U P A
an international journal
Cation distribution study of Nd^ substituted Zn-Mg spinel ferrites by structural refinement method
B P L a d g a o n k a r , P N V a s a m b e k a r a ^ d A S V a in g a n k a r * Department of Electronics, Shi>^ji University,
Kolhapur>4l6 004, Maharasjltrik India
E 'l n a i l : a n iL v a in g a n k a r tij 'jjr a h o o .c o n i
A h .t r .c t : A s s u m in g p r e fe r e n t ia l d is t n b u t io n o f m a g n e s iu m io n a m o n g teira h etira l ( A ) an d o c ta h e d r a l ( B ) s it e th e c a tio n d is tr ib u tio n is p r e d ic te d i„, N d ’- su b s titu te d Z n - M g f e m i e s . C a tio n d is tr ib u tio n is in v e s t ig a t e d b y a m e th o d w h e r e in s ir u c lu ia l r er in eitK n l i s a p p lie d T h e th e o r e tic a l in te n sity ll X lay r e t le c t io n s . w h ic h fo u n d t o d e p e n d o n s it e o c c u p a n c y , w a s c a lc u la t e d T h e d e p e n d e n c e o l in t e n s it y o f
„ ,n m e le r w a s s tu d ie d w h ic h s u g g e s t s th at th e in t e n s it y o f ( 2 2 0 ) an d ( 4 2 2 ) r e f le c t io n s a re s e n s it iv e t o A - s it e , w h e r e a s th at 0 ^ 2 2 . ) an d ( 4 0 0 ) t o the I' MIC C lo s e a g r e e m e n t o f th e t h e o r e t ic a lly c a lc u la t e d a n d e x p e r i m e n t a lly o b s e r v e d in t e n s it y s u p p o r ts th e p r e d ic t e d c a t io n d is lr i u lio n . o
t , u l the s im p h f ie d m e th o d w h e r e in g r a p h o f th e o r e tic a l in t e n s it y o f ( 2 2 0 ) r e n e c t io n s is p lo tte d a g a in s t d is tr ib u tio n p a r a m e te r B y p lo t tin g o b s e i^ e d
,y ot
r
s a m e p la n e th e e x a c t L t n b u t . o n p a r a m e te r is d e e d e d w it h the- h e lp o f th is p lo t T h e p lo t o f r e lia b ilit y f a c o r . R a g a m s . d .s t n b u io n ,>« m icici s h o w s d e e p n e a r a b o u t e x a c t d is tr ib u tio n p a r a m e te r , w h ic h s u p p o r ts th e e x a c t n e s s o l c a tio n d is tn b u tio n T h e in v e s t ig a t e d c a n o n "„ \ c a l s that 7in c io n L w s its str o n g o c c u p a n c y o n A - s it e an d m a g n e s iu m io n d istr ib u te s p a rtia lly a m o n g A an d B s it e s in d ic a tin g m w im u m o c c u p a n c y i,n A site l o r X ^ 0 2 0 T h e s u b s titu te d N d'" lu n r e s id e s o n B - s it e d is p la c in g p ro p o r tio n a l amount o f m a g n e s iu m fr o m B s it e to A s u e .
Kt> words . Folycrystalhne ferriic, cation distribution. X-ray intensity P\CS Nos. 75.50 Gg. 61.I0.N/, 6l.66.-f
1. Intnxiuction
Spinel fe r rite s h a v e tw o m a g n e t ic s u b l a tt ic c s , te tr a h e d r a l A - s ite and o c ta h e d ra l B - s i te . T h e s t r u c tu r a l, e le c tr i c a l a n d m a g n e t ic properties, u p o n w h ic h its a p p li c a ti o n d e p e n d s , a r c f o u n d to b e sensitive to d is t r i b u t i o n o f c a t i o n s a m o n g th e s e s ite s [1]. In t'rder to in te r p r e t th e r e s u lts r e g a r d in g th e s e in tr in s ic p r o p e r tie s , ilic k n o w le d g e o f c a ti o n d is t r i b u t i o n tu r n s o u t to b e e s s e n tia l, riierefo rc, in v e s ti g a ti o n o f c a ti o n d is tr i b u ti o n in f e r r ite s s y s te m is o f in te re s t. T h e c a ti o n d i s tr i b u ti o n c a n b e in v e s ti g a te d b y th e
^iclii’o sta tis tic a l m o d e l in w h ic h th r e e m a g n e tic io n s p e r lo r m u la unit is c o n s i d e r e d [2 J . H o w e v e r , th e p r e s e n t .sy stem d o e s n o t consist th r e e m a g n e t ic io n s p e r f o r m u la u n its . U p a d h y a y a n d b a ld h a [3] h a v e s u g g e s t e d th e m e t h o d t o e s t i m a t e c a t i o n d istrib u tio n , a s s u m i n g r e l a t i v e w e ig h te d m a g n e t ic in te r a c tio n per fo rm u la u n it. T h is w a s f u r th e r m o d if ie d b y V a s a m b e k a r
et al
K] fo r tr iv a le n t s u b s t i t u t i o n .
B y p r o c e s s o f s t r u c t u r a l r e f i n e m e n t o f X - r a y p o w d e r dififacto g ram s, m u c h stru c tu r a l in f o r m a tio n c a n b e o b ta in e d [5 ,6 ].
The in te n s ity o f X - r a y r e f l e c t i o n s p r o v i d e s th e in f o r m a t io n Corresponding Author
r e g a r d in g o c c u p a n c y o f c a tio n s a m o n g th e s e s ite s [ 1 , 7 ] , w h e r e a s fu ll w id th at h a l f m a x im u m ( F W H M ) g iv e s p a r tic le s iz e 15]. T h e in te n s ity o f 2 2 0 a n d 4 2 2 r e f le c t io n s s tr o n g ly d e p e n d s o n c a tio n s o f te t r a h e d r a l s ite [7 ], w h ile th a t o f 2 2 2 a n d 4 0 0 is s e n s itiv e to c a ti o n s o f o c ta h e d r a l s ite |« ] . A s s u m in g th is d e p e n d e n c e , th e s tr u c tu r a l r e f in e m e n t m e t h o d is u s e d a n d th e r e s u lts r e g a r d in g t h e s t u d y o f c a t i o n d i s t r i b u t i o n in v e s t i g a t i o n b y s t r u c t u r a l r e f in e m e n t fo r N d^^ s u b s tit u te d Z n - M g f e r r it e s a r e r e p o r te d .
2. Experimental
C o m p o s i ti o n s o f p o ly c r y s ta l li n e f e r r ite s , Z n ^ M g , , / c2. N d^ 0 4
(x
= O.CX), 0 . 2 0 , 0 . 4 0 , 0 . 6 0 , 0 . 8 0 a n d 1 .0 0 ; y = 0 .0 0 a n d 0 .0 5 ) w e re p r e p a r e d b y s ta n d a r d c e r a m ic m e t h o d , w h e r e in th e A R g r a d e o x i d e s Z n O , M g O , a n d N d ^ O , w e r e e m p l o y e d . T h e s in te r in g te m p e r a tu r e w a s c o n tr o lle d a t i0(X)‘'C f o r 2 4 h o u r s a n d th e f u r n a c e w a s s l o w ly c o o le d . T o c o n f i r m th e c o m p l e ti o n o f s o lid s ta te r e a c t io n , th e c o m p o s i t i o n s w e r e c h a r a c t e r i z e d b y s t a n d a r d t o o l s i.e . X - r a y , F I R a b s o r p t i o n a n d S E M . T h e d if f r a c l o g r a m s w e r e f u r th e r s u b j e c te d f o r s t r u c tu r a l r e f in e m e n t to in v e s tig a te th e c a ti o n d is tr i b u ti o n .©2001 lACS
352 B P Ladgaonkar, P N Vasambekar and A S Vaingankar
3. Results and discussion
T h e X - r a y d i f f r a c t o g r a m s o f p o w d e r e d c o m p o s i t i o n s r e v e a l th e f o r m a t i o n o f s i n g l e p h a s e c u b i c s p i n e ls , s h o w i n g w e ll d e f i n e d r e f le c tio n s o f a llo w e d p la n e s . O n r e f in e m e n t o f th e d if f r a c to g r a m s , th e e x t r a c t e d s t r u c t u r a l d a t a a r e p r e s e n t e d in T a b le 1. T h e la t ti c e c o n s t a n t , a s i n d i c a t e d in T a b le 1, e x h i b i t s l i n e a r r e l a t i o n s h i p w ith c o n c e n t r a t i o n o b e y i n g V e g a r d ’s la w . T h i s m a y b e d u e to l a r g e io n i c r a d i u s o f io n = 0 .8 3
A),
w h ic h w h e n s u b s t i t u t e d r e s i d e s o n te t r a h e d r a l A - s i t e a n d d i s p l a c e s s m a l l e rF e ^
io n = 0 .6 7A)
f r o mA
s ite toB
s ite . T h is s u g g e s t s th e s t r o n g o c c u p a n c y o fZn^'^
io n o n t e t r a h e d r a l A - s i t e [91. D u e toNd^'*'
s u b s t i t u t i o n th e la t t i c e c o n s t a n t is f o u n d to b e d e c r e a s i n g s l ig h t ly . S u c h r e d u c t i o n in t h e l a t t i c e c o n s t a n t in r a r e - e a r t hs u b s t i t u t e d f e r r i t e s s y s t e m w a s r e p o r t e d b y R e z l e s c u and R e z l e s c u [ 1 0 ] , s u g g e s t i n g th e o c c u p a n c y o f r a r e - e a r t h io n on B- s i te .
T h e p h y s i c a l d e n s i t i e s
(dp)
o f t h e c o m p o s i t i o n s were m e a s u r e d b y u s i n g l i q u i d m e t h o d a n d a r c r e p o r t e d in T able ) a l o n g w ith X - r a y d e n s i t y(dx)
a n d p o r o s i t y ( P ) . T h e caiu^n- o x y g e n b o n d l e n g t h s f o r t e t r a h e d r a l A - s i t e , ( > 4 - 0 ) a n d for o c t a h e d r a l B - s i t e(B-O)
w e r e c a l c u l a t e d b y u s i n g relatio n sA ~ O = (w - 1 / 8) flV 3 a n d
B - 0
= ( 5 / 8 - U ) a a n d a r c presented in T a b le 1. T h eA-O
b o n d l e n g t h s h o w s in c r e a s i n g tr e n d wnh Zn^**^ c o n c e n t r a t i o n , w h i l e B - 0 b o n d l e n g t h d e c r e a s e s with i n c r e a s i n gZri^'^
i o n . T h i s c a n b e a t t r i b u t e d t o th e strong o c c u p a n c y o f io n o n A - s i t e . T e t r a h e d r a l s i te(R^)
and Table 1. Structural data for the compositions of Zn^Mg^ yNd^O^ ferrites system.C o m p o s it i o n s
Parameters
Lattice constants, (a) A No. of Formula unit, (Z) Fonnula weight, (w) gm.
X-ray Density, (dx) gm/cm' Physical I>ensity, <dp) gm/cm' Porosity (P) %
Bond distance, (A-O) A Bond distance, (B-O) A Tetrahedral Radius. (R^) A Octahedral Radius, (R^) A
R-Factors R^
R,
S
Oxygen ion param eter (U) A
0 00 020 0.40 0 60 0.80 1.00
y = 0.00 8 33
8 200.02
3.99 4 64 13 89 1.72 2-13 0.37 0.783 0 0 0 4 S 0.0051 0,017 0.056 0 369
8.53 8 208.23
4.01 4.79 16.36 1.78 2 11 0.43 0 755 0.0197 0 0233 0.042 0 123 0 373
8.37 8 216 44
4.22 4.95 14.44 1.82 2.09 0 47 0.739 0.0108 0 0127 0.023 0.125 0.355
8.39 8 224 65
4.54 5.10 10.39 1.86 2.08 0 51 0 727 0.0065 0.0066 0.012 0 064 0.377
8.41
8
232 8 4.64 5.27 1 1 98 1.87 2 08 0.52 0.725 0.0069 0 0068 0.018 0.097 0.378
8.43 8 241.08
4.81 5.40 1100 1 94 2-04 0-59 0 691 0.0183 0 0178 0.035 0 190 0.383 y=0.05
Lattice constants, (a) A 8.31 8.33 8.35 8.37 8 39 8.4!
No. of Formula unit, (Z) 8 8 8 8 8 8
Formula weight, (w) gm. 204.23 212.44 220.66 228.87 237.08 245.29
X-ray !3cnsity. (dx) gm/cm' 4.13 4.15 4.39 4 45 4.50 4.79
Physical Density, (dp) gm/cm^ 4.65 4.82 4.99 5.16 5.33 5.49
Porosity. (P) % 11.26 13.75 11 86 13.67 15.48 12.57
Bond distance, (A-O) A 1.71 1.78 1.81 1.85 1.87 1.92
Bond distance, (B-O) A 2.13 2.10 2.08 2.07 2.07 2.05
Tetrahedral Radius. (R^) A 0.36 0.43 0.46 0.5 0 0.52 0.57
Octahedral Radius, (R^) A 0.782 0.751 0.736 0.727 0.719 0.695
R-Factors 0.0228 0.0201 0,0174 0.0092 0.0260 0.0319
R. 0.0212 0.0209 0.0116 0.0103 0.0248 0.0304
R^p 0.057 0.044 0 .050 0.026 0.056 0.069
S 0.305 0.231 0.266 0.142 0.299 0.370
Oxygen ion parameter, (U) A 0.368 0.373 0.375 0.377 0.378 0.382
th e in te n s ity o f 2 2 2 a n d 4 0 0 re f le c t io n s in c r e a s e s w ith in c r e a s in g
S-
T h i s m a y b e a t t r i b u t e d to th e s e n s i t i v i t y o f 2 2 0 a n d 4 2 2 r e f le c t io n to th e c a ti o n s o f tc u - a h c d ra l A - s i tc a n d th a t o f 2 2 2 a n d (K iahedral s i te(Rg)
r a d i i h a v e b e e n c a l c u l a t e d b y u s i n g r e l a ti o niroiii S m i t h a n d W i j n f l l ] , = ( u - 1 / 4 ) a V s - / ? „ a n d
R g = ( 5 /S - u ) a - R
q,
w h e r eR^
is th e r a d i u s o f o x y g e n a n du
is the o x y g e n io n p a r a m e t e r . O n c l o s e i n s p e c t i o n o f T a b le 1, it is lound th a t th e t e t r a h e d r a l r a d i u s in c r e a s e s w i t h i n c r e a s i n gZn^*
,-,m centration, w h e r e a s t h a t o f o c t a h e d r a l s i te d e c r e a s e s . T h i s ,iis() s u p p o r ts th e o c c u p a n c y o f
Zv?*
io n o n A - s i te .X -ra y p o w d e r d i f f r a c t o g r a m s c o n s i s t s m u c h s t r u c t u r a l
mlormation,
w h ic h c a n b e e x p l o r e d b y s t r u c t u r a l r e f i n e m e n t(5, hi According
to R ie t v e ld [5 ] , th e in te n s ity o f r e f le c t io n o b s e r v e d atBragg's
p o s i t i o n 0 * is g i v e n b y/, = e x p [ - Co( 2 0 * ) 2 / / / , ' ] , (D
where l/^ l" - is th e to t a l s t r u c t u r e f a c t o r o b t a i n e d b y s u m m i n g
!he a to m ic s c a t t e r i n g f a c t o r s o f a ll 5 6 a t o m s a l o n g w ith t h e i r pnsiiional c o - o r d i n a t e s . S i n c e t h e c u b i c s p i n e l h a s s p a c e g r o u p f d?!Ti [7 J, th e p o s i t i o n a l c o - o r d i n a t e s u s e d a r e 8 a a n d I 6 c f o r cations o f t e t r a h e d r a l a n d o c t a h e d r a l s i te r e s p e c t i v e l y a n d 3 2 c loi o x y g e n io n [ 1 J. T h e a t o m i c s c a t t e r i n g f a c t o r s w e r e o b ta i n e d Iromcq. (15)
/ ( i ) = ] ^ a , e x p (- /> ,s ^ ) + c , , (
2
)(3) whore
a^,
a n d c a r e th e c o e f f i c i e n t o b t a i n e d f r o m le a s t c u r v e tilt in g -1\
is th e m u l t i p l i c i t y o f th e r e f l e c t i o n s a n dLj^
is L o r e n l / p o la riz a tio n fa c to r. S in c e th e G a u s s i a n d is tr i b u ti o n f u n c tio n w a s lo n s k lc rc d a s p r o f ile f u n c t i o n , t h e c o n s t a n t C o c o u l d b e e q u a l U) 41og2 [1 2 ] . T h e te r m is F u ll W i d t h a t H a l f M a x i m u m (1 W H M ) , t a k e s a c c o u n t o f p e a k b r o a d e n i n g r e s u l t i n g f r o m p a rticle s i / e a n d is g i v e n b y = a t a n ^ 04* v ta n 0 4 * M \ w h e r e /f. I and vv' a r c th e h a l f w id th p a r a m e t e r s . T h e r e l i a b i l i t y o f stiu ciu ral r e f i n e m e n t is u s u a l l y e x p r e .s s e d in t e r m s o f r e l ia b i li ty i.K fo rsRj^
,R^^^
a n d 5 , th e g o o d n e s s o f fit [ 1 3 ,1 4 ] . T h e s e la u n rs h a v e b e e n c a l c u l a t e d a n d p r e s e n te d in T a b le 1, T h e v a lu e s‘>1 the p a r a m e te r s a r c f o u n d to b e le s s th a n 0 .1 5 , th e li m i t o f re lia b ility [1 5 , 1 6 ], w h ic h s u p p o r t s th e r e f in e m e n t.
A s s u m in g p r e f e r e n ti a l o c c u p a n c y o f io n o n e it h e r s ite s , the fo r m u la p r o p o s e d f o r c a t i o n d i s t r i b u t i o n is
Distribution parameter 6
F i g u r e 1 T h e o r e t i c a l i n t e n s it y o f r c f l e c l i o n vs d is t r ib u t io n p a r a m e te r s
4 0 0 r e f l e c t i o n s to th e c a t i o n s o f o c t a h e d r a l B - s i te . I f a m o u n t o f l i g h t e r io n
(S)
in c r e a s e s , th e n e q u a l a m o u n t o f h e a v ie r io n s h i f ts f r o m A - s i te to B - s i te . T h is r e s u l t s in t o d e c r e a s e in th e to ta l s t r u c tu r e f a c t o r(F^)
o f A - s i tc a n d in c r e a s e in to ta l s t r u c tu r e (F ^ ) o f B - s i tc . T h e c l u b e d in t e n s i ty / ^ j , vi n d e p e n d e n t o n h o w e v e r , it s h o w s in c r e a s i n g tr e n d w ith o x y g e n io n p a r a m e t e r ( u ) , a s s h o w n in F ig u r e 2 . T h e o x y g e n io n p a r a m e t e r w a s d e c i d e d b y p l a c i n g o b s e r v e d in t e n s i ty o f -f o n th is p lo t. T h u s o b t a i n e d u - p a r a m e t e r s a r c r e p o r te d in T a b le 1.
w here
g
is th e d i s t r i b u t i o n p a r a m e t e r , w h i c h g iv e s a m o u n t o f io n o c c u p y i n g t e t r a h e d r a l A - s i te . B y u s i n g c q . ( 1 ) , th e th eo retical i n t e n s i ti e s o f r e f l e c t i o n s w e r e c a lc u la te d a n d th e r a tio f o r i n t e r p r e t a t i o n o f th e r e s u lts . In o r d e r to c o n f i r m the d e p e n d e n c e o f i n t e n s i t y o f r e f l e c t i o n s o n s i te o c c u p a n c y , ihc in te n s itie s o f v a r i o u s r e f l e c t i o n s h a v e b e e n c a l c u l a t e d a s a function o f d i s t r i b u t i o n p a r a m e t e r 5 in th e r a n g e f o r m 0 top lo tte d a g a i n s t d i s t r i b u t i o n p a r a m e t e r 5 , a s d e p i c t e d in i^tgurc I . O n i n s p e c t i o n o f F i g u r e 1, it is o b s e r v e d t h a t in t e n s i ty 2 2 0 a n d 4 2 2 r e f l e c t i o n d e c r e a s e s w ith i n c r e a s i n g 5 , w h e r e a s
F i g u r e 2 . I n t e n s it y o f + I ,, , r e n e c l i o n e.v o x y g e n io n U -p a r a m e te r
T h e i n t e n s i ty o f 2 2 0 r e f l e c t i o n b e in g s e n s i t i v e to A - s i te , is c a lc u la te d a s a f u n c t io n f o r d i s t r i b u t i o n p a r a m e t e r
g
a n d p lo t te d v e r s u sg.
T h e e x p a n d e d p a r t o f th i s p lo t is s h o w n in F ig u r e 3, ty p i c a l l y f o rx
= 0 . 4 0 ; y = 0.(X ) a n d 0 .0 5 . T h e e x a c t v a lu e o f d i s t r i b u t i o n p a r a m e t e rg
is o b t a i n e d b y p l a c i n g o b s e r v e d in t e n s i ty o f 2 2 0 r e f l e c t i o n o n th e s a m e p lo t , a s i n d i c a te d in th e F ig u r e 3 . T h e s e v a l u e s o f e x a c t d i s t r i b u t i o n p a r a m e t e rg
a r c354 B P Ladgaonkar, P N Vasambekar and A S VainganLir
u s e d to p r e d i c t c a t i o n d i s t r i b u t i o n . T h e r e f i n e m e n t f a c t o r s w e r e a l s o c a l c u l a t e d a s a f u n c t i o n o f
S
a n d p lo t te d a g a i n s tS
a s d e p i c t e d in F i g u r e 3 . B y in s p e c t i o n o f F ig u r e 3, it is f o u n d t h a t th e r e f i n e m e n t f a c t o r s h o w s th e d i p n e a r a b o u t e x a c t v a lu e o fS-
Distribution param eter 6
o
I.
ccFigure 3. Theoretical intensity of 220 reflection and reliability index vs distribution parameter d. (a) x = 0.40 ; y = 0.00 and (b) x = 0.40 ; y = 0.05.
T h i s d i p in th e r e f i n e m e n t f a c t o r s u p p o r t s th e e x a c t n e s s o f (he d is tr i b u ti o n p a r a m e t e r
S
a n d h e n c e p r o p o s e d c a ti o n d istribution T h e i n v e s t i g a t e d c a t i o n d i s t r i b u t i o n is p r e s e n t e d in T able : T h e c a t i o n d i s t r i b u t i o n p r e s e n t e d in T a b l e 2 s h o w s good a g r e e m e n t w ith th e p r e v i o u s r e p o r t s f o r M g F c2 0^ f e ir itc j 1 7| T h e o c c u p a n c y o f m a g n e s i u m io n o n te t r a h e d r a l s ite increases w ith c o n c e n t r a ti o n (x ) u p to x = 0 . 2 0 a n d d e c r e a s e thereafter O n Nd^"*^ s u b s t i t u i o n , th e a m o u n t o f M g ^ ‘*‘ io n o c c u p y in g A sue in c r e a s e s . T h i s a l s o s u p p o r t s th e o c c u p a n c y o n Nd-^"^ io n on[]
s ite .
4* Conclusion
S t r u c tu r a l r e f i n e m e n t m e t h o d c a n b e u s e d to e s t i m a t e th e exact c a t i o n d i s t r i b u t i o n . T h e i n t e n s i t y o f r e f l e c t i o n s h o w s ns d e p e n d e n c e o n s i te o c c u p a n c y a n d o x y g e n io n p a ra m e te r . The e x a c t d i s t r i b u t i o n p a r a m e t e r c a n b e d e c i d e d b y comparing:
o b s e r v e d i n t e n s i t y w ith c a l c u l a t e d o n e . T h e r e f in e m e n t facioi s h o w s a d e e p n e a r a b o u t th e e x a c t d is tr i b u ti o n p a r a m e te r s , whiUi s u p p o r t th e e x a c t n e s s o f th e m e t h o d . T h e c a ti o n d istrib u u o n i n v e s t i g a t i o n s h o w s t h a t th e o c c u p a n c y o f m a g n e s iu m ion on t e t r a h e d r a l s i te in c r e a s e s u p l o . r = 0 . 2 a n d d e c r e a s e s thercalicr T h e s u b s t i t u t e d Nd^**" io n r e s i d e s o n B - s i t e a n d resu lts mi<
in c r e a s e o f m a g n e s i u m io n o n A - s i te . R e fe re n c e s
[1] B P Ladgaonkar and A S Vaingankar Muter, Chem Pltw S(v'\
280 (1998)
[2] M A G ellio J Phys. Chem Sol 13 (I960)
[3] R V Upadhyay and G L Baldha Indian J, Phvs. A63 83.S i ivs (4J P N Vasambekar, C B Kolekar and A S Vaingankar J Mhk>'
Magn. Mater 186 333 (1998)
|5 ] H M Riclvcld J Appi Cryst 2 65 (1969) [6] H M Reitveld Acta Cryst. 22 151 (1967) Table 2. Gallon distribution for the compositions of Zn^Mg, ^Fe,yNd^O^ ferrites system
cone. Nd*"* cone. Cation distribution Distribution
X y
parameter 5
0 . 0 0 . 0 0 124^^0 ^ 4 0 .1 2 4
0 .2 (Zn,„„M go
,^Fe.,,„)nMg,.,„Fe, ,«,Nd„
0 .1 8 60 .4
(Zn,,„Mg„ ,,,Nd,
0 .1 7 60 . 6 0 .0 6 3
0 .8 141^ »OM^*^nOt»l ^4 0 .0 0 9
1.0 ^^**1 «0^ 8o.»wof^^051^)^1^ 80000^^2 «KI(»^^0(Jo)*^4 0 .0 0 0
0 .0 I25^®0»75)''t^8o.l»75^®I 075^^0.051*^4 0 .1 2 5
0 .2 0 .0 5 602^^1 V4*h^4(, 0 .1 9 8
0 .4 ^^*^0 40^80141^^^0407)^1^ 80407^^®! 141^^0 0l)*f)4 0 .1 9 3
0 . 6 14)^800H6^®0 314)^1 ^ 8 0 1 .ftl4»l^*lo.Os)*^4 0 .0 8 6
0 .8 ^^*'0.«0^8o 024^®0.l7ft)'^f^8o 176^® 1 774^*^0,05)* ^4 0 .0 2 4
1.0 <Zn, ooMgo.oooJ'Co!»o)''lMg„^Fc,„^Nd,„]“0 , 0 .0 0 0
