\Part[
    \eng{Condensed matter physics}
    \ger{Festkörperphysik}
    ]{cm}
    \TODO{Bonds, hybridized orbitals, tight binding}
\Section[
    \eng{Bravais lattice}
    \ger{Bravais-Gitter}
    ]{bravais}

    % \begin{ttext}
    %     \eng{

    %     }
    %     \ger{

    %     }
    % \end{ttext}

    \eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
    \ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}

    \eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
    \ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}

    \Eng[lattice_system]{Lattice system}
    \Ger[lattice_system]{Gittersystem}
    \Eng[crystal_family]{Crystal system}
    \Ger[crystal_family]{Kristall-system}
    \Eng[point_group]{Point group}
    \Ger[point_group]{Punktgruppe}
    \eng[bravais_lattices]{Bravais lattices}
    \ger[bravais_lattices]{Bravais Gitter}

    \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
    \renewcommand\tabularxcolumn[1]{m{#1}}
    \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
    \begin{table}[H]
        \centering
        \caption{\gt{bravais_table2}}
        \label{tab:bravais2}
    
        \begin{adjustbox}{width=\textwidth}
        \begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
            \hline
            \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
                                                 & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
            \GT{monoclinic} (m) & $\text{C}_\text{2}$   & \bvimg{mp} & \\ \hline
            \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
            \GT{tetragonal} (t) & $\text{D}_\text{4}$   & \bvimg{tp} & \\ \hline
            \GT{hexagonal} (h) & $\text{D}_\text{6}$    & \bvimg{hp} & \\ \hline
        \end{tabularx}
        \end{adjustbox}
    \end{table}
    


    \begin{table}[H]
        \centering
        \caption{\gt{bravais_table3}}
        \label{tab:bravais3}
    
        % \newcolumntype{g}{>{\columncolor[]{0.8}}}
        \begin{adjustbox}{width=\textwidth}
            % \begin{tabularx}{\textwidth}{|c|}
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            % \end{tabularx}
            % \begin{tabular}{|c|}
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            % \end{tabular}
            % \\
        \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
            \hline
            \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
                                                 & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
            \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP}  &  &  &  \\  \hline
            \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS}  &  &  \\ \hline
            \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
            \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} &  & \bvimg{tI} & \\ \hline
            \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} &  &  & \\ \cline{2-7}
             & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} &  &  & \\ \hline
            \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} &  & \bvimg{cI} & \bvimg{cF} \\ \hline
        \end{tabularx}
        \end{adjustbox}
    \end{table}
    \TODO{FCC, BCC, diamond/Zincblende wurtzize cell/lattice vectors}
    \TODO{primitive unit cell: contains one lattice point}\\

family of plane that are equivalent due to crystal symmetry
    \begin{formula}{miller}
        \desc{Miller index}{}{}
        \desc[german]{Millersche Indizes}{}{}
        \eq{
            (hkl) & \text{\GT{plane}}\\
            [hkl] & \text{\GT{direction}}\\
            \{hkl\} & \text{\GT{millerFamily}}
        }
    \end{formula}
    

\Section[
    \eng{Reciprocal lattice}
    \ger{Reziprokes Gitter}
    ]{reci}
    \begin{ttext}
        \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
        \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
    \end{ttext}

    \begin{formula}{vectors}
        \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
        \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
        \eq{
            \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
            \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
            \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
        }
    \end{formula}

    \Subsection[
        \eng{Scattering processes}
        \ger{Streuprozesse}
        ]{scatter}
        \begin{formula}{matthiessen}
            \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{$\mu$ mobility, $\tau$ scattering time}
            \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{$\mu$ Moblitiät, $\tau$ Streuzeit}
            \eq{
                \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
                \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
            }
        \end{formula}
    

\Section[
    \eng{Free electron gas}
    \ger{Freies Elektronengase}
]{free_e_gas}
    \begin{ttext}
        \eng{Assumptions: electrons can move freely and independent of each other.}
        \ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.}
    \end{ttext}

    \begin{formula}{drift_velocity}
        \desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity}
        \desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit}
        \eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}}
    \end{formula}

    \begin{formula}{mean_free_time}
        \desc{Mean free time}{}{}
        \desc[german]{Streuzeit}{}{}
        \eq{\tau}
    \end{formula}

    \begin{formula}{mean_free_path}
        \desc{Mean free path}{}{}
        \desc[german]{Mittlere freie Weglänge}{}{}
        \eq{\ell = \braket{v} \tau}
    \end{formula}

    \begin{formula}{mobility}
        \desc{Electrical mobility}{}{$q$ charge, $m$ mass}
        \desc[german]{Beweglichkeit}{}{$q$ Ladung, $m$ Masse}
        \eq{\mu = \frac{q \tau}{m}}
    \end{formula}

    \Subsection[
        \eng{2D electron gas}
        \ger{2D Elektronengas}
        ]{2deg}

        \begin{ttext}
            \eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
            \ger{
                Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird.
            }
        \end{ttext}
        \begin{formula}{confinement_energy}
            \desc{Confinement energy}{Raises ground state energy}{}
            \desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{}
            \eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}}
        \end{formula}

        \Eng[plain_wave]{plain wave}
        \Ger[plain_wave]{ebene Welle}
        \begin{formula}{energy}
            \desc{Energy}{}{}
            \desc[german]{Energie}{}{}
            \eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}}
        \end{formula}

    \Subsection[
        \eng{1D electron gas / quantum wire}
        \ger{1D Eleltronengas / Quantendraht}
        ]{1deg}

        \begin{formula}{energy}
            \desc{Energy}{}{}
            \desc[german]{Energie}{}{}
            \eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2}
        \end{formula}
        
    \Subsection[
        \eng{0D electron gas / quantum dot}
        \ger{0D Elektronengase / Quantenpunkt}
        ]{0deg}

        \TODO{TODO}


\Section[
    \eng{\GT{misc}}
    \ger{\GT{misc}}
]{misc}

