\documentclass{article}

\usepackage{Engineering}
\usepackage{multicol}
\usepackage{tcolorbox}
\usepackage{titlesec}
\usepackage{titling}
\usepackage{etoolbox}
\usepackage{tabularx}

% === METADATA ===
\pdftitle{EFPLab2 Cheatsheet}

% === HEADER/FOOTER ===
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\lhead{Matteo Frongillo}
\chead{\nouppercase Materials Lab}
\rhead{\thepage}

\renewcommand{\sectionmark}[1]{\markboth{#1}{}}

% === CUSTOM BOX COMMANDS ===
\definecolor{BoxBG}{HTML}{F0F8FF}
\definecolor{BoxBorder}{HTML}{3B83BD}

\newtcolorbox{theorybox}[1][]{
  colback=BoxBG,
  colframe=BoxBorder,
  fonttitle=\bfseries,
  left=1mm,right=1mm,top=1mm,bottom=1mm,
  boxrule=0.8pt,
  arc=1.5mm,
  title={\ifstrempty{#1}{}{\begingroup\intheoryboxtitletrue #1\endgroup\intheoryboxtitlefalse}}
}

\newtcolorbox{examplebox}[1]{
  colback=gray!10!white,
  colframe=gray!80!black,
  coltitle=white,
  fonttitle=\bfseries,
  left=1mm,right=1mm,top=1mm,bottom=1mm,
  boxrule=0.8pt,
  arc=1.5mm,
  title={#1}
}

\newtcolorbox{formula}[1]{
  colback=red!10!white,
  colframe=red!90!black!75,
  fonttitle=\bfseries,
  left=1mm,right=1mm,top=1mm,bottom=1mm,
  boxrule=0.8pt,
  arc=1.5mm,
  title={#1}
}

% === SECTION TITLE FORMATTING ===
\newif\ifintheoryboxtitle
\intheoryboxtitlefalse

\titleformat{\part}
  {\ifintheoryboxtitle\color{white}\else\color{BoxBorder}\fi\huge\bfseries}
  {\thepart}{0.5em}{}

\titleformat{\section}
  {\ifintheoryboxtitle\color{white}\else\color{BoxBorder}\fi\Large\bfseries}
  {\thesection}{0.5em}{}

\titleformat{\subsection}
  {\ifintheoryboxtitle\color{white}\else\color{BoxBorder}\fi\bfseries}
  {\thesubsection}{0.5em}{}

\titleformat{\subsubsection}
  {\ifintheoryboxtitle\color{white}\else\color{BoxBorder}\fi\small\bfseries}
  {\thesubsubsection}{0.5em}{}

% === DOCUMENT ===
\begin{document}
\begin{multicols}{2}
\setlength{\columnsep}{1pt}

% === CONTENT ===
%   \section{Preambule}
%   \begin{theorybox}{Theory box}
%       Lorem ipsum dolor sit amet.
%   \end{theorybox}
%   
%   \begin{formula}{Formula box}
%       Lorem ipsum dolor sit amet.
%   \end{formula}
%   
%   \begin{examplebox}{Lab/examples box}
%       Lorem ipsum dolor sit amet.
%   \end{examplebox}

\vspace*{-1.4cm}
\part{Physical metallurgy}
\section{Classes and properties}
\begin{theorybox}[Material classes and typical properties]
  \centering
  \renewcommand{\arraystretch}{1.5}
  \begin{tabular}{|c|l|}
    \hline Class & Typical properties\\
    \hline \makecell{Metal\\Alloys} & \makecell[l]{1) Thermal + electric conductivity\\2) Ductility\\3) Castable\\4) Reflective}\\
    \hline Ceramics & \makecell[l]{1) High T resistance\\(High E, low $\alpha$)\\2) High compression strength\\3) Thermal + electric insulator\\4) Wear resistance}\\
    \hline Polymers & \makecell[l]{1) Cheap\\2) Thermal + electric insulator\\3) Corrosion resistance\\4) Moldable}\\
    \hline
  \end{tabular}
\end{theorybox}

\subsection{Structural model of metals}
\begin{theorybox}
  \begin{center}
    $\phi = \dfrac{\text{Volume occupied by atoms in unit cell}}{\text{Total volume of unit cell}}$
  \end{center}

  \subsubsection{FCC (Face-centered cubic)}
  \begin{center}
    \includegraphics[width=.4\linewidth]{media/fcc.png}\\[1.5ex]
    \begin{itemize}
      \item Packing efficiency:\\
        $\phi \approx 74\%$
      \item Many slip systems (12)
      \item Closest pack direction
    \end{itemize}

    \subsubsection{BCC (Body-centered cubic)}
    \includegraphics[width=.4\linewidth]{media/bcc.png}\\[1.5ex]
    \begin{itemize}
      \item Packing efficiency:\\
        $\phi \approx 68\%$
      \item Many slip systems (6)
      \item Not closest pack direction
      \item Cottrell atmosphere
    \end{itemize}
  \end{center}
\end{theorybox}

\vfill
\phantom{}
\columnbreak

\begin{theorybox}
  \subsubsection{HCP (Hexagonal close-packed)}
  \begin{center}
    \includegraphics[width=.4\linewidth]{media/hcp.png}\\[1.5ex]
    \begin{itemize}
      \item Packing efficiency:\\
        $\phi \approx 74\%$
      \item Very few slip systems (3)
      \item Closest pack direction
    \end{itemize}
  \end{center}
\end{theorybox}

\subsection{Structural odel of ceramics}
\begin{itemize}
  \item Ionic bonding, complex crystal structures (ceramics), amorphous (glasses)
  \item Brittle, but high chemical and thermal resistance
  \item Insulators
  \item Wear-resistant (e.g. ferro-/piezoelectricity)
\end{itemize}

\subsection{Amorphous and crystalline materials}
\begin{center}
  \includegraphics[width=\linewidth]{media/mono-poly-amorph.png}
\end{center}
\begin{theorybox}
  \subsubsection{Amorpohus materials}
  \begin{itemize}
    \item No crystal lattice (e.g. quartz glass, polymers)
    \item Atomic distances defined by chemical bonds
    \item Bond angles are variable
  \end{itemize}

  \subsubsection{Crystalline materials}
  \begin{itemize}
    \item Crystal lattice (e.g. metals, ceramics, quartz)
    \item Atomic distances and bonding angles are defined
  \end{itemize}
\end{theorybox}

\vfill
\phantom{}
\end{multicols}

\newpage
\begin{multicols}{2}
\setlength{\columnsep}{1pt}

\subsection{Directionals depenence}
\begin{theorybox}
  \subsubsection{Anisotropy and Isotropy}
  \textbf{Anisotropic}:\\
  properties depend on the direction

  \textbf{Isotropic}:\\
  properties do not depend on direction

  \textbf{Quasi-isotropic}:\\
  properties microscopically depend on the direction but not macroscopically
\end{theorybox}

\subsubsection{Miller indices for crystal directions}
\begin{center}
  \includegraphics[width=.7\linewidth]{media/miller.png}
\end{center}



\vfill
\phantom{}
\end{multicols}

\end{document}