On the activity of MnO in MnO-SiO 2 melts
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Zone Axis
Reflection
lnterplanar Angles
g Ratios
u
v
w
h
k
1
g (/%-1)
dA
Radians
Degrees
0
0
1
0 1 1
2 -1 1
0 0 0
0.1111 0.1184 0.1184
9.000 8.445 8.445
2.059 1.083 0.977
180.0 (1-2) 62.0 (1-3) 56.0 (2-3)
0.9383 (1/2) 0.9383 (1/3) 1.000 (2/3)
1.0657 (2/1) 1.0657 (3/1) 1.000 (3/2)
The diffraction pattern given is from the [001] zone axis. The column headed g is the reciprocal lattice vector magnitude for each reflection (the latter denoted by the plane's Miller indices hkl) while d is the equivalent interplanar spacing in the direct lattice. The figures in parentheses after the angles indicate which set of indices the angle refers to, (1-2) means the angle between the first and second set of indices. A similar notation follows the "g Ratios" to show which pair of g are referred to. The second of these columns is the reciprocal of the first.
s p a c e g and g ' (which is the t n t e r p l a n a r angle in d i r e c t s p a c e ) is given b y : 3
3
.~ .~ Gi~gigj c o s 0 = z=l ~--a
Igl'lg']
[2]
Since t h i s a p p l i e s to a l l l a t t i c e s no s p e c i a l s y m m e t r y a r r a n g e m e n t s a r e n e c e s s a r y and the e f f i c i e n c y of c o m p u t e r s in handling m a t r i x c a l c u l a t i o n s is u t i l i z e d . In the p r o g r a m , a f t e r i n i t i a l t e s t i n g f o r e r r o r s in the data, Eq. [1] is u s e d to c o m p u t e a l l g v e c t o r s up to (555) which a r e then s o r t e d into i n c r e a s i n g o r d e r of m a g n i t u d e and then p r i n t e d t o g e t h e r with t h e i r r e c i p rocals the d-spacings. All zone a x e s up to [555] a r e then l i s t e d and the l i s t of g - v e c t o r s is s e a r c h e d for the t h r e e l a r g e s t which l i e in the p l a n e n o r m a l to the zone a x i s . The i n d i c e s of t h e s e a r e l i s t e d t o g e t h e r with t h e i r r a t i o s and t h e i r i n t e r p l a n a r a n g l e s , T a b l e I. T h i s p r o v i d e s s u f f i c i e n t i n f o r m a t i o n f o r the m i c r o s c o p i s t to c h a r a c t e r i z e a complete reciprocal lattice plane. In the c a s e of h e x a g o n a l , cubic and t e t r a g o n a l a x e s the d u p l i c a t i o n of e q u i v a l e n t zone a x e s i s e l i m i n a t e d to r e d u c e the output. In the t e t r a g o n a l c a s e the a x e s a r e a l t e r e d s o that a = b r c if t h i s i s n e c e s s a r y , to f a c i l i t a t e t h i s . F o r a l l s t r u c t u r e s m u l t i p l e s of m o r e primitive directions are ignored. The a b s e n t r e f l e c t i o n s f o r the B r a v a i s l a t t i c e s a r e o m i t t e d f r o m the l i s t of g - v e c t o r s b y using a d a t a c a r d which r e a d s in the a p p r o p r i a t e l a t t i c e c h o i c e . In a d d i tion, f o r b i d d e n r e f l e c t i o n s f r o m the c o m m o n nonB r a v a i s l a t t i c e s d i a m o n d cubic and c.p.h, m a y be d e l e t e d b y a s u i t a b l e c h o i c e of d a t a c a r d . A p l a c e in the prog
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