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	<id>https://en.formulasearchengine.com/index.php?action=history&amp;feed=atom&amp;title=Universal_one-way_hash_function</id>
	<title>Universal one-way hash function - Revision history</title>
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	<updated>2026-05-23T08:56:40Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Universal_one-way_hash_function&amp;diff=246403&amp;oldid=prev</id>
		<title>134.60.77.114: /* Definition */</title>
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		<updated>2014-12-15T08:24:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Definition&lt;/span&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 10:24, 15 December 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The writer is called Wilber Pegues&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;To play lacross is the thing &lt;/del&gt;I &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;adore most of all&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Distributing manufacturing &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where my primary income comes from and it&#039;s &lt;/del&gt;something I &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;truly appreciate. My wife &lt;/del&gt;and I &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reside in Kentucky&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Feel free to visit my &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blog ... psychics online (&lt;/del&gt;[http://&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1.234&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;36&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;240&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fxac&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;m001_2/7330 click the next page&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;)&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I would like to introduce myself to you, I am Andrew and my spouse doesn&#039;t like it at all&lt;/ins&gt;. I&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;ve always loved residing in Alaska&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;To climb &lt;/ins&gt;is something &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;she would never give up. &lt;/ins&gt;I &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;am an invoicing officer &lt;/ins&gt;and I&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;ll be promoted soon&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Feel free to visit my &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;web page :: &lt;/ins&gt;[http://&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;herandkingscounty&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;content&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;information-and-facts-you-must-know-about-hobbies psychic phone&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>134.60.77.114</name></author>
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	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Universal_one-way_hash_function&amp;diff=246402&amp;oldid=prev</id>
		<title>en&gt;BDD: removing deleted article</title>
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		<updated>2014-03-03T19:14:53Z</updated>

		<summary type="html">&lt;p&gt;removing deleted article&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 21:14, 3 March 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cleanup|date=April 2012}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;writer &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;called Wilber Pegues&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;To play lacross &lt;/ins&gt;is the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;thing I adore &lt;/ins&gt;most of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;all&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Distributing manufacturing &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where my primary income comes from &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it&#039;s something I &lt;/ins&gt;truly &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;appreciate&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;My wife &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I reside &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Kentucky&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Feel free &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;visit my blog &lt;/ins&gt;... &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;psychics online &lt;/ins&gt;([http://&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;234&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;36&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;240&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fxac&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;m001_2&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7330 click &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;next page&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[File:Slip system.gif|right|thumb|Schematic view of slip mechanism]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In materials science, &#039;&#039;&#039;slip&#039;&#039;&#039; is the process by which a [[dislocation]] motion produces [[plastic deformation]]. An external force makes parts of the [[crystal lattice]] glide along each other, changing the material&#039;s geometry. Depending on the type of lattice, different slip systems are present in the material. More specifically, slip occurs between planes containing the smallest [[Burgers vector]]. &lt;/del&gt;The &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;picture on the right shows a schematic view of the slip mechanism.The slip planes and slip directions in a crystal have specific crystallographic forms. The slip planes are normally the planes with the highest density of atoms, i.e., those most widely spaced, and the direction of the slip &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the direction in the slip plane that corresponds to one of the shortest lattice translation vectors&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Often, this &lt;/del&gt;is the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;direction in which atoms are &lt;/del&gt;most &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;closely spaced. A slip plane and a slip direction constitute a slip system. A characteristic shear stress is required to initiate a slip.&amp;lt;ref name=&quot;Hull and Bacon&quot;&amp;gt;, Hull D., Bacon, D.J (2001); &quot;Introduction to Dislocations&quot;, ISBN 0-75076-4681-0&amp;lt;/ref&amp;gt; &lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Slip is an important mode &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;deformation mechanism in crystals. Slip induces plasticity in most of the metals.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Slip systems==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;===fcc===&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[File:Lattice face centered cubic.svg|left|upright|thumb|Unit cell of an fcc material.]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[File:FCC Lattice.svg|upright|thumb|Lattice configuration of the close packed slip plane in an fcc material. The arrow represents the burgers vector in this dislocation glide system&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Slip in [[Face-centered cubic|face centered cubic]] (fcc) crystals occurs along the [[Close-packing of spheres|close packed plane]]. Specifically, the slip plane &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;of type {111}, &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the direction is of type &amp;lt;{{overline|1}}10&amp;gt;. In the diagram, the specific plane and direction are (111) and [{{overline|1}}10], respectively. Given the permutations of the slip plane types and direction types, fcc crystals have 12 slip systems. In the fcc lattice, the [[norm (mathematics)|norm]] of the Burgers vector, b, can be calculated using the following equation:&amp;lt;ref name=VanVliet&amp;gt;[http://ocw.mit.edu/OcwWeb/Materials-Science-and-Engineering/3-032Fall-2007/CourseHome/index.htm Van Vliet, Krystyn J. (2006); &quot;3.032 Mechanical Behavior of Materials&quot;]&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&amp;lt;math&amp;gt;|b|= \frac {a}{2}|&amp;lt;110&amp;gt;|= \frac{a}{\sqrt 2}&amp;lt;/math&amp;gt;&amp;lt;ref name=VanVliet&amp;gt;[http://www.stellar.mit.edu/S/course/3/fa06/3.032/index.html Van Vliet, Krystyn J. (2006); &quot;3.032 Mechanical Behavior of Materials&quot;]&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Where a is the lattice constant of the unit cell.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;===bcc===&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[File:Lattice body centered cubic.svg|left|upright||thumb|Unit cell of a bcc material.]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[File:BCC Lattice.JPG|upright|thumb|Lattice configuration of the slip plane in a bcc material. The arrow represents the burgers vector in this dislocation glide system.]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Slip in [[body-centered cubic]] (bcc) crystals occurs along the plane of shortest [[Burgers vector]] as well; however, unlike fcc, there are no &lt;/del&gt;truly &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;close-packed planes in the bcc crystal structure. Thus, a slip system in bcc requires heat to activate. Some bcc materials (e.g. α-Fe) can contain up to 48 slip systems. There are six slip planes of type {110}, each with two &amp;lt;111&amp;gt; directions (12 systems)&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;There are 24 {123} &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12 {112} planes each with one &amp;lt;111&amp;gt; direction (36 systems, for a total of 48). While the {123} and {112} planes are not exactly identical &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;activation energy to {110}, they are so close in energy that for all intents and purposes they can be treated as identical&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In the diagram on the right the specific slip plane and direction are (110) and [{{overline|1}}11], respectively.&amp;lt;ref name=&quot;VanVliet&quot;/&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|b|= \frac {a}{2}|&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;111&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|= \frac{\sqrt 3a}{2}&amp;lt;/math&amp;gt;&amp;lt;ref name=VanVliet&amp;gt;[http://www.stellar.mit.edu/S/course/3/fa06/3.032/index.html Van Vliet, Krystyn J. (2006); &quot;3.032 Mechanical Behavior of Materials&quot;]&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elemental metals in the bcc [[crystal structure]] include [[lithium]], [[sodium]], [[potassium]], [[vanadium]], [[chromium]], [[manganese]], [[iron]], [[rubidium]], [[niobium]], [[molybdenum]], [[cesium]], [[barium]], [[tantalum]], [[tungsten]], [[radium]], and [[europium]]. Compound materials with the bcc crystal structure include the [[cesium halides]] (other than [[CsF]]).&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;===hcp===&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Slip in [[hexagonal close packed]] (hcp) metals is much more limited than in bcc and fcc crystal structures. This is because few active slip systems exist in hcp metals. The result of the small number of slip systems is that the metal is generally brittle.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Cadmium]], [[zinc]], [[magnesium]], [[titanium]], and [[beryllium]] have a slip plane at {0001} and a slip direction of &amp;lt;11{{overline|2}}0&amp;gt;. This creates a total of three slip systems, depending on orientation. (Remember that a slip system is a combination of a slip plane and a slip direction) Other combinations are also possible.&amp;lt;ref name=Callister&amp;gt;Callister, William D., Jr. (2007); &quot;Materials Science and Engineering: An Introduction&quot;, ISBN 0-471-73696-1&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;There are two types of dislocations in crystals that can induce slip-edge dislocations and screw dislocations. Edge dislocations have the direction of the burgers vector perpendicular &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the dislocation line, while screw dislocations have the direction of the burgers vector parallel to the dislocation line&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The type of dislocations generated largely depends on the direction of the applied stress, temperature and other factors&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Screw dislocations can easily cross slip from one plane to another if the other slip plane contains the direction of the burgers vector&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ref name=&quot;Hull and Bacon&quot;&amp;gt;, Hull D., Bacon, D.J &lt;/del&gt;(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2001); &quot;Introduction to Dislocations&quot;, ISBN 0-75076-4681-0&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==See also==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;*[[Miller indices]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{reflist}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==External links==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;*&lt;/del&gt;[http://&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;doitpoms&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ac&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;uk&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tlplib&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;slip&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;index.php An online tutorial on slip], explained on a promotional site for [[materials science]] at &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[University of Cambridge]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Materials science]&lt;/del&gt;]&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;BDD</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Universal_one-way_hash_function&amp;diff=12676&amp;oldid=prev</id>
		<title>en&gt;Sadeq: /* Definition */</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Universal_one-way_hash_function&amp;diff=12676&amp;oldid=prev"/>
		<updated>2012-05-06T03:31:04Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Definition&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{cleanup|date=April 2012}}&lt;br /&gt;
&lt;br /&gt;
[[File:Slip system.gif|right|thumb|Schematic view of slip mechanism]]&lt;br /&gt;
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In materials science, &amp;#039;&amp;#039;&amp;#039;slip&amp;#039;&amp;#039;&amp;#039; is the process by which a [[dislocation]] motion produces [[plastic deformation]]. An external force makes parts of the [[crystal lattice]] glide along each other, changing the material&amp;#039;s geometry. Depending on the type of lattice, different slip systems are present in the material. More specifically, slip occurs between planes containing the smallest [[Burgers vector]]. The picture on the right shows a schematic view of the slip mechanism.The slip planes and slip directions in a crystal have specific crystallographic forms. The slip planes are normally the planes with the highest density of atoms, i.e., those most widely spaced, and the direction of the slip is the direction in the slip plane that corresponds to one of the shortest lattice translation vectors. Often, this is the direction in which atoms are most closely spaced. A slip plane and a slip direction constitute a slip system. A characteristic shear stress is required to initiate a slip.&amp;lt;ref name=&amp;quot;Hull and Bacon&amp;quot;&amp;gt;, Hull D., Bacon, D.J (2001); &amp;quot;Introduction to Dislocations&amp;quot;, ISBN 0-75076-4681-0&amp;lt;/ref&amp;gt; &lt;br /&gt;
Slip is an important mode of deformation mechanism in crystals. Slip induces plasticity in most of the metals.&lt;br /&gt;
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==Slip systems==&lt;br /&gt;
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===fcc===&lt;br /&gt;
[[File:Lattice face centered cubic.svg|left|upright|thumb|Unit cell of an fcc material.]]&lt;br /&gt;
[[File:FCC Lattice.svg|upright|thumb|Lattice configuration of the close packed slip plane in an fcc material. The arrow represents the burgers vector in this dislocation glide system.]]&lt;br /&gt;
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Slip in [[Face-centered cubic|face centered cubic]] (fcc) crystals occurs along the [[Close-packing of spheres|close packed plane]]. Specifically, the slip plane is of type {111}, and the direction is of type &amp;lt;{{overline|1}}10&amp;gt;. In the diagram, the specific plane and direction are (111) and [{{overline|1}}10], respectively. Given the permutations of the slip plane types and direction types, fcc crystals have 12 slip systems. In the fcc lattice, the [[norm (mathematics)|norm]] of the Burgers vector, b, can be calculated using the following equation:&amp;lt;ref name=VanVliet&amp;gt;[http://ocw.mit.edu/OcwWeb/Materials-Science-and-Engineering/3-032Fall-2007/CourseHome/index.htm Van Vliet, Krystyn J. (2006); &amp;quot;3.032 Mechanical Behavior of Materials&amp;quot;]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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:&amp;lt;math&amp;gt;|b|= \frac {a}{2}|&amp;lt;110&amp;gt;|= \frac{a}{\sqrt 2}&amp;lt;/math&amp;gt;&amp;lt;ref name=VanVliet&amp;gt;[http://www.stellar.mit.edu/S/course/3/fa06/3.032/index.html Van Vliet, Krystyn J. (2006); &amp;quot;3.032 Mechanical Behavior of Materials&amp;quot;]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Where a is the lattice constant of the unit cell.&lt;br /&gt;
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===bcc===&lt;br /&gt;
[[File:Lattice body centered cubic.svg|left|upright||thumb|Unit cell of a bcc material.]]&lt;br /&gt;
[[File:BCC Lattice.JPG|upright|thumb|Lattice configuration of the slip plane in a bcc material. The arrow represents the burgers vector in this dislocation glide system.]]&lt;br /&gt;
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Slip in [[body-centered cubic]] (bcc) crystals occurs along the plane of shortest [[Burgers vector]] as well; however, unlike fcc, there are no truly close-packed planes in the bcc crystal structure. Thus, a slip system in bcc requires heat to activate. Some bcc materials (e.g. α-Fe) can contain up to 48 slip systems. There are six slip planes of type {110}, each with two &amp;lt;111&amp;gt; directions (12 systems). There are 24 {123} and 12 {112} planes each with one &amp;lt;111&amp;gt; direction (36 systems, for a total of 48). While the {123} and {112} planes are not exactly identical in activation energy to {110}, they are so close in energy that for all intents and purposes they can be treated as identical. In the diagram on the right the specific slip plane and direction are (110) and [{{overline|1}}11], respectively.&amp;lt;ref name=&amp;quot;VanVliet&amp;quot;/&amp;gt;&lt;br /&gt;
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:&amp;lt;math&amp;gt;|b|= \frac {a}{2}|&amp;lt;111&amp;gt;|= \frac{\sqrt 3a}{2}&amp;lt;/math&amp;gt;&amp;lt;ref name=VanVliet&amp;gt;[http://www.stellar.mit.edu/S/course/3/fa06/3.032/index.html Van Vliet, Krystyn J. (2006); &amp;quot;3.032 Mechanical Behavior of Materials&amp;quot;]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Elemental metals in the bcc [[crystal structure]] include [[lithium]], [[sodium]], [[potassium]], [[vanadium]], [[chromium]], [[manganese]], [[iron]], [[rubidium]], [[niobium]], [[molybdenum]], [[cesium]], [[barium]], [[tantalum]], [[tungsten]], [[radium]], and [[europium]]. Compound materials with the bcc crystal structure include the [[cesium halides]] (other than [[CsF]]).&lt;br /&gt;
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===hcp===&lt;br /&gt;
Slip in [[hexagonal close packed]] (hcp) metals is much more limited than in bcc and fcc crystal structures. This is because few active slip systems exist in hcp metals. The result of the small number of slip systems is that the metal is generally brittle.&lt;br /&gt;
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[[Cadmium]], [[zinc]], [[magnesium]], [[titanium]], and [[beryllium]] have a slip plane at {0001} and a slip direction of &amp;lt;11{{overline|2}}0&amp;gt;. This creates a total of three slip systems, depending on orientation. (Remember that a slip system is a combination of a slip plane and a slip direction) Other combinations are also possible.&amp;lt;ref name=Callister&amp;gt;Callister, William D., Jr. (2007); &amp;quot;Materials Science and Engineering: An Introduction&amp;quot;, ISBN 0-471-73696-1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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There are two types of dislocations in crystals that can induce slip-edge dislocations and screw dislocations. Edge dislocations have the direction of the burgers vector perpendicular to the dislocation line, while screw dislocations have the direction of the burgers vector parallel to the dislocation line. The type of dislocations generated largely depends on the direction of the applied stress, temperature and other factors. Screw dislocations can easily cross slip from one plane to another if the other slip plane contains the direction of the burgers vector.&amp;lt;ref name=&amp;quot;Hull and Bacon&amp;quot;&amp;gt;, Hull D., Bacon, D.J (2001); &amp;quot;Introduction to Dislocations&amp;quot;, ISBN 0-75076-4681-0&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==See also==&lt;br /&gt;
*[[Miller indices]]&lt;br /&gt;
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==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
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==External links==&lt;br /&gt;
*[http://www.doitpoms.ac.uk/tlplib/slip/index.php An online tutorial on slip], explained on a promotional site for [[materials science]] at the [[University of Cambridge]]&lt;br /&gt;
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[[Category:Materials science]]&lt;/div&gt;</summary>
		<author><name>en&gt;Sadeq</name></author>
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