11institutetext: University of Catania
Department of Mathematics and Computer Science
Viale Andrea Doria, 6 - 95125 - Catania, ITALY
11email: {giampaolo.bella, domenico.cantone,
marianna.nicolosiasmundo<EMAIL_ADDRESS>22institutetext: The
Sicilian Wheat Bank S.p.A, 22email<EMAIL_ADDRESS>
# Blockchains through ontologies: the case study of the Ethereum ERC721
standard in OASIS (Extended Version)

Giampaolo Bella  Domenico Cantone 11 Cristiano Longo 11
Marianna Nicolosi Asmundo 22 Daniele Francesco Santamaria 1111

###### Abstract

Blockchains are gaining momentum due to the interest of industries and people
in _decentralized applications_ (Dapps), particularly in those for trading
assets through digital certificates secured on blockchain, called tokens. As a
consequence, providing a clear unambiguous description of any activities
carried out on blockchains has become crucial, and we feel the urgency to
achieve that description at least for trading. This paper reports on how to
leverage the _Ontology for Agents, Systems, and Integration of Services_
(“OASIS”) as a general means for the semantic representation of smart
contracts stored on blockchain as software agents. Special attention is paid
to non-fungible tokens (NFTs), whose management through the ERC721 standard is
presented as a case study.

##  1 Introduction

The last decade reports vast interest on blockchain technology and related
applications from various realms, including economic, social, business, and
academic ones. Beyond the financial speculation concerning cryptocurrencies,
the interest in blockchain technologies is mainly motivated by the fact that
they realize decentralized and publicly shared ledgers, where third-party
intermediaries demanding the client’s total and unquestioned trust are no
longer required. Blockchain technologies [6] were precisely introduced to
allow users to interact and run programs in a distributed way without the
requirement of trusted entities, yet guaranteeing ownership, transparency,
traceability, availability, continuity, and immutability of digital shared
assets. Applications of blockchain technologies range from the _Internet of
Things_ (IoT) and robotics [18], to commerce, healthcare, insurance, energy,
laws, and communications.

One of the most popular applications of Turing-complete blockchains such as
Ethereum [15] is the _smart contract_. Smart contracts are self-executing and
immutable programs, autonomously running and verified on a distributed and
decentralized public network, which implement decentralized applications on
blockchain systems called _Dapps_. In 2020, Dapps have particularly grown as
an exchange tool for non-fungible tokens (NFTs), namely digital certificates
stored on the blockchain representing predetermined rights on certain unique
assets. NFTs are mainly used as a proof of ownership of physical or digital
products. Such tokens are routinely exchanged by users to witness that assets
whose uniqueness is hard to demonstrate (for example, digital images) are
owned in an exclusive way. At the end of 2020, the market capitalization of
NFTs reached the amount of 338 millions of U.S.
dollars.111https://www.statista.com/statistics/1221742/nft-market-
capitalization-worldwide/ (last access: 08/07/2021). However, one of the main
limitations of blockchains is the hard-coded nature of the transactions stored
on them. As a consequence, it is hard to probe a blockchain, for example, to
find smart contracts trading specific NFTs that satisfy certain requirements
in terms of quality or quantity.

Therefore, a formal semantic knowledge representation capturing the blockchain
smart contracts as well as the activities carried out on it facilitates the
understanding of blockchain concepts, the interlinking with other out-of-chain
information, and also formal reasoning. Moreover, a semantic conception of
blockchains enables the automatic discovery of smart contracts, the
interconnection of services running on different blockchains (i.e., cross-
chain integration) and the integration between on-chain and off-chain
services. These features turn out to be more interesting when smart contracts
are implemented as mechanisms for generating and exchanging tokens. A
desirable feature of token exchange systems is a precise and intelligent query
mechanism capable of determining what, when, and how certain assets have been
generated, exchanged or destroyed. For example, intelligent systems may be
aware of the activation of smart contracts for generating tokens with specific
characteristics, e.g., of the type of exchanged asset, of the exchange of
particular tokens at certain conditions, or of their destruction. More in
general, intelligent systems may be aware of the activation of smart contracts
and of all the related activities over the blockchain.

Beyond a semantic representation of transactions and information stored in
blocks, a real, semantically represented blockchain is effectively achievable
if smart contracts are interpreted as reactive agents operating on a common
environment, with a fully specified semantics of available operations,
committed actions, and stored data.

The representation of blockchain actors requires ontological capabilities for
fully representing agents and their interactions in a detailed way. This paper
adopts the _Ontology for Agents, Systems, and Integration of Services_
(“OASIS”) towards the full, semantic representation of the Ethereum blockchain
and the smart contracts running on it, with a special focus on the smart
contracts compliant with the ERC721
standard222https://ethereum.org/it/developers/docs/standards/tokens/erc-721/
for NFTs management.

The paper is organized as follows. Section 2 presents related work. Section 3
outlines OASIS, whereas Sections 4 and 5 depict the ontology implementing the
OASIS representation of, respectively, the Ethereum blockchain and the ERC721
standard. Finally, Section 6 draws some conclusions and delineates future
research directions.

##  2 Related works

Interest in symbiotically combining semantic web technologies and blockchains
is quite recent [7, 3]. One of the areas of investigation concentrates in
developing a characterization of blockchain concepts and technologies through
ontologies and of blocks and transactions meta-data. An ontological albeit
theoretical approach at blockchain representation exists [11]. Ruta _et al._
propose a blockchain framework for _semantic web of things_ (SWoT) contexts
settled as a _Service-Oriented Architecture_ (SOA), where nodes can exploit
smart contracts for registering, discovering, and selecting annotated services
and resources [14].

Blockchain technologies are also exploited as a secure and public storage
system for small data, including linked data, and to realize a more resilient
architecture for the Semantic Web [7].

Other works aim at representing ontologies within a blockchain context. In
[10], ontologies are used as common data format for blockchain-based
applications such as the proposed provenance traceability ontology, but are
limited to implementation aspects of the blockchain.

Fill discusses blockchains applied for tracking the provenance of knowledge,
for establishing delegation schemes, and for ensuring the existence of
patterns in formal conceptualizations using zero-knowledge proofs [8].

A semantic interpretation of smart contracts as services bases on the _Ethon_
ontology [12] exist [1]. The main limitation of that approach is the poor
semantic description of smart contracts, thus hindering the discovery of
unknown smart contracts and of the related operations fulfilled during their
life-span.

The _Blockchain Ontology with Dynamic Extensibility_ (BLONDiE) project [16]
provides a comprehensive vocabulary that covers the structure of different
components (wallets, transactions blocks, accounts, etc.) of blockchain
platforms (Bitcoin and Ethereum) and that can be easily extended to other
alternative systems.

Finally, in [5] the authors illustrated how the ontology OASIS is applied for
ontologically describing digital contracts (called _ontological smart
contracts_), intended as agreement among agents, and how they can be secured
on Ethereum.

In this contribution, the definition of digital contracts in [5] is
generalized to include blockchain smart contracts, intended as programs
running on the blockchain and interpreted as digital agents in the OASIS
fashion.

##  3 Preliminaries

The _Ontology for Agents, Systems, and Integration of Services_ (“OASIS”) [4]
is an OWL 2 ontology for representing agents and their activities. On one
hand, the ontology models (web) agents and, in particular, the way they
interact and operate in a collaborative environment, regardless of the
framework and language adopted for their implementation. Agents are mainly
represented by means of the mentalistic notion of agent behavior inspired by
[2], encompassing goals and tasks that are achievable (either publicly
available or exposed on request) by the agent, together with actions, sensors,
and actuators used to perform operations. On the other hand, OASIS is used to
define actions that may be requested to other agents and their related
information such as operation inputs and outputs. Such requests are submitted
by exchanging suitable fragments of OASIS, whereas agents whose capabilities
are compatible with the requested actions are discovered by means of SPARQL
queries performed over their behaviors. OASIS was applied to build a TRL3
prototype of a home assistant that activates and manages applications,
devices, and users interacting with each other within the environment [4].
OASIS was also used to define agent agreements and store these in the IPFS
file system [13] in order to reduce the transaction data stored directly on
blockchain [5].

Figure 1: Agent representation in OASIS

OASIS models agents by publicly representing their behaviors. By exposing
behaviors, agents report to the communication peers the set of operations that
they are able to perform and, eventually, the type of data required to execute
these and the expected output. The representation of agents and their
interactions in OASIS is carried out along three main steps. The first step
consists in defining the template for agent behaviour: templates are high-
level descriptions of behaviors of abstract agents that can be implemented to
define more specific and concrete behaviors of real agents. For example, a
template may be designed for agents to sell and ship products to buyers, and
it may be implemented by any phone seller that ships its products using the
Fedex courier: templates are useful to guide developers to define the most
suitable representation of their agents. The second step consists in
implementing a template, which requires a specification of the full
operational details about the sought behavior.

As depicted in Fig. 1, agent behaviors are represented by the goals to
achieve, which in turn are related with their constitutional elements, namely
tasks. Tasks represent atomic operations that agents execute, and are
described by the actions to be performed. Actions are drawn from a shared and
common vocabulary, and can be simple or composed, eventually associated with
requested input parameters and expected outputs. Finally, agent behaviors in
OASIS may be associated with conditionals [5], adding constraints on the
execution of actions and ensuring that certain conditions are verified before
or after a task is executed. OASIS conditionals are OWL sentences that have
the fashion of _Semantic Web Rule Language_ (SWRL) rules [17], describing
operations that must be triggered when certain conditions hold.

##  4 Representing Ethereum through OASIS

In this section, we describe how the Ethereum blockchain is modelled in
OASIS.333The ontology is reachable at
https://www.dmi.unict.it/santamaria/projects/oasis/sources/ether-oasis.owl
OASIS provides a different representation of blockchains with respect to Ethon
[12] and BLONDiE [16], since the description of blockchain has to be aligned
with the definitions of agent and agent behavior.

Ethereum is represented in OASIS by following the schema illustrated in Fig.
2. Ethereum blocks embedding transactions are represented by instances of the
class EthereumBlock (subclass of BlockchainBlock) and connected to the
transactions contained in them by means of the object-property embeds. Each
Ethereum transaction is identified by an instance of the class
EthereumTransaction (subclass of BlockchainTransaction), encapsulating all the
transaction information.

Block miners are identified by instances of the class EthereumNode (subclass
of BlockchainNode) and linked to the mined block through the object-property
mines: instances of BlockchainNode are also instances of the class Agent,
representing agents and provided with a behavior as in the OASIS fashion.
Moreover, instances of BlockchainNode (resp., EthereumNode) are connected to
instances of the class System (resp., EthereumSystem) by means of the object-
property constitutes. Such a characterization of nodes, blocks, and
transactions is the main difference with analogous approaches such as Ethon
and BLONDiE, since it allows one to describe activities carried out by both
in-chain and out-of-chain agents, thus providing a higher-level model of the
two ecosystems and a means to unify them. Specifically, Ethereum activities
are classified into two main categories, namely, deployments of smart
contracts, represented by instances of the class EthereumSmartContratCreation
(subclass of BlockchainSmartContractCreation), and interactions with smart
contracts, represented by instances of the class
EthereumSmartContractInteraction (subclass of the
BlockchainSmartContractInteraction).

In OASIS, smart contracts deployed into the Ethereum blockchain correspond to
agents with well-defined behaviors: interactions with smart contracts are
represented by OASIS _plan executions_ and linked to the behavior that induced
the action. Specifically, a smart contract creation is represented by an
instance of the class BlockchainSmartContractCreation, which is related with
the description of the agent describing its behavior by the object-property
describes, the latter represented by an instance of the class
BlockchainSmartContractAgent (subclass of the class Agent). Instances of
BlockchainSmartContractCreation are also associated by means of the object-
property associatedWith with the related Ethereum accounts, represented by
instances of the class EthereumSmartContractAccounts (sublcass of the class
BlockchainSmartContractAccount, which, in turn, is a subclass of
BlockchainAccount). Users are instead associated with _Ethereum externally
owned accounts_ (EOA) represented by instances of the class EOA-
EthereumAccount (sublcass of EOA-BlockchainAccount, which is a subclass of
BlockchainAccount).

OASIS identifies four main general categories of smart contract agents: a)
smart contracts providing non-fungible token exchange mechanisms compatible
with the Ethereum standard ERC721, which are represented by instances of the
class EthereumERC721SmartContractAgent (subclass of the class
NonFungibleBlockchainSmartContractAgent); b) smart contracts providing
fungible token exchange mechanisms compatible with the Ethereum standard
ERC20, which are represented by instances of the class
EthereumERC20SmartContractAgent (subclass of the class
FungibleBlockchainSmartContractAgent); c) agents responsible for exchanging
Ether cryptocurrency, which are represented by instances of the class
EtherExchangeSmartContractAgent (subclass of the class
CryptocurrencyExchangeBlockchainSmartContractAgent); d) general purpose and
user-defined smart contract agents that do not enjoy the characteristics of
the aforementioned smart contracts, which are introduced by instances of the
class GeneralPurposeBlockchainSmartContractAgent.

In OASIS, agents may perform actions autonomously or as response to requests
of executing some operations submitted by a peer. Concerning the blockchain
ecosystem, we mainly limit ourselves to take into account only requests that
modify the state of the chain (both internal and external), and hence induce
transactions, even through _view functions_ , namely functions that do not
modify the state of the chain may be represented as well.

The transactions (represented by instances of the class EthereumTransaction)
induced by interaction requests submitted to smart contracts are related with
instances of the class EthereumContractInteraction (subclass of the class
SmartContractInteraction) by means of the object-property describes. Instances
of EthereumContractInteraction introduce plan descriptions as in the OASIS
fashion by means of the object-property describes. Plan descriptions are ways
of characterizing requests of actions and the related actions performed by
agents. The most notable subclass of EthereumContractInteraction is the class
EtherExchangeSmartContractInteraction, representing the transferring of Ether
cryptocurrency from a wallet to another. The class
EtherExchangeSmartContractInteraction is also a subclass of the class
CryptocurrencyExchangeBlockchainSmartContractInteraction, which in turn is a
subclass of the class BlockchainSmartContractInteraction.

An example of representing Ethereum transactions in OASIS is illustrated in
Appendix A.

Figure 2: Representing the Ethereum blockchain in OASIS

##  5 The ERC721 protocol in OASIS

In this section we show how OASIS represents the main ERC721 standard
functions for managing non-fungible tokens on the Ethereum blockchain. For
space limitations, we illustrate how the ERC721 standard for minting non-
fungible tokens is modelled in OASIS, whereas the ERC721 functions for
transferring tokens, burning tokens, granting ownership of single tokens, of
all the tokens stored in the wallet, and to verify the ownership of tokens, as
represented in OASIS, are described in Appendices B, C, D, E, and F,
respectively. Finally, ERC721 tokens are described in Appendix G.

As seen in the previous section, the smart contracts defined for the ERC721
token management are introduced by means of instances of the class
EthereumERC721SmartContractAgent (subclass of the class Agent). In OASIS,
agents having similar behaviors inherit the representation of their behavior
from a common template providing general descriptions that may be customized
by single agents. For this purpose, OASIS provides a template for the ERC721
standard introduced by the individual
ethereum_ERC721_smart_contract_behavior_template, which describes the
behaviors of agents minting, burning, and transferring Ethereum NFTs according
to the guidelines of the standard. Other functions admitted by the standard
ERC721, namely the _approve_ function (delegating wallets for managing single
tokens), the _setApprovalForAll_ function (delegating wallets for managing all
the tokens owned), and _ownerOf_ (for retrieving the owner of a given token),
are also represented in OASIS.

Figure 3: OASIS behavior template for the ERC721 minting function

Fig. 3 illustrates the behavior template provided by OASIS describing the
ERC721 function for generating new tokens. The behavior template consists of a
single goal, which in turn consists of a single task. Tasks comprise four
elements. The first element is the task operator, providing the description of
the action to be performed, namely minting. The latter is introduced by means
of the individual mint (instance of the class Action), through the the object-
property refersExactlyTo. We recall that in OASIS the object-properties
refersExacltyTo and refersAsNewTo are introduced to describe the way how
constituting elements of agent behaviors must be matched when a verification
of compatible behaviors occurs. The object-property refersExactlyTo introduces
well-known entities whose IRIs must correspond to the IRIs of the matched
entities or for which the OWL object-property sameAs has been expressed. On
the contrary, the object-property refersAsNewTo introduces entities (instances
of the class ReferenceTemplate) that are used as general descriptions
encapsulating the features that the matching entities must satisfy.

The second element of the ERC721 token minting task is the operator argument
introducing the individual blockchain_digital_token by means of the object-
property refersExactlyTo. Operators and operator arguments identify
unambiguously that the referred operation consists in the generation of
(digital) tokens on the blockchain. The third and the fourth elements
represent the recipient and the outcome of the operation, respectively. The
recipient is introduced by means of a template of the task object, whereas the
outcome is introduced by means of a template of the output parameter of the
task. The object template and the output parameter are both connected through
the object-property refersAsNewTo to the entity mint_ERC721_token, which
describes the features that the recipient of the action must have, i.e., being
an instance of the class EthereumTokenERC721.

##  6 Conclusions

This paper leveraged the OASIS ontology towards the representation of the
Ethereum blockchain and the smart contracts deployed on it. Specific focus was
on those that comply with the ERC721 standard for NFTs management. OASIS is
exploited as a means of semantically representing Ethereum with the aim of
probing the blockchain for locating smart contracts and related NFTs by
specifying the desired features. In particular, the ontological representation
of OASIS allows one to find smart contracts and related NFTs by inspecting
their behavioural descriptions through purposely crafted SPARQL queries. It
was already clear that the OASIS approach to semantic representation had the
power of generality but our findings demonstrate it at an applied level.

Future work is dense. The very next step is to extend OASIS so as to model the
standard protocols ERC20 and ERC1155 for fungible and semi-fungible tokens,
respectively, and to represent different blockchains such as Stellar Lumens.
Moreover, we intend to take up the design of a search engine exploiting OASIS
to find desired smart contracts and tokens using a mechanism of auto-
generating parametric _ad-hoc_ SPARQL queries that could be borrowed from
sibling applications [4]. The present work supports the claim that the
potential of the semantic representation of blockchains has much to be
unveiled in the near future.

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## Appendix A - Example of Ethereum transaction in OASIS

Fig. 4 shows an Ethereum transaction storing the smart contract for emitting
NFTs of the Sicilian Wheat Bank (SWB)
S.p.A.444https://www.bancadelgrano.it/en/ The individual
block_node_10452395_tran_1 represents the Ethereum transaction and is related
with the individual SWB_SmartContractCreation describing the smart contract by
means of the object-property describes. The description of the agent
identifying the SWB smart contract is introduced by the individual
SWB_smart_contract_agent which is linked to SWB_smart_contract_creation by
means of the object-property describes. Finally, the node (SparkPool) that
mines the block (block_node_10452395) including the transaction is also
associated to the Ethereum main-net (ethereum_mainnet) by means of the object-
property constitutes.

Figure 4: Example of representing an Ethereum transaction in OASIS

## Appendix B - ERC721 transferring function in OASIS

The behaviour for the ERC721 function for transferring tokens is depicted in
Fig. 5. It provides three input parameters, one for the token to be
transferred and one for each externally owned account involved in the
transferring of the token, namely the source wallet and the destination
wallet. The source and destination wallets are introduced by exploiting the
object-property refersAsNewTo by means of two individuals instances of the
class EOA-EthereumAccount, namely, transfer-2_ERC721_EOA-account (the source)
and transfer-3_ERC721_EOA-account (the destination). To ensure that the token
is transferred from the wallet identified as source to the wallet identified
as destination, the conditional illustrated in Fig. 6 is provided.

Figure 5: OASIS behaviour template for the ERC721 transfer function

The conditional ensures the existence of a transfer activity for each token to
be transferred. The conditional has as conditional object a fresh transfer
activity and as operator the individual exist. In its turn, the transfer
activity indicates as transfer source the wallet used as first parameter in
the token transferring, as transfer destination the wallet used as second
parameter, and as transferred object the token passed as input parameter.

Figure 6: Conditional for the ERC721 transfer function

## Appendix C - ERC721 token burning function in OASIS

The behaviour for the burning function of the ERC721 standard is depicted in
Fig. 7. In this case, the individual
ethereum_ERC721_smart_contract_behavior_template (representing the ERC721
behaviour template) is also connected to the behaviour describing the burning
function, whose structure is analogous to the minting function but with a
different action and with an input parameter template instead of an output
parameter template. The action introduced in the burning function is the
individual burn, whereas the input parameter template is connected with an
individual representing the token to be burnt that is passed as input to the
burning function.

Figure 7: OASIS behaviour template for the ERC721 burning function

## Appendix D - ERC721 token approve function in OASIS

The standard ERC721 allows the owner of tokens to delegate wallets to manage
tokens on his behalf. Authorizations may be carried out either on a single
token or on any token stored in his wallet. The ERC721 function approve and
setApprovalForAll are introduced for the former and the latter case,
respectively.

In case that an externally owned account is authorized to manage a single
token, the behaviour in Fig. 8 is adopted. Specifically, the behaviour
introduces as input parameter the account to be authorized and the granted
token, as operator the instance delegate, and as operator argument the
instance ownership. The conditional in Fig. 9 ensures that only the operation
of burning and transferring may be pursued when the wallet is authorized to
operate on behalf of his owner. Such a condition is guaranteed by the
existence of a delegation activity (instance of DelegationActivity), having as
delegation property the instances burn and transfer. The subject and the
object of the delegation activity are the authorized wallet and the granted
token, respectively.

Figure 8: OASIS behaviour template for the ERC721 approve function Figure 9:
Conditional for the ERC721 approve function

## Appendix E - ERC721 setApprovalForAll function in OASIS

The Ethereum ERC721 standard allows wallet owners to authorize an account to
manage all the tokens owned. The corresponding behaviour is illustrated in
Fig. 10. The behaviour is close to the behaviour for granting a single token,
with the only difference that there is no input parameter concerning the
granted token. In such a case, the conditional in Fig. 11 ensures that
authorization is extended to each token owned. Indeed, the delegation object
expresses the object-property hasSpecificity with value the individual any.

Figure 10: OASIS behaviour template for the ERC721 _setApprovalForAll_
function

Figure 11: Conditional for the ERC721 approve-all function

## Appendix F - ERC721 token ownership retrieval function in OASIS

The Ethereum ERC721 standard allows one to retrieve the wallet owner of a
token. The corresponding behaviour is illustrated in Fig. 12.

The behaviour is related with a task description providing as recipient and as
input parameter the selected token, whose owner has to be retrieved. The
conditional in Fig. 13 ensures that the wallet retrieved is the effective
owner of the token considered.

Figure 12: OASIS behaviour template for the ERC721 function for retrieving the
token’s owner

Figure 13: OASIS conditional for the ERC721 function for retrieving the
token’s owner

## Appendix G - ERC721 token representation in OASIS

Tokens are depicted in Fig. 14. There are four main types of token:

  * •

non-fungible tokens, represented by instances of the class
EthereumSemiFungibleToken, the latter containing the class EthereumTokenERC721
that represents non-fungible tokens compliant with the ERC721 standard
protocol;

  * •

fungible tokens, represented by instances of the class EthereumFungibleToken,
the latter containing the class EthereumTokenERC20 that represents fungible
tokens compliant with the ERC20 standard protocol;

  * •

semi-fungible tokens, represented by instance of the class
EthereumSemiFungibleToken, the latter containing the class
EthereumTokenERC1155 that represents semi-fungible tokens compliant with the
ERC1155 standard protocol;

  * •

custom user-defined tokens not compliant with the ERC standard protocols,
represented by instances of the class EthereumCustomToken.

Figure 14: Ethereum token representation in OASIS

The four mentioned classes are defined as subclass of the class EthereumToken.
Additionally, tokens that have been definitively destroyed are also instances
of the class BurnedEthereumToken.

Tokens carry two types of features [9], a) perdurant features such as the
token ID, that never change and are embedded with the entity representing the
token and b) endurant features, that change during the life-span of the token
and are associated with an instance of the class EthereumTokenEndurantFeatures
(subclass of EndurantFeature), by means of the object-property
hasEthereumTokenEndurantFeature. The most notable subclass of EndurantFeature
is the class EthereumWalletOwnerEndurantFeature, which describes the wallet of
the token’s owner (by means of the data-properties isInTheWalletOf). When the
endurant features of a token are modified by the smart contract managing it,
they became deprecated and replaced by a new set of features by means of a
modification activity. Those new features are introduced by means of a fresh
instance of the class EndurantFeature. Modification of tokens is allowed only
if it involves endurant features and hence perdurant features cannot change.
Endurant features may be replaced with other endurant features by introducing
an instance of the class EthereumTokenFeatureModificationActivity which is
connected with:

  * •

the changed endurant feature, which is also instance of the class
DeprecatedEthereumTokenEndurantFeature, by means of the object-property
hasEthereumTokenFeatureModificationSource;

  * •

the new endurant feature, by means of the object-property
hasEthereumTokenFeatureModificationResult.

Moreover, the modified endurant feature is connected with the endurant feature
that replaces it by means of the object-property isEthereumTokenFeature
ModifiedIn, whereas the token embedding the features is connected with the new
endurant feature by means of the object-property
hasEthereumTokenEndurantFeature as described above.


2021 [supp-]supplementary

[1]Ralf Drautz

[1]ICAMS, Ruhr-Universität Bochum, Universitätsstraße 150, Bochum, 44801,
Germany

2]Max Planck Institut für Eisenforschung, Max Planck Straße 1, Düsseldorf,
40237, Germany

# Atomic cluster expansion for Pt-Rh catalysts: From ab initio to the
simulation of nanoclusters in few steps

Yanyan Liang<EMAIL_ADDRESS>Matous Mrovec<EMAIL_ADDRESS>Yury
Lysogorskiy<EMAIL_ADDRESS>Miquel Vega-Paredes<EMAIL_ADDRESS>Christina Scheu<EMAIL_ADDRESS><EMAIL_ADDRESS>*  [

###### Abstract

Insight into structural and thermodynamic properties of nanoparticles is
crucial for designing optimal catalysts with enhanced activity and stability.
We present a semi-automated workflow for parameterizing the atomic cluster
expansion (ACE) from ab initio data. The main steps of the workflow are the
generation of training data from accurate electronic structure calculations,
an efficient fitting procedure supported by active learning and uncertainty
indication, and a thorough validation. We apply the workflow to the simulation
of binary Pt-Rh nanoparticles that are important for catalytic applications.
We demonstrate that the Pt-Rh ACE is able to reproduce accurately a broad
range of fundamental properties of the elemental metals as well as their
compounds while retaining an outstanding computational efficiency. This
enables a direct comparison of simulations to high resolution experiments.

###### keywords:

atomic cluster expansion, machine learning, atomistic simulations, platinum-
rhodium catalyst, nanoclusters

##  1 Introduction

In the field of catalysis, noble metals play a key role. Among them, platinum
(Pt) and rhodium (Rh) are used extensively as heterogeneous catalysts due to
their superior activity and stability li2011characterization . For example,
Pt-Rh based materials are widely used as effective vehicle exhaust catalysts
to reduce emissions of harmful pollutants CO and NO${}_{\text{x}}$ into less
harmful CO2 and N2 eley1998advances ; ravindra2004platinum . Furthermore, they
have also been employed in fuel cells jung2014pt ; ramli2018platinum  to
enhance the oxygen reduction and hydrogen oxidation reactions.

These catalytic materials are typically applied in the form of nanoparticles
or nanoclusters to maximize the active surface area where the chemical
reactions take place sun2021advancements . An important aspect of the
nanoparticles is their microstructure that can be tailored to optimize
functional properties as well as stability. In multicomponent systems, the
goal is often not to achieve a random distribution of chemical elements as in
a solid solution, but to design nanoparticles with specific morphologies
ghosh2012core ; gawande2015core . For instance, despite the fact that Pt and
Rh are miscible elements with face-centered cubic (fcc) structures their
nanoparticles have usually been prepared in the form of concentric composites,
typically with a spherical Rh core surrounded by a Pt-rich shell layer. Such
core-shell morphologies can be prepared using a wet chemical approach, where
the core is synthesized first and the surface is coated afterwards
ghosh2012core ; gawande2015core . They can exhibit an enhanced catalytic
activity and structural stability compared to traditional alloyed catalysts
ghosh2012core  as a result of their non-equilibrium crystal structures
garzon2018controlling  or shapes. However, the non-equilibrium nanoparticles
may not be stable under operating conditions and undergo transformations that
lead to deterioration of the catalytic activity.

In Fig. 1, an example of a Pt-Rh core-shell nanoparticle with a distorted
octahedral shape is shown vega2023 . The high angle annular dark field (HAADF)
micrograph and energy dispersive X-ray spectroscopy (EDS) map acquired in a
scanning transmission electron microscope (STEM) reveal a varying Pt shell
thickness of 3-5 monolayers. STEM is widely used for characterizing catalyst
nanoparticles, since it can provide information on the atomic arrangement and
composition su2017advanced . However, investigations of dynamic processes at
elevated temperatures requires to carry out challenging and time consuming in-
situ experiments that are often limited by beam-induced artefacts
manjon2022exploring . Therefore, it is desirable to complement the
experimental characterization with atomistic modeling to obtain a deeper
understanding of the thermodynamic and kinetic phenomena governing the
structure of nanoparticles.

Figure 1: STEM-HAADF micrograph (a) and corresponding EDS composition map (b)
of a Rh-Pt core shell nanoparticle. Pt is in blue and Rh in green. In (a) the
crystallographic facets are indicated.

Atomistic simulations can provide valuable information about energetics of
particular structural features, such as formation energies of point defects or
various surface facets, but also directly follow the dynamical evolution of
the entire system using molecular dynamics (MD) or explore the thermodynamic
stability using Monte Carlo (MC) methods. Even though it is nowadays possible
to study systems of millions of atoms, approaching realistic dimensions of
nanoparticles, the essential prerequisite for reliable quantitative
predictions is an accurate and efficient description of interatomic
interactions. However, there exist, to our best knowledge, no interatomic
potentials for the Pt-Rh binary system that could be applied in large-scale MD
or MC studies of thermodynamic and kinetic phenomena.

In this work, we developed an atomic cluster expansion (ACE) parametrization
for Pt-Rh using a semi-automatic workflow consisting of the generation of a
training dataset based on accurate density functional theory (DFT)
hohenberg1964inhomogeneous ; kohn1965self  calculations, efficient fitting and
validation procedures lysogorskiy2021performant , and uncertainty indication
and active learning (AL) algorithms lysogorskiy2022active  that can be
employed to improve the model if necessary. ACE has successfully been applied
to model metallic, covalent and ionic materials and was shown to offer
superior accuracy and computational efficiency lysogorskiy2021performant ;
lysogorskiy2022active ; qamar2022atomic .

The ACE methodology combines the advantages of machine-learned (ML) methods
and physically based models of interatomic interactions. We summarize only the
essentials of ACE and refer to original publications for more details
drautz2019atomic ; drautz2020atomic ; dusson2022atomic ;
lysogorskiy2021performant ; bochkarevefficientpara ; bochkarev2022multilayer .

One of the key features of ACE is a complete and hierarchical set of basis
functions ${B}_{i{\bm{v}}}$ that span the space of local atomic environments.
This enables to expand an atomic property $\varphi_{i}^{(p)}$ such as the
energy of atom $i$ as

$\varphi_{i}^{(p)}=\sum_{{\bm{v}}}^{n_{{\bm{v}}}}c_{{\bm{v}}}^{(p)}{B}_{i{\bm{v}}}\,,$
(1)

with expansion coefficients $c_{{\bm{v}}}^{(p)}$ where ${{\bm{v}}}$ is
composed of several indices. The basis functions fulfill fundamental
translation, rotation, inversion and permutation (TRIP) invariances for the
representation of scalar variables, or equivariances for the expansion of
vectorial or tensorial quantities.

In the simplest case, the energy is evaluated linearly as

$E_{i}=\varphi_{i}^{(1)}\,,$ (2)

but most ACE parametrizations to date, including the presented Pt-Rh model,
use two atomic properties with a Finnis-Sinclair square-root embedding,

$E_{i}=\varphi_{i}^{(1)}+\sqrt{\varphi_{i}^{(2)}}\,.$ (3)

We demonstrate that Pt-Rh ACE provides not only an accurate description of
fundamental properties for both elemental metals as well as their compounds,
but that it is well suited for large-scale atomistic simulations of
nanoclusters.

##  2 Results and discussion

###  2.1 Training of ACE

Figure 2: Energy per atom of structures in the Pt-Rh training set as a
function of the nearest neighbour distance (NNB).

Figure 3: Comparison of energies and forces predicted by ACE with respect to
the reference training DFT data. The “Low” subset includes data within a
distance of 1 eV/atom above the convex hull.

The parameterization of ACE models requires a consistent set of reference DFT
data. For the Pt-Rh system, we generated about 30 000 atomic configurations
and evaluated their energies and forces using the Vienna ab-initio simulation
package (VASP) kressabinitio1993 ; kresse1996efficiency ; kresse1996efficient
and the PBE functional for approximating exchange and correlationPBEXC . The
considered structures span a wide portion of the configuration space for both
elemental metals and their binary compounds. The configurations include
perfect bulk structures, common defects, e.g., vacancies, surfaces and grain
boundaries, and small random clusters. For all these configurations, we varied
their volumes and randomly displaced atoms away from their equilibrium
positions to sample vibrational degrees of freedom. A summary of energies per
atom for all structures as a function of the nearest neighbour distance in
each structure is shown in Fig. 2. The training data corresponds to 29800
structures with 437157 atoms, spanning nearest neighbour distances from 1.8 up
to 6.3 Å and sampling the energy space from about $-6.3$ eV/atom to $+2$
eV/atom.

The ACE parameterization was carried out using the pacemaker package
bochkarevefficientpara . In the fitting process, a hierarchical basis
extension scheme with a sequential addition of ACE basis functions was
adopted. For the radial basis functions, spherical Bessel functions were used.
Structures within an energy window of 1 eV/atom above the convex hull were
assigned significantly larger weights in the loss function optimization, while
structures with higher energy were given smaller weights.

After initial training, we employed AL to ensure a reliable description of Pt-
Rh surfaces as these are crucial for simulations of core-shell nanoclusters
(see below). This was achieved by computing the extrapolation grade $\gamma$
based on the D-optimality criterion lysogorskiy2022active  for a number of
(100), (110) and (111) fcc surface slabs containing up to 56 atoms with two
compositions (Pt0.3Rh0.7 and Pt0.7Rh0.3). The slab configurations were
obtained using a hybrid MD-MC method in the $NVT$ ensemble at three different
temperatures (300, 500 and 800 K). Structures with large values of the
extrapolation grade ($\gamma>5$) were selected using the MaxVol algorithm.
These structures were then computed with DFT, added to the training set, and
the ACE potential was retrained. See Section 4.4 for more details.

In Fig. 3, the energies and forces predicted by ACE are compared with the
reference DFT data for the training set. The ACE model reproduces the DFT
energies and forces with good accuracy. Obtained root mean square errors
(RMSE) for the energy and force components are 13 meV/atom and 57 meV/Å for
the training set and 36 meV/atom and 140 meV/Å for the test set, respectively.
The relativley large errors in the energies are due to the very low weights
that were assigned to high energy structures with atoms at close distance as
these structures have no relevance for the simulation of the nanoparticles. In
fact, for the lower energy structures within the 1 eV window above the convex
hull that are most significant in the simulations, the RMSE are only 6
meV/atom and 30 meV/Å for the training set and 6 meV/atom and 26 meV/Å for the
test set, respectively.

###  2.2 Validation of the Pt-Rh ACE

For an initial validation of the parameterized potential, various fundamental
properties of the elemental metals were examined and compared to DFT and
experimental data in Table 1. For both Pt and Rh, the equilibrium lattice
parameters predicted by ACE are in excellent agreement with DFT, while being
slightly larger than the experimental values. The elastic constants and bulk
moduli also agree well with those of DFT, with somewhat larger discrepancies
observed for $C_{11}$ and $C_{44}$ for Pt. The differences however remain
comparable to those between DFT and experiment. The larger lattice constants
and mostly smaller elastic moduli predicted by DFT and ACE in comparison with
experiment are likely caused by the PBE-GGA exchange-correlation functional
that leads to underbinding for nonmagnetic fcc metals graboskiabinitio .

The formation and migration energies of the mono-vacancy are in close
agreement with the reference DFT values and comparable with the available
experimental measurements for Rh. For Pt, the large discrepancy between the
theoretical and experimental values is due to deficiencies in the description
of the exchange-correlation contributions at metallic surfaces thomasvacancy .
A better agreement can be obtained after correcting for this intrinsic surface
error, but the correction term depends on the electronic structure of the
metal thomasvacancy  and cannot be employed in classical atomistic models.

We also examined energies of surfaces with low-index orientations. As
illustrated in Table 1, ACE captures correctly the ordering of Pt surface
energies in comparison to DFT, as
$\gamma_{(100)}>\gamma_{(110)}>\gamma_{(111)}$. However, DFT strongly
underestimate the absolute values of surface energies in comparison to
experiment. The underlying reason for this discrepancy is identical as in the
case of vacancies. For Rh, the stability of the lowest energy $(111)$ surface
is reproduced by ACE, but the energies of the $(100)$ and $(110)$ are almost
degenerate according to DFT while ACE predicts the latter to have a slightly
higher energy. Besides these common surface orientations, we also evaluated
other surface configurations provided in the Crystalium
databasetran2016surface ; tran2019anisotropic ; zheng2020grain  and compared
them to the available DFT data in Fig. 4. A close agreement is seen between
ACE and DFT with a slight overestimation of Rh surface energies by ACE. When
comparing both metals, it is evident that Pt has smaller surface energies than
Rh, which is relevant for the structure of nanoclusters (see below).

Table 1: Comparison of various properties of elemental Pt and Rh obtained from ACE, DFT and experiment. For the vacancy, $E_{f}$ and $E_{m}$ represent the formation and migration energies, respectively. For surface energies, the experimental values are for average orientations. | Platinum | Rhodium
---|---|---
| ACE | DFT | Exp | ACE | DFT | Exp
Lattice constant |  |  |  |  |  |
$a_{0}$ (Å) | 3.97 | 3.97 | 3.92waseda1975high  | 3.83 | 3.83 | 3.80nuding1997influence
Elastic moduli |  |  |  |  |  |
$C_{11}$ (GPa) | 267 | 308 | 347simmons1965single  | 422 | 409 | 422simmons1965single
$C_{12}$ (GPa) | 227 | 222 | 251simmons1965single  | 169 | 182 | 192simmons1965single
$C_{44}$ (GPa) | 50 | 70 | 77simmons1965single  | 192 | 186 | 194simmons1965single
$B$ (GPa) | 241 | 251 | 228$-$275darling1966anon  | 253 | 258 | 276buch1999pure
Vacancy |  |  |  |  |  |
$E_{f}$ (eV) | 0.69 | 0.68thomasvacancy  | 1.15$-$1.60cahn1996physical  | 1.84 | 1.82 | 1.71de1988cohesion
$E_{m}$ (eV) | 1.06 | 1.24angsten2014elemental  | 1.43balluffi1978vacancy  | 1.87 | 1.79angsten2014elemental  | –
Surface energy |  |  |  |  |  |
$\gamma_{(100)}$ (mJ/m2) | 1847 | 1856Ptosti_1189002  |  | 2386 | 2350Rhosti_1287920  |
$\gamma_{(110)}$ (mJ/m2) | 1685 | 1681Ptosti_1189002  | 2490tyson1977surface  | 2466 | 2331Rhosti_1287920  | 2659tyson1977surface
$\gamma_{(111)}$ (mJ/m2) | 1417 | 1488Ptosti_1189002  |  | 2073 | 1984Rhosti_1287920  |
Figure 4: Comparison of various surface energies obtained from ACE and DFT.
The reference DFT data are taken from the Crystalium databasetran2016surface ;
tran2019anisotropic ; zheng2020grain .

The phase stabilities of various bulk phases over a broad range of volumes are
examined for both metals in Fig. 5. It can be seen that the agreement between
ACE and DFT is excellent up to the dissociation limit, which is often not the
case for ML models lysogorskiy2022active ; qamar2022atomic . Both Pt and Rh
are most stable in the fcc phase. The closely related hexagonal close-packed
(hcp) phases have only slightly higher energies ($\Delta E_{\text{hcp-
fcc}}=79$ meV/atom for Pt and $\Delta E_{\text{hcp-fcc}}=36$ meV/atom for Rh).
The ACE model correctly reproduces the energetic ordering of other low-energy
phases, namely,
$E_{\text{sc}}>E_{\text{A15}}>E_{\text{bcc}}>E_{\text{hcp}}>E_{\text{fcc}}$
for Pt and
$E_{\text{sc}}>E_{\text{bcc}}>E_{\text{A15}}>E_{\text{hcp}}>E_{\text{fcc}}$
for Rh, where the subtle differences of $E_{\text{bcc}-\text{hcp}}=18$
meV/atom for Pt and $E_{\text{bcc}-\text{A15}}=49$ meV/atom for Rh are all
correctly captured and bcc and sc correspond to body-centered cubic and simple
cubic phases, respectively.

Phonon dispersions along high symmetry directions of the Brillouin zone and
phonon densities of states for the fcc phases of Pt and Rh are shown in Fig.
6. ACE exhibits a close agreement with DFT for both elemental metals.

Apart from the properties of the elemental metals, we evaluated the
equilibrium lattice parameters of random Pt-Rh fcc alloys as a function of
temperature and compared them with available experimental data in Fig. 7(a).
The linear decrease of the lattice parameter with increasing Rh concentration
is well reproduced by ACE. As mentioned above, the overestimation of the
values of the lattice parameters predicted by theory are due to the
underbinding of the PBE exchange-correlation functional used for the DFT
training data.

There exists experimental evidence for ordering tendencies in the Pt-Rh system
steiner_PhysRevB.71.104204  but no unequivocal confirmation of the existence
of distinct ordered phases. Nevertheless, several theoretical studies
turchi_PhysRevB.74.064202 ; curtarolo2005accuracy ; lu1991long ;
lu1995ordering ; pohl2009phase  predicted a possible occurrence of ordered
phases at low temperatures. The D022 phase and the so-called ”phase 40” (NbP
prototype, Pearson symbol tI8, space group I41/amd) were identified as the
lowest energy phases for the PtRh3 and PtRh stoichiometries, respectively.
More recently, Hart et al. hartcomprehensive  reported the Pd2Ti prototype
(Pearson symbol oI6, space group Immm) to be a stable phase on the convex hull
for the PtRh2 stoichiometry.

We calculated the formation energies of these ordered structures using ACE and
compared them with the reference DFT data in Fig. 7 (b). In addition, the plot
contains formation energies of fcc random solid solutions. ACE predictions for
the three ordered phases agree closely with the DFT results, reproducing
correctly the convex hull. All random solid solutions lie above the convex
hull, but their formation energies remain negative.

(a) Pt

(b) Rh

Figure 5: Energy as a function of the nearest neighbour distance (NNB) for
various bulk phases of (a) Pt and (b) Rh. The lines represent ACE predictions
while the dots correspond to the reference DFT data. The insets depict low-
energy regions around the fcc ground state.

Figure 6: Phonon dispersion for the ground state fcc structure of (a) Pt and
(b) Rh.

Figure 7: (a) Lattice constants of Pt-Rh alloys as a function of chemical
composition at different temperatures. The square symbols represent the
experimental values at $T=300$ K raub1959metals . (b) Formation energies of
most stable ordered phases from DFT (blue diamonds) hartcomprehensive  and
their ACE predictions (red crosses). ACE predictions for fcc random solid
solutions are marked by red circles.

###  2.3 Simulations of Pt-Rh nanoclusters

As the Pt-Rh nanoclusters appear to be terminated predominantly with (111) and
(100) planes (see Fig. 1), we started our simulations using truncated
octahedrons that contain six (100) and eight (111) planes. The initial focus
of the simulations was to examine the surface segregation that may play a role
in stabilization of the core-shell geometry. We investigated two compositions
of $\text{Pt}_{30}\text{Rh}_{70}$ and $\text{Pt}_{45}\text{Rh}_{55}$, with a
random initial distribution of both species in the nanoclusters (see
supplementary Fig. S3). The simulations were done at $T=500$ K using a hybrid
MD/MC procedure for efficiently reaching thermodynamic equilibrium.

Figure 8 shows the final cluster configurations for both compositions. In both
cases, we observed a strong tendency of the Pt atoms (blue spheres) to
segregate to the surface and to form a continuous monolayer across the whole
cluster surface. Based on the results for the Pt-poor composition
$\text{Pt}_{30}\text{Rh}_{70}$, we surmise that the segregation of Pt occurs
preferentially on the (111) facets as the coverage of the (100) facets remains
incomplete (see the top left configuration in Fig. 8). For the Pt-rich
composition $\text{Pt}_{45}\text{Rh}_{55}$, all surfaces of the cluster are
covered completely by Pt (see the top right configuration in Fig. 8).
Interestingly, the excess Pt atoms in this case do not continue to segregate
to adjacent subsurface layers but remain randomly dispersed in the cluster
interior. While the formation of a Pt surface layer can be related to the low
surface energies of Pt (cf. Fig. 4), experimental observations of the core-
shell particles show a thicker coverage of 3-5 layers of Pt at the surface
vega2023 . However, according to our simulations Rh atoms have a slight
preference for the occupation of the second subsurface layer (see the bottom
right configuration in Fig. 8).

To analyze this discrepancy in more detail, we performed additional DFT
calculations of Pt-Rh surface slabs with different orientations. All slabs
consisted of ten atomic planes with two Pt and eight Rh layers. One of the Pt
layers was located at the surface while the position of the second Pt layer
was varied, from being the adjacent subsurface layer, i.e., forming two Pt
layers on the surface to the opposite surface of the slab, i.e., a Rh slab
with both surfaces covered by Pt layers. These calculations confirm that the
single Pt layers on both slab surfaces corresponds to energetically most
favorable configuration, see supplementary Fig. S4. In contrast, the formation
of two adjacent Pt surface layers results mostly in configurations with higher
energies than when the Pt layers are farther apart. The energetics of these
interactions is described well by ACE, confirming the reliability of ACE
predictions in the large-scale MD simulations. This analysis shows that in
thermodynamic equilibrium a multilayer segregation of Pt atoms on the surface
of the Pt-Rh nanoclusters is likely not favorable. This suggests that the
core-shell morphologies with a Rh core and a thicker Pt shell observed in some
STEM experiments are kinetically stabilized. This corroborates with the fact
that the experimental synthesis procedure creates the core first followed by
the coating of the surface element.

(a) $\text{Pt}_{30}\text{Rh}_{70}$

(b) $\text{Pt}_{45}\text{Rh}_{55}$

Figure 8: Visualization of the surface segregation in Pt-Rh octahedron
nanoclusters with (a) $\text{Pt}_{30}\text{Rh}_{70}$ and (b)
$\text{Pt}_{45}\text{Rh}_{55}$ composition. Pt atoms are colored in blue and
Rh atoms in green. Top figures show the front view of truncated octahedron
with four (111) and one (100) surface facets. Bottom figures show mid cross-
sections of the clusters with four (111) and two (100) surface planes.

To obtain a complementary view on the stability of the core-shell clusters, we
performed additional MD simulations at elevated temperatures. In contrast to
the hybrid MD-MC simulations presented above, we generated the initial
clusters as spheres with a Rh core and a Pt shell, to mimic real experimental
geometries. The thickness of the shell was set to approximately three Pt
layers. The clusters were then annealed at temperatures of 1000 and 1500 K.

In Fig. 9, the nanoclusters are visualized after 2 ns of annealing. At the
lower temperature of 1000 K, the cluster undergoes small shape changes but its
core-shell morphology remains intact. When the temperature is increased to
1500 K, we start observing diffusion events leading to a gradual intermixing
of the Rh atoms from the core into the Pt shell. The duration of the MD
simulation is too short to reach thermodynamic equilibrium and supports our
conclusion that the experimentally observed Rh core and Pt shell structure is
metastable.

(a) $T=1000$ K, $t=2$ ns

(b) $T=1500$ K, $t=2$ ns

Figure 9: Visualization of core-shell nanocluster after $t=2$ ns annealing at
(a) 1000 K and (b) 1500 K. Rh atoms in green, Pt atoms in transparent blue.

##  3 Conclusion

We presented the development and application of ACE for the Pt-Rh binary
system. Our approach utilized a semi-automatic workflow combining high-
throughput DFT calculations, efficient fitting and validation procedures, and
active learning using uncertainty indication based on the D-optimality
criterion. The resulting ACE potential accurately describes fundamental
properties of the Pt-Rh system with ab initio accuracy and is suitable for
large-scale atomistic simulations.

We applied the ACE to investigate structural stability of various Pt-Rh
nanoclusters using hybrid MC/MD simulations. Our results show a strong surface
segregation of Pt and a preference to form a single monolayer coverage of the
whole cluster. This is in contrast to experimental observations, where core-
shell nanoclusters with thicker Pt shells were reported. By carrying out MD
simulations at elevated temperatures, we showed that the core-shell cluster
morphologies consisting of a Rh core with a thicker Pt shell observed in
experiments are not thermodynamically favorable but rather kinetically
stabilized.

The accuracy of ACE cannot exceed the accuracy of the reference DFT
calculations. DFT predicts surface and defect energies in Pt poorly, which
suggests that the simulations for Pt-Rh nanoclusters are limited primarily by
the DFT reference data. This highlights that improved exchange correlation
functionals that are suitable for high-ghroughput database generation are
urgently required.

##  4 Methods

###  4.1 DFT calculations

All reference DFT calculations were done using the Vienna ab-initio simulation
package (VASP) kressabinitio1993 ; kresse1996efficiency ; kresse1996efficient
with projector augmented waves Blochlprojectoraugemented . For the description
of the exchange-correlation functional, we employed the Perdew-Burke-Ernzerhof
(PBE) functional PBEXC . For energy and force calculations parameters were
chosen with a tight settings to obtain an converged accurate results. A plane-
wave cutoff energy of $E_{\text{cut}}=500$ eV and Gaussian smearing of
$\sigma=0.1$ eV were used in all calculations. A dense $\Gamma$ centered
k-point mesh with a spacing of 0.125 Å-1 was used to sample the Brillouin
zone.

###  4.2 ACE parametrization

The ACE model was parameterized using the pacemaker package
bochkarevefficientpara . In the first stage, fitting was performed using a
hierarchical basis extension, resulting in the ACE potential consisting of
8874 basis functions and 20 688 parameters with a maximum order $\nu=4$,
corresponding to five-body interactions. Additional details of the model are
summarized in Table 2. Relative weights of different structures in the loss
function were distributed based on their distance to the convex hull. This
method prioritized structures with lower energies, giving them a greater
contribution to the loss function bochkarevefficientpara . In addition, the
weights of non-periodic clusters were reduced by a factor of ten to provide
regularization to the ACE model. The initial parametrization was improved
using active learning as described in Section 4.4.

Table 2: Details of the ACE parametrization: $r_{c}$ denotes the cutoff radius; RBF the type of radial basis function; ”#func. /element” represents the maximum number of functions per element for each body order $\nu$. System |  $r_{c}$ (Å) | RBF | $n_{\text{max}}$ | $l_{\text{max}}$ | #func. /element
---|---|---|---|---|---
Pt-Rh | 6.3 | SBessel | 28/5/4/1 | 0/6/4/1 | 56/385/3976/20

###  4.3 MD and MC simulations

The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package
LAMMPS  with the ML_PACE lysogorskiy2021performant  and MC sadighscalable
packages was used for the MD and MC atomistic simulations. We adopted an
integration time step of $\Delta t=1$ fs for the MD simulations. All
simulations were equilibrated at the target temperature/pressure for
$t_{eq}=50$ ps before production runs. For MD simulations of lattice
parameters of Pt-Rh alloys, we used a simulation cell containing 2048 atoms
that corresponds to an $8\times 8\times 8$ conventional fcc cell. Simulations
were conducted at two temperatures $T=300$ K and $T=800$ K in an isothermal-
isobaric ($NPT$) ensemble with a pressure of $P=0$ bar for $t=500$ ps. Nosé-
Hoover thermostat and barostat were used to control temperature and pressure.
Damping parameters were 0.1 ps for temperature and 1 ps for pressure to ensure
the temperature and pressure fluctuations are appropriate.

Two nanocluster geometries were created using the Atomistic Simulation
Environment (ASE) ase-paper : a truncated octahedron for the surface
segregation phenomena and a spherical nanocluster for annealing of
nanoclusters. The truncated octahedron comprises six $(100)$ and eight $(111)$
surfaces and contained 2406 atoms. Different chemical compositions were
initialized by randomly assigning Pt or Rh to the atomic positions. A
spherical nanocluster was created with 3577 atoms consisting of a Rh core
(1058 atoms) covered by three layers of Pt (2519 atoms). All simulations of
nanoparticles were performed in the canonical ($NVT$) ensemble using the Nosé-
Hoover thermostat with a damping parameter of 0.1 ps.

A Monte Carlo scheme was used for the simulation of surface segregation using
the MC sadighscalable  packages implemented in LAMMPS to allow for atomic
swapping between different types of atoms. The simulations were performed for
$t=200$ ps for surface segregation and $t=2$ ns for annealing of
nanoparticles. The open visulization tool OVITO stukowski2009visualization
was used for the visulization of nanoclusters.

###  4.4 Active learning

To capture atomic environments relevant for nanoclusters, we used small fcc
surface structures with different crystallographic orientations and sizes,
namely, slabs with the (100) surface orientation containing 32 atoms, the
(110) surface of 56 atoms, and (111) surface orientation containing 36 atoms,
respectively. To sample different slab configurations, we employed a hybrid
MD-MC approach in the $NVT$ ensemble, running each simulation for 100 ps at
three different temperatures (300, 500 and 800 K). We calculated on-the-fly
the extrapolation grade $\gamma$ for each atom every 100th simulation step
using the D-optimality criterion. Structures with $\gamma$ values greater than
5 were selected as extrapolative structures, resulting in a few thousand
candidate structures. All simulations were performed using the LAMMPS version,
which calculates the extrapolation grades for ACE lysogorskiy2022active . To
select the most representative atomic environments, we utilized the MaxVol
algorithm to construct a new active set from the structures generated in the
previous step. We gave priority to structures that had multiple atoms that
entered the new active set lysogorskiy2022active  and selected the top hundred
candidates for data efficiency. These selected structures were computed with
DFT, added to the original training set, and used to upfit the ACE potential.
As a result of the above approach, we observed a significant decrease in the
extrapolation grades for representative nanocluster (see Supplementary Fig.
S3), and a reduction in the error metrics for the energy and forces of the
selected surface structures. The energy root mean square error (RMSE)
decreased from 31 to 3 meV/atom and the force RMSE from 172 to 84 meV/Å(see
Supplementary Fig. S1).

###  4.5 STEM characterization

A probe corrected Titan Themis 60-300 operated at 300 kV was used for the STEM
characterization. For imaging, a HAADF detector with a collection angle of
78-200 mrad was used. The EDS composition maps were acquired with a Brucker
Super X detector.

Supplementary information

The supplementary information is provided in the following PDF file.

Acknowledgments The authors acknowledge computation time by Center for
Interface-Dominated High Performance Materials (ZGH) at Ruhr-Universität
Bochum, Germany.

Funding This work was in part supported by the German Science Foundation
(DFG), projects 405621081 and 405621217.

Data availability DFT reference data that was used for training and the ACE
potential file are available upon request.

Conflict of interest On behalf of all authors, the corresponding author states
that there is no conflict of interest.

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