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<title>Atomic diffusion</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Atomic diffusion</span></span>

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<p>In <a href="Chemical_physics" title="Chemical physics">chemical physics</a>, <b>atomic diffusion</b> is a <a href="Diffusion" title="Diffusion">diffusion</a> process whereby the random, <a href="Thermal_energy" title="Thermal energy">thermally-activated</a> movement of <a href="Atom" title="Atom">atoms</a> in a <a href="Solid" title="Solid">solid</a> results in the net transport of atoms. For example, <a href="Helium" title="Helium">helium</a> atoms inside a balloon can diffuse through the wall of the balloon and escape, resulting in the balloon slowly deflating. Other air <a href="Molecule" title="Molecule">molecules</a> (e.g. <a href="Oxygen" title="Oxygen">oxygen</a>, <a href="Nitrogen" title="Nitrogen">nitrogen</a>) have lower mobilities and thus diffuse more slowly through the balloon wall. There is a <a href="Concentration_gradient" class="mw-redirect" title="Concentration gradient">concentration gradient</a> in the balloon wall, because the balloon was initially filled with helium, and thus there is plenty of helium on the inside, but there is relatively little helium on the outside (helium is not a major component of <a href="Air" class="mw-redirect" title="Air">air</a>). The rate of transport is governed by the <a href="Mass_diffusivity" title="Mass diffusivity">diffusivity</a> and the concentration gradient.

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<div class="mw-heading mw-heading2"><h2 id="In_crystals">In crystals</h2></div>

<p>In the crystal solid state, diffusion within the crystal lattice occurs by either <a href="Interstitial_defect" title="Interstitial defect">interstitial</a> or substitutional mechanisms and is referred to as <a href="Lattice_diffusion_coefficient" title="Lattice diffusion coefficient">lattice diffusion</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In interstitial lattice diffusion, a diffusant (such as C in an iron alloy), will diffuse in between the lattice structure of another crystalline element. In substitutional lattice diffusion (<a href="Self-diffusion" title="Self-diffusion">self-diffusion</a> for example), the atom can only move by substituting place with another atom. Substitutional lattice diffusion is often contingent upon the availability of <a href="Crystallographic_defect" title="Crystallographic defect">point vacancies</a> throughout the crystal lattice. Diffusing particles migrate from point vacancy to point vacancy by the rapid, essentially random jumping about

(<a href="Jump_diffusion" title="Jump diffusion">jump diffusion</a>).

</p><p>Since the prevalence of point vacancies increases in accordance with the <a href="Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a>, the rate of crystal solid state diffusion increases with temperature.

</p><p>For a single atom in a defect-free crystal, the movement can be described by the "<a href="Random_walk" title="Random walk">random walk</a>" model. In 3-dimensions it can be shown that after <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

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<annotation encoding="application/x-tex">{\displaystyle n}</annotation>

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</math></span><img src="./a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> jumps of length <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">

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<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

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</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> the atom will have moved, on average, a distance of:

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<annotation encoding="application/x-tex">{\displaystyle r=\alpha {\sqrt {n}}.}</annotation>

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</math></span><img src="./fb9192037bba45b15c826f7686af3cd79a66e91f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.612ex; height:3.009ex;" alt="{\displaystyle r=\alpha {\sqrt {n}}.}" loading="lazy"></span></dd></dl>

<p>If the jump frequency is given by <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span> (in jumps per second) and time is given by <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}">

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<annotation encoding="application/x-tex">{\displaystyle t}</annotation>

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</math></span><img src="./65658b7b223af9e1acc877d848888ecdb4466560.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}" loading="lazy"></span>, then <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}">

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<annotation encoding="application/x-tex">{\displaystyle r}</annotation>

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</math></span><img src="./0d1ecb613aa2984f0576f70f86650b7c2a132538.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" loading="lazy"></span> is proportional to the square root of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Tt}">

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<annotation encoding="application/x-tex">{\displaystyle Tt}</annotation>

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</math></span><img src="./64f833ef155db2cdf6ff0a08cd4899ee753cb784.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.476ex; height:2.176ex;" alt="{\displaystyle Tt}" loading="lazy"></span>:

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<annotation encoding="application/x-tex">{\displaystyle r\sim {\sqrt {Tt}}.}</annotation>

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</math></span><img src="./3d65ee6f2c3f10c25ac45944a152a6c9ab281bb8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.206ex; height:3.009ex;" alt="{\displaystyle r\sim {\sqrt {Tt}}.}" loading="lazy"></span></dd></dl>

<p>Diffusion in <a href="Polycrystalline" class="mw-redirect" title="Polycrystalline">polycrystalline</a> materials can involve short circuit diffusion mechanisms. For example, along the grain boundaries and certain crystalline defects such as dislocations there is more open space, thereby allowing for a lower activation energy for diffusion. Atomic diffusion in polycrystalline materials is therefore often modeled using an <a href="Effective_diffusion_coefficient" title="Effective diffusion coefficient">effective diffusion coefficient</a>, which is a combination of lattice, and <a href="Grain_boundary_diffusion_coefficient" title="Grain boundary diffusion coefficient">grain boundary diffusion coefficients</a>. In general, <a href="Surface_diffusion" title="Surface diffusion">surface diffusion</a> occurs much faster than <a href="Grain_boundary_diffusion_coefficient" title="Grain boundary diffusion coefficient">grain boundary diffusion</a>, and <a href="Grain_boundary_diffusion_coefficient" title="Grain boundary diffusion coefficient">grain boundary diffusion</a> occurs much faster than <a href="Lattice_diffusion_coefficient" title="Lattice diffusion coefficient">lattice diffusion</a>.

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<ul><li><a href="Kirkendall_effect" title="Kirkendall effect">Kirkendall effect</a></li>

<li><a href="Mass_diffusivity" title="Mass diffusivity">Mass diffusivity</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFHeitjansKarger2005" class="citation book cs1">Heitjans, P.; Karger, J., eds. (2005). <i>Diffusion in condensed matter: Methods, Materials, Models</i> (2nd ed.). Birkhauser. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>3-540-20043-6</bdi>.</cite></span>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://dragon.unideb.hu/~zerdelyi/Diffusion-on-the-nanoscale/index.html">Classical and nanoscale diffusion (with figures and animations)</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2023-04-08" href="https://en.wikipedia.org/wiki/?title=Atomic_diffusion&oldid=1148781012">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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