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	<id>http://gisaxs.com/index.php?action=history&amp;feed=atom&amp;title=Lattice%3ADiamond</id>
	<title>Lattice:Diamond - Revision history</title>
	<link rel="self" type="application/atom+xml" href="http://gisaxs.com/index.php?action=history&amp;feed=atom&amp;title=Lattice%3ADiamond"/>
	<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;action=history"/>
	<updated>2026-04-08T18:07:51Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.31.7</generator>
	<entry>
		<id>http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5599&amp;oldid=prev</id>
		<title>KevinYager: /* See Also */</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5599&amp;oldid=prev"/>
		<updated>2016-11-13T22:45:59Z</updated>

		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;See Also&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 22:45, 13 November 2016&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-l196&quot; &gt;Line 196:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 196:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==See Also==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==See Also==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [http://en.wikipedia.org/wiki/Diamond_cubic Diamond Cubic (Wikipedia)]&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [http://en.wikipedia.org/wiki/Diamond_cubic Diamond Cubic (Wikipedia)]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;* [[Lattice:Hexagonal &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Diamond&lt;/del&gt;|Hexagonal Diamond Lattice]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; 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;* [[Lattice:Hexagonal &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;diamond&lt;/ins&gt;|Hexagonal Diamond Lattice]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5589&amp;oldid=prev</id>
		<title>KevinYager at 22:27, 13 November 2016</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5589&amp;oldid=prev"/>
		<updated>2016-11-13T22:27:03Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 22:27, 13 November 2016&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=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;The diamond lattice, which consists of tetrahedrally-arranged atoms/particles, has [[Lattice:Simple Cubic|simple cubic]] symmetry.&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; 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 diamond &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[&lt;/ins&gt;lattice&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]]&lt;/ins&gt;, which consists of tetrahedrally-arranged atoms/particles, has [[Lattice:Simple Cubic|simple cubic]] &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[&lt;/ins&gt;symmetry&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]]&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Diamond00.png]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Diamond00.png]]&lt;/div&gt;&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-l5&quot; &gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;Along an appropriate axis, the lattice has six-fold symmetry (hexagonal).&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; 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;Along an appropriate axis, the lattice has six-fold symmetry (&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[&lt;/ins&gt;hexagonal&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]]&lt;/ins&gt;).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Canonical Diamond==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Canonical Diamond==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5587&amp;oldid=prev</id>
		<title>KevinYager: /* Nano */</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5587&amp;oldid=prev"/>
		<updated>2016-11-13T22:22:57Z</updated>

		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nano&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 22:22, 13 November 2016&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-l51&quot; &gt;Line 51:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 51:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====Nano====&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====Nano====&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;* Liu, W.; Tagawa, M.; Xin, H.L.; Wang, T.; Emamy, H. Li, H.; [[Yager, K.G.]]; Starr, F.W.; Tkachenko, A.V.; Gang, O. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;&lt;/del&gt;Diamond family of nanoparticle superlattices&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot; &lt;/del&gt;Science 2016, 351, 582–586.&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; 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 class=&quot;diffchange diffchange-inline&quot;&gt;* [[Lattices of nano-objects|Nanoparticle superlattice]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; 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 class=&quot;diffchange diffchange-inline&quot;&gt;*&lt;/ins&gt;* Liu, W.; Tagawa, M.; Xin, H.L.; Wang, T.; Emamy, H. Li, H.; [[Yager, K.G.]]; Starr, F.W.; Tkachenko, A.V.; Gang, O. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[http://science.sciencemag.org/content/351/6273/582 &lt;/ins&gt;Diamond family of nanoparticle superlattices&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;] &amp;#039;&amp;#039;&lt;/ins&gt;Science&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#039;&amp;#039; &amp;#039;&amp;#039;&amp;#039;&lt;/ins&gt;2016&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#039;&amp;#039;&amp;#039;&lt;/ins&gt;, 351, 582–586. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[http://dx.doi.org/10.1126/science.aad2080 doi: 10.1126/science.aad2080]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Diamond-like Two-particle==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Diamond-like Two-particle==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5586&amp;oldid=prev</id>
		<title>KevinYager: /* Nano */</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5586&amp;oldid=prev"/>
		<updated>2016-11-13T22:20:24Z</updated>

		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nano&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 22:20, 13 November 2016&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-l51&quot; &gt;Line 51:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 51:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====Nano====&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====Nano====&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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 class=&quot;diffchange diffchange-inline&quot;&gt;TBD&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; 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 class=&quot;diffchange diffchange-inline&quot;&gt;Liu, W.; Tagawa, M.; Xin, H.L.; Wang, T.; Emamy, H. Li, H.; [[Yager, K.G.]]; Starr, F.W.; Tkachenko, A.V.; Gang, O. &amp;quot;Diamond family of nanoparticle superlattices&amp;quot; Science 2016, 351, 582–586.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Diamond-like Two-particle==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Diamond-like Two-particle==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5584&amp;oldid=prev</id>
		<title>KevinYager at 22:18, 13 November 2016</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5584&amp;oldid=prev"/>
		<updated>2016-11-13T22:18:14Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 22:18, 13 November 2016&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-l4&quot; &gt;Line 4:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 4:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;[[Image:Diamond01.png]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;[[Image:Diamond02.png]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;[[Image:Diamond03.png]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;[[Image:Diamond04.png]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;[[Image:Diamond06.png]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; 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;[[Image:Diamond07.png]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Along an appropriate axis, the lattice has six-fold symmetry (hexagonal).&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Along an appropriate axis, the lattice has six-fold symmetry (hexagonal).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5583&amp;oldid=prev</id>
		<title>KevinYager: Created page with &quot;The diamond lattice, which consists of tetrahedrally-arranged atoms/particles, has simple cubic symmetry.  Image:Diamond00.png   Image:Diamond01...&quot;</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Lattice:Diamond&amp;diff=5583&amp;oldid=prev"/>
		<updated>2016-11-13T22:17:47Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;The diamond lattice, which consists of tetrahedrally-arranged atoms/particles, has &lt;a href=&quot;/index.php/Lattice:Simple_Cubic&quot; class=&quot;mw-redirect&quot; title=&quot;Lattice:Simple Cubic&quot;&gt;simple cubic&lt;/a&gt; symmetry.  &lt;a href=&quot;/index.php/File:Diamond00.png&quot; title=&quot;File:Diamond00.png&quot;&gt;Image:Diamond00.png&lt;/a&gt;   Image:Diamond01...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;The diamond lattice, which consists of tetrahedrally-arranged atoms/particles, has [[Lattice:Simple Cubic|simple cubic]] symmetry.&lt;br /&gt;
&lt;br /&gt;
[[Image:Diamond00.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Image:Diamond01.png]]&lt;br /&gt;
[[Image:Diamond02.png]]&lt;br /&gt;
[[Image:Diamond03.png]]&lt;br /&gt;
&lt;br /&gt;
[[Image:Diamond04.png]]&lt;br /&gt;
[[Image:Diamond06.png]]&lt;br /&gt;
[[Image:Diamond07.png]]&lt;br /&gt;
&lt;br /&gt;
Along an appropriate axis, the lattice has six-fold symmetry (hexagonal).&lt;br /&gt;
&lt;br /&gt;
==Canonical Diamond==&lt;br /&gt;
A canonical diamond lattice (single atom/particle type arranged as shown above) has symmetry &amp;#039;&amp;#039;Fd3m&amp;#039;&amp;#039;. The atoms occupy the positions (0,0,0;1/4,1/4,1/4)+face-centering.&lt;br /&gt;
===Symmetry===&lt;br /&gt;
* Crystal Family: Cubic&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Lattice_system Crystal System]: [[Lattice:Cubic|Cubic]]&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Bravais_lattice#Bravais_lattices_in_3_dimensions Bravais Lattice]: F (fcc)&lt;br /&gt;
* Crystal class: Hexoctahedral&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Crystallographic_point_group Point Group]: d3m &lt;br /&gt;
* Space Group: Fd3m&lt;br /&gt;
* Particles per unit cell: &amp;lt;math&amp;gt;n=8&amp;lt;/math&amp;gt;&lt;br /&gt;
* Volume of unit cell: &amp;lt;math&amp;gt;V_d=a^3&amp;lt;/math&amp;gt;&lt;br /&gt;
* Dimensionality: &amp;lt;math&amp;gt;d=3&amp;lt;/math&amp;gt;&lt;br /&gt;
* Projected &amp;#039;&amp;#039;d&amp;#039;&amp;#039;-dimensional volume: &amp;lt;math&amp;gt;v_d=a^3&amp;lt;/math&amp;gt;&lt;br /&gt;
* Solid angle: &amp;lt;math&amp;gt;\Omega_d=4\pi&amp;lt;/math&amp;gt;&lt;br /&gt;
* Nearest-neighbor distance: &amp;lt;math&amp;gt;d_{nn}=\sqrt{3}a/4 \approx 0.433 a&amp;lt;/math&amp;gt;&lt;br /&gt;
* Assuming spherical particles of radius &amp;#039;&amp;#039;R&amp;#039;&amp;#039;:&lt;br /&gt;
** Particle [[Lattice:Packing fraction|volume fraction]]: &amp;lt;math&amp;gt;\phi=32 \pi R^3/\left(3a^3\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** Maximum volume fraction: &amp;lt;math&amp;gt;\phi_{max}=\pi\sqrt{3}/16\approx0.340&amp;lt;/math&amp;gt; when &amp;lt;math&amp;gt;R=a\sqrt{3}/8&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Structure===&lt;br /&gt;
The lattice may be thought of as two interpenetrating FCC lattices.&lt;br /&gt;
===Particle Positions===&lt;br /&gt;
There are 18 positions. In total there are 8 particles in the unit cell:&lt;br /&gt;
* &amp;lt;math&amp;gt; 8 \, \mathrm{corners} \, \times \, \frac{1}{8} = 1&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,0,0\right),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0),(1,1,1)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 6 \, \mathrm{faces} \, \times \, \frac{1}{2} = 3&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},0,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},0\right),\left(1,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},1,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},1\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{internal \,\, tetrahedral \,\, sites} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+(0,0,0)=\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(0,\frac{1}{2},\frac{1}{2}\right)=\left(\frac{1}{4},\frac{3}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},0,\frac{1}{2}\right)=\left(\frac{3}{4},\frac{1}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},\frac{1}{2},0\right)=\left(\frac{3}{4},\frac{3}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Examples===&lt;br /&gt;
====Elemental====&lt;br /&gt;
: 6. [http://en.wikipedia.org/wiki/Carbon Carbon (C)] (&amp;#039;&amp;#039;a&amp;#039;&amp;#039; = 3.567 Å)&lt;br /&gt;
: 14. [http://en.wikipedia.org/wiki/Silicon Silicon (Si)] (&amp;#039;&amp;#039;a&amp;#039;&amp;#039; = 5.431 Å)&lt;br /&gt;
: 32. [http://en.wikipedia.org/wiki/Germanium Germanium (Ge)] (&amp;#039;&amp;#039;a&amp;#039;&amp;#039; = 5.657 Å)&lt;br /&gt;
: 50. [http://en.wikipedia.org/wiki/Tin Gray Tin (Sn)] (&amp;#039;&amp;#039;a&amp;#039;&amp;#039; = 6.491 Å)&lt;br /&gt;
&lt;br /&gt;
====Atomic====&lt;br /&gt;
* TBD&lt;br /&gt;
&lt;br /&gt;
====Nano====&lt;br /&gt;
* TBD&lt;br /&gt;
&lt;br /&gt;
==Diamond-like Two-particle==&lt;br /&gt;
Also known as &amp;#039;&amp;#039;&amp;#039;zincblende&amp;#039;&amp;#039;&amp;#039;. This is effectively &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Image:Diamond-2particle.png|300px]]&lt;br /&gt;
&lt;br /&gt;
===Examples===&lt;br /&gt;
====Atomics====&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Gallium_arsenide Gallium arsenide (GaAs)]&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Zinc_sulfide Zinc sulfide (ZnS)], a.k.a. [http://cst-www.nrl.navy.mil/lattice/struk/b3.html zincblende]&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Indium_phosphide Indium phosphide (InP)]&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Silicon_carbide Cubic silicon carbide (CSi)]&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Gallium_nitride Cubic gallium nitride (GaN)]&lt;br /&gt;
&lt;br /&gt;
==Double-filled Diamond-like Two-particle==&lt;br /&gt;
The diamond lattice includes 8 &amp;quot;tetrahedral holes&amp;quot;, with only 4 occupied in a &amp;#039;normal&amp;#039; diamond structure. A two-particle lattice can be formed by filling all 8 internal holes with the 2nd particle-type, in which case the particles exist in a 1:2 ratio. This is often called a &amp;#039;&amp;#039;&amp;#039;CaF&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039;&amp;#039; lattice.&lt;br /&gt;
&lt;br /&gt;
[[Image:Double diamond01.png|300px]]&lt;br /&gt;
&lt;br /&gt;
===Particle Positions===&lt;br /&gt;
There are 22 positions. In total there are 12 particles in the unit cell:&lt;br /&gt;
* &amp;lt;math&amp;gt; 8 \, \mathrm{corners} \, \times \, \frac{1}{8} = 1&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,0,0\right),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0),(1,1,1)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 6 \, \mathrm{faces} \, \times \, \frac{1}{2} = 3&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},0,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},0\right),\left(1,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},1,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},1\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{principal \,\, tetrahedral \,\, sites} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+(0,0,0)=\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(0,\frac{1}{2},\frac{1}{2}\right)=\left(\frac{1}{4},\frac{3}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},0,\frac{1}{2}\right)=\left(\frac{3}{4},\frac{1}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},\frac{1}{2},0\right)=\left(\frac{3}{4},\frac{3}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{tetrahedral \,\, holes} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-(0,0,0)=\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-\left(0,\frac{1}{2},\frac{1}{2}\right)=\left(\frac{3}{4},\frac{1}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-\left(\frac{1}{2},0,\frac{1}{2}\right)=\left(\frac{1}{4},\frac{3}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-\left(\frac{1}{2},\frac{1}{2},0\right)=\left(\frac{1}{4},\frac{1}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
===Neighbors===&lt;br /&gt;
There are 12 particles in the unit cell: 4 of type A, and 8 of type B. The type A particles each connect to 8 particles of type B. The type B particles each connect (tetrahedrally) to 4 particles of type A.&lt;br /&gt;
&lt;br /&gt;
[[Image:Double diamond03.png|300px]]&lt;br /&gt;
&lt;br /&gt;
The lattice may also be thought of as having cubes of type B with a connected type A particle at the center. However the extended lattice is not BCC-like, since only every second &amp;quot;BCC cube&amp;quot; has a central particle of type A.&lt;br /&gt;
&lt;br /&gt;
[[Image:Double diamond02.png|300px]]&lt;br /&gt;
&lt;br /&gt;
===Examples===&lt;br /&gt;
====Atomics====&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Calcium_fluoride Calcium fluoride (CaF&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;)] (&amp;#039;&amp;#039;a&amp;#039;&amp;#039; = 5.46 Å)&lt;br /&gt;
&lt;br /&gt;
==Double Inter-penetrating Diamond Two-Particle==&lt;br /&gt;
This lattice is formed from two diamond lattices that inter-penetrate. It is often called the &amp;#039;&amp;#039;&amp;#039;NaTl&amp;#039;&amp;#039;&amp;#039; lattice.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Image:NaTl-diamond04.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Particle Positions===&lt;br /&gt;
There are 36 positions. In total there are 16 particles in the unit cell, 8 of each type.&lt;br /&gt;
====Particle Type A====&lt;br /&gt;
* &amp;lt;math&amp;gt; 8 \, \mathrm{corners} \, \times \, \frac{1}{8} = 1&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,0,0\right),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0),(1,1,1)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 6 \, \mathrm{faces} \, \times \, \frac{1}{2} = 3&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},0,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},0\right),\left(1,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},1,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},1\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{internal \,\, tetrahedral \,\, sites} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+(0,0,0)=\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(0,\frac{1}{2},\frac{1}{2}\right)=\left(\frac{1}{4},\frac{3}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},0,\frac{1}{2}\right)=\left(\frac{3}{4},\frac{1}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},\frac{1}{2},0\right)=\left(\frac{3}{4},\frac{3}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Particle Type B====&lt;br /&gt;
* &amp;lt;math&amp;gt; 12 \, \mathrm{edges} \, \times \, \frac{1}{4} = 3&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{2},0,0\right) , \left(0,\frac{1}{2},0\right) , \left(0,0,\frac{1}{2}\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(1,0,\frac{1}{2}\right) , \left(1,1,\frac{1}{2}\right) , \left(0,1,\frac{1}{2}\right) , \left(\frac{1}{2},1,0\right) , \left(1,\frac{1}{2},0\right) , \left(\frac{1}{2},0,1\right) , \left(0,\frac{1}{2},1\right), \left(1,\frac{1}{2},1\right) , \left(\frac{1}{2},1,1\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 1 \, \mathrm{central} \, \times \, 1 = 1&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{internal \,\, tetrahedral \,\, sites} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-(0,0,0)=\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-\left(0,\frac{1}{2},\frac{1}{2}\right)=\left(\frac{3}{4},\frac{1}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-\left(\frac{1}{2},0,\frac{1}{2}\right)=\left(\frac{1}{4},\frac{3}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{3}{4},\frac{3}{4},\frac{3}{4}\right)-\left(\frac{1}{2},\frac{1}{2},0\right)=\left(\frac{1}{4},\frac{1}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Examples===&lt;br /&gt;
====Atomics====&lt;br /&gt;
* Sodium Thallium crystal ([http://cst-www.nrl.navy.mil/lattice/struk/b32.html NaTl])&lt;br /&gt;
====Nanoparticles====&lt;br /&gt;
* Au NPs and proteins: Petr Cigler, Abigail K. R. Lytton-Jean, Daniel G. Anderson, M. G. Finn &amp;amp; Sung Yong Park [http://www.nature.com/nmat/journal/v9/n11/abs/nmat2877.html DNA-controlled assembly of a NaTl lattice structure from gold nanoparticles and protein nanoparticles]     Nature Materials 9, 918–922 (2010) [http://dx.doi.org/10.1038/nmat2877 doi:10.1038/nmat2877]&lt;br /&gt;
*: [[Image:Lit-NaTL-NPs.png|thumb|center|300px]]&lt;br /&gt;
&lt;br /&gt;
==Cristobalite==&lt;br /&gt;
[http://en.wikipedia.org/wiki/Cristobalite Cristobalite] is a diamond-like lattice formed in [http://en.wikipedia.org/wiki/Silicon_dioxide silicon dioxide] (SiO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;). The Si atoms bond tetradrally, each to four O atoms. Each O atom is bonded to 2 Si atoms, effectively acting as a bridge.&lt;br /&gt;
&lt;br /&gt;
===Structure===&lt;br /&gt;
Can be thought of as a diamond lattice, where the tetrahedral species sit on the positions of the canonical diamond sites, and the two-bonded species sites at the midway point of each bond.&lt;br /&gt;
&lt;br /&gt;
[[Image:Cristobalite01.png|300px]] [[Image:Cristobalite13.png|300px]] [[Image:Cristobalite35.png|300px]]&lt;br /&gt;
&lt;br /&gt;
The tetrahedral species sit on the 14 &amp;quot;FCC&amp;quot; sites, plus 4 &amp;quot;internal&amp;quot; diamond sites. The two-bonded species sit on the 16 internal bonds in the unit cell. The tetrahedral species sit at a distance from one another of:&lt;br /&gt;
* Next-nearest-neighbor distance: &amp;lt;math&amp;gt;d_{nnn}=\sqrt{3}a/4 \approx 0.433 a&amp;lt;/math&amp;gt;&lt;br /&gt;
The different species thus have a distance of half that:&lt;br /&gt;
* Nearest-neighbor distance: &amp;lt;math&amp;gt;d_{nn}=\sqrt{3}a/8 \approx 0.217 a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Particle Positions===&lt;br /&gt;
There are 34 positions (24 in unit cell)&lt;br /&gt;
====Particle Type A (bond tetrahedrally)====&lt;br /&gt;
There are 18 positions. In total there are 8 particles in the unit cell:&lt;br /&gt;
* &amp;lt;math&amp;gt; 8 \, \mathrm{corners} \, \times \, \frac{1}{8} = 1&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,0,0\right),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0),(1,1,1)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 6 \, \mathrm{faces} \, \times \, \frac{1}{2} = 3&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(0,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},0,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},0\right),\left(1,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},1,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},1\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{internal \,\, tetrahedral \,\, sites} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+(0,0,0)=\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(0,\frac{1}{2},\frac{1}{2}\right)=\left(\frac{1}{4},\frac{3}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},0,\frac{1}{2}\right)=\left(\frac{3}{4},\frac{1}{4},\frac{3}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},\frac{1}{2},0\right)=\left(\frac{3}{4},\frac{3}{4},\frac{1}{4}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
====Particle Type B (two-fold bonded)====&lt;br /&gt;
There are 16 positions (all 16 in the unit cell):&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{level \,\, one} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ (0,0,0)+\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right) }{2} =\left(\frac{1}{8},\frac{1}{8},\frac{1}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ \left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)+\left(\frac{1}{2},\frac{1}{2},0 \right) }{2} =\left(\frac{3}{8},\frac{3}{8},\frac{1}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ \left(\frac{1}{2},\frac{1}{2},0 \right) + \left(\frac{3}{4},\frac{3}{4},\frac{1}{4}\right) }{2} =\left(\frac{5}{8},\frac{5}{8},\frac{1}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ \left(\frac{3}{4},\frac{3}{4},\frac{1}{4}\right) + (1,1,0) }{2} =\left(\frac{7}{8},\frac{7}{8},\frac{1}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{level \,\, two} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{1}{4},\frac{1}{4},\frac{1}{4} \right) + \left(\frac{1}{2},0,\frac{1}{2} \right) }{2} =\left(\frac{3}{8},\frac{1}{8},\frac{3}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{1}{4},\frac{1}{4},\frac{1}{4} \right) + \left(0,\frac{1}{2},\frac{1}{2} \right) }{2} =\left(\frac{1}{8},\frac{3}{8},\frac{3}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{3}{4},\frac{3}{4},\frac{1}{4} \right) + \left(1,\frac{1}{2},\frac{1}{2} \right) }{2} =\left(\frac{7}{8},\frac{5}{8},\frac{3}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{3}{4},\frac{3}{4},\frac{1}{4} \right) + \left(\frac{1}{2},1,\frac{1}{2} \right) }{2} =\left(\frac{5}{8},\frac{7}{8},\frac{3}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{level \,\, three} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{3}{4},\frac{1}{4},\frac{3}{4} \right) + \left(\frac{1}{2},0,\frac{1}{2} \right) }{2} =\left(\frac{5}{8},\frac{1}{8},\frac{5}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{3}{4},\frac{1}{4},\frac{3}{4} \right) + \left(1,\frac{1}{2},\frac{1}{2} \right) }{2} =\left(\frac{7}{8},\frac{3}{8},\frac{5}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{1}{4},\frac{3}{4},\frac{3}{4} \right) + \left(0,\frac{1}{2},\frac{1}{2} \right) }{2} =\left(\frac{1}{8},\frac{5}{8},\frac{5}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{1}{4},\frac{3}{4},\frac{3}{4} \right) + \left(\frac{1}{2},1,\frac{1}{2} \right) }{2} =\left(\frac{3}{8},\frac{7}{8},\frac{5}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt; 4 \, \mathrm{level \,\, four} \, \times \, 1 = 4&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ (1,0,1) + \left(\frac{3}{4},\frac{1}{4},\frac{3}{4}\right) }{2} =\left(\frac{7}{8},\frac{1}{8},\frac{7}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ \left(\frac{3}{4},\frac{1}{4},\frac{3}{4}\right) + \left(\frac{1}{2},\frac{1}{2},1 \right) }{2} =\left(\frac{5}{8},\frac{3}{8},\frac{7}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{ \left(\frac{1}{2},\frac{1}{2},1 \right) + \left(\frac{1}{4},\frac{3}{4},\frac{3}{4}\right) }{2} =\left(\frac{3}{8},\frac{5}{8},\frac{7}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
** &amp;lt;math&amp;gt;\frac{  \left(\frac{1}{4},\frac{3}{4},\frac{3}{4} \right) + (0,1,1) }{2} =\left(\frac{1}{8},\frac{7}{8},\frac{7}{8}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Examples===&lt;br /&gt;
====Atomics====&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Cristobalite Cristobalite] form of [http://en.wikipedia.org/wiki/Silicon_dioxide silicon dioxide] (SiO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;)&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
* [http://en.wikipedia.org/wiki/Diamond_cubic Diamond Cubic (Wikipedia)]&lt;br /&gt;
* [[Lattice:Hexagonal Diamond|Hexagonal Diamond Lattice]]&lt;/div&gt;</summary>
		<author><name>KevinYager</name></author>
		
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