Simetríacristalina
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MINERALOGÍA Y
PETROLOGÍA
ING . PERCY HAROLD GUERRERO DÍAZ
CAP. I.2 : SIMETRÍA CRISTALINA
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HABRÁ SIMETRÍA EN LOS CRISTALES?
POR QUE SERÁ IMPORTANTE CONOCER LA
SIMETRÍA DE LOS CRISTALES?
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AL FINAL DE LA SESIÓN, EL ESTUDIANTE REALIZA UNA PRACTICA
SOBRE SOBRE SIMETRÍA CRISTALINA, TENIENDO EN CUENTA LA
CLASIFICACIÓN SEGÚN TIPOS SISTEMAS CRISTALINOS.
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ESTRUCTURA INTERNA DE LOS
CRISTALES
Max Von Lave 1912, científico queutilizó los rayos X para difractar loscristales
Descubrió la interferencia de losrayos X en los cristales, lo que lepermitió determinar con exactitud laslongitudes de onda de dichos rayos ysentar las bases para el estudio de laestructura interna de los cristales
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Eje de Simetría
Plano de Simetría
Centro de Simetría
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Línea imaginaria que atravieza elcristal sobre el cual se hace girar1,2,3,4 o 6 veces, repitiendo suapariencia durante una rotacióncompleta
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EJES DE SIMETRÍA
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EJES DE SIMETRÍA
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EJES DE SIMETRÍA
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Punto interno del cristal por el cualpasa toda recta que une a dos puntosiguales
Esta operación se conoce con elnombre de Inversión
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6
6
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Todos los sistemas cristalinos, con excepción del cúbico, presentan ejes
cristalográficos de longitud diferente
Se obtienen calculando las intersecciones (h, k, l), o número de traslaciones, con los
tres ejes fundamentales del cristal
Posteriormente se invierten y se eliminan denominadores
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(hkl) nombra el plano dado
{hkl} indica todos los planos
homólogos que resultan de aplicar
los elementos de simetría del
cristal al plano (hkl)
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Deducir las intersecciones de cada plano conlos ejes cristalográficos a, b y c. Es decir,contar el número de traslaciones t1, t2 y t3que ocupa el plano sobre los ejes a, b y c
Ejemplo
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SOLUCIÓN
• El plano ABD ocupa:
2t1 en el eje a, 2t2en el eje b, y 4t3en el eje c
• El plano EBD ocupa:
4t1 en el eje a, 2t2en el eje b, y 4t3en el eje c
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SOLUCIÓN
Para calcular los índices de Miller de
cada plano, a partir de estas
intersecciones, se invierten los valores
y, si es necesario, se reducen las
fracciones
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SOLUCIÓN
El plano ABD corta a los ejes en 2, 2 y 4
Su inversión es: 1/2, 1/2, 1/4
Reducimos fracciones, quitandodenominadores: 2/4, 2/4, 1/4. Sin denominadoresqueda 221
Índices de Miller: (221)
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Sistemas Cristalinos
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Albita (NaAlSi308): Sistema Triclínico
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Sistema Cúbico
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Sistema Cúbico
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Olivino (Mg,Fe)2(SiO4): Sistema Rómbico
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Apatito(Ca5[(F, OH, Cl)/(PO4)3] ) Sistema Hexagonal
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Casiterita (SnO2): Sistema Tetragonal
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Dolomita (CaMg(CO3)2): Sistema Trigonal
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Sistema Monoclínico
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GRACIAS