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%----------------------- AUTHORS -------------------------------------
\author{Aleksandra Khanina}
\affiliation{National University of Science and Technology MISIS, Leninsky Av.~4, Moscow, 119049, Russia.}
\email{khanina.as@misis.ru}
\author{Tatyana Sviridova}
\affiliation{National University of Science and Technology MISIS, Leninsky Av.~4, Moscow, 119049, Russia.}
\author{Alexandra Ivanova}
\affiliation{National University of Science and Technology MISIS, Leninsky Av.~4, Moscow, 119049, Russia.}
\author{Andrey Voronin}
\affiliation{National University of Science and Technology MISIS, Leninsky Av.~4, Moscow, 119049, Russia.}
\author{Vladimir Khovaylo}
\affiliation{National University of Science and Technology MISIS, Leninsky Av.~4, Moscow, 119049, Russia.}
\alsoaffiliation{National University of Science and Technology MISIS, Leninsky Av.~4, Moscow, 119049, Russia.}
\email{khovaylo@misis.ru}

%----------------TITLE-----------------------------
\title{
--- Supplementary Information --- \\
Mechanochemical Synthesis of Ba-Doped \ch{BiCuSeO} Oxyselenides: Influence of Processing Conditions on Phase Formation}

\begin{document}
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%-------------------------------------------------------------------
\clearpage
\section{Phase and elemental analysis}

\begin{figure}[h!]
    \centering
    \includegraphics[width=1\linewidth]{figures SI/Fig.S1 XRD (HBM-PLS).pdf}
    \caption{Powder XRD patterns of the Bi$_{1-x}$Ba$_x$CuSeO ($x$ = 0, 0.075, 0.125, 0.175) samples after MS and PLS. Bragg’s reflections for the BiCuSeO phase are indicated by gray ticks on the top part of the figure.
    }
    \label{Fig:XRD-time}
\end{figure}

\begin{table*}[h!]
    \centering
    \begin{tabular}{ c|c|c c c c c}
        \hline
                \parbox[c][2.3em][c]{2.25cm}{powder-to-ball\\mass ratio}&  Nominal composition& $a, b$ (\AA) & $c$ (\AA) & \parbox[c][2.3em][c]{2.5cm}{(Bi + Ba):Cu:Se\\ratios} & Ba/(Bi + Ba)  & $d_{\mathrm{CS}}$ (\AA) \\
        \hline
        \multirow{4}{*}{1:10} & BiCuSeO & 3.929 & 8.931 & 1.08:0.86:1.05 & 0  & 201 \\
        & Bi$_{0.925}$Ba$_{0.075}$CuSeO & 3.946 & 9.013 & 1.05:0.93:1.02 & 0.07 & 344 \\
        & Bi$_{0.875}$Ba$_{0.125}$CuSeO & 3.953 & 9.041 & 1.04:0.96:1.01 & 0.12  & 269 \\
        & Bi$_{0.825}$Ba$_{0.175}$CuSeO & 3.959 & 9.074 & 1.03:0.99:0.98 & 0.16 & 256 \\
        \hline
        \multirow{4}{*}{1:20} & BiCuSeO & 3.928 & 8.948 & 1.02:0.94:0.99 & 0  & 250 \\
        & Bi$_{0.925}$Ba$_{0.075}$CuSeO & 3.939 & 8.992 & 1.01:0.99:0.98 & 0.07  & 219 \\
        & Bi$_{0.875}$Ba$_{0.125}$CuSeO & 3.947 & 9.030 & 1.02:0.99:0.99 & 0.12  & 209 \\
        & Bi$_{0.825}$Ba$_{0.175}$CuSeO & 3.954 & 9.064 & 1.01:0.99:0.99 & 0.16  & 225 \\
        \hline
        \multirow{4}{*}{1:40} & BiCuSeO & 3.926 & 8.950 & 1.03:0.99:0.98 & 0  & 225 \\
        & Bi$_{0.925}$Ba$_{0.075}$CuSeO & 3.943 & 9.000 & 1.02:0.99:0.99 & 0.07  & 213 \\
        & Bi$_{0.875}$Ba$_{0.125}$CuSeO & 3.950 & 9.041 & 1.02:1.00:0.98 & 0.11  & 196 \\
        & Bi$_{0.825}$Ba$_{0.175}$CuSeO & 3.957 & 9.075 & 1.02:1.00:0.99 & 0.17  & 210 \\
        \hline
    \end{tabular}
    \caption{Refined lattice constants from Rietveld analysis of X-ray diffraction data and EDS results for the Bi$_{1-x}$Ba$_x$CuSeO ($x$ = 0, 0.075, 0.125, 0.175) samples grounded in different powder-to-ball mass ratios after MS}
     \label{Tab:XRD-EDS}
\end{table*}

%-------------------------------------------------------------------

\clearpage
\section{Particle size distribution}

\begin{figure}[h!]
    \centering
    \includegraphics{figures SI/Fig.S2 DLS.pdf}
    \caption{Particle size distribution of BiCuSeO powders milled at different powder-to-ball mass ratios.}
    \label{Fig:XRD-PLS}
\end{figure}

\clearpage
\section{Microstructure characterization}

\begin{figure}[h]
    \centering
    \includegraphics[width=1\linewidth]{figures SI/Fig.S3 SEMp.pdf}
    \caption{SEM micrographs of the polished surfaces for Bi$_{1-x}$Ba$_x$CuSeO ($x$ = 0.075, 0.125, 0.175) powders. The dark areas are CuO phases.}
    \label{Fig:SEMp}
\end{figure}

\begin{figure}[H]
    \centering
    \includegraphics[width=1\linewidth]{figures SI/Fig.S4 SEMf.pdf}
    \caption{SEM micrographs of the fractured cross-sections for BiCuSeO bulk samples.}
    \label{Fig:SEMf}
\end{figure}

\clearpage
\section{Thermal conductivity and figure of merit}

\begin{figure}[h!]
    \centering
    \includegraphics[width=0.5\linewidth]{figures SI/Fig.S5 TE.pdf}
    \caption{Concentration and powder-to-ball mass ratio dependence of the (a, b)~total thermal conductivity $\kappa_{tot}$, (c, d)~lattice thermal conductivity $\kappa_{lat}$ and (e, f)  electrical thermal conductivity $\kappa_{el}$ and (g, h) figure of merit $zT$ for Bi$_{1-x}$Ba$_x$CuSeO ($x$ = 0, 0.075, 0.125, 0.175) samples consolidated by PLS. Literature data for other Bi$_{1-x}$Ba$_x$CuSeO-based oxyselenides are also shown for comparison 
    (Bhaskar et al.,\cite{bhaskar2017}
    Feng et al.,\cite{feng2018, feng2016}
    Hong et al.,\cite{hong2022}
    Lan et al.,\cite{lan2013}
    Liu et al.,\cite{liu2013}
    Jiang et al.,\cite{jiang2021}
    Kim et al.,\cite{kim2021}
    Lei et al.,\cite{lei2021, lei2022}
    Li et al.,\cite{li2012, li2012Ba}
    Liang et al.,\cite{liang2023}
    Park et al.,\cite{park2019}
    Luu et al.,\cite{luu2013}
    Pei et al.,\cite{pei2014}
    Novitskii et al,\cite{novitskii2022Sm}
    Wen et al.,\cite{wen2017}
    Yang et al.,\cite{yang2016}
    Zeng et al.\cite{zeng2023}).
    All displayed data points correspond to values obtained at 300 K.}
    \label{Fig:TE}
\end{figure}

\clearpage

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