Nonstoichiometry, Order, and Disorder in Fluorite-Related Materials

14 Nonstoichiometry, Order, and Disorder in Fluorite-Related Materials for Energy Conversion

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LEROY EYRING Department of Chemistry and the Center for Solid State Science, Arizona State University, Tempe, Ariz. 85281

Ordered intermediate phases in fluorite-related model systems and in materials useful as fast ion conductors and nuclear energy sources are reviewed. The rare earth oxides are emphasized as models of extended defects and ordering in such materials. Modern high resolution (3.5 Å) electron optical methods are used to deduce unit cells, suggest structures, and reveal reaction mechanisms. The relationships between ordered structures in the ternary and binary oxides are emphasized; nevertheless, a wide range of order and disorder is observed. Electron micrographs are presented to illustrate the range of direct observations possible and to underline the importance of the technique in elucidating not only structural defects but reaction mechanisms at the unit cell level.

T h e

s t r u c t u r e of a m a t e r i a l is a n e n c y c l o p e d i a o n t h e p r o p e r t i e s of its

constituent atoms a n d is therefore at t h e root of a l l its c h e m i c a l a n d p h y s i c a l p r o p e r t i e s . W e m e a n , of course, t h e structure o f t h e r e a l m a t e r i a l , w h i c h i n c l u d e s its defects most r e s p o n s i b l e f o r t h e r e a c t i v i t y a n d d y n a m i c s of c h e m i c a l a n d p h y s i c a l c h a n g e .

M e c h a n i s m i n reactions c a n

n o t b e u n d e r s t o o d w i t h o u t k n o w l e d g e o f t h e defect s t r u c t u r e .

Under

s t a n d i n g c a n l e a d to i m p r o v e d c o n t r o l o f r e a c t i o n p r o p e r t i e s a n d t o t h e a b i l i t y to d e s i g n n e w m a t e r i a l s .

E l u c i d a t i o n of t h e s t r u c t u r e o f r e a l

m a t e r i a l s of p r a c t i c a l i m p o r t a n c e i n t h e m o s t d i r e c t w a y p o s s i b l e is therefore i m p o r t a n t , a n d these studies w i l l serve as a basis f o r f u r t h e r u n d e r s t a n d i n g . W e seek h e r e n o t a s h a l l o w classification b u t d e e p i n s i g h t of s u b t l e s h a d i n g . 240

Goodenough and Whittingham; Solid State Chemistry of Energy Conversion and Storage Advances in Chemistry; American Chemical Society: Washington, DC, 1977.

14.

EYRiNG

Nonstoichiometry,

Order,

and

241

Disorder

F l u o r i t e - r e l a t e d m a t e r i a l s are a m o n g those c o m m o n l y e n c o u n t e r e d i n e n e r g y c o n v e r s i o n a n d storage. T h e i r v a r i e d usefulness a n d t h e i r l i m i t a tions c a n b e best u n d e r s t o o d i n terms of t h e i r s t r u c t u r e , w h i c h is a palpable

expression

of

their nature.

The

fluorite

structure m a y

be

v i s u a l i z e d i n m a n y w a y s . F o r e x a m p l e , i f a l l the t e t r a h e d r a l interstices i n a c u b i c c l o s e - p a c k e d a r r a y of atoms are

filled

b y atoms of a different

k i n d , the fluorite s t r u c t u r e results. T h e l a t t i c e is f a c e - c e n t e r e d (Fm3m)

cubic

w i t h m e t a l atoms ( M ) at (0, 0, 0 ) a n d the n o n m e t a l atoms

at ( VA, VA, VA ) a n d ( V A , V A , V A )

(X)

a n d e q u i v a l e n t positions. T h i s gives f o u r

f o r m u l a u n i t s p e r u n i t c e l l . A n a l t e r n a t i v e w a y of v i s u a l i z i n g the s t r u c t u r e is to c o n s i d e r the c o o r d i n a t i o n cubes of the m e t a l atoms ( M X ) s h a r i n g Downloaded by TUFTS UNIV on October 21, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch014

8

a l l edges i n a t h r e e - d i m e n s i o n a l c h e s s b o a r d n e t w o r k . C o o r d i n a t i o n t e t r a h e d r a of n o n m e t a l atoms

( X M ) share a l l edges i n a n o n s p a c e - f i l l i n g 4

t h r e e - d i m e n s i o n a l n e t w o r k . S t i l l a n o t h e r w a y of e x p r e s s i n g this s t r u c t u r e is to c o n s i d e r i t as a s t a c k i n g of c l o s e - p a c k e d layers of atoms a l o n g the [1 1 1] d i r e c t i o n i n t h e sequence

α Β γ β Ο α γ Α β α Β γ β Ο α . . .

w h e r e R o m a n capitals represent m e t a l atoms a n d G r e e k letters n o n m e t a l , e a c h i n e q u a l l y s p a c e d c u b i c c l o s e - p a c k e d layers. F i g u r e 1 illustrates a u n i t c e l l of

fluorite

w h e r e circles represent m e t a l a t o m positions a n d

triangles represent n o n m e t a l a t o m positions. T h e o c t a h e d r a l interstices r e p r e s e n t e d b y the d i a m o n d s are a l l e m p t y . T e x t b o o k examples of the fluorite s t r u c t u r e are u s u a l l y the

fluorides

of C a , Sr, a n d B a a n d the oxides of T h a n d U . T o this list m u s t b e a d d e d m a n y others w h e r e the a t o m r a d i u s r a t i o of m e t a l / n o n m e t a l >

0.73.

T h e s e w o u l d i n c l u d e m a n y of the h y d r i d e s a n d oxides of t h e r a r e e a r t h a n d a c t i n i d e elements.

F u r t h e r m o r e , w h e n w e c o n s i d e r a d d i n g or s u b

t r a c t i n g atoms of either t y p e to g i v e

fluorite-related

d e f e c t structures

w h i c h m a y b e o r d e r e d or d i s o r d e r e d , the p o s s i b i l i t i e s b o g g l e t h e m i n d . F l u o r i t e - r e l a t e d m a t e r i a l s h a v e a k n o w n c o m p o s i t i o n a l v a r i a t i o n at least f r o m M 4 X 9 ( M X . 2

2 5

) to M X . A l t h o u g h t h e r e are m a n y other

r e l a t e d m a t e r i a l s of i m p o r t a n c e i n energy c o n v e r s i o n , s u c h as the

fluoritefluorides

Figure 1. The fluorite structure. The large circles represent metal atom positions; the triangles represent nonmetal positions; and the diamonds represent the empty octahedral posi tions in the cubic dose-packed struc ture.


242

SOLID STATE

CHEMISTRY

a n d h y d r i d e s , h e r e w e s h a l l focus a t t e n t i o n almost e x c l u s i v e l y o n o x y g e n deficient phases i n t h e c o m p o s i t i o n r a n g e M O a . ( 2 . 0 > χ > 1.5)

where

t h e o x y g e n d e f i c i e n c y is e i t h e r o r d e r e d o r d i s o r d e r e d . I n these phases a g o o d a p p r o x i m a t i o n is to c o n s i d e r t h e m e t a l a t o m s u b s t r u c t u r e i n t a c t as i n fluorite w i t h s m a l l d i s p l a c e m e n t s

understood.

T h e o x y g e n s u b s t r u c t u r e is t h e n c h a r a c t e r i z e d as possessing

vacancies

o n n o r m a l sites w h i c h m a y b e o r d e r e d i n l o n g o r short r a n g e o r d i s o r d e r e d . T h i s m e a n s t h a t there w i l l a l w a y s b e c o h e r e n c e , b u t t h e r e m a y b e

a

regular or p e r i o d i c variation i n oxygen composition i n the structure. M a n y m e t a l s c a p a b l e of t e t r a v a l e n c y f o r m e x t r e m e l y t h e r m a l l y stable Downloaded by TUFTS UNIV on October 21, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch014

fluorite-related

oxides. I n d e e d , T h 0

( 3 3 0 0 ° db 1 0 0 ° C ) .

2

is t h e h i g h e s t m e l t i n g o x i d e k n o w n

T h e c o n g r u e n t l y m e l t i n g c o m p o s i t i o n s of a l l these

r e f r a c t o r y oxides i n v a c u u m are l o w e r t h a n the d i o x i d e ( e v e n f o r T h 0 ) . 2

Ce0 a

2

loses o x y g e n i n v a c u u m to a c o m p o s i t i o n of C e O i . i at 2 0 0 0 ° C i n 5

tungsten cell, a n d P r a n d T b 0

2

lose o x y g e n

to

substoichiometric

ΜΟι.υ.δ at t h e m e l t i n g p o i n t . T h e m e l t i n g p o i n t of r e d u c e d

substances

is > 2 0 0 0 ° C . T h e e n t h a l p i e s of f o r m a t i o n of the oxides f o r the elements forming

fluorite-related

phases are v e r y h i g h , ^ 2 1 0 - 2 6 0 k c a l / g a t o m of

metal. A f e w o t h e r g e n e r a l statements a b o u t p r o p e r t i e s s h o u l d also b e m a d e . D i f f u s i o n coefficients of m e t a l atoms are g e n e r a l l y v e r y l o w u p to t e m peratures i n excess of o n e - h a l f t h e m e l t i n g p o i n t ; i n contrast, the d i f f u s i o n coefficients of the o x y g e n atoms are r e l a t i v e l y l a r g e . U n d e r these same c o n d i t i o n s the v a p o r i n e q u i l i b r i u m w i t h t h e s o l i d is o x y g e n . M u c h h i g h e r t e m p e r a t u r e s m u s t b e a t t a i n e d b e f o r e m e t a l - c o n t a i n i n g v a p o r species are d e t e c t a b l e . I n short, t h e m e t a l s u b s t r u c t u r e is rigid a n d n o n v o l a t i l e , w h i l e t h e n o n m e t a l s u b s t r u c t u r e is m o b i l e a n d v o l a t i l e .

Fluorite-Related

Materials

in Energy-Winning

Roles

T h e r e is a r o m a n t i c h i s t o r y a n d great l i t e r a t u r e o n these deficient

fluorite-related

anion

phases. T h i s i n c l u d e s W e l s b a c h gas m a n t l e s a n d

N e r n s t g l o w e r s . T h i s c h a p t e r is n o t i n t e n d e d to b e c o m p r e h e n s i v e ; r a t h e r , references

are m a d e a r b i t r a r i l y to t h a t w o r k w h i c h h i g h l i g h t s c u r r e n t

efforts t o c l a r i f y t h e s t r u c t u r a l p r i n c i p l e s b e h i n d d e f e c t

fluorite-related

materials. Solid Electrolytes.

ZTRCONIA- A N D H A F N I A - B A S E D M A T E R I A L S .

When

z i r c o n i a o r h a f n i a react w i t h t h e a l k a l i n e e a r t h oxides ( e s p e c i a l l y c a l c i a ) o r r a r e e a r t h oxides, p s e u d o b i n a r y v a c a n c i e s are f o r m e d .

fluorite-related

phases

with

anion

A t h i g h t e m p e r a t u r e s t h e p h a s e fields are b r o a d

c u b i c s o l i d solutions, a l t h o u g h i n some cases there m a y b e

considerable

diffuse scatter i n t h e i r d i f f r a c t i o n patterns. T h e s e m a t e r i a l s are t e c h n i c a l l y


14.

EYRiNG

Nonstoichiometry,

Order,

and

Disorder

243

i m p o r t a n t b e c a u s e of t h e r a p i d t r a n s p o r t of o x i d e ions at m o d e r a t e l y h i g h temperatures w i t h o u t electronic or cationic conduction.

T h i s ensures a

v a r i e t y of h i g h t e m p e r a t u r e e l e c t r o m e c h a n i c a l uses. A t h i g h e r t e m p e r a t u r e s c u b i c phases o f c o n t i n u o u s l y c h a n g i n g c o m position cover the

field.

A t lower temperatures (
r v a cancy pairs w i t h a cation between.

A l l p r e s s et a l . suggest t h a t these

clusters m a y coalesce to f o r m finite g r o u p s i n Φι o r e x t e n d e d c h a i n s i n Φ . 2

This information was obtained f r o m p o w d e r diffraction data w h i c h p r o v i d e only l i m i t e d conclusions about vacancy ordering. E l e c t r o n d i f f r a c t i o n p a t t e r n s of c a l c i a - s t a b i l i z e d h a f n i a a n d z i r c o n i a s h o w diffuse s c a t t e r i n g i n a d d i t i o n to t h e s r t o n g reflections f r o m t h e


244

SOLID S T A T E

fluorite and

CHEMISTRY

s u b c e l l . A l l p r e s s a n d R o s s e l l ( 8 ) h a v e a n a l y z e d this diffuse scatter

h a v e o b t a i n e d g o o d a g r e e m e n t w i t h the e x p e c t e d d i f f r a c t i o n f r o m

specimens w i t h d o m a i n s of t h e Φι phase of 3 0 - A d i a m e t e r c o h e r e n t l y e m b e d d e d i n specific orientations w i t h i n t h e c u b i c m a t r i x . T h i s is r e m i n i s c e n t of t h e d o m a i n s of C a r t e r a n d R o t h

(2).

Lefevre (9) noted ordering i n Z r 0 - S c 0 2

t u r n e d out to b e r h o m b o h e d r a l Z r S c O i 3

4

2

2

3

c a u s e d b y a phase w h i c h

( J O ) a n d t w o others w i t h w i d e r

c o m p o s i t i o n w i d t h s as w e l l as h i g h e r Ζ ι Ό

2

content.

Bevan ( J J )

and

c o - w o r k e r s h a v e d e t e r m i n e d t h a t the c o m p o s i t i o n w i d t h of these phases is less t h a n at first t h o u g h t a n d h a v e a s s i g n e d t h e m t h e i d e a l f o r m u l a s Zr Sc Oi , Zri Sc O , and Z r Downloaded by TUFTS UNIV on October 21, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch014

3

4

0

2

4

2 6

isomorphous w i t h M O i 7

4 8

Sci Ou . Zr Sc Oi 4

7

3

4

w a s f o u n d (12)

2

to b e

i n the b i n a r y phases to b e d e s c r i b e d later. T h e

2

s t r u c t u r a l feature e m p h a s i z e d i n these results is a s t r i n g of o x y g e n v a c a n cies a l o n g t h e [ 1 1 1 ]

w h i c h gives units of M O i

F

7

2

c o m p o s e d of a s i x -

c o o r d i n a t e d M a t o m s u r r o u n d e d w i t h t r i g o n a l s y m m e t r y b y six s e v e n c o o r d i n a t e d M atoms.

T h e s e u n i t s are s e p a r a t e d b y a f u l l y o x i d i z e d

M O i 4 g r o u p a l o n g [ 1 1 l ] - l i k e beads of t w o types i n a s t r i n g t o f o r m 7

F

the s t r u c t u r e o f Z r i S c O 0

4

2 6

( s p a c e g r o u p R3).

T h e s e b e a d e d strings, a l l

o r i e n t e d p a r a l l e l to the t h r e e f o l d axis, are e d g e - s h a r e d to f o r m a n i n t e r p e n e t r a t i n g n e t w o r k of t h e t w o k i n d s of u n i t s .

T h e Z r a n d S c atoms

o c c u p y the m e t a l sites r a n d o m l y i n b o t h structures. I n the Z r Y b O i 3

4

2

p h a s e (13),

m o d i f i c a t i o n s are o b s e r v e d .

w h e r e the l a r g e r Y b is present, t w o

O n e is i s o s t r u c t u r a l w i t h Z r S c O i , a n d t h e 3

4

2

o t h e r ( a l o w t e m p e r a t u r e f o r m ) has some o r d e r i n g of m e t a l atoms w i t h Z r o c c u p y i n g t h e s i x - c o o r d i n a t e d m e t a l sites a n d r a n d o m o c c u p a n c y

of

the s e v e n - c o o r d i n a t e d sites. I n the other r a r e e a r t h z i r c o n i a s o l i d s o l u tions (11),

w h e r e the size d i s c r e p a n c y b e t w e e n the atoms increases, t h e r e

is l i t t l e e v i d e n c e of o r d e r i n g . T h e o r d e r e d phases of s i m i l a r c o m p o s i t i o n o b s e r v e d b y K o m e s s a r o v a and

S p i r i d i n o v (14)

i n t h e H f O ^ S c ^ O s system a n d i n d e x e d as r h o m b o

h e d r a l u n i t cells a r e p r o b a b l y closely r e l a t e d to these Z r 0 · S c 0 2

2

3

phases.

C o l l o n g u e s a n d c o - w o r k e r s (JO, J 5 ) as w e l l as m a n y others ( J ) h a v e f o u n d p y r o c h l o r e phases i n these t e r n a r y o x i d e systems. phase, Α

2

3 +

Β

2

4

A l t h o u g h this

Ό , is r e l a t e d to fluorite, the shifts i n o x y g e n positions are 7

so great t h a t t h e s t r u c t u r e is best c o n s i d e r e d as i n t e r p e n e t r a t i n g f r a m e w o r k s of [ A 0 ] 2

a n d [ B O ] w i t h the A i n l i n e a r c o o r d i n a t i o n a n d Β i n

octahedral coordination.

e

T h e radius ratio, r( A

3 +

)/r(B

) , is

4 +

between

ca. 1.20 a n d 1.60. T H O R I A - R A R E E A R T H OXIDE SYSTEMS.

S o l i d solutions b e t w e e n t h o r i a

a n d the r a r e e a r t h oxides a r e w e l l k n o w n a n d h a v e b e e n u s e d f o r years as o x y g e n - c o n d u c t i n g s o l i d electrolytes. I n e a c h case s t u d i e d t h e r e is a w i d e - r a n g e s o l i d s o l u t i o n h a v i n g a fluorite s t r u c t u r e u p to a m a x i m u m at m o d e r a t e t e m p e r a t u r e s of a b o u t 4 0 %

( M 0 ) i n T h 0 . N o ordered 2

3

2


14.

Nonstoichiometry,

EYRiNG

i n t e r m e d i a t e phases

Order,

i n this s y s t e m

and at l o w

Disorder

245

temperatures

have

been

described. On and

the M 0 - r i c h side at v e r y h i g h t e m p e r a t u r e s , h o w e v e r , S i b i e u d e 2

F o e x ( 16)

3

h a v e f o u n d e v i d e n c e of a r e m a r k a b l e c o m p l e x i t y s h o w i n g

phases r e l a t e d to t h e A - , B - , C - , X - , a n d Η-type sesquioxides of v a r i a b l e c o m p o s i t i o n as w e l l as to n u m e r o u s other h e x a g o n a l phases of a p p a r e n t l y n a r r o w c o m p o s i t i o n . T h e C - t y p e phase is, of course,

fluorite-related,

but

n o o r d e r e d i n t e r m e d i a t e n a r r o w c o m p o s i t i o n phases h a v e b e e n i n d i c a t e d i n t h e t e r n a r y system thus far. U R A N I U M DIOXIDE—RARE E A R T H OXIDE SYSTEMS.


W e i t z e l and

h a v e r e c e n t l y p r e p a r e d s e v e r a l oxides of c o m p o s i t i o n

(17)

Keller

(M .5Uo.5)0 0

w h e r e M is a r a r e e a r t h a t o m ; t h e y h a v e s h o w n t h e m to b e s t r i c t l y

2

fluorite

i n spite of the u n u s u a l presence of U ( V ) a n d U ( V I ) i n e i g h t - c o o r d i n a t i o n . M a n y studies h a v e s h o w n t h e f o r m a t i o n of fluorite s o l i d solutions of wide

composition

UYeOi

2

range.

O u r a t t e n t i o n is d r a w n to

3Y 0 -U0 2

3

It is i s o s t r u c t u r a l w i t h t h e Z r M O i 3

4

?

(18).

phases d i s c u s s e d a b o v e a n d w i t h t h e

2

b i n a r y oxides of c o m p o s i t i o n M O i

or

3

w h i c h w a s the first c r y s t a l of this s t r u c t u r e d e t e r m i n e d

2

to b e d i s c u s s e d b e l o w as t h e s t r u c

t u r a l e n d m e m b e r of the h o m o l o g o u s series i n the r a r e e a r t h h i g h e r oxides. These

are t h e o n l y k n o w n o r d e r e d

fluorite-related

t e r n a r y oxides

in

this f a m i l y . M a n y reactor

Fluorite-Related Oxides for the Nuclear Industry. fuels a n d r a d i a t i o n p o w e r sources are

fluorite-related

oxides.

These sub

stances c h a r a c t e r i s t i c a l l y m u s t operate i n p l a c e for l o n g p e r i o d s of t i m e , at h i g h t e m p e r a t u r e s , i n s t r o n g r a d i a t i o n fields, a n d w i t h g r o w i n g levels of i m p u r i t y . U n d e r l y i n g a n y r a t i o n a l l y b a s e d p r o g r a m to i m p r o v e t h e p e r f o r m a n c e characteristics of these m a t e r i a l s m u s t b e a s o u n d k n o w l e d g e of t h e i r s t r u c t u r e a n d texture, e s p e c i a l l y t h e i r defect s t r u c t u r e , as a f u n c t i o n of t e m p e r a t u r e , pressure of o x y g e n , r a d i a t i o n

field,

and level

of

impurity. A t t e n t i o n w i l l b e f o c u s e d h e r e o n t h e structures of fluorite-related Pu0

2

(U, Pu)0

2

2

2

as w e l l as the p l u t o n i u m oxides.

FLUORITE Μ0 .δ. 2

Cm,

oxygen-deficient

oxides of the a c t i n i d e elements. T h e s e i n c l u d e U 0 , T h 0 , D i o x i d e s are k n o w n for T h , P a , U , N p , P u , A m ,

B k , a n d C f . T h e l a t t i c e p a r a m e t e r s are c o m p a r e d i n F i g u r e 2.

enormous oxygen

The

v a r i a t i o n of the t h e r m o d y n a m i c s t a b i l i t y is reflected i n t h e

a c t i v i t y r e q u i r e d to m a i n t a i n s t o i c h i o m e t r y at 1000 ° C

which

varies m o r e t h a n 20 orders of m a g n i t u d e . Th0

2

is o n l y s l i g h t l y s u b s t o i c h i o m e t r i c i n the presence of T h e v e n

near the m e l t i n g point.

U0

2

b e g i n s to lose o x y g e n a p p r e c i a b l y i n t h e

p r e s e n c e of U at ~ 1 5 0 0 ° C a n d reaches a m o n o t e c t i c c o m p o s i t i o n of ~ U O i . . 6 5

at 2 5 0 0 ° C at a

T h e heavier actinide dioxides typically show

l i t t l e d e v i a t i o n f r o m s t o i c h i o m e t r y u n t i l a t e m p e r a t u r e of a f e w h u n d r e d


246

SOLID STATE

CHEMISTRY


A C T I N I D E OXIDE

LANTHANIDE Figure 2.

OXIDE

Lattice parameters for fluorite-related rare earth and actiniae

oxides

degrees is r e a c h e d , a n d t h e n q u i t e s u d d e n l y t h e y enter a p h a s e of w i d e c o m p o s i t i o n r a n g e of fluorite structure. A n u n d e r s t a n d i n g o f the d e g r e e a n d n a t u r e of s h o r t - or l o n g - r a n g e o r d e r i n g of defects i n these

Μ0 .δ 2

phases has not p r o g r e s s e d v e r y far. A b r i e f r e v i e w of w o r k u p to a b o u t 1970 a l o n g these lines offers p h a s e d i a g r a m s a n d references ( 19). R e c e n t l y S0rensen

(20)

has u n d e r t a k e n m e a s u r e m e n t s

(and

the

c o r r e l a t i o n of the w o r k of o t h e r s ) of t h e p a r t i a l m o l a r t h e r m o d y n a m i c q u a n t i t i e s f o r o x y g e n i n nônstoichiometric p l u t o n i u m a n d p l u t o n i u m u r a n i u m oxides. H e has p r e v i o u s l y d o n e a s i m i l a r analysis o n the C e 0 _ e 2

s y s t e m (21).

I n e a c h of these systems a c a r e f u l analysis of t h e t h e r m o

d y n a m i c d a t a shows s u r p r i s i n g d e v i a t i o n s f r o m i d e a l s o l u t i o n . I n e a c h case a d e r i v e d p h a s e d i a g r a m i n d i c a t e s s e v e r a l subregions i n the M 0 . e 2

p h a s e i n w h i c h the slopes of A G

0 2

VS. log X have characteristic values.

I n t h e C e 0 . 6 p h a s e i n a d d i t i o n to n u m e r o u s nônstoichiometric subregions 2

w i t h i n w h i c h consistent t h e r m o d y n a m i c p r o p e r t i e s are o b s e r v e d , are s u p e r i m p o s e d i n d i c a t i o n s of b e l o n g i n g to a h o m o l o g o u s s u c h subregions

there

s t a b i l i t y at p a r t i c u l a r s t o i c h i o m e t r i c s

series M 0 n

2 n

_ . 2

I n t h e P u O * system t h r e e

( f r o m P u O ^ - P u O i ^ ) a n d t w o t w o - p h a s e regions are

i n d i c a t e d . T h e t w o - p h a s e regions are i n t h e c o m p o s i t i o n r a n g e PuOi.9945 a n d P u O i 999 . T h e ( U , P u ) 0 . « phase separates, b y the same t r e a t m e n t , 8

2

i n t o five subregions w i t h n o i n d i c a t i o n of s p e c i a l s t a b i l i t y at a n y n a r r o w c o m p o s i t i o n . T h e results c o v e r t h e c o m p o s i t i o n r a n g e 2.00 > χ > H i g h t e m p e r a t u r e x - r a y d i f f r a c t i o n observations

(20,

21)

1.85. i n these

systems h a v e s h o w n superstructures of m o n o c l i n i c s y m m e t r y a b o u t 9 0 0 ° C


14.

Nonstoichiometry,

EYRiNG

Order, and

247

Disorder

i n the C e 0 . 6 system. H o w e v e r , i n P u 0 . 6 o r w i t h a n a d m i x t u r e of u r a n i a 2

2

o n l y fluorite structures w e r e f o r m e d . I t seems a p p a r e n t t h a t e v e n at these h i g h t e m p e r a t u r e s ( a l t h o u g h o n l y u p to l i t t l e m o r e t h a n o n e - h a l f t h e m e l t i n g t e m p e r a t u r e s ) there is c o n s i d e r a b l e o r d e r , at least short-range order.

T h i s o r d e r exists i n spite of a h i g h m o b i l i t y o f o x y g e n

atoms

w h i c h at t h e h i g h e s t t e m p e r a t u r e s m u s t s p e n d a g o o d d e a l of t i m e b e t w e e n positions o f m i n i m u m e n e r g y ( 2 2 ) . The M O 7

i 2

p h a s e has d e f i n i t e l y b e e n e s t a b l i s h e d f o r C m a n d C f ( 2 3 ,

2 4 ) , a n d t h e r e is clear e v i d e n c e f o r o r d e r i n i n t e r m e d i a t e regions i n t h e CmOi.

8 2

a n d at t w o c o m p o s i t i o n s i n t h e B k 0 _ 6 system ( 2 5 ) . 2


T a b l e I s u m m a r i z e s t h e k n o w n i n t e r m e d i a t e phases

among the

a c t i n i d e oxides i n M O * , 1.5 < χ < 2.0. T h e names of the phases are u s e d a d v i s e d l y f o l l o w i n g t h e n o m e n c l a t u r e f o r t h e l a n t h a n i d e oxides. Table I. Μ

I n t e r m e d i a t e Phases a m o n g t h e A c t i n i d e O x i d e s

ΜΟ^Β(σ)

Th Pa U Νρ Pu Am Cm Bk Cf

M0 (i) lm71

M0 è(i)

ΜΟ . -δ(α)

1M±

2 00

Χ

Χ Χ Χ Χ χ

i

Triclinic

a b c a 0 7

= 13.8A = 16.2A —12.1A = 107.4° — 100.1° = 92.2°

ROisis

11

Triclinic

a = 6.5 A b = 9.9A c = 6.5A a = 90.0° β = 99.6° γ=96.3°

TbOi.833

12

Pn

a =

,

P

(

r

T l

.

0

1

W

l

h b

n u

7

1

4

)

χ " i * )

6.7A

6 = 23.2A c = 15.5A 0 = 125.2° PrOi.833

12

Pn

a 6 c 0

R0 .ooo

00

Fm3m

a =

5.393A

(Pr0 )

a =

5.220A

(TbOi.95)

2

= 6.687A = 11.602A = 15.470A = 125°15' 2

If a phase occurs in the PrO* as well as in the TbO* system R is used, otherwise the specific symbol is used. β


14.

EYWNG

Nonstoichiometry,

Order, and Disorder

251

Intermediate Rare E a r t h Oxide Phases


Relation

to Basic Structure

a =

2a,

a

=

at +

1/26, -

l/2c

α =

a, +

1/26,

6 =

3/26, +

c =

l / 2 a , — 1/26,

a =

a, +

6 =

5 / 2 ( - 6 ,

—

CHEMISTRY

moderate

300°C).

T h e u n i t ceUs f o r s e v e r a l m e m b e r s of t h e h o m o l o g o u s series M 0 n

where η =

d i f f r a c t i o n a n d h a v e b e e n a d d e d to those a l r e a d y k n o w n f o r η = oo.

2 n

-2

7, 9, 10, 11, a n d 12 h a v e b e e n d e t e r m i n e d ( 2 9 ) u s i n g e l e c t r o n

T h e s e are s h o w n i n p r o j e c t i o n a l o n g [211]

4 and

i n F i g u r e 3 a n d are

d e s c r i b e d i n d e t a i l i n T a b l e I I I . I n a d d i t i o n , p o l y m o r p h i s m occurs i n t h e zeta ( n =

9 ) p h a s e a n d p e r h a p s i n others.

A l l t h e phases h a v e t h e same a axis. T h e a r r a n g e m e n t of v a c a n c i e s a l o n g this axis, w h i c h is a v e c t o r of t h e k i n d V i [ 2 1 1 ] , are s h o w n i n F


F i g u r e 4. T h i s feature of t h e i o t a s t r u c t u r e is c o n s i d e r e d t h e largest h e l d i n c o m m o n b y t h e m e m b e r s of t h e h o m o l o g o u s series of b i n a r y oxides ( n = 7, 9 , 1 0 , 11, 1 2 ) . T h e o d d m e m b e r s of the series also h a v e t h e same c axis a n d h e n c e t h e i o t a ac p l a n e ( 135 )

F

as a c o m m o n f e a t u r e . A s F i g u r e

3 s h o w s , t h e e v e n m e m b e r s h a v e a n ac p l a n e i n c o m m o n also, b u t c is different i n this case.

A n o t h e r e l e m e n t w h i c h w e n t i n t o this s t r u c t u r a l

p r i n c i p l e hypothesis was the h i g h resolution structure images of the delta

10 Figure 3. Projections of the unit cells of members of the homologous series along the common a axis, [211] F



14.

Nonstoichiometry,

EYRiNG

Figure

4.

Order, and

253

Disorder

Arrangement of vacancy pairs along the a axis, common to members of the homologous series

[211]

F

p h a s e ( T b n 0 o ) w h i c h a p p e a r e d to s h o w ( F i g u r e 5 ) the positions of t h e 2

vacancies i n the u n i t c e l l as w o u l d b e p r e d i c t e d ( F i g u r e 6 ) . D e s p i t e this a p p a r e n t success, a p p l i c a t i o n of h i g h r e s o l u t i o n c r y s t a l s t r u c t u r e i m a g i n g to structures s u c h as the

fluorite

type h a d not been

d e v e l o p e d p r e v i o u s l y ; h e n c e great care m u s t b e t a k e n i n the i n t e r p r e t a t i o n of the images o b t a i n e d . H i g h r e s o l u t i o n c r y s t a l s t r u c t u r e i m a g i n g is c a p a b l e of g i v i n g a t w o d i m e n s i o n a l p o i n t - t o - p o i n t i m a g e of the c r y s t a l p o t e n t i a l to a r e s o l u t i o n of a b o u t 3.5 A . T h i s is possible for crystals w h e n there is a short axis of o n l y o n e - c o o r d i n a t i o n p o l y h e d r o n i n the d i r e c t i o n of v i e w i n g a n d r a t h e r l a r g e axes i n the other t w o directions.

S u c h a structure exhibits l a r g e

v a r i a t i o n s i n p o t e n t i a l w h e n v i e w e d d o w n this short axis. I n a d d i t i o n , t h e c r y s t a l m u s t b e t h i n ( < 100 A ) , o r i e n t e d w i t h i n ~ 0.1°, a n d v i e w e d at the correct defocus. U n d e r these c o n d i t i o n s c r y s t a l s t r u c t u r e images of structures b a s e d o n t h e R e 0

3

s t r u c t u r e , for e x a m p l e , c a p a b l e of i n t u i t i v e

interpretation have been produced The

fluorite

(31).

superstructures, o n t h e other h a n d , are n o t l i k e l y

exhibit large potential variations i n any direction. A n a d d e d

to

disadvantage

is that t h e shortest axis for these m a t e r i a l s is the 6.75 A a axis. T h i s strains the t h i n phase object a p p r o x i m a t i o n o n w h i c h the c a l c u l a t i o n s are b a s e d a n d h e n c e requires that the t e c h n i q u e b e s h o w n to a p p l y . T o a d d t o t h e



254

SOLID STATE

Figure 5.

Figure 6.

Crystal structure image of Tb O . enhanced. tl

u

Possible structures of delta (Pr O ) n

20

Dark field,

CHEMISTRY

optically

projected down

[211]


F

14.

Nonstoichiometry,

EYRiNG

Order,

and

255

Disorder

difficulty, the r e c i p r o c a l l a t t i c e axes p e r p e n d i c u l a r to t h e p r o j e c t i o n axis are r a t h e r l o n g , p r o d u c i n g f e w b e a m s i n a r e a s o n a b l e s i z e d a p e r t u r e . T h e stakes i n success are h i g h , h o w e v e r , since t h i s t e c h n i q u e a l o n e c a n r e v e a l t e x t u r a l details d i r e c t l y , a n d t h e c a p a b i l i t y of t r e a t i n g a n y i m p o r t a n t class of substances s u c h as the

fluorite

m a t e r i a l s is v i t a l .

In

v i e w of s u c h u n f a v o r a b l e c i r c u m s t a n c e s i t is i m p e r a t i v e to c o m p a r e c a l c u l a t e d a n d o b s e r v e d images to a v o i d serious errors i n the i n t e r p r e t a t i o n . W i t h this i n m i n d S k a r n u l i s , S u m m e r v i l l e , a n d E y r i n g

(32)

have

t e s t e d t h e a p p l i c a b i l i t y of t h e m e t h o d o n t h e p r o t o t y p e of t h e h o m o l o g u o s series, t h e i o t a p h a s e ( P r O i ) , the o n l y one of the i n t e r m e d i a t e phases 7


for w h i c h complete

2

s t r u c t u r a l d a t a are a v a i l a b l e ( 3 3 ) .

m u l t i s l i c e m e t h o d of C o w l e y a n d M o o d i e (34)

The

n-beam

is t h e basis of t h e i m a g e

contrast c a l c u l a t i o n s . Calculated

Images

of

(Pr Oi ), [211] 7

2

atoms for P r O i 7

M0

2

the

Iota

Zone.

F

Phase

F i g u r e 7 shows the p r o j e c t i o n of t h e i d e a l

w h e n v i e w e d d o w n the (111)F a n d t h e ( 2 1 1 ) axes.

The

F

c o o r d i n a t i o n c u b e is also s h o w n to f a c i l i t a t e o r i e n t a t i o n .

8

C a l c u l a t e d η-beam images of t h e [211] z o n e for 25-, 165-, a n d 235-Â t h i c k crystals are s h o w n i n F i g u r e 8 u s i n g i o n i c s c a t t e r i n g factors.

The

d e f e c t of focus of t h e m i c r o s c o p e is t a k e n to b e —1000 A . T h e o r i g i n is p l a c e d at t h e top left c o r n e r w i t h t w o of t h e axes (a = figure

b =

along the

c)

edges.

T h e c a l c u l a t e d t h i n c r y s t a l images at 1000-A u n d e r f o c u s

correspond

to t h e p r o j e c t i o n of t h e c o l u m n s of o x y g e n v a c a n c i e s i n t h e s t r u c t u r e — t h e r e b e i n g t w o p e r u n i t c e l l i n this case.

M a n y v a r i e d images

c a l c u l a t e d w h e n m a n y thicknesses a n d defects of focus are u s e d

are (32),

b u t t h i c k e r crystals t e n d to s h o w o n l y one w h i t e spot p e r u n i t c e l l ( e.g., at 2 3 5 - A t h i c k n e s s , 1000-A u n d e r f o c u s

w i t h ionic scattering

factors).

T h i s f e a t u r e correlates w i t h t h e strings of s i x - c o o r d i n a t e d m e t a l atoms. T h e i m a g e s f o r t h i c k e r crystals d o n o t h a v e a one-to-one c o r r e l a t i o n w i t h the projected potential a n d hence cannot be considered true crystal s t r u c t u r e i m a g e s . T h e y do, h o w e v e r , h a v e the p e r i o d i c i t y a n d s y m m e t r y of t h e s t r u c t u r e a n d f o r this r e a s o n are p o w e r f u l tools i n i d e n t i f y i n g a n d c o r r e l a t i n g o b s e r v e d images. Zr Sc Oi , 3

4

2

[211]

F

Zone.

T h i s p h a s e is i s o s t r u c t u r a l w i t h

Pr Oi , 7

2

a n d f o r this r e a s o n differences i n t h e images m a y b e u s e d to i n f e r differ ences i n f o r m factors of t h e m e t a l atoms.

T h e η-beam c a l c u l a t i o n s f o r

this phase u s i n g a t o m i c s c a t t e r i n g factors are s h o w n i n F i g u r e 8. generalizations can be made.

A s i n the case for P r O i 7

2

Some

the thin crystal

images c o r r e l a t e d w e l l w i t h t h e p r o j e c t e d p o t e n t i a l ( e.g., 24r-48-A t h i c k ness, 9 0 0 - 1 0 0 0 - A u n d e r f o c u s , a t o m i c s c a t t e r i n g f a c t o r s )

(32).

T h e same


256

SOLID STATE

CHEMISTRY

CATION AND ANION SITES

^

AT RELATIVE INTERVALS

•

OF

8 [111], TO E A C H

— Δ

OTHER

COLUMNS

OF


VACANCIES

ANION

·

AND

OCTAHEDRAL

CATIONS

Figure 7. Projections of the ideal atom positions of Pr 0 down (a) the [111] axis where the line intersections, filled triangles, and empty triangles represent columns of metal and nonmetal sites at rehtive intervals of 1/12[111 ] to each other. The columns of nonmetal vacancies and six-coordinated metal atoms are indicated by filled circles and (b) the [211] axis where metal atom sites are marked with a plus sign; the nonmetal sites are marked by a multiplication sign; nonmetal vacancies are marked with a square; and filled circles again indi cate columns of six-coordinated metal atoms. M0 cubes are also outlined to facilitate interpretation. 1

1%

F

F

F

8

is t r u e except f o r a shift i n o r i g i n f o r crystals a b o u t 165 A t h i c k as observed for P r O i . 7

2

T h e images d e r i v e d u s i n g i o n i c s c a t t e r i n g factors

h a v e m o r e f r i n g e , b u t i m a g e s s h o w i n g t w o spots p e r u n i t c e l l o c c u r at 1 2 0 - 1 4 4 - A a n d 1 0 0 0 - A u n d e r f o c u s ( 3 2 ) .

I n b o t h cases t h e t h i c k e s t

crystals s h o w one spot p e r u n i t c e l l Calculated Images of P r O i , [ H 1 ] F Zone. T h e s e i m a g e s s h o w i n g 7

2

a n h e x a g o n a l a r r a y of spots at a l l thicknesses a n d defects of focus a l m o s t



14.

EYRiNG

Nonstoichiometry,

Order, and

257

Disorder

Figure 8. Calculated images of Pr 0 and Zr Scfi . The type of scattering factors and the defect of focus are shown at the bottom, while the number of slices (~ 6.75À per slice) is shown at the left. 7

lt

s

12

u n i f o r m a l l y i n d i c a t e one spot p e r u n i t c e l l , a l t h o u g h there is a n o r i g i n shift i n some cases. Observed Images of the Iota Phase Images o f R7O12 Phases, [ 2 1 1 ] Z o n e . t y p i c a l i m a g e s of P r O i 7

Figure 9(a)

w i t h o n e spot p e r u n i t c e l l .

2

and (b)

show

S u c h images are

c o m p a r a b l e to some of those c a l c u l a t e d f o r t h i c k crystals. F i g u r e s h o w s a n i m a g e of Z r S c O i 3

4

2

9(c)

i n w h i c h t w o spots p e r u n i t c e l l a p p e a r i n

Figure 9. Observed (100) crystal structure images of Pr 0 and Zr Sc A : (a) typical image of Pr O ; (b) thick-crystal image of Pr Ô , and (c) thincrystal image of Zr Sc 0 showing vacancy arrangement 7

7

7

tf

lt

7

s

4

s

12

12


4

lt


258

SOLID STATE

CHEMISTRY

Figure 10. Observed (111) images of Pr 0 and Zr Sc 0 : (a) typical image, (b) two twin orientations of Zr Sc^0 with a region of C-type oxide between 7

7

s

lt

s

4

lt

lt

t h e u p p e r r i g h t s i d e . T h i s c o u l d b e a r e a s o n a b l y t h i n c r y s t a l , e.g., 1 2 0 144 A t o c o r r e l a t e w i t h t h e c a l c u l a t e d images.

I n g e n e r a l the o b s e r v e d

i m a g e s of t h e i o t a p h a s e s h o w v a r i a t i o n s as d o the c a l c u l a t e d i m a g e s ; h o w e v e r , t h e correlations are sometimes a m b i g u o u s . Images of P r 0 7

1 2

Phases, (111)

Zone.

T h e r e is g o o d

agreement

b e t w e e n c a l c u l a t e d a n d o b s e r v e d images i n t h i s z o n e ; F i g u r e 10(a) the observed image.

c o o r d i n a t e d cations i n t h e d i r e c t i o n of the b e a m . m a y o b s e r v e t w o regions of Z r S c 0 3

of M 0 2

3

shows

T h e spots c a n b e c o r r e l a t e d w i t h c o l u m n s of s i x -

4

1 2

In Figure 10(b)

one

i n t w i n orientation w i t h an overlay

( C - t y p e ) at t h e t w i n b o u n d a r y . T h e [ 1 1 1 ] z o n e axis is c o m m o n F

t o a l l three regions. Discussion of the Iota Phase Images.

D e s p i t e its l i m i t a t i o n s this

t e c h n i q u e shows great p r o m i s e i n c o r r e l a t i n g c a l c u l a t e d a n d

observed

images

projected

even i f the point-to-point correspondence

w i t h the

p o t e n t i a l does n o t exist f o r t h e t h i c k crystals i m a g e d so far. I t is difficult i n these o x y g e n l a b i l e m a t e r i a l s t o observe t h i n crystals w i t h o u t c o m p o s i t i o n c h a n g e i n t h e v a c u u m of t h e m i c r o s c o p e u n d e r the h e a t i n g of t h e e l e c t r o n b e a m . A t t h e least a n u n a m b i g u o u s i d e n t i f i c a t i o n c a n b e m a d e o f e a c h phase, a n d the i m a g e , w h i l e n o t i n t u i t i v e l y interprétable, c a n g i v e s o m e h e l p i n s o r t i n g out t h e s t r u c t u r e since images c a l c u l a t e d f r o m w r o n g structures d o n o t agree w e l l . I n t h e case of p a s s i v e crystals, t h i n e n o u g h samples c o u l d b e u s e d t o observe images w i t h contrast a g r e e i n g w i t h t h e projected potential.


14.

EYRiNG

Nonstoichiometry,

Images of Beta, Epsilon, Observations.

Order,

and

Disorder

259

and Zeta Phases

Summerville a n d E y r i n g (55)

have continued h i g h

r e s o l u t i o n c r y s t a l s t r u c t u r e i m a g i n g of o t h e r o r d e r e d i n t e r m e d i a t e phases i n a n a t t e m p t to c l a r i f y the s t r u c t u r a l p r i n c i p l e w h i c h w o u l d e l u c i d a t e the h o m o l o g o u s series i n these

fluorite-related

materials.

T h e existence of a b i f u r c a t e d , e v e n - o d d , h o m o l o g o u s series i n t h e r a r e e a r t h oxides w a s c l e a r l y i n d i c a t e d i n e a r l i e r w o r k ( 2 9 ) . to i m a g e m e m b e r s of the e v e n g r o u p . ( P r 4 0 4 ) are s h o w n i n F i g u r e 11. 4

T h e s t r o n g spots at t h e corners of a


2

It was important

S o m e images of t h e b e t a p h a s e

Figure 11.

(100)

lt

Crystal structure images of beta


260

SOLID S T A T E

rectangle (nearly a square)

CHEMISTRY

c o r r e s p o n d to o n e u n i t c e l l i n t h i s

[211]

p r o j e c t i o n ( F i g u r e 3 ) . T h e r e is c o n s i d e r a b l e contrast w i t h i n t h e u n i t c e l l . If the W c l i n i c unit cell w i t h η =

12 s h o w n i n p r o j e c t i o n i n F i g u r e 3

were t w i n n e d along ( 1 1 0 ) , the unit c e l l actually observed w o u l d result. r

S u c h a unit cell w i t h expected

v a c a n c i e s is s h o w n i n F i g u r e 12 i n

projection. I m a g e s c a l c u l a t e d o n t h e basis of this s t r u c t u r e , except t h a t t h e m e t a l atoms a b o u t t h e v a c a n c i e s w e r e a l l o w e d to r e l a x just as t h e y d o i n i o t a p h a s e ( 3 2 ) , are s h o w n i n F i g u r e 13 f o r three thicknesses a n d a — 9 0 0 - A d e f e c t of focus.

T h e o x y g e n atoms a r e n o t s h i f t e d i n this c a l c u l a t i o n


except to r e m o v e those c o r r e s p o n d i n g to the v a c a n c i e s . T h e c a l c u l a t e d i m a g e s f o r t h i n crystals at — 9 0 0 - A defocus c o r r e s p o n d t o t h e p r o j e c t e d a n i o n v a c a n c i e s of t h e m o d e l as t h e y d i d i n the case of i o t a p h a s e ; h o w e v e r , i m a g e s f o r t h i c k e r crystals are q u i t e different. T h e o b s e r v e d i m a g e s o f F i g u r e 11 c o r r e l a t e w e l l w i t h those c a l c u l a t e d at a d e f o c u s of — 9 0 0 - A a n d at 162- a n d 2 4 3 - A t h i c k n e s s r e s p e c t i v e l y as shown.

A l l t h i n g s c o n s i d e r e d , t h e a g r e e m e n t is b e t t e r t h a n s h o u l d b e

expected.

A t least t h e PI s t r u c t u r e of F i g u r e 12 is c o m p a t i b l e w i t h the

observations. T h e t h e r m a l d e c o m p o s i t i o n t e m p e r a t u r e of m e m b e r s of t h e h o m o logous series decreases f r o m i o t a to b e t a , w h i c h is the last of the series o b s e r v e d i n P r O * except f o r P r 0 . 2

°

oxygen

vacancy

T h i s decrease

of t h e r m a l s t a b i l i t y

·

seven c o o r d i n a t e

•

eight

coordinate

cation cation

Figure 12. Diagrammatic representations of the proposed structures of the beta phase, (a) Model with symmetry P I . (b) Model with symmetry P m . Indices refer to fluorite subcell.



14.

EYRiNG

Nonstoichiometry,

Order,

and

Disorder

261

Figure 13. Calculated images of beta phase with the defect of focus and the thickness of the crystal indicated suggests t h e p o s s i b i l i t y of d i s o r d e r i n these phases. F i g u r e s 14 a n d 15 i l l u s t r a t e s u c h d i s o r d e r . I n one case t h e r e is a s h i f t i n t h e i n t e n s i t y o f c e r t a i n spots a l o n g a definite b o u n d a r y , a n d i n t h e o t h e r t h e r e is a loss of the regular pattern over one unit cell.

Figure 14. Crystal structure image from (100) , showing image variations which may correspond to domains of each of the proposed polymorphs of beta Jt



262

SOLID STATE

Figure

IS.

Figure

Crystal structure image of beta from a (100) apparent stacking faults

lt

16.

Crystal structure image from a (100)

10

CHEMISTRY

zone

zone of

showing

epsilon


14.

EYEING

Nonstoichiometry,

Order,

and

A n i m a g e of t h e e p s i l o n phase ( P r i O 0

1 8

Disorder

263

) is s h o w n i n F i g u r e 16. T h e

corners of t h e u n i t c e l l are s h a r p spots w i t h c o n s i d e r a b l e d e t a i l i n t h e contrast w i t h i n t h e u n i t c e l l . Images for this p h a s e are p r e s e n t l y b e i n g c a l c u l a t e d , b u t t h e results a r e n o t f a r e n o u g h a l o n g t o m e r i t d i s c u s s i o n . F i g u r e 17 d e p i c t s i m a g e s of z e t a phase. A t t h e t o p of t h e figure a p r o j e c t i o n of t h e be p l a n e is o b s e r v e d to b e f a i r l y r e g u l a r l y s p a c e d b u t w i t h o b v i o u s fluctuation of t h e intensities. A n i n t e r g r o w t h of i o t a a n d z e t a w i t h a repeat d i s t a n c e of b

7

&9 Is c l e a r l y d i s c e r n e d at t h e b o t t o m b u t

i n this case w i t h t h e ab p l a n e p r o j e c t e d .

T h e z e t a u n i t cells h a v e t w o

spots p e r u n i t c e l l , w h e r e a s t h e y are n o t r e s o l v e d i n i o t a . C a l c u l a t i o n s


h a v e n o t b e e n m a d e for z e t a , b u t s i n c e t w o spots p e r u n i t c e l l are seen i n t h e i m a g e s of t h e d e l t a p h a s e ( F i g u r e 5 ) , i t m a y n o t b e s u r p r i s i n g to see t h e m i n z e t a . D i s c u s s i o n o f t h e O b s e r v e d R e s u l t s . T h e i n t e r p r e t a t i o n s as set f o r w a r d here (32)

e x t e n d t h e s t r u c t u r a l m o d e l of K u n z m a n n a n d E y r i n g

Figure 17.

(211)

F

crystal structure image of the zeta phase


264 (29)

SOLID STATE

CHEMISTRY

a n d are consistent w i t h t h e v i e w t h a t i n t h e o d d m e m b e r s of the

series every n t h ( 1 3 5 )

F

p l a n e of cations is s i x - c o o r d i n a t e d , w i t h

those

i n between b e i n g a l l seven- or eight-coordinated. T h e oxygen vacancies o n e a c h s i x - c o o r d i n a t e d c a t i o n o c c u r a l o n g t h e b o d y d i a g o n a l [111] t h e c o o r d i n a t i o n c u b e at a n a n g l e of 73° to t h e ( 135 )

F

I n the e v e n m e m b e r s t w i n n i n g at t h e u n i t c e l l l e v e l a l o n g produces

puckered {135}

F

of

plane. (110)

F

planes s u c h t h a t t h e i r a v e r a g e d i r e c t i o n is

p a r a l l e l to ( 1 1 0 ) . I n the case of b e t a , f o r e x a m p l e , t h e r e are a l t e r n a t e F

segments of ( 1 3 5 )

F

and (531)

planes of s i x - c o o r d i n a t e d cations w h i c h

F

m a k e u p the &-face of the m o n o c l i n i c u n i t c e l l .

T h e s e are ( 1 0 1 )

F

on


average. Images of Phase Transformations Fluarite-Related

Binary

and Intergrowth

in

Oxide Systems

W h e n the rare e a r t h oxides w h i c h h a v e a p p r e c i a b l e o x y g e n d i s s o c i a t i o n pressures at m o d e r a t e t e m p e r a t u r e s a r e s t u d i e d i n t h e v a c u u m of t h e m i c r o s c o p e u n d e r t h e h e a t i n g of the e l e c t r o n b e a m , phase reactions are n o t o n l y possible, t h e y are i n e v i t a b l e . T h e r e f o r e , w h i l e i m a g e s of t h e o r d e r e d phases w e r e o b s e r v e d , specimens i n the act of t r a n s f o r m a t i o n were recorded.

Summerville a n d E y r i n g (32)

have observed numerous

cases, a f e w of w h i c h w i l l b e r e h e a r s e d h e r e . Diffraction Patterns. S t r e a k i n g a l o n g b* is a l w a y s o b s e r v e d i n t h e d i f f r a c t i o n p a t t e r n w h e n d i s o r d e r is o b s e r v e d i n the i m a g e .

Before the

s t r e a k i n g b e c o m e s extensive, i t is r e p l a c e d b y t h e d i f f r a c t i o n spots of t h e n e w phase.

I t is v e r y c o m m o n to find d i f f r a c t i o n patterns c o n t a i n i n g

d i f f r a c t i o n spots f r o m t w o o r m o r e phases i n t h e same z o n e i n d i c a t i n g the t o p o t a c t i c i n t e r g r o w t h of these phases.

T h e s e observations suggest t h a t

d u r i n g r e a c t i o n t h e r e is d i s o r d e r a l o n g b w h i c h is soon r e p l a c e d b y o r d e r i n this d i r e c t i o n b u t b y m o r e t h a n one phase. T h e n finally the n e w p h a s e occurs alone.

T h e s e changes i n the h o m o l o g o u s

series o c c u r w i t h a n

a d v a n c i n g front p a r a l l e l to { 1 3 5 } o r to t h e p u c k e r e d planes i f t h e r e a c t i o n F

occurs b e t w e e n e v e n m e m b e r s . C o n v e n t i o n a l d o m a i n s are

Images of Systems in Phase Reactions.

r a r e l y seen i n images of these m a t e r i a l s . A s m e n t i o n e d a b o v e a n d as s h o w n i n F i g u r e 1 8 ( a ) , a m o n g the h o m o l o g o u s series a p l a n a r r e a c t i o n f r o n t seems m o s t t y p i c a l . I n this case t h e z e t a p h a s e is d e c o m p o s i n g

to

i o t a , a n d a l t e r n a t i n g layers one u n i t c e l l w i d e suggest.the m e c h a n i s m of r e a c t i o n . O n the o t h e r h a n d , i n the Ρ Γ 0 Ι 2 - Ρ Γ 0 3 phase r e g i o n w h e r e the 7

2

structures are not so closely r e l a t e d , coherent i n t e r g r o w t h results f r o m nucleation and growth i n a more conventional w a y Figures 18(b)

a n d 19.

as i l l u s t r a t e d i n

T h e l a t t e r is of a Zr^ScyO* c o m p o s i t i o n of

^

Μ Ο ι . . T h e e d g e of the c o n v e n t i o n a l d o m a i n s are seen to b e q u i t e c l e a n β 4



14.

EYRiNG

Nonstoichiometry,

Order,

and

Figure 18. (a) Crystal structure showing intergrowth with iota, (b) ture image showing a domain of which is largely sigma

265

Disorder

image from (100) (HI)ρ Crystal struc Fr O in a crystal phase. 9

1

it

w i t h l i t t l e d i s t u r b a n c e i n the s e m i c o h e r e n t interface. I n F i g u r e 19 p e r f e c t register b e t w e e n t h e [111] d i r e c t i o n of b o t h phases is o b s e r v e d t h e Z r S c 0 i 2 substrate a n d t h e S c 0 8

4

2

3

between

i n c l u s i o n s of 70Â i n d i a m e t e r .

D i s o r d e r i n Images. T h e o c c u r r e n c e of fine scale d i s o r d e r i n i m a g e s is c o m m o n l y o b s e r v e d . A t e q u i l i b r i u m the Z r * a n d S c 4

3 +

in Zr Sc Oi 8

4

2

are

r a n d o m a n d the o x y g e n l a t t i c e is r e g u l a r . F i g u r e 20 s h o w s d i s o r d e r w h i c h m a y arise f r o m i n c o m p l e t e r a n d o m i z a t i o n of the Z r * a n d S c 4

Zr Sc Oi 3

4

2

3 +

i n the

s p e c i m e n w h i c h leads t o d i s o r d e r i n t h e o x y g e n s u b s t r u c t u r e .

I n o t h e r cases d i s o r d e r is a p p a r e n t o n a l a r g e r scale, g i v i n g a l m o s t a s u p e r s t r u c t u r e repeat p a t t e r n . F i g u r e 21 shows n o t o n l y this k i n d of d i order i n the P r O i 7

2

m a t r i x b u t also e p s i l o n a n d b e t a ( a n d p e r h a p s Φ')

i n a c r y s t a l of i o t a . T h e p e r i o d i c i t y characteristics of t h e o r d e r e d i n c l u sions c h a n g e w i t h t i m e . F i g u r e 2 2 shows t h e r e l a t i v e o r i e n t a t i o n o f t h e i n t e r g r o w n regions i n the s p e c i m e n of F i g u r e 2 1 .



266

SOLID STATE

Figure

19.

Domains

Figure 20.

of Sc O t

s

in a matrix of Zr Sc 0 images s

4

lt

Disorder evident in (111) images of 7

CHEMISTRY

as seen in

Zr Sc 0 s

k

19


(H1)

F


EYRiNG

Nonstoichiometry,

Figure 21.

Order, and

Intergrowth

in Pr O . n

tn

267

Disorder

t

[211 ]

F

zone

Figure 22. Schematic representation of the intergrowth phases shown in Figure 21


268

SOLID S T A T E

Comments on the Results of Structure Fluorite-Related (a) from

Rare Earth

Imaging

CHEMISTRY

of

Oxides

C r y s t a l s t r u c t u r e images of g o o d r e s o l u t i o n h a v e b e e n o b t a i n e d

crystals of s e v e r a l phases i n t h e h o m o l o g o u s series

of

fluorite-

r e l a t e d oxides. (b)

T h e c a l c u l a t e d images of t h i n crystals c o r r e s p o n d t o the p r o

j e c t e d p o t e n t i a l of t h e k n o w n structure. (c)

T h e o b s e r v e d images correlate w e l l w i t h those c a l c u l a t e d f o r

t h i c k crystals i n w h i c h t h e s t r u c t u r e is k n o w n . (d)

T h e t h i c k c r y s t a l images d o n o t p r o v i d e a n i n t u i t i v e l y i n t e r


prétable p i c t u r e , b u t t h e c o r r e l a t i o n of p e r i o d i c i t y a n d s y m m e t r y

affords

u n e q u i v o c a l i d e n t i f i c a t i o n of t h e phases o b s e r v e d . (e)

P h a s e reactions c a n b e f o l l o w e d i n s u b s t a n t i a l d e t a i l ; h o w e v e r ,

m o r e m u s t b e d o n e to m o d e l t h e m a c c u r a t e l y . (f)

I t w i l l b e necessary

to c o n t i n u e u s i n g c a l c u l a t e d i m a g e s

to

m i n i m i z e errors i n i n t e r p r e t a t i o n . (g)

I n systems i n w h i c h t h i n crystals m a y b e o b s e r v e d i n t u i t i v e

i n t e r p r e t a t i o n s h o u l d b e possible e v e n to t h e p o i n t of l o c a t i n g o x y g e n vacancies i n General

fluorite-related

crystals.

Comments

F l u o r i t e - r e l a t e d materials are i m p o r t a n t to n e w e n e r g y a n d storage p r o c e d u r e s .

conversion

S o m e of these are b i n a r y , others t e r n a r y , or e v e n

m o r e c o m p l e x . T h e y i n v o l v e m a n y m e t a l atoms a n d u s u a l l y o x y g e n , rine, or hydrogen.

fluo

Significant i m p r o v e m e n t i n e x i s t i n g m a t e r i a l s a n d t h e

c r e a t i o n of n e w materials are r e q u i r e d as fossil fuels, w h i c h h a v e b e e n t h e c o n v e n t i o n a l sources of energy, are d i s p l a c e d . C e n t r a l to this material's e v o l u t i o n is a k n o w l e d g e of s t r u c t u r a l details at the u n i t c e l l l e v e l .

S u c h i n f o r m a t i o n is n e e d e d t o u n d e r s t a n d t h e i r

f u n c t i o n a n d f a i l u r e a n d to d i r e c t t h e process of g e n e r a t i n g alternatives. A l t h o u g h t h e fluorite structure itself is u b i q u i t o u s a n d s i m p l e , a l m o s t a l l u s a b l e m a t e r i a l s h a v i n g structures r e l a t e d to i t h a v e e x t e n d e d defects. A r e v i e w of these o r d e r e d a n d d i s o r d e r e d

phases has b e e n

r e v e a l i n g a m u l t i t u d e of phases of fine scale c o m p o s i t i o n a l

sketched, variability

w i t h u n d o u b t e d short-range o r d e r a n d , i n a d d i t i o n , a m u l t i t u d e of o r d e r e d intermediate

phases w h i c h are often

h o m o l o g o u s series M 0 n

2 n

compositionally

m e m b e r s of

an

-2.

M a n y details of the h o m o l o g o u s series i n t h e r a r e e a r t h o x i d e s y s t e m h a v e b e e n d i s c u s s e d — p r i n c i p a l l y those aspects w h i c h h a v e b e e n d i s c o v e r e d b y m e a n s of h i g h r e s o l u t i o n e l e c t r o n o p t i c a l t e c h n i q u e s .

This

has i n c l u d e d the d e t e r m i n a t i o n of t h e u n i t cells of the h o m o l o g u e s .

The

use of c a l c u l a t i o n s to g i v e c o n f i d e n c e to i m a g e i n t e r p r e t a t i o n has b e e n


14.

EYRiNG

Nonstoichiometry,

Order and Disorder

269

d e m o n s t r a t e d . T h e images c a n t h e n b e u s e d t o s h o w r e a c t i o n patterns a n d d i s o r d e r i n phase reactions. F i n a l l y recent results o n t h e C e 0 - 2 series w e r e p r e s e n t e d to i l l u strate that e v e n i n this closely r e l a t e d o x i d e system n o t a l l t h e h o m o l o g u e s h a v e t h e same structure as those o f P r O * o r T b O * . M u c h remains to b e d o n e b e f o r e a c l e a r u n d e r s t a n d i n g o f t h e m a n i f o l d of structures w h i c h a r e c a l l e d fluorite-related is e v o k e d , b u t t h e quest w i l l b e w o r t h t h e effort. n

2 n


Acknowledgment T h e c u r r e n t s u p p o r t of t h e U . S . E n e r g y R e s e a r c h a n d D e v e l o p m e n t Administration ( a n d earlier support of the U . S . A t o m i c E n e r g y C o m m i s s i o n ) f o r that p a r t o f the w o r k d e s c r i b e d here a n d a t t r i b u t e d to t h e a u t h o r a n d his co-workers is g r a t e f u l l y a c k n o w l e d g e d .

Literature Cited 1. Duclot, M., Vicat, J., Deporter, C., J. Solid State Chem. (1970) 2, 236. 2. Carter, R. E., Roth, W. L., in "Electrochemical Force Measurements in High Temperature Systems," C. B. Alcock, Ed., pp. 125-144, Institution of Mining and Metallurgy, London, 1968. 3. Delamarre, C., Rev. Int. Hautes Temp. Refract. (1972) 9, 209. 4. Michel, D., Mater. Res. Bull. (1972) 8, 943. 5. Allpress, J. G., Rossell, H. J., Scott, H. G., Mater. Res. Bull. (1974) 9, 455. 6. Rossell, H. J., Scott, H. G., J. Solid State Chem. (1975) 13, 345. 7. Allpress, J. G., Rossell, H. J., Scott, H. G., J. Solid State Chem. (1975) 14, 264. 8. Allpress, J. G., Rossell, H. J., J. Solid State Chem. (1975) 15, 68. 9. Lefevre, J., Ann. Chem. (1963) 8, 135. 10. Collongues, R., Queipoux, F., Perez y Jorba, M., Gilles, J. C., Bull. Soc. Chim. Fr. (1965) 1141. 11. Thornber, M. R., Bevan, D. J. M., Summerville, E., J. Solid State Chem. (1970) 1, 545. 12. Thornber, M. R., Bevan, D. J. M., Graham, J., Acta Cryst. (1968) B24, 1183. 13. Thornber, M. R., Bevan, D. J. M., J. Solid State Chem. (1970) 1, 536. 14. Komissarova, L. N., Spiridinov, F. M., Dokl. Akad. Nauk SSSR (1968) 182, 834. 15. Collongues, R., Perez y Yorba, M., Lefevre, J., Bull. Soc. Chim. Fr. (1961) 70. 16. Sibieude, F., Foëx, M., J. Nucl. Mater. (1975) 56, 229. 17. Weitzel, H., Keller, C., J. Solid State Chem. (1975) 13, 136. 18. Bartram, S. F., Inorg. Chem. (1965) 5, 749. 19. Eyring, L., in "Solid State Chemistry," C. N . R. Rao, Ed., pp. 565-634, Marcel Dekker, New York, 1974. 20. Sørensen, Proc. Int. Conf. Plutonium and Other Actinides, 5th, Sept. 1975, Baden-Baden, Germany 21. Sørensen, O. T., J. Solid State Chem. (1976) 18, 217. 22. O'Keeffe, M., in "Fast Ion Transport," W. van Gool, Ed., pp. 233-247, North Holland, 1973.


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23. Chikalla, T. D., Turcotte, R. P., Natl. Bur. Stand. (U.S.) Spec. Publ. 364 (1972) 319.

24. Turcotte, R. P., Haire, R. G., private communication. 25. Turcotte, R. P., Chikalla, T. D., Eyring, L., J. Inorg. Nucl. Chem. (1971) 33, 3749.

26. McCarthy, G. J., Fischer, R. D., Johnson, G. G., Jr., Gooden, C. E., in Natl. Bur. Stand. Spec. Publ. 364 (1972) 397. 27. Ray, S. P., Cox, D. E., J. Solid State Chem. (1975) 15, 333. 28. Ray, S. P., Nowick, A. S., Cox, D. E., J. Solid State Chem. (1975) 15, 344. 29. Kunzmann, P., Eyring, L., J. Solid State Chem. (1975) 14, 229. 30. Height, T. M., Bevan, D. J. M., private communication. 31. Iijima, S., Acta Cryst. (1973) A 2 9 , 18. 32. Skarnulis, A. J., Summerville, E., Eyring, L., to be published. 33. Von Dreele, R. B., Eyring, L., Bowman, A . L., Yarnell, J. L., Acta Cryst. Downloaded by TUFTS UNIV on October 21, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch014

(1975) B 3 1 , 971.

Cowley, J. M., Moodie, A . F., Acta Cryst. (1957) 35. Summerville, E., Eyring, L., to be published.

34.

RECEIVED

July

10, 609.

27, 1976.


Nonstoichiometry, Order, and Disorder in Fluorite-Related Materials

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