formelsammlung/src/cm/misc.tex
2025-02-02 22:59:33 +01:00

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\Section[
\eng{Band theory}
\ger{Bändermodell}
]{band}
\Subsection[
\eng{Hybrid orbitals}
\ger{Hybridorbitale}
]{hybrid_orbitals}
\begin{ttext}
\eng{Hybrid orbitals are linear combinations of other atomic orbitals.}
\ger{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.}
\end{ttext}
% chemmacros package
\begin{formula}{sp3}
\desc{sp3 Orbital}{\GT{eg} \ce{CH4}}{}
\desc[german]{sp3 Orbital}{}{}
\eq{
1\text{s} + 3\text{p} = \text{sp3}
\orbital{sp3}
}
\end{formula}
\begin{formula}{sp2}
\desc{sp2 Orbital}{}{}
\desc[german]{sp2 Orbital}{}{}
\eq{
1\text{s} + 2\text{p} = \text{sp2}
\orbital{sp2}
}
\end{formula}
\begin{formula}{sp}
\desc{sp Orbital}{}{}
\desc[german]{sp Orbital}{}{}
\eq{
1\text{s} + 1\text{p} = \text{sp}
\orbital{sp}
}
\end{formula}
\Section[
\eng{Diffusion}
\ger{Diffusion}
]{diffusion}
\begin{formula}{diffusion_coefficient}
\desc{Diffusion coefficient}{}{}
\desc[german]{Diffusionskoeffizient}{}{}
\quantity{D}{\m^2\per\s}{s}
\end{formula}
\begin{formula}{particle_current_density}
\desc{Particle current density}{Number of particles through an area}{}
\desc[german]{Teilchenstromdichte}{Anzahl der Teilchen durch eine Fläche}{}
\quantity{J}{1\per\s^2}{s}
\end{formula}
\begin{formula}{einstein_relation}
\desc{Einstein relation}{Classical}{\QtyRef{diffusion_coefficient}, \mu \qtyRef{mobility}, \QtyRef{temperature}, $q$ \qtyRef{charge}}
\desc[german]{Einsteinrelation}{Klassisch}{}
\eq{D = \frac{\mu \kB T}{q}}
\end{formula}
\begin{formula}{concentration}
\desc{Concentration}{A quantity per volume}{}
\desc[german]{Konzentration}{Eine Größe pro Volumen}{}
\quantity{c}{x\per\m^3}{s}
\end{formula}
\begin{formula}{fick_law_1}
\desc{Fick's first law}{Particle movement is proportional to concentration gradient}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}}
\desc[german]{Erstes Ficksches Gesetz}{Teilchenbewegung ist proportional zum Konzentrationsgradienten}{}
\eq{J = -D\frac{c}{x}}
\end{formula}
\begin{formula}{fick_law_2}
\desc{Fick's second law}{}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}}
\desc[german]{Zweites Ficksches Gesetz}{}{}
\eq{\pdv{c}{t} = D \pdv[2]{c}{x}}
\end{formula}
\Section[
\eng{\GT{misc}}
\ger{\GT{misc}}
]{misc}
\begin{formula}{work_function}
\desc{Work function}{Lowest energy required to remove an electron into the vacuum}{}
\desc[german]{Austrittsarbeit}{eng. "Work function"; minimale Energie um ein Elektron aus dem Festkörper zu lösen}{}
\quantity{W}{\eV}{s}
\eq{W = \Evac - \EFermi}
\end{formula}
\begin{formula}{electron_affinity}
\desc{Electron affinity}{Energy required to remove one electron from an anion with one negative charge.\\Energy difference between vacuum level and conduction band}{}
\desc[german]{Elektronenaffinität}{Energie, die benötigt wird um ein Elektron aus einem einfach-negativ geladenen Anion zu entfernen. Entspricht der Energiedifferenz zwischen Vakuum-Niveau und dem Leitungsband}{}
\quantity{\chi}{\eV}{s}
\eq{\chi = \left(\Evac - \Econd\right)}
\end{formula}
\begin{formula}{laser}
\desc{Laser}{Light amplification by stimulated emission of radiation}{}
\desc[german]{Laser}{}{}
\ttxt{
\eng{\textit{Gain medium} is energized \textit{pumping energy} (electric current or light), light of certain wavelength is amplified in the gain medium}
}
\end{formula}