2009-10-27.lyx

#LyX 1.6.3 created this file. For more info see http://www.lyx.org/
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\options 10pt
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\language ngerman
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\graphics default
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\pdf_title "HM-VD-Übersichtszettel"
\pdf_author "Julian Gethmann"
\pdf_subject "Höheremathematik Vordiplom"
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\author "" 
\author "" 
\end_header

\begin_body

\begin_layout Section
Kovalente Bindungen
\end_layout

\begin_layout Standard
\begin_inset Formula $1s^{2}2s^{2}2p^{2}\to1\overbrace{s^{2}\underbrace{2s2p_{x}2p_{y}2p_{z}}_{4\times sp^{3}}}^{\text{Hybridorbitale}}\to2p_{z}+3\times sp^{2}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula \begin{eqnarray*}
CH_{4}\\
\text{Methan}\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Standard
GRAFIK
\end_layout

\begin_layout Standard
\begin_inset Note Note
status open

\begin_layout Plain Layout
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{tikzpicture}[mindmap,concept color=white!50]  
\end_layout

\begin_layout Plain Layout


\backslash
node [concept] {C^{-}}  child[grow=top] {node[concept] {Hˆ{+}}};
\end_layout

\begin_layout Plain Layout


\backslash
end{tikzpicture}  
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
FOLIEN
\end_layout

\begin_layout Subsection
Kristalle: 
\begin_inset Formula $C$
\end_inset

 (Diamant), 
\begin_inset Formula $Si,\, Ge$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $A^{III}B^{V}\to In\ Sb;\ Ga\ As$
\end_inset


\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
3D Graphit
\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
2D Graphen (2004)
\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
1D Kohlensotff-Nanoröhren (1991) 
\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
0D Fulleren 
\begin_inset Formula $\underbrace{C_{60}}_{\varnothing7,1\,\AA}$
\end_inset

/
\begin_inset Formula $C_{70}$
\end_inset

 (1985)
\end_layout

\begin_layout Subsection
Metallische Bindung
\end_layout

\begin_layout Standard
Valenzelektronen sind delokalisiert
\end_layout

\begin_layout Standard
\begin_inset Formula $\to$
\end_inset

 Elektronengas
\end_layout

\begin_layout Standard
\begin_inset Formula $Li$
\end_inset

-Ionen: 
\begin_inset Formula $r_{1}\sim0,6\,\AA$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $Li$
\end_inset

-Kristall: 
\begin_inset Formula $R_{0}\sim3\,\AA$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\left.\dfrac{R_{0}}{r_{i}}\right|_{Cu}\sim1,33,\quad\left.\dfrac{R_{0}}{r_{i}}\right|\approx1,05$
\end_inset


\end_layout

\begin_layout Subsection
Wasserstoffbrückenbindung
\end_layout

\begin_layout Standard
\begin_inset Formula $\left.U_{i}\right|_{H}\sim13,6\,\text{eV};\quad\left.U_{i}\right|_{Na}\approx5,1\,\text{eV}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $H\to$
\end_inset

 Kovalente bindung nur mit 
\bar under
einem 
\bar default
Nachbarn
\end_layout

\begin_layout Standard
GRAFIK
\end_layout

\begin_layout Standard
DNA Ammoniak 
\begin_inset Formula $NH_{3}$
\end_inset


\end_layout

\begin_layout Section
Struktur der Kristalle
\end_layout

\begin_layout Standard

\bar under
Symmetrie: 
\bar default
Transformationen 
\begin_inset Quotes gld
\end_inset

unverändert
\begin_inset Quotes grd
\end_inset

 erscheinen
\end_layout

\begin_layout Standard
Mathematik 
\begin_inset Formula $\to$
\end_inset

 Gruppentheorie
\end_layout

\begin_layout Enumerate
Punktgruppen (mindestens 1 Punkt ist fest)
\end_layout

\begin_deeper
\begin_layout Enumerate
z.
\begin_inset space \thinspace{}
\end_inset

B.
 Drehung um eine Drehachse GRAFIK, FOLIE
\end_layout

\begin_layout Enumerate
Spiegelung um eine Spiegelebene GRAFIK
\end_layout

\begin_layout Enumerate
Punktspiegelung GRAFIK
\end_layout

\end_deeper
\begin_layout Standard
Spiegelung + Drehung
\end_layout

\begin_layout Standard
GRAFIK
\end_layout

\begin_layout Standard
Drehinversion
\end_layout

\begin_layout Standard
GRAFIK
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
setcounter{enumi}{2} 
\end_layout

\end_inset


\end_layout

\begin_layout Enumerate
Raumgruppen (translative Symmetrieoperationen)
\end_layout

\begin_deeper
\begin_layout Enumerate
Gleitspiegelebene GRAFIK
\end_layout

\begin_layout Enumerate
Schraubung/Torsion GRAFIK
\end_layout

\end_deeper
\begin_layout Standard
Kristallstruktur=Gitter+Basis
\end_layout

\begin_layout Standard
GRAFIK
\end_layout

\begin_layout Standard
\begin_inset Formula $\underbrace{U(\vec{r})}_{\text{Umgebung}}=U(\vec{r}+\vec{R})$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\vec{R}=n_{1}\vec{a}+n_{2}\vec{b}+n_{3}\vec{c},\;\vec{a},\vec{b},\vec{c}\text{ sind Baisvektoren}$
\end_inset


\end_layout

\begin_layout Standard
GRAFIK
\end_layout

\end_body
\end_document