The domain structure of β-In2S3 “single crystals” due to the ordering of indium vacancies

Mat. Res. Bull. Vol. 3, pp. 519-528, 1968. in the United States.

THE DOMAIN

STRUCTURE

P e r g a m o n P r e s s , Inc.

OF B-In2S 3 "SINGLE CRYSTALS"

DUE TO THE

a)

ORDERING

Printed

OF INDIUM VACANCIES

J. Van Landuyt I), H. Hatwell 2), S. Amelinckx I)3) i) Rijksuniversitair Centrum Antwerpen (Belgium) :2) Union Carbide European Research Associates SA Brussels (Belgium) 13) S.C.K. - C . E . N . Mol (Belgium).

(Received April 29, 1968; Communicated by S. Amelinckx) ABSTRACT In2S 3 h a s a defective spinel structure. The indium ions in tetrahedral interstices disorder at 420 ° C whereas the indium ions in octahedral interstices disorder at 780 ° C. The order-disorder process is observed in the electron microscope and different types of interfaces resulting from the ordering of indium ions (or indium vacancies) are studied. It was possible to identify twins and anti-phase boundaries due to the ordering of tetrahedral indium ions and anti-phase boundaries resulting from the ordering of octahedral indium ions.

The Klinger

structure

the symbol

nated)

spinel

(In(4),[])

interstices,

structure. dral

8-In2S 3 has been determined

(i) and refined by Rooymans

It is a defective hedral

of

(2) and King

structure which are occupied

The indium ions occupy

(six-coordinated)as

(3).

can be represented

In(6)S3 where [] represents which

by Hahn and

vacant

in the normal

tetraspinel

as well part of the octahe-

part of the tetrahedral

(four-coordi-

interstices.

a) Work performed under the auspices S.C.K. - R.U.C.A.

519

by

of the Association

520

DOMAIN STRUCTURE OF ;3-1n2S 3

As a result of the stoichiometry which would be occupied be expressed by saying tice of tetrahedral vacancies

interstices

along rows which

As a result of the ordering tains in fact [001]

direction

The structure fying the stacking tinguish

two

Doublet

hedral

symbol

the

coinciding with

layers.

One can dis-

of two successive

hereafter. indium ions only.

(capital

latin letters

represent

i.

of the octahedral

One fourth of the

remains

unfilled;

denotes

a particular

rent repartition Mixed doublet tetrahedral

we therefore fraction

re-

indium in octa-

layers

interstices

Yi where

of all

the index

the y - positions between

the diffe-

spinel only

1/4

as well octahedral

The stacking

symbol

latin letters interstices).

are occupied.

This

is shown

different

symbols

dral indium ions.

top down)

sites in a

in each doublet

schematically

layers

Even in the

layer and only 1/4 of the tetrahedral (top up,

as

for these

denote

of the octahedral

of each kind two

note

containing

indium ions.

(iii)

octahedral

possibilities.

of indium ions in tetrahedral complete

indium ions is shown

differentiates

is of the type BceibC(small

where

spinel,

coordination.

fig.

given

the

spinel.

consisting

letters

and at the same time

(ii)

lattice

(iii)

is AYiB

greek

The arrangement in

lost;

The unit cell con-

filled with octahedral

sulfur,

is

can most simply be described by speci-

called doublets

The stacking

to the

(2).

the normal

of the basic

in successive

layers

present

of

kinds of lamella

sulfur layers, (i)

c/~ = 3.

of the tetragonal

one of the cube directions

are parallel

the cubic symmetry

three unit cells

can

structure.Th~9~

{iii} planes

tetragonal with

This

are present in the lat-

of the spinel

sulfur rows in the

crystal becomes

spinel (with composi-

in the In2S 3 structure.

that vacancies

are ordered

close packed

not all interstices

in the complete

tion In3S4)can be occupied

Vol. 3, No. 6

sites layer

in fig.

2

are used for the tetrahe-

Vol. 3, No. 6

DOMAIN STRUCTURE OF fi-In2S 3

521

J /

O:

pp~ @

m

FIG.

1

M

FIG.

2

i) O c t a h e d r a l d o u b l e t layers in In2S ~ structure. a) Two c l o s e - p a c k e d (S)-layers ar~ shown with the indium ions in o c t a h e d r a l position. One quarter of the a v a i l a b l e sites is vacant. b) Cut p e r p e n d i c u l a r to the (iii) - planes as v i e w e d along a [112] direction. c) Symbols.

2) M i x e d d o u b l e t layer. a) One c l o s e - p a c k e d (S) layer is shown, t o g e t h e r with the ind i u m ions in o c t a h e d r a l an t e t r a ~ e d r a l position. 43- of the o c t a h e d r a l sites are v a c a n t and ~ of the available tetrah e d r a l sltes are vacant. For the t e t r a h e d r a l sites, only the v a c a n c i e s with respect to the normal spinel structure are m a r k e d (by an open circle). b) Cut p e r p e n d i c u l a r to the (iii) - planes, as seen along a [112] direction. The two s u l f u r - l a y e r s limiting the m i x e d d o u b l e t layer are illustrated. Here the layers of top-up and top-down t e t r a h e d r a l sites can be clearly d i s t i n g u i shed. c) Symbols.

522

DOMAnW STRUCTURE OF ~-Ln2S3

Vol. 3, No. 6

If one takes into account the presence of the unmixed doublet layers, the occupancy of the tetrahedral sites per layer 1 becomes ~ for each kind. In the defective

spinel In2S 3 the tetrahedral interstices marked 2 1 1 by a small empty circle remain vacant reducing to ~ . ~ = ~-~ the fraction of tetrahedral

interstices occupied in each layer. The 1 3 1 1 2 total fraction of indium ions is then ~(~ + ~)+ 2 . ~ = ~ which

corresponds to the stoichiometry of In2S 3.

It is clear that one

can now consider rows of tetrahedral vacancies parallel to the close packed direction of the sulfur matrix.

From fig. 2 it

also follows that the rows of tetrahedral vacancies in the mixed layer are constituted alternatively of vacant sites with the top of the tetrahedron up, respectively down. are not equidistant.

The complete

Consequently the rows

structure now consists of an

alternating stacking of octahedral and mixed the way schematized by the stacking symbol

doublet layers

in

(the asterisk at the

small letters indicates a different repartition of the vacancies) Ay%B c ~% b C 8% A b~ 7% a B ~% C a i B% c 2 / A 7% B ... This stacking sequence is illustrated in fig. 3.

S

B

S

C

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

FIG. 3 Stacking sequence perpendicular to the close packed planes illustrating the terminology used.

Vol. 3, No. 6

DOMAIN STRUCTURE OF fl-In2S 3

It w a s

shown

(4) by m e a n s of o b s e r v a t i o n s

light that the lattice

of t e t r a h e d r a l

some k i n d of "melting",

i.e.

disordering

with

second t r a n s i t i o n

the d i s o r d e r i n g

at 420 ° C, w h e r e a s

was

to e l u c i d a t e

lattice

microscopic

in detail

of i n d i u m ions

close p a c k e d

from

hedral

resulting f r o m the

in a r i g i d m a t r i x of face

the structure

Interfaces

that one can c o n s i d e r

due to the f i l l i n g

(or to the o r d e r i n g

dral i n t e r s t i c e s

in b o t h

of

doublet

Since only 1/2 of the o c t a h e d r a l in the o c t a h e d r a l se b o u n d a r i e s

hedral

inter-

of v a c a n c i e s ) .

the a r r a n g e m e n t

of o c t a h e -

layers

is n o t ex-

twinning

interstices.

interstices

are f i l l e d ( 3 / 4

layer and 1/4 in the m i x e d

layer)antipha-

are p o s s i b l e

is shown

however.One

schematically

antiphase

boundaries

the d i s o r d e r i n g

temperature

ling of the t e t r a h e d r a l

of the

in fig.

i n d i u m ions are n o t taken

that these

of octa-

of t e t r a h e d r a l

as a r e s u l t of the filling of o c t a h e d r a l

bilities

centered

due to mistakes in the filling

In view of the s y m m e t r y

above

of the indium sub-

interstices.

stices

pected

r e p o r t e d here

of interfaces.

(i) I n t e r f a c e s

(ii)

structure

The pur-

sulfur.

It is clear two c l a s s e s

observations

point

associated

i n d i u m ions.

the d i s o r d e r i n g

and to study the domain

ordering

The m e l t i n g

is p r e s u m a b l y

of the o c t a h e d r a l

pose of the e l e c t r o n

in p o l a r i z e d

i n d i u m ions u n d e r g o e s

a second t r a n s i t i o n w a s n o t e d at 750 ° C. is iiO0 ° C. T h i s

523

several

4a w h e r e

into account. would

remain

of 420 ° C

interstices

with

possi-

the tetraIt is clear

in place even where

the fil-

indium becomes

at

random. The f i l l i n g rise

of the t e t r a h e d r a l

to the f o r m a t i o n

can

give

of two types of interfaces.

(a) If the rows of i n d i u m v a c a n c i e s rent close p a c k e d d i r e c t i o n s twins result.

interstices

of the sulfur

This was already

(3) w h o also o b s e r v e d

are p a r a l l e l

the twins

to d i f f e sublattice

n o t e d by H a t w e l l in p o l a r i z e d

et al

light.

524

DOMAIN STRUCTURE OF fl-In2S 3

Vol. 3, No. 6

(b) If the rows occupied by vacancies and hence also these occupied by tetrahedral

indium are out of step different ty-

pes of anti-phase boundaries now parallel, An example

are formed.

but displaced on both

is shown in fig.

4b.

interfaces can be identified

The lattices are

sides of the boundary.

These different types of

in the

electron

microscope

using the following criteria.

o

0

,d d ,, 0" ,"d / O' •d o

o

,"

/'

o

,

o

/

o

~

o

0

o

o

,'

o

d

,,"

o

,"

o

o

d o' o o ,, d o,,

/,

o

,"

0

/

o 0 (a)

o

d

oo

•

o~,.

0 o, , /

Q

O/• • 0¢."0 d o,'

0 ,"0

/o

•

o/o

0 •

."

0

¢

•

O P ,'O ¢~

o"

."0

o,'

•

,

~'

•

O'Oo

0,','

•

, , 0 • 0 A,,R .'-~----~"

q," o 0,o.

o

, ,"0" •

'o

o

.

0.,'o 0 , ~,.,"0 ,

0," 0 ~--w=;--~ " ~

•

,,

•

0,. O°,'"O°O, ' 0 ~ • ,' •

qm

o

,'

o

0

•

o

•

o

(b)

FIG.

4a, b

a) Anti-phase boundary(APB) in the octahedral sublattice. The arrangement of the octahedral indiums in a mixed doublet layer was used to illustrate the defect. The tetrahedral ions have been omit~d for clarity reasons. b) A n t i - p h a s e b o u n d a r y (APB) in the sublattice due to the cations in tetrahedral sites. Notice how the sublattice due to the cations in octahedral sites remains continuous across the APB. For anti-phase b o u n d a r i e s

the contrast should remain

the

same accross the boundary for any orientation of the foil, whereas

for twin b o u n d a r i e s

the contrast is different on both

sides for most reflections.

Also the diffraction pattern will

be the same on both sides of anti-phase b o u n d a r i e s , b u t same foil orientation twin boundary.

it will be different on both

f o r t he

sides of a

Vol. 3, No. 6

DOMAIN STRUCTURE OF ~-In2S 3

The two types of a n t i - p h a s e shed by o b s e r v i n g certain

the

the t e m p e r a t u r e

anti-phase

rature w h e r e

ordering

boundaries

the twins b e c o m e

structure

boundaries

can be d i s t i n g u i -

behaviour.

become mobile.

ions,

It is f o u n d that

mobile

at the same tempe-

Since

that the twin i n t e r f a c e s

of the t e t r a h e d r a l

anti-phase

boundaries

525

it is clear

from

are a s s o c i a t e d w i t h the

one can conclude

are also a s s o c i a t e d w i t h

that these

tetrahedral

in-

d i u m ions. The a n t l - p h a s e octahedral

interstices

" The m e m o r y mably

boundaries

should remain

the p r e s e n c e

boundary

although

revealed

in t r a n s m i s s i o n

three

configuration observations

below

evidence discussed

(4) is presu-

such b o u n d a r i e s

for

the p r e s e n c e

above.

Fig.

DI, D 2 and D 3.

the s p e c i m e n was h e a t e d temperature

ones.

figuration

of b o u n d a r i e s

background

i n t e n s i t y we c o n c l u d e

of the

from~he

Between

the two

in the m i c r o s c o p e

of the t e t r a h e d r a l

that of the o c t a h e d r a l

It is clear

has changed.

that the con-

F r o m the d i f f e r e n c e

in

that the s t e p p e d b o u n d a r y

is

taken on b o t h

sides of the boundary.

This b o u n d a r y

has c l e a r l y m o v e d b e t w e e n

The b o u n d a r i e s well

BI,

B2,

This follows

B 5 have

remained

B 3 and B 4 and B 5 are a n t i - p h a s e

B 6 connect vations B 3 are

two d i s l o c a t i o n s

are c o n s i s t e n t w i t h tetrahedral

octahedral

pattern.

it is clear

immobile.

Whereas

in the b a s i c

boundaries

b o u n d a r i e s . This

boundaries

B 4 and

that B 5 and

lattice.These

the i n t e r p r e t a t i o n

obser-

that BI,B 2 and

whereas

B 4 and B5are

interpretation

also ex-

by twin b o u n d a r i e s

of the t e t r a h e d r a l

as

the b o u n d a r i e s

that the b o u n d a r i e s

p l a i n s w h y B 4 and B 5 can be i n t e r s e c t e d by a n t i - p h a s e

characteristics

It is f u r t h e r e v i d e n t

anti-phase

anti-phase

pattern

the two o b s e r v a t i o n s .

from the image

as f r o m the d i f f r a c t i o n

BI,B 2 and B 3 have m o v e d

above

indium ionshut

a twin boundary. This was c o n f i r m e d by the d i f f r a c t i o n

boundaries.

are

5a and b are

of the same area as can be c o n c l u d e d

of d i s l o c a t i o n s

the d i s o r d e r i n g

et al

750 ° C.

optical microscopy.

shall now p r e s e n t

two p h o t o g r a p h s

up to

of the

of this type of a n t i - p h a s e

it is n o t e v i d e n t w h y

types of i n t e r f a c e

the f i l l i n g

immobile

" e f f e c t o b s e r v e d by H a t w e l l

associated with

We

associated with

type.

and

526

DOMAIN STRUCTURE OF ~-/n2S 3

Vol. 3, No. 6

FIG. 5a & b Successive stages of a heating sequence. In between the two exposures (a & b) this area was heated above 4200 C. The grown in dislocations D I, D 9 and D~ serve as reference points. A jogged twin boundary can b~ ob@erved delineating two regions of different background intensity. This twin boundary has moved in (b). In (b)one also notices the presence of anti-phase boundaries B , B 2 and B 3. The boundaries B~ and B E remained immobile troughout t~e heating experiment. They are p~est~ned to be associated with ordering in the "octahedral" sublattiee.

Vol. 3, No. 6 Also

DOMAIN STRUCTURE OF fl-In2S 3

it a c c o u n t s

immobile

octahedral

Since lel w i t h

for the i n t e r a c t i o n

the

[001]

anti-phase

are p o s s i b l e w h i c h

orientations

are v i s i b l e

in Fig.6.

shown as an inset,

Diffraction

includes

spots c o r r e s p o n d i n g

lattice

of the b a s i c

are twin

with

as seen in Fig.5

axis of the t e t r a g o n a l

orientations

pattern

of twin b o u n d a r i e s

boundaries

any of the cube d i r e c t i o n s

527

at Bg

can be paral-

structure,three

related.

These

three

The area for the d i f f r a c t i o n the three o r i e n t a t i o n s .

to the twin r e l a t e d

areas

can be

distinguished.

FIG.

the

6

R e g i o n c o n t a i n i n g the three p o s s i b l e o r i e n t a t i o n s of the superlattice. A d i f f e r e n c e in b a c k g r o u n d i n t e n s i t y can be observed. The d i f f r a c t i o n p a t t e r n (shown as an inset) was taken o v e r areas i, 2,and 3, and c o n t a i n s spots due to the three o r i e n t a t i o n s in twin r e l a t i o n s h i p w i t h resp e c t to each other.

528

DOMAIN STRUCTURE OF fl-In2S3

Vol. 3, No. 6

The observations presented here clearly confirm the conclusions inferred by Hatwell et al optical observation.

(5) on the basis of their

Moreover they present evidence for the

occurence of two independent types of anti-phase boundaries: octahedral and tetrahedral anti-phase boundaries.

References i. H. Hahn and W. Klinger, 2. C.J.M.

Rooymans,

Z. anorg, al%em.

J. Inorg.

and Nucl.

3. G.D.S. King, Acta Cryst. 15, 512 4. H. Hatwell, C.R. Acad. 5. H. Hatwell, C.R. Acad.

G. Offergeld, Sc. 258, 553 G. Offergeld, Sc. 252, 3586

Chem.

chem. ii,

260, 97 (1949). 78

(1959).

(1962).

C. Herinckx and J. Van Cakenberghe (1962). C. Herinckx and J. Van Cakenberghe 6961).