{"id":9750,"date":"2020-04-06T11:39:07","date_gmt":"2020-04-06T14:39:07","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=9750"},"modified":"2021-03-19T16:28:39","modified_gmt":"2021-03-19T19:28:39","slug":"redes-de-bravais","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/redes-de-bravais\/","title":{"rendered":"Redes de Bravais"},"content":{"rendered":"<hr \/>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As sete c\u00e9lulas primitivas apresentadas anteriormente permitem elementos f\u00edsicos <span id='easy-footnote-1-9750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/redes-de-bravais\/#easy-footnote-bottom-1-9750' title=' \u00e1tomos, mol\u00e9culas, etc, '><sup>1<\/sup><\/a><\/span>apenas nos seus v\u00e9rtices. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Contudo, ser\u00e1 a menor c\u00e9lula unit\u00e1ria sempre a melhor c\u00e9lula? <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Ou, ser\u00e1 poss\u00edvel escolher uma c\u00e9lula unit\u00e1ria maior.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A escolha da C\u00e9lula unit\u00e1ria deve levar em considera\u00e7\u00e3o os seguintes aspectos:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Deve ser a menor poss\u00edvel, isto significa que deve possuir o menor volume;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Deve respeitar a simetria da rede cristalina, isto \u00e9, os lados da c\u00e9lula devem estar paralelos aos eixos de simetria ou perpendiculares aos planos de simetria;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Os eixos da c\u00e9lula devem ser ortogonais ou hexagonais sempre que poss\u00edvel<\/span>;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O papel de parede serve como exemplo para explicar os conceitos de Cristalografia. Inicialmente, observa-se que existem duas figuras distintas que se repetem, uma maior envolta por um c\u00edrculo e outra menor com quatro pontos. Essas duas figuras podem representar \u00e1tomos, mol\u00e9culas, ou grupos quaisquer de materiais.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 1 apresenta quatro possibilidades<span id='easy-footnote-2-9750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/redes-de-bravais\/#easy-footnote-bottom-2-9750' title=' outras talvez existam'><sup>2<\/sup><\/a><\/span> de c\u00e9lulas &#8211; preta, vermelha, verde e azul &#8211; e quatro eixos de simetria &#8211; linhas pontilhadas.<\/span><\/p>\n<figure id=\"attachment_9721\" aria-describedby=\"caption-attachment-9721\" style=\"width: 1024px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-1.png\"><img decoding=\"async\" class=\"wp-image-9721 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-1.png\" alt=\"\" width=\"1024\" height=\"1024\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-1.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-1-300x300.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-1-150x150.png 150w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-1-768x768.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption id=\"caption-attachment-9721\" class=\"wp-caption-text\">Figura 1. Escolha de C\u00e9lulas<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A c\u00e9lula vermelha possui a menor \u00e1rea &#8211; a<sup>2 <\/sup><span id='easy-footnote-3-9750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/redes-de-bravais\/#easy-footnote-bottom-3-9750' title=' considerando &lt;em&gt;a&lt;\/em&gt; como sendo a dist\u00e2ncia entre os v\u00e9rtices da c\u00e9lula. O volume seria a&lt;sup&gt;3&lt;\/sup&gt;'><sup>3<\/sup><\/a><\/span> , \u00e9 ortogonal, mas viola a condi\u00e7\u00e3o de poder completar a figura apenas com transla\u00e7\u00e3o sem deixar espa\u00e7os vazios.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A c\u00e9lula verde tamb\u00e9m possui \u00e1rea igual- a<sup>2<\/sup>, mas n\u00e3o completa a figura com movimentos de transla\u00e7\u00e3o, e\u00a0 n\u00e3o \u00e9 ortogonal nem hexagonal.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A c\u00e9lula preta possui\u00a0 \u00e1rea duas vezes maior- 2a<sup>2<\/sup>, completa a figura com movimentos de transla\u00e7\u00e3o diagonais, \u00e9 ortogonal, mas exige a exist\u00eancia de um elemento adicional no cento da figura, que n\u00e3o existe nas c\u00e9lulas primitivas anteriores.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente, a c\u00e9lula azul possui a maior \u00e1rea &#8211; 4a<sup>2<\/sup>, completa a figura com movimentos de transla\u00e7\u00e3o, \u00e9 ortogonal, mas tamb\u00e9m exige a exist\u00eancia de um elemento adicional no cento da figura.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 2 apresenta as quatro possibilidades de incorporar elementos nas c\u00e9lulas primitivas fora dos v\u00e9rtices. Portanto, como existem sete (7) c\u00e9lulas primitivas e quatro(4) novas possibilidades, ter\u00edamos um total de vinte e oito (28) estruturas cristalinas poss\u00edveis.<\/span><\/p>\n<figure id=\"attachment_9734\" aria-describedby=\"caption-attachment-9734\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/Bravais_2_1.png\"><img decoding=\"async\" class=\"wp-image-9734 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/Bravais_2_1.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/Bravais_2_1.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/Bravais_2_1-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/Bravais_2_1-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9734\" class=\"wp-caption-text\">Figura 2. Redes de Bravais<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Contudo, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Auguste_Bravais\" target=\"_blank\" rel=\"noopener\">Auguste Bravais<\/a> demonstrou em 1848 que existiam apenas catorze (14) redes cristalinas \u00fanicas e diferentes no espa\u00e7o tridimensional, que passaram a ser denominadas de <\/span><span style=\"font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/en.wikipedia.org\/wiki\/Bravais_lattice\" target=\"_blank\" rel=\"noopener\">Redes de Bravais,<\/a> conforme mostra a Tabela 2.<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Tabela 2. Rede de Bravais\n<div class=\"wpdt-c wdt-skin-aqua\">\n    \n    <input type=\"hidden\" id=\"wdtNonceFrontendServerSide_41\" name=\"wdtNonceFrontendServerSide_41\" value=\"c7574cd43b\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/blog\/wp-json\/wp\/v2\/pages\/9750\" \/><input type=\"hidden\" id=\"wdtFrontendelementorNonce_41\" name=\"wdtFrontendelementorNonce_41\" value=\"a84dcd21ee\" \/>    <input type=\"hidden\" id=\"table_1_desc\"\n           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integer  column-wdt_id&quot;,&quot;aTargets&quot;:[0]},{&quot;sType&quot;:&quot;string&quot;,&quot;wdtType&quot;:&quot;string&quot;,&quot;bVisible&quot;:true,&quot;orderable&quot;:true,&quot;searchable&quot;:true,&quot;InputType&quot;:&quot;text&quot;,&quot;name&quot;:&quot;newcolumn&quot;,&quot;origHeader&quot;:&quot;newcolumn&quot;,&quot;notNull&quot;:false,&quot;conditionalFormattingRules&quot;:[],&quot;transformValueRules&quot;:&quot;&quot;,&quot;className&quot;:&quot; column-newcolumn&quot;,&quot;aTargets&quot;:[1]},{&quot;sType&quot;:&quot;string&quot;,&quot;wdtType&quot;:&quot;string&quot;,&quot;bVisible&quot;:true,&quot;orderable&quot;:true,&quot;searchable&quot;:true,&quot;InputType&quot;:&quot;text&quot;,&quot;name&quot;:&quot;restricoesnasdimensoes&quot;,&quot;origHeader&quot;:&quot;restricoesnasdimensoes&quot;,&quot;notNull&quot;:false,&quot;conditionalFormattingRules&quot;:[],&quot;transformValueRules&quot;:&quot;&quot;,&quot;className&quot;:&quot; 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   <table id=\"table_1\"\n           class=\" scroll responsive display nowrap wdt-no-display data-t data-t wpDataTable wpDataTableID-41 \"\n           style=\"\"\n           data-described-by='table_1_desc'\n           data-wpdatatable_id=\"41\">\n        \n        <!-- Table header -->\n        \n<thead>\n<tr>\n                    <th\n                        class=\" wdtheader sort numdata integer \"\n        style=\"\">        wdt_ID<\/th>        <th\n        data-class=\"expand\"                class=\" wdtheader sort \"\n        style=\"\">        Sistema<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Primitivo - P<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Centrado em Face \u00danica - C<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Centrado no Interior - I<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Centrado em Todas as Faces - F<\/th>    <\/tr>\n<\/thead>\n        <!-- \/Table header -->\n\n        <!-- Table body -->\n        \n<tbody>\n<!-- Table body -->\n<div data-id=\"41\"\n     class=\"wdt-timeline-item wdt-timeline-table_1\"\n     style=\"\">\n    <div class=\"wdt-table-loader\">\n        <div class=\"wdt-table-loader-row wdt-table-loader-header\">\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n        <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n            <\/div>\n<\/div><!-- \/Table body -->\n                    <tr id=\"table_41_row_0\"\n            data-row-index=\"0\">\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">Tricl\u00ednico<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                    <\/tr>\n                            <tr id=\"table_41_row_1\"\n            data-row-index=\"1\">\n                            <td style=\"\">2<\/td>\n                            <td style=\"\">Monocl\u00ednico<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                    <\/tr>\n                            <tr id=\"table_41_row_2\"\n            data-row-index=\"2\">\n                            <td style=\"\">3<\/td>\n                            <td style=\"\">Ortorr\u00f4mbico<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">Sim<\/td>\n                    <\/tr>\n                            <tr id=\"table_41_row_3\"\n            data-row-index=\"3\">\n                            <td style=\"\">4<\/td>\n                            <td style=\"\">Tetragonal<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                    <\/tr>\n                            <tr id=\"table_41_row_4\"\n            data-row-index=\"4\">\n                            <td style=\"\">5<\/td>\n                            <td style=\"\">Trigonal<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">?<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                    <\/tr>\n                            <tr id=\"table_41_row_5\"\n            data-row-index=\"5\">\n                            <td style=\"\">6<\/td>\n                            <td style=\"\">Hexagonal<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                    <\/tr>\n                            <tr id=\"table_41_row_6\"\n            data-row-index=\"6\">\n                            <td style=\"\">7<\/td>\n                            <td style=\"\">C\u00fabico<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">N\u00e3o<\/td>\n                            <td style=\"\">Sim<\/td>\n                            <td style=\"\">Sim<\/td>\n                    <\/tr>\n            <\/tbody>        <!-- \/Table body -->\n\n        <!-- Table footer -->\n        \n        <!-- \/Table footer -->\n    <\/table>\n\n<\/div><style>\ntable.wpDataTable td.numdata { text-align: right !important; }\n<\/style>\n<style>\n                    \n                                                      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Contudo, ser\u00e1 a menor c\u00e9lula unit\u00e1ria sempre a melhor c\u00e9lula? Ou, ser\u00e1 poss\u00edvel escolher uma c\u00e9lula unit\u00e1ria maior. A escolha da C\u00e9lula unit\u00e1ria deve levar em considera\u00e7\u00e3o os seguintes aspectos: Deve ser a menor poss\u00edvel, isto significa que deve possuir o menor [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":9479,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-9750","page","type-page","status-publish","has-post-thumbnail","hentry"],"uagb_featured_image_src":{"full":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1.png",1200,280,false],"thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1-150x150.png",150,150,true],"medium":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1-300x70.png",300,70,true],"medium_large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1-768x179.png",580,135,true],"large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1-1024x239.png",580,135,true],"1536x1536":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1.png",1200,280,false],"2048x2048":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1.png",1200,280,false],"post-thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1.png",1200,280,false],"twentytwenty-fullscreen":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristais_1.png",1200,280,false]},"uagb_author_info":{"display_name":"admin","author_link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/author\/admin\/"},"uagb_comment_info":0,"uagb_excerpt":"As sete c\u00e9lulas primitivas apresentadas anteriormente permitem elementos f\u00edsicos apenas nos seus v\u00e9rtices. Contudo, ser\u00e1 a menor c\u00e9lula unit\u00e1ria sempre a melhor c\u00e9lula? Ou, ser\u00e1 poss\u00edvel escolher uma c\u00e9lula unit\u00e1ria maior. A escolha da C\u00e9lula unit\u00e1ria deve levar em considera\u00e7\u00e3o os seguintes aspectos: Deve ser a menor poss\u00edvel, isto significa que deve possuir o menor&hellip;","_links":{"self":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/9750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/comments?post=9750"}],"version-history":[{"count":6,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/9750\/revisions"}],"predecessor-version":[{"id":40049,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/9750\/revisions\/40049"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media\/9479"}],"wp:attachment":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media?parent=9750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}