The domain structure of the δ-phase alloy NiMo

Mat. Res. Bull. Vol. 8, pp. 721-732, 1973. in the United States.

THE D O M A I N

STRUCTURE

OF THE

Pergamon Press, Inc.

6-PHASE A L L O Y NiMo::

G . V a n T e n d e l o o and S . A m e l i n c k x :~:: of A n t w e r p R U C A , M i d d e l h e i m l a a n i, A n t w e r p

University

Printed

B2020,Belgiu~,

(Received April 4, 1973; Communicated by S. Amelinckx)

ABSTRACT E l e c t r o n d i f f r a c t i o n and e l e c t r o n m i c r o s c o p y are u s e d to study the d o m a i n s t r u c t u r e in the 6-phase NiMo. A r e m a r k a b l e m i c r o - s t r u c t u r e due to the s i m u l t a n e o u s p r e sence of a n t i p h a s e b o u n d a r i e s , i n v e r s i o n d o m a i n s and p e r m u t a t i o n twins has b e e n o b s e r v e d and c o u l d be a n a lysed by c o n t r a s t e x p e r i m e n t s .

Introduction In the c o u r s e of a s y s t e m a t i c alloys

characterized

of the

6-phase N i M o was

electron microscopy. structures

lacking

study of d o m a i n

by c o o r d i n a t i o n examined

attention

in

the s u b s t r u c t u r e

in some detail,

In p a r t i c u l a r

a centre

polyhedra

structures

by m e a n s

of

focused

on

was

of symmetry.

Structure The s t r u c t u r e Shoemaker

[i].

of the

6-phase was d e t e r m i n e d

It is s h o w n

The unit cell o

is o r t h o r h o m b i c o

identical

impossible small

in length;

pseudotetragonal

with

o

by m e a n s

to d i f f e r e n t i a t e

differences

and

in fig.l.

a = 9,108 A, b = 9,108 A, c = 8,852 A. most

by S h o e m a k e r

in length.

between

The a and b axes are al-

of e l e c t r o n these

diffraction

two axes

The s t r u c t u r e

it is

in v i e w of the

is f u r t h e r m o r e

non-

centrosymmetrical. :: W o r k p e r f o r m e d u n d e r the a u s p i c e s :":"Also at SCK-CEN, Mol, B e l g i u m

721

of the a s s o c i a t i o n

RUCA-SCK

722

6-PHASE ALLOY

NiMo

Vol. 8, No. 6

@

@

4o0

095

140

530 ~

0 22

280

~'

@

o,, @

550

~

036

720 4;,0

06,, 090

C

©

~

~0

@ Oo~

®

470

® 280

036

®

@

530 ~

O Io

720

005

@ ®

a 0-,8

s50 280

078

600

,a~

@

078 Ooa

@

@

097

860

095 0 22

@

, .@----

~

@

4o0 ,40 b~

0 22

o @

O,0

280

~

0 95

'40

0'

450

o e®

C

@

e720

003

4o0

3

@ 4o0 ,40

064

4~o

O~o

095 0~2 0-,8

@

e

0°3

®

FIG.I The

6-phase structure of NiMo; p r o j e c t i o n down the z-axis Large circles : Mo Small circles : Ni Intermediate circles:various mixtures of Mo and Ni The numbers at the circles are the z-coordinates in h u n d r e d t h of the c-parameter (after Shoemaker and Shoemaker [i]). Domain structure Three different types of domain boundaries on purely geometrical

grounds

(i) Antiphase boundaries; the structure

:

characterized

which the structures (3) Twin boundaries,

i.e. boundaries between domains of are related by an inversion operation.

c h a r a c t e r i z e d by the interchange of the a-

i.e. the structures

ly over 90 ° .

by a d i s p l a c e m e n t vector;

in the two domains being parallel.

(2) Inversion boundaries;

and b-axis,

can be p r e d i c t e d

This

are rotated very a p p r o x i m a t e -

is a consequence of the very exceptional

Vol. 8, No. 6

5-PHASE ALLOY NiMo

circumstances

that a and b are p r a c t i c a l l y

in this p a r t i c u l a r

structure.

We shall

723 equal

call

in l e n g t h

them p e r m u t a t i o n

twins. The p o s s i b i l i t i e s whereas

(2) and

one can v i s u a l i z e

From group theory riants

a large n u m b e r

considerations

can also be d e r i v e d

The o b s e r v a t i o n s is not a f f e c t e d operations

lattice,

clearly

primitive

2/m 2/m 2/m. tetragonal

pointgroup

G(4/m

the s t r u c t u r e

The

decomposing

of d i f f e r e n t

structure

variants

structure.

symmetry

operations

E

symmetry

ope-

is "by chance"

hand the p o i n t g r o u p

can be d e r i v e d

G of the l a t t i c e

which

of the

of the four v a r i a n t s

one o p e r a t i o n

original

for the

fact that of the of

Using

by t a k i n g

is 16 and de-

structure

to the

shown in f i g . 2 a

of G can be r e p r e s e n t e d

as

by

subgroup

from e a c h of the c o s e t s

the n o t a t i o n

H,which

can be o b t a i n e d

the g r o u p G into c o s e t s w i t h r e s p e c t

H, and by a p p l y i n g

in a n o t h e r

are those of the

is in a c t u a l

this by the o r d e r of the p o i n t g r o u p

is 4 [2].

The

(space g r o u p P212121).

the o r d e r of the p o i n t g r o u p vide

to that

the l a t t i c e

On the o t h e r

pattern

structure.

operations

lattice

since

its s y m m e t r y

is H(222)

The n u m b e r

However

(i).

of va-

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

The r o t a t i o n

orthorhombic

2/m 2/m).

that

symmetry

for the structure.

number

for

:

in one d o m a i n

be r o t a t i o n

r a t i o n of the p r i m i t i v e

of p o s s i b i l i t i e s

of the d o m a i n

the s t r u c t u r e

therefore

but not

pointgroup

demonstrate

to two variants,

the m a x i m u m

as f o l l o w s

by the p r e s e n c e

relating

domain must

(3) e a c h give rise

to the the 16

:

: identity

I : inversion C 2, C~, C~,

C~'

rotations

m,

m"'

reflections

m', m,"

1 C 4 , C~, ~,

C~

rotations

180 ° a b o u t t w o f o l d

in v e r t i c a l

a b o u t the

~ , C 4 ~ o rotation-inversion axis;

The d e c o m p o s i t i o n where

over

mirror

fourfold operation

as

planes

axis a b o u t the f o u r f o l d

o is in fact a h o r i z o n t a l

of G can then be w r i t t e n

axis

mirror.

: G=H+IH+G~H+m'H

: =

IH =

c 2,

(I, m, m"

=

;

o)

m'H =

(m', C~ , ~9q ; m"') 4

724

6 - P H A S E ALLOY NiMo

Vol. 8, No. 6

0 2

c;

%

m oo

(a)

H(2 2 2)

422 Representation of the pointgroup of the NiMo lattice G(~ ~ ~) and the pointgroup of the structure H(222).

/j

inversion ~ x

-...

Permutation

I

Permutation inversion

"11"

Permutation

l

xy_ nr

z

IV

inversion I

(b)

y

FIG.2 Schematic representation of the mutual relations between the four possible variants occuring in the 6-phase. The same symbols are used as in fig.2a. The four variants

are now obtained by applying the operations E,

I, C~ and m' to the original schematically If

structure;

they are represented

in fig.2b.

(I) is considered

to describe the normal structure by giving

the position vector ~j of the atoms,

then the other variants

generated by means of the same set of position vectors, respect to the indicated reference Although

in principle

six different

are

but with

systems. interfaces

can be considered

Vol. 8, No. 6 between

b-PHASE ALLOY NiMo

four v a r i a n t s ,

ly three e s s e n t i a l l y pected.

they are two by two e q u i v a l e n t

different

We shall call

(a) i n v e r s i o n

Evidence

reasons

: (1) v e r s u s

"

(c) p e r m u t a t i o n

types of i n t e r f a c e s

t h e m for o b v i o u s

boundaries

(b) p e r m u t a t i o n

725

(II) or

: (I) v e r s u s

inversion: boundaries

for t h e s e p r e d i c t i o n s

are to be ex-

: (III)

versus

(IV)

or

(II)

versus

(IV)

(IV) or

(II)

versus

(III)

(III)

(I) v e r s u s

so that o n -

will

be i l l u s t r a t e d

by ob-

servations. Contrast

effects

The d i f f e r e n t wing grounds

interfaces

boundaries

the c o n t r a s t

side of the b o u n d a r y

diffraction

condition,

structures

only differ

dary

itself

possible

is a l w a y s

as well

by a p a r a l l e l

(2) The i n v e r s i o n

boundaries

pattern

ations.

shown

symmetry

whereas

trast differences

situations.

the b r i g h t

the d a r k between

the d i f f r a c t i o n (3) The p e r m u t a t i o n differences

Apart pattern

be d i f f e r e n t two domains.

for

there w i l l be no

by m a k i n g beam

field

of u - l i k e

situ-

for r e f l e c -

rise to a c e n t e r of image will p r o d u c e

the two domains.

exhibit

strong

no

con-

The b o u n d a r i e s

fringes,also no v i s i b l e

it-

in m u l t i p l e effect

on

is to be expected. in p r i n c i p l e

give rise to c o n t r a s t

on e i t h e r

is b e c a u s e

for s i m u l t a n e o u s l y

be l a r g e s t

for t h o s e r e f l e c t i o n s

the v a l u e s

of s t r u c t u r e

side as well

in the

the d e p t h p e r i o d i c i t y

operating

More quantitatively

khl are largest.

The b o u n Except

in this case,

from satellites

twins w i l l

This

the

[4].

f i e l d image m a y

in the two d o m a i n s

DF as in the BF.

[3].

law in m u l t i p l e

[5] t h a t

self will be i m a g e d by m e a n s beam

since

displacement.

to a zone w h i c h g i v e s

in p r o j e c t i o n ;

contrast,

the

can o n l y be m a d e v i s i b l e

of F r i e d e l ' s

not b e l o n g i n g

the same, w h a t e v e r

satellites,

use of the v i o l a t i o n It has b e e n

on

of u - f r i n g e s

dependent

on the d i f f r a c t i o n

in the two d o m a i n s

in BF as in DF,

is i m a g e d by m e a n s

orientation

influence

tions

on the f o l l o -

:

(i) For a n t i p h a s e either

can be d i s t i n g u i s h e d

reflections

the c o n t r a s t

will

in the

is l i k e l y

to

for w h i c h the d i f f e r e n c e s

amplitudes

corresponding

to hkl and

in

726

6 - P H A S E ALLOY NiMo In p r i n c i p l e difference since

spot d o u b l i n g

between

in e l e c t r o n

the c e n t e r

Vol. 8, No. 6

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

a and b; the d i f f e r e n c e diffraction

and large

camera

even using lengths

m u s t be v e r y

reflections

this

small

far from

spot s p l i t t i n g

c o u l d not be d e t e c t e d . Schematically

the s i t u a t i o n Contrast

can be s u m m a r i z e d

between

domains

as f o l l o w s

in

BF

DF

Antiphase

boundaries

no

no

Inversion

boundaries

no

yes

yes

yes

Permutation

twins

:

Experimental Specimen

preparation

The m a t e r i a l ther

was p r e p a r e d

in an arc f u r n a c e . T h e

however

it c o n t a i n s

transmission sheets

resulting

ethylglycol,

Foils

for

by e l e c t r o p o l i s h i n g

in a b a t h c o n t a i n i n g

38cm 3 p e r c h l o r i c

The foils w e r e heat t r e a t e d

toge-

is not h o m o g e n e o u s ,

constituent.

are o b t a i n e d

such p r e c i p i t a t e s

38cm 3 h y d r o f l u o r i c ,

the c o n s t i t u e n t s

material

as the m a j o r

electron microscopy

containing

of water.

NiMo

by m e l t i n g

for m a n y

264 cm 3

a c i d and 18cm 3

hours b e t w e e n

ii00 and 1200°C. Observations We shall

now p r e s e n t

faces p r e d i c t e d in ~-NiMo

evidence

on g e o m e t r i c a l

and s t r u c t u r a l

and can be i d e n t i f i e d

Fig.3a, figuration to c o n t r a s t

that the four

differences

ever the d i f f r a c t i o n fied as a n t i p h a s e D do give rise

Some

between

the d o m a i n s

conditions.

to d i f f e r e n c e s

example

interfaces,such

boundaries.

grounds,

by u s i n g the c o n t r a s t

b and c shows a typical

of domains.

kinds

of i n t e r do o c c u r

effects.

of an o b s e r v e d

as A do not g i v e rise on e i t h e r

side,

They are u n a m b i g e o u s l y

Other

interfaces,

in c o n t r a s t

con-

what-

identi-

such as B, C and

under c e r t a i n

imaging

conditions. F r o m the c o n t r a s t domains

behaviour

in fig.3a

I, II and III s h o u l d be d i f f e r e n t ,

triple point.

Such a b e h a v i o u r

it is clear moreover

c a n n o t be e x p l a i n e d

that the

these

form a

by a s s u m i n g

Vol. 8, No. 6

5 - P H A S E A L L O Y NiMo

the e x i s t e n c e since

of e i t h e r

three v a r i a n t s

between

boundary

Indeed

the d o m a i n s

there

as w e l l

larger

Since

where

small.

is an i n v e r s i o n

mains

too.

in s t r u c -

shows a BF and DF for a

structure

f a c t o r FO32

6-NiMo

difference

even

is 5

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

is P 2 1 2 1 2 1

projected

for a 422 r e f l e c t i o n

due to p e r m u t a t i o n

of a and b is

at B in the D.F.

in b a c k g r o u n d

image

structure

symmetry

analysis

boundary

in p r o -

d o w n the c - a x i s , O; 4'

of the d o m a i n

configu-

in fig.4.

f r o m fig.5

in the BF and a s y m m e t r i c a l

of the n a t u r e of

from w h i c h

is i m a g e d by s - t y p e

it is clear

fringes,

symme-

in the DF.

the c r y s t a l l o g r a p h y that as well

the space

shows

at 4' O;

for the i d e n t i f i c a t i o n

can be o b t a i n e d

has b e e n o b s e r v e d

the

do-

as long as

Indeed

the p r o j e c t i o n

centr~of

are s c h e m a t i s e d evidence

are excited.

[i] hence e.g.

due to i n v e r s i o n

beam situations,



of the c o n t r a s t

inversion

Concerning

showsunambigeously

twin and an i n v e r s i o n

were m a d e

contrast

are required,

B or C has to be

(BF and DF)

in m u l t i p l e

of the type

The r e s u l t s r a t i o n of fig.3

3 variants

of a p e r m u t a t i o n

in DF no d i f f e r e n c e

on fig.l has 3 1 and ~, 3"

trical

Fig.3c

a c e n t r e of s y m m e t r y

that the

is e x p e c t e d

contrast.

only reflections

jection

Fig.3b

configuration

The o b s e r v e d

is noticed,

g r o u p of

field.

is a s t r o n g d i f f e r e n c e

these m i c r o g r a p h s

the c o n t r a s t

Moreover

intensity

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

boundary

since

extremely

as in dark

the c a l c u l a t e d

that B is a s u p e r p o s i t i o n

where

in b r i g h t

field

difference

than F302.

one has to c o n c l u d e

boundary

contrast

(k h i).

condi-

h a n d B and C are p e r m u t a t i o n

is a p r o n o u n c e d

there

for this p r e s e n t

an i n v e r s i o n

alone,

a contrast

are the d i f f r a c t i o n

in b a c k g r o u n d

for w h i c h

(h k i) and

302 r e f l e c t i o n

one n e v e r o b s e r v e s

the o t h e r

a large d i f f e r e n c e

ture f a c t o r

boundaries

D in fig.3 m u s t be a p u r e

I and II w h a t e v e r

since

for r e f l e c t i o n s

times

in B.F.

and c ) . O n

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

that boundary

since

the d o m a i n s

tions(fig.3a,b

or ~ e r m u t a t i o n

are required.

One can c o n c l u d e inversion

inversion

727

of the d o m a i n

antiphase

structure

boundaries

it

as i n v e r s i o n

728

5-PHASE ALLOY NiMo

Vol. 8, No. 6

Bright field (B.F.) and dark field (D.F.) images of a domain configuration showing clearly three different domains. A is the only boundary at which no d i f f e r e n c e in background intensity is observed.

FIG.3 b

Same region as in fig.3a, illustrating the large change in contrast at boundaries B and C for a 302 reflection.

Vol. 8, No. 6

5 - P H A S E ALLOY NtMo

729

FIG.3 B.F. a n d D.F. i m a g e s h o w i n g unambigeously the inversion cont r a s t at b o u n d a r i e s B and D for a 422 r e f l e c t i o n for which no c o n t r a s t d u e to a p e r m u t a t i o n of a a n d b is to be e x p e c t e d .

C

aL

b

®

°L a

....!..B

A\

\\\\\\\\\\\\ a

@

FIG.4

Schematic representation of the results obtained l y s i s of t h e c o n f i g u r a t i o n s h o w n in figs.3 + : direct structure - : inverted structure

from

the

ana-

730

6-PHASE ALLOYNiMo

Vol. 8, No. 6

FIG.5 Fringe patterns at inversion domain boundaries. The configuration shown in a) was oriented in b) and c) for illustrating the a-type fringe pattern at the inversion boundary I.

FIG.6 Antiphase boundaries, permutation twins and inversion boundaries all lying approximatively in the (i00) or (O10) plane; proving the existence of four orientation variants.

Vol. 8, No. 6

5 - P H A S E ALLOY NiMo

domain boundaries lie almost (fig.6). deduced

731

and p e r m u t a t i o n twins are nearly planar

invariably

in the basal planes

The d i s p l a c e m e n t from e x t i n c £ i o n s

vector

(iOO),

and

(010) or

(O01)

for the A P B ( e . g . A

in fig.3) as 1 turned out to be of the type ~[ii0]; it

is in a g r e e m e n t with a theoretical model. From these m i c r o g r a p h s variants

it also follows

(marked i, 2, 3, 4 in fig.6)

predicted

from structural

do occur

considerations.

m a x i m u m number of variants

that four o r i e n t a t i o n in the alloy,

as

Four was also the

ever e n c o u n t e r e d

during the investi-

gation. Conclusions The

6-phase of NiMo presents

due to the simultaneous sion domains

a remarkable domain structure

presence of antiphase boundaries

and p e r m u t a t i o n

twins.

Different types of domains

could be identified by means of contrast experiments. twins

show a structure

in dark field,

while

inver-

factor contrast

as well

Permutation

in bright

field as

inversion domains were identified using the

b r e a k d o w n of F r i e d e l ' s

law in the d i f f r a c t e d beam.

tailed account with the c r y s t a l l o g r a p h i c structure will be p u b l i s h e d

A more de-

analysis of the domain

forthcommingly.

Acknowledgements Thanks are due to Dr.J.Van Landuyt and to D r . P . D e l a v i g n e t t e for useful

discussions

and for help w i t h the experiments.

References i. C . B . S h o e m a k e r 2. G.Van Tendeloo

and D.P.Shoemaker,

Acta Cryst.l_~6, 997

(1963)

et al,to be p u b l i s h e d

3. R.Gevers, J.Van L a n d u y t and S.Amelinckx, 689 (1965)

Phys.Stat. Sol.l!l ,

4. R.Gevers, J.Van Landuyt and S.Amelinckx, 343 (1966)

Phys.Stat. Sol.18,

5. R.Serneels

et al, to be published.