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Created February 6, 2019 10:30
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bonding.html
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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title class="next-head">「02-bonding」</title><link rel="shortcut icon" type="image/ico" href="http://127.0.0.1:8830/_static/favicon.ico" class="next-head"><link rel="stylesheet" href="./bonding_files/page.css" class="next-head"><link rel="stylesheet" href="./bonding_files/markdown.css" class="next-head"><link rel="stylesheet" href="./bonding_files/highlight.css" class="next-head"><link rel="stylesheet" href="./bonding_files/katex@0.5.1.css" class="next-head"><script type="text/javascript" src="./bonding_files/tweenlite.min.js" class="next-head"></script><script type="text/javascript" src="./bonding_files/mermaid.min.js" class="next-head"></script><link rel="preload" href="./bonding_files/index.js" as="script"><link rel="preload" href="./bonding_files/_app.js" as="script"><link rel="preload" href="./bonding_files/_error.js" as="script"><link rel="preload" href="./bonding_files/webpack-42652fa8b82c329c0559.js" as="script"><link rel="preload" href="./bonding_files/commons.1c1b5ebd55cbcad2529a.js" as="script"><link rel="preload" href="./bonding_files/main-94dad8183cac85e3af97.js" as="script"><style type="text/css">/* Chart.js */
@-webkit-keyframes chartjs-render-animation{from{opacity:0.99}to{opacity:1}}@keyframes chartjs-render-animation{from{opacity:0.99}to{opacity:1}}.chartjs-render-monitor{-webkit-animation:chartjs-render-animation 0.001s;animation:chartjs-render-animation 0.001s;}</style></head><body><div id="__next"><div id="page-ctn"><header id="page-header"><h3><svg viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path fill-rule="evenodd" d="M3 5h4v1H3V5zm0 3h4V7H3v1zm0 2h4V9H3v1zm11-5h-4v1h4V5zm0 2h-4v1h4V7zm0 2h-4v1h4V9zm2-6v9c0 .55-.45 1-1 1H9.5l-1 1-1-1H2c-.55 0-1-.45-1-1V3c0-.55.45-1 1-1h5.5l1 1 1-1H15c.55 0 1 .45 1 1zm-8 .5L7.5 3H2v9h6V3.5zm7-.5H9.5l-.5.5V12h6V3z"></path></svg>02-bonding</h3></header><section class="markdown-body"><h2 class="source-line" data-source-line="0">Bonding</h2>
<p class="source-line" data-source-line="2">Solids can form through different kinds of bonding:</p>
<ol>
<li class="source-line" data-source-line="4"><strong>Van-der-Waals</strong></li>
</ol>
<ul>
<li class="source-line" data-source-line="6">bonding energy between 10 and 100 meV (not stable at room temperature)</li>
<li class="source-line" data-source-line="7">most dominant only in noble gas crystals</li>
<li class="source-line" data-source-line="8">close-packaging of equal spheres, electrons are bound</li>
<li class="source-line" data-source-line="9">current fluctuations create a temporal dipole which induce a dipole in another atom</li>
</ul>
<ol start="2">
<li class="source-line" data-source-line="11"><strong>Hydrogenic</strong></li>
</ol>
<ul>
<li class="source-line" data-source-line="13">bonding energy around 100 meV</li>
<li class="source-line" data-source-line="14">occurs at atoms with high electronegativity (hydrogen bonds)</li>
<li class="source-line" data-source-line="15">very important in biological processes</li>
<li class="source-line" data-source-line="16">of ionic character (electron removed from hydrogen atom)</li>
</ul>
<ol start="3">
<li class="source-line" data-source-line="18"><strong>Metallic</strong></li>
</ol>
<ul>
<li class="source-line" data-source-line="20">bonding energy between 1 and 5 eV</li>
<li class="source-line" data-source-line="21">electrons can move freely</li>
<li class="source-line" data-source-line="22">relative large distance between nuclei</li>
<li class="source-line" data-source-line="23">classical not stable but quantum mechanical because <em>kinetic energy of electrons is lowered??</em></li>
</ul>
<ol start="4">
<li class="source-line" data-source-line="25"><strong>Ionic</strong></li>
</ol>
<ul>
<li class="source-line" data-source-line="27">bonding energy between 5 and 10 eV</li>
<li class="source-line" data-source-line="28">complete ionisation of one atom (electron transfer)</li>
<li class="source-line" data-source-line="29">electrostatic force between cations and anions</li>
<li class="source-line" data-source-line="30">close-packaging of equal spheres, electrons are bound</li>
</ul>
<ol start="5">
<li class="source-line" data-source-line="32"><strong>Covalent</strong></li>
</ol>
<ul>
<li class="source-line" data-source-line="34">electron pair bonding / overlap of neighboring orbitals</li>
<li class="source-line" data-source-line="35"><em>Linear Combination of Atomic Orbitals</em></li>
<li class="source-line" data-source-line="36">sp2 / sp3 hybridisation</li>
</ul>
<h3 class="source-line" data-source-line="38">Models</h3>
<ol>
<li class="source-line" data-source-line="40"><strong>Van-der-Waals</strong></li>
</ol>
<p class="source-line" data-source-line="42">The <strong>Lennard-Jones</strong> potential, $$V®=A/r^{12} - B/r^6$$, models the
attractive dipole interactions of the <strong>Van-der-Waals</strong> forces between two
neutral atoms as well as the repulsive force due to the Pauli exclusion
principle.</p>
<ol start="2">
<li class="source-line" data-source-line="47"><strong>Hard-Sphere</strong></li>
</ol>
<p class="source-line" data-source-line="49">Sometimes the repulsive force due to the Pauli exclusion principle is also
modeled by $$V®=Ae^{r/\rho}.$$</p>
<ol start="3">
<li class="source-line" data-source-line="52"><strong>Ionic</strong></li>
</ol>
<h1 class="source-line" data-source-line="54">In order to model the ionic bonding energy one has to account for the
contribution of neighboring ions as the <strong>Coulomb</strong> potential is long range.
The potential energy can be written as $$V®</h1>
<p class="source-line" data-source-line="58">\sum_{i\neq j}
\left(\frac{A}{r^{12}}\pm\frac{e_0^2}{4\pi\epsilon_0r_{ij}}\right)
\approx
\frac{A}{R^{12}}-\frac{e_0^2}{4\pi\epsilon_0}\sum_{i\neq j}\frac{\pm1}{r_{ij}}
,</p>
wherein the first term is again due to the short-range Pauli exclusion
principle.
### Missing
* energy diagrams of the potentials
* sketch of how the atoms arange
### Keywords
* cohesive energy
### Questions
&gt; Why do lattice structures form (at room temperature)?
&gt; What is the phycics behind Van-der-Waals interactions?
One the one hand side an atom can induce a dipole on another atom which leads
to an attractive $r^{-6}$ potential. One the other hand the Pauli exclusion
principle acts as a repulsive force with $r^{-12}$ dependency.
&gt; What is the adiabatic / Born-Oppenheimer approximation?
In the adiabatic approximation one assumes nuclei and electron dynamics occur
at different time scales. Nuclei dynamics occur at slow time scales while
electron dynamics occur almost instantly. *This allows one to postulate a
static lattice.*
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