Solid State Chemistry: A Contemporary Overview - American

2 Some Uses of High-Resolution Electron Microscopy in Solid State Chemistry

Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1970-0186.ch002

LEROY

EYRING

Department of Chemistry and the Center for Solid State Science, A r i z o n a State University, Tempe, A Z 85281

The

principles

to permit

of electron

an evaluation

of high-resolution ReO -related

techniques

very selectively interval

formation

are briefly

sketched

use and

limitations

to solid state chemistry.

systems have been extensively

3

the

microscopy

of the potential

reviewed

MO3 and

to

studied

and illustrated.

MO 2

are

5

destruction

of point

and

extended

of regular

and the ordering

of the latter into new phases are

These

phases

block

include

bronzes

structures

phases suited

electron

investigated. described

deficient

variable

The

representative materials

microscopy results

and illustrated,

tetragonal

and

of

for

including

the

larger

study

ordinary

class

where conventional

methods have failed, defects,

and phase

trans-

have

been

materials

structure

forms of extended

the

composition.

are

determination

new phases,

various

transformations.

O o l i d state c h e m i s t r y is c o m p r e h e n s i v e i n its c o n c e r n . ^

also

high-resolution

(HRTEM)

on these

defects observed.

of varied

5

the

defects.

with

MO3,

composition, 2

less ideally

mission

oxygen

elements

such as H-Nb O

Fluorite-related of

of

in

including

The intergrowth

tungsten

are

Compositions

described,

structural

The and

I t deals, at t h e

molecular level, w i t h composition, structure, bonding, reaction charac

teristics, a n d t h e r m o d y n a m i c p r o p e r t i e s of solids, as is t y p i c a l of c h e m i s t r y of gases a n d solutions.

the

I n a d d i t i o n , a n d i n p a r t i c u l a r , i t is

c o n c e r n e d w i t h the p r o p e r t i e s of m a t e r i a l s t h a t d e r i v e f r o m t h e i r solidness. F o r these m a t e r i a l s t h r e e - d i m e n s i o n a l s t r u c t u r e a n d s t r u c t u r a l are at the root

of

their composition

a n d properties.

The

0-8412-0472-1 /80/33-186-027$09.00/1 © 1980 American Chemical Society In Solid State Chemistry: A Contemporary Overview; Holt, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980.

defects

range

of

28

SOLID S T A T E C H E M I S T R Y :

A CONTEMPORARY

OVERVIEW

c h e m i c a l v a r i a t i o n is g r e a t l y e n l a r g e d i n t h e s o l i d state because of

the

r e l a x a t i o n of s t o i c h i o m e t r y r e q u i r e m e n t s , a n d h e n c e f r o m t h i s f a c t is d e r i v e d the p o s s i b i l i t y of i n f i n i t e c o m p o s i t i o n a l v a r i a b i l i t y a n d

aniso

t r o p i c r e a c t i o n alternatives. It w o u l d b e difficult to overestimate t h e i m p o r t a n c e of

exhaustive

s t r u c t u r a l c h a r a c t e r i z a t i o n . N o one needs to b e c o n v i n c e d of t h e v a l u e of a n X - r a y or n e u t r o n d i f f r a c t i o n i n v e s t i g a t i o n , w h i c h reveals t h e r e p e a t i n g u n i t , h e n c e the l o n g - r a n g e

o r d e r , i n c r y s t a l l i n e m a t e r i a l s — t h i s is the

b e g i n n i n g of almost a n y s t u d y .

H o w e v e r , t h e i n t i m a t e details of

the

s t r u c t u r e of r e a l solids, i n c l u d i n g t h e i r defects a n d i m p e r f e c t i o n s , g r e a t l y


influence t h e i r c h e m i c a l p r o p e r t i e s .

Classical diffraction methods

give

l i m i t e d i n f o r m a t i o n f r o m s u c h s m a l l regions of space; therefore, w e m u s t look elsewhere for a t e c h n i q u e that y i e l d s this s t r u c t u r a l i n f o r m a t i o n . M o s t chemists f e e l less at h o m e i n r e c i p r o c a l space, since t h e i r v i e w of s t r u c t u r e i n v o l v e s the s p a t i a l c o n f i g u r a t i o n of atoms d e s c r i b e d i n terms of the l e n g t h a n d d i r e c t i o n s of c h e m i c a l b o n d s or of d i s p l a c e d or m o v i n g atoms.

I n these terms the c o m p o s i t i o n , s t r u c t u r e , s t a b i l i t y , r e a c t i v i t y , or

m e c h a n i s m of r e a c t i o n are c o n c e i v e d i n terms of l i t e r a l m o d e l s of atoms i n fixed or transient p o s i t i o n s . T o the extent t h a t this is t r u e , a n i n s t r u m e n t t h a t w o u l d m a g n i f y a r e g i o n of space sufficiently a n d i n a t i m e frame c o m p a t i b l e to h u m a n o b s e r v a t i o n (so t h a t i n d i v i d u a l atoms c o u l d b e i d e n t i f i e d a n d l o c a t e d i n space a n d f o l l o w e d occur)

w o u l d be

the u l t i m a t e i n s t r u m e n t of

high-resolution electron microscope tial.

I t is o u r p u r p o s e

here

as c h e m i c a l

( H R E M ) has this a u d a c i o u s

to s k e t c h , of

changes

c h e m i c a l analysis.

necessity

The

poten

s u p e r f i c i a l l y , the

present state of these t e c h n i q u e s as t h e y are u s e d to i l l u m i n a t e s o l i d state c h e m i s t r y . T h e a d v a n t a g e of d i r e c t v i s u a l i z a t i o n of the structure of r e a l solids, i n c l u d i n g t h e i r defects,

b e c o m e s a p p a r e n t w h e n one r e v i e w s t h e t o r

turous p a t h b y w h i c h i n d i r e c t m e t h o d s y i e l d u n c e r t a i n i d e n t i f i c a t i o n of the p r i n c i p a l defects i n a n y m a t e r i a l . O n e m u s t not o v e r s e l l H R E M as a d i r e c t means of f o l l o w i n g the course of c h e m i c a l r e a c t i o n i n solids, b u t the v a l u e of b e i n g a b l e to v i s u a l i z e the types of defects a n d t h e i r j u x t a p o s i t i o n i n a n y m a t e r i a l is enormous.

T h e i m p a c t of H R E M

on

our

k n o w l e d g e of s t r u c t u r e a n d m e c h a n i s m i n s o l i d state c h e m i s t r y has b e e n profound. I t has b e e n m o r e t h a n a score of years since M e n t e r ( I )

anticipated

the e l u c i d a t i o n of s t r u c t u r e b a s e d o n l a t t i c e i m a g i n g . H i s d r e a m has b e e n realized i n large measure today w h e n two-dimensional images

capable

of p o i n t - t o - p o i n t i n t u i t i v e i n t e r p r e t a t i o n at a r e s o l u t i o n of 3.5 A or b e t t e r are b e i n g t a k e n . T h e t e c h n i q u e is flourishing b o t h i n p r a c t i c e a n d t h e o r y , e x p a n d i n g d a i l y its r a n g e of a p p l i c a t i o n to solids. W e w i l l n o w

quali

t a t i v e l y e x a m i n e the m e t h o d s of this t e c h n i q u e i n o r d e r to assess t h e i r

In Solid State Chemistry: A Contemporary Overview; Holt, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980.

2.

EYRING

High-Resolution

Electron

29

Microscopy

usefulness a n d l i m i t a t i o n s . T h i s w i l l b e f o l l o w e d b y a g l i m p s e of d i v e r s e types of studies of interest to the s o l i d state c h e m i s t . F i n a l l y , a n a t t e m p t w i l l be m a d e to see d i r e c t i o n s the field m i g h t take i n the i m m e d i a t e f u t u r e . HREM

Imaging

U n d e r 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 p o s s i b l e to i m a g e a c r y s t a l i n t w o d i m e n s i o n s w i t h a p o i n t - t o - p o i n t r e s o l u t i o n of a b o u t 2 A .

I t has

b e e n p o s s i b l e to i m a g e crystals at a r e s o l u t i o n of a b o u t 3.5 A f o r t h e past s e v e r a l years u s i n g r e l a t i v e l y i n e x p e n s i v e , c o m m e r c i a l l y a v a i l a b l e instruments.

I t is to be h o p e d t h a t w i t h i n the next d e c a d e i t w i l l


r o u t i n e to i m a g e crystals at a b o u t 1.5 A . T h i s means t h a t , w h e r e a s

be now

details of s t r u c t u r e , i n c l u d i n g defects, are r e v e a l e d m i c r o s c o p i c a l l y at t h e s u b u n i t c e l l l e v e l (say, t h e l e v e l of c o o r d i n a t i o n p o l y h e d r a ) , i t s h o u l d be p o s s i b l e to o b s e r v e solids at the a t o m i c l e v e l . C l e a r l y these a d v a n c e s i n t e c h n i q u e h a v e u n f a t h o m e d significance for s o l i d state c h e m i s t r y . F o r a t h o r o u g h d i s c u s s i o n of e l e c t r o n m i c r o s c o p e i m a g i n g of c r y s t a l structures, the b o o k " D i f f r a c t i o n P h y s i c s " b y J o h n M . C o w l e y is s u g gested ( 2 ) .

M o r e a b b r e v i a t e d sources, s u c h as C o w l e y ( 3 ) , A l l p r e s s ( 4 ) ,

A l l p r e s s a n d Sanders ( 5 ) , A l l p r e s s et a l . ( 6 ) , a n d O ' K e e f e et a l . ( 7 , 8 ) , s h o u l d b e c o n s u l t e d f o r references to the p r i m a r y l i t e r a t u r e a n d for t h e d e t a i l e d m a t h e m a t i c a l , e x p e r i m e n t a l , a n d c a l c u l a t i o n a l details of m i c r o s copic imaging. A t present, most of the w o r k b e i n g d o n e is w i t h c o n v e n t i o n a l beam high-resolution transmission electron microscopy ( H R T E M ) a t i n g at 100 k e V .

These microscopes

fixed oper

are d i r e c t analogues of o p t i c a l

m i c r o s c o p e s : p a r t i c l e s f r o m a n e l e c t r o n g u n are a c c e l e r a t e d a n d c o n c e n trated on the sample to be imaged.

T h e effective size of t h e source is

normally a few microns i n diameter

(2).

T h e r e s o l u t i o n a n d contrast of the i m a g e are l a r g e l y d e t e r m i n e d i n the i n i t i a l stage of m a g n i f i c a t i o n b y the objective lens. S p h e r i c a l a b e r r a tion, w h i c h depends beams

o n p h a s e r e t a r d a t i o n , increases v e r y r a p i d l y for

d i f f r a c t e d at i n c r e a s i n g B r a g g angles.

Lenses i n common

use

h a v e a s p h e r i c a l a b e r r a t i o n constant of 1-3 m m , l i m i t i n g t h e r e s o l u t i o n to

a few

angstroms.

This, rather than high-voltage

i n s t a b i l i t i e s , is the p r i n c i p a l l i m i t a t i o n to r e s o l u t i o n ( 2 ) .

or

lens-current

Electromagnetic

stigmators are a d j u s t e d to correct a n y a s t i g m a t i s m . E l e c t r o n m i c r o s c o p y is e n h a n c e d b e c a u s e of the ease w i t h w h i c h b o t h selected area e l e c t r o n d i f f r a c t i o n a n d a n i m a g e of the same r e g i o n of a c r y s t a l c a n b e r e c o r d e d . F i g u r e 1 illustrates b o t h m o d e s of o p e r a t i o n of

a

t y p i c a l three-lens

g e o m e t r i c optics.

m a g n i f y i n g system, u s i n g the

symbolism

of

T h e r e g i o n of t h e s p e c i m e n to b e v i e w e d is b a t h e d

b y the n e a r l y p a r a l l e l electron b e a m after i t has p a s s e d t h r o u g h t h e condenser lens system.

T h e scattered electrons f r o m the s p e c i m e n are


30

CHEMISTRY:

A CONTEMPORARY

OVERVIEW


SOLID STATE

Figure 1. The ray paths in an electron microscope used (a) to produce a high-magnification image or (b) to produce a diffraction pattern of a selected area of the specimen. focused

o n t h e b a c k f o c a l p l a n e of t h e objective

diffraction pattern.

lens to p r o d u c e t h e

T h i s is t h e first F o u r i e r t r a n s f o r m of t h e object.

T h e s e electrons interfere a g a i n i n t h e G a u s s i a n i m a g e p l a n e t o p r o d u c e a n i m a g e . T h e a m p l i t u d e d i s t r i b u t i o n i n t h e i m a g e is a F o u r i e r t r a n s f o r m of that i n t h e b a c k f o c a l p l a n e . T h e f o c a l l e n g t h of the i n t e r m e d i a t e lens m a y b e c h a n g e d

[as i n

F i g u r e 1 ( b ) ] so t h a t i n s t e a d of t h e i m a g e p l a n e t h e b a c k f o c a l p l a n e of


2.

EYRING

High-Resolution

Electron

Microscopy

31

the objective is i m a g e d at t h e object p l a n e of the p r o j e c t o r lens, w h e r e it m a y b e v i e w e d o n a

fluorescent

screen or p h o t o g r a p h e d .

A s m a l l a p e r t u r e p l a c e d i n ' t h e i m a g e p l a n e of the o b j e c t i v e lens w i l l select o n l y p a r t of the i m a g e to b e m a g n i f i e d .

S i n c e a s w i t c h i n the

i n t e r m e d i a t e lens w i l l not c h a n g e the area selected i n the a p e r t u r e , t h e d i f f r a c t i o n p a t t e r n p r o d u c e d i n the d i f f r a c t i o n m o d e w i l l represent o n l y the selected area. T h i s selected area e l e c t r o n d i f f r a c t i o n c a p a b i l i t y is of i m m e n s e i m p o r t a n c e , e s p e c i a l l y w i t h c r y s t a l l i n e specimens, since i t p e r mits c o r r e l a t i o n of the d i f f r a c t i o n p a t t e r n w i t h the same r e g i o n of contrast o b s e r v e d i n the i m a g e .

T h e m i n i m u m area selected is l i m i t e d b y

the


s p h e r i c a l a b e r r a t i o n of the lens to regions a b o u t 0.5 / m i i n d i a m e t e r at 100 k e V . T h e Formation of the Image.

A s indicated above, the image

is

f o r m e d b y interference of the e l e c t r o n beams i n the i m a g e p l a n e of the objective

lens.

A n objective

a p e r t u r e is u s e d to select the

beams t h a t w i l l b e u s e d to f o r m the i m a g e . for t w o f u n d a m e n t a l reasons.

diffracted

T h e a p e r t u r e is i m p o r t a n t

F i r s t , because the p h a s e r e t a r d a t i o n of a

d i f f r a c t e d b e a m varies as t h e f o u r t h p o w e r of the a n g l e of t r a v e r s a l of the lens ( 5 ) , i t is advanatgeous to l i m i t the beams to those scattered at l o w e r angles. S e c o n d , since there is a finite r e s o l u t i o n of the

microscope,

contrast is i m p r o v e d i f those beams are r e m o v e d that are f r o m i n t e r p l a n a r spacings less t h a n the r e s o l u t i o n of the m i c r o s c o p e

and hence w o u l d

s i m p l y c o n t r i b u t e to t h e b a c k g r o u n d . If o n l y one d i f f r a c t e d b e a m is i n c l u d e d w i t h the d i r e c t b e a m , i n t e r ference w i l l

produce

s i m p l y a set of

fringes, w h i c h u n d e r

suitable

c o n d i t i o n s w i l l c o r r e s p o n d to the set of p l a n e s i n r e a l space that g i v e rise to the d i f f r a c t i o n spot.

M o r e often, m a n y beams are u s e d w i t h the

d i r e c t b e a m to f o r m a b r i g h t - f i e l d , t w o - d i m e n s i o n a l i m a g e ( 2 ) .

I n some

instances i t m a y b e d e s i r e d to e x c l u d e the d i r e c t b e a m a n d o b t a i n a n i m a g e o n l y f r o m interference of the d i f f r a c t e d beams p r o d u c i n g a d a r k field i m a g e . I n this case a h i g h e r r e s o l u t i o n has b e e n o b s e r v e d Other Experimental Conditions.

(9).

I t is necessary t o r e d u c e c o n t a m i

n a t i o n of t h e s p e c i m e n as m u c h as possible.

T h i s is a c c o m p l i s h e d

by

p r o v i d i n g surfaces c o o l e d to l i q u i d n i t r o g e n t e m p e r a t u r e s i n t h e v i c i n i t y of the s p e c i m e n .

I n some cases i t is necessary to i m p r o v e the v a c u u m ,

a n d this a u t o m a t i c a l l y reduces the rate of c o n t a m i n a t i o n . I n o r d e r to h a v e images t h a t c a n b e i n t e r p r e t e d i n t u i t i v e l y , i t is necessary to h a v e specimens less t h a n 100 A t h i c k . T h i s is a c c o m p l i s h e d i n a n y of several w a y s . sputtered

films.

M e t a l s m a y b e p r e p a r e d i n t h i n , e v a p o r a t e d , or

B r i t t l e , n o n m e t a l l i c specimens

grinding—sometimes

may

be

prepared

at l i q u i d n i t r o g e n t e m p e r a t u r e s — p r o d u c i n g

by

frag

ments t h i n e n o u g h to b e i m a g e d . I n a n y case, i o n t h i n n i n g m a y b e u s e d , a n d i f the s t r u c t u r a l features of interest are not affected b y this t r e a t m e n t , s u i t a b l y t h i n specimens m a y b e o b t a i n e d .


32


The

specimens

are s u p p o r t e d

A CONTEMPORARY

OVERVIEW

frequently on holey carbon

grids,

w h e r e a t h i n e d g e of s u i t a b l e characteristics is f o u n d p r o j e c t i n g o v e r a h o l e i n the s u p p o r t

film.

F o r h i g h - r e s o l u t i o n i m a g i n g of crystals i t is necessary

to h a v e a

d o u b l e - t i l t i n g s p e c i m e n h o l d e r that c a n o r i e n t the c r y s t a l a l o n g a n y of s e v e r a l z o n e axes as d e s i r e d . I n o r d e r to h a v e g o o d contrast i n a n i m a g e w h i c h is also i n t e r p r e t a b l e , t h e c o r r e c t a p e r t u r e a n d thinness of c r y s t a l m u s t be c o m b i n e d w i t h a c a r e f u l l y a d j u s t e d focus. 900 A

(10).

U s u a l l y this r e q u i r e s a n u n d e r f o c u s

Absorption produces

of

about

n o contrast i n the G a u s s i a n i m a g e


p l a n e i f the a p e r t u r e is u n r e s t r i c t e d ( 5 ) . T h e Calculation of Images.

I n o r d e r for H R T E M to b e u s e f u l i n

the d e t e r m i n a t i o n of s t r u c t u r e , the images p r o d u c e d , w h i c h are a n a r r a y of l i g h t a n d d a r k spots, m u s t b e i n t e r p r e t a b l e i n terms of the t y p e a n d l o c a t i o n of t h e atoms i n the s p e c i m e n . be a two-dimensional projection

I d e a l l y the i m a g e w o u l d s i m p l y

of the a t o m i c a r r a n g e m e n t , e n a b l i n g

t h e contrast to be i n t e r p r e t e d i n t u i t i v e l y ( F i g u r e 2 ) .

U n d e r carefully

c o n t r o l l e d c o n d i t i o n s of s p e c i m e n a n d m i c r o s c o p e , this has b e e n to b e possible

found

(10).

S a t i s f y i n g a l l these c o n d i t i o n s is m o r e l i m i t i n g t h a n is d e s i r a b l e , a n d one w o u l d l i k e to b e a b l e to use i m a g e contrast w h e r e these stringent r e q u i r e m e n t s are not f u l l y met.

S u c h images are n o t i n t e r p r e t a b l e w i t h

confidence i n terms of a t o m positions unless t h e y c a n b e s h o w n to agree w i t h c a l c u l a t e d images over a range of c o n d i t i o n s (8). necessary to c a l c u l a t e images that c o r r e s p o n d

T h e r e f o r e , i t is

to t h e orientations a n d

thicknesses of t h e s p e c i m e n of k n o w n or p o s t u l a t e d s t r u c t u r e a n d c o m p a r e these w i t h those o b s e r v e d .

I n o r d e r to m a k e t h e c a l c u l a t i o n s the

c o n d i t i o n s of focus of the m i c r o s c o p e the b e a m d i v e r g e n c e , m u s t b e k n o w n (8).

m u s t h a v e specified v a l u e s , a n d

a p e r t u r e size, a n d s p h e r i c a l a b e r r a t i o n constant E v e n i f the details of s t r u c t u r e c a n n o t b e

deter

m i n e d w i t h assurance, the characteristics of the i m a g e a l l o w 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 w i t h a p a r t i c u l a r phase.

F o r most c h e m i c a l studies this

i n f o r m a t i o n is e n o u g h , a n d i t c a n n o t be o b t a i n e d i n other w a y s . C o m p u t e r packages n o w h a v e b e e n d e v e l o p e d

that enable

image

c a l c u l a t i o n s to b e m a d e b a s e d o n n - b e a m m u l t i s l i c e d y n a m i c a l t h e o r y (8,11).

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

o b s e r v e d images, as w i l l b e i l l u s t r a t e d b e l o w . High-Voltage H R T E M .

T h e o p t i m u m r e s o l u t i o n of a

microscope

is g i v e n b y t h e e q u a t i o n d = 0.6A

3 / 4

C

B

1 / 4

w h e r e d is t h e h a l f - w i d t h of t h e s p r e a d f u n c t i o n , A is t h e w a v e l e n g t h of the electron, a n d C

8

is the s p h e r i c a l a b e r r a t i o n coefficient

(2,3).


Good,


2.

EYRING

High-Resolution

Electron

33

Microscopy

Figure 2. A print by M . C. Escher showing about one and a half unit cells. Light and dark patches are intuitively interpretable in terms of the elements of the structure. Even out of focus, the relative distances and symmetries are preserved. The more perverse will find satisfaction in viewing it upside down (31). stable, h i g h - v o l t a g e supplies n o w c a n b e m a d e a n d u s e d w i t h v e r y stable lens c u r r e n t s , so t h a t i t s h o u l d b e p o s s i b l e to increase t h e r e s o l u t i o n b y d e c r e a s i n g A, t h a t is, b y g o i n g to h i g h - v o l t a g e electrons. A t 500 k e V one expects to o b t a i n 1.7 A p o i n t - t o - p o i n t r e s o l u t i o n . T h e r e are s e v e r a l a d v a n t a g e s to u s i n g h i g h - v o l t a g e m i c r o s c o p e s s u c h as t h e a b i l i t y to s t u d y specimens t h r e e or f o u r t i m e s as t h i c k w i t h t h e same ease of i n t e r p r e t a t i o n as i n 1 0 0 - k e V m a c h i n e s .

Contrast w i l l

be

e n h a n c e d b y a f a c t o r of t w o or three, w i t h t h e same c l a r i t y a n d w i t h less damage

d u e to i n e l a s t i c s c a t t e r i n g .

T h e p r i n c i p a l advantage for

the

c h e m i s t , h o w e v e r , w i l l b e t h e p o s s i b i l i t y of fitting c o n t r o l l e d a t m o s p h e r e s p e c i m e n stages i n t h e m u c h l a r g e r m i c r o s c o p e lens c h a n n e l s . T h e m o r e p e n e t r a t i n g e l e c t r o n b e a m w i l l b e less affected b y the t h i n gaseous e n v i r o n m e n t p r o v i d e d for the s p e c i m e n at e q u i l i b r i u m . A r e s o l u t i o n of atoms


34

SOLID STATE C H E M I S T R Y :

A CONTEMPORARY

OVERVIEW

conjures u p the n o t i m p o s s i b l e feat of o b s e r v i n g t h e t r a n s p o r t of atoms i n crystals. T h i s s h o u l d also a d v a n c e t h e c a p a b i l i t y of d e t e r m i n i n g s t r u c t u r e b y direct imaging. T h e results of 1 - M e V m i c r o s c o p e

studies of several m a t e r i a l s a n d

t h e i n s t r u m e n t itself h a v e b e e n d e s c r i b e d b y H o r i u c h i a n d h i s c o - w o r k e r s T h e r e s o l u t i o n i m p r o v e m e n t over 1 0 0 - k e V i n s t r u m e n t s is

(12,13,14). dramatic.

W i t h a 2 - A r e s o l u t i o n , one c a n v i r t u a l l y resolve t h e

atoms

at t h e t e t r a h e d r a l sites b e t w e e n the crossed shear planes i n t h e

block

structure N b i 0 9 . H o w e v e r , these i n s t r u m e n t s are e x t r e m e l y 2

2

a n d w i l l r e q u i r e a great d e a l of d e v e l o p m e n t

expensive

b e f o r e t h e y b e c o m e as


p r a c t i c a l l y u s e f u l as the 1 0 0 - k e V i n s t r u m e n t s .

Applications

of HRTEM

to Solid State

Chemistry

T h e d e v e l o p m e n t of the field of e l e c t r o n m i c r o s c o p y is of

enormous

significance to t h e s o l i d state chemist. I t is a m a z i n g to c o n t e m p l a t e t h a t a l l t h e h i g h - r e s o l u t i o n studies ever m a d e h a v e e x a m i n e d o n l y a b o u t mm

2

1

of s p e c i m e n area w i t h a mass of a b o u t 0.2 fig of m a t e r i a l . T h e r e is

a l o t m o r e to b e seen! E v e n w i t h t h i s s m a l l mass, studies h a v e i n c l u d e d t h e o b s e r v a t i o n of u l t r a s t r u c t u r e a n d defects i n a great v a r i e t y of m i n e r a l specimens ( 1 5 ) , c a r b o n i n m a n y f o r m s i n c l u d i n g d i a m o n d , g r a p h i t e , a n d e v e n s i n g l e - a t o m - t h i c k sheets (16), n o n c r y s t a l l i n e i n o r g a n i c solids

a n d a w i d e r a n g e of c r y s t a l l i n e a n d

(17).

W e w i l l discuss h e r e o n l y t w o types of studies o n c r y s t a l l i n e oxides. T h e first i n c l u d e s e x a m i n a t i o n o f m a n y s t r u c t u r a l types a n d defects i n R e 0 - b a s e d crystals ( m o s t w o r k has b e e n d o n e o n these almost i d e a l l y 3

s u i t e d m a t e r i a l s ) a n d t h e s e c o n d i n c l u d e s studies of the

fluorite-related

b i n a r y r a r e e a r t h oxides to i l l u s t r a t e the v a l u e of t h e t e c h n i q u e i n a m o r e o r d i n a r y b u t less w e l l s u i t e d c r y s t a l t y p e . Structures Based on the R e 0 tallographic Shear.

The R e 0

3

3

Structure T y p e — R e g i o n of C r y s -

s t r u c t u r e is one of t h e easiest to v i s u a l i z e .

I t consists of m e t a l atoms o c t a h e d r a l l y c o o r d i n a t e d w i t h o x y g e n in w h i c h a l l corners of the c o o r d i n a t i o n o c t a h e d r a are s h a r e d i n t h r e e d i r e c t i o n s . T h i s c u b i c n e t w o r k has t h e same a p p e a r a n c e p r o j e c t e d a l o n g a n y of the p r i n c i p a l axes—that

is, m e t a l - f i l l e d o c t a h e d r a

i n square outline

with

alternate squares u n f i l l e d i n a c h e c k e r b o a r d f a s h i o n . T h e u n f i l l e d squares are elements of square t u n n e l s i n a l l t h r e e d i r e c t i o n s . T h e u n i t cells of these r e l a t e d structures are one c o o r d i n a t i o n o c t a h e d r o n t h i c k 4.8 A )

(about

a n d f r e q u e n t l y q u i t e l a r g e i n t h e other d i r e c t i o n s ; h e n c e t h e y

are almost i d e a l subjects f o r h i g h - r e s o l u t i o n s t u d y . T h e i n v e s t i g a t i o n s w e w i l l discuss i n v o l v e r e d u c e d W 0 containing M o or N b .

N b is t h e m o s t c o m m o n

reduced materials investigated.

3

sometimes

metal i n the highly

T h e oxides n e a r M 0

3

in

composition


2.

EYRING

High-Resolution

Electron

h a v e defects c a l l e d c r y s t a l l o g r a p h i c shear ( C S ) . composition

35

Microscopy

T h o s e of i n t e r m e d i a t e

h a v e defects i n v o l v i n g o c t a h e d r a t h a t h a v e s h e a r e d i n a

c y l i n d r i c a l f a s h i o n , p r o v i d i n g p e n t a g o n a l t u n n e l s a l o n g the axis of shear. The

most

reduced

oxides

are s h e a r e d

i n two

directions.

A l l these

materials preserve the o c t a h e d r a l c o o r d i n a t i o n of the m e t a l atoms

by

i n c r e a s i n g edge s h a r i n g of the c o o r d i n a t i o n o c t a h e d r a as t h e m e t a l - t o o x y g e n r a t i o is i n c r e a s e d b y r e d u c t i o n . CS in W 0 Figures 3(b)

has b e e n s t u d i e d b y I i j i m a

3

and 3(c).

Figure 3(b)

(18)

a n d is i d e a l i z e d i n

shows a p r o j e c t i o n of R e 0

the c-axis. I m a g i n e r e m o v a l of a l l oxygens i n a (210)

3

along

plane and closing


the s t r u c t u r e to r e g a i n the same o x y g e n s t r u c t u r e b y a s h e a r i n g a c t i o n 1/2

[110].

S u c h a n o p e r a t i o n is r e p r e s e n t e d b y

is the c r e a t i o n of a W a d s l e y defect ( 1 9 ) . m i c r o g r a p h of

such a Wadsley

defect

(210) 1 / 2 [ 1 1 0 ] .

This

F i g u r e 3a is a h i g h r e s o l u t i o n (18).

T h e m a i n features

are

u n m i s t a k a b l e even t h o u g h the r e a l e d g e - s h a r i n g o c t a h e d r a are consider ably distorted.

I i j i m a f o u n d that u n d e r o t h e r t h a n o p t i m u m i m a g i n g

c o n d i t i o n s , the d e t a i l is not so e v i d e n t .

N e v e r t h e l e s s , t h e defects

are

easily r e c o g n i z e d , a n d t h e i r f o r m a t i o n a n d d e p l o y m e n t i n this s t r u c t u r e can be observed.

Figure 3. (a) High-resolution electron micrograph of a WO _s crystal obtained with the electron beam incident parallel to the c-axis. A prominent feature of the contrast shows the (210) CS plane, across which square arrays of the dark dots (indicating W atom positions) are shifted. The contrast distributions are in good accordance with the idealized model of the (210) CS plane (b). However, the image showed that edge-sharing octahedra (shaded) are considerably distorted, so that the distance X of (c) is much larger than in the ideal model (18). s



36

SOLID S T A T E

CHEMISTRY:

A CONTEMPORARY

OVERVIEW

Figure 4. (a) Oscillatory dark and light contrast bands running parallel to the CS plane on both sides, (b) With further electron beam irradiation, new CS planes develop with the same periodicity as that of the oscillatory contrast in (a) (18). There

is

a

clear

premonitory

behavior

before

develop d u r i n g electron irradiation [ F i g u r e 4 ( a ) ] .

the

C S

planes

T h i s manifests itself

as w a v e s of c o n t r a s t v a r i a t i o n of a r e g u l a r s p a c i n g , w h i c h t h e n d e v e l o p into

[Figure 4 ( b ) ] .

This

a p p e a r a n c e of l i n e a r p a r a l l e l lines of b l o t c h e s of c o n t r a s t a l o n g t h e

C S defects

p a r a l l e l to

a n o r i g i n a l defect

[102]

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

These

d a r k strain fields d i s a p p e a r w h e n t h e shear occurs.

A s W a d s l e y defects

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

purge

themselves o f k i n k s , w h i c h a p p e a r f r e q u e n t l y i n t h e e a r l y stages. T h i s b e h a v i o r is consistent w i t h a g g r e g a t i o n of o x y g e n v a c a n c i e s o n a disk, surrounded b y partial dislocations, w h i c h can expand a n d m o v e l o n g i t u d i n a l l y as suggested b y A n d e r s o n a n d H y d e Iijima observed only (210) a n d (210)

(20).

C S planes i n material reduced

at 1 0 2 2 ° C . T h e r e w e r e n o p l a n e s o b s e r v e d i n t h e [010]

zone.

O n the

o t h e r h a n d , d u r i n g e l e c t r o n b e a m h e a t i n g , C S occurs o n ( 2 0 1 ) a n d ( 2 0 1 ) . T h i s a n i s o t r o p i c b e h a v i o r is c o n s i d e r e d to be d u e to t h e d i s t o r t i o n of monoclinic W 0

3

structures f r o m t h e c u b i c R e 0 . 3

T h e d i s t o r t i o n is a

f u n c t i o n of t e m p e r a t u r e , as are t h e p r e f e r r e d d i r e c t i o n s of shear.

I n no

case w e r e ( 1 0 2 ) p l a n e s p r e f e r r e d . T H E REGION O F T H E TETRAGONAL TUNGSTEN BRONZE T Y P E OF STRUC

TURES.

I i j i m a a n d A l l p r e s s (21,22)

a n d defects i n W 0

3

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

structures

c o n t a i n i n g p e n t a v a l e n t cations ( N b ) i n c o n s i d e r a b l e

concentration, together w i t h the concomitant oxygen

deficiency.


2.

EYRING

High-Resolution

Electron

37

Microscopy

I n these structures, as i n R e 0 , o n l y c o r n e r s h a r i n g of c o o r d i n a t i o n 3

o c t a h e d r a occurs, b u t c o l u m n s of f o u r o r m o r e strings of o c t a h e d r a shear c y l i n d r i c a l l y a l o n g c s u c h t h a t w h e n c o r n e r s h a r i n g is r e e s t a b l i s h e d , triangular a n d pentagonal tunnels have been created along the periphery of the shear surface. T h e t u n n e l s c a n b e filled b y strings of — N b — O — N b — i n o r d e r e d w a y s to generate a v a r i e t y of superstructures. F i g u r e 5 illustrates 4Nb 0 2

5

these

•9W0

3

phenomena and 2 N b O 2

s

i n tetragonal

tungsten

bronze

(TTB),

• 7W0 . 3

T h e v a r i o u s T T B - l i k e elements m a y o c c u r i n d i v i d u a l l y as e x t e n d e d defects, b e o r d e r e d i n t o a definite s t r u c t u r e , o r b e i n t e r g r o w n w i t h t h e Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1970-0186.ch002

W0

3

m a t r i x to a c c o m m o d a t e a n y c o m p o s i t i o n . T h i s is o b s e r v e d as c l e a r l y

s h o w n i n F i g u r e 6, w h e r e regions of 4 N b 0 2

5

• 9W0

3

are s e p a r a t e d b y -

Acta Crystallographica

Figure 5. Structural elements encountered in the binary system Nb^Og • WO . Each hatched square represents an M0 octahedron, which shares its corner oxygen atoms with neighboring octahedra to form a lattice of composition MO . (a) The cubic ReO. structure, (b) The host lattice of the tetragonal tungsten bronze (TTB). (c) The structure of 4Nb O • 9WO contains three TTB subcells, and the superlattice is a consequence of the ordered occupation of one-third of the pentagonal tunnels by -O-M-O-M-Ostrings parallel to c (filled circles) (21). s

6

s

2

s


s


38

SOLID S T A T E

CHEMISTRY:

A CONTEMPORARY

OVERVIEW

Figure 6. (a) Lattice image from a crystal of 4Nb 0 • 9WO containing a zigzag, out-of~phase boundary (marked with arrows). Rectangles outline the unit cells of the ordered structure, and circles within the boundary mark TTB subcells in which all four pentagonal tunnels are empty. The presence of the boundary causes a displacement of 1/3 [010] in the ordered structure, (b) Model of the boundary structure, derived from the contrast in (a). The host lattice of the corner-shared octahedra is continuous, but the pattern of occupied tunnels (full circles) is interrupted at the boundary (21). 2

a

zigzag,

out-of-phase boundary.

5

T h e correlation

s

between the

thin

c r y s t a l i m a g e contrast a n d the structure is c l e a r l y s h o w n . I t has b e e n p o s s i b l e f r o m these studies to e x p l o r e the c o m p o s i t i o n l i m i t s of e a c h p h a s e b y o b s e r v i n g d i r e c t l y the o c c u p a n c y of t h e tunnels w h e n p h a s e s e p a r a t i o n o c c u r r e d . I t has b e e n p o s s i b l e to see a v a r i e t y of i n t e r g r o w t h p a t t e r n s , a n d i t has b e e n p o s s i b l e to d e t e r m i n e n e w structures by direct observation. The Block Structures.

I f t h e o x y g e n d e f i c i e n c y is f u r t h e r i n c r e a s e d

b y c o n t i n u e d increase of N b

5 +

ions, the R e 0 - r e l a t e d structures s w i t c h 3

once m o r e i n t o a different r e g i m e , i n t h i s case t h e c r y s t a l l o g r a p h i c shear c h a r a c t e r i s t i c of t h e m o d e r a t e l y r e d u c e d W 0

3

occurs i n t w o directions


2.

EYRING

High-Resolution

Electron

to g i v e infinite c o l u m n s of R e 0

3

39

Microscopy

s t r u c t u r e of s m a l l d i m e n s i o n s i n t w o

d i r e c t i o n s s h i f t e d w i t h respect to e a c h other a l o n g the c o l u m n s u c h t h a t e d g e s h a r i n g occurs at t h e i r b o u n d a r i e s . Figure 7

(23)

gives a sqhematic r e p r e s e n t a t i o n of

b l o c k s t r u c t u r e of the p o l y m o r p h H - N b 0 2

5

the idealized

b o t h as a p r o j e c t i o n of e d g e -

a n d c o r n e r - s h a r i n g o c t a h e d r a a n d as a n abstract r e p r e s e n t a t i o n s h o w i n g o n l y t h e b l o c k s a n d the c o l u m n s of t e t r a h e d r a l l y c o o r d i n a t e d N b atoms. N o t i c e that 3 X 4 X

o c t a h e d r a l c o l u m n s are r e g u l a r l y i n t e r s p e r s e d w i t h 3

4 c o l u m n s s h e a r e d a n d s h i f t e d one-half a n o c t a h e d r a l distance

to

p e r m i t edge s h a r i n g . I n F i g u r e 8 ( 2 3 ) a t h i n c r y s t a l , w h i c h is p r i m a r i l y of t h e H - N b 0 Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1970-0186.ch002

2

structure, is i n t e r r u p t e d b y a f a u l t i n w h i c h t w o 3 X 4

5

c o l u m n s are

i n t e r g r o w n . T h i s is s i m i l a r to a s t a c k i n g f a u l t of layers of atoms.

Notice

that t h e a p p a r e n t r e d u c t i o n r e s u l t i n g i n i n c r e a s e d edge s h a r i n g has b e e n a c c o m m o d a t e d i n a most i n g e n i o u s w a y , p r e s e r v i n g the o c t a h e d r a l c o o r d i n a t i o n o f most of the m e t a l atoms.

Acta Crystallographica

Figure 7. (a) Idealized model of the structure of H-Nb 0 and (b) its simple representation. The darker and lighter squares, which form 3 X 5 and 3X4 blocks by their corner sharing, are centered about the two levels perpendicular to the b-axis and are 1.9 A apart. The black circles represent the tetrahedrally coordinated Nb atoms. The unit cell is outlined (a = 21.2, b = 3.8, c = 19.4Aandp = 120°) (23). 2

5



Figure

8.

Two-dimensional

2

s

lattice image of H-Nb O showing defects parallel to the c-axis. Inset corresponds to the enclosed area (23).


o w

Hi

o 2

O

3

w K H

a

n

C/J

o r e

2.

EYRING

High-Resolution

Electron

41

Microscopy

T h e studies so f a r i l l u s t r a t e d h a v e e s t a b l i s h e d that w h e n a s u i t a b l e c r y s t a l is v i e w e d i n a h i g h - r e s o l u t i o n m i c r o s c o p e

w i t h the appropriate

o r i e n t a t i o n a n d w i t h t h e correct a d j u s t m e n t o f t h e e l e c t r o n optics a n d p h y s i c a l c h o i c e o f reflections, a n i m a g e is o b t a i n e d that c a n b e i n t e r p r e t e d i n t u i t i v e l y i n terms of t h e t w o - d i m e n s i o n a l p r o j e c t e d crystal.

potential of the

F u r t h e r m o r e , this h i g h - r e s o l u t i o n i m a g e reveals defects

when

t h e y o c c u r b e y o n d t h e p o i n t - t o - p o i n t r e s o l u t i o n , w h i c h is u s u a l l y 3.5 A or better i n m i c r o s c o p e s p r e s e n t l y a v a i l a b l e . B e y o n d t h e r a t h e r t w o - d i m e n s i o n a l defects just d i s c u s s e d , i t h a s


b e e n p o s s i b l e to observe p o i n t defects i n some o f these b l o c k structures. S u c h defects h a v e b e e n d e s c r i b e d , f o r e x a m p l e , b y I i j i m a et a l .

(24).

I n F i g u r e 9 ( a ) a p o i n t defect is c l e a r l y s h o w n i n t h e 3 X 4

block

structure of N b i 0 9 , w h e r e a w h i t e spot i n d i c a t i n g o n e of t h e square 2

2

tunnels is r e p l a c e d b y a b l a c k spot, r e s u l t i n g f r o m a shift i n t h e a t o m i c positions.

F i g u r e 9 ( b ) gives t h e i r i n t e r p r e t a t i o n o f t h e a n a t o m y of t h e

d e f e c t — t w o d i s p l a c e d i n t e r s t i t i a l m e t a l atoms a n d t w o excess atoms.

oxygen

F i g u r e 9 ( c ) shows t h e locations of t h e d i s p l a c e d m e t a l atoms i n

t h e p e r f e c t s t r u c t u r e , s u g g e s t i n g t h a t t h e defects c o u l d b e a n n e a l e d o u t ( o r p r o d u c e d i n r a r e cases) b y h e a t i n g w i t h t h e e l e c t r o n b e a m .

That

this is t r u e is i l l u s t r a t e d i n F i g u r e 10, w h e r e i n the s e q u e n c e ( a ) , ( b ) , (c),

defects a p p e a r a n d , m o r e often, d i s a p p e a r as a f u n c t i o n o f t i m e

i r r a d i a t e d i n the e l e c t r o n b e a m .

STATES O F AMERICA

T h e p o i n t defects a r e t h o u g h t t o b e d u e t o o n l y a f e w atoms a n d n o t to a f e w c o l u m n s of atoms.

F u r t h e r m o r e , t h e defects c o u l d b e a s c r i b e d

Figure 9a. Enlarged image of the black spot appearing in Figure 10(c). The position of the spot corresponds to one of the 2X3 channels in a block (24).


42

A CONTEMPORARY

OVERVIEW



Figure

9c.

Perfect structure corresponding

to the one in Figure

9b


(24)

2.

EYRING

High-Resolution

Electron

43

Microscopy

A s has b e e n p o i n t e d o u t ,

H R T E M on Fluorite-Related Structures.

H R T E M t e c h n i q u e s are best a p p l i e d to crystals w h o s e i n t e r e s t i n g s t r u c t u r a l r e l a t i o n s h i p s are s h o w n i n p r o j e c t i o n w h e n v i e w e d a l o n g a v e r y short axis. T h i s is true b o t h i n t h e o r y a n d p r a c t i c e . T h e systems of R e 0 3

r e l a t e d structures d i s c u s s e d so f a r a r e n e a r l y i d e a l i n this respect, a n d t h e y h a v e r e v e a l e d t h e i n t i m a t e details of t h e i r s t r u c t u r a l r e l a t i o n s h i p s a n d i m p e r f e c t i o n s i n a 'shameless w a y . W e n o w demonstrate t h e use of H R T E M o n a m o r e c o m m o n t y p e of s t r u c t u r e , w h i c h does n o t h a v e a v e r y short axis i n one d i r e c t i o n w i t h l a r g e d i m e n s i o n s i n t h e o t h e r t w o a n d h e n c e strains t h e assumptions o f t h e present c a l c u l a t i o n a l a b i l i t i e s


and

t h e c a p a b i l i t i e s of t h e m i c r o s c o p e .

F o r this p u r p o s e

w o r k d o n e o n t h e r a r e ejirth oxides, w h i c h are T h e structures of i n t e r m e d i a t e phases

fluorite-related

i n the

we review systems.

fluorite-related

rare

e a r t h oxides h a d b e e n s t u d i e d b y c o n v e n t i o n a l d i f f r a c t i o n means a n d b y i n d i r e c t means, s u c h as e l e c t r i c a l c o n d u c t i v i t y a n d t h e pressure d e p e n d ence of c o m p o s i t i o n , for m a n y years w i t h o u t a p p r o a c h i n g a satisfactory u n d e r s t a n d i n g o f t h e s t r u c t u r a l basis of t h e h o m o l o g o u s series of i n t e r m e d i a t e phases.

F o r a n u n d e r s t a n d i n g of t h e c h e m i s t r y of a n y m a t e r i a l ,

the s t r u c t u r a l p r i n c i p l e r e l a t i n g d i s t i n c t phases a n d t h e n a t u r e of t h e

Figure

10. (a,b,c) Series of pictures taken at several-minute intervals, showing the effect of electron irradiation on the black spots (24)



44

SOLID

STATE

CHEMISTRY:

A CONTEMPORARY

OVERVIEW

12

t 10

12'

t Journal of Solid State Chemistry

Figure 11. Projections of the unit cells of the fluorite-related homologous series of the rare earth oxides along the common a-axis, [211 ] . Notice that the unit cell of monoclinic 12 is obtained by twinning the primitive 12 about (110) and that 12' is formed when 12 is further twinned about (Oil). The monoclinic unit cell of 10 is formed analogously to 12' from the primitive 10. The monoclinic unit cells all have a common ac plane, different from that common to the primitive unit cells (26). F


EYRING

High-Resolution

Electron

Microscopy

45


2.

Figure 12. Calculated n-beam crystal structure images for the (100) zone of PryOtg. Calculations were made with atomic-scattering factors (6X6 unit cells). Notice that the image at 27-A thickness and 900-A underfocus is a projection of the actual arrangement of two columns of oxygen vacancies per unit cell. A similar image recurs at about 135-A thickness. The other most prevalent image has one spot per unit cell and, although unequivocably recognizable, does not correspond to the projected potential (11). 7


In Solid State Chemistry: A Contemporary Overview; Holt, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980. 7

J2

12

7

7

Figure 13. Observed (100) image of Pr 0 spot per unit cell, (b) A thick image of Pr 0 . cancy arrangement 3

4

12

3

k

12

7

12

and Zr Sc 0 . (a) A typical image of Pr 0 with one (c) A thin-crystal image of Zr Sc 0 , showing the vaon the right-hand side (11).


EYRiNG

High-Resolution

Electron

Microscopy


pq

a. 3.3

*s ο s

8-fill

II




48

Figure

A CONTEMPORARY

OVERVIEW

15. Observed (100) image of Pr 0 . Inset shows the correspondence of the image to that calculated for a thin crystal (28). 9

9

16

i s o l a t e d defects i n v o l v e d i n a n y associated delineated.

S u s t a i n e d efforts

to

get

chemical change must

this i n f o r m a t i o n h a d

been

be only

m a r g i n a l l y successful before H R T E M w a s a p p l i e d . T H E INTERMEDIATE PHASES.

C o m p o s i t i o n a l l y , the h i g h e r oxides

of

the rare earths ( C e , P r , a n d T b ) h a d b e e n s h o w n to b e l o n g to a h o m o l o g o u s series R 0 N

4 < Ce 0 4

n < 6

2 n

- 2 , w i t h R m e a n i n g rare e a r t h , a n d n a n integer,

oo ( n =

and P r 0 4

fluorite-related,

4 , 7 , 9 , 1 0 , 1 1 , 1 2 , oo k n o w n ) .

E x c e p t for h e x a g o n a l

( h i g h t e m p e r a t u r e ) , a l l the phases w e r e k n o w n to b e

6

but

determination

of

t h e i r t r u e u n i t cells h a d

been

i m p o s s i b l e . T h e p r o b l e m s t e m m e d m a i n l y f r o m t h e difficulty i n g r o w i n g single crystals of

s u i t a b l e size a n d p e r f e c t i o n

without

unmanageable


In Solid State Chemistry: A Contemporary Overview; Holt, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980. tl

2

Figure 16. Calculated n-beam crystal structure images of the proposed model of delta-phase Tb O 0' The image at a thickness of 26 A at 900-A underfocus corresponds to the projected potential of the proposed structure (28).



50

SOLID S T A T E

CHEMISTRY:

A CONTEMPORARY

OVERVIEW

Figure 17. Observed image of Tb O . There are clearly two spots per unit cell corresponding closely to the proposed structure (inset is calculated thin-crystal image) (28). lt

twinning.

20

T h e e l e c t r o n m i c r o s c o p e is q u i t e c a p a b l e of e x a m i n i n g t h i n

crystals 1 y? i n area, w h i c h are t y p i c a l l y u n t w i n n e d a n d q u i t e s u i t a b l e for observation. A s t u d y o f a l l t h e t h e n - k n o w n phases i n the P r O ^ a n d TbOa- systems w e r e m a d e b y K u n z m a n n a n d E y r i n g (26), niques.

using electron optical tech

T h i s s t u d y r e v e a l e d the u n i t cells of a l l t h e e s t a b l i s h e d phases

a n d suggested a s t r u c t u r a l p r i n c i p l e for the o d d m e m b e r s of t h e series. T h e researchers f o u n d that i f the crystals w e r e v i e w e d d o w n t h e i r a-axis ( i n the ( 2 1 1 ) z o n e , w h e r e F stands f o r fluorite i n d i c e s ) , t h e y e x h i b i t e d F

a r e g u l a r l y v a r y i n g p r o j e c t i o n p r o f i l e , as i l l u s t r a t e d i n F i g u r e 11. i n d i c a t e s t h a t t h e a-axis is c o m m o n to a l l t h e h o m o l o g o u s

This

series, a n d i n

t h a t l i m i t e d sense i t is t h e largest fluorite d e f e c t feature t h a t a l l phases have i n common. F u r t h e r e x a m i n a t i o n reveals, h o w e v e r , that t h e series is d i c h o t o m o u s w i t h the o d d - n g r o u p c h a r a c t e r i z e d b y a c o m m o n

ac p l a n e a n d t h e

e v e n m e m b e r s also w i t h a c o m m o n b u t different ac p l a n e . T h a t i s , t h e o d d m e m b e r s also h a v e a c-axis i n c o m m o n , a n d t h e e v e n m e m b e r s a c o m m o n b u t different c-axis. I n d e e d , t h e e v e n m e m b e r s are f o r m e d b y


2.

EYRING

High-Resolution

Electron

Microscopy

51

.4

(a)


ir''' °

oxygtn

(b)

i " ' '

•

tlx-coordlnate

vacancy

•

tcvon-coordlnata

cation

• tiaht-coordlnatt

cation cation

Figure 18. Projection in (211) of two possible structures of Pr tO (n = 12). (a) Model with PI symmetry, (b) Model with Pm symmetry (29). F

2

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

(and shown i n

F i g u r e 1 1 ) , at the u n i t c e l l l e v e l , g i v i n g a f o l d e d defect feature folds are r e l a t e d to t h e ac p l a n e s of the o d d m e m b e r s .

u

whose

T h i s ac p l a n e is

c h a r a c t e r i z e d b y h a v i n g a l l the m e t a l atoms i t contains six- ( r a t h e r t h a n s e v e n - or e i g h t - ) c o o r d i n a t e d w i t h the t w o v a c a n t o x y g e n p o s i t i o n s across t h e b o d y d i a g o n a l of t h e i r 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 ac plane.

T h e r e f o r e , the largest feature i n c o m m o n

to a l l t h e phases is

this ac p l a n e , w h i c h , i n the e v e n m e m b e r s , is f o l d e d i n a z i g z a g w a y .

Figure 19. Crystal structure image in (211) of a thin crystal of Pr p The inset is a calculated image from the PI structural mole, Figure 18 (29). F


2}

w

In Solid State Chemistry: A Contemporary Overview; Holt, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980. 2k

hk9

n

kk

Figure 20. Calculated image for Tb O a polymorph of Fr O . Notice the shift in the rows of undulating oxygen vacancy pairs in the images at a thickness of 26 A and a 900-A underfocus with respect to the inset of Figure 19 (28).


2.

EYRING

High-Resolution

T h e s t r u c t u r e of P r O i 7

of n e u t r o n p o w d e r

Electron

53

Microscopy

has b e e n d e t e r m i n e d b y t o t a l profile analysis

2

diffraction data.

T h i s has s e r v e d as t h e basis

p r e d i c t i o n of m e t a l a t o m shifts i n t h e t r i a l structures F r o m observed

a n d c a l c u l a t e d h i g h - r e s o l u t i o n i m a g e s , i t has

p o s s i b l e to d e t e r m i n e structures f o r t h e o d d m e m b e r s Tbu0 o

(PrnO

2

unit cell). 12-17.

T h e calculated and observed 7

9

6

Pr Oi , 7

been

Pr Oi ,

2

9

6

is o b s e r v e d to h a v e a q u i t e different a n d v e r y l a r g e

2 0

T h e s t u d y of P r O i

t h a t of P r O i

of

(27).

2

images are g i v e n i n F i g u r e s

w a s d o n e b y S k a r n u l i s et a l . ( I I ) ,

while

was made by Tuenge and E y r i n g (28), a n d T b n O

studied b y K u n z m a n n and E y r i n g (26)

2 0

and Tuenge and E y r i n g

was (28).

I n t h e case of P r O i , w h o s e s t r u c t u r e is k n o w n ( 2 7 ) , t h e r e s o l u t i o n of Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1970-0186.ch002

7

the microscope

2

is not q u i t e sufficient to separate t h e r o w s of

spots t h a t are c a l c u l a t e d for t h i n crystals a n d t h a t r e c u r at thicknesses.

vacancy greater

T h e s e r o w s of v a c a n c i e s are c l e a r l y r e s o l v e d , h o w e v e r , i n

t h e h i g h e r m e m b e r s , a n d t h e r e is satisfactory a g r e e m e n t b e t w e e n c a l c u -

Figure

21.

Observed crystal structure image of Tb fi , Figure 20 (28) 2

u

calculated


in

54

SOLID S T A T E C H E M I S T R Y : A C O N T E M P O R A R Y

OVERVIEW

Weight c h a n g e , mg 30


20

1.50

40

1.65

50

1.70

60

1.75

70

80

90

1.95

1.80

Composition, x in PrO

2.00

x

Figure 22. Phase diagram of the PrO -0 system. Prominent features are the homologous series R 0 -2> 4 < n < oo, and two nonstoichiometric phases a and 7 h a v e v e r y s i m i l a r d e f e c t structures,

d i f f e r i n g o n l y b y the s p a c i n g of p l a n a r d e f e c t features, yet the i s o m o r p h i n the t h r e e series is R O i . 7

2

F o r e x a m p l e , for n =

only

12 t h e

one p o l y m o r p h seen so far i n the PrO^. system is different f r o m a n y of the three or m o r e seen i n the T b O ^ system.


H R T E M in the Study of Phase Reactions.

I t is c l e a r b y n o w t h a t

H R T E M c a n b e u s e d to get s t r u c t u r a l i n f o r m a t i o n o n a v a r i e t y of phases. I n this case the s p e c i m e n a n d m i c r o s c o p e c o n d i t i o n s m u s t b e k n o w n a n d controlled very carefully.

I n m a n y other

cases,

however,

where

structures are k n o w n , u n k n o w n , or i m m a t e r i a l , the phases, phase

the rela

t i o n s h i p s , a n d the i n t e r g r o w t h characteristics are c l e a r l y i d e n t i f i a b l e b y the c e l l p a r a m e t e r s or s y m m e t r y characteristics, w h i c h are r e v e a l e d

by

t h e i n t e n s i t y d i s t r i b u t i o n i n the i m a g e b u t w h i c h do not c o r r e s p o n d

to

the a r r a y of the c h a r g e d e n s i t y of the c r y s t a l . It is p r o b a b l e t h a t the c o n t r i b u t i o n of H R T E M to s o l i d state c h e m i s t r y w i l l be greatest i n these

Figure 23. Image of Zr Sc O in the (1H)F zone. Notice domains of the n = 4 phase about 70 A across imbedded in a matrix of an n = 7 phase. The large hexagonal pattern is due to an overlay of the two phases in perfect register. 029

0m71

lm6Ji


56

CHEMISTRY:

A CONTEMPORARY

OVERVIEW


SOLID S T A T E

Figure 24. Image of intergrowths of members of the homologous series, (a) Lattice image from (100) , showing intergrowth with iota. Domains of n = 4 with n = 7 phase. Notice the thinness of the interface between these phases of different structures, (b) (lll)p lattice image, showing a domain of Pr 0 in a crystal that is largely sigma phase. An intimate intergrowth between n = 7 and n = 9 phases. These phases are perfectly coherent, having the same ac planes at the interface and differing only in the width of the slab—in this case, one unit cell wide for a few cycles (32). 9

9

12



11

20

x

n

F

2n 2

Figure 25. An image of multiple-phased TbO down [211 ] . The specimen was prepared by reduction of Tb O in the microscope. Integers indicate n in Tb 0 . for cell projections in the various parts. Strain fields are apparent in the n = 7, n = 11 phase interface (28).



58

SOLID S T A T E

CHEMISTRY:

A CONTEMPORARY

OVERVIEW

Figure 26. An image of inter grown slabs of n = 12 and n = 11 phases in highly oxidized TbO . In this projection the body diagonal of n = I I is the same length as the edge of n = 12, permitting almost perfect coherence (28). x

latter cases w h e r e r e a c t i o n i n f o r m a t i o n , i f n o t s t r u c t u r a l i n f o r m a t i o n , is g i v e n d i r e c t l y . C h e m i c a l r e a c t i o n i n the s o l i d state is a c c o m p a n i e d b y the r e d i s t r i b u t i o n of m a t e r i a l , a n d this is r e c o r d e d d i r e c t l y b y H R T E M . T h e use of H R T E M to g i v e i n f o r m a t i o n a b o u t t h e i n d i v i d u a l defects i n solids, w h i c h are t h e agents of c h e m i c a l c h a n g e , h a v e b e e n r e p e a t e d l y m e n t i o n e d i n t h e p a r a g r a p h s a b o v e w h e r e t h e R E 0 - r e l a t e d structures 3

w e r e d i s c u s s e d . W e close o u r d i s c u s s i o n w i t h some examples of crystals of t h e

fluorite-related

materials undergoing change.

T h e p h a s e d i a g r a m of the P r O ^ system is s h o w n i n F i g u r e 22.

Of

interest h e r e are i m a g e s of t r a n s f o r m a t i o n events i n t h e t w o - p h a s e d


Microscopy

59

regions. I n F i g u r e 23 the i n t e r g r o w t h of t h e n =

4 a n d n ^= 7 phases

2.

EYRING

High-Resolution

Electron

i n the r e l a t e d system Zr^ScyOs are o b s e r v e d i n t h e ( l l l ) p z o n e ; w e h e r e t h e p e r f e c t t o p o t a x i a l r e l a t i o n s h i p a n d the coherence phases.

T h e r e is a m a t r i x of R O i 7

2

see

of t h e t w o

i n w h i c h d o m a i n s of R 0 4

of

6

about

7 0 - A d i a m e t e r are d i s p e r s e d . T h e s e t w o phases are different e n o u g h i n s t r u c t u r e t h a t t h e y d o n o t seem to i n t e r g r o w at t h e u n i t c e l l l e v e l . M i c r o g r a p h s of p u r e PrOa. i n this c o m p o s i t i o n r e g i o n are s i m i l a r {see

Figure

24(b)]. In Figure 24(a)

the i n t e r g r o w t h of the n =

7 and n =

9 phases

I n these cases t h e structures are v e r y s i m i l a r , d i f f e r i n g o n l y


is o b s e r v e d .

Figure 27. Sequential images from a (211)p zone, showing nucleation and growth of sheets of n = 7 into ann = 9 phase of PrO . Time between images about 2 min (30). x


60

SOLID S T A T E C H E M I S T R Y : A C O N T E M P O R A R Y O V E R V I E W

b y a small variance i n the

fc-axis,

and have

i n t e r g r o w t h of

variable

thickness across t h e c o m m o n ac planes. I m a g e s r e s e m b l e structures w i t h f r e q u e n t s t a c k i n g faults. T h e a l t e r n a t i n g of n =

7 and n =

9, one u n i t

c e l l t h i c k , c a n b e r e a d i l y d i s c e r n e d for a short distance. I n the T b O a . - 0 n =

7 and n =

t w o phases. n =

2

system, t h e p r i n c i p l e t w o - p h a s e r e g i o n is b e t w e e n

11. F i g u r e 25 shows a r e g i o n of i n t e r g r o w t h of

these

B e t w e e n lines of g o o d register, one c a n observe 11 r o w s of

7 a n d 7 r o w s of n =

11, w i t h t h e r e g i o n b e t w e e n c l e a r l y m a r k e d

b y d a r k s t r a i n fields. F i g u r e 26 shows a r e g i o n of i n t e r g r o w t h of n = and n =

11, w h e r e the p r o j e c t e d b o d y d i a g o n a l of n =


e d g e of n =

12

11 equals t h e c e l l

12.

I n c e r t a i n cases c h e m i c a l c h a n g e c a n b e f o l l o w e d h i g h r e s o l u t i o n . F i g u r e 27 ( 3 0 ) a few minutes apart (the

exposure

d e c o m p o s i t i o n of a c r y s t a l of n = a n d r a p i d g r o w t h of t h e n =

as i t o c c u r s at

gives a sequence of images t a k e n o n l y t i m e is a b o u t 7 sec)

d u r i n g the

9, s h o w i n g d r a m a t i c a l l y the n u c l e a t i o n 7 p h a s e o c c u r r i n g a l o n g the ac

plane.

T h e r e is m u c h s l o w e r g r o w t h a l o n g b.

Conclusion T h e t e c h n i q u e a n d use of H R T E M i n b r o a d studies of the m o r e o r less i d e a l s t r u c t u r a l systems, b a s e d u p o n the R e 0

3

s t r u c t u r e , has b e e n

i l l u s t r a t e d . I n this case i n d i v i d u a l e x t e n d e d a n d p o i n t defects h a v e b e e n seen i n s p l e n d i d d e t a i l , i n c l u d i n g f o r m a t i o n a n d d e s t r u c t i o n ; regions

of

coherent i n t e r g r o w t h of c o m p o n e n t parts h a v e b e e n o b s e r v e d at the l e v e l of r e s o l u t i o n of c o o r d i n a t i o n o c t a h e d r a ; a n d the i n d i v i d u a l phases

have

b e e n d i s p l a y e d w i t h images f a i t h f u l to the c h a r g e d e n s i t y p r o j e c t i o n

to

a r e s o l u t i o n of 3.5 A . I n some cases n e w structures h a v e b e e n d i r e c t l y indicated. I n a d d i t i o n , s i m i l a r studies of a n o r d i n a r y system n o t so i d e a l l y s u i t e d to H R T E M , the f l u o r i t e - r e l a t e d system, h a v e b e e n d e s c r i b e d .

In

this case w e n o t e that the best s t r u c t u r a l i n f o r m a t i o n a v a i l a b l e f o r t h e i n t e r m e d i a t e phases is o b t a i n e d b y d i r e c t o b s e r v a t i o n of i m a g e contrast. A l s o , the details of p h a s e reactions are s h o w n t o b e r e v e a l e d d i r e c t l y b y H R T E M images. I n this case, too, n e w phases are o b s e r v e d a n d c h a r a c t e r i z e d for t h e first t i m e . C o m p u t e r packages

for t h e c a l c u l a t i o n of i m a g e s are a v a i l a b l e t o

m a k e m o n i t o r i n g of results possible, a n d m i c r o s c o p e s are b e i n g i m p r o v e d and

invented.

There should be a bright future for the application of

this t e c h n i q u e to the s t u d y of s o l i d state p r o b l e m s .

The number

cases s t u d i e d so f a r is m i n i s c u l e c o m p a r e d to the o b v i o u s a p p l i c a t i o n s .


of

2.

EYRING

High-Resolution

Electron

Microscopy

61

Glossary of Symbols H R T E M = high-resolution transmission electron microscopy H R E M = high-resolution electron microscope d = h a l f w i d t h of the s p r e a d f u n c t i o n A = w a v e l e n g t h of the e l e c t r o n C

s

=

s p h e r i c a l a b e r r a t i o n coefficient

k e V = volts X 10" MeV = =


[uvw]

3

volts X 10"

6

i n d i c e s of a d i r e c t i o n i n the d i r e c t l a t t i c e ( z o n e a x i s )

(uvw)

= i n d i c e s of a " f o r m " of z o n e axis

(hid)

=

CS = a, b c = y

n =

i n d i c e s of a set of p a r a l l e l planes c r y s t a l l o g r a p h i c shear u n i t - c e l l vectors a n i n t e g e r m a r k i n g a m e m b e r of a h o m o l o g o u s series

R = rare earth element

i= R 0 , n = 7 £= R 0 , n— 9 €

_

R

7

1 2

9

1 6

1 0

O

8= R O u

1 8

2 0

, n =

10

, n — 11

P = Ri 022, n = 12 2

Literature

Cited

1. Menter, J. W. Proc. R. Soc. London, Ser. A 1956, 236, 119. 2. Cowley, J . M. "Diffraction Physics"; N o r t h - H o l l a n d : Amsterdam, 1975; Chapters 13, 17, 18. 3. Cowley, J. M. Annu. Rev. Phys. Chem. 1978, 29, 251. 4. Allpress, J. A. Nat. Bur. Stand. (U.S.) Spec. Publ. 1972, 364, 87. 5. Allpress, J. A.; Sanders, J. V. J. Appl. Crystallogr. 1973, 6, 165. 6. Allpress, J. A.; H e w a t , E. A.; Moodie, A . F.; Sanders, J. V. Acta Crystallogr., Sect. A 1972, 28, 528. 7. O'Keefe, M. A. Acta Crystallogr., Sect. A 1973, 29, 322. 8. O'Keefe, M. A.; Buseck, P. R.; Iijima, S. Nature 1978, 274, 322. 9. Pierce, L.; Buseck, P. R. Science 1974, 186, 1209. 10. Iijima, S. J. Appl. Phys. 1971, 42, 5891. 11. Skarnulis, A . J.; Summerville, E.; E y r i n g , L. J. Solid State Chem. 1978. 23, 59. 12. H o r i u c h i ; S.; Matsui, Y.; Bando, Y . Jpn. J. Appl. Phys. 1976, 15, 2483. 13. H o r i u c h i , S.; K i k u c h i , T . ; Goto, M. Acta Crystallogr., Sect. A 1977, 33, 701. 14. H o r i u c h i , S.; Matsui, Y . ; Bando, Y . ; Sekikawa, Y . ; Sakaguchi, K . Proc. Intern. Conf. High-Voltage Microscopy, 5th, Kyoto, 1977. 15. V e b l e n , D. R.; Buseck, P . R.; B u r n h a m , C . W . Science 1977, 198, 359. 16. M i l l w a r d , G . R.; Jefferson, D . A.; Thomas, J. M. J. Microscopy 1978, 113, 1. 17. Cowley, J. M. Annu. Rev. Mater. Sci. 1976, 6, 53. 18. Iijima, S. J. Solid State Chem. 1975, 14, 52. 19. Andersson, S. " T h e Chemistry of Extended Defects in Nonmetallic Solids"; E y r i n g , L.; O'Keeffe, M., E d s . ; N o r t h - H o l l a n d : Amsterdam, 1970.


62 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.


30. 31. 32.


A CONTEMPORARY

OVERVIEW

Anderson, J. S.; H y d e , B . G . J. Phys. Chem. Solids 1967, 28, 1393. Iijima, S.; Allpress, J . A. Acta Crystallogr., Sect. A 1974, 30, 22. I b i d . , 29. Iijima, S. Acta Crystallogr., Sect. A 1973, 29, 18. Iijima, S.; K i m u r a , S.; Goto, M. Acta Crystallogr., Sect. A 1973, 29, 632. Skarnulis, A. J.; Iijima, S.; Cowley, J . M. Acta Crystallogr., Sect. A 1976, 32, 799. K u n z m a n n , P . ; E y r i n g , L. J. Solid State Chem. 1975, 14, 229. V o n Dreele, R. B.; E y r i n g , L.; B o w m a n , A. L.; Yarnell, J. L. Acta Crystallogr., Sect. B 1975, 31, 971. Tuenge, R. T.; E y r i n g , L. J. Solid State Chem. 1979, 29, 165. Summerville, E.; Tuenge, R. T . ; E y r i n g , L. J. Solid State Chem. 1978, 24, 21. Inaba, H.; Lin, S. H.; E y r i n g , L., unpublished data. Escher, M. C . Eight Heads; Escher Foundation, Haags Gemeentemuseum: T h e H a g u e , Grauenhage, Denmark. Goodenough, J . B.; W h i t t i n g h a m , M. S., E d s . I n " S o l i d State Chemistry of Energy Conversion and Storage," Adv. Chem. Ser. 1977, 163.

RECEIVED

September 18, 1978.


Solid State Chemistry: A Contemporary Overview - American

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