{"id":2519,"date":"2015-03-09T10:51:59","date_gmt":"2015-03-09T13:51:59","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=2519"},"modified":"2023-06-17T14:50:33","modified_gmt":"2023-06-17T17:50:33","slug":"cristais","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/","title":{"rendered":"Estruturas Cristalinas"},"content":{"rendered":"<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif;\">&#8220;<span style=\"font-size: 14pt;\"><strong><em>Um <span style=\"font-size: 14pt;\">diamante<\/span> com falhas vale mais do que um seixo sem imperfei\u00e7\u00f5es&#8221;<\/em><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\">Prov\u00e9rbio Chin\u00eas<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As estruturas cristalinas dos s\u00f3lidos afetam todas as propriedades dos materiais, e a cristalografia fornece a base te\u00f3rica para o estudo das propriedades dos materiais.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Simetrias internas e for\u00e7as externas afetam as propriedades dos materiais, e t<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">odos os materiais possuem algum tipo de simetria interna, mesmo que n\u00e3o sejam cristalinos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os materiais cristalinos apresentam 32 tipos estruturas cristalinas decorrentes das simetrias poss\u00edveis, m<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">ateriais amorfos<span id='easy-footnote-1-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-1-2519' title='Exemplos de materiais amorfos: l\u00edquidos e vidros. '><sup>1<\/sup><\/a><\/span> possuem apenas uma simetria; a esf\u00e9rica. Materiais com simetria esf\u00e9rica possuem propriedades isotr\u00f3picas, isto \u00e9, independem da dire\u00e7\u00e3o espacial.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Cer\u00e2micas, metais, rochas e s\u00f3lidos policristalinos tamb\u00e9m possuem simetria esf\u00e9rica. Por outro lado, m<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">ateriais fibrosos apresentam simetria cil\u00edndrica com eixo na dire\u00e7\u00e3o das fibras.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As principais for\u00e7as externas que atuam nos materiais s\u00e3o:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">tens\u00e3o mec\u00e2nica;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">campo el\u00e9trico;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">campo magn\u00e9tico;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">temperatura.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0A simetria dos campos, el\u00e9trico e magn\u00e9tico, e das tens\u00f5es, mec\u00e2nica e de cisalhamento, dependem de configura\u00e7\u00f5es externas. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Isto significa que esses elementos externos podem apresentar comportamento anisotr\u00f3pico<span id='easy-footnote-2-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-2-2519' title='&lt;span class=&quot;lg&quot; role=&quot;text&quot;&gt;&lt;span class=&quot;sj&quot;&gt;\u00a0&lt;\/span&gt;&lt;\/span&gt;&lt;span class=&quot;df&quot; role=&quot;text&quot;&gt;caracter\u00edstica de um meio, ou de um material, em que certas propriedades f\u00edsicas diferem com as dire\u00e7\u00f5es espaciais'><sup>2<\/sup><\/a><\/span><\/span><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, a<\/span><span style=\"font-family: verdana, geneva, sans-serif;\"> temperatura, por ser um escalar, possui simetria esf\u00e9rica e, consequentemente, possui comportamento isotr\u00f3pico<span id='easy-footnote-3-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-3-2519' title=' &lt;span class=&quot;df&quot; role=&quot;text&quot;&gt;qualidade de alguns meios ou materiais de possu\u00edrem as mesmas propriedades f\u00edsicas em todas as dire\u00e7\u00f5es'><sup>3<\/sup><\/a><\/span><\/span><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, o estudo das estruturas cristalinas se tornou importante porque materiais anisotr\u00f3picos apresentam propriedades distintas dependendo da orienta\u00e7\u00e3o espacial e deve-se levar em considera\u00e7\u00e3o este detalhe no projeto de m\u00e1quinas e equipamentos que utilizam estes materiais.\u00a0<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Existem cristais de todos os tamanhos; gigantescos ou min\u00fasculos.<\/span><\/p>\n<figure id=\"attachment_9519\" aria-describedby=\"caption-attachment-9519\" style=\"width: 950px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/mine_salt.png\"><img decoding=\"async\" class=\"wp-image-9519 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/mine_salt.png\" alt=\"\" width=\"950\" height=\"652\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/mine_salt.png 950w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/mine_salt-300x206.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/mine_salt-768x527.png 768w\" sizes=\"(max-width: 950px) 100vw, 950px\" \/><\/a><figcaption id=\"caption-attachment-9519\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 1. Cristais Gigantes na Cueva de los Cristales no M\u00e9xico Fonte:https:\/\/science.howstuffworks.com\/environmental\/earth\/geology\/mexico-giant-crystal-cave.htm<\/span><\/figcaption><\/figure>\n<figure id=\"attachment_9521\" aria-describedby=\"caption-attachment-9521\" style=\"width: 550px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/menor_cristal.png\"><img decoding=\"async\" class=\"wp-image-9521 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/menor_cristal.png\" alt=\"\" width=\"550\" height=\"410\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/menor_cristal.png 550w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/menor_cristal-300x224.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/a><figcaption id=\"caption-attachment-9521\" class=\"wp-caption-text\">Figura 2. Menor cristal de neve do mundo com 275 mol\u00e9culas de \u00e1gua Fonte:https:\/\/www.themarysue.com\/275-water-molecule-ice-crystal\/<\/figcaption><\/figure>\n<figure id=\"attachment_9534\" aria-describedby=\"caption-attachment-9534\" style=\"width: 220px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_silicio.png\"><img decoding=\"async\" class=\"wp-image-9534 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_silicio.png\" alt=\"\" width=\"220\" height=\"588\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_silicio.png 220w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_silicio-112x300.png 112w\" sizes=\"(max-width: 220px) 100vw, 220px\" \/><\/a><figcaption id=\"caption-attachment-9534\" class=\"wp-caption-text\">Figura 3. Cristal de Sil\u00edcio para fabrica\u00e7\u00e3o de semicondutores<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, no\u00e7\u00f5es de Cristalografia, a ci\u00eancia que estuda os cristais, tornam-se indispens\u00e1veis para a compreens\u00e3o das propriedades dos materiais.<\/span><\/p>\n<h2 id='rede-cristalina'  id=\"boomdevs_1\">Rede Cristalina<\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>Materiais cristalinos<\/strong> apresentam uma estrutura denominada de <strong>Rede Cristalina<\/strong>, que se caracteriza pela repeti\u00e7\u00e3o infinita de <strong>grupos de \u00e1tomos<\/strong>\u00a0exatamente iguais quando vistos de qualquer um dos pontos da Rede. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, torna-se imposs\u00edvel distinguir pontos ou regi\u00f5es em materiais cristalinos.\u00a0<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O grupo que se repete denomina-se de <strong>Base<\/strong> e o <strong>conjunto dos pontos no espa\u00e7o<\/strong> que determinam a localiza\u00e7\u00e3o da Base denomina-se <strong>Rede<\/strong>.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por exemplo, a Figura 4 mostra um papel de parede formado por desenhos sofisticados que se repetem no plano. <\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Quantos grupos existem?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Onde se encontra a Rede?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Voc\u00ea consegue determinar o in\u00edcio e o fim do desenho?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Como os grupos se repetem?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Esta figura poderia representar uma Rede Cristalina?<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<figure id=\"attachment_9679\" aria-describedby=\"caption-attachment-9679\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1.png\"><img decoding=\"async\" class=\"wp-image-9679\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1.png\" alt=\"\" width=\"800\" height=\"800\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-300x300.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-150x150.png 150w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/papel_parede_1-768x768.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9679\" class=\"wp-caption-text\">Figura 4. Papel de parede ou rede cristalina?<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por outro lado, a Figura 5 representa a estrutura cristalina da mol\u00e9cula de um material condutor fict\u00edcio. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Se aplicarmos uma corrente el\u00e9trica na dire\u00e7\u00e3o das setas individualmente, mediremos valores distintos de tens\u00e3o porque o n\u00famero de mol\u00e9culas pretas e vermelhas em s\u00e9rie depende da dire\u00e7\u00e3o escolhida.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Isto significa que a resistividade deste material depender\u00e1 da dire\u00e7\u00e3o espacial e deixar\u00e1 de ser uma constante. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O mesmo racioc\u00ednio se aplica a outras propriedades do material, tais como a resistividade t\u00e9rmica e o coeficiente de elasticidade.<\/span><\/p>\n<figure id=\"attachment_9527\" aria-describedby=\"caption-attachment-9527\" style=\"width: 1024px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_1.png\"><img decoding=\"async\" class=\"wp-image-9527 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_1.png\" alt=\"\" width=\"1024\" height=\"768\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_1.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_1-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/cristal_1-768x576.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption id=\"caption-attachment-9527\" class=\"wp-caption-text\">Figura 5. Estrutura Cristalina<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Cristalografia estuda a estrutura dos \u00e1tomos nos s\u00f3lidos cristalinos atrav\u00e9s dos seguintes m\u00e9todos:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Difra\u00e7\u00e3o de Raio-x;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"> Difra\u00e7\u00e3o de El\u00e9trons;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">e Difra\u00e7\u00e3o de N\u00eautrons.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Cada uma dessas radia\u00e7\u00f5es interage de forma diferente com a mat\u00e9ria. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Raio-X interage com a distribui\u00e7\u00e3o espacial dos El\u00e9trons nos \u00c1tomos. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por sua vez, feixes de El\u00e9trons reagem \u00e0 distribui\u00e7\u00e3o de cargas dos El\u00e9trons e N\u00facleo dos \u00c1tomos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Finalmente, N\u00eautrons, imunes a campos el\u00e9tricos, desviam dos n\u00facleos at\u00f4micos afetados pela For\u00e7a Forte. Por\u00e9m, como os N\u00eautrons possuem momento magn\u00e9tico, campos magn\u00e9ticos afetam sua trajet\u00f3ria. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os videos abaixo descrevem a difra\u00e7\u00e3o por raios-X, o m\u00e9todo mais utilizado na Cristalografia.<\/span><\/p>\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]wtvs1t3YZPw[\/wpdevart_youtube]<\/p>\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]QHMzFUo0NL8[\/wpdevart_youtube]<\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A partir da difra\u00e7\u00e3o de Raios X, a Cristalografia se desenvolveu<span id='easy-footnote-4-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-4-2519' title=' Anteriormente, o estudo dos cristais se baseava em observa\u00e7\u00f5es com lentes de aumento'><sup>4<\/sup><\/a><\/span> porque permitiu medir as dimens\u00f5es dos cristais com precis\u00e3o nunca anteriormente poss\u00edvel.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> A Figura 6 mostra como o feixe de uma radia\u00e7\u00e3o eletromagn\u00e9tica permite medir a dist\u00e2ncia entre elementos do cristal utilizando a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Bragg%27s_law\" target=\"_blank\" rel=\"noopener\">Lei de Bragg<\/a> &#8211; Equa\u00e7\u00e3o 1.<\/span><\/p>\n<figure id=\"attachment_22648\" aria-describedby=\"caption-attachment-22648\" style=\"width: 247px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/bragg.png\"><img decoding=\"async\" class=\"wp-image-22648 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/bragg.png\" alt=\"\" width=\"247\" height=\"96\" \/><\/a><figcaption id=\"caption-attachment-22648\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 1. Lei de Bragg<\/span><\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:\u00a0<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n \u00e9 um n\u00famero inteiro;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bb \u00e9 o comprimento de onda da radia\u00e7\u00e3o incidente;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">d \u00e9 a dist\u00e2ncia entre elementos do cristal;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b8 \u00e9 o \u00e2ngulo medido da radia\u00e7\u00e3o refletida.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<figure id=\"attachment_9497\" aria-describedby=\"caption-attachment-9497\" style=\"width: 499px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/braggs_law.png\"><img decoding=\"async\" class=\"wp-image-9497 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/braggs_law.png\" alt=\"\" width=\"499\" height=\"345\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/braggs_law.png 499w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/braggs_law-300x207.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/a><figcaption id=\"caption-attachment-9497\" class=\"wp-caption-text\">Figura 6. Difra\u00e7\u00e3o de radia\u00e7\u00e3o eletromagn\u00e9tica nos materiais<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Cristalografia de Raios X comprovou que os \u00e1tomos e\/ou mol\u00e9culas dos cristais formavam estruturas geom\u00e9tricas peri\u00f3dicas, e a matem\u00e1tica fornece ferramentas para o estudo dessas figuras geom\u00e9tricas.\u00a0<\/span><\/p>\n<h2 id='c\u00e9lula-cristalogr\u00e1fica'  id=\"boomdevs_2\">C\u00e9lula Cristalogr\u00e1fica<\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A <strong>Cristalografia<\/strong> baseia-se nos conceitos de <strong>Rede, Grupo e C\u00e9lulas<\/strong>.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Vetores de posi\u00e7\u00e3o definem os<strong> pontos da Rede<\/strong> da seguinte maneira:<\/span><\/p>\n<figure id=\"attachment_9916\" aria-describedby=\"caption-attachment-9916\" style=\"width: 438px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/ponto_cristal.png\"><img decoding=\"async\" class=\"size-full wp-image-9916\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/ponto_cristal.png\" alt=\"\" width=\"438\" height=\"53\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/ponto_cristal.png 438w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/ponto_cristal-300x36.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/a><figcaption id=\"caption-attachment-9916\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Pontos da Rede Cristalina<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">P \u00e9 o ponto da Rede Cristalina;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n<sub>i<\/sub> s\u00e3o as coordenadas do ponto;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a, b e c s\u00e3o os vetores unit\u00e1rios que geram a Rede Cristalina.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00c1lgebra Linear fornece os fundamentos para os vetores unit\u00e1rios, sendo os sistemas ortogonais, cil\u00edndricos e esf\u00e9ricos os mais conhecidos. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, existem outros sistemas, que se relacionam atrav\u00e9s de transforma\u00e7\u00f5es matem\u00e1ticas matriciais.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As coordenadas n s\u00e3o n\u00fameros que representam a dist\u00e2ncia existentes entre a origem do sistema de coordenadas[efn]A origem do sistema de coordenadas pode ser qualquer ponto da Rede[\/efn_note] e o ponto em cada uma das dire\u00e7\u00f5es a, b e c. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Denomina-se de <strong>Rede Primitiva<\/strong> a rede onde as coordenadas n s\u00e3o n\u00fameros inteiros e todos os pontos da rede podem ser obtidos como transla\u00e7\u00e3o dos vetores unit\u00e1rios. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, os pontos da Rede Cristalina necessitam de refer\u00eancia, e o <\/span><strong style=\"font-family: verdana, geneva, sans-serif;\">sistema de coordenadas<\/strong><span style=\"font-family: verdana, geneva, sans-serif;\"> define a refer\u00eancia<\/span><strong style=\"font-family: verdana, geneva, sans-serif;\">\u00a0geom\u00e9trica.\u00a0<\/strong><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O\u00a0<\/span><strong style=\"font-family: verdana, geneva, sans-serif;\">sistema de coordenadas\u00a0<\/strong><span style=\"font-family: verdana, geneva, sans-serif;\">pode ser <strong>cartesiano<\/strong><\/span><span style=\"font-family: verdana, geneva, sans-serif;\">, <\/span><strong style=\"font-family: verdana, geneva, sans-serif;\">esf\u00e9rico<\/strong><span style=\"font-family: verdana, geneva, sans-serif;\"> ou <b>cil\u00edndrico<\/b>, e<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0a orienta\u00e7\u00e3o dos eixos obedece a regra da m\u00e3o direita ou esquerda, dependendo do referencial escolhido.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Normalmente, utiliza-se o referencial da m\u00e3o direita.\u00a0<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A determina\u00e7\u00e3o da Base da estrutura cristalina ocorre ap\u00f3s a identifica\u00e7\u00e3o dos eixos da Rede Cristalina.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por exemplo, a Figura 7 apresenta poss\u00edveis eixos para a estrutura cristalina, por\u00e9m apenas os vermelhos poderiam ser utilizados. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O eixo azul viola o princ\u00edpio da Rede Primitiva.<\/span><\/p>\n<figure id=\"attachment_9924\" aria-describedby=\"caption-attachment-9924\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/bases_cristal.png\"><img decoding=\"async\" class=\"wp-image-9924 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/bases_cristal.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/bases_cristal.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/bases_cristal-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/bases_cristal-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9924\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 7. Eixos da Estrutura Cristalina<\/span><\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A quantidade de \u00e1tomos ou mol\u00e9culas na Base pode ser maior ou igual a um e ajusta-se \u00e0 origem dos eixos para coincidir com o centro de um dos \u00e1tomos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>A C\u00e9lula<\/strong> representa o elemento geom\u00e9trico b\u00e1sico da rede cristalina e pode ser composto por:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00e1tomos iguais;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">grupos de \u00e1tomos diferentes;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">mol\u00e9culas;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00edons;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">grupos de mol\u00e9culas diferentes.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 id='c\u00e9lula-unit\u00e1ria'  id=\"boomdevs_3\">C\u00e9lula Unit\u00e1ria<\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Define-se <strong>C\u00e9lula Unit\u00e1ria <\/strong>como\u00a0<strong>figura geom\u00e9trica regular, formada por pontos da Rede Cristalina,<\/strong> <strong>capaz de formar outras formas geom\u00e9tricas apenas por transla\u00e7\u00e3o<\/strong> e sem deixar <strong>nenhum espa\u00e7o vazio<\/strong>.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, a natureza nos contempla com diversas formas, que preferem formas mais compactas, sim\u00e9tricas e resistentes.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por exemplo, o casco das tartarugas apresenta hex\u00e1gonos, paralelogramos, e trap\u00e9zios, todas figuras geom\u00e9tricas regulares capazes de formar uma figura geom\u00e9trica complexa, mas finita.<\/span><\/p>\n<figure id=\"attachment_9688\" aria-describedby=\"caption-attachment-9688\" style=\"width: 1024px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/casco_tartaruga.png\"><img decoding=\"async\" class=\"wp-image-9688 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/casco_tartaruga.png\" alt=\"\" width=\"1024\" height=\"854\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/casco_tartaruga.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/casco_tartaruga-300x250.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/casco_tartaruga-768x641.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption id=\"caption-attachment-9688\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 8. Casco de Tartaruga<\/span><\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As abelhas constroem suas colmeias como hex\u00e1gonos iguais h\u00e1 milhares de anos, que podem se estender infinitamente.<\/span><\/p>\n<figure id=\"attachment_9689\" aria-describedby=\"caption-attachment-9689\" style=\"width: 1303px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel.png\"><img decoding=\"async\" class=\"wp-image-9689 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel.png\" alt=\"\" width=\"1303\" height=\"1197\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel.png 1303w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel-300x276.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel-1024x941.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel-768x706.png 768w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/favos_mel-1200x1102.png 1200w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" \/><\/a><figcaption id=\"caption-attachment-9689\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 9. Colmeia<\/span><\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Aranhas criam teias extremamente resistentes com fios em <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/catenaria\/\">caten\u00e1rias<\/a>, que apresentam limita\u00e7\u00f5es de crescimento.<\/span><\/p>\n<figure id=\"attachment_9693\" aria-describedby=\"caption-attachment-9693\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/teia_aranha.png\"><img decoding=\"async\" class=\"wp-image-9693\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/teia_aranha.png\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/teia_aranha.png 960w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/teia_aranha-300x200.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/teia_aranha-768x511.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9693\" class=\"wp-caption-text\">Figura 10. Teia de aranha<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">E a natureza criou cristais maravilhosos a partir de formas geom\u00e9tricas b\u00e1sicas.<\/span><\/p>\n<figure id=\"attachment_9695\" aria-describedby=\"caption-attachment-9695\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/cristais_foto.png\"><img decoding=\"async\" class=\"wp-image-9695\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/cristais_foto.png\" alt=\"\" width=\"800\" height=\"451\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/cristais_foto.png 816w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/cristais_foto-300x169.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/04\/cristais_foto-768x433.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9695\" class=\"wp-caption-text\">Figura 11. Cristais<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Mas qual seria a forma geom\u00e9trica capaz satisfazer a condi\u00e7\u00e3o de <strong>possuir geometria regular e formar outras formas geom\u00e9tricas apenas por transla\u00e7\u00e3o sem deixar nenhum espa\u00e7o vazio<\/strong>?\u00a0 <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Apenas o Paralelep\u00edpedo<span id='easy-footnote-5-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-5-2519\" title=\" n\u00e3o o paralelep\u00edpedo de rua, mas sim o geom\u00e9trico\"><sup>5<\/sup><\/a><\/span><\/span><span style=\"font-family: verdana, geneva, sans-serif;\"> &#8211; Figura 12, que possui seis faces formadas por paralelogramos, sendo tr\u00eas pares congruentes e paralelos. <span id='easy-footnote-6-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-6-2519\" title=\" &lt;\/span&gt;&lt;\/p&gt;\n&lt;p&gt;&lt;span style=&quot;font-family: verdana, geneva, sans-serif;&quot;&gt;A Figura 12 mostra em verde um dos pares em face opostas. \"><sup>6<\/sup><\/a><\/span> Os tr\u00eas \u00e2ngulos &#8211; \u03b1, \u03b2, \u03b3 &#8211; e os tr\u00eas comprimentos &#8211; a, b, c &#8211; caracterizam a c\u00e9lula e denominam-se constantes da c\u00e9lula ou rede.<\/span><\/p>\n<figure id=\"attachment_9593\" aria-describedby=\"caption-attachment-9593\" style=\"width: 1200px\" class=\"wp-caption aligncenter\"><a style=\"font-weight: bold; background-color: transparent; text-align: inherit;\" href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/celu_uni.png\"><img decoding=\"async\" class=\"wp-image-9593 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/celu_uni.png\" alt=\"\" width=\"1200\" height=\"800\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/celu_uni.png 1200w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/celu_uni-300x200.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/celu_uni-1024x683.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/celu_uni-768x512.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/a><figcaption id=\"caption-attachment-9593\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 12. C\u00e9lula Unit\u00e1ria<\/span><\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que os eixos do sistema cartesiano utilizam a orienta\u00e7\u00e3o da regra da m\u00e3o direita<span id='easy-footnote-7-2519' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/cristais\/#easy-footnote-bottom-7-2519\" title=\" Com a m\u00e3o direita, fazendo o movimento com os dedos no sentido de x para y, o polegar dever\u00e1 apontar o sentido positivo de z. Se fizermos o mesmo com a m\u00e3o esquerda, o sentido do eixo z ficar\u00e1 invertido. \"><sup>7<\/sup><\/a><\/span> Adicionalmente, os eixos de refer\u00eancia da c\u00e9lula unit\u00e1ria encontram-se paralelos \u00e0s faces do paralelep\u00edpedo e, consequentemente, n\u00e3o s\u00e3o necessariamente ortogonais.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Toda a teoria dos cristais se baseou em geometria e matem\u00e1tica. Por isso, deve-se seguir rigorosamente as conven\u00e7\u00f5es e as regras envolvidas.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Mas onde ficam os \u00e1tomos e mol\u00e9culas na c\u00e9lula unit\u00e1ria? Para que a representa\u00e7\u00e3o represente o material desejado,\u00a0<strong>a c\u00e9lula unit\u00e1ria dever\u00e1 conter a f\u00f3rmula qu\u00edmica da mol\u00e9cula que desejamos representar<\/strong>.<\/span><\/p>\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]NYVSI83KiKU[\/wpdevart_youtube]<\/p>\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]Rm-i1c7zr6Q[\/wpdevart_youtube]<\/p>\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]F4Du4zI4GJ0[\/wpdevart_youtube]<\/p>\n<h2 id='refer\u00eancias'  id=\"boomdevs_4\"><span style=\"font-family: verdana, geneva, sans-serif;\">Refer\u00eancias<\/span><\/h2>\n<ol>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">QUINN, J.J., TI K.S., <strong>Solid State Physics &#8211; Principles and Modern Applications<\/strong>, Springer-Verlag, 2009.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">NEWNHAM, R.E., <strong>Properties of Materials &#8211; Anisotropy, Symmetry, Structure<\/strong>, Oxford University Press, 2005.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">KITTEL, C., <strong>Introduction to Solid State Physics<\/strong>, Wiley, 2005.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">ASHCROFT,N.W., MERMIN, D.,\u00a0 <strong>Solid State Physics<\/strong>, Harcourt, 1976.<\/span><\/li>\n<\/ol>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Um diamante com falhas vale mais do que um seixo sem imperfei\u00e7\u00f5es&#8221; Prov\u00e9rbio Chin\u00eas As estruturas cristalinas dos s\u00f3lidos afetam todas as propriedades dos materiais, e a cristalografia fornece a base te\u00f3rica para o estudo das propriedades dos materiais. Simetrias internas e for\u00e7as externas afetam as propriedades dos materiais, e todos os materiais possuem algum [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":9479,"parent":2473,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-2519","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":"&#8220;Um diamante com falhas vale mais do que um seixo sem imperfei\u00e7\u00f5es&#8221; Prov\u00e9rbio Chin\u00eas As estruturas cristalinas dos s\u00f3lidos afetam todas as propriedades dos materiais, e a cristalografia fornece a base te\u00f3rica para o estudo das propriedades dos materiais. Simetrias internas e for\u00e7as externas afetam as propriedades dos materiais, e todos os materiais possuem algum&hellip;","_links":{"self":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/2519","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=2519"}],"version-history":[{"count":173,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/2519\/revisions"}],"predecessor-version":[{"id":44462,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/2519\/revisions\/44462"}],"up":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/2473"}],"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=2519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}