How many tetrahedral and octahedral voids are possible if the number of close packed sphere in two layers is N

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Solution

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$T h e n u m b e r o f t e t r a h e d r a l v o i d s i s f o r m e d t w i c e a s t h e n u m b e r o f o c t a h e d r a l v o i d s w h i l e c l o s e p a c k i n g o f a t o m s i n c c p a n d h c p s t r u c t u r e s . T h u s, i f n u m b e r o f c l o s e p a c k e d s p h e r e s i s e q u a l t o' N' . T h e r e f o r e, n u m b e r o f o c t a h e d r a l v o i d s f o r m e d = N . A n d, t h e n u m b e r o f t e t r a h e d r a l v o i d s f o r m e d = 2 N .$

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