UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
“LABORATORIO DE CRISTALOGRAFIA”
2013 – B
INFORME N°6: PROYECCION ESTEREOGRÁFICA
CODIGO
NOMBRE DE LOS INTEGRANTES
101186C
QUILICHE GALV!" RONAL#
1011$%F
BAYONA HUERTA" MANUEL NICOLÁS
102$120323
VIERA CASTILLO" VICTOR MANUEL
NOMBRE DEL PROFESOR
QUI&ONE! MONTEVER#E" CARLOS CARLOS
FECHA DE SESION
30'10'13
FECHA DE ENTREGA DEL INFORME
0('10'13
PROYECCION ESTEREOGRÁFICA
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
1) RESUMEN: Para el presente informe de cristalografía, procederemos a detallar un tema importantísimo; el cual nos permitirá definir la simetría de las caras de un cristal (las caras externas). Esta es la llamada proyección estereográfica; la cual es una proyección respecto a una proyección esfé esféri rica, ca, dond donde e la matr matriz iz de esta esta proy proyec ecci ción ón esta estarí ría a en el círcu círculo lo máxi máximo mo ue ue enci encier erra ra la proyección esférica. !racias a este plano ue di"ide a la esfera, se podrán u#icar los planos del cristal, esto de#ido a ue los planos cristalográficos tam#ién se pueden presentar como normales a estos mismos planos. Estas normales se intersectarían en la proyección esférica, y de esta manera procedemos a u#icar estas proyecciones proyecciones esféricas esféricas en la proyección proyección estereográfica. estereográfica. $demás de#emos tener en cuenta cuenta ue la proyección estereográfica solo es una representación de los planos, direcciones y otros elementos de simetría del cristal en una plataforma de dos dimensiones. %ale decir ue a pesar de ue podremos notar los elementos de simetría y los planos del cristal, no "amos a poder "erlos realmente como son; para eso los ángulos asignados a cada punto de la proyección esférica (son dos ángulos) representan además la dimensión de cada punto (distancia entre el meridiano #ase y distancia entre el paralelo #ase) de esta manera podremos imaginarnos donde se u#ica el punto de la proyección estereográfica en una proyección esférica. &am#ié m#ién n util utiliz izar arem emos os todo todos s los los elem elemen ento tos s de la "ent "entan ana a Stereo Stereo
estereográ estereográfica) fica),,
el cual cual pert perten enec ece e a la plat plataf afor orma ma de
Projection Projection (proyecció (proyección n
CaRIne CaRIne Crysta Crystallo llogra graphy phy 3.0 . 'os
adecuaremos a representar dos tipos de cristales El 'al y el sl (am#os del sistema cu#ico), representaremos las características de las caras como sus respecti"os ángulos, representaremos sus polos, colocaremos a ue simetría pertenece cada polo, etc. $l concluir este informe detallaremos algunas particularidades y algunas o#ser"aciones
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
-#tener la respecti"a representación estereográfica para un cristal cu#ico usando el programa
CaRIne Crystallography 3.0. ealizar aplicaciones a una proyección estereográfica con las funciones usando las funciones del comando Stereo Projection. “Recordar que esta experiencia, ayudara a interpretar cualquier simetría de cristal; pero antes debemos tomar como referencia aquellos cristales de simetría cubica, ya que son mas didácticos para trabajar
3) IN INTR TROD ODUC UCCI CION ON:: REPRESENT REPRES ENTACION ACIONES ES DE UN CRISTAL
REPRESENTACION ESFERICA
Para este tipo de representación, se realiza en la plataforma de una esfera, donde se procede a colocar al cristal en el centro de la esfera. Posteriormente se traza una línea perpendicular a cada cara del cristal. +a intersección de la línea con la superficie de la esfera forma un punto denominado 2POLO”. 3ond 3onde e cada cada cara cara es un punt punto o (pol (polo), o), ademá además s tridimensional
dire diremo mos s ue ue la repres represent entac ació ión n es
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
FIGURA 2: REPRESENTACION DE LAS CARAS DE UN CRISTAL EN UNA P.E.
REPRESENTACION REPRESENTACION ESTEREOGRAFICA EST EREOGRAFICA
Para poder representar las caras y di"ersos elementos de simetría de un cristal; lo más adecuado seria tra#a*ar con esta proyección, ya ue nos da a entender con más facilidad la u#icación de cada elemento, además nos #usca reducir a una superficie plana (dos dimensiones).
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
$demás entendemos ue esta proyección necesita como #ase, un punto el cual c ual notamos en la figura 4, se encuentra en la #ase de la esfera. on este punto de referencia se trazan líneas, todas dirigidas a este punto, respecto de los polos. 3e esta manera al intersectarse con el plano ecuatorial de la representación esférica, suponen una serie de puntos, los cuales son la representación estereográfica de los llamados 2P-+-56
FIGURA 4: VISTA DE UNA PROYECCION ESTEREOGRAFICA
5in em#argo 7emos dic7o ue la medida de los ángulos de cada cara de un cristal, es crucial para imaginarnos al cristal cristal en forma real; lo más con"eniente a7ora es utilizar 2 La !" "! #$%%” & 'R!"
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
FIGURA 0: REPRESENTACION DE UNA NED UFF
3e esta esta mane manera ra se puede pueden n repr represe esent ntar ar los los elem elemen ento tos s de sime simetr tría ía y a"eri a"erigu guar ar los los ángu ángulo los s respect respecti"o i"os, s, sin ning8n ning8n incon" incon"eni enient ente; e; ya ue sa#emo sa#emos s además además ue la red de 9uff 9uff tiene tiene una dimensión de :0 por :0 en cada celda. $ continuación "eremos la representación de los elementos de simetría de un cristal.
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
4) PROC PROCED EDIM IMIE IENT NTO: O:
argamos el programa el programa CaRIne CaRIne Crystallography Crystallography !" y a#rimos la celda del cloruro de sodio ya realizada, como muestra los pasos de las figuras .
%entana de arine 4..
omando open cell.
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%entana %entana elda unitaria un itaria del 'al. +uego de 7a#er a#ierto la celda y 7a#erle dado algunos efectos como muestran las figuras > y ? procedemos procedemos a #uscar en la #arra de 7erramientas 7erramientas la pesta=a Ca$ para luego realizar la acti"idad ue reuerimos.
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
FIGURA : CELDA CRISTALOGRAFICA DEL NaC
5eleccionar el comando S!*!& P*&5!-& del men8 S6!-a( para desplegar la "entana de funciones, como se muestra en la @igura A.4.
FIGURA 7: VENTANA DE FUNCIONES STEREO PROJECTION
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$ continuación presionamos en el #otón P&!( y en el #otón T*a!(9 y en D-*!-&( para definir el rango de direcciones u, ", 9 (7, B, l) ue desea d esea considerar.
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FIGURA ;: VENTANA STEREO PROJECTION DEFINIDA “#o es necesario definir la secci$n de direcciones; ya que sabemos que para cada plano tiene sus índices de %ra&ais, y estos son los mismos para las direcciones; como tambi'n sabemos que la representaci$n de la cara de un cristal es perpendicular a dicha cara, la direcci$n toma la mima direcci$n y por ende tendrán la misma proyecci$n estereográfica(
5eleccionar el comando S!*!& P*&5!-& del men8 S6!-a( y elegir la opción C*!a-& para "isualizar la proyección estereográfica creada.
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POLO 1 POLO 2
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E5! "! &a
A6a*!! &a
&a
FIGURA 12: TRAA DEL EJE DE ONA
N& a6a*!! &a
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E5! "! (-8!*a !*a*-&
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0) TAREA: *+! *+! R R -A PR* R*CCI CCI/ / S! S!1A 1AR R (200 (200)) 11- CRI CRIS!A S!A- C+I +IC* ACAC-,, &*S!RA1* !*1*S -*S P*-*S 1 -A 4*R&A 52006, 52206, 52226 -AS !RA7AS !R --*S. omo en general ya 7emos tra#a*ado con el cristal cu#ico 'al, y *ustamente la proyección estándar en la parte del procedimiento es (G), procederemos a indicar los polos de la forma HGI, HGGI y HGGGI.
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UNIVERSIDAD NACIONAL DEL CALLAO UNIVERSIDAD FACULTAD CIENCIAS NATURALES Y MATEMÁTICAS ESCUELA PROFESIONAL DE FÍSICA
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