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\vspace{0.7cm}
\begin{center}
\textbf{\LARGE Supplementary information}

\vspace{0.3cm}

\textbf{\LARGE Coalescence of AuPd nanoalloys in implicit
environments}

\vspace{0.5cm} %& \vspace{0.3cm}

\Large{Sofia Zinzani,\textit{$^{a}$} Francesca Baletto\textit{$^{a\ddag}$}}

\vspace{0.3cm}
\small{\textit{$^{a}$~Università degli Studi di Milano - Dipartimento di Fisica; Via Celoria 16; Milano I-20133; Italy.}} \\
%\vspace{0.1cm} \\
\small{\textit{$^{\ddag}$~ E-mail: francesca.baletto@unimi.it }}

\end{center}
\label{sec:suppl_info}

\section{Introduction}
Below we include other characterization quantities, a table summarising the parameters adopted in the various simulations and the graphs obtained for all quantities analysed, for all sets. For the sake of clarity, they have not been reported in the main text, but form an essential part of this work. The results obtained are ordered as follow:
\begin{itemize}
    \item \ref{subsec:S1} contains a table showing all sets of $\eta_{\alpha}$ and $\rho_{\alpha}$ parameters we chose for the MEIs.
    \item \ref{subsec:S2} contains others characterization quantities used for the analysis but not reported in detail in the main text.
    \item \ref{subsec:S3} contains all the figures for the simulations for the smaller systems, composed of 55 atoms of gold and 55 of palladium, both icosahedral.
    \item \ref{subsec:S4} contains all the figures for the simulations for the bigger systems, composed of 561 atoms of gold and 561 of palladium, both icosahedral.
\end{itemize}


\section{MEI-Set selection}
\label{subsec:S1}
In the table \ref{tab:set} are reported all the sets of simulation performed for $Au_{55}^{Ih}$ - $Pd_{55}^{Ih}$. Referring to the main text of this article: set0 represents simulations performed in vacuum. Sets 1 to 34 environments of type AP, sets 101 to 134 environments of type P, and set 201 to 234 environments of type A.
For $Au_{561}^{Ih}$ - $Pd_{561}^{Ih}$ simulations only: \texttt{set0, set1, set2, set3, set4, set21, set24, set31, set34, set134}, has been performed, due to the large computational time required, highlighted in violet in the table.

\begin{table}[h]
\centering
\begin{minipage}{.3\textwidth} % Prima colonna
%\centering
\begin{tabular}{|c|c|c|c|c|}
\hline Set name & $\rho_{\mathrm{Au}}$ & $\rho_{\mathrm{Pd}}$ & $\eta_{\mathrm{Au}}[\mathrm{eV}]$ & $\eta_{\mathrm{Pd}}[\mathrm{eV}]$ \\
\hline \rowcolor{azzurrino} set 0 & \multicolumn{4}{c|}{ Vacuum } \\
\hline \rowcolor{azzurrino} set 1 & 0.5 & 0.5 & 0.02 & 0.02 \\
\hline \rowcolor{azzurrino} set 2 & 0.5 & 0.5 & 0.02 & 0.04 \\
\hline \rowcolor{azzurrino} set 3 & 0.5 & 0.5 & 0.02 & 0.06 \\
\hline \rowcolor{azzurrino} set 4 & 0.5 & 0.5 & 0.02 & 0.08 \\
\hline set 11 & 0.5 & 0.75 & 0.02 & 0.02 \\
\hline set 12 & 0.5 & 0.75 & 0.02 & 0.04 \\
\hline set 13 & 0.5 & 0.75 & 0.02 & 0.06 \\
\hline set 14 & 0.5 & 0.75 & 0.02 & 0.08 \\
\hline \rowcolor{azzurrino} set 21 & 0.5 & 1.0 & 0.02 & 0.02 \\
\hline set 22 & 0.5 & 1.0 & 0.02 & 0.04 \\
\hline set 23 & 0.5 & 1.0 & 0.02 & 0.06 \\
\hline \rowcolor{azzurrino} set 24 & 0.5 & 1.0 & 0.02 & 0.08 \\
\hline set 28 & 1.0 & 1.0 & 0.02 & 0.2 \\
\hline \rowcolor{azzurrino} set 31 & 0.5 & 1.5 & 0.02 & 0.02 \\
\hline set 32 & 0.5 & 1.5 & 0.02 & 0.04 \\
\hline set 33 & 0.5 & 1.5 & 0.02 & 0.06 \\
\hline \rowcolor{azzurrino} set 34 & 0.5 & 1.5 & 0.02 & 0.08 \\
%\hline \multicolumn{5}{|c|}{  } \\
\hline set 201 & 0.5 & 0 & 0.02 & 0 \\
\hline set 204 & 0.5 & 0 & 0.08 & 0 \\
\hline set 221 & 1.0 & 0 & 0.02 & 0 \\
\hline set 224 & 1.0 & 0 & 0.08 & 0 \\
\hline set 231 & 1.5 & 0 & 0.02 & 0 \\
\hline set 234 & 1.5 & 0 & 0.08 & 0 \\
\hline set 101 & 0 & 0.5 & 0 & 0.02 \\
\hline set 104 & 0 & 0.5 & 0 & 0.08 \\
\hline set 106 & 0 & 0.5 & 0 & 0.2 \\
\hline set 121 & 0 & 1.0 & 0 & 0.02 \\
\hline set 124 & 0 & 1.0 & 0 & 0.08 \\
\hline set 126 & 0 & 1.0 & 0 & 0.2 \\
\hline set 131 & 0 & 1.5 & 0 & 0.02 \\
\hline set 133 & 0 & 1.5 & 0 & 0.06 \\
\hline \rowcolor{azzurrino} set 134 & 0 & 1.5 & 0 & 0.08 \\
\hline 
\end{tabular}
\end{minipage}
\centering
\caption{Sets of simulations at 400K performed for both nanoalloys composed of 55 atoms of gold and 55 of palladium and in light purple for nanoalloys composed of 561 atoms of gold and 561 of palladium at 600K. In the first columns, we reported the set name corresponding to the chosen parameters $\rho_{Au}$, $\rho_{Pd}$, $\eta_{Au}$, $\eta_{Pd}$ given in columns 2,3,4,5 respectively.}
\label{tab:set}
\end{table}




%

\section{Supplementary characterization methods: PDDF in \texttt{Sapphire}}
\label{subsec:S2}

In \texttt{Sapphire}\cite{art:sapphire}, the PDDF is calculated via a Kernel function, $K\left(d_{i j}, d ; h\right)$ over the $d_{i j}$ variable, constructed from \textit{n} observations:
\begin{equation}
\operatorname{PDDF}\left[K\left(d_{i j}, d ; h\right)\right]=\frac{1}{N h} \sum_i^N \sum_{j \neq i} K\left(\frac{d_{i j}-d}{h}\right) \mbox{~~~,}
\label{eq:PDDF}
\end{equation}
where $d_{i j}$ is the pair-distance between atom $i$ and $j$ in Cartesian coordinates, $d_{i j}=\sqrt{\left(x_i-x_j\right)^2+\left(y_i-y_j\right)^2+\left(z_i-z_j\right)^2} \mbox{~~~.}$
The parameter $h$ is the bandwidth that defines the tightness of the kernel function. 
Setting the bandwidth is a delicate step.\cite{Delgado2021, art:sapphire}  We select $h= 0.05$ of the bulk lattice as it has been proven to be sufficiently broad to smooth the sharp Dirac peaks from having a finite sample, and to sufficiently resolve key features. A detailed discussion is available elsewhere \cite{ThesisRobert, art:sapphire}.



\clearpage
\section{${Au_{55}^{Ih}}$-${Pd_{55}^{Ih}}$}
\label{subsec:S3}
%
\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/Gyr_HalfMax.png}
  \caption{Time evolution of radius of gyration of the whole cluster (in black) and half maximum pair distance $R_{max} = D_{max}/2$ (in pink), for ${Au_{55}^{Ih}}$-${Pd_{55}^{Ih}}$ in vacuum (set0) and in the environment (all the others sets) with $\rho_{Au}$, $\rho_{Pd}$, $\eta_{Au}$ eV and $\eta_{Pd}$ eV varing with associated set names as in table \ref{tab:set}. 
  Each graph represents the average over four independent simulations of the quantities mentioned. The mean value is represented by the solid line, while the shadow represents the standard deviation.}
  \label{fig:55_Gyr_HalfMax_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Gyr_HalfMax.png}
  \caption{Time evolution of the radius of gyration of the whole cluster (in black) and half maximum pair distance $R_{max} = D_{max}/2$ (in pink), for ${Au_{55}^{Ih}}$-${Pd_{55}^{Ih}}$ in vacuum (set0) and in the environment (all the others sets) with $\rho_{Au}$, $\rho_{Pd}$, $\eta_{Au}$ eV and $\eta_{Pd}$ eV varing with associated set names as in table \ref{tab:set}.
  Each graph represents the average over four independent simulations of the quantities mentioned. The mean value is represented by the solid line, while the shadow represents the standard deviation.}
  \label{fig:55_Gyr_HalfMax_P}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=12.cm]{Figure/Supplementar_Information/55/Env_AP/Gyr_HalfMax.png}
  \caption{Time evolution of radius of gyration of the whole cluster (in black) and half maximum pair distance $R_{max} = D_{max}/2$ (in pink), for ${Au_{55}^{Ih}}$-${Pd_{55}^{Ih}}$ in vacuum (set0) and in the environment (all the others sets) with $\rho_{Au}$, $\rho_{Pd}$, $\eta_{Au}$ eV and $\eta_{Pd}$ eV varing with associated set names as in table \ref{tab:set}.
  Each graph represents the average over four independent simulations of the quantities mentioned. The mean value is represented by the solid line, while the shadow represents the standard deviation.}
  \label{fig:55_Gyr_HalfMax_AP}
\end{figure}




\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/Sapph_PDF_Tot.png}
  \caption{Pair distance distribution function mean of whole cluster. In black is represented the PDDF at initial time (equal to the contact time) while in green is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Tot_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Sapph_PDF_Tot.png}
  \caption{Pair distance distribution function mean of whole cluster. In black is represented the PDDF at initial time (equal to the contact time) while in green is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Tot_P}
\end{figure}

\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_AP/Sapph_PDF_Tot.png}
  \caption{Pair distance distribution function mean of whole cluster. In green is represented the PDDF at initial time (equal to the contact time) while in black is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Tot_AP}
\end{figure}



\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/Sapph_PDF_Au.png}
  \caption{Pair distance distribution function mean of Au atoms. In yellow is represented the PDDF at initial time (equal to the contact time) while in red is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Au_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Sapph_PDF_Au.png}
  \caption{Pair distance distribution function mean of Au atoms. In yellow is represented the PDDF at initial time (equal to the contact time) while in red is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Au_P}
\end{figure}

\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_AP/Sapph_PDF_Au.png}
  \caption{Pair distance distribution function mean of Au atoms. In yellow is represented the PDDF at initial time (equal to the contact time) while in red is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Au_AP}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/Sapph_PDF_Pd.png}
  \caption{Pair distance distribution function mean of Au atoms. In light blue is represented the PDDF at initial time (equal to the contact time) while in blue is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Pd_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Sapph_PDF_Pd.png}
  \caption{Pair distance distribution function mean of Au atoms. In light blue is represented the PDDF at initial time (equal to the contact time) while in blue is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Pd_P}
\end{figure}

\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_AP/Sapph_PDF_Pd.png}
  \caption{Pair distance distribution function mean of Au atoms. In light blue is represented the PDDF at initial time (equal to the contact time) while in blue is represented the PDDF at final time. Final time is equal to 10 ns.}
  \label{fig:55_Sapph_PDF_Pd_AP}
\end{figure}

\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/All_Surf.png}
  \caption{Time evolution percentage of Au atoms (in red) and Pd atoms (in dark blue),
compared to the total number of surface atoms. Surface atoms were identified by their atop generalized coordination number. The shaded areas correspond to the variations on the simulations, while the solid line represents the average of the percentages. Also shown in light blue is the percentage of surface palladium atoms to the total number of palladium atoms and in orange the percentage of gold on the surface compared to the total number of atoms of gold. }
  \label{fig:55_All_Surf_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/All_Surf.png}
  \caption{Time evolution percentage of Au atoms (in red) and Pd atoms (in dark blue),
compared to the total number of surface atoms. Surface atoms were identified by their atop generalized coordination number. The shaded areas correspond to the variations on the simulations, while the solid line represents the average of the percentages. Also shown in light blue is the percentage of surface palladium atoms to the total number of palladium atoms and in orange the percentage of gold on the surface compared to the total number of atoms of gold. }
  \label{fig:55_All_Surf_P}
\end{figure}

\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_AP/All_Surf.png}
  \caption{Time evolution percentage of Au atoms (in red) and Pd atoms (in dark blue),
compared to the total number of surface atoms. Surface atoms were identified by their atop generalized coordination number. The shaded areas correspond to the variations on the simulations, while the solid line represents the average of the percentages. Also shown in light blue is the percentage of surface palladium atoms to the total number of palladium atoms and in orange the percentage of gold on the surface compared to the total number of atoms of gold. }
  \label{fig:55_All_Surf_AP}
\end{figure}




\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/Gyr_Au_Pd.png}
  \caption{Time evolution radius of gyration of the two chemical species: in orange is represented the mean radius of gyration of Au and in blue that of Pd.}
  \label{fig:55_Gyr_Au_Pd_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Gyr_Au_Pd.png}
  \caption{Time evolution radius of gyration of the two chemical species: in orange is represented the mean radius of gyration of Au and in blue that of Pd.}
  \label{fig:55_Gyr_Au_Pd_P}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Gyr_Au_Pd.png}
  \caption{Time evolution radius of gyration of the two chemical species: in orange is represented the mean radius of gyration of Au and in blue that of Pd.}
  \label{fig:55_Gyr_Au_Pd_AP}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/Mixing_parameter.png}
  \caption{Time evolution mixing parameter $\mu$.}
  \label{fig:55_Mixing_parameter_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/Mixing_parameter.png}
  \caption{Time evolution mixing parameter $\mu$.}
  \label{fig:55_Mixing_parameter_P}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_AP/Mixing_parameter.png}
  \caption{Time evolution mixing parameter $\mu$.}
  \label{fig:55_Mixing_parameter_AP}
\end{figure}


%Set 234 is truly peculiar, we observe a systematic decrease of LAE$_{Au}$=0, meaning number of Au atoms without Pd atoms in their first shell of coordination. Associated with the decrease of LAE$_{Au}$=0, Set 234 favours drastically the mixing. 
%Similarly, set134 is the only MEI where only Au/Pd interacts showing a significant  change in the LAE, with again both LAE$_{\alpha}$=0 almost zero for both chemical species. Moreover, for set 134 the number of LAE$_{Pd}$ is not zero, suggesting that individual Pd atom starts to be fully encapsulated in the Au matrix. The MEIs where at least a few Pd atoms are dispersed in the Au region are set34, set23, set24, set11 e set12, set134, MEIs for which LAE$_{Au}$=0 less than 10\%: set224, set234; set134; set34 is at 15\%. This could be that Au atoms diffuse over the Pd core, we do expect a larger R-gyr for Au.
%LAE must discuss more in details and gathered into some information for the main text.


\begin{figure}[h]
\centering
\includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_A/LAE_tail.png}
  \caption{LAE distribution for Au$_{55}$Pd$_{55}$ after 10 ns in MEIs where only Au interacts. Local atomic environments for Au atoms are in red-orange-yellow; while Pd-LAE are in blue-light-blue-cyan. }
  \label{fig:55_LAE_tail_A}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_P/LAE_tail.png}
  \caption{LAE distribution for Au$_{55}$Pd$_{55}$ after 10 ns in MEIs where only Pd interacts. Local atomic environments for Au atoms are in red-orange-yellow; while Pd-LAE are in blue-light-blue-cyan. }
  \label{fig:55_LAE_tail_P}
\end{figure}

\begin{figure}[h]
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/55/Env_AP/LAE_tail.png}
  \caption{LAE distribution for Au$_{55}$Pd$_{55}$ after 10 ns in MEIs where both Au and Pd interacts. Local atomic environments for Au atoms are in red-orange-yellow; while Pd-LAE are in blue-light-blue-cyan.}
  \label{fig:55_LAE_tail_AP}
\end{figure}

\clearpage
\section{${Au_{561}^{Ih}}$-${Pd_{561}^{Ih}}$}
\label{subsec:S4}

\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/Gyr_HalfMax.png}
  \caption{Time evolution radius of gyration of the whole cluster (in black) and half maximum pair distance $R_{max} = D_{max}/2$ (in pink), for ${Au_{55}^{Ih}}$-${Pd_{55}^{Ih}}$ in the environment with $\rho_{Au}$, $\rho_{Pd}$, $\eta_{Au}$ eV and $\eta_{Pd}$ eV varying as in table \ref{tab:set}.
  Each graph represents the average over four independent simulations of the quantities mentioned. The mean value is represented by the solid line, while the shadow represents the standard deviation.}
  \label{fig:561_Gyr_HalfMax_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/Gyr_HalfMax.png}
  \caption{Time evolution radius of gyration of the whole cluster (in black) and half maximum pair distance $R_{max} = D_{max}/2$ (in pink), for ${Au_{55}^{Ih}}$-${Pd_{55}^{Ih}}$ in the environment with $\rho_{Au}$, $\rho_{Pd}$, $\eta_{Au}$ eV and $\eta_{Pd}$ eV varying as in table \ref{tab:set}.
  Each graph represents the average over four independent simulations of the quantities mentioned. The mean value is represented by the solid line, while the shadow represents the standard deviation.}
  \label{fig:561_Gyr_HalfMax_AP}
\end{figure}



\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/Sapph_PDF_Tot.png}
  \caption{Pair distance distribution function mean of whole cluster. In green is represented the PDDF at initial time (equal to the contact time) while in black is represented the PDDF at final time. Final time is equal to 20 ns}
  \label{fig:561_Sapph_PDF_Tot_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/Sapph_PDF_Tot.png}
  \caption{Pair distance distribution function mean of whole cluster. In green is represented the PDDF at initial time (equal to the contact time) while in black is represented the PDDF at final time. Final time is equal to 20 ns}
  \label{fig:561_Sapph_PDF_Tot_AP}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/Sapph_PDF_Au.png}
  \caption{Pair distance distribution function mean of Au atoms. In yellow is represented the PDDF at initial time (equal to the contact time) while in red is represented the PDDF at final time. Final time is equal to 20 ns}
  \label{fig:561_Sapph_PDF_Au_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/Sapph_PDF_Au.png}
  \caption{Pair distance distribution function mean of Au atoms. In yellow is represented the PDDF at initial time (equal to the contact time) while in red is represented the PDDF at final time. Final time is equal to 20 ns}
  \label{fig:561_Sapph_PDF_Au_AP}
\end{figure}




\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/Sapph_PDF_Pd.png}
  \caption{Pair distance distribution function mean of Pd atoms. In light blue is represented the PDDF at initial time (equal to the contact time) while in blue is represented the PDDF at final time. Final time is equal to 20 ns.}
  \label{fig:561_Sapph_PDF_Pd_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/Sapph_PDF_Pd.png}
  \caption{Pair distance distribution function mean of Pd atoms. In light blue is represented the PDDF at initial time (equal to the contact time) while in blue is represented the PDDF at final time. Final time is equal to 20 ns.}
  \label{fig:561_Sapph_PDF_Pd_AP}
\end{figure}



\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/All_Surf.png}
  \caption{Time evolution percentage of Au atoms (in red) and Pd atoms (in dark blue), compared to the total number of surface atoms. Surface atoms were identified by their atop generalized coordination number. The shaded areas correspond to the variations on the simulations, while the solid line represents the average of the percentages. Also shown in light blue is the percentage of surface palladium atoms to the total number of palladium atoms and in orange the percentage of gold on the surface compared to the total number of atoms of gold.
}
  \label{fig:561_All_Surf_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/All_Surf.png}
  \caption{Time evolution percentage of Au atoms (in red) and Pd atoms (in dark blue), compared to the total number of surface atoms. Surface atoms were identified by their atop generalized coordination number. The shaded areas correspond to the variations on the simulations, while the solid line represents the average of the percentages. Also shown in light blue is the percentage of surface palladium atoms to the total number of palladium atoms and in orange the percentage of gold on the surface compared to the total number of atoms of gold.
}
  \label{fig:561_All_Surf_AP}
\end{figure}



\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/Gyr_Au_Pd.png}
  \caption{Time evolution radius of gyration of the two chemical species: in orange is represented the mean radius of gyration of Au and in blue that of Pd.}
  \label{fig:561_Gyr_Au_Pd_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/Gyr_Au_Pd.png}
  \caption{Time evolution radius of gyration of the two chemical species: in orange is represented the mean radius of gyration of Au and in blue that of Pd.}
  \label{fig:561_Gyr_Au_Pd_AP}
\end{figure}





\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/Mixing_parameter.png}
  \caption{Time evolution mixing parameter $\mu$.}
  \label{fig:561_Mixing_parameter_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/Mixing_parameter.png}
  \caption{Time evolution mixing parameter $\mu$.}
  \label{fig:561_Mixing_parameter_AP}
\end{figure}


\begin{figure}[h]
\centering
  \includegraphics[width=4.5cm]{Figure/Supplementar_Information/561/Env_P/LAE_tail.png}
  \caption{LAE distribution for Au$_{561}$Pd$_{561}$ after 20 ns in MEIs where only Au interacts. Local atomic environments for Au atoms are in red-orange-yellow; while Pd-LAE are in blue-light-blue-cyan.}
  \label{fig:561_LAE_tail_P}
\centering
  \includegraphics[width=12.0cm]{Figure/Supplementar_Information/561/Env_AP/LAE_tail.png}
  \caption{LAE distribution for Au$_{561}$Pd$_{561}$ after 20 ns in MEIs where only Au interacts. Local atomic environments for Au atoms are in red-orange-yellow; while Pd-LAE are in blue-light-blue-cyan.}
  \label{fig:561_LAE_tail_AP}
\end{figure}




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