<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2007000200009</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Reciprocity relations for Bollmann's o-lattice]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gómez Rodríguez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Romeu Casajuana]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Física Departamento de Materia Condensada]]></institution>
<addr-line><![CDATA[México D.F]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2007</year>
</pub-date>
<volume>53</volume>
<numero>2</numero>
<fpage>139</fpage>
<lpage>143</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2007000200009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2007000200009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2007000200009&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[A reciprocity relation for Bollmann's O-lattice is introduced. This result completes the existing Grimmer's reciprocity results between coincidence sites and displacement shift complete lattices. We show that the lattice generated by a*i - b*i (i = 1, 2, 3) is reciprocal to the O-lattice. This result, supported by Multislice calculations, indicates that it is possible to observe the O-lattice under an electron microscope using annular apertures, thus allowing the study of strain fields existing in interfaces or between a thin film growing onto a crystalline substrate.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Se presenta una relación de reciprocidad para las redes O de Bollmann. Este resultado complementa el obtenido por Grimmer quien estableció relaciones de reciprocidad entre las redes de coincidencia y las redes DSC. Demostramos que la red generada por a*i - b*i (i = 1, 2, 3) es recíproca a la red O. Este resultado, apoyado en simulaciones por el método multicapas, indica que podría ser factible observar la red O en el microscopio electrónico usando aperturas anulares, permitiendo con ello el estudio de los campos de esfuerzos en interfaces o entre una película delgada y el sustrato sobre el que crece]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[O-lattices]]></kwd>
<kwd lng="en"><![CDATA[grain boundaries]]></kwd>
<kwd lng="es"><![CDATA[Redes O]]></kwd>
<kwd lng="es"><![CDATA[fronteras de grano]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="center"><font face="verdana" size="4"><b>Reciprocity relations for Bollmann's o&#150;lattice</b></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>A. G&oacute;mez Rodr&iacute;guez and D. Romeu Casajuana</b></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><i>Departamento de Materia Condensada, Instituto de F&iacute;sica, Universidad Nacional Aut&oacute;noma de M&eacute;xico, </i><i>M&eacute;xico 04510 D.F</i></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">Recibido el 11 de diciembre de 2006    <br> Aceptado el 26 de marzo de 2007</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">A reciprocity relation for Bollmann's O&#150;lattice is introduced. This result completes the existing Grimmer's reciprocity results between coincidence sites and displacement shift complete lattices. We show that the lattice generated by <i>a*<sub>i</sub> &#151; b<i>*<sub>i</sub></i> </i>(<i>i</i> = 1, 2, 3) is reciprocal to the O&#150;lattice. This result, supported by Multislice calculations, indicates that it is possible to observe the O&#150;lattice under an electron microscope using annular apertures, thus allowing the study of strain fields existing in interfaces or between a thin film growing onto a crystalline substrate.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords:  </b>O&#150;lattices; grain boundaries.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     <p align="justify"><font face="verdana" size="2">Se presenta una relaci&oacute;n de reciprocidad para las redes O de Bollmann. Este resultado complementa el obtenido por Grimmer quien estableci&oacute; relaciones de reciprocidad entre las redes de coincidencia y las redes DSC. Demostramos que la red generada por <i>a<i>*<sub>i</sub> </i> &#151; b<i>*<sub>i</sub> </i> </i>(<i>i</i> = 1, 2, 3) es rec&iacute;proca a la red O. Este resultado, apoyado en simulaciones por el m&eacute;todo multicapas, indica que podr&iacute;a ser factible observar la red O en el microscopio electr&oacute;nico usando aperturas anulares, permitiendo con ello el estudio de los campos de esfuerzos en interfaces o entre una pel&iacute;cula delgada y el sustrato sobre el que crece.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores:</b> Redes O; fronteras de grano.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">PACS:61.72.Mm;68.37&#150;d</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmf/v53n2/v53n2a9.pdf">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Acknowledgements</b></font></p>     <p align="justify"><font face="verdana" size="2">The authors wish to thank L.M. Beltr&aacute;n del R&iacute;o for assistance with the SimulaTem simulations.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. S. Ranganathan, Acta <i>Cryst. </i><b>21</b> (1966) 197.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8332034&pid=S0035-001X200700020000900001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">2. W. 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