diff --git a/scripts/ch_elchem.py b/scripts/ch_elchem.py
index 6e9ff5d..8b9c07f 100644
--- a/scripts/ch_elchem.py
+++ b/scripts/ch_elchem.py
@@ -1,47 +1,80 @@
 #!/usr/bin env python3
-from formulasheet import *
+from formulary import *
 from scipy.constants import gas_constant, Avogadro, elementary_charge
 
 Faraday = Avogadro * elementary_charge
 
 @np.vectorize
-def fbutler_volmer_left(ac, z, eta, T):
+def fbutler_volmer_anode(ac, z, eta, T):
     return np.exp((1-ac)*z*Faraday*eta/(gas_constant*T))
 
 @np.vectorize
-def fbutler_volmer_right(ac, z, eta, T):
+def fbutler_volmer_cathode(ac, z, eta, T):
     return -np.exp(-ac*z*Faraday*eta/(gas_constant*T))
 
 def fbutler_volmer(ac, z, eta, T):
-    return fbutler_volmer_left(ac, z, eta, T) + fbutler_volmer_right(ac, z, eta, T)
+    return fbutler_volmer_anode(ac, z, eta, T) + fbutler_volmer_cathode(ac, z, eta, T)
 
 def butler_volmer():
     fig, ax = plt.subplots(figsize=size_half_third)
-    ax.set_xlabel("$\\eta$")
-    ax.set_ylabel("$i/i_0$")
+    ax.set_xlabel("$\\eta$ [V]")
+    ax.set_ylabel("$j/j_0$")
     etas = np.linspace(-0.1, 0.1, 400)
     T = 300
     z = 1.0
     # other a
-    alpha2, alpha3 = 0.2, 0.8
+    ac2, ac3 = 0.2, 0.8
     i2 = fbutler_volmer(0.2, z, etas, T)
     i3 = fbutler_volmer(0.8, z, etas, T)
-    ax.plot(etas, i2, color="blue", linestyle="dashed", label=f"$\\alpha={alpha2}$")
-    ax.plot(etas, i3, color="green", linestyle="dashed", label=f"$\\alpha={alpha3}$")
+    ax.plot(etas, i2, color="blue", linestyle="dashed", label=f"$\\alpha_\\text{{C}}={ac2}$")
+    ax.plot(etas, i3, color="green", linestyle="dashed", label=f"$\\alpha_\\text{{C}}={ac3}$")
     # 0.5
     ac = 0.5
-    irel_left = fbutler_volmer_left(ac, z, etas, T)
-    irel_right = fbutler_volmer_right(ac, z, etas, T)
-    ax.plot(etas, irel_left,  color="gray")
-    ax.plot(etas, irel_right, color="gray")
-    ax.plot(etas, irel_right + irel_left, color="black", label=f"$\\alpha=0.5$")
+    irel_anode = fbutler_volmer_anode(ac, z, etas, T)
+    irel_cathode = fbutler_volmer_cathode(ac, z, etas, T)
+    ax.plot(etas, irel_anode,  color="gray")
+    ax.plot(etas, irel_cathode, color="gray")
+    ax.plot(etas, irel_cathode + irel_anode, color="black", label=f"$\\alpha_\\text{{C}}=0.5$")
     ax.grid()
     ax.legend()
     ylim = 6
     ax.set_ylim(-ylim, ylim)
     return fig
 
+@np.vectorize
+def ftafel_anode(ac, z, eta, T):
+    return 10**((1-ac)*z*Faraday*eta/(gas_constant*T*np.log(10)))
+
+@np.vectorize
+def ftafel_cathode(ac, z, eta, T):
+    return -10**(-ac*z*Faraday*eta/(gas_constant*T*np.log(10)))
+
+def tafel():
+    i0 = 1
+    ac = 0.2
+    z = 1
+    T = 300
+    eta_max = 0.2
+    etas = np.linspace(-eta_max, eta_max, 400)
+    i = np.abs(fbutler_volmer(ac, z, etas ,T))
+    iright = i0 * np.abs(ftafel_cathode(ac, z, etas, T))
+    ileft = i0 * ftafel_anode(ac, z, etas, T)
+
+    fig, ax = plt.subplots(figsize=size_half_third)
+    ax.set_xlabel("$\\eta$ [V]")
+    ax.set_ylabel("$\\log_{10}\\left(\\frac{|j|}{j_0}\\right)$")
+    # ax.set_ylabel("$\\log_{10}\\left(|j|/j_0\\right)$")
+    ax.set_yscale("log")
+    # ax.plot(etas, linear, label="Tafel slope")
+    ax.plot(etas[etas >= 0], ileft[etas >= 0],  linestyle="dashed", color="gray", label="Tafel Approximation")
+    ax.plot(etas[etas <= 0], iright[etas <= 0], linestyle="dashed", color="gray")
+    ax.plot(etas, i, label=f"Butler-Volmer $\\alpha_\\text{{C}}={ac:.1f}$")
+    ax.legend()
+    ax.grid()
+    return fig
+
 if __name__ == '__main__':
     export(butler_volmer(), "ch_butler_volmer")
+    export(tafel(), "ch_tafel")
 
 
diff --git a/scripts/cm_phonons.py b/scripts/cm_phonons.py
index 7219a63..5d6487a 100644
--- a/scripts/cm_phonons.py
+++ b/scripts/cm_phonons.py
@@ -1,5 +1,5 @@
 #!/usr/bin env python3
-from formulasheet import *
+from formulary import *
 
 def fone_atom_basis(q, a, M, C1, C2):
     return np.sqrt(4*C1/M * (np.sin(q*a/2)**2 + C2/C1 * np.sin(q*a)**2))
diff --git a/scripts/distributions.py b/scripts/distributions.py
index 2164dcb..3e49df3 100644
--- a/scripts/distributions.py
+++ b/scripts/distributions.py
@@ -1,5 +1,5 @@
 from numpy import fmax
-from formulasheet import *
+from formulary import *
 import itertools
 
 
diff --git a/scripts/formulasheet.py b/scripts/formulasheet.py
deleted file mode 100644
index c6be793..0000000
--- a/scripts/formulasheet.py
+++ /dev/null
@@ -1,71 +0,0 @@
-#!/usr/bin env python3
-import os
-import matplotlib.pyplot as plt
-import numpy as np
-import math
-import scipy as scp
-
-if __name__ == "__main__":  # make relative imports work as described here: https://peps.python.org/pep-0366/#proposed-change
-    if __package__ is None:
-        __package__ = "formulasheet"
-        import sys
-        filepath = os.path.realpath(os.path.abspath(__file__))
-        sys.path.insert(0, os.path.dirname(os.path.dirname(filepath)))
-
-from util.mpl_colorscheme import set_mpl_colorscheme
-import util.colorschemes as cs
-# SET THE COLORSCHEME
-# hard white and black
-# cs.p_gruvbox["fg0"] = "#000000"
-# cs.p_gruvbox["bg0"] = "#ffffff"
-COLORSCHEME = cs.gruvbox_dark()
-# print(COLORSCHEME)
-# COLORSCHEME = cs.GRUVBOX_DARK
-
-tex_src_path = "../src/"
-img_out_dir = os.path.join(tex_src_path, "img")
-filetype = ".pdf"
-skipasserts = False
-
-full = 8
-size_half_half = (full/2, full/2)
-size_third_half = (full/3, full/2)
-size_half_third = (full/2, full/3)
-
-def assert_directory():
-    if not skipasserts:
-        assert os.path.abspath(".").endswith("scripts"), "Please run from the `scripts` directory"
-
-def texvar(var, val, math=True):
-    s = "$" if math else ""
-    s += f"\\{var} = {val}"
-    if math: s += "$"
-    return s
-
-def export(fig, name, notightlayout=False):
-    assert_directory()
-    filename = os.path.join(img_out_dir, name + filetype)
-    if not notightlayout:
-        fig.tight_layout()
-    fig.savefig(filename) #, bbox_inches="tight")
-
-@np.vectorize
-def smooth_step(x: float, left_edge: float, right_edge: float):
-    x = (x - left_edge) / (right_edge - left_edge)
-    if x <= 0: return 0.
-    elif x >= 1: return 1.
-    else: return 3*(x*2) - 2*(x**3)
-
-
-# run even when imported
-set_mpl_colorscheme(COLORSCHEME)
-
-if __name__ == "__main__":
-    assert_directory()
-    s = \
-    """% This file was generated by scripts/formulasheet.py\n% Do not edit it directly, changes will be overwritten\n""" + cs.generate_latex_colorscheme(COLORSCHEME)
-    filename = os.path.join(tex_src_path, "util/colorscheme.tex")
-    print(f"Writing tex colorscheme to {filename}")
-    with open(filename, "w") as file:
-        file.write(s)
-
diff --git a/scripts/qubits.py b/scripts/qubits.py
index e6b2595..9b725e2 100644
--- a/scripts/qubits.py
+++ b/scripts/qubits.py
@@ -1,4 +1,4 @@
-from formulasheet import *
+from formulary import *
 import scqubits as scq
 import qutip as qt
 
diff --git a/scripts/readme.md b/scripts/readme.md
index 4e9571b..bfc5912 100644
--- a/scripts/readme.md
+++ b/scripts/readme.md
@@ -1,9 +1,16 @@
 # Scripts
 Put all scripts that generate plots or tex files here.
+You can run all files at once using `make scripts`
 
 ## Plots
 For plots with `matplotlib`:
-1. import `plot.py` 
+1. import `formulary.py` 
 2. use one of the preset figsizes
 3. save the image using the `export` function in the `if __name__ == '__main__'` part
 
+## Colorscheme
+To ensure a uniform look of the tex source and the python plots, 
+the tex and matplotlib colorschemes are both handled in `formulary.py`.
+Set the `COLORSCHEME` variable to the desired colors.
+Importing `formulary.py`  will automatically apply the colors to matplotlib,
+and running it will generate `util/colorscheme.tex` for LaTeX.
diff --git a/scripts/stat-mech.py b/scripts/stat-mech.py
index 9661d0d..18c1c34 100644
--- a/scripts/stat-mech.py
+++ b/scripts/stat-mech.py
@@ -1,5 +1,5 @@
 #!/usr/bin env python3
-from formulasheet import *
+from formulary import *
 
 def flennard_jones(r, epsilon, sigma):
     return 4 * epsilon * ((sigma/r)**12 - (sigma/r)**6)
diff --git a/scripts/util/colorschemes.py b/scripts/util/colorschemes.py
index fdb6fb1..753a072 100644
--- a/scripts/util/colorschemes.py
+++ b/scripts/util/colorschemes.py
@@ -65,7 +65,7 @@ p_gruvbox = {
     "alt-gray":     "#7c6f64",
 }
 
-def grubox_light():
+def gruvbox_light():
     GRUVBOX_LIGHT = { "fg0": p_gruvbox["fg0-hard"], "bg0": p_gruvbox["bg0-hard"] } \
         | {f"fg{n}": p_gruvbox[f"fg{n}"] for n in range(1,5)} \
         | {f"bg{n}": p_gruvbox[f"bg{n}"] for n in range(1,5)} \
@@ -177,14 +177,3 @@ def stupid():
         | { f"fg-{n}": brightness(c, 2.0) for n,c in p_stupid.items() }
     return LEGACY
 
-# UTILITY
-def color_latex_def(name, color):
-    # name = name.replace("-", "_")
-    color = color.strip("#")
-    return "\\definecolor{" + name + "}{HTML}{" + color + "}"
-
-def generate_latex_colorscheme(palette, variant="light"):
-    s = ""
-    for n, c in palette.items():
-        s += color_latex_def(n, c) + "\n"
-    return s
diff --git a/src/ch/ch.tex b/src/ch/ch.tex
index da2b008..c1fc103 100644
--- a/src/ch/ch.tex
+++ b/src/ch/ch.tex
@@ -7,305 +7,3 @@
     \ger{Periodensystem}
 ]{ptable}
     \drawPeriodicTable
-
-\Section[
-    \eng{Electrochemistry}
-    \ger{Elektrochemie}
-]{el}
-
-    \eng[std_cell]{standard cell potential}
-    \ger[std_cell]{Standardzellpotential}
-    \eng[electrode_pot]{electrode potential}
-    \ger[electrode_pot]{Elektrodenpotential}
-    \begin{formula}{chemical_potential}
-        \desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{gibbs_free_energy}, \QtyRef{amount}}
-        \desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
-        \quantity{\mu}{\joule\per\mol;\joule}{is}
-        \eq{
-            \mu_i \equiv \pdv{G}{n_i}_{n_j\neq n_i,p,T}
-        }
-    \end{formula}
-
-    \begin{formula}{standard_chemical_potential}
-        \desc{Standard chemical potential}{In equilibrium}{\QtyRef{chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}, \QtyRef{activity}}
-        \desc[german]{Standard chemisches Potential}{}{}
-        \eq{\mu_i = \mu_i^\theta + RT \Ln{a_i}}
-    \end{formula}
-
-    \begin{formula}{chemical_equilibrium}
-        \desc{Chemical equilibrium}{}{\QtyRef{chemical_potential}, \QtyRef{stoichiometric_coefficient}}
-        \desc[german]{Chemisches Gleichgewicht}{}{}
-        \eq{\sum_\text{\GT{products}} \nu_i \mu_i = \sum_\text{\GT{educts}} \nu_i \mu_i}
-    \end{formula}
-
-    \begin{formula}{activity}
-        \desc{Activity}{relative activity}{\QtyRef{chemical_potential}, \QtyRef{standard_chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}}
-        \desc[german]{Aktivität}{Relative Aktivität}{}
-        \quantity{a}{}{s}
-        \eq{a_i = \Exp{\frac{\mu_i-\mu_i^\theta}{RT}}}
-    \end{formula}
-
-    \begin{formula}{electrochemical_potential}
-        \desc{Electrochemical potential}{Chemical potential with electrostatic contributions}{\QtyRef{chemical_potential}, $z$ valency (charge), \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvani Potential)}
-        \desc[german]{Elektrochemisches Potential}{Chemisches Potential mit elektrostatischen Enegiebeiträgen}{\QtyRef{chemical_potential}, $z$ Ladungszahl, \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvanisches Potential)}
-        \quantity{\muecp}{\joule\per\mol;\joule}{is}
-        \eq{\muecp_i \equiv \mu_i + z_i F \phi}
-    \end{formula}
-
-    \begin{formula}{nernst_equation}
-        \desc{Nernst equation}{Elektrode potential for a half-cell reaction}{$E$ electrode potential, $E^\theta$ \gt{std_cell}, \ConstRef{universal_gas}, \ConstRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \QtyRef{activity}, \QtyRef{stoichiometric_coefficient}}
-        \desc[german]{Nernst-Gleichung}{Elektrodenpotential für eine Halbzellenreaktion}{}
-        \eq{E = E^\theta + \frac{RT}{zF} \Ln{\frac{ \left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{oxidized}}{\left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{reduced}}}}
-    \end{formula}
-
-    \begin{formula}{cell}
-        \desc{Electrochemical cell}{}{}
-        \desc[german]{Elektrochemische Zelle}{}{}
-        \ttxt{
-            \eng{
-                \begin{itemize}
-                    \item Electrolytic cell: Uses electrical energy to force a chemical reaction
-                    \item Galvanic cell: Produces electrical energy through a chemical reaction
-                \end{itemize}
-            }
-            \ger{
-                \begin{itemize}
-                    \item Elektrolytische Zelle: Nutzt elektrische Energie um eine Reaktion zu erzwingen
-                    \item Galvanische Zelle: Produziert elektrische Energie durch eine chemische Reaktion 
-                \end{itemize}
-            }
-        }
-    \end{formula}
-    \begin{formula}{standard_cell_potential}
-        \desc{Standard cell potential}{}{$\Delta_\txR G^\theta$ standard \qtyRef{gibbs_free_energy} of reaction, $n$ number of electrons, \ConstRef{faraday}}
-        \desc[german]{Standard Zellpotential}{}{$\Delta_\txR G^\theta$ Standard \qtyRef{gibbs_free_energy} der Reaktion, $n$ Anzahl der Elektronen, \ConstRef{faraday}}
-        \eq{E^\theta_\text{rev} = \frac{-\Delta_\txR G^\theta}{nF}}
-    \end{formula}
-
-    \begin{formula}{she}
-        \desc{Standard hydrogen electrode (SHE)}{}{}
-        \desc[german]{Standard Wasserstoffelektrode}{}{}
-        \ttxt{
-            \eng{Defined as reference for measuring half-cell potententials}
-            \ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
-        }
-        $a_{\ce{H+}} =1 \, (\text{pH} = 0)$, $p_{\ce{H2}} = \SI{100}{\kilo\pascal}$
-    \end{formula}
-
-   \eng[galvanic]{galvanic}
-    \ger[galvanic]{galvanisch}
-    \eng[electrolytic]{electrolytic}
-    \ger[electrolytic]{electrolytisch}
-    \begin{formula}{cell_efficiency}
-        \desc{Thermodynamic cell efficiency}{}{$P$ \fqEqRef{ed:el:power}}
-        \desc[german]{Thermodynamische Zelleffizienz}{}{}
-        \eq{
-            \eta_\text{cell} &= \frac{P_\text{obtained}}{P_\text{maximum}} = \frac{E_\text{cell}}{E_\text{cell,rev}} & & \text{\gt{galvanic}} \\
-            \eta_\text{cell} &= \frac{P_\text{minimum}}{P_\text{applied}} = \frac{E_\text{cell,rev}}{E_\text{cell}} & & \text{\gt{electrolytic}}
-        }
-    \end{formula}
-
-    \Subsection[
-        \eng{Ionic conduction in electrolytes}
-        \ger{Ionische Leitung in Elektrolyten}
-    ]{ion_cond}
-        \eng[z]{charge number}
-        \ger[z]{Ladungszahl}
-        \eng[of_i]{of ion $i$}
-        \ger[of_i]{des Ions $i$}
-         
-        \begin{formula}{diffusion}
-            \desc{Diffusion}{caused by concentration gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{diffusion_constant} \gt{of_i}, \QtyRef{concentration} \gt{of_i}}
-            \desc[german]{Diffusion}{durch Konzentrationsgradienten}{}
-            \eq{ i_\text{diff} = \sum_i -z_i F D_i \left(\odv{c_i}{x}\right) }
-        \end{formula}
-
-        \begin{formula}{migration}
-            \desc{Migration}{caused by potential gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ potential gradient in the solution}
-            \desc[german]{Migration}{durch Potentialgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ Potentialgradient in der Lösung}
-            \eq{ i_\text{mig} = \sum_i -z_i^2 F^2 \, c_i \, \mu_i \, \nabla\Phi_\txs }
-        \end{formula}
-
-        \begin{formula}{convection}
-            \desc{Convection}{caused by pressure gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} in flowing electrolyte}
-            \desc[german]{Convection}{durch Druckgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} im fliessenden Elektrolyt}
-            \eq{ i_\text{conv} = \sum_i -z_i F \, c_i \, v_i^\text{flow} }
-        \end{formula}
-
-        \begin{formula}{ionic_conductivity}
-            \desc{Ionic conductivity}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ charge number, \qtyRef{concentration} and \qtyRef{mobility} of the positive (+) and negative (-) ions}
-            \desc[german]{Ionische Leitfähigkeit}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ Ladungszahl, \qtyRef{concentration} und \qtyRef{mobility} der positiv (+) und negativ geladenen Ionen}
-            \quantity{\kappa}{\per\ohm\cm=\siemens\per\cm}{}
-            \eq{\kappa = F^2 \left(z_+^2 \, c_+  \, \mu_+ + z_-^2 \, c_- \, \mu_-\right)}
-        \end{formula}
-
-        \begin{formula}{ionic_resistance}
-            \desc{Ohmic resistance of ionic current flow}{}{$L$ \qtyRef{length}, $A$ \qtyRef{area}, \QtyRef{ionic_conductivity}}
-            \desc[german]{Ohmscher Widerstand für Ionen-Strom}{}{}
-            \eq{R_\Omega = \frac{L}{A\,\kappa}}
-        \end{formula}
-
-        \begin{formula}{ionic_mobility}
-            \desc{Ionic  mobility}{}{$v_\pm$ steady state drift \qtyRef{velocity}, $\phi$ \qtyRef{electric_scalar_potential}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{charge}, \QtyRef{viscosity}, $r_\pm$ ion radius}
-            \desc[german]{Ionische Moblilität}{}{}
-            \quantity{u_\pm}{\cm^2\mol\per\joule\s}{}
-            % \eq{u_\pm = - \frac{v_\pm}{\nabla \phi \,z_\pm F} = \frac{e}{6\pi F \eta_\text{dyn} \r_\pm}}
-        \end{formula}
-
-        \begin{formula}{transference}
-            \desc{Transference number}{Ion transport number \\Fraction of the current carried by positive / negative ions}{$i_{+/-}$ current through positive/negative charges}
-            \desc[german]{Überführungszahl}{Anteil der positiv / negativ geladenen Ionen am Gesamtstrom}{$i_{+/-}$ Strom durch positive / negative Ladungn}
-            \eq{t_{+/-} = \frac{i_{+/-}}{i_+ + i_-}}
-        \end{formula}
-
-        \eng[csalt]{electrolyte \qtyRef{concentration}}
-        \eng[csalt]{\qtyRef{concentration} des Elektrolyts}
-        \begin{formula}{molar_conductivity}
-            \desc{Molar conductivity}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{csalt}}
-            \desc[german]{Molare Leitfähigkeit}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{salt}}
-            \quantity{\Lambda_\txM}{\siemens\cm^2\per\mol=\ampere\cm^2\per\volt\mol}{ievs}
-            \eq{\Lambda_\txM = \frac{\kappa}{c_\text{salt}}}
-        \end{formula}
-
-        \begin{formula}{kohlrausch_law}
-            \desc{Kohlrausch's law}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} at infinite dilution, $c_\text{salt}$ \gt{csalt}, $K$ \GT{constant}}
-            \desc[german]{}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} bei unendlicher Verdünnung, $\text{salt}$ \gt{csalt} $K$ \GT{constant}}
-            \eq{\Lambda_\txM = \Lambda_\txM^0 - K \sqrt{c_\text{salt}}}
-        \end{formula}
-        
-    % Electrolyte conductivity
-        \begin{formula}{molality}
-            \desc{Molality}{}{\QtyRef{amount} of the solute, \QtyRef{mass} of the solvent}
-            \desc[german]{Molalität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{mass} des Lösungsmittels}
-            \quantity{b}{\mol\per\kg}{}
-            \eq{b = \frac{n}{m}}
-        \end{formula}
-
-        \begin{formula}{molarity}
-            \desc{Molarity}{\GT{see} \qtyRef{concentration}}{\QtyRef{amount} of the solute, \QtyRef{volume} of the solvent}
-            \desc[german]{Molarität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{volume} des Lösungsmittels}
-            \quantity{c}{\mol\per\litre}{}
-            \eq{c = \frac{n}{V}}
-        \end{formula}
-
-        \begin{formula}{ionic_strength}
-            \desc{Ionic strength}{Measure of the electric field in a solution through solved ions}{\QtyRef{molality}, \QtyRef{molarity}, $z$ \qtyRef{charge_number}}
-            \desc[german]{Ionenstärke}{Maß eienr Lösung für die elektrische Feldstärke durch gelöste Ionen}{}
-            \quantity{I}{\mol\per\kg;\mol\per\litre}{}
-            \eq{I_b &= \frac{1}{2} \sum_i b_i z_i^2 \\ I_c &= \frac{1}{2} \sum_i c_i z_i^2}
-        \end{formula}
-
-        \begin{formula}{debye_screening_length}
-            \desc{Debye screening length}{}{\ConstRef{avogadro}, \ConstRef{charge}, \QtyRef{ionic_strength}, \QtyRef{permittivity}, \ConstRef{boltzmann}, \QtyRef{temperature}}
-            \desc[german]{Debye-Länge / Abschirmlänge}{}{}
-            \eq{\lambda_\txD = \sqrt{\frac{\epsilon \kB T}{2\NA e^2 I_C}}}
-        \end{formula}
-
-        \begin{formula}{mean_ionic_activity}
-            \desc{Mean ionic activity coefficient}{Accounts for decreased reactivity because ions must divest themselves of their ion cloud before reacting}{}
-            \desc[german]{Mittlerer ionischer Aktivitätskoeffizient}{Berücksichtigt dass Ionen sich erst von ihrer Ionenwolke lösen müssen, bevor sie reagieren können}{}
-            \quantity{\gamma}{}{s}
-            \eq{\gamma_\pm = \left(\gamma_+^{\nu_+} \, \gamma_-^{\nu_-}\right)^{\frac{1}{\nu_+ + \nu_-}}}
-        \end{formula}
-
-        \begin{formula}{debye_hueckel_law}
-            \desc{Debye-Hückel limiting law}{For an infinitely dilute solution}{\QtyRef{mean_ionic_activity}, $A$ solvent dependant constant, $z$ \qtyRef{charge_number}, \QtyRef{ionic_strength} in [\si{\mol\per\kg}]}
-            \desc[german]{Debye-Hückel Gesetz}{Für eine unendlich verdünnte Lösung}{}
-            \eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
-        \end{formula} 
-
-    \Subsection[
-        \eng{Kinetics}
-        \ger{Kinetik}
-        ]{kin}
-        \begin{formula}{overpotential}
-            \desc{Overpotential}{}{$E_\text{electrode}$ potential at which the reaction starts $E_\text{ref}$ thermodynamic potential of the reaction}
-            \desc[german]{Überspannung}{}{$E_\text{electrode}$ Potential bei der die Reaktion beginnt, $E_\text{ref}$ thermodynamisches Potential der Reaktion}
-            \eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
-        \end{formula}
-
-        \begin{formula}{activation_overpotential}
-            \desc{Activation overpotential}{}{}
-            \desc[german]{Aktivierungsüberspannung}{}{}
-            \eq{}
-        \end{formula}
-
-        \begin{formula}{concentration_overpotential}
-            \desc{Concentration overpotential}{}{}
-            \desc[german]{Konzentrationsüberspannung}{}{}
-            \eq{\eta_\text{conc} = -\frac{RT}{(1-\alpha) nF} \ln \left(\frac{c_\text{ox}^0}{c_\text{ox}^\txS}\right)} 
-        \end{formula}
-
-        \begin{formula}{diffusion_overpotential}
-            \desc{Diffusionoverpotential}{}{}
-            \desc[german]{Diffusionsüberspannung}{}{}
-            \eq{}
-        \end{formula}
-        \begin{formula}{roughness_factor}
-            \desc{Roughness factor}{Surface area related to electrode geometry}{}
-            \eq{\rfactor}
-        \end{formula}   
-
-        \begin{formula}{butler_volmer}
-            \desc{Butler-Volmer equation}{Reaction kinetics near the equilibrium potentential}
-            {$j$ \qtyRef{current_density}, $j_0$ exchange current density, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txc/\txa}$ cathodic/anodic charge transfer coefficient}
-            %Current through an electrode iof a unimolecular redox reaction with both anodic and cathodic reaction occuring on the same electrode
-            \desc[german]{Butler-Volmer-Gleichung}{Reaktionskinetik in der Nähe des Gleichgewichtspotentials}
-            {$j$ \qtyRef{current_density}, $j_0$ Austauschstromdichte, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txc/\txa}$ Ladungstransferkoeffizient an der Kathode/Anode}
-            \begin{gather}
-                j = j_0 \,\rfactor\, \left[ \Exp{\frac{(1-a_\txc) z F \eta}{RT}} - \Exp{-\frac{\alpha_\txc z F \eta}{RT}}\right]
-                \intertext{\GT{with}}
-                \alpha_\txa = 1 - \alpha_\txc
-            \end{gather}
-            \separateEntries
-            \fig{img/ch_butler_volmer.pdf}
-        \end{formula}
-        
-
-
-\Section[
-    \eng{misc}
-    \ger{misc}
-]{misc}
-    \begin{formula}{std_condition}
-        \desc{Standard temperature and pressure}{}{}
-        \desc[german]{Standardbedingungen}{}{}
-        \eq{
-            T &= \SI{273.15}{\kelvin} = \SI{0}{\celsius} \\
-            p &= \SI{100000}{\pascal} = \SI{1.000}{\bar}
-        }
-    \end{formula}
-    \begin{formula}{ph}
-        \desc{pH definition}{}{$a_{\ce{H+}}$ hyrdrogen ion \qtyRef{activity}}
-        \desc[german]{pH-Wert definition}{}{$a_{\ce{H+}}$ Wasserstoffionen-\qtyRef{activity}}
-        \eq{\pH = -\log_{10}(a_{\ce{H+}})}
-    \end{formula}
-
-    \begin{formula}{ph_rt}
-        \desc{pH}{At room temperature \SI{25}{\celsius}}{}
-        \desc[german]{pH-Wert}{Bei Raumtemperatur \SI{25}{\celsius}}{}
-        \eq{
-            \pH > 7 &\quad\tGT{basic} \\
-            \pH < 7 &\quad\tGT{acidic} \\
-            \pH = 7 &\quad\tGT{neutral}
-        }
-    \end{formula}
-
-    \begin{formula}{covalent_bond}
-        \desc{Covalent bond}{}{}
-        \desc[german]{Kolvalente Bindung}{}{}
-        \ttxt{
-            \eng{Bonds that involve sharing of electrons to form electron pairs between atoms.}
-            \ger{Bindungen zwischen Atomen die durch geteilte Elektronen, welche Elektronenpaare bilden, gebildet werden.}
-        }
-    \end{formula}
-
-    \begin{formula}{grotthuss}
-        \desc{Grotthuß-mechanism}{}{}
-        \desc[german]{Grotthuß-Mechanismus}{}{}
-        \ttxt{
-            \eng{The mobility of protons in aqueous solutions is much higher than that of other ions because they can "move" by breaking and reforming covalent bonds of water molecules.}
-            \ger{The Moblilität von Protononen in wässrigen Lösungen ist wesentlich größer als die anderer Ionen, da sie sich "bewegen" können indem die Wassertsoffbrückenbindungen gelöst und neu gebildet werden.}
-        }
-    \end{formula}
-
diff --git a/src/ch/el.tex b/src/ch/el.tex
new file mode 100644
index 0000000..eb988a8
--- /dev/null
+++ b/src/ch/el.tex
@@ -0,0 +1,511 @@
+\Section[
+    \eng{Electrochemistry}
+    \ger{Elektrochemie}
+]{el}
+\begin{formula}{chemical_potential}
+    \desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{gibbs_free_energy}, \QtyRef{amount}}
+    \desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
+    \quantity{\mu}{\joule\per\mol;\joule}{is}
+    \eq{
+        \mu_i \equiv \pdv{G}{n_i}_{n_j\neq n_i,p,T}
+    }
+\end{formula}
+
+\begin{formula}{standard_chemical_potential}
+    \desc{Standard chemical potential}{In equilibrium}{\QtyRef{chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}, \QtyRef{activity}}
+    \desc[german]{Standard chemisches Potential}{}{}
+    \eq{\mu_i = \mu_i^\theta + RT \Ln{a_i}}
+\end{formula}
+
+\begin{formula}{chemical_equilibrium}
+    \desc{Chemical equilibrium}{}{\QtyRef{chemical_potential}, \QtyRef{stoichiometric_coefficient}}
+    \desc[german]{Chemisches Gleichgewicht}{}{}
+    \eq{\sum_\text{\GT{products}} \nu_i \mu_i = \sum_\text{\GT{educts}} \nu_i \mu_i}
+\end{formula}
+
+\begin{formula}{activity}
+    \desc{Activity}{relative activity}{\QtyRef{chemical_potential}, \QtyRef{standard_chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}}
+    \desc[german]{Aktivität}{Relative Aktivität}{}
+    \quantity{a}{}{s}
+    \eq{a_i = \Exp{\frac{\mu_i-\mu_i^\theta}{RT}}}
+\end{formula}
+
+\begin{formula}{electrochemical_potential}
+    \desc{Electrochemical potential}{Chemical potential with electrostatic contributions}{\QtyRef{chemical_potential}, $z$ valency (charge), \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvani Potential)}
+    \desc[german]{Elektrochemisches Potential}{Chemisches Potential mit elektrostatischen Enegiebeiträgen}{\QtyRef{chemical_potential}, $z$ Ladungszahl, \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvanisches Potential)}
+    \quantity{\muecp}{\joule\per\mol;\joule}{is}
+    \eq{\muecp_i \equiv \mu_i + z_i F \phi}
+\end{formula}
+
+
+\Subsection[
+    \eng{Electrochemical cell}
+    \ger{Elektrochemische Zelle}
+]{cell}
+    \eng[galvanic]{galvanic}
+    \ger[galvanic]{galvanisch}
+    \eng[electrolytic]{electrolytic}
+    \ger[electrolytic]{electrolytisch}
+
+    \begin{formula}{schematic}
+        \desc{Schematic}{}{}
+        \desc[german]{Aufbau}{}{}
+        \begin{tikzpicture}
+            \pgfmathsetmacro{\width}{3}
+            \pgfmathsetmacro{\height}{4}
+            \pgfmathsetmacro{\elWidth}{\width/9}
+
+            \draw[thick] (0,0) rectangle (\width,\height);
+            \fill[bg-blue] (-2,-2) rectangle (2,0.5);
+
+            % Electrodes
+            \draw[thick, red] (-1,2) -- (-1,-1.2); % Reference electrode
+            \draw[thick, green] (0,2) -- (0,-1); % Counter electrode
+            \draw[thick, gray] (1,2) -- (1,-1.5); % Working electrode
+
+            % Labels
+            \node[left] at (-1,0) {Reference electrode};
+            \node[left] at (0,-0.5) {Counter electrode};
+            \node[right] at (1,-1) {Working electrode};
+            \node[left] at (-2,-1.5) {Electrolyte};
+
+            % Potentiostat
+            \draw[thick] (-2.5,3) rectangle (2.5,4);
+            \node at (0,3.5) {Potentiostat};
+
+            % Wires
+            \draw[thick] (-1,2) -- (-1,3);
+            \draw[thick] (0,2) -- (0,3);
+            \draw[thick] (1,2) -- (1,3);
+
+            % Ammeter and Voltmeter
+            \draw[thick] (-1,2) to[ammeter] (-1,3);
+            \draw[thick] (0,2) -- (0,3);
+            \draw[thick] (1,2) to[voltmeter] (1,3);
+
+        % Connecting to potentiostat
+        \draw[thick] (-1,3.8) -- (-1,4);
+        \draw[thick] (1,3.8) -- (1,4);
+    \end{tikzpicture}
+    \end{formula}
+
+    \begin{formula}{cell}
+        \desc{Electrochemical cell types}{}{}
+        \desc[german]{Arten der Elektrochemische Zelle}{}{}
+        \ttxt{
+            \eng{
+                \begin{itemize}
+                    \item Electrolytic cell: Uses electrical energy to force a chemical reaction
+                    \item Galvanic cell: Produces electrical energy through a chemical reaction
+                \end{itemize}
+            }
+            \ger{
+                \begin{itemize}
+                    \item Elektrolytische Zelle: Nutzt elektrische Energie um eine Reaktion zu erzwingen
+                    \item Galvanische Zelle: Produziert elektrische Energie durch eine chemische Reaktion 
+                \end{itemize}
+            }
+        }
+    \end{formula}
+
+    % todo group together
+    \begin{formula}{faradaic}
+        \desc{Faradaic process}{}{}
+        \desc[german]{Faradäischer Prozess}{}{}
+        \ttxt{
+            \eng{Charge transfers between the electrode bulk and the electrolyte.}
+            \ger{Ladung wird zwischen Elektrode und dem Elektrolyten transferiert.}
+        }
+    \end{formula}
+    \begin{formula}{non-faradaic}
+        \desc{Non-Faradaic (capacitive) process}{}{}
+        \desc[german]{Nicht-Faradäischer (kapazitiver) Prozess}{}{}
+        \ttxt{
+            \eng{Charge is stored at the electrode-electrolyte interface.}
+            \ger{Ladung lagert sich am Elektrode-Elektrolyt Interface an.}
+        }
+    \end{formula}
+
+
+    \begin{formula}{electrode_potential}
+        \desc{Electrode potential}{}{}
+        \desc[german]{Elektrodenpotential}{}{}
+        \quantity{E}{\volt}{s}
+    \end{formula}
+
+    \begin{formula}{standard_cell_potential}
+        \desc{Standard cell potential}{}{$\Delta_\txR G^\theta$ standard \qtyRef{gibbs_free_energy} of reaction, $n$ number of electrons, \ConstRef{faraday}}
+        \desc[german]{Standard Zellpotential}{}{$\Delta_\txR G^\theta$ Standard \qtyRef{gibbs_free_energy} der Reaktion, $n$ Anzahl der Elektronen, \ConstRef{faraday}}
+        \eq{E^\theta_\text{rev} = \frac{-\Delta_\txR G^\theta}{nF}}
+    \end{formula}
+
+
+    \begin{formula}{nernst_equation}
+        \desc{Nernst equation}{Electrode potential for a half-cell reaction}{\QtyRef{electrode_potential}, $E^\theta$ \secEqRef{standard_cell_potential}, \ConstRef{universal_gas}, \ConstRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \QtyRef{activity}, \QtyRef{stoichiometric_coefficient}}
+        \desc[german]{Nernst-Gleichung}{Elektrodenpotential für eine Halbzellenreaktion}{}
+        \eq{E = E^\theta + \frac{RT}{zF} \Ln{\frac{ \left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{oxidized}}{\left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{reduced}}}}
+    \end{formula}
+
+    \begin{formula}{cell_efficiency}
+        \desc{Thermodynamic cell efficiency}{}{$P$ \fqEqRef{ed:el:power}}
+        \desc[german]{Thermodynamische Zelleffizienz}{}{}
+        \eq{
+            \eta_\text{cell} &= \frac{P_\text{obtained}}{P_\text{maximum}} = \frac{E_\text{cell}}{E_\text{cell,rev}} & & \text{\gt{galvanic}} \\
+            \eta_\text{cell} &= \frac{P_\text{minimum}}{P_\text{applied}} = \frac{E_\text{cell,rev}}{E_\text{cell}} & & \text{\gt{electrolytic}}
+        }
+    \end{formula}
+
+
+\Subsection[
+    \eng{Ionic conduction in electrolytes}
+    \ger{Ionische Leitung in Elektrolyten}
+]{ion_cond}
+    \eng[z]{charge number}
+    \ger[z]{Ladungszahl}
+    \eng[of_i]{of ion $i$}
+    \ger[of_i]{des Ions $i$}
+     
+    \begin{formula}{diffusion}
+        \desc{Diffusion}{caused by concentration gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{diffusion_constant} \gt{of_i}, \QtyRef{concentration} \gt{of_i}}
+        \desc[german]{Diffusion}{durch Konzentrationsgradienten}{}
+        \eq{ i_\text{diff} = \sum_i -z_i F D_i \left(\odv{c_i}{x}\right) }
+    \end{formula}
+
+    \begin{formula}{migration}
+        \desc{Migration}{caused by potential gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ potential gradient in the solution}
+        \desc[german]{Migration}{durch Potentialgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ Potentialgradient in der Lösung}
+        \eq{ i_\text{mig} = \sum_i -z_i^2 F^2 \, c_i \, \mu_i \, \nabla\Phi_\txs }
+    \end{formula}
+
+    \begin{formula}{convection}
+        \desc{Convection}{caused by pressure gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} in flowing electrolyte}
+        \desc[german]{Convection}{durch Druckgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} im fliessenden Elektrolyt}
+        \eq{ i_\text{conv} = \sum_i -z_i F \, c_i \, v_i^\text{flow} }
+    \end{formula}
+
+    \begin{formula}{ionic_conductivity}
+        \desc{Ionic conductivity}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ charge number, \qtyRef{concentration} and \qtyRef{mobility} of the positive (+) and negative (-) ions}
+        \desc[german]{Ionische Leitfähigkeit}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ Ladungszahl, \qtyRef{concentration} und \qtyRef{mobility} der positiv (+) und negativ geladenen Ionen}
+        \quantity{\kappa}{\per\ohm\cm=\siemens\per\cm}{}
+        \eq{\kappa = F^2 \left(z_+^2 \, c_+  \, \mu_+ + z_-^2 \, c_- \, \mu_-\right)}
+    \end{formula}
+
+    \begin{formula}{ionic_resistance}
+        \desc{Ohmic resistance of ionic current flow}{}{$L$ \qtyRef{length}, $A$ \qtyRef{area}, \QtyRef{ionic_conductivity}}
+        \desc[german]{Ohmscher Widerstand für Ionen-Strom}{}{}
+        \eq{R_\Omega = \frac{L}{A\,\kappa}}
+    \end{formula}
+
+    \begin{formula}{ionic_mobility}
+        \desc{Ionic  mobility}{}{$v_\pm$ steady state drift \qtyRef{velocity}, $\phi$ \qtyRef{electric_scalar_potential}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{charge}, \QtyRef{viscosity}, $r_\pm$ ion radius}
+        \desc[german]{Ionische Moblilität}{}{}
+        \quantity{u_\pm}{\cm^2\mol\per\joule\s}{}
+        \eq{u_\pm = - \frac{v_\pm}{\nabla \phi \,z_\pm F} = \frac{e}{6\pi F \eta_\text{dyn} r_\pm}}
+    \end{formula}
+
+    \begin{formula}{stokes_friction}
+        \desc{Stokes's law}{Frictional force exerted on spherical objects moving in a viscous fluid at low Reynolds numbers}{$r$ particle radius, \QtyRef{viscosity}, $v$ particle \qtyRef{velocity}}
+        \desc[german]{Gesetz von Stokes}{Reibungskraft auf ein sphärisches Objekt in einer Flüssigkeit bei niedriger Reynolds-Zahl}{$r$ Teilchenradius, \QtyRef{viscosity}, $v$ Teilchengeschwindigkeit}
+        \eq{F_\txR = 6\pi\,r \eta v}
+    \end{formula}
+
+    \begin{formula}{transference}
+        \desc{Transference number}{Ion transport number \\Fraction of the current carried by positive / negative ions}{$i_{+/-}$ current through positive/negative charges}
+        \desc[german]{Überführungszahl}{Anteil der positiv / negativ geladenen Ionen am Gesamtstrom}{$i_{+/-}$ Strom durch positive / negative Ladungn}
+        \eq{t_{+/-} = \frac{i_{+/-}}{i_+ + i_-}}
+    \end{formula}
+
+    \eng[csalt]{electrolyte \qtyRef{concentration}}
+    \eng[csalt]{\qtyRef{concentration} des Elektrolyts}
+    \begin{formula}{molar_conductivity}
+        \desc{Molar conductivity}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{csalt}}
+        \desc[german]{Molare Leitfähigkeit}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{salt}}
+        \quantity{\Lambda_\txM}{\siemens\cm^2\per\mol=\ampere\cm^2\per\volt\mol}{ievs}
+        \eq{\Lambda_\txM = \frac{\kappa}{c_\text{salt}}}
+    \end{formula}
+
+    \begin{formula}{kohlrausch_law}
+        \desc{Kohlrausch's law}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} at infinite dilution, $c_\text{salt}$ \gt{csalt}, $K$ \GT{constant}}
+        \desc[german]{}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} bei unendlicher Verdünnung, $\text{salt}$ \gt{csalt} $K$ \GT{constant}}
+        \eq{\Lambda_\txM = \Lambda_\txM^0 - K \sqrt{c_\text{salt}}}
+    \end{formula}
+    
+% Electrolyte conductivity
+    \begin{formula}{molality}
+        \desc{Molality}{}{\QtyRef{amount} of the solute, \QtyRef{mass} of the solvent}
+        \desc[german]{Molalität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{mass} des Lösungsmittels}
+        \quantity{b}{\mol\per\kg}{}
+        \eq{b = \frac{n}{m}}
+    \end{formula}
+
+    \begin{formula}{molarity}
+        \desc{Molarity}{\GT{see} \qtyRef{concentration}}{\QtyRef{amount} of the solute, \QtyRef{volume} of the solvent}
+        \desc[german]{Molarität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{volume} des Lösungsmittels}
+        \quantity{c}{\mol\per\litre}{}
+        \eq{c = \frac{n}{V}}
+    \end{formula}
+
+    \begin{formula}{ionic_strength}
+        \desc{Ionic strength}{Measure of the electric field in a solution through solved ions}{\QtyRef{molality}, \QtyRef{molarity}, $z$ \qtyRef{charge_number}}
+        \desc[german]{Ionenstärke}{Maß eienr Lösung für die elektrische Feldstärke durch gelöste Ionen}{}
+        \quantity{I}{\mol\per\kg;\mol\per\litre}{}
+        \eq{I_b &= \frac{1}{2} \sum_i b_i z_i^2 \\ I_c &= \frac{1}{2} \sum_i c_i z_i^2}
+    \end{formula}
+
+    \begin{formula}{debye_screening_length}
+        \desc{Debye screening length}{}{\ConstRef{avogadro}, \ConstRef{charge}, \QtyRef{ionic_strength}, \QtyRef{permittivity}, \ConstRef{boltzmann}, \QtyRef{temperature}}
+        \desc[german]{Debye-Länge / Abschirmlänge}{}{}
+        \eq{\lambda_\txD = \sqrt{\frac{\epsilon \kB T}{2\NA e^2 I_C}}}
+    \end{formula}
+
+    \begin{formula}{mean_ionic_activity}
+        \desc{Mean ionic activity coefficient}{Accounts for decreased reactivity because ions must divest themselves of their ion cloud before reacting}{}
+        \desc[german]{Mittlerer ionischer Aktivitätskoeffizient}{Berücksichtigt dass Ionen sich erst von ihrer Ionenwolke lösen müssen, bevor sie reagieren können}{}
+        \quantity{\gamma}{}{s}
+        \eq{\gamma_\pm = \left(\gamma_+^{\nu_+} \, \gamma_-^{\nu_-}\right)^{\frac{1}{\nu_+ + \nu_-}}}
+    \end{formula}
+
+    \begin{formula}{debye_hueckel_law}
+        \desc{Debye-Hückel limiting law}{For an infinitely dilute solution}{\QtyRef{mean_ionic_activity}, $A$ solvent dependant constant, $z$ \qtyRef{charge_number}, \QtyRef{ionic_strength} in [\si{\mol\per\kg}]}
+        \desc[german]{Debye-Hückel Gesetz}{Für eine unendlich verdünnte Lösung}{}
+        \eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
+    \end{formula} 
+
+\Subsection[
+    \eng{Kinetics}
+    \ger{Kinetik}
+]{kin}
+    \begin{formula}{transfer_coefficient}
+        \desc{Transfer coefficient}{}{}
+        \desc[german]{Durchtrittsfaktor}{Transferkoeffizient\\Anteil des Potentials der sich auf die freie Reaktionsenthalpie des anodischen Prozesses auswirkt}{}
+        \eq{
+            \alpha_\txA &= \alpha \\
+            \alpha_\txC &= 1-\alpha
+        }
+    \end{formula}
+
+    \begin{formula}{overpotential}
+        \desc{Overpotential}{}{}
+        \desc[german]{Überspannung}{}{}
+        \ttxt{
+            \eng{Potential deviation from the equilibrium cell potential}
+            \ger{Abweichung der Spannung von der Zellspannung im Gleichgewicht}
+        }
+    \end{formula}
+    \begin{formula}{activation_overpotential}
+        \desc{Activation verpotential}{}{$E_\text{electrode}$ potential at which the reaction starts $E_\text{ref}$ thermodynamic potential of the reaction}
+        \desc[german]{Aktivierungsüberspannung}{}{$E_\text{electrode}$ Potential bei der die Reaktion beginnt, $E_\text{ref}$ thermodynamisches Potential der Reaktion}
+        \eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
+    \end{formula}
+
+    \begin{formula}{concentration_overpotential}
+        \desc{Concentration overpotential}{Due to concentration gradient near the electrode, the ions need to \hyperref[f:ch:el:ion_cond:diffusion]{diffuse} to the electrode before reacting}{\ConstRef{universal_gas}, \QtyRef{temperature}, $\c_{0/\txS}$ ion concentration in the electrolyte / at the double layer, $z$ \qtyRef{charge_number}, \ConstRef{faraday}}
+        \desc[german]{Konzentrationsüberspannung}{Durch einen Konzentrationsgradienten an der Elektrode müssen Ionen erst zur Elektrode \hyperref[f:ch:el:ion_cond:diffusion]{diffundieren}, bevor sie reagieren können}{}
+        \eq{
+            \eta_\text{conc,anodic} &= -\frac{RT}{\alpha \,zF} \ln \left(\frac{c_\text{red}^0}{c_\text{red}^\txS}\right) \\
+            \eta_\text{conc,cathodic} &= -\frac{RT}{(1-\alpha) zF} \ln \left(\frac{c_\text{ox}^0}{c_\text{ox}^\txS}\right)
+        }
+    \end{formula}
+
+    \begin{formula}{diffusion_overpotential}
+        \desc{Diffusion overpotential}{}{}
+        \desc[german]{Diffusionsüberspannung}{}{}
+        \eq{\eta_\text{diff} = \frac{RT}{nF} \ln \left( \cfrac{\cfrac{c^\txs_\text{ox}}{c^0_\text{ox}}}{\cfrac{c^\txs_\text{red}}{c^0_\text{red}}} \right)}
+    \end{formula}
+
+    \begin{formula}{diffusion_layer}
+        \desc{Cell layers}{}{}
+        \desc[german]{Zellschichten}{}{}
+        \begin{tikzpicture}
+            \tikzset{
+                label/.style={color=fg1,anchor=center,rotate=90},
+            }
+            \pgfmathsetmacro{\tkW}{8}               % Total width
+            \pgfmathsetmacro{\tkH}{5}               % Total height
+            \pgfmathsetmacro{\edW}{1}               % electrode width              
+            \pgfmathsetmacro{\hhW}{1}               % helmholtz width
+            \pgfmathsetmacro{\ndW}{2}               % nernst diffusion with
+            \pgfmathsetmacro{\eyW}{\tkW-\edW-\hhW-\ndW}     % electrolyte width
+            \pgfmathsetmacro{\edX}{0}               % electrode width              
+            \pgfmathsetmacro{\hhX}{\edW}            % helmholtz width
+            \pgfmathsetmacro{\ndX}{\edW+\hhW}       % nernst diffusion with
+            \pgfmathsetmacro{\eyX}{\tkW-\eyW}       % electrolyte width
+
+            \draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
+            \draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east]  {$c$};
+            \path[fill=bg-orange]        (\edX,0) rectangle (\edX+\edW,\tkH); \node[label] at (\edX+\edW/2,\tkH/2) {\GT{electrode}};
+            \path[fill=bg-green!90!bg0]  (\hhX,0) rectangle (\hhX+\hhW,\tkH); \node[label] at (\hhX+\hhW/2,\tkH/2) {\GT{helmholtz_layer}};
+            \path[fill=bg-green!60!bg0]  (\ndX,0) rectangle (\ndX+\ndW,\tkH); \node[label] at (\ndX+\ndW/2,\tkH/2) {\GT{nernst_layer}};
+            \path[fill=bg-green!20!bg0]  (\eyX,0) rectangle (\eyX+\eyW,\tkH); \node[label] at (\eyX+\eyW/2,\tkH/2) {\GT{elektrolyte}};
+            \draw (\hhX,2) -- (\ndX,3) -- (\tkW,3);
+            \tkYTick{2}{$c^\txS$};
+            \tkYTick{3}{$c^0$};
+        \end{tikzpicture}
+    \end{formula}
+    \Eng[c_surface]{surface \qtyRef{concentration}}
+    \Eng[c_bulk]{bulk \qtyRef{concentration}}
+    \Ger[c_surface]{Oberflächen-\qtyRef{concentration}}
+    \Ger[c_bulk]{Bulk-\qtyRef{concentration}}
+
+
+    \begin{formula}{diffusion_layer_thickness}
+        \desc{Nerst Diffusion layer thickness}{}{$c^0$ \GT{c_bulk}, $c^\txs$ \GT{c_surface}}
+        \desc[german]{Dicke der Nernstschen Diffusionsschicht}{}{}
+        \eq{\delta_\txN = \frac{c^0 - c^\txs}{\odv{c}{x}_{x=0}}}
+    \end{formula}
+
+    \begin{formula}{roughness_factor}
+        \desc{Roughness factor}{Surface area related to electrode geometry}{}
+        \eq{\rfactor}
+    \end{formula}   
+
+    \begin{formula}{butler_volmer}
+        \desc{Butler-Volmer equation}{Reaction kinetics near the equilibrium potentential}
+        {$j$ \qtyRef{current_density}, $j_0$ exchange current density, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txC/\txA}$ cathodic/anodic charge transfer coefficient}
+        %Current through an electrode iof a unimolecular redox reaction with both anodic and cathodic reaction occuring on the same electrode
+        \desc[german]{Butler-Volmer-Gleichung}{Reaktionskinetik in der Nähe des Gleichgewichtspotentials}
+        {$j$ \qtyRef{current_density}, $j_0$ Austauschstromdichte, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txC/\txA}$ Ladungstransferkoeffizient an der Kathode/Anode}
+        \begin{gather}
+            j = j_0 \,\rfactor\, \left[ \Exp{\frac{(1-a_\txC) z F \eta}{RT}} - \Exp{-\frac{\alpha_\txC z F \eta}{RT}}\right]
+            \intertext{\GT{with}}
+            \alpha_\txA = 1 - \alpha_\txC
+        \end{gather}
+        \separateEntries
+        \fig{img/ch_butler_volmer.pdf}
+    \end{formula}
+
+    % \Subsubsection[
+    %     \eng{Tafel approximation}
+    %     \ger{Tafel Näherung}
+    % ]{tafel}
+
+    % \begin{formula}{slope}
+    %     \desc{Tafel slope}{}{}
+    %     \desc[german]{Tafel Steigung}{}{}
+    %     \eq{}
+    % \end{formula}
+
+    \begin{formula}{equation}
+        \desc{Tafel approximation}{For slow kinetics: $\abs{\eta} > \SI{0.1}{\volt}$}{}
+        \desc[german]{Tafel Näherung}{Für langsame Kinetik: $\abs{\eta} > \SI{0.1}{\volt}$}{}
+        \eq{
+            \Log{j} &\approx \Log{j_0} + \frac{\alpha_\txC zF \eta}{RT\ln(10)} && \eta \gg \SI{0.1}{\volt}\\
+            \Log{\abs{j}} &\approx \Log{j_0} - \frac{(1-\alpha_\txC) zF \eta}{RT\ln(10)} && \eta \ll -\SI{0.1}{\volt}
+        }
+        \fig{img/ch_tafel.pdf}
+    \end{formula}
+
+
+
+\Subsection[
+    \eng{Techniques}
+    \ger{Techniken}
+]{tech}
+
+    \Subsubsection[
+        \eng{Reference electrodes}
+        \ger{Referenzelektroden}
+    ]{ref}
+        \begin{ttext}
+            \eng{Defined as reference for measuring half-cell potententials}
+            \ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
+        \end{ttext}
+
+        \begin{formula}{she}
+            \desc{Standard hydrogen elektrode (SHE)}{}{$p=\SI{e5}{\pascal}$, $a_{\ce{H+}}=\SI{1}{\mol\per\litre}$ (\Rightarrow $\pH=0$)}
+            \desc[german]{Standardwasserstoffelektrode (SHE)}{}{}
+            \ttxt{
+                \eng{Potential of the reaction: \ce{2H^+ +2e^- <--> H2}}
+                \ger{Potential der Reaktion: \ce{2H^+ +2e^- <--> H2}}
+            }
+        \end{formula}
+
+        \begin{formula}{rhe}
+            \desc{Reversible hydrogen electrode (RHE)}{RHE Potential does not change with the pH value}{$E^0\equiv \SI{0}{\volt}$, \QtyRef{activity}, \QtyRef{pressure}, \GT{see} \fqEqRef{ch:el:cell:nernst_equation}}
+            \desc[german]{Reversible Wasserstoffelektrode (RHE)}{Potential ändert sich nicht mit dem pH-Wert}{}
+            \eq{
+                E_\text{RHE} &= E^0 + \frac{RT}{F} \Ln{\frac{a_{\ce{H^+}}}{p_{\ce{H2}}}} \\
+                             &= \SI{0}{\volt} - \SI{0.059}{\volt}
+            }
+        \end{formula}
+    
+    
+
+    \Subsubsection[
+        \eng{Cyclic voltammetry}
+        \ger{Zyklische Voltammetrie}
+    ]{cycl_v}
+        \begin{formula}{duck}
+            \desc{Cyclic voltammogram}{}{}
+            % \desc[german]{}{}{}
+            \begin{tikzpicture}
+                \pgfmathsetmacro{\Ax}{-2.3}
+                \pgfmathsetmacro{\Ay}{ 0.0}
+                \pgfmathsetmacro{\Bx}{ 0.0}
+                \pgfmathsetmacro{\By}{ 1.0}
+                \pgfmathsetmacro{\Cx}{ 0.4}
+                \pgfmathsetmacro{\Cy}{ 1.5}
+                \pgfmathsetmacro{\Dx}{ 2.0}
+                \pgfmathsetmacro{\Dy}{ 0.5}
+                \pgfmathsetmacro{\Ex}{ 0.0}
+                \pgfmathsetmacro{\Ey}{-1.5}
+                \pgfmathsetmacro{\Fx}{-0.4}
+                \pgfmathsetmacro{\Fy}{-2.0}
+                \pgfmathsetmacro{\Gx}{-2.3}
+                \pgfmathsetmacro{\Gy}{-0.3}
+                \begin{axis}[ymin=-3,ymax=3,xmax=3,xmin=-3,
+                    % equal axis,
+                    minor tick num=1,
+                    xlabel={$U$}, xlabel style={at={(axis description cs:0.5,+0.02)}},
+                    ylabel={$I$}, ylabel style={at={(axis description cs:0.1,0.5)}},
+                    anchor=center, at={(0,0)},
+                    axis equal image,clip=false,
+                ]
+                    % CV with beziers
+                    \draw[thick, fg-blue]                                                       (axis cs:\Ax,\Ay) coordinate (A) node[left]  {A}
+                        ..controls (axis cs:\Ax+1.8, \Ay+0.0) and (axis cs:\Bx-0.2, \By-0.4) .. (axis cs:\Bx,\By) coordinate (B) node[left]  {B}
+                        ..controls (axis cs:\Bx+0.1, \By+0.2) and (axis cs:\Cx-0.3, \Cy+0.0) .. (axis cs:\Cx,\Cy) coordinate (C) node[above] {C}
+                        ..controls (axis cs:\Cx+0.5, \Cy+0.0) and (axis cs:\Dx-1.3, \Dy+0.1) .. (axis cs:\Dx,\Dy) coordinate (D) node[right] {D}
+                        ..controls (axis cs:\Dx-2.0, \Dy-0.1) and (axis cs:\Ex+0.3, \Ey+0.8) .. (axis cs:\Ex,\Ey) coordinate (E) node[right] {E}
+                        ..controls (axis cs:\Ex-0.1, \Ey-0.2) and (axis cs:\Fx+0.2, \Fy+0.0) .. (axis cs:\Fx,\Fy) coordinate (F) node[below] {F}
+                        ..controls (axis cs:\Fx-0.2, \Fy+0.0) and (axis cs:\Gx+1.5, \Gy-0.2) .. (axis cs:\Gx,\Gy) coordinate (G) node[left]  {G};
+                    \node[above] at (A) {\rightarrow};
+                \end{axis}
+            \end{tikzpicture}
+        \end{formula}
+
+        \begin{formula}{upd}
+            \desc{Underpotential deposition (UPD)}{}{}
+            \desc[german]{}{}{}
+            \ttxt{Reversible deposition of metal onto a foreign metal electrode at potentials positive of the Nernst potential \TODO{clarify}}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Rotating disk electrodes}
+        % \ger{}
+    ]{rde}
+        \begin{formula}{viscosity}
+            \desc{Dynamic viscosity}{}{}
+            \desc[german]{Dynamisch Viskosität}{}{}
+            \quantity{\eta,\mu}{\pascal\s=\newton\s\per\m^2=\kg\per\m\s}{}
+        \end{formula}
+
+        \begin{formula}{kinematic_viscosity}
+            \desc{Kinematic viscosity}{\qtyRef{viscosity} related to density of a fluid}{\QtyRef{viscosity}, \QtyRef{density}}
+            \desc[german]{Kinematische Viskosität}{\qtyRef{viscosity} im Verhältnis zur Dichte der Flüssigkeit}{}
+            \quantity{\nu}{\cm^2\per\s}{}
+            \eq{\nu = \frac{\eta}{\rho}}
+        \end{formula}
+
+        \begin{formula}{diffusion_layer_thickness}
+            \desc{Diffusion layer thickness}{\TODO{Where does 1.61 come from}}{$D$ \qtyRef{diffusion_coefficient}, $\nu$ \qtyRef{kinematic_viscosity}, \QtyRef{angular_frequency}}
+            \desc[german]{Diffusionsshichtdicke}{}{}
+            \eq{\delta_\text{diff}= 1.61 D{^\frac{1}{3}} \nu^{\frac{1}{6}} \omega^{-\frac{1}{2}}}
+        \end{formula}
+
+        \begin{formula}{limiting_current}
+            \desc{Limiting current}{}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \secEqRef{diffusion_layer_thickness}, $\nu$ \qtyRef{kinematic_viscosity}, \QtyRef{angular_frequency}}
+            % \desc[german]{Limitierender Strom}{}{}
+            \eq{j^\infty = nFD \frac{c^0}{\delta_\text{diff}} = \frac{1}{1.61} nFD^{\frac{2}{3}}  v^{\frac{-1}{6}} c^0 \sqrt{\omega}}
+        \end{formula}
+
diff --git a/src/ch/misc.tex b/src/ch/misc.tex
new file mode 100644
index 0000000..0c5eec2
--- /dev/null
+++ b/src/ch/misc.tex
@@ -0,0 +1,107 @@
+\Section[
+    \eng{Thermoelectricity}
+    \ger{Thermoelektrizität}
+]{thermo}
+    \begin{formula}{seebeck}
+        \desc{Seebeck coefficient}{}{$V$ voltage, \QtyRef{temperature}}
+        \desc[german]{Seebeck-Koeffizient}{}{}
+        \quantity{S}{\micro\volt\per\kelvin}{s}
+        \eq{S = -\frac{\Delta V}{\Delta T}}
+    \end{formula}
+    \begin{formula}{seebeck_effect}
+        \desc{Seebeck effect}{Elecromotive force across two points of a material with a temperature difference}{\QtyRef{conductivity}, $V$ local voltage, \QtyRef{seebeck}, \QtyRef{temperature}}
+        \desc[german]{Seebeck-Effekt}{}{}
+        \eq{\vec{j} = \sigma(-\Grad V - S \Grad T)}
+    \end{formula}
+
+    \begin{formula}{thermal_conductivity}
+        \desc{Thermal conductivity}{Conduction of heat, without mass transport}{\QtyRef{heat}, \QtyRef{length}, \QtyRef{area}, \QtyRef{temperature}}
+        \desc[german]{Wärmeleitfähigkeit}{Leitung von Wärme, ohne Stofftransport}{}
+        \quantity{\kappa,\lambda,k}{\watt\per\m\K=\kg\m\per\s^3\kelvin}{s}
+        \eq{\kappa = \frac{\dot{Q} l}{A\,\Delta T}}
+        \eq{\kappa_\text{tot} = \kappa_\text{lattice} + \kappa_\text{electric}}
+    \end{formula}
+
+    \begin{formula}{wiedemann-franz}
+        \desc{Wiedemann-Franz law}{}{Electric \QtyRef{thermal_conductivity}, $L$ in \si{\watt\ohm\per\kelvin} Lorentz number, \QtyRef{conductivity}}
+        \desc[german]{Wiedemann-Franz Gesetz}{}{Elektrische \QtyRef{thermal_conductivity}, $L$ in \si{\watt\ohm\per\kelvin} Lorentzzahl, \QtyRef{conductivity}}
+        \eq{\kappa = L\sigma T}
+    \end{formula}
+
+    \begin{formula}{zt}
+        \desc{Thermoelectric figure of merit}{Dimensionless quantity for comparing different materials}{\QtyRef{seebeck}, \QtyRef{conductivity}, }
+        \desc[german]{Thermoelektrische Gütezahl}{Dimensionsoser Wert zum Vergleichen von Materialien}{}
+        \eq{zT = \frac{S^2\sigma}{\lambda} T}
+    \end{formula}
+
+
+\Section[
+    \eng{misc}
+    \ger{misc}
+]{misc}
+
+    % TODO: hide
+    \begin{formula}{stoichiometric_coefficient}
+        \desc{Stoichiometric coefficient}{}{}
+        \desc[german]{Stöchiometrischer Koeffizient}{}{}
+        \quantity{\nu}{}{s}
+    \end{formula}
+
+    \begin{formula}{std_condition}
+        \desc{Standard temperature and pressure}{}{}
+        \desc[german]{Standardbedingungen}{}{}
+        \eq{
+            T &= \SI{273.15}{\kelvin} = \SI{0}{\celsius} \\
+            p &= \SI{100000}{\pascal} = \SI{1.000}{\bar}
+        }
+    \end{formula}
+    \begin{formula}{ph}
+        \desc{pH definition}{}{$a_{\ce{H+}}$ hyrdrogen ion \qtyRef{activity}}
+        \desc[german]{pH-Wert definition}{}{$a_{\ce{H+}}$ Wasserstoffionen-\qtyRef{activity}}
+        \eq{\pH = -\log_{10}(a_{\ce{H+}})}
+    \end{formula}
+
+    \begin{formula}{ph_rt}
+        \desc{pH}{At room temperature \SI{25}{\celsius}}{}
+        \desc[german]{pH-Wert}{Bei Raumtemperatur \SI{25}{\celsius}}{}
+        \eq{
+            \pH > 7 &\quad\tGT{basic} \\
+            \pH < 7 &\quad\tGT{acidic} \\
+            \pH = 7 &\quad\tGT{neutral}
+        }
+    \end{formula}
+
+    \begin{formula}{covalent_bond}
+        \desc{Covalent bond}{}{}
+        \desc[german]{Kolvalente Bindung}{}{}
+        \ttxt{
+            \eng{Bonds that involve sharing of electrons to form electron pairs between atoms.}
+            \ger{Bindungen zwischen Atomen die durch geteilte Elektronen, welche Elektronenpaare bilden, gebildet werden.}
+        }
+    \end{formula}
+
+    \begin{formula}{grotthuss}
+        \desc{Grotthuß-mechanism}{}{}
+        \desc[german]{Grotthuß-Mechanismus}{}{}
+        \ttxt{
+            \eng{The mobility of protons in aqueous solutions is much higher than that of other ions because they can "move" by breaking and reforming covalent bonds of water molecules.}
+            \ger{The Moblilität von Protononen in wässrigen Lösungen ist wesentlich größer als die anderer Ionen, da sie sich "bewegen" können indem die Wassertsoffbrückenbindungen gelöst und neu gebildet werden.}
+        }
+    \end{formula}
+
+
+    \Eng[cyanide]{Cyanide}
+    \Ger[cyanide]{Zyanid}
+    \Eng[ammonia]{Ammonia}
+    \Ger[ammonia]{Ammoniak}
+
+    \begin{formula}{common_chemicals}
+        \desc{Common chemicals}{}{}
+        \desc[german]{Häufige Chemikalien}{}{}
+        \begin{tabular}{l|c}
+            \GT{name} & \GT{formula} \\ \hline\hline
+            \GT{cyanide} & \ce{CN} \\ \hline
+            \GT{ammonia} & \ce{NH3}
+        \end{tabular}
+    \end{formula}
+
diff --git a/src/cm/crystal.tex b/src/cm/crystal.tex
index a38a8b6..deed6f7 100644
--- a/src/cm/crystal.tex
+++ b/src/cm/crystal.tex
@@ -6,11 +6,7 @@
     \eng{Bravais lattice}
     \ger{Bravais-Gitter}
 ]{bravais}
-    \eng[table2D]{In 2D, there are 5 different Bravais lattices}
-    \ger[table2D]{In 2D gibt es 5 verschiedene Bravais-Gitter}
 
-    \eng[table3D]{In 3D, there are 14 different Bravais lattices}
-    \ger[table3D]{In 3D gibt es 14 verschiedene Bravais-Gitter}
 
     \Eng[lattice_system]{Lattice system}
     \Ger[lattice_system]{Gittersystem}
@@ -24,56 +20,43 @@
     \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
-        \expandafter\caption\expandafter{\gt{table2D}}
-        \label{tab:bravais2}
-    
+
+    \begin{bigformula}{2d}
+        \desc{2D}{In 2D, there are 5 different Bravais lattices}{}
+        \desc[german]{2D}{In 2D gibt es 5 verschiedene Bravais-Gitter}{}
         \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}
+            \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}
+    \end{bigformula}
     
 
-
-    \begin{table}[H]
-        \centering
-        \caption{\gt{table3D}}
-        \label{tab:bravais3}
-    
+    \begin{bigformula}{3d}
+        \desc{3D}{In 3D, there are 14 different Bravais lattices}{}
+        \desc[german]{3D}{In 3D gibt es 14 verschiedene Bravais-Gitter}{}
         % \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}
+            \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}
+    \end{bigformula}
 
     \begin{formula}{lattice_constant}
         \desc{Lattice constant}{Parameter (length or angle) describing the smallest unit cell}{}
diff --git a/src/cm/mat.tex b/src/cm/mat.tex
index 1fece32..66f351c 100644
--- a/src/cm/mat.tex
+++ b/src/cm/mat.tex
@@ -12,3 +12,17 @@
         \tau &= \frac{l}{L}
     }
 \end{formula}
+
+\begin{formula}{stress}
+    \desc{Stress}{Force per area}{\QtyRef{force}, \QtyRef{area}}
+    \desc[german]{Spannung}{(Engl. "stress") Kraft pro Fläche}{}
+    \quantity{\sigma}{\newton\per\m^2}{v}
+    \eq{\ten{\sigma}_{ij} = \frac{F_i}{A_j}}
+\end{formula}
+
+\begin{formula}{strain}
+    \desc{Strain}{}{$\Delta x$ distance from reference position $x_0$}
+    \desc[german]{Dehnung}{(Engl. "strain")}{$\Delta x$ Auslenkung aus der Referenzposition $x_0$}
+    \quantity{\epsilon}{}{s}
+    \eq{\epsilon = \frac{\Delta x}{x_0}}
+\end{formula}
diff --git a/src/cm/techniques.tex b/src/cm/techniques.tex
index 2013d3b..77973ab 100644
--- a/src/cm/techniques.tex
+++ b/src/cm/techniques.tex
@@ -13,54 +13,53 @@
         \eng{Raman spectroscopy}
         \ger{Raman Spektroskopie}
     ]{raman}
-        % \begin{minipagetable}{raman}
-        %     \entry{name}{
-        %         \eng{Raman spectroscopy}
-        %         \ger{Raman-Spektroskopie}
-        %     }
-        %     \entry{application}{
-        %         \eng{Vibrational modes, Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqName{cm:misc:vdw_material}}
-        %         \ger{Vibrationsmoden, Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqName{cm:misc:vdw_material}}
-        %     }
-        %     % \entry{how}{
-        %     %     \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, inelastic scattering because of rotation-, vibration-, phonon and spinflip-processes, plot spectrum as shift of the laser light (in \si{\per\cm})}
-        %     %     \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, inelastische Streuung durch Rotations-, Schwingungs-, Phonon und Spin-Flip-Prozesse, plotte Spektrum als Verschiebung gegen das Laser Licht (in \si{\per\cm}) }
-        %     % }
-        % \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
+
+    % TODO remove fqname from minipagetable?
+
+    \begin{bigformula}{raman}
+        \desc{Raman spectroscopy}{}{}
+        \desc[german]{Raman-Spektroskopie}{}{}
+        \begin{minipagetable}{raman}
+            \tentry{application}{
+                \eng{Vibrational modes, Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqRef{cm:misc:vdw_material}}
+                \ger{Vibrationsmoden, Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqRef{cm:misc:vdw_material}}
+            }
+            \tentry{how}{
+                \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, inelastic scattering because of rotation-, vibration-, phonon and spinflip-processes, plot spectrum as shift of the laser light (in \si{\per\cm})}
+                \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, inelastische Streuung durch Rotations-, Schwingungs-, Phonon und Spin-Flip-Prozesse, plotte Spektrum als Verschiebung gegen das Laser Licht (in \si{\per\cm}) }
+            }
+        \end{minipagetable}
+        \begin{minipage}{0.45\textwidth}
             \begin{figure}[H]
                 \centering
                 % \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
                 % \caption{\cite{Bian2021}}
             \end{figure}
         \end{minipage}
+    \end{bigformula}
 
-        \expandafter\detokenize\expandafter{\fqname}
-        \GT{cm:meas:raman:raman:application}
 
-        \separateEntries
-
-        % \begin{minipagetable}{pl}
-        %     \entry{name}{
-        %         \eng{Photoluminescence spectroscopy}
-        %         \ger{Photolumeszenz-Spektroskopie}
-        %     }
-        %     \entry{application}{
-        %         \eng{Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqName{cm:misc:vdw_material}}
-        %         \ger{Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqName{cm:misc:vdw_material}}
-        %     }
-        %     \entry{how}{
-        %         \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, electrons are excited, relax to the conduction band minimum and finally accross the band gap under photon emission}
-        %         \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, Elektronen werden angeregt und relaxieren in das Leitungsband-Minimum und schließlich über die Bandlücke unter Photonemission}
-        %     }
-        % \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
+    \begin{bigformula}{pl}
+        \desc{Photoluminescence spectroscopy}{}{}
+        \desc[german]{Photolumeszenz-Spektroskopie}{}{}
+        \begin{minipagetable}{pl}
+            \tentry{application}{
+                \eng{Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqRef{cm:misc:vdw_material}}
+                \ger{Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqRef{cm:misc:vdw_material}}
+            }
+            \tentry{how}{
+                \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, electrons are excited, relax to the conduction band minimum and finally accross the band gap under photon emission}
+                \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, Elektronen werden angeregt und relaxieren in das Leitungsband-Minimum und schließlich über die Bandlücke unter Photonemission}
+            }
+        \end{minipagetable}
+        \begin{minipage}{0.45\textwidth}
             \begin{figure}[H]
                 \centering
                 % \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
                 % \caption{\cite{Bian2021}}
             \end{figure}
         \end{minipage}
+    \end{bigformula}
 
 
     \Subsection[
@@ -82,63 +81,63 @@
         \end{ttext}
 
 
+    \begin{bigformula}{amf}
+        \desc{Atomic force microscopy (AMF)}{}{}
+        \desc[german]{Atomare Rasterkraftmikroskopie (AMF)}{}{}
         \begin{minipagetable}{amf}
-            \entry{name}{
-                \eng{Atomic force microscopy (AMF)}
-                \ger{Atomare Rasterkraftmikroskopie (AMF)}
-            }
-            \entry{application}{
+            \tentry{application}{
                 \eng{Surface stuff}
                 \ger{Oberflächenzeug}
             }
-            \entry{how}{
+            \tentry{how}{
                 \eng{With needle}
                 \ger{Mit Nadel}
             }
         \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
+        \begin{minipage}{0.45\textwidth}
             \begin{figure}[H]
                 \centering
                 \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
                 \caption{\cite{Bian2021}}
             \end{figure}
         \end{minipage}
+    \end{bigformula}
 
 
 
 
+    \begin{bigformula}{stm}
+        \desc{Scanning tunneling microscopy (STM)}{}{}
+        \desc[german]{Rastertunnelmikroskop (STM)}{}{}
         \begin{minipagetable}{stm}
-            \entry{name}{
-                \eng{Scanning tunneling microscopy (STM)}
-                \ger{Rastertunnelmikroskop (STM)}
-            }
-            \entry{application}{
+            \tentry{application}{
                 \eng{Surface stuff}
                 \ger{Oberflächenzeug}
             }
-            \entry{how}{
+            \tentry{how}{
                 \eng{With TUnnel}
                 \ger{Mit TUnnel}
             }
         \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
+        \begin{minipage}{0.45\textwidth}
             \begin{figure}[H]
                 \centering
                 \includegraphics[width=0.8\textwidth]{img/cm_stm.pdf}
                 \caption{\cite{Bian2021}}
             \end{figure}
         \end{minipage}
+    \end{bigformula}
 
 \Section[
     \eng{Fabrication techniques}
     \ger{Herstellungsmethoden}
-    ]{fab}
+]{fab}
+
+    \begin{bigformula}{cvd}
+    \desc{Chemical vapor deposition (CVD)}{}{}
+    \desc[german]{Chemische Gasphasenabscheidung (CVD)}{}{}
     \begin{minipagetable}{cvd}
-        \entry{name}{
-            \eng{Chemical vapor deposition (CVD)}
-            \ger{Chemische Gasphasenabscheidung (CVD)}
-        }
-        \entry{how}{
+        \tentry{how}{
             \eng{
                 A substrate is exposed to volatile precursors, which react and/or decompose on the heated substrate surface to produce the desired deposit.
                 By-products are removed by gas flow through the chamber.
@@ -148,7 +147,7 @@
                 Nebenprodukte werden durch den Gasfluss durch die Kammer entfernt.
             }
         }
-        \entry{application}{
+        \tentry{application}{
             \eng{
                 \begin{itemize}
                     \item Polysilicon \ce{Si}
@@ -167,10 +166,11 @@
             }
         }
     \end{minipagetable}
-    \begin{minipage}{0.5\textwidth}
+    \begin{minipage}{0.45\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img/cm_cvd_english.pdf}
     \end{minipage}
+\end{bigformula}
 
 
     \Subsection[
@@ -182,31 +182,31 @@
             \ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
         \end{ttext}
 
-        \begin{minipagetable}{mbe}
-            \entry{name}{
-                \eng{Molecular Beam Epitaxy (MBE)}
-                \ger{Molekularstrahlepitaxie (MBE)}
-            } 
-            \entry{how}{
-                \eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
-                \ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
-            }
-            \entry{application}{
-                \eng{
-                    \begin{itemize}
-                        \item Gallium arsenide \ce{GaAs}
-                    \end{itemize}
-                    \TODO{Link to GaAs}
+        \begin{bigformula}{mbe}
+            \desc{Molecular Beam Epitaxy (MBE)}{}{}
+            \desc[german]{Molekularstrahlepitaxie (MBE)}{}{}
+            \begin{minipagetable}{mbe}
+                \tentry{how}{
+                    \eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
+                    \ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
                 }
-                \ger{
-                    \begin{itemize}
-                        \item Galliumarsenid \ce{GaAs}
-                    \end{itemize}
+                \tentry{application}{
+                    \eng{
+                        \begin{itemize}
+                            \item Gallium arsenide \ce{GaAs}
+                        \end{itemize}
+                        \TODO{Link to GaAs}
+                    }
+                    \ger{
+                        \begin{itemize}
+                            \item Galliumarsenid \ce{GaAs}
+                        \end{itemize}
+                    }
                 }
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \centering
-            \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
-        \end{minipage}
+            \end{minipagetable}
+            \begin{minipage}{0.45\textwidth}
+                \centering
+                \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
+            \end{minipage}
+        \end{bigformula}
 
diff --git a/src/cm/topo.tex b/src/cm/topo.tex
index 191f716..f51b19d 100644
--- a/src/cm/topo.tex
+++ b/src/cm/topo.tex
@@ -56,17 +56,17 @@
         \eq{\gamma_n = \oint_C \d \vec{R} \cdot A_n(\vec{R}) = \int_S \d\vec{S} \cdot \vec{\Omega}_n(\vec{R})}
     \end{formula}
 
-    \begin{ttext}[chern_number_desc]
-        \eng{The Berry flux through any 2D closed surface is quantized by the \textbf{Chern number}.
-            If there is time-reversal symmetry, the Chern-number is 0.
-        }
-        \ger{Der Berry-Fluß durch eine geschlossene 2D Fl[cher is quantisiert durch die \textbf{Chernzahl}
-            Bei erhaltener Zeitumkehrungssymmetrie ist die Chernzahl 0.
-        }
-    \end{ttext}
     \begin{formula}{chern_number}
         \desc{Chern number}{Eg. number of Berry curvature monopoles in the Brillouin zone (then $\vec{R} = \vec{k}$)}{$\vec{S}$ closed surface in $\vec{R}$-space. A \textit{Chern insulator} is a 2D insulator with $C_n \neq 0$}
         \desc[german]{Chernuzahl}{Z.B. Anzahl der Berry-Krümmungs-Monopole in der Brilouinzone (dann ist $\vec{R} = \vec{k}$). Ein \textit{Chern-Isolator} ist ein 2D Isolator mit $C_n\neq0$}{$\vec{S}$ geschlossene Fläche im $\vec{R}$-Raum}
+        \ttxt{
+            \eng{The Berry flux through any 2D closed surface is quantized by the \textbf{Chern number}.
+                If there is time-reversal symmetry, the Chern-number is 0.
+            }
+            \ger{Der Berry-Fluß durch eine geschlossene 2D Fl[cher is quantisiert durch die \textbf{Chernzahl}
+                Bei erhaltener Zeitumkehrungssymmetrie ist die Chernzahl 0.
+            }
+        }
         \eq{C_n = \frac{1}{2\pi} \oint \d \vec{S}\ \cdot \vec{\Omega}_n(\vec{R})}
     \end{formula}
 
@@ -76,10 +76,14 @@
         \eq{\vec{\sigma}_{xy} = \sum_n \frac{e^2}{h} \int_\text{\GT{occupied}} \d^2k\, \frac{\Omega_{xy}^n}{2\pi} = \sum_n C_n \frac{e^2}{h}}
     \end{formula}
 
-    \begin{ttext}
-        \eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}.}
-        \ger{Ein 2D Isolator mit einer Chernzahl ungleich 0 wird \textbf{topologischer Isolator} genannt.}
-    \end{ttext}
+    \begin{formula}{topological_insulator}
+        \desc{Topological insulator}{}{}
+        \desc[german]{Topologischer Isolator}{}{}
+        \ttxt{
+            \eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}.}
+            \ger{Ein 2D Isolator mit einer Chernzahl ungleich 0 wird \textbf{topologischer Isolator} genannt.}
+        }
+    \end{formula}
 
 
 
diff --git a/src/comp/ad.tex b/src/comp/ad.tex
index 8d38ddd..d7dec09 100644
--- a/src/comp/ad.tex
+++ b/src/comp/ad.tex
@@ -2,86 +2,373 @@
     \eng{Atomic dynamics}
     % \ger{}
 ]{ad}
-    \Subsection[
-        \eng{Born-Oppenheimer Approximation}
-        \ger{Born-Oppenheimer Näherung}
-    ]{bo}
-        \begin{formula}{hamiltonian}
-            \desc{Electron Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:elsth:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:elsth:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
-            \desc[german]{Hamiltonian der Elektronen}{}{}
-            \eq{\hat{H}_\txe = \hat{T}_\txe + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe}}
+\begin{formula}{hamiltonian}
+    \desc{Electron Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:est:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
+    \desc[german]{Hamiltonian der Elektronen}{}{}
+    \eq{\hat{H}_\txe = \hat{T}_\txe + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe}}
+\end{formula}
+\begin{formula}{ansatz}
+    \desc{Wave function ansatz}{}{$\psi_\text{en}^n$ eigenstate $n$ of \fqEqRef{comp:est:hamiltonian}, $\psi_\txe^i$ eigenstate $i$ of \fqEqRef{comp:ad:bo:hamiltonian}, $\vecr,\vecR$ electron/nucleus positions, $\sigma$ electron spin, $c^{ni}$ coefficients}
+    \desc[german]{Wellenfunktion Ansatz}{}{}
+    \eq{\psi_\text{en}^n\big(\{\vecr,\sigma\},\{\vecR\}\big) = \sum_i c^{ni}\big(\{\vecR\}\big)\, \psi_\txe^i\big(\{\vecr,\sigma\},\{\vecR\}\big)}
+\end{formula}
+\begin{formula}{equation}
+    \desc{Equation}{}{}
+    % \desc[german]{}{}{}
+    \eq{
+        \label{eq:\fqname}
+        \left[E_\txe^j\big(\{\vecR\}\big) + \hat{T}_\txn + V_{\txn \leftrightarrow \txn} - E^n \right]c^{nj} = -\sum_i \Lambda_{ij} c^{ni}\big(\{\vecR\}\big)
+    }
+\end{formula}
+\begin{formula}{coupling_operator}
+    \desc{Exact nonadiabtic coupling operator}{Electron-phonon couplings / electron-vibrational couplings}{$\psi^i_\txe$ electronic states, $\vecR$ nucleus position, $M$ nucleus \qtyRef{mass}}
+    % \desc[german]{}{}{}
+    \begin{multline}
+        \Lambda_{ij} = \int \d^3r (\psi_\txe^j)^* \left(-\sum_I \frac{\hbar^2\nabla_{\vecR_I}^2}{2M_I}\right) \psi_\txe^i \\
+        + \sum_I \frac{1}{M_I} \int\d^3r \left[(\psi_\txe^j)^* (-i\hbar\nabla_{\vecR_I})\psi_\txe^i\right](-i\hbar\nabla_{\vecR_I})
+    \end{multline}
+\end{formula}
+
+\Subsection[
+    \eng{Born-Oppenheimer Approximation}
+    \ger{Born-Oppenheimer Näherung}
+]{bo}
+    \begin{formula}{adiabatic_approx}
+        \desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move (\absRef{adiabatic_theorem})}{$\Lambda_{ij}$ \fqEqRef{comp:ad:coupling_operator}} 
+        \desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{}
+        \eq{\Lambda_{ij} = 0 \quad \text{\GT{for} } i\neq j}
+    \end{formula}
+    \begin{formula}{approx}
+        \desc{Born-Oppenheimer approximation}{Electrons are not influenced by the movement of the atoms}{\GT{see} \fqEqRef{comp:ad:equation}, $V_{\txn \leftrightarrow \txn} = \const$ absorbed into $E_\txe^j$}
+        \desc[german]{Born-Oppenheimer Näherung}{Elektronen werden nicht durch die Bewegung der Atome beeinflusst}{}
+        \begin{gather}
+            \Lambda_{ij} = 0
+            \shortintertext{\fqEqRef{comp:ad:bo:equation} \Rightarrow}
+            \left[E_e^i\big(\{\vecR\}\big) + \hat{T}_\txn - E^n\right]c^{ni}\big(\{\vecR\}\big) = 0
+        \end{gather}
+    \end{formula}
+    \begin{formula}{surface}
+        \desc{Born-Oppenheimer surface}{Potential energy surface (PES)\\ The nuclei follow Newtons equations of motion on the BO surface if the system is in the electronic ground state}{$E_\txe^0, \psi_\txe^0$ lowest eigenvalue/eigenstate of \fqEqRef{comp:ad:bo:hamiltonian}}
+        \desc[german]{Born-Oppenheimer Potentialhyperfläche}{Die Nukleonen Newtons klassichen Bewegungsgleichungen auf der BO Hyperfläche wenn das System im elektronischen Grundzustand ist}{$E_\txe^0, \psi_\txe^0$ niedrigster Eigenwert/Eigenzustand vom \fqEqRef{comp:ad:bo:hamiltonian}}
+        \begin{gather}
+            V_\text{BO}\big(\{\vecR\}\big) = E_\txe^0\big(\{\vecR\}\big) \\
+            M_I \ddot{\vecR}_I(t) = - \Grad_{\vecR_I} V_\text{BO}\big(\{\vecR(t)\}\big)
+        \end{gather}
+    \end{formula}
+    \begin{formula}{ansatz}
+        \desc{Ansatz for \secEqRef{approx}}{Product of single electronic and single nuclear state}{}
+        \desc[german]{Ansatz für \secEqRef{approx}}{Produkt aus einem einzelnen elektronischen Zustand und einem Nukleus-Zustand}{}
+        \eq{
+            \psi_\text{BO} = c^{n0} \big(\{\vecR\}\big) \,\psi_\txe^0 \big(\{\vecr,\sigma\},\{\vecR\}\big)
+        }
+    \end{formula}
+
+    \begin{formula}{limitations}
+        \desc{Limitations}{}{$\tau$ passage of time for electrons/nuclei, $L$ characteristic length scale of atomic dynamics, $\dot{\vec{R}}$ nuclear velocity, $\Delta E$ difference between two electronic states}
+        \desc[german]{Limitationen}{}{}
+        \ttxt{
+            \eng{ 
+                \begin{itemize}
+                    \item Nuclei velocities must be small and electron energy state differences large
+                    \item Nuclei need spin for effects like spin-orbit coupling
+                    \item Nonadiabitc effects in photochemistry, proteins
+                \end{itemize}
+                Valid when Massey parameter $\xi \gg 1$
+            }
+        }
+        \eq{
+            \xi = \frac{\tau_\txn}{\tau_\txe} = \frac{L \Delta E}{\hbar \abs{\dot{\vecR}}}
+        }
+    \end{formula}   
+
+\Subsection[
+    \eng{Structure optimization}
+    \ger{Strukturoptimierung}
+]{opt}
+    \begin{formula}{forces}
+        \desc{Forces}{}{}
+        \desc[german]{Kräfte}{}{}
+        \eq{\vec{F}_I = -\Grad_{\vecR_I} E \explOverEq{\fqEqRef{qm:se:hellmann_feynmann}} -\Braket{\psi(\vecR_I) | \left(\Grad_{\vecR_I} \hat{H}(\vecR_I)\right) | \psi(\vecR) }}
+    \end{formula}
+    \begin{formula}{ionic_cycle}
+        \desc{Ionic cycle}{\fqEqRef{comp:est:dft:ks:scf} for geometry optimization}{}
+        \desc[german]{}{}{}
+        \ttxt{
+            \eng{
+                \begin{enumerate}
+                    \item Initial guess for $n(\vecr)$
+                    \begin{enumerate}
+                        \item Calculate effective potential $V_\text{eff}$
+                        \item Solve \fqEqRef{comp:est:dft:ks:equation}
+                        \item Calculate density $n(\vecr)$
+                        \item Repeat b-d until self consistent
+                    \end{enumerate}
+                    \item Calculate \secEqRef{forces}
+                    \item If $F\neq0$, get new geometry by interpolating $R$ and restart
+                \end{enumerate}
+            }
+        }
+    \end{formula}
+
+    \begin{formula}{transformation}
+        \desc{Transformation of atomic positions under stress}{}{$\alpha,\beta=1,2,3$ position components, $R$ position, $R(0)$ zero-strain position, $\ten{\epsilon}$ \qtyRef{strain} tensor}
+        \desc[german]{Transformation der Atompositionen unter Spannung}{}{$\alpha,\beta=1,2,3$ Positionskomponenten, $R$ Position, $R(0)$ Position ohne Dehnung, $\ten{\epsilon}$ \qtyRef{strain} Tensor}
+        \eq{R_\alpha(\ten{\epsilon}_{\alpha\beta}) = \sum_\beta \big(\delta_{\alpha\beta} + \ten{\epsilon}_{\alpha\beta}\big)R_\beta(0)}
+    \end{formula}
+
+    \begin{formula}{stress_tensor}
+        \desc{Stress tensor}{}{$\Omega$ unit cell volume, \ten{\epsilon} \qtyRef{strain} tensor}
+        \desc[german]{Spannungstensor}{}{}
+        \eq{\ten{\sigma}_{\alpha,\beta} = \frac{1}{\Omega} \pdv{E_\text{total}}{\ten{\epsilon}_{\alpha\beta}}_{\ten{\epsilon}=0}}
+    \end{formula}
+
+    \begin{formula}{pulay_stress}
+        \desc{Pulay stress}{}{}
+        \desc[german]{Pulay-Spannung}{}{}
+        \eq{
+            N_\text{PW} \propto E_\text{cut}^\frac{3}{2} \propto \abs{\vec{G}_\text{max}}^3
+        }
+        \ttxt{\eng{
+            Number of plane waves $N_\text{PW}$ depends on $E_\text{cut}$.
+            If $G$ changes during optimization, $N_\text{PW}$ may change, thus the basis set can change.
+            This typically leads to too small volumes.
+        }}
+    \end{formula}
+
+\Subsection[
+    \eng{Lattice vibrations}
+    \ger{Gitterschwingungen}
+]{latvib}
+    \begin{formula}{force_constant_matrix}
+        \desc{Force constant matrix}{}{}
+        % \desc[german]{}{}{}
+        \eq{\Phi_{IJ}^{\mu\nu} = \pdv{V(\{\vecR\})}{R_I^\mu,R_J^\nu}_{\{\vecR_I\}=\{\vecR_I^0\}}}
+    \end{formula}
+
+    \begin{formula}{harmonic_approx}
+        \desc{Harmonic approximation}{Hessian matrix, 2nd order Taylor expansion of the \fqEqRef{comp:ad:bo:surface} around every nucleus position $\vecR_I^0$}{$\Phi_{IJ}^{\mu\nu}$ \secEqRef{force_constant_matrix}, $s$ displacement}
+        \desc[german]{Harmonische Näherung}{Hesse matrix, Taylor Entwicklung der \fqEqRef{comp:ad:bo:surface} in zweiter Oddnung um Atomposition $\vecR_I^0$}{}
+        \eq{ V^\text{BO}(\{\vecR_I\}) \approx V^\text{BO}(\{\vecR_I^0\}) + \frac{1}{2} \sum_{I,J}^N \sum_{\mu,\nu}^3 s_I^\mu s_J^\nu \Phi_{IJ}^{\mu\nu} }
+    \end{formula}
+    
+    % solving difficult becaus we need to calculate (3N)^2 derivatives, Hellmann-Feynman cant be applied directly
+    % -> DFPT
+
+    % finite-difference method
+    \Subsubsection[
+        \eng{Finite difference method}
+        % \ger{}
+    ]{fin_diff}
+
+        \begin{formula}{approx}
+            \desc{Approximation}{Assume forces in equilibrium structure vanish}{$\Delta s$ displacement of atom $J$}
+            % \desc[german]{}{}{}
+            \eq{\Phi_{IJ}^{\mu\nu} \approx \frac{\vecF_I^\mu(\vecR_1^0, \dots, \vecR_J^0+\Delta s_J^\nu,\dots, \vecR_N^0)}{\Delta s_J^\nu}}
         \end{formula}
-        \begin{formula}{ansatz}
-            \desc{Wave function ansatz}{}{$\psi_\text{en}^n$ eigenstate $n$ of \fqEqRef{comp:elst:hamiltonian}, $\psi_\txe^i$ eigenstate $i$ of \fqEqRef{comp:ad:bo:hamiltonian}, $\vecr,\vecR$ electron/nucleus positions, $\sigma$ electron spin, $c^{ni}$ coefficients}
-            \desc[german]{Wellenfunktion Ansatz}{}{}
-            \eq{\psi_\text{en}^n\big(\{\vecr,\sigma\},\{\vecR\}\big) = \sum_i c^{ni}\big(\{\vecR\}\big)\, \psi_\txe^i\big(\{\vecr,\sigma\},\{\vecR\}\big)}
+        \begin{formula}{dynamical_matrix}
+            \desc{Dynamical matrix}{Mass reduced \absRef[fourier transform]{fourier_transform} of the \fqEqRef{comp:ad:latvib:force_constant_matrix}}{$\vec{L}$ vector from origin to unit cell $n$, $\alpha/\beta$ atom index in th unit cell, $\vecq$ \qtyRef{wave_vector}, $\Phi$ \fqEqRef{comp:ad:latvib:force_constant_matrix}, $M$ \qtyRef{mass}}
+            % \desc[german]{}{}{}
+            \eq{D_{\alpha\beta}^{\mu\nu} = \frac{1}{\sqrt{M_\alpha M_\beta}} \sum_{n^\prime} \Phi_{\alpha\beta}^{\mu\nu}(n-n^\prime) \e^{\I \vec{q}(\vec{L}_n - \vec{L}_{n^\prime})}}
         \end{formula}
-        \begin{formula}{equation}
-            \desc{Equation}{}{}
+
+        \begin{formula}{eigenvalue_equation}
+            \desc{Eigenvalue equation}{For a periodic crystal, reduces number of equations from $3N_p\times N$ to $3N_p$. Eigenvalues represent phonon band structure.}{$N_p$ number of atoms per unit cell, $\vecc$ displacement amplitudes, $\vecq$ \qtyRef{wave_vector}, $\mat{D}$ \secEqRef{dynamical_matrix}}
+            \desc[german]{Eigenwertgleichung}{}{}
+            \eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) }
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Anharmonic approaches}
+        \ger{Anharmonische Ansätze}
+    ]{anharmonic}
+
+        \begin{formula}{qha}
+            \desc{Quasi-harmonic approximation}{}{}
+            \desc[german]{}{}{}
+            \ttxt{\eng{
+                Include thermal expansion by assuming \fqEqRef{comp:ad:bo:surface} is volume dependant.
+            }}
+        \end{formula}
+
+        \begin{formula}{pertubative}
+            \desc{Pertubative approaches}{}{}
+            % \desc[german]{Störungs}{}{}
+            \ttxt{\eng{
+                Expand \fqEqRef{comp:ad:latvib:force_constant_matrix} to third order.
+            }}
+        \end{formula}
+
+    
+
+
+\Subsection[
+    \eng{Molecular Dynamics}
+    \ger{Molekulardynamik}
+]{md} \abbrLink{md}{MD}
+    \begin{formula}{desc}
+        \desc{Description}{}{}
+        \desc[german]{Beschreibung}{}{}
+        \ttxt{\eng{
+            \begin{itemize}
+                \item Exact (within previous approximations) approach to treat anharmonic effects in materials.
+                \item Computes time-dependant observables.
+                \item Assumes fully classical nuclei.
+                \item Macroscropical observables from statistical ensembles 
+                \item System evolves in time (ehrenfest). Number of points to consider does NOT scale with system size.
+                \item Exact because time dependance is studied explicitly, not via harmonic approx.
+            \end{itemize}
+            \TODO{cleanup}
+        }}
+    \end{formula}
+
+    \begin{formula}{procedure}
+        \desc{MD simulation procedure}{}{}
+        \desc[german]{Ablauf von MD Simulationen}{}{}
+        \ttxt{\eng{
+            \begin{enumerate}
+                \item Initialize with optimized geometry, interaction potential, ensemble, integration scheme, temperature/pressure control
+                \item Equilibrate to desired temperature/pressure (eg with statistical starting velocities)
+                \item Production run, run MD long enough to calculate desired observables
+            \end{enumerate}
+        }}
+    \end{formula}
+
+    \Subsubsection[
+        \eng{Ab-initio molecular dynamics}
+        \ger{Ab-initio molecular dynamics}
+    ]{ab-initio}
+        \begin{formula}{bomd}
+            \abbrLabel{BOMD}
+            \desc{Born-Oppenheimer MD (BOMD)}{}{}
+            \desc[german]{Born-Oppenheimer MD (BOMD)}{}{}
+            \ttxt{\eng{
+                \begin{enumerate}
+                    \item Calculate electronic ground state of current nucleui configuration $\{\vecR(t)\}$ with \abbrRef{ksdft}
+                    \item \hyperref[f:comp:ad:opt:forces]{Calculate forces} from the \fqEqRef{comp:ad:bo:surface} 
+                    \item  Update positions and velocities
+                \end{enumerate}
+                \begin{itemize}
+                    \gooditem "ab-inito" - no empirical information required
+                    \baditem Many expensive \abbrRef{dft} calculations
+                \end{itemize}
+            }}
+        \end{formula}
+
+        \begin{formula}{cpmd}
+            \desc{Car-Parrinello MD (CPMD)}{}{$\mu$ electron orbital mass, $\varphi_i$ \abbrRef{ksdft} eigenststate, $\lambda_{ij}$ Lagrange multiplier}
+            \desc[german]{Car-Parrinello MD (CPMD)}{}{}
+            \ttxt{\eng{
+                Evolve electronic wave function $\varphi$ (adiabatically) along with the nuclei \Rightarrow only one full \abbrRef{ksdft} 
+            }}
+            \begin{gather}
+                M_I \odv[2]{\vecR_I}{t} = -\Grad_{\vecR_I} E[\{\varphi_i\},\{\vecR_I\}] \\
+                % not using pdv because of comma in parens
+                % E[\{\varphi_i\}\{\vecR_I\}] = \Braket{\psi_0|H_\text{el}^\text{KS}|\psi_0}
+                \mu \odv[2]{\varphi_i(\vecr,t)}{t} = - \frac{\partial}{\partial\varphi_i^*(\vecr,t)} E[\{\varphi_i\},\{\vecR_I\}] + \sum_j \lambda_{ij} \varphi_j(\vecr,t)
+            \end{gather}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Force-field MD}
+        \ger{Force-field MD}
+    ]{ff}
+
+        \begin{formula}{ffmd}
+            \desc{Force field MD (FFMD)}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{\eng{
+                \begin{itemize}
+                    \item Use empirical interaction potential instead of electronic structure
+                    \baditem Force fields need to be fitted for specific material \Rightarrorw not transferable 
+                    \gooditem Faster than \abbrRef{bomd}
+                    \item Example: \absRef{lennard_jones}
+                \end{itemize}
+            }}
+        \end{formula}
+
+
+
+    \Subsubsection[
+        \eng{Integration schemes}
+        % \ger{}
+    ]{scheme}
+        \begin{ttext} 
+            \eng{Procedures for updating positions and velocities to obey the equations of motion.}
+        \end{ttext}
+        
+        \begin{formula}{euler}
+            \desc{Euler method}{First-order procedure for solving \abbrRef{ode}s with a given initial value.\\Taylor expansion of $\vecR/\vecv (t+\Delta t)$}{}
+            \desc[german]{Euler-Verfahren}{Prozedur um gewöhnliche DGLs mit Anfangsbedingungen in erster Ordnung zu lösen.\\Taylor Entwicklung von $\vecR/\vecv (t+\Delta t)$}{}
+            \eq{
+                \vecR(t+\Delta t) &= \vecR(t) + \vecv(t) \Delta t + \Order{\Delta t^2} \\
+                \vecv(t+\Delta t) &= \vecv(t) + \veca(t) \Delta t + \Order{\Delta t^2}
+            }
+            \ttxt{\eng{
+                Cumulative error scales linearly $\Order{\Delta t}$. Not time reversible.
+            }}
+        \end{formula}
+
+        \begin{formula}{verlet}
+            \desc{Verlet integration}{Preverses time reversibility, does not require velocity updates}{}
+            \desc[german]{Verlet-Algorithmus}{Zeitumkehr-symmetrisch}{}
+            \eq{
+                \vecR(t+\Delta t) = 2\vecR(t) -\vecR(t-\Delta t) + \veca(t) \Delta t^2 + \Order{\Delta t^4}
+            }
+        \end{formula}
+        
+        \begin{formula}{velocity-verlet}
+            \desc{Velocity-Verlet integration}{}{}
             % \desc[german]{}{}{}
             \eq{
-                \label{eq:\fqname}
-                \left[E_\txe^j\big(\{\vecR\}\big) + \hat{T}_\txn + V_{\txn \leftrightarrow \txn} - E^n \right]c^{nj} = -\sum_i \Lambda_{ij} c^{ni}\big(\{\vecR\}\big)
+                \vecR(t+\Delta t) &= \vecR(t) + \vecv(t)\Delta t + \frac{1}{2} \veca(t) \Delta t^2 + \Order{\Delta t^4} \\
+                \vecv(t+\Delta t) &= \vecv(t) + \frac{\veca(t) + \veca(t+\Delta t)}{2} \Delta t + \Order{\Delta t^4} 
             }
         \end{formula}
-        \begin{formula}{coupling_operator}
-            \desc{Exact nonadiabtic coupling operator}{Electron-phonon couplings / electron-vibrational couplings}{$\psi^i_\txe$ electronic states, $\vecR$ nucleus position, $M$ nucleus \qtyRef{mass}}
+        
+        \TODO{leapfrog}
+
+    \Subsubsection[
+        \eng{Thermostats and barostats}
+        \ger{Thermostate und Barostate}
+    ]{stats}
+        \begin{formula}{velocity_rescaling}
+            \desc{Velocity rescaling}{Thermostat, keep temperature at $T_0$ by rescaling velocities. Does not allow temperature fluctuations and thus does not obey the \absRef{c_ensemble}}{$T$ target \qtyRef{temperature}, $M$ \qtyRef{mass} of nucleon $I$, $\vecv$ \qtyRef{velocity}, $f$ number of degrees of freedom, $\lambda$ velocity scaling parameter, \ConstRef{boltzmann}}
             % \desc[german]{}{}{}
-            \begin{multline}
-                \Lambda_{ij} = \int \d^3r (\psi_\txe^j)^* \left(-\sum_I \frac{\hbar^2\nabla_{\vecR_I}^2}{2M_I}\right) \psi_\txe^i \\
-                + \sum_I \frac{1}{M_I} \int\d^3r \left[(\psi_\txe^j)^* (-i\hbar\nabla_{\vecR_I})\psi_\txe^i\right](-i\hbar\nabla_{\vecR_I})
-            \end{multline}
-        \end{formula}
-        \begin{formula}{adiabatic_approx}
-            \desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move}{$\Lambda_{ij}$ \fqEqRef{comp:ad:bo:coupling_operator}} 
-            \desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleich}{}
-            \eq{\Lambda_{ij} = 0 \quad \text{\GT{for} } i\neq j}
-        \end{formula}
-        \begin{formula}{approx}
-            \desc{Born-Oppenheimer approximation}{}{\GT{see} \fqEqRef{comp:ad:bo:equation}}
-            \desc[german]{Born-Oppenheimer Näherung}{}{}
-            \begin{gather}
-                \Lambda_{ij} = 0
-                \shortintertext{\fqEqRef{comp:ad:bo:equation} \Rightarrow}
-                \left[E_e^i\big(\{\vecR\}\big) + \hat{T}_\txn - E^n\right]c^{ni}\big(\{\vecR\}\big) = 0
-            \end{gather}
-        \end{formula}
-
-        \begin{formula}{surface}
-            \desc{Born-Oppenheimer surface}{Potential energy surface (PES)\\ The nuclei follow Newtons equations of motion on the BO surface if the system is in the electronic ground state}{$E_\txe^0, \psi_\txe^0$ lowest eigenvalue/eigenstate of \fqEqRef{comp:ad:bo:hamiltonian}}
-            \desc[german]{Born-Oppenheimer Potentialhyperfläche}{Die Nukleonen Newtons klassichen Bewegungsgleichungen auf der BO Hyperfläche wenn das System im elektronischen Grundzustand ist}{$E_\txe^0, \psi_\txe^0$ niedrigster Eigenwert/Eigenzustand vom \fqEqRef{comp:ad:bo:hamiltonian}}
-            \begin{gather}
-                V_\text{BO}\big(\{\vecR\}\big) = E_\txe^0\big(\{\vecR\}\big) \\
-                M_I \ddot{\vecR}_I(t) = - \Grad_{\vecR_I} V_\text{BO}\big(\{\vecR(t)\}\big)
-                \shortintertext{\GT{ansatz} \GT{for} \fqEqRef{comp:ad:bo:approx}}
-                \psi_\text{BO} = c^{n0} \big(\{\vecR\}\big) \,\psi_\txe^0 \big(\{\vecr,\sigma\},\{\vecR\}\big)
-            \end{gather}
-        \end{formula}
-
-        \begin{formula}{limitations}
-            \desc{Limitations}{}{}
-            \desc[german]{Limitationen}{}{}
-            \ttxt{
-                \eng{ 
-                    \begin{itemize}
-                        \item Nuclei velocities must be small and electron energy state differences large
-                        \item Nuclei need spin for effects like spin-orbit coupling
-                        \item Nonadiabitc effects in photochemistry, proteins
-                    \end{itemize}
-                }
+            \eq{
+                \Delta T(t) &= T_0 - T(t) \\
+                            &= \sum_I^N \frac{M_I\,(\lambda \vecv_I(t))^2}{f\kB} - \sum_I^N \frac{M_I\,\vecv_I(t)^2}{f\kB} \\
+                            &= (\lambda^2 - 1) T(t)
             }
-        \end{formula}   
-        \TODO{geometry optization?, lattice vibrations (harmionic approx, dynamical matrix)}
+            \eq{\lambda = \sqrt{\frac{T_0}{T(t)}}}
+        \end{formula}
 
+        \begin{formula}{berendsen}
+            \desc{Berendsen thermostat}{Does not obey \absRef{c_ensemble} but efficiently brings system to target temperature}{}
+            % \desc[german]{}{}{}
+            \eq{\odv{T}{t} = \frac{T_0-T}{\tau}}
+        \end{formula}
 
-        \Subsection[
-            \eng{Molecular Dynamics}
-            \ger{Molekulardynamik}
-        ]{md}
-        \begin{ttext}
-            \eng{Statistical method}
-            
-        \end{ttext}
+        \begin{formula}{nose-hoover}
+            \desc{Nosé-Hoover thermostat}{Control the temperature with by time stretching with an associated mass.\\Compliant with \absRef{c_ensemble}}{$s$ scaling factor, $Q$ associated "mass", $\mathcal{L}$ \absRef{lagrangian}, $g$ degrees of freedom}
+            \desc[german]{Nosé-Hoover Thermostat}{}{}
+            \begin{gather}
+                \d\tilde{t} = \tilde{s}\d t \\
+                \mathcal{L} = \sum_{I=1}^N \frac{1}{2} M_I \tilde{s}^2 v_i^2 - V(\tilde{\vecR}_1, \ldots, \tilde{\vecR}_I, \ldots, \tilde{\vecR}_N) + \frac{1}{2} Q \dot{\tilde{s}}^2 - g \kB T_0 \ln \tilde{s}
+            \end{gather}
+        \end{formula}
 
-        \TODO{ab-initio MD, force-field MD}
+    \Subsubsection[
+        \eng{Calculating observables}
+        \ger{Berechnung von Observablen}
+    ]{obs}
+        \begin{formula}{spectral_density}
+            \desc{Spectral density}{Wiener-Khinchin theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{$C$ \absRef{autocorrelation}}
+            \desc[german]{Spektraldichte}{Wiener-Khinchin Theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{}
+            \eq{S(\omega) = \int_{-\infty}^\infty \d\tau C(\tau) \e^{-\I\omega t} }
+        \end{formula}
 
+        \begin{formula}{vdos} \abbrLabel{VDOS}
+            \desc{Vibrational density of states (VDOS)}{}{$S_{v_i}$ velocity \secEqRef{spectral_density} of particle $I$}
+            \desc[german]{Vibrationszustandsdicht (VDOS)}{}{}
+            \eq{g(\omega) \sim \sum_{I=1}^N M_I S_{v_I}(\omega)}
+        \end{formula}
diff --git a/src/comp/elsth.tex b/src/comp/elsth.tex
deleted file mode 100644
index 38748e4..0000000
--- a/src/comp/elsth.tex
+++ /dev/null
@@ -1,183 +0,0 @@
-\Section[
-    \eng{Electronic structure theory}
-    % \ger{}
-]{elst}
-    \begin{formula}{kinetic_energy}
-        \desc{Kinetic energy}{of species $i$}{$i$ = nucleons/electrons, $N$ number of particles, $m$ \qtyRef{mass}}
-        \desc[german]{Kinetische Energie}{von Spezies $i$}{$i$ = Nukleonen/Elektronen, $N$ Teilchenzahl, $m$ \qtyRef{mass}}
-        \eq{\hat{T}_i &= -\sum_{n=1}^{N_i} \frac{\hbar^2}{2 m_i} \vec{\nabla}^2_n}
-    \end{formula}
-    \begin{formula}{potential_energy}
-        \desc{Electrostatic potential}{between species $i$ and $j$}{$i,j$ = nucleons/electrons, $r$ particle position, $Z_i$ charge of species $i$, \ConstRef{charge}}
-        \desc[german]{Elektrostatisches Potential}{zwischen Spezies $i$ und $j$}{}
-        \eq{\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j e^2}{\abs{\vecr_k - \vecr_l}}}
-    \end{formula}
-    \begin{formula}{hamiltonian}
-        \desc{Electronic structure Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:elsth:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:elsth:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
-        \eq{\hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe} + V_{\txn \leftrightarrow \txn}}
-    \end{formula}
-    \begin{formula}{mean_field}
-        \desc{Mean field approximation}{Replaces 2-particle operator by 1-particle operator}{Example for Coulumb interaction between many electrons}
-        \desc[german]{Molekularfeldnäherung}{Ersetzt 2-Teilchen Operator durch 1-Teilchen Operator}{Beispiel für Coulumb Wechselwirkung zwischen Elektronen}
-        \eq{
-            \frac{1}{2}\sum_{i\neq j} \frac{e^2}{\abs{\vec{r}_i - \vec{r}_j}} \approx \sum_{i} V_\text{eff}(\vec{r}_i)
-        }
-    \end{formula}
-
-
-\Subsection[
-    \eng{Tight-binding}
-    \ger{Modell der stark gebundenen Elektronen / Tight-binding}
-]{tb}
-    \begin{formula}{assumptions}
-        \desc{Assumptions}{}{}
-        \desc[german]{Annahmen}{}{}
-        \ttxt{
-            \eng{
-                \begin{itemize}
-                    \item Atomic wave functions are localized \Rightarrow Small overlap, interaction cutoff
-                \end{itemize}
-            }
-        }
-    \end{formula}
-    \begin{formula}{hamiltonian}
-        \desc{Tight-binding Hamiltonian}{in second quantized form}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} create/destory an electron on site $i$, $\epsilon_i$ on-site energy, $t_{i,j}$ hopping amplitude, usually $\epsilon$ and $t$ are determined from experiments or other methods}
-        \desc[german]{Tight-binding Hamiltonian}{in zweiter Quantisierung}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} erzeugen/vernichten ein Elektron auf Platz $i$, $\epsilon_i$ on-site Energie, $t_{i,j}$ hopping Amplitude, meist werden $\epsilon$ und $t$ aus experimentellen Daten oder anderen Methoden bestimmt}
-        \eq{\hat{H} = \sum_i \epsilon_i \hat{a}_i^\dagger \hat{a}_i - \sum_{i,j} t_{i,j} \left(\hat{a}_i^\dagger \hat{a}_j + \hat{a}_j^\dagger \hat{a}_i\right)}
-    \end{formula}
-    
-
-
-\Subsection[
-    \eng{Density functional theory (DFT)}
-    \ger{Dichtefunktionaltheorie (DFT)}
-]{dft}
-    \Subsubsection[
-        \eng{Hartree-Fock}
-        \ger{Hartree-Fock}
-    ]{hf}
-        \begin{formula}{description}
-            \desc{Description}{}{}
-            \desc[german]{Beschreibung}{}{}
-            \begin{ttext}
-                \eng{
-                    \begin{itemize}
-                        \item \fqEqRef{comp:elst:mean_field} theory obeying the Pauli principle
-                        \item Self-interaction free: Self interaction is cancelled out by the Fock-term
-                    \end{itemize}
-                }
-            \end{ttext}
-        \end{formula}
-        \begin{formula}{equation}
-            \desc{Hartree-Fock equation}{}{
-                $\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
-                $\hat{T}$ kinetic electron energy,
-                $\hat{V}_{\text{en}}$ electron-nucleus attraction,
-                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential},
-            }
-            \desc[german]{Hartree-Fock Gleichung}{}{
-                $\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
-                $\hat{T}$ kinetische Energie der Elektronen,
-                $\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
-                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}
-            }
-            \eq{
-                \left(\hat{T} + \hat{V}_{\text{en}} + \hat{V}_{\text{HF}}^\xi\right)\varphi_\xi(x) = \epsilon_\xi \varphi_\xi(x)
-            }
-        \end{formula}
-        \begin{formula}{potential}
-            \desc{Hartree-Fock potential}{}{}
-            \desc[german]{Hartree Fock Potential}{}{}
-            \eq{
-                V_{\text{HF}}^\xi(\vecr) = 
-                \sum_{\vartheta} \int \d x' 
-                \frac{e^2}{\abs{\vecr - \vecr'}}
-                \left(
-                    \underbrace{\abs{\varphi_\xi(x')}^2}_{\text{Hartree-Term}}
-                    - \underbrace{\frac{\varphi_{\vartheta}^*(x') \varphi_{\xi}(x') \varphi_{\vartheta}(x)}{\varphi_\xi(x)}}_{\text{Fock-Term}}
-                \right)
-            }
-        \end{formula}
-        \begin{formula}{scf}
-            \desc{Self-consistent field cycle}{}{}
-            % \desc[german]{}{}{}
-            \ttxt{
-                \eng{
-                    \begin{enumerate}
-                        \item Initial guess for $\psi$
-                        \item Solve SG for each particle
-                        \item Make new guess for $\psi$
-                    \end{enumerate}
-                }
-            }
-        \end{formula}
-
-    \Subsubsection[
-        \eng{Hohenberg-Kohn Theorems}
-        \ger{Hohenberg-Kohn Theoreme}
-    ]{hk}
-        \begin{formula}{hk1}
-            \desc{Hohenberg-Kohn theorem (HK1)}{}{}
-            \desc[german]{Hohenberg-Kohn Theorem (HK1)}{}{}
-            \ttxt{
-                \eng{For any system of interacting electrons, the ground state electron density $n(\vecr)$ determines $\hat{V}_\text{ext}$ uniquely up to a trivial constant. }
-                \ger{Die Elektronendichte des Grundzustandes $n(\vecr)$ bestimmt ein einzigartiges $\hat{V}_{\text{ext}}$ eines Systems aus interagierenden Elektronen bis auf eine Konstante.}
-            }
-        \end{formula}
-        \begin{formula}{hk2}
-            \desc{Hohenberg-Kohn theorem (HK2)}{}{}
-            \desc[german]{Hohenberg-Kohn Theorem (HK2)}{}{}
-            \ttxt{
-                \eng{Given the energy functional $E[n(\vecr)]$, the ground state density and energy can be obtained variationally. The density that minimizes the total energy is the ecxact ground state density. }
-                \ger{Für ein Energiefunktional $E[n(\vecr)]$ kann die Grundzustandsdichte und Energie durch systematische Variation bestimmt werden. Die Dichte, welche die Gesamtenergie minimiert ist die exakte Grundzustandsichte. }
-            }
-        \end{formula}
-
-    \Subsubsection[
-        \eng{Kohn-Sham DFT}
-        \ger{Kohn-Sham DFT}
-    ]{ks}
-        \begin{formula}{map}
-            \desc{Kohn-Sham map}{}{}
-            \desc[german]{Kohn-Sham Map}{}{}
-            \ttxt{
-                \eng{Maps fully interacting system of electrons to a system of non-interacting electrons with the same ground state density $n^\prime(\vecr) = n(\vecr)$}
-            }
-            \eq{n(\vecr) = \sum_{i=1}^N \abs{\phi_i(\vecr)}^2}
-        \end{formula}
-        \begin{formula}{functional}
-            \desc{Kohn-Sham functional}{}{$T_\text{KS}$ kinetic enery, $V_\text{ext}$ external potential, $E_\txH$ \hyperref[f:comp:elst:dft:hf:potential]{Hartree term}, $E_\text{XC}$ exchange correlation functional}
-            \desc[german]{Kohn-Sham Funktional}{}{}
-            \eq{E_\text{KS}[n(\vecr)] = T_\text{KS}[n(\vecr)] + V_\text{ext}[n(\vecr)] + E_\text{H}[n(\vecr)] + E_\text{XC}[n(\vecr)] }
-        \end{formula}   
-
-        \begin{formula}{equation}
-            \desc{Kohn-Sham equation}{Solving it uses up a large portion of supercomputer resources}{$\phi_i^\text{KS}$ KS orbitals}
-            \desc[german]{Kohn-Sham Gleichung}{Die Lösung der Gleichung macht einen großen Teil der Supercomputer Ressourcen aus}{}
-            \begin{multline}
-                \biggr\{
-                    -\frac{\hbar^2\nabla^2}{2m} 
-                    + v_\text{ext}(\vecr)
-                    + e^2 \int\d^3 \vecr^\prime \frac{n(\vecr^\prime)}{\abs{\vecr-\vecr^\prime}} \\
-                    + \pdv{E_\txX[n(\vecr)]}{n(\vecr)} 
-                    + \pdv{E_\txC[n(\vecr)]}{n(\vecr)}
-                \biggr\} \phi_i^\text{KS}(\vecr) =\\
-                = \epsilon_i^\text{KS} \phi_i^\text{KS}(\vecr)
-            \end{multline}
-        \end{formula}
-        \begin{formula}{scf}
-            \desc{Self-consistent field cycle for Kohn-Sham}{}{}
-            % \desc[german]{}{}{}
-            \ttxt{
-                \itemsep=\parsep
-                \eng{
-                    \begin{enumerate}
-                        \item Initial guess for $n(\vecr)$
-                        \item Calculate effective potential $V_\text{eff}$
-                        \item Solve \fqEqRef{comp:elst:dft:ks:equation}
-                        \item Calculate density $n(\vecr)$
-                        \item Repeat 2-4 until self consistent
-                    \end{enumerate}
-                }
-            }
-        \end{formula}
diff --git a/src/comp/est.tex b/src/comp/est.tex
new file mode 100644
index 0000000..542036c
--- /dev/null
+++ b/src/comp/est.tex
@@ -0,0 +1,289 @@
+\Section[
+    \eng{Electronic structure theory}
+    % \ger{}
+]{est}
+
+\begin{formula}{kinetic_energy}
+    \desc{Kinetic energy}{of species $i$}{$i$ = nucleons/electrons, $N$ number of particles, $m$ \qtyRef{mass}}
+    \desc[german]{Kinetische Energie}{von Spezies $i$}{$i$ = Nukleonen/Elektronen, $N$ Teilchenzahl, $m$ \qtyRef{mass}}
+    \eq{\hat{T}_i &= -\sum_{n=1}^{N_i} \frac{\hbar^2}{2 m_i} \vec{\nabla}^2_n}
+\end{formula}
+\begin{formula}{potential_energy}
+    \desc{Electrostatic potential}{between species $i$ and $j$}{$i,j$ = nucleons/electrons, $r$ particle position, $Z_i$ charge of species $i$, \ConstRef{charge}}
+    \desc[german]{Elektrostatisches Potential}{zwischen Spezies $i$ und $j$}{}
+    \eq{\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j e^2}{\abs{\vecr_k - \vecr_l}}}
+\end{formula}
+\begin{formula}{hamiltonian}
+    \desc{Electronic structure Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:est:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
+    \eq{\hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe} + V_{\txn \leftrightarrow \txn}}
+\end{formula}
+\begin{formula}{mean_field}
+    \desc{Mean field approximation}{Replaces 2-particle operator by 1-particle operator}{Example for Coulomb interaction between many electrons}
+    \desc[german]{Molekularfeldnäherung}{Ersetzt 2-Teilchen Operator durch 1-Teilchen Operator}{Beispiel für Coulomb Wechselwirkung zwischen Elektronen}
+    \eq{
+        \frac{1}{2}\sum_{i\neq j} \frac{e^2}{\abs{\vec{r}_i - \vec{r}_j}} \approx \sum_{i} V_\text{eff}(\vec{r}_i)
+    }
+\end{formula}
+
+
+\Subsection[
+    \eng{Tight-binding}
+    \ger{Modell der stark gebundenen Elektronen / Tight-binding}
+]{tb}
+    \begin{formula}{assumptions}
+        \desc{Assumptions}{}{}
+        \desc[german]{Annahmen}{}{}
+        \ttxt{
+            \eng{
+                \begin{itemize}
+                    \item Atomic wave functions are localized \Rightarrow Small overlap, interaction cutoff
+                \end{itemize}
+            }
+        }
+    \end{formula}
+    \begin{formula}{hamiltonian}
+        \desc{Tight-binding Hamiltonian}{in second quantized form}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} create/destory an electron on site $i$, $\epsilon_i$ on-site energy, $t_{i,j}$ hopping amplitude, usually $\epsilon$ and $t$ are determined from experiments or other methods}
+        \desc[german]{Tight-binding Hamiltonian}{in zweiter Quantisierung}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} erzeugen/vernichten ein Elektron auf Platz $i$, $\epsilon_i$ on-site Energie, $t_{i,j}$ hopping Amplitude, meist werden $\epsilon$ und $t$ aus experimentellen Daten oder anderen Methoden bestimmt}
+        \eq{\hat{H} = \sum_i \epsilon_i \hat{a}_i^\dagger \hat{a}_i - \sum_{i,j} t_{i,j} \left(\hat{a}_i^\dagger \hat{a}_j + \hat{a}_j^\dagger \hat{a}_i\right)}
+    \end{formula}
+    
+
+
+\Subsection[
+    \eng{Density functional theory (DFT)}
+    \ger{Dichtefunktionaltheorie (DFT)}
+]{dft}
+    \abbrLink{dft}{DFT}
+    \Subsubsection[
+        \eng{Hartree-Fock}
+        \ger{Hartree-Fock}
+    ]{hf}
+        \begin{formula}{description}
+            \desc{Description}{}{}
+            \desc[german]{Beschreibung}{}{}
+            \begin{ttext}
+                \eng{
+                    \begin{itemize}
+                        \item Assumes wave functions are \fqEqRef{qm:other:slater_det} \Rightarrow Approximation
+                        \item \fqEqRef{comp:est:mean_field} theory obeying the Pauli principle
+                        \item Self-interaction free: Self interaction is cancelled out by the Fock-term
+                    \end{itemize}
+                }
+            \end{ttext}
+        \end{formula}
+        \begin{formula}{equation}
+            \desc{Hartree-Fock equation}{}{
+                $\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
+                $\hat{T}$ kinetic electron energy,
+                $\hat{V}_{\text{en}}$ electron-nucleus attraction,
+                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential},
+            }
+            \desc[german]{Hartree-Fock Gleichung}{}{
+                $\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
+                $\hat{T}$ kinetische Energie der Elektronen,
+                $\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
+                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}
+            }
+            \eq{
+                \left(\hat{T} + \hat{V}_{\text{en}} + \hat{V}_{\text{HF}}^\xi\right)\varphi_\xi(x) = \epsilon_\xi \varphi_\xi(x)
+            }
+        \end{formula}
+        \begin{formula}{potential}
+            \desc{Hartree-Fock potential}{}{}
+            \desc[german]{Hartree Fock Potential}{}{}
+            \eq{
+                V_{\text{HF}}^\xi(\vecr) = 
+                \sum_{\vartheta} \int \d x' 
+                \frac{e^2}{\abs{\vecr - \vecr'}}
+                \left(
+                    \underbrace{\abs{\varphi_\xi(x')}^2}_{\text{Hartree-Term}}
+                    - \underbrace{\frac{\varphi_{\vartheta}^*(x') \varphi_{\xi}(x') \varphi_{\vartheta}(x)}{\varphi_\xi(x)}}_{\text{Fock-Term}}
+                \right)
+            }
+        \end{formula}
+        \begin{formula}{scf}
+            \desc{Self-consistent field cycle}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{
+                \eng{
+                    \begin{enumerate}
+                        \item Initial guess for $\psi$
+                        \item Solve SG for each particle
+                        \item Make new guess for $\psi$
+                    \end{enumerate}
+                }
+            }
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Hohenberg-Kohn Theorems}
+        \ger{Hohenberg-Kohn Theoreme}
+    ]{hk}
+        \begin{formula}{hk1}
+            \desc{Hohenberg-Kohn theorem (HK1)}{}{}
+            \desc[german]{Hohenberg-Kohn Theorem (HK1)}{}{}
+            \ttxt{
+                \eng{For any system of interacting electrons, the ground state electron density $n(\vecr)$ determines $\hat{V}_\text{ext}$ uniquely up to a trivial constant. }
+                \ger{Die Elektronendichte des Grundzustandes $n(\vecr)$ bestimmt ein einzigartiges $\hat{V}_{\text{ext}}$ eines Systems aus interagierenden Elektronen bis auf eine Konstante.}
+            }
+        \end{formula}
+        \begin{formula}{hk2}
+            \desc{Hohenberg-Kohn theorem (HK2)}{}{}
+            \desc[german]{Hohenberg-Kohn Theorem (HK2)}{}{}
+            \ttxt{
+                \eng{Given the energy functional $E[n(\vecr)]$, the ground state density and energy can be obtained variationally. The density that minimizes the total energy is the ecxact ground state density. }
+                \ger{Für ein Energiefunktional $E[n(\vecr)]$ kann die Grundzustandsdichte und Energie durch systematische Variation bestimmt werden. Die Dichte, welche die Gesamtenergie minimiert ist die exakte Grundzustandsichte. }
+            }
+        \end{formula}
+
+        \begin{formula}{density}
+            \desc{Ground state electron density}{}{}
+            \desc[german]{Grundzustandselektronendichte}{}{}
+            \eq{n(\vecr) = \Braket{\psi_0|\sum_{i=1}^N \delta(\vecr-\vecr_i)|\psi_0}}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Kohn-Sham DFT}
+        \ger{Kohn-Sham DFT}
+    ]{ks}
+        \abbrLink{ksdft}{KS-DFT}
+        \begin{formula}{map}
+            \desc{Kohn-Sham map}{}{}
+            \desc[german]{Kohn-Sham Map}{}{}
+            \ttxt{
+                \eng{Maps fully interacting system of electrons to a system of non-interacting electrons with the same ground state density $n^\prime(\vecr) = n(\vecr)$}
+            }
+            \eq{n(\vecr) = \sum_{i=1}^N \abs{\phi_i(\vecr)}^2}
+        \end{formula}
+        \begin{formula}{functional}
+            \desc{Kohn-Sham functional}{}{$T_\text{KS}$ kinetic enery, $V_\text{ext}$ external potential, $E_\txH$ \hyperref[f:comp:est:dft:hf:potential]{Hartree term}, $E_\text{XC}$ \fqEqRef{comp:est:dft:xc:xc}}
+            \desc[german]{Kohn-Sham Funktional}{}{}
+            \eq{E_\text{KS}[n(\vecr)] = T_\text{KS}[n(\vecr)] + V_\text{ext}[n(\vecr)] + E_\text{H}[n(\vecr)] + E_\text{XC}[n(\vecr)] }
+        \end{formula}   
+
+        \begin{formula}{equation}
+            \desc{Kohn-Sham equation}{Exact single particle \abbrRef{schroedinger_equation} (though often exact $E_\text{XC}$ is not known)\\ Solving it uses up a large portion of supercomputer resources}{$\phi_i^\text{KS}$ KS orbitals, $\int\d^3r v_\text{ext}(\vecr)n(\vecr)=V_\text{ext}[n(\vecr)]$}
+            \desc[german]{Kohn-Sham Gleichung}{Exakte Einteilchen-\abbrRef{schroedinger_equation} (allerdings ist das exakte $E_\text{XC}$ oft nicht bekannt)\\ Die Lösung der Gleichung macht einen großen Teil der Supercomputer Ressourcen aus}{}
+            \begin{multline}
+                \biggr\{
+                    -\frac{\hbar^2\nabla^2}{2m} 
+                    + v_\text{ext}(\vecr)
+                    + e^2 \int\d^3 \vecr^\prime \frac{n(\vecr^\prime)}{\abs{\vecr-\vecr^\prime}} \\
+                    + \pdv{E_\txX[n(\vecr)]}{n(\vecr)} 
+                    + \pdv{E_\txC[n(\vecr)]}{n(\vecr)}
+                \biggr\} \phi_i^\text{KS}(\vecr) =\\
+                = \epsilon_i^\text{KS} \phi_i^\text{KS}(\vecr)
+            \end{multline}
+        \end{formula}
+        \begin{formula}{scf}
+            \desc{Self-consistent field cycle for Kohn-Sham}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{
+                \itemsep=\parsep
+                \eng{
+                    \begin{enumerate}
+                        \item Initial guess for $n(\vecr)$
+                        \item Calculate effective potential $V_\text{eff}$
+                        \item Solve \fqEqRef{comp:est:dft:ks:equation}
+                        \item Calculate density $n(\vecr)$
+                        \item Repeat 2-4 until self consistent
+                    \end{enumerate}
+                }
+            }
+        \end{formula}
+
+        \Subsubsection[
+            \eng{Exchange-Correlation functionals}
+            \ger{Exchange-Correlation Funktionale}
+        ]{xc}
+            \begin{formula}{xc}
+                \desc{Exchange-Correlation functional}{}{}
+                \desc[german]{Exchange-Correlation Funktional}{}{}
+                \eq{ E_\text{XC}[n(\vecr)] = \Braket{\hat{T}} - T_\text{KS}[n(\vecr)] + \Braket{\hat{V}_\text{int}} - E_\txH[n(\vecr)] }
+                \ttxt{\eng{
+                    Accounts for:
+                    \begin{itemize}
+                            \item Kinetic energy difference between interaction and non-interacting system
+                            \item Exchange energy due to Pauli principle
+                            \item Correlation energy due to many-body Coulomb interaction (not accounted for in mean field Hartree term $E_\txH$)
+                    \end{itemize}
+                }}
+            \end{formula}
+            \begin{formula}{lda}
+                \desc{Local density approximation (LDA)}{Simplest DFT functionals}{$\epsilon_\txX$ calculated exchange energy from \hyperref[f:comp:qmb:models:heg]{HEG model}, $\epsilon_\txC$ correlation energy calculated with \fqSecRef{comp:qmb:methods:qmonte-carlo}}
+                \desc[german]{}{}{}
+                \abbrLabel{LDA}
+                \eq{E_\text{XC}^\text{LDA}[n(\vecr)] = \int \d^3r\,n(r) \Big[\epsilon_\txX[n(\vecr)] + \epsilon_\txC[n(\vecr)]\Big]}
+            \end{formula}
+
+            \begin{formula}{gga}
+                \desc{Generalized gradient approximation (GGA)}{}{$\epsilon_\txX$ calculated exchange energy from \hyperref[f:comp:qmb:models:heg]{HEG model}, $F_\text{XC}$ function containing exchange-correlation energy dependency on $n$ and $\Grad n$}
+                \desc[german]{}{}{}
+                \abbrLabel{GGA}
+                \eq{E_\text{XC}^\text{GGA}[n(\vecr)] = \int \d^3r\,n(r) \epsilon_\txX[n(\vecr)]\,F_\text{XC}[n(\vecr), \Grad n(\vecr)]}
+            \end{formula}
+
+            \TODO{PBE}
+
+            \begin{formula}{hybrid}
+                \desc{Hybrid functionals}{}{}
+                \desc[german]{Hybride Funktionale}{}{$\alpha$ mixing paramter, $E_\txX$ exchange energy, $E_\txC$ correlation energy}
+                \eq{\alpha E_\txX^\text{HF} + (1-\alpha) E_\txX^\text{GGA} + E_\txC^\text{GGA}}
+                \ttxt{\eng{
+                    Include \hyperref[f:comp:dft:hf:potential]{Fock term} (exact exchange) in other functional, like \abbrRef{gga}. Computationally expensive
+                }}
+
+            \end{formula}
+
+
+            \begin{formula}{range-separated-hybrid}
+                \desc{Range separated hyrid functionals (RSH)}{Here HSE as example}{$\alpha$ mixing paramter, $E_\txX$ exchange energy, $E_\txC$ correlation energy}
+                % \desc[german]{}{}{}
+                \begin{gather}
+                    \frac{1}{r} = \frac{\erf(\omega r)}{r} + \frac{\erfc{\omega r}}{r} \\
+                    E_\text{XC}^\text{HSE} = \alpha E_\text{X,SR}^\text{HF}(\omega) + (1-\alpha)E_\text{X,SR}^\text{GGA}(\omega) + E_\text{X,LR}^\text{GGA}(\omega) + E_\txC^\text{GGA}
+                \end{gather}
+                \separateEntries
+                \ttxt{\eng{
+                        Use \abbrRef{gga} and \hyperref[comp:est:dft:hf:potential]{Fock} exchange for short ranges (SR) and only \abbrRef{GGA} for long ranges (LR).
+                        \abbrRef{GGA} correlation is always used. Useful when dielectric screening reduces long range interactions, saves computational cost.
+                }}
+            \end{formula}   
+
+            \begin{formula}{comparison}
+                \desc{Comparison of DFT functionals}{}{}
+                \desc[german]{Vergleich von DFT Funktionalen}{}{}
+                \begin{tabular}{l|c}
+                    \hyperref[f:comp:est:dft:hf:potential]{Hartree-Fock} & only exchange, no correlation \Rightarrow upper bound of GS energy \\
+                    \abbrRef{lda} & understimates e repulsion \Rightarrow Overbinding \\
+                    \abbrRef{gga} & underestimate band gap \\
+                    hybrid & underestimate band gap
+                \end{tabular}
+            \end{formula}
+    
+    \Subsubsection[
+        \eng{Basis sets}
+        \ger{Basis-Sets}
+    ]{basis}
+        \begin{formula}{plane_wave}
+            \desc{Plane wave basis}{Plane wave ansatz in \fqEqRef{comp:est:dft:ks:equation}\\Good for periodic structures, allows computation parallelization over a sample points in the \abbrRef{brillouin_zone}}{}
+            \desc[german]{Ebene Wellen als Basis}{}{}
+            \eq{\sum_{\vecG^\prime} \left[\frac{\hbar^2 \abs{\vecG+\veck}^2}{2m} \delta_{\vecG,\vecG^\prime} + V_\text{eff}(\vecG-\vecG^\prime)\right] c_{i,\veck,\vecG^\prime} = \epsilon_{i,\veck} c_{i,\veck,\vecG}}
+        \end{formula}
+        \begin{formula}{plane_wave_cutoff}
+            \desc{Plane wave cutoff}{Number of plane waves included in the calculation must be finite}{}
+            % \desc[german]{}{}{}
+            \eq{E_\text{cutoff} = \frac{\hbar^2 \abs{\veck+\vecG}^2}{2m}}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Pseudo-Potential method}
+        \ger{Pseudopotentialmethode}
+    ]{pseudo}
+        \begin{formula}{ansatz}
+            \desc{Ansatz}{}{}
+            \desc[german]{Ansatz}{}{}
+            \ttxt{\eng{
+                Core electrons are absorbed into the potential since they do not contribute much to interesting properties.
+            }}
+        \end{formula}
diff --git a/src/comp/ml.tex b/src/comp/ml.tex
index c481ca4..ed8b7f8 100644
--- a/src/comp/ml.tex
+++ b/src/comp/ml.tex
@@ -80,5 +80,5 @@
         \eng{Gradient descent}
         \ger{Gradientenverfahren}
     ]{gd}
-        \TODO{TODO}
+        \TODO{in lecture 30 CMP}
 
diff --git a/src/comp/qmb.tex b/src/comp/qmb.tex
index bd6c3e4..26c88a1 100644
--- a/src/comp/qmb.tex
+++ b/src/comp/qmb.tex
@@ -2,6 +2,28 @@
     \eng{Quantum many-body physics}
     \ger{Quanten-Vielteilchenphysik}
 ]{qmb}
+    \Subsection[
+        \eng{Quantum many-body models}
+        \ger{Quanten-Vielteilchenmodelle}
+    ]{models}
+        \begin{formula}{heg}
+            \desc{Homogeneous electron gas (HEG)}{Also "Jellium"}{}
+            \desc[german]{}{}{}
+            \ttxt{
+                \eng{Both positive (nucleus) and negative (electron) charges are distributed uniformly.}
+            }
+        \end{formula}
+        
+    \Subsection[
+        \eng{Methods}
+        \ger{Methoden}
+    ]{methods}
+        \Subsubsection[
+            \eng{Quantum Monte-Carlo}
+            \ger{Quantum Monte-Carlo}
+        ]{qmonte-carlo}
+        
+
 \TODO{TODO}
     \Subsection[
         \eng{Importance sampling}
diff --git a/src/constants.tex b/src/constants.tex
index cce5235..4b4dd12 100644
--- a/src/constants.tex
+++ b/src/constants.tex
@@ -40,7 +40,7 @@
         \desc{Faraday constant}{Electric charge of one mol of single-charged ions}{\ConstRef{avogadro}, \ConstRef{boltzmann}}
         \desc[german]{Faraday-Konstante}{Elektrische Ladungs von einem Mol einfach geladener Ionen}{}
         \constant{F}{def}{
-            \val{9.64853321233100184}{\coulomb\per\mol}
+            \val{9.64853321233100184\xE{4}}{\coulomb\per\mol}
             \val{\NA\,e}{}
         }
     \end{formula}
diff --git a/src/ed/misc.tex b/src/ed/misc.tex
index 1204d16..ccd05b7 100644
--- a/src/ed/misc.tex
+++ b/src/ed/misc.tex
@@ -98,19 +98,7 @@
     
 
     \TODO{sort}
-    \begin{formula}{impedance_c}
-        \desc{Impedance of a capacitor}{}{}
-        \desc[german]{Impedanz eines Kondesnators}{}{}
-        \eq{Z_{C} = \frac{1}{i\omega C}}
-    \end{formula}
 
-    \begin{formula}{impedance_l}
-        \desc{Impedance of an inductor}{}{}
-        \desc[german]{Impedanz eines Induktors}{}{}
-        \eq{Z_{L} = i\omega L}
-    \end{formula}
-
-    \TODO{impedance addition for parallel / linear}
 
 \Section[
     \eng{Dipole-stuff}
@@ -129,3 +117,25 @@
         \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
     \end{formula}
 
+\Section[
+    \eng{misc}
+    \ger{misc}
+]{misc}
+    \begin{formula}{impedance_r}
+        \desc{Impedance of an ohmic resistor}{}{\QtyRef{resistance}}
+        \desc[german]{Impedanz eines Ohmschen Widerstands}{}{}
+        \eq{Z_{R} = R}
+    \end{formula}
+    \begin{formula}{impedance_c}
+        \desc{Impedance of a capacitor}{}{\QtyRef{capacity}, \QtyRef{angular_velocity}}
+        \desc[german]{Impedanz eines Kondensators}{}{}
+        \eq{Z_{C} = \frac{1}{\I\omega C}}
+    \end{formula}
+
+    \begin{formula}{impedance_l}
+        \desc{Impedance of an inductor}{}{\QtyRef{inductance}, \QtyRef{angular_velocity}}
+        \desc[german]{Impedanz eines Induktors}{}{}
+        \eq{Z_{L} = \I\omega L}
+    \end{formula}
+
+    \TODO{impedance addition for parallel / linear}
diff --git a/src/main.tex b/src/main.tex
index aa8bc53..fe722a8 100644
--- a/src/main.tex
+++ b/src/main.tex
@@ -25,7 +25,7 @@
 \setlist{noitemsep}                 % no vertical space between items
 \setlist[1]{labelindent=\parindent} % < Usually a good idea
 \setlist[itemize]{leftmargin=*}
-\setlist[enumerate]{labelsep=*, leftmargin=1.5pc}  % horizontal indent of items
+% \setlist[enumerate]{labelsep=*, leftmargin=1.5pc}  % horizontal indent of items
 
 \usepackage{titlesec}   % colored titles
 \usepackage{array}      % more array options
@@ -37,11 +37,14 @@
 \input{util/colorscheme.tex}
 \input{util/colors.tex} % after colorscheme
 % GRAPHICS
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.18}
 \usepackage{tikz}       % drawings
 \usetikzlibrary{decorations.pathmorphing}
 \usetikzlibrary{decorations.pathreplacing} % braces
 \usetikzlibrary{calc}
 \usetikzlibrary{patterns}
+\usetikzlibrary{patterns}
 \input{util/tikz_macros}
 % speed up compilation by externalizing figures
 % \usetikzlibrary{external}
@@ -90,113 +93,6 @@
 \newcommand{\TODO}[1]{{\color{fg-red}TODO:#1}}
 \newcommand{\ts}{\textsuperscript}
 
-\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
-
-% "automate" sectioning
-% start <section>, get heading from translation, set label
-% fqname is the fully qualified name: the keys of all previous sections joined with a ':'
-% [1]: code to run after setting \fqname, but before the \part, \section etc
-% 2: key
-\newcommand{\Part}[2][desc]{
-    \newpage
-    \def\partName{#2}
-    \def\sectionName{}
-    \def\subsectionName{}
-    \def\subsubsectionName{}
-    \edef\fqname{\partName}
-    #1
-    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
-    \part{\fqnameText} 
-    \label{sec:\fqname}
-}
-\newcommand{\Section}[2][]{
-    \def\sectionName{#2}
-    \def\subsectionName{}
-    \def\subsubsectionName{}
-    \edef\fqname{\partName:\sectionName}
-    #1
-    % this is necessary so that \section takes the fully expanded string. Otherwise the pdf toc will have just the fqname
-    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
-    \section{\fqnameText}
-    \label{sec:\fqname}
-}
-% \newcommand{\Subsection}[1]{\Subsection{#1}{}}
-\newcommand{\Subsection}[2][]{
-    \def\subsectionName{#2}
-    \def\subsubsectionName{}
-    \edef\fqname{\partName:\sectionName:\subsectionName}
-    #1
-    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
-    \subsection{\fqnameText}
-    \label{sec:\fqname}
-}
-\newcommand{\Subsubsection}[2][]{
-    \def\subsubsectionName{#2}
-    \edef\fqname{\partName:\sectionName:\subsectionName:\subsubsectionName}
-    #1
-    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
-    \subsubsection{\fqnameText}
-    \label{sec:\fqname}
-}
-\edef\fqname{NULL}
-
-\newcommand\luaDoubleFieldValue[3]{%
-    \directlua{
-        if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
-            tex.sprint(#1[#2][#3])
-            return
-        end
-        luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
-        tex.sprint("???")
-    }%
-}
-% REFERENCES
-% All xyzRef commands link to the key using the translated name
-% Uppercase (XyzRef) commands have different link texts, but the same link target
-% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
-% Equations/Formulas
-% <name>
-% \newrobustcmd{\fqEqRef}[1]{%
-\newrobustcmd{\fqEqRef}[1]{%
-    % \edef\fqeqrefname{\GT{#1}}
-    % \hyperref[eq:#1]{\fqeqrefname}
-    \hyperref[f:#1]{\GT{#1}}%
-}
-
-% Section
-% <name>
-\newrobustcmd{\fqSecRef}[1]{%
-    \hyperref[sec:#1]{\GT{#1}}%
-}
-% Quantities
-% <symbol>
-\newrobustcmd{\qtyRef}[1]{%
-    \edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"fqname"}}%
-    \hyperref[qty:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
-}
-% <symbol> <name>
-\newrobustcmd{\QtyRef}[1]{%
-    $\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
-}
-% Constants
-% <name>
-\newrobustcmd{\constRef}[1]{%
-    \edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"fqname"}}%
-    \hyperref[const:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
-}
-% <symbol> <name>
-\newrobustcmd{\ConstRef}[1]{%
-    $\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
-}
-% Element from periodic table
-% <symbol>
-\newrobustcmd{\elRef}[1]{%
-    \hyperref[el:#1]{{\color{fg0}#1}}%
-}
-% <name>
-\newrobustcmd{\ElRef}[1]{%
-    \hyperref[el:#1]{\GT{el:#1}}%
-}
 
 % \usepackage{xstring}
 
@@ -218,6 +114,7 @@
     \immediate\write\luaAuxFile{\noexpand\directlua{\detokenize{#1}}}
     \directlua{#1}
 }
+
 % read
 \IfFileExists{\jobname.lua.aux}{%
   \input{\jobname.lua.aux}%
@@ -240,6 +137,8 @@
 }
 \AtEndDocument{\immediate\closeout\labelsFile}
 
+
+\input{util/fqname.tex}
 \input{circuit.tex}
 \input{util/macros.tex}
 \input{util/environments.tex}   % requires util/translation.tex to be loaded first
@@ -284,7 +183,7 @@
 
 \input{util/translations.tex}
 
-% \InputOnly{ch}
+% \InputOnly{comp}
 
 \Input{math/math}
 \Input{math/linalg}
@@ -314,6 +213,7 @@
 \Input{cm/misc}
 \Input{cm/techniques}
 \Input{cm/topo}
+\Input{cm/mat}
 
 
 \Input{particle}
@@ -322,18 +222,25 @@
 
 \Input{comp/comp}
 \Input{comp/qmb}
-\Input{comp/elsth}
+\Input{comp/est}
 \Input{comp/ad}
 \Input{comp/ml}
 
 \Input{ch/periodic_table}  % only definitions
 \Input{ch/ch}
+\Input{ch/el}
+\Input{ch/misc}
 
 \newpage
 \Part[
     \eng{Appendix}
     \ger{Anhang}
 ]{appendix}
+\begin{formula}{world}
+    \desc{World formula}{}{}
+    \desc[german]{Weltformel}{}{}
+    \eq{E = mc^2 +\text{AI}}
+\end{formula}
 \Input{quantities}
 \Input{constants}
 
diff --git a/src/math/calculus.tex b/src/math/calculus.tex
index c89c70a..1685109 100644
--- a/src/math/calculus.tex
+++ b/src/math/calculus.tex
@@ -20,7 +20,7 @@
             \eng{Fourier series}
             \ger{Fourierreihe}
         ]{series}
-            \begin{formula}{series}
+        \begin{formula}{series} \absLabel[fourier_series]
                 \desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
                 \desc[german]{Fourierreihe}{Komplexe Darstellung}{}
                 \eq{f(t) = \sum_{k=-\infty}^{\infty} c_k \Exp{\frac{2\pi \I kt}{T}}}
@@ -58,7 +58,7 @@
             \eng{Fourier transformation}
             \ger{Fouriertransformation}
         ]{trafo}
-            \begin{formula}{transform}
+            \begin{formula}{transform} \absLabel[fourier_transform]
                 \desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
                 \desc[german]{Fouriertransformierte}{}{}
                 \eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
diff --git a/src/math/probability_theory.tex b/src/math/probability_theory.tex
index e48437c..256b1ea 100644
--- a/src/math/probability_theory.tex
+++ b/src/math/probability_theory.tex
@@ -54,10 +54,10 @@
         \eq{p_X(x) = P(X = x)}
     \end{formula}
 
-    \begin{formula}{autocorrelation}
-        \desc{Autocorrelation}{Correlation of $f$ to itself at an earlier point in time, $C$ is a covariance function}{}
-        \desc[german]{Autokorrelation}{Korrelation vonn $f$ zu sich selbst zu einem früheren Zeitpunkt. $C$ ist auch die Kovarianzfunktion}{}
-        \eq{C_A(\tau) = \lim_{T \to \infty} \frac{1}{2T}\int_{-T}^{T} f(t+\tau) f(t) \d t) = \braket{f(t+\tau)\cdot f(t)}}
+    \begin{formula}{autocorrelation} \absLabel
+        \desc{Autocorrelation}{Correlation of $f$ to itself at an earlier point in time, $C$ is a covariance function}{$\tau$ lag-time}
+        \desc[german]{Autokorrelation}{Korrelation vonn $f$ zu sich selbst zu einem früheren Zeitpunkt. $C$ ist auch die Kovarianzfunktion}{$\tau$ Zeitverschiebung}
+        \eq{C_A(\tau) &= \lim_{T \to \infty} \frac{1}{2T}\int_{-T}^{T} f(t+\tau) f(t) \d t) \\ &= \braket{f(t+\tau)\cdot f(t)}}
     \end{formula}
 
     \begin{formula}{binomial_coefficient}
diff --git a/src/mechanics.tex b/src/mechanics.tex
index 0bbc319..4527215 100644
--- a/src/mechanics.tex
+++ b/src/mechanics.tex
@@ -66,7 +66,7 @@
             Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
         }
     \end{ttext}
-    \begin{formula}{lagrangian}
+    \begin{formula}{lagrangian} \absLabel
         \desc{Lagrange function}{}{$T$ kinetic energy, $V$ potential energy }
         \desc[german]{Lagrange-Funktion}{}{$T$ kinetische Energie, $V$ potentielle Energie}
         \eq{\lagrange = T - V}
diff --git a/src/particle.tex b/src/particle.tex
index 67e3607..5b33a9c 100644
--- a/src/particle.tex
+++ b/src/particle.tex
@@ -11,6 +11,17 @@
         }
     \end{formula}
 
+    \begin{formula}{spin}
+        \desc{Spin}{}{}
+        \desc[german]{Spin}{}{}
+        \quantity{\sigma}{}{v}
+    \end{formula}
+
+    \begin{bigformula}{standard_model}
+        \desc{Standard model}{}{}
+        \desc[german]{Standartmodell}{}{}
+        \centering
+
 \tikzset{%
           label/.style = { black, midway, align=center },
        toplabel/.style = { label, above=.5em, anchor=south },
@@ -82,7 +93,7 @@
     \draw [->] (-0.7, 0.35) node [legend] {\qtyRef{mass}}  -- (-0.5, 0.35);
     \draw [->] (-0.7, 0.20) node [legend] {\qtyRef{spin}}  -- (-0.5, 0.20);
     \draw [->] (-0.7, 0.05) node [legend] {\qtyRef{charge}} -- (-0.5, 0.05);
-    \draw [->] (-0.7,-0.10) node [legend] {\qtyRef{colors}} -- (-0.5,-0.10);
+    \draw [->] (-0.7,-0.10) node [legend] {\GT{colors}} -- (-0.5,-0.10);
     
     \draw [brace,draw=\colorQuarks] (-0.55, 0.5) -- (-0.55,-1.5) node[leftlabel,color=\colorQuarks] {\gt{quarks}};
     \draw [brace,draw=\colorLepton] (-0.55,-1.5) -- (-0.55,-3.5) node[leftlabel,color=\colorLepton] {\gt{leptons}};
@@ -99,3 +110,5 @@
     \node at (2,0.85) [generation] {\small III};
     \node at (1,1.05) [generation] {\small generation};
 \end{tikzpicture}
+
+    \end{bigformula}
diff --git a/src/qm/qm.tex b/src/qm/qm.tex
index 5fc8b38..ff39b5e 100644
--- a/src/qm/qm.tex
+++ b/src/qm/qm.tex
@@ -206,9 +206,18 @@
         \begin{formula}{schroedinger_equation}
             \desc{Schrödinger equation}{}{}
             \desc[german]{Schrödingergleichung}{}{}
+            \abbrLabel{SE}
             \eq{i\hbar\frac{\partial}{\partial t}\psi(x, t) = (- \frac{\hbar^2}{2m} \vec{\nabla}^2 + \vec{V}(x)) \psi(x)}
         \end{formula}
 
+        \begin{formula}{hellmann_feynmann} \absLabel
+            \desc{Hellmann-Feynman-Theorem}{Derivative of the energy to a parameter}{}
+            \desc[german]{Hellmann-Feynman-Theorem}{Abletiung der Energie nach einem Parameter}{}
+            \eq{
+                \odv{E_\lambda}{\lambda} = \int \d^3r \psi^*_\lambda \odv{\hat{H}_\lambda}{\lambda} \psi_\lambda = \Braket{\psi(\lambda)|\odv{\hat{H}_{\lambda}}{\lambda}|\psi(\lambda)}
+            }
+        \end{formula}
+
         \Subsection[
             \eng{Time evolution}
             \ger{Zeitentwicklug}
@@ -232,13 +241,6 @@
                 \eq{\dot{\rho} = \underbrace{-\frac{i}{\hbar} [\hat{H}, \rho]}_\text{reversible} + \underbrace{\sum_{n.m} h_{nm} \left(\hat{A}_n\rho \hat{A}_{m^\dagger} - \frac{1}{2}\left\{\hat{A}_m^\dagger \hat{A}_n,\rho \right\}\right)}_\text{irreversible}}
             \end{formula}
 
-            \begin{formula}{hellmann_feynmann}
-                \desc{Hellmann-Feynman-Theorem}{Derivative of the energy to a parameter}{}
-                \desc[german]{Hellmann-Feynman-Theorem}{Abletiung der Energie nach einem Parameter}{}
-                \eq{
-                    \odv{E_\lambda}{\lambda} = \int \d^3r \psi^*_\lambda \odv{\hat{H}_\lambda}{\lambda} \psi_\lambda = \Braket{\psi(\lambda)|\odv{\hat{H}_{\lambda}}{\lambda}|\psi(\lambda)}
-                }
-            \end{formula}
 
 
             \TODO{unitary transformation of time dependent H}
@@ -292,14 +294,15 @@
                 \end{formula}
                 % \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time}
 
-            \Subsection[
-                \ger{Korrespondenzprinzip}
-                \eng{Correspondence principle}
-                ]{correspondence_principle}
-                \begin{ttext}[desc]
+            % TODO: wo gehört das hin?
+            \begin{formula}{correspondence_principle}
+                \desc{Correspondence principle}{}{}
+                \desc[german]{Korrespondenzprinzip}{}{}
+                \ttxt{
                     \ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
                     \eng{The classical mechanics can be derived from quantum mechanics in the limit of large quantum numbers.}
-                \end{ttext}
+                }
+            \end{formula}
                 
 
 
@@ -308,8 +311,8 @@
         \ger{Störungstheorie}
         ]{qm_pertubation}
         \begin{ttext}
-            \eng[desc]{The following holds true if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}
-            \ger[desc]{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}
+            \eng{The following holds true if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}
+            \ger{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}
         \end{ttext}
         \begin{formula}{pertubation_hamiltonian}
             \desc{Hamiltonian}{}{}
@@ -566,6 +569,15 @@
             \eq{\Delta\omega \coloneq \abs{\omega_0 - \omega_\text{L}} \ll \abs{\omega_0 + \omega_\text{L}} \approx 2\omega_0}
         \end{formula}
 
+        \begin{formula}{adiabatic_theorem} \absLabel
+            \desc{Adiabatic theorem}{}{}
+            \desc[german]{Adiabatentheorem}{}{}
+            \ttxt{
+                \eng{A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.}
+                \ger{Ein quantenmechanisches System bleibt in im derzeitigen Eigenzustand falls eine Störung langsam genug wirkt und der Eigenwert durch eine Lücke vom Rest des Spektrums getrennt ist.}
+            }
+        \end{formula}
+
         \begin{formula}{slater_det}
             \desc{Slater determinant}{Construction of a fermionic (antisymmetric) many-particle wave function from single-particle wave functions}{}
             \desc[german]{Slater Determinante}{Konstruktion einer fermionischen (antisymmetrischen) Vielteilchen Wellenfunktion aus ein-Teilchen Wellenfunktionen}{}
diff --git a/src/quantities.tex b/src/quantities.tex
index c2766f4..01903eb 100644
--- a/src/quantities.tex
+++ b/src/quantities.tex
@@ -124,7 +124,7 @@
     \end{formula}
     \begin{formula}{angular_frequency}
         \desc{Angular frequency}{}{\QtyRef{time_period}, \QtyRef{frequency}}
-        \desc[german]{Winkelgeschwindigkeit}{}{}
+        \desc[german]{Kreisfrequenz}{}{}
         \quantity{\omega}{\radian\per\s}{s}
         \eq{\omega = \frac{2\pi/T}{2\pi f}}
     \end{formula}
diff --git a/src/quantum_computing.tex b/src/quantum_computing.tex
index 61804c9..5992888 100644
--- a/src/quantum_computing.tex
+++ b/src/quantum_computing.tex
@@ -433,7 +433,7 @@
         \begin{formula}{rabi_oscillation}
             \desc{Rabi oscillations}{}{$\omega_{21}$ resonance frequency of the energy transition, $\Omega$ Rabi frequency}
             \desc[german]{Rabi-Oszillationen}{}{$\omega_{21}$ Resonanzfrequenz des Energieübergangs, $\Omega$ Rabi-Frequenz}
-            \eq{\Omega_ TODO}
+            \eq{\Omega_ \text{\TODO{TODO}}}
         \end{formula}
 
         \Subsection[
diff --git a/src/statistical_mechanics.tex b/src/statistical_mechanics.tex
index b4b0f5f..d690410 100644
--- a/src/statistical_mechanics.tex
+++ b/src/statistical_mechanics.tex
@@ -346,24 +346,76 @@
     \eng{Ensembles}
     \ger{Ensembles}
 ]{ensembles}
+    \Eng[const_variables]{Constant variables}
+    \Ger[const_variables]{Konstante Variablen}
 
+    \begin{bigformula}{nve} \absLabel[mc_ensemble]
+        \desc{Microcanonical ensemble}{}{}
+        \desc[german]{Mikrokanonisches Ensemble}{}{}
+        \begin{minipagetable}{nve}
+            \entry{const_variables} {$E$, $V,$ $N$           }
+            \entry{partition_sum}   {$\Omega = \sum_n 1$     }
+            \entry{probability}     {$p_n = \frac{1}{\Omega}$}
+            \entry{td_pot}          {$S = \kB\ln\Omega$      }
+            \entry{pressure}        {$p = T \pdv{S}{V}_{E,N}$}
+            \entry{entropy}         {$S = \kB = \ln\Omega$   }
+        \end{minipagetable}
+    \end{bigformula}
 
+    \begin{bigformula}{nvt} \absLabel[c_ensemble]
+        \desc{Canonical ensemble}{}{}
+        \desc[german]{Kanonisches Ensemble}{}{}
+        \begin{minipagetable}{nvt}
+            \entry{const_variables} {$T$, $V$, $N$                    }
+            \entry{partition_sum}   {$Z = \sum_n \e^{-\beta E_n}$     }
+            \entry{probability}     {$p_n = \frac{\e^{-\beta E_n}}{Z}$}
+            \entry{td_pot}          {$F = - \kB T \ln Z$              }
+            \entry{pressure}        {$p = -\pdv{F}{V}_{T,N}$          }
+            \entry{entropy}         {$S = -\pdv{F}{T}_{V,N}$          }
+        \end{minipagetable}
+    \end{bigformula}
+
+    \begin{bigformula}{mvt} \absLabel[gc_ensemble]
+        \desc{Grand canonical ensemble}{}{}
+        \desc[german]{Grosskanonisches Ensemble}{}{}
+        \begin{minipagetable}{mvt}
+            \entry{const_variables} {$T$, $V$, $\mu$                                      }
+            \entry{partition_sum}   {$Z_\text{g} = \sum_{n} \e^{-\beta(E_n - \mu N_n)}$   }
+            \entry{probability}     {$p_n = \frac{\e^{-\beta (E_n - \mu N_n}}{Z_\text{g}}$}
+            \entry{td_pot}          {$ \Phi = - \kB T \ln Z$                              }
+            \entry{pressure}        {$p = -\pdv{\Phi}{V}_{T,\mu} = -\frac{\Phi}{V}$       }
+            \entry{entropy}         {$S = -\pdv{\Phi}{T}_{V,\mu}$                         }
+        \end{minipagetable}
+    \end{bigformula}
+
+    \begin{bigformula}{npt}
+        \desc{Isobaric-isothermal}{Gibbs ensemble}{}
+        % \desc[german]{Kanonisches Ensemble}{}{}
+        \begin{minipagetable}{npt}
+            \entry{const_variables} {$N$, $p$, $T$}
+            \entry{partition_sum}   {}
+            \entry{probability}     {$p_n ? \frac{\e^{-\beta(E_n + pV_n)}}{Z}$}
+            \entry{td_pot}          {}
+            \entry{pressure}        {}
+            \entry{entropy}         {}
+        \end{minipagetable}
+    \end{bigformula}
+
+    \begin{bigformula}{nph}
+        \desc{Isonthalpic-isobaric ensemble}{Enthalpy ensemble}{}
+        % \desc[german]{Kanonisches Ensemble}{}{}
+        \begin{minipagetable}{nph}
+            \entry{const_variables} {}
+            \entry{partition_sum}   {}
+            \entry{probability}     {}
+            \entry{td_pot}          {}
+            \entry{pressure}        {}
+            \entry{entropy}         {}
+        \end{minipagetable}
+    \end{bigformula}
+
+    \TODO{complete, link potentials}
 
-    \begin{table}[H]
-        \centering
-        \caption{caption}
-        \label{tab:\fqname}
-    
-        \begin{tabular}{l|c|c|c}
-             &  \gt{mk} & \gt{k}  & \gt{gk}  \\ \hline
-            \GT{variables} & $E$, $V,$ $N$ & $T$, $V$, $N$ & $T$, $V$, $\mu$ \\ \hline
-            \GT{partition_sum} & $\Omega = \sum_n 1$ & $Z = \sum_n \e^{-\beta E_n}$ & $Z_\text{g} = \sum_{n} \e^{-\beta(E_n - \mu N_n)}$ \\ \hline
-            \GT{probability} & $p_n = \frac{1}{\Omega}$ & $p_n = \frac{\e^{-\beta E_n}}{Z}$ & $p_n = \frac{\e^{-\beta (E_n - \mu N_n}}{Z_\text{g}}$ \\ \hline
-            \GT{td_pot} & $S = \kB\ln\Omega$ & $F = - \kB T \ln Z$ & $ \Phi = - \kB T \ln Z$ \\ \hline
-            \GT{pressure} & $p = T \pdv{S}{V}_{E,N}$ &$p = -\pdv{F}{V}_{T,N}$ & $p = -\pdv{\Phi}{V}_{T,\mu} = -\frac{\Phi}{V}$ \\ \hline
-            \GT{entropy} & $S = \kB = \ln\Omega$ & $S = -\pdv{F}{T}_{V,N}$ & $S = -\pdv{\Phi}{T}_{V,\mu}$ \\ \hline
-        \end{tabular}
-    \end{table}
 
     \begin{formula}{ergodic_hypo}
         \desc{Ergodic hypothesis}{Over a long periode of time, all accessible microstates in the phase space are equiprobable}{$A$ Observable}
@@ -560,7 +612,7 @@
             % b - \frac{a}{\kB T}}
         \end{formula}
 
-        \begin{formula}{lennard_jones}
+        \begin{formula}{lennard_jones} \absLabel
             \desc{Lennard-Jones potential}{Potential between two molecules. Attractive for $r > \sigma$, repulsive for $r < \sigma$.\\ In condensed matter: Attraction due to Landau Dispersion \TODO{verify} and repulsion due to Pauli exclusion principle.}{}
             \desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$.\\ In Festkörpern: Anziehung durch Landau-Dispersion und Abstoßung durch Pauli-Prinzip.}{}
             \fig[0.7]{img/potential_lennard_jones.pdf}
diff --git a/src/util/colorscheme.tex b/src/util/colorscheme.tex
index 67baf99..c8d0b47 100644
--- a/src/util/colorscheme.tex
+++ b/src/util/colorscheme.tex
@@ -1,28 +1,28 @@
-% This file was generated by scripts/formulasheet.py
+% This file was generated by scripts/formulary.py
 % Do not edit it directly, changes will be overwritten
-\definecolor{fg0}{HTML}{f9f5d7}
-\definecolor{bg0}{HTML}{1d2021}
-\definecolor{fg1}{HTML}{ebdbb2}
-\definecolor{fg2}{HTML}{d5c4a1}
-\definecolor{fg3}{HTML}{bdae93}
-\definecolor{fg4}{HTML}{a89984}
-\definecolor{bg1}{HTML}{3c3836}
-\definecolor{bg2}{HTML}{504945}
-\definecolor{bg3}{HTML}{665c54}
-\definecolor{bg4}{HTML}{7c6f64}
-\definecolor{fg-red}{HTML}{fb4934}
-\definecolor{fg-orange}{HTML}{f38019}
-\definecolor{fg-yellow}{HTML}{fabd2f}
-\definecolor{fg-green}{HTML}{b8bb26}
-\definecolor{fg-aqua}{HTML}{8ec07c}
-\definecolor{fg-blue}{HTML}{83a598}
-\definecolor{fg-purple}{HTML}{d3869b}
-\definecolor{fg-gray}{HTML}{a89984}
-\definecolor{bg-red}{HTML}{cc241d}
-\definecolor{bg-orange}{HTML}{d65d0e}
-\definecolor{bg-yellow}{HTML}{d79921}
-\definecolor{bg-green}{HTML}{98971a}
-\definecolor{bg-aqua}{HTML}{689d6a}
-\definecolor{bg-blue}{HTML}{458588}
-\definecolor{bg-purple}{HTML}{b16286}
-\definecolor{bg-gray}{HTML}{928374}
+\definecolor{fg0}{HTML}{1d2021}
+\definecolor{bg0}{HTML}{f9f5d7}
+\definecolor{fg1}{HTML}{3c3836}
+\definecolor{fg2}{HTML}{504945}
+\definecolor{fg3}{HTML}{665c54}
+\definecolor{fg4}{HTML}{7c6f64}
+\definecolor{bg1}{HTML}{ebdbb2}
+\definecolor{bg2}{HTML}{d5c4a1}
+\definecolor{bg3}{HTML}{bdae93}
+\definecolor{bg4}{HTML}{a89984}
+\definecolor{fg-red}{HTML}{9d0006}
+\definecolor{fg-orange}{HTML}{af3a03}
+\definecolor{fg-yellow}{HTML}{b57614}
+\definecolor{fg-green}{HTML}{79740e}
+\definecolor{fg-aqua}{HTML}{427b58}
+\definecolor{fg-blue}{HTML}{076678}
+\definecolor{fg-purple}{HTML}{8f3f71}
+\definecolor{fg-gray}{HTML}{7c6f64}
+\definecolor{bg-red}{HTML}{fb4934}
+\definecolor{bg-orange}{HTML}{f38019}
+\definecolor{bg-yellow}{HTML}{fabd2f}
+\definecolor{bg-green}{HTML}{b8bb26}
+\definecolor{bg-aqua}{HTML}{8ec07c}
+\definecolor{bg-blue}{HTML}{83a598}
+\definecolor{bg-purple}{HTML}{d3869b}
+\definecolor{bg-gray}{HTML}{a89984}
diff --git a/src/util/environments.tex b/src/util/environments.tex
index 93e1316..07d0f1d 100644
--- a/src/util/environments.tex
+++ b/src/util/environments.tex
@@ -83,6 +83,19 @@
         \ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
     }
     \directlua{n_formulaEntries = 0}
+
+    % makes this formula referencable with \abbrRef{<name>}
+    % [1]: label to use
+    % 2: Abbreviation to use for references
+    \newcommand{\abbrLabel}[2][#1]{
+        \abbrLink[f:\fqname]{##1}{##2}
+    }
+    % makes this formula referencable with \absRef{<name>}
+    % [1]: label to use
+    \newcommand{\absLabel}[1][#1]{
+        \absLink[f:\fqname]{##1}
+    }
+
     \newcommand{\newFormulaEntry}{
         \directlua{
             if n_formulaEntries > 0 then
@@ -229,11 +242,13 @@
         \par\noindent\ignorespaces
         % \textcolor{gray}{\hrule}
         % \vspace{0.5\baselineskip}
-        \IfTranslationExists{\fqname:#1}{%
-                \raggedright
-                \GT{\fqname:#1}
+        \textbf{
+            \IfTranslationExists{\fqname:#1}{%
+                    \raggedright
+                    \GT{\fqname:#1}
             }{\detokenize{#1}}
-            \IfTranslationExists{\fqname:#1_desc}{
+        }
+        \IfTranslationExists{\fqname:#1_desc}{
                : {\color{fg1} \GT{\fqname:#1_desc}}
         }{}
         \hfill
@@ -414,15 +429,24 @@
         entries = {}
     }
 
+    % Normal entry
+    % 1: field name (translation key)
+    % 2: entry text
+    \newcommand{\entry}[2]{
+        \directlua{
+            table.insert(entries, {key = "\luaescapestring{##1}", value = [[\detokenize{##2}]]})
+        }
+    }
+    % Translation entry
     % 1: field name (translation key)
     % 2: translation define statements (field content)
-    \newcommand{\entry}[2]{
+    \newcommand{\tentry}[2]{
         % temporarily set fqname so that the translation commands dont need an explicit key
         \edef\fqname{\tmpFqname:#2:##1}
         ##2
         \edef\fqname{\tmpFqname}
         \directlua{
-            table.insert(entries, "\luaescapestring{##1}")
+            table.insert(entries, {key = "\luaescapestring{##1}", value = "\\gt{" .. table_name .. ":\luaescapestring{##1}}"})
         }
     }
 }{
@@ -436,8 +460,8 @@
             \begin{tabularx}{\textwidth}{|l|X|}
             \hline
             \directlua{
-                for _, k in ipairs(entries) do
-                    tex.print("\\GT{" .. k .. "} & \\gt{"..table_name..":"..k .."}\\\\")
+                for _, kv in ipairs(entries) do
+                    tex.print("\\GT{" .. kv.key .. "} & " .. kv.value .. "\\\\")
                 end
             }
             \hline
diff --git a/src/util/fqname.tex b/src/util/fqname.tex
new file mode 100644
index 0000000..b017ad9
--- /dev/null
+++ b/src/util/fqname.tex
@@ -0,0 +1,180 @@
+% Everything related to referencing stuff
+
+\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
+
+% SECTIONING
+% start <section>, get heading from translation, set label
+% secFqname is the fully qualified name of sections: the keys of all previous sections joined with a ':'
+% fqname is secFqname:<key> where <key> is the key/id of some environment, like formula
+% [1]: code to run after setting \fqname, but before the \part, \section etc
+% 2: key
+\newcommand{\Part}[2][desc]{
+    \newpage
+    \def\partName{#2}
+    \def\sectionName{}
+    \def\subsectionName{}
+    \def\subsubsectionName{}
+    \edef\fqname{\partName}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \part{\fqnameText} 
+    \label{sec:\fqname}
+}
+\newcommand{\Section}[2][]{
+    \def\sectionName{#2}
+    \def\subsectionName{}
+    \def\subsubsectionName{}
+    \edef\fqname{\partName:\sectionName}
+    \edef\secFqname{\fqname}
+    #1
+    % this is necessary so that \section takes the fully expanded string. Otherwise the pdf toc will have just the fqname
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \section{\fqnameText}
+    \label{sec:\fqname}
+}
+% \newcommand{\Subsection}[1]{\Subsection{#1}{}}
+\newcommand{\Subsection}[2][]{
+    \def\subsectionName{#2}
+    \def\subsubsectionName{}
+    \edef\fqname{\partName:\sectionName:\subsectionName}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \subsection{\fqnameText}
+    \label{sec:\fqname}
+}
+\newcommand{\Subsubsection}[2][]{
+    \def\subsubsectionName{#2}
+    \edef\fqname{\partName:\sectionName:\subsectionName:\subsubsectionName}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \subsubsection{\fqnameText}
+    \label{sec:\fqname}
+}
+\edef\fqname{NULL}
+
+\newcommand\luaDoubleFieldValue[3]{%
+    \directlua{
+        if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
+            tex.sprint(#1[#2][#3])
+            return
+        end
+        luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
+        tex.sprint("???")
+    }%
+}
+% REFERENCES
+% All xyzRef commands link to the key using the translated name
+% Uppercase (XyzRef) commands have different link texts, but the same link target
+% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
+
+% Equations/Formulas
+% \newrobustcmd{\fqEqRef}[1]{%
+\newrobustcmd{\fqEqRef}[1]{%
+    % \edef\fqeqrefname{\GT{#1}}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[f:#1]{\GT{#1}}%
+}
+% Formula in the current section
+\newrobustcmd{\secEqRef}[1]{%
+    % \edef\fqeqrefname{\GT{#1}}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[f:\secFqname:#1]{\GT{\secFqname:#1}}%
+}
+
+% Section
+% <name>
+\newrobustcmd{\fqSecRef}[1]{%
+    \hyperref[sec:#1]{\GT{#1}}%
+}
+% Quantities
+% <symbol>
+\newrobustcmd{\qtyRef}[1]{%
+    \edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"fqname"}}%
+    \hyperref[qty:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\QtyRef}[1]{%
+    $\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
+}
+% Constants
+% <name>
+\newrobustcmd{\constRef}[1]{%
+    \edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"fqname"}}%
+    \hyperref[const:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\ConstRef}[1]{%
+    $\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
+}
+% Element from periodic table
+% <symbol>
+\newrobustcmd{\elRef}[1]{%
+    \hyperref[el:#1]{{\color{fg0}#1}}%
+}
+% <name>
+\newrobustcmd{\ElRef}[1]{%
+    \hyperref[el:#1]{\GT{el:#1}}%
+}
+
+
+
+% "LABELS"
+% These currently do not place a label,
+% instead they provide an alternative way to reference an existing label
+\directLuaAux{
+    if absLabels == nil then
+        absLabels = {}
+    end
+}
+% [1]: target (fqname to point to)
+% 2: key
+\newcommand{\absLink}[2][sec:\fqname]{
+    \directLuaAuxExpand{
+        absLabels["#2"] = [[#1]] 
+    } 
+}
+\directLuaAux{
+    if abbrLabels == nil then
+        abbrLabels = {}
+    end
+}
+% [1]: target (fqname to point to)
+% 2: key
+% 3: label (abbreviation)
+\newcommand{\abbrLink}[3][sec:\fqname]{
+    \directLuaAuxExpand{
+        abbrLabels["#2"] = {}
+        abbrLabels["#2"]["abbr"] = [[#3]] 
+        abbrLabels["#2"]["fqname"] = [[#1]] 
+    } 
+}
+% [1]: 
+\newrobustcmd{\absRef}[2][\relax]{%
+    \directlua{
+        if absLabels["#2"] == nil then
+            tex.sprint("\\detokenize{#2}???")
+        else
+            if "#1" == "" then  %-- if [#1]  is not given, use translation of key as text, else us given text
+                tex.sprint("\\hyperref[" .. absLabels["#2"] .. "]{\\GT{" .. absLabels["#2"] .. "}}")
+            else
+                tex.sprint("\\hyperref[" .. absLabels["#2"] .. "]{\luaescapestring{#1}}")
+            end
+        end
+    }
+}
+\newrobustcmd{\abbrRef}[1]{%
+    \directlua{
+        if abbrLabels["#1"] == nil then
+            tex.sprint("\\detokenize{#1}???")
+        else
+            tex.sprint("\\hyperref[" .. abbrLabels["#1"]["fqname"] .. "]{" .. abbrLabels["#1"]["abbr"] .. "}")
+        end
+    }
+}
+
+
+
+
diff --git a/src/util/macros.tex b/src/util/macros.tex
index 2a9cb20..aa4caf6 100644
--- a/src/util/macros.tex
+++ b/src/util/macros.tex
@@ -1,6 +1,7 @@
+% use \newcommand instead of \def because we want to throw an error if a command gets redefined
 \newcommand\smartnewline[1]{\ifhmode\\\fi}  % newline only if there in horizontal mode
-\def\gooditem{\item[{$\color{fg-red}\bullet$}]}
-\def\baditem{\item[{$\color{fg-green}\bullet$}]}
+\newcommand\gooditem{\item[{$\color{fg-green}\bullet$}]}
+\newcommand\baditem{\item[{$\color{fg-red}\bullet$}]}
 
 % Functions with (optional) paranthesis
 % 1: The function (like \exp, \sin etc.)
@@ -24,11 +25,11 @@
 
 % COMMON SYMBOLS WITH SUPER/SUBSCRIPTS, VECTOR ARROWS ETC.
 % \def\laplace{\Delta} % Laplace operator
-\def\laplace{\bigtriangleup} % Laplace operator
+\newcommand\laplace{\bigtriangleup} % Laplace operator
 % symbols
-\def\Grad{\vec{\nabla}}       
-\def\Div {\vec{\nabla} \cdot} 
-\def\Rot {\vec{\nabla} \times}
+\newcommand\Grad{\vec{\nabla}}       
+\newcommand\Div {\vec{\nabla} \cdot} 
+\newcommand\Rot {\vec{\nabla} \times}
 % symbols with parens
 \newcommand\GradS[1][\relax]{\CmdInParenthesis{\Grad}{#1}}
 \newcommand\DivS [1][\relax]{\CmdInParenthesis{\Div} {#1}}
@@ -37,100 +38,96 @@
 \newcommand\GradT[1][\relax]{\CmdWithParenthesis{\text{grad}\,}{#1}}
 \newcommand\DivT[1][\relax] {\CmdWithParenthesis{\text{div}\,} {#1}}
 \newcommand\RotT[1][\relax] {\CmdWithParenthesis{\text{rot}\,} {#1}}
-\def\vecr{\vec{r}}
-\def\vecR{\vec{R}}
-\def\veck{\vec{k}}
-\def\vecx{\vec{x}}
-\def\kB{k_\text{B}}         % boltzmann
-\def\NA{N_\text{A}}         % avogadro
-\def\EFermi{E_\text{F}}     % fermi energy
-\def\Efermi{E_\text{F}}     % fermi energy
-\def\Evalence{E_\text{v}}   % val vand energy
-\def\Econd{E_\text{c}}      % cond. band nergy
-\def\Egap{E_\text{gap}}     % band gap energy
-\def\Evac{E_\text{vac}}     % vacuum energy
-\def\masse{m_\text{e}}      % electron mass
-\def\Four{\mathcal{F}}      % Fourier transform
-\def\Lebesgue{\mathcal{L}}  % Lebesgue
-\def\O{\mathcal{O}}         % order
-\def\PhiB{\Phi_\text{B}}    % mag. flux
-\def\PhiE{\Phi_\text{E}}    % electric flux
-\def\nreal{n^{\prime}}            % refraction real part
-\def\ncomplex{n^{\prime\prime}}        % refraction index complex part
-\def\I{i}                   % complex unit
-\def\crit{\text{crit}}      % crit (for subscripts)
-\def\muecp{\overline{\mu}}  % electrochemical potential
-\def\pH{\text{pH}}          % pH
-\def\rfactor{\text{rf}}     % rf roughness_factor
+\newcommand\kB{k_\text{B}}         % boltzmann
+\newcommand\NA{N_\text{A}}         % avogadro
+\newcommand\EFermi{E_\text{F}}     % fermi energy
+\newcommand\Efermi{E_\text{F}}     % fermi energy
+\newcommand\Evalence{E_\text{v}}   % val vand energy
+\newcommand\Econd{E_\text{c}}      % cond. band nergy
+\newcommand\Egap{E_\text{gap}}     % band gap energy
+\newcommand\Evac{E_\text{vac}}     % vacuum energy
+\newcommand\masse{m_\text{e}}      % electron mass
+\newcommand\Four{\mathcal{F}}      % Fourier transform
+\newcommand\Lebesgue{\mathcal{L}}  % Lebesgue
+% \newcommand\O{\mathcal{O}}         % order
+\newcommand\PhiB{\Phi_\text{B}}    % mag. flux
+\newcommand\PhiE{\Phi_\text{E}}    % electric flux
+\newcommand\nreal{n^{\prime}}            % refraction real part
+\newcommand\ncomplex{n^{\prime\prime}}        % refraction index complex part
+\newcommand\I{i}                   % complex/imaginary unit
+\newcommand\crit{\text{crit}}      % crit (for subscripts)
+\newcommand\muecp{\overline{\mu}}  % electrochemical potential
+% \newcommand\pH{\text{pH}}          % pH, already defined by one of the chem packages
+\newcommand\rfactor{\text{rf}}     % rf roughness_factor
 
 
 % SYMBOLS
-\def\R{\mathbb{R}}
-\def\C{\mathbb{C}}
-\def\Z{\mathbb{Z}}
-\def\N{\mathbb{N}}
-\def\id{\mathbb{1}}
+\newcommand\R{\mathbb{R}}
+\newcommand\C{\mathbb{C}}
+\newcommand\Z{\mathbb{Z}}
+\newcommand\N{\mathbb{N}}
+\newcommand\id{\mathbb{1}}
 % caligraphic
-\def\E{\mathcal{E}}  % electric field
-% upright
-\def\txA{\text{A}}
-\def\txB{\text{B}}
-\def\txC{\text{C}}
-\def\txD{\text{D}}
-\def\txE{\text{E}}
-\def\txF{\text{F}}
-\def\txG{\text{G}}
-\def\txH{\text{H}}
-\def\txI{\text{I}}
-\def\txJ{\text{J}}
-\def\txK{\text{K}}
-\def\txL{\text{L}}
-\def\txM{\text{M}}
-\def\txN{\text{N}}
-\def\txO{\text{O}}
-\def\txP{\text{P}}
-\def\txQ{\text{Q}}
-\def\txR{\text{R}}
-\def\txS{\text{S}}
-\def\txT{\text{T}}
-\def\txU{\text{U}}
-\def\txV{\text{V}}
-\def\txW{\text{W}}
-\def\txX{\text{X}}
-\def\txY{\text{Y}}
-\def\txZ{\text{Z}}
-
-\def\txa{\text{a}}
-\def\txb{\text{b}}
-\def\txc{\text{c}}
-\def\txd{\text{d}}
-\def\txe{\text{e}}
-\def\txf{\text{f}}
-\def\txg{\text{g}}
-\def\txh{\text{h}}
-\def\txi{\text{i}}
-\def\txj{\text{j}}
-\def\txk{\text{k}}
-\def\txl{\text{l}}
-\def\txm{\text{m}}
-\def\txn{\text{n}}
-\def\txo{\text{o}}
-\def\txp{\text{p}}
-\def\txq{\text{q}}
-\def\txr{\text{r}}
-\def\txs{\text{s}}
-\def\txt{\text{t}}
-\def\txu{\text{u}}
-\def\txv{\text{v}}
-\def\txw{\text{w}}
-\def\txx{\text{x}}
-\def\txy{\text{y}}
-\def\txz{\text{z}}
+\newcommand\E{\mathcal{E}}  % electric field
+% upright, vector
+\newcommand\txA{\text{A}}  \newcommand\vecA{\vec{A}}  
+\newcommand\txB{\text{B}}  \newcommand\vecB{\vec{B}}
+\newcommand\txC{\text{C}}  \newcommand\vecC{\vec{C}}
+\newcommand\txD{\text{D}}  \newcommand\vecD{\vec{D}}
+\newcommand\txE{\text{E}}  \newcommand\vecE{\vec{E}}
+\newcommand\txF{\text{F}}  \newcommand\vecF{\vec{F}}
+\newcommand\txG{\text{G}}  \newcommand\vecG{\vec{G}}
+\newcommand\txH{\text{H}}  \newcommand\vecH{\vec{H}}
+\newcommand\txI{\text{I}}  \newcommand\vecI{\vec{I}}
+\newcommand\txJ{\text{J}}  \newcommand\vecJ{\vec{J}}
+\newcommand\txK{\text{K}}  \newcommand\vecK{\vec{K}}
+\newcommand\txL{\text{L}}  \newcommand\vecL{\vec{L}}
+\newcommand\txM{\text{M}}  \newcommand\vecM{\vec{M}}
+\newcommand\txN{\text{N}}  \newcommand\vecN{\vec{N}}
+\newcommand\txO{\text{O}}  \newcommand\vecO{\vec{O}}
+\newcommand\txP{\text{P}}  \newcommand\vecP{\vec{P}}
+\newcommand\txQ{\text{Q}}  \newcommand\vecQ{\vec{Q}}
+\newcommand\txR{\text{R}}  \newcommand\vecR{\vec{R}}
+\newcommand\txS{\text{S}}  \newcommand\vecS{\vec{S}}
+\newcommand\txT{\text{T}}  \newcommand\vecT{\vec{T}}
+\newcommand\txU{\text{U}}  \newcommand\vecU{\vec{U}}
+\newcommand\txV{\text{V}}  \newcommand\vecV{\vec{V}}
+\newcommand\txW{\text{W}}  \newcommand\vecW{\vec{W}}
+\newcommand\txX{\text{X}}  \newcommand\vecX{\vec{X}}
+\newcommand\txY{\text{Y}}  \newcommand\vecY{\vec{Y}}
+\newcommand\txZ{\text{Z}}  \newcommand\vecZ{\vec{Z}}
+                           
+\newcommand\txa{\text{a}}  \newcommand\veca{\vec{a}}
+\newcommand\txb{\text{b}}  \newcommand\vecb{\vec{b}}
+\newcommand\txc{\text{c}}  \newcommand\vecc{\vec{c}}
+\newcommand\txd{\text{d}}  \newcommand\vecd{\vec{d}}
+\newcommand\txe{\text{e}}  \newcommand\vece{\vec{e}}
+\newcommand\txf{\text{f}}  \newcommand\vecf{\vec{f}}
+\newcommand\txg{\text{g}}  \newcommand\vecg{\vec{g}}
+\newcommand\txh{\text{h}}  \newcommand\vech{\vec{h}}
+\newcommand\txi{\text{i}}  \newcommand\veci{\vec{i}}
+\newcommand\txj{\text{j}}  \newcommand\vecj{\vec{j}}
+\newcommand\txk{\text{k}}  \newcommand\veck{\vec{k}}
+\newcommand\txl{\text{l}}  \newcommand\vecl{\vec{l}}
+\newcommand\txm{\text{m}}  \newcommand\vecm{\vec{m}}
+\newcommand\txn{\text{n}}  \newcommand\vecn{\vec{n}}
+\newcommand\txo{\text{o}}  \newcommand\veco{\vec{o}}
+\newcommand\txp{\text{p}}  \newcommand\vecp{\vec{p}}
+\newcommand\txq{\text{q}}  \newcommand\vecq{\vec{q}}
+\newcommand\txr{\text{r}}  \newcommand\vecr{\vec{r}}
+\newcommand\txs{\text{s}}  \newcommand\vecs{\vec{s}}
+\newcommand\txt{\text{t}}  \newcommand\vect{\vec{t}}
+\newcommand\txu{\text{u}}  \newcommand\vecu{\vec{u}}
+\newcommand\txv{\text{v}}  \newcommand\vecv{\vec{v}}
+\newcommand\txw{\text{w}}  \newcommand\vecw{\vec{w}}
+\newcommand\txx{\text{x}}  \newcommand\vecx{\vec{x}}
+\newcommand\txy{\text{y}}  \newcommand\vecy{\vec{y}}
+\newcommand\txz{\text{z}}  \newcommand\vecz{\vec{z}}
 
 % SPACES
-\def\sdots{\,\dots\,}
-\def\qdots{\quad\dots\quad}
-\def\qRarrow{\quad\Rightarrow\quad}
+\newcommand\sdots{\,\dots\,}
+\newcommand\qdots{\quad\dots\quad}
+\newcommand\qRarrow{\quad\Rightarrow\quad}
 
 % ANNOTATIONS
 % put an explanation above an equal sign
@@ -188,12 +185,12 @@
 \newcommand\Order[1]{\CmdWithParenthesis{\mathcal{O}}{#1}}
 
 % VECTOR, MATRIX and TENSOR
-% use vecA to force an arrow
-\NewCommandCopy{\vecA}{\vec}
+% use vecAr to force an arrow
+\NewCommandCopy{\vecAr}{\vec}
 % extra {} assure they can b directly used after _
 %% arrow/underline
 \newcommand\mat[1]{{\ensuremath{\underline{#1}}}}
-\renewcommand\vec[1]{{\ensuremath{\vecA{#1}}}}
+\renewcommand\vec[1]{{\ensuremath{\vecAr{#1}}}}
 \newcommand\ten[1]{{\ensuremath{[#1]}}}
 \newcommand\complex[1]{{\ensuremath{\tilde{#1}}}}
 %% bold
diff --git a/src/util/periodic_table.tex b/src/util/periodic_table.tex
index af3fa21..d74f7ee 100644
--- a/src/util/periodic_table.tex
+++ b/src/util/periodic_table.tex
@@ -54,10 +54,11 @@
     \vspace{0.5\baselineskip}
     \begingroup
         % label it only once
+        % \detokenize{\label{el:#1}}
         \directlua{ 
             if elements["#1"]["labeled"] == nil then
                 elements["#1"]["labeled"] = true
-                tex.print("\\label{el:#1}")
+                tex.print("\\phantomsection\\label{el:#1}")
             end
         }
         \NameWithDescription[\descwidth]{\elementName}{\elementName_desc}
diff --git a/src/util/tikz_macros.tex b/src/util/tikz_macros.tex
index 11df2d3..9ad5717 100644
--- a/src/util/tikz_macros.tex
+++ b/src/util/tikz_macros.tex
@@ -103,3 +103,12 @@
   \draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
   \draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east] {$E$};
 }
+
+\newcommand\tkXTick[2]{
+  \pgfmathsetmacro{\tickwidth}{0.1}
+  \draw (#1, -\tickwidth/2) -- (#1, \tickwidth/2) node[anchor=north] {#2};
+}
+\newcommand\tkYTick[2]{
+  \pgfmathsetmacro{\tickwidth}{0.1}
+  \draw (-\tickwidth/2, #1) -- (\tickwidth/2,#1) node[anchor=east] {#2};
+}