), noted γ sa cubo (k), is done leading to (see Sec. VII of the Supplemental Material):

γ sa cubo (k) ≈ γ sa ∞ + 6 [2γ e -(3/2)γ 100 -(4/3)γ 111 ] kd 2 (25π) 1/3 (7) γ sa ∞ = 3γ 100 + 2γ 111 d 2 (25π) 1/3
As seen in Fig 1b, we confirm an almost constant variation of γ(k) around 1.20 J/m 2 . Such observation is in agreement with MC simulations where the discrepancy in the plateau is mainly due to the assumption of considering only surface sites in the analytical approach. Unfortunately, the variation of γ with size is not straightforward contrary to the exact calculation discussed previously. Indeed, nothing can be concluded about the importance of the predominant term in the numerator of Eq 17. In the particular case of Cu, it is close to zero explaining the stability of γ with size. To generalise this result, the estimation of the numerator has been extended to other noble metals (Ag and Au) confirming this trend (see Table I). Within the spherical approximation, our analytical calculations therefore suggest that the surface energy does not vary with the size and is equal to γ sa ∞ (i.e. for k → ∞ in Eq. 17).

In the following, we analyse the error made in the spherical approximation where two strong assumptions were established. The first one was to determine R(k) from the atomic density where all the atoms constituting the NP contribute equally. However, as seen in Sec. VI of the Supplemental Material, ρ ∞ is correctly reproduced (at least to first order) when only considering that the surface atoms, N surf (k), contribute half compared to the core atoms. In the definition of R(k), this is equivalent to consider that the total number of atoms is N (k) -N surf (k)/2. In this corrected spherical approximation (csa), the surface area becomes S csa (k) = S sa (1 -1/k). By applying this new surface formulation to the MC simulations, a significant variation of the surface energy with the size of the NPs is found. The result (corrected MC) presented in the Fig. 1b shows a decrease for NPs smaller than 20 Å to reach a plateau in the order of 1.20 J/m 2 . As seen in Fig. 1b, the same trend is observed for the analytical model, γ csa cubo (k), where S csa (k) is considered. In other words, by using this simple surface area correction to the spherical approximation, it is possible to restore the energy dependence obtained with an exact description of the surface area. The second assumption comes from the morphology, i.e. sphere rather than cuboctahedron. Actually, the following relationship γ csa cubo (k) ≈ 1.10γ exact cubo (k) can be established (see Sec. VII of the Supplemental Material). Thereby, the only difference between the exact calculation and the corrected spherical approximation ones results in a morphological factor due to the difference between a sphere and a cuboctahedron. To conclude, the spherical approximation is very appropriate for large sizes (with a constant form factor) but must be corrected for small sizes by a factor modifying the radius of the NP, which itself depends on the size and takes into account the specific contribution of the surface atoms.

Let us now consider liquid NPs by applying the approach developed for solid NPs to determine E ref and A in Eq. 4. For the reference energy, it is simply a question of calculating the average energy of a bulk system at 1500 K (see Sec. II of the Supplemental Material). To determine the surface area, one can no longer rely on an exact calculation. Moreover, the corrected spherical approximation allows a precise determination of this area by assuming that the number of surface atoms is very close to that in the solid state. Meanwhile, the usual spherical approximation is subject to the same disadvantage as in the solid state, i.e. an overestimation of the volume (and therefore of the radius) of the NP at small sizes, which is even greater the smaller the size is. Figure 4a shows that the variation of the surface energy with the size of the NP in the liquid state is very similar to that observed in the solid state. Thus the calculation with the usual spherical approximation shows a constant surface energy close to 1.15 J/m 2 , whereas the corrected spherical approximation gives a strong increase of γ when the size decreases, a variation slightly higher than that observed in the solid state. This significant variation may seem very surprising if we refer to the solid state where the weight of highly energetic sites (edges and vertices) decreases in favour of that of the facets when the size increases. However, vertices, edges and facets no longer exist in the liquid state and it is tempting to think that the surface energy distribution is relatively homogeneous. To address this issue, we determined the local energies in terms of spatial distribution in the liquid state. As seen in Fig. 4b, we show the local energies for two NP sizes (561 and 5083 atoms). The particles do adopt a quasi-spherical shape without the presence of facets and edges in agreement with TEM observations (see Fig. 2a). Nevertheless, the energy analysis shows a strong surface heterogeneity. There is a difference of about 0.8 eV between the most energetic and the least energetic surface atoms, compared to a difference of about 0.6 eV in the solid state between vertices and facets {111}. This unexpected presence in the liquid state of highly energetic surface atoms whose weight decreases with increasing size (cf. Fig. 4b) is at the origin of the strong variation of γ with size, as in the solid state. The determination of the statistics of these sites as a of size and temperature remains to be done. As proposed in case of solid NPs, this result therefore suggests that a heterogeneous surface necessarily tends to a variation in the value of γ.

Based on both numerical simulations and analytical developments, this study explains the origin of the disagreements regarding the evolution of the surface energy with the size of the NPs [START_REF] Müller | The dependence of the surface energy of regular clusters and small crystallites on the particle size[END_REF][START_REF] Medasani | Theoretical study of the surface energy, stress, and lattice contraction of silver nanoparticles[END_REF][START_REF] Xiong | Modeling size effects on the surface free energy of metallic nanoparticles and nanocavities[END_REF][START_REF] Yao | Size effect of the sur-face energy density of nanoparticles[END_REF][START_REF] Jiang | Modeling the effects of size and surface broken bond on surface energy of nanocrystals[END_REF][START_REF] Molleman | Size and shape dependency of the surface energy of metallic nanoparticles: Unifying the atomic and thermodynamic approaches[END_REF]. A strong dependence is obtained when the exact surface of the NP is considered, which is possible for simple forms. In contrast, using the classical spherical approximation, we obtain a surface energy that is almost independent of the size of the NP. If we correct the classical spherical approximation by taking into account the specific contribution of the surface atoms, we obtain a very good agreement with the exact calculation within one morphological factor. This result is particularly useful for dealing with liquid NPs, for which the exact surface area can hardly be calculated. How then can we explain the success of thermodynamic or kinetic approaches that use the classical spherical approximation and that reproduce well the experimental data, while neglecting the variation of γ with size [3][4][5][6][7][START_REF] Chmielewski | Reshaping dynamics of gold nanoparticles under H2 and O2 at atmospheric pressure[END_REF]]?

The answer is that they rely on the expression of the chemical potential which involves the product γA and where the excess energy of the NP is considered to be localised at the surface (and does not contain core contributions as for the icosahedron). In these approaches, it is therefore essential to respect the consistency of the calculations of γ and A. This product can be evaluated either by considering the exact value of the surface area A and the exact variation of γ with size, or by considering the value of A given by the classical spherical approximation and the value of γ consistent with this calculation of A, namely a constant value equal to that of a semiinfinite bulk. In this latter case, even if the variations of γ and A are not exact, the product is correct explaining the success of thermodynamic or kinetic approaches based on the classical spherical approximation. This work therefore represents a significant achievement on an essential but difficult to define physical property at the nanoscale while proposing simple approaches to improve the thermodynamic and kinetic models developed so far in the future.

Sec. I. Methodology

Within the tight-binding (TB) framework [1,2], the total energy of an atom n is splitted in two parts, a band structure term that describes the formation of an energy band when atoms are put together and a repulsive term that empirically accounts for the ionic and electronic repulsions : E n tot = E n band + E n rep . The total energy of the system containing N atoms, E tot , then writes

E tot = n=1,N E n
tot . The band energy, E n band is given by :

E n band = - m =n ξ 2 exp -2q( r nm r 0 -1) (8)
and the repulsive contribution, E n rep , is chosen to have a pairwise Born-Mayer form :

E n rep = m =n A exp -p( r nm r 0 -1) (9)
with r nm the distance between atoms at sites n and m and r 0 corresponds to the equilibrium distance between first neighbors in the pure metal. ξ is the effective hopping integral between atoms. The parameters (ξ, A, q and p) used in this study are fitted to reproduce several bulk physical properties. More details concerning the fitting procedure can be found in our previous works dealing with the structural and thermodynamic properties of metallic nanoparticles [3,4]. This atomic interaction model is implemented in a Monte Carlo (MC) code in the canonical ensemble, based on the Metropolis algorithm, which allows to relax the structures at finite temperature [5]. In the canonical ensemble, MC trials correspond to random displacements. The average quantities are calculated over 10 6 MC macrosteps, a similar number of macrosteps being used to reach equilibrium. A MC macrostep corresponds to N propositions of random atomic displacement, N being the total number of atoms of the cluster. Such approach is perfectly adapted to deal with large systems and to reproduce the main energetic properties of transition and noble metals.

Sec. II. Energy profiles along the radius of solid and liquid NPs

In Figure S1, we present the energy profiles along the radius of the different nanoparticles (147, 923 and 5083 atoms) in solid and liquid states. Such an analysis is made possible by the calculation of local energies derived directly from the TB model. Interestingly, we can clearly identify two populations, i.e. core (grey area) and surface atoms (blue area). In case of solid NPs, the first corresponds to the core atoms which have energies around -3.50 eV/atom. The second population corresponds to surface atoms which are less stable and have energies reaching -2.60 eV/atom. The discontinuous aspect of the curve is mainly due to the layer structure of solid NP giving rise to this type of profile. For liquid NPs, the energy profiles along the particle are obviously more continuous.

Here again, two populations of atoms are observed. The slice views shown in Figure S2 for solid and liquid NPs provide a direct insight into the distribution within the nanoparticle and confirms the presence of two populations where the excess energy is located at the surface.

Consequently, E ref is simply the average energy of atoms identified in core position whatever the state of the NPs. In principle, it would be relevant to determine a different core energy for all sizes of NP. However, as the variation is very small (less than 10 meV/atom between Cu 147 and Cu 5083 ), we choose to determine E ref from the largest NP where the plateau corresponding to the core atoms is more clearly defined. In case of solid NP, E ref is equal to -3.50 eV/at for solid NP which is exactly the total energy of a face-centered cubic bulk Cu in our TB model. In case of liquid NPs, E ref is equal to -3.18 eV/at and corresponds to an infinite system in the liquid state at 1500 K.

Sec. III. Analysis of the local energies in solid nanoparticles

As an example, we plot the histogram of local energies for Cu NPs with total number of atoms, N = 147, 923 and 5083 atoms. Different populations of atoms can be identified (Fig S3a). The energies lie between -3.6 and -3.4 eV/atom are due to the bulk atoms which have 12 neighbors. The second population corresponds to the surface atoms which energies are below -3.2 eV/atom. As expected, the contribution of surface atoms decreases as the cluster size increases from Cu 147 to Cu 5083 . Moreover, a local analysis presented in Fig. S3b provides a spatial representation of the different surface sites with the following hierarchy :

E {111} < E {100} < E e < E v .
This result is not surprising since it is directly related to the coordination number (Z i ) of each site. The larger Z i is, the higher the cohesion energy is. Finally, it is particularly interesting to note that local energies are independent on the size and remain constant whatever the nanoparticle under consideration.

Sec. IV. Calculation of surface energy from the exact definition of the surface area: γ exact cubo (k)

A cuboctahedral NP with k shells contains 12 vertices (v), 24(k-1) atoms in edges (e), 6(k-1) 2 and 4(k-2)(k-1) atoms on {100} and {111} facets (f ), respectively. The total number of atoms N (k), the volume V (k) and the surface S(k) are given by the following equations :

N (k) = 10 3 k 3 + 5k 2 + 11 3 k + 1 (10)
V (k) = 5 √ 2 3 (kd) 3 (11)
S(k) = 2(3 + √ 3)(kd) 2 (12)
In this section, we detail the analytical calculation of the surface energy which is written as follows:

γ cubo (k) = i n i γ i A , (13)
γ i represents the local excess energy for each surface site i (i = v, e, f ) defined as E i -E ref .

As for the surface area A, different approaches are possible. Here, A is considered as the exact surface S(k) of the cuboctahedral nanoparticle. According to Eq. 13 and precise identification of surface sites, the surface energy is given by :

γ exact cubo (k) = 12γ v + 24(k -1)γ e 2k 2 d 2 (3 + √ 3) + 6(k -1) 2 γ 100 + 4(k -2)(k -1)γ 111 2k 2 d 2 (3 + √ 3)
From this we get :

γ exact cubo (k) = 3γ 100 + 2γ 111 d 2 (3 + √ 3) + 1 d 2 (3 + √ 3) × 6 k (2γ e -γ 100 -γ 111 ) + 6γ v -12γ e + 3γ 100 + 4γ 111 k 2
By limiting to the first-order Taylor approximation of γ exact cubo (k), we obtain :

γ exact cubo ≈ γ exact ∞ + 6 [2γ e -γ 100 -γ 111 ] kd 2 (3 + √ 3) γ exact ∞ = 3γ 100 + 2γ 111 d 2 (3 + √ 3)
Sec. V. Synthesis and TEM observations of solid and liquid NPs

The temperature serie of Transmission Electron Microscopy (TEM) images of the Cu NPs was acquired using a JEOL JEM-ARM200F spherical aberration corrected electron microscope equipped with a cold field emission gun operated at 80 kV here and a ultrafast Gatan OneView camera. For in situ TEM heating, we used a slightly modified version of the Atmosphere TEM environmental gas cell from Protochips Inc. with high temperature heating capabilities up to 1273 K [6].

The Cu NPs were synthesized by alternated pulsed laser deposition (PLD) technique in a high vacuum chamber at 10 -5 Pa according to an experimental procedure detailed in [7]. The NPs was carried out directly on the 50-nm thick electron transparent silicon nitride membrane of the small heating E-chip that composes the Protochips gas cell. The nominal thickness of metal deposited was fixed at 2 nm and the SiN substrate was held at 723 K during metal deposition in order to obtain NPs with diameter below 10 nm. TEM observations were performed in vacuum with the SiN membrane of the larger E-chip of the gas cell removed.

Sec. VI. Calculation of the atomic density, ρ

In this section, we present the different approaches to calculate the atomic density for NPs, an important quantity which is taken into account in the γ calculation.

• Infinite system

In case of bulk, there is no particular difficulty since it can be straightforward determined from a face-centered cubic structure of lattice parameter a containing four atoms per cell. As a result, the atomic density of a bulk system is given by the following equation :

ρ ∞ = √ 2 d 3 , (14)
where d corresponds to the equilibrium distance between first neighbors in pure metals. Knowing that the lattice parameter of Cu is equal to 3.62 Å, we obtain ρ 0.084 atom/ Å3 . In case of simulations at 1500 K, thermal expansion is taken into account leading to ρ 0.076 atom/ Å3 . While this calculation seems trivial for an infinite volume, it has been ignored when using the spherical approximation in nanoparticles in literature.

• Nanoparticle

Atomic density from the total number of atoms N (k)

In case of a cuboctahedron NP, the number of atoms N (k) and the volume V (k) are known exactly. If we do not distinguish between core and surface sites and if we apply the following relation ρ(k) = N (k)/V (k), the atomic density is simply given by :

ρ(k) = 10k 3 + 15k 2 + 11k + 3 5 √ 2(kd) 3
By limiting to the first-order Taylor expansion of ρ(k), we obtain :

ρ(k) ≈ ρ ∞ 1 + 3 2k
The fact that the atomic density of the NP is different from that of the bulk system before any relaxation clearly shows that the formula ρ(k) = N (k)/V (k) should be corrected by differentiating the contribution of each type of site.

Atomic density by distinguishing between surface and bulk atoms

Let us consider N ef f (k) the number of atoms in the NP where surface atoms N surf (k), counting for half, are removed : N ef f (k) = N (k) -N surf (k)/2 where :

N surf (k) = 6(k -1) + 4(k -2)(k -1) + 24(k -1) + 12
By limiting to the second-order Taylor expansion of ρ(k) = N ef f (k)/V (k), we obtain :

ρ(k) ≈ ρ ∞ 1 + 11 10k 2 (15)
In this case, the atomic density is equal to that of the bulk system at the first order.

This simple calculation on the cuboctahedron shows that it is essential to specifically take into account the contribution of the surface atoms to correctly obtain the atomic density of a nanoparticle. This is particularly useful and crucial when using the spherical approximation for NPs to calculate γ.

Sec. VII. Calculation of surface energy from the spherical approximation of the surface: γ sa cubo (k) and γ csa cubo (k)

Spherical approximation

To determine the radius of a NP in the classical spherical approximation (sa), we use the relation N = ρV considering ρ ∞ the density of the infinite system and N (k) the total number of atoms of the NP, without discriminating the contribution of core and surface atoms. As a result,

R sa (k) = 3d 3 N (k) 4π √ 2 1/3
Knowing N (k), the surface area within the spherical approximation is noted S sa and can be expressed as :

S sa (k) = 4πd 2 3 4π √ 2 2/3 × 1 + k 3 (10k 2 + 15k + 11) 2/3 (16)
From R sa (k) and S sa (k): It can be noted that in a simple manner the following relationship can be obtained :

γ sa cubo (k) = 1 - 1 k + 31 60 k 2 × 1 25π
γ sa ∞ ≈ 1.10γ exact ∞

Corrected spherical approximation

To correct the classical spherical approximation, we now distinguish between the contribution of core and surface atoms using N ef f (k). A second-order Taylor expansion of N ef f (k) leads to :

N ef f (k) ≈ N (k) 1 - 3 2k + 9 4k 2
Using this relation, we get :

R csa (k) ≈ 3 4πρ ∞ N (k) 1 - 3 2k + 9 4k 2 1/3 S csa (k) ≈ 4π 3 4πρ ∞ N (k) 1 - 3 2k + 9 4k 2 2/3 (17)
From the definition of S sa (k) (Eq. 16), S csa (k) can be written :

S csa (k) ≈ S sa (k) 1 - 3 2k + 9 4k 2 2/3
, leading to the following relationship between S csa (k) and S sa (k) by limiting to the first-order Taylor expansion :

S csa (k) ≈ S sa (k) 1 - 1 k . ( 18
)
As seen in this equation, the corrected spherical approximation thus leads to a decrease in surface area relative to that of the spherical approximation.

In the following, we note γ csa cubo (k) the surface energy obtained from the corrected spherical approximation. Considering previous equations, we simply get :

γ csa cubo (k) ≈ γ sa cubo (k) 1 + 1 k . ( 19
)
Moreover, from the initial definition of γ sa cubo (k) and by limiting Eq. 19 to the first-order Taylor expansion of γ csa cubo (k), we obtain : (1/3)

γ csa cubo (k) = 1 d 2 (25π)
The corrected spherical approximation is in very good agreement with the exact calculation with a constant form factor coming from the relation: S csa (k) = (1/1.10)S(k). Note that the value of 1.10 depends on the metal element.

Calculations of the radius for solid and liquid nanoparticles

Depending on its degree of accuracy, the spherical approximation gives rise to two calculations of radii in case of solid NPs, namely R sa and R csa . As seen in Table II, the difference is most significant for small NPs.

FIG. 1 .

 1 FIG. 1. Calculated surface energies for cuboctahedron Cu NPs as a function of size based on an (a) exact surface S(k) and (b) a spherical (sa) approximation as well as corrected spherical approximation (csa). Both figures present analytical and MC results.

FIG. 2 .

 2 FIG.2. Spherical approximation to determine the effective surface area from TEM images of Cu NPs in (a) solid (facetted NPs at 573 K) and (b) liquid states (non-facetted NPs with a spherical shape at 1073 K). On the right : comparison of the sphere of radius R obtained from the atomic density (ρ∞) with configurations from MC simulations for different sizes and states of NPs containing 55 atoms, 561 atoms and 2869 atoms. For the liquid cases, it is obvious that a snapshot is not so representative of the situation since the particle is strongly deformed during the simulation.

8 FIG. 4 .

 84 FIG. 4. (a) Calculated surface energies for liquid Cu NPs as a function of size within a spherical approximation and corrected spherical approximation. (b) Analysis of the local energies on surface of liquid NPs containing 561 and 5083 atoms. Energies are in eV.

  The support from the French research funding agency (ANR) under Grant No. 18-CE09-0014-01 (GIANT) is gratefully acknowledged. The authors are grateful to Région Ile de France for convention SESAME E1845 for the support of the JEOL electron microscope installed at Universit Paris. J.N. acknowledges funding from the French National Research Agency through the TOTEM project, Grant Number ANR-17-CE07-0031. H.A and B.L thank F. Ducastelle for fruitful discussions. SUPPLEMENTARY MATERIAL OF : IS THERE REALLY A SIZE EFFECT ON THE SURFACE ENERGY OF NANOPARTICLES ?

  FIG. S1. Energy profiles along the radius of NPs containing 147, 923 and 5083 atoms (from top to bottom). Left : solid NPs (T =5 K) and right : liquid NPs (T =1500 K). The grey and blue areas represent the core and surface atoms, respectively.

5 FIG

 5 FIG. S2. Slice views showing the presence of core and surface populations for NPs containing 923 atoms in (a) solid and (b) liquid states. In case of solid NP, the contribution of subsurface atoms can be identified. Energies are in eV.

20 FIG

 20 FIG. S3. (a) Analysis of the local energies in a histogram form for Cu solid NPs containing 147, 923 and 5083 atoms at 5K. For the sake of clarity, the values for the number of atoms in case of the NP147 have been increased by a factor of 10. (b) Analysis of the local energies on surface sites of solid Cu923 NP where different populations can be identified according to the following hierarchy : E f < Ee < Ev. Note that the distinction between the different facets ({111} and {100}) is not visible at this scale. Energies are in eV/at.

2 / 3 × 2

 232 (3γ 100 + 2γ 111 ) + 6 k (2γ e -γ 100 -γ 111 ) + 6γ v -12γ e + 3γ 100 -4γ 111 k By limiting to the first-order Taylor expansion of γ sa cubo (k), we obtain : γ sa cubo (k) ≈ γ sa ∞ + 6 [2γ e -(3/2)γ 100 -(4/3)γ 111 ] kd 2 (25π) 1/3 γ sa ∞ = 3γ 100 + 2γ 111 d 2 (25π) 1/3 ,

+ 6 (

 6 3γ 100 + 2γ 111 + 6 k (2γ e -γ 100 -γ 111 ) ≈ 1.10 γ exact ∞ 2γ e -γ 100 -γ 111 ) kd 2 (3 + √ 3) ≈ 1.10γ exact cubo (k)

N

  55 147 309 561 923 2869 5083 6525 10179 17885 24739 R sa 5.3 7.4 9.5 11.6 13.7 20.1 24.3 26.4 30.7 37.0 41.3 R csa 3.8 6.1 8.3 10.4 12.6 19.0 23.2 25.3 29.6 35.9 40.2

TABLE II .

 II For each NP containing N atoms, R is obtained within the spherical approximation and corrected spherical approximation in solid state. Values are given in Å.