Dislocations stopped by the Σ = 9 (122 ) grain boundary in Si. An HREM study of thermal activation

HAL Id: jpa-00211079

https://hal.archives-ouvertes.fr/jpa-00211079

Submitted on 1 Jan 1989

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Dislocations stopped by the Σ = 9 (122 ) grain

boundary in Si. An HREM study of thermal activation

J. Thibault-Desseaux, J.L. Putaux, A. Bourret, H.O.K. Kirchner

To cite this version:

J. Thibault-Desseaux, J.L. Putaux, A. Bourret, H.O.K. Kirchner. Dislocations stopped by the Σ = 9

(122 ) grain boundary in Si. An HREM study of thermal activation. Journal de Physique, 1989, 50

(18), pp.2525-2540. �10.1051/jphys:0198900500180252500�. �jpa-00211079�

Dislocations

_{stopped by}

the 03A3

=

9 (122 )

grain

boundary

in

Si.

An HREM

_study

of thermal activation

J. Thibault-Desseaux

_(1),

J. L. Putaux

_(1),

A. Bourret

₍₁₎

and H. O. K. Kirchner

₍₂₎

(1)

Département

de Recherche Fondamentale, Service de

_Physique,

Centre d’Etudes Nucléaires, 85X, 38041 Grenoble Cedex, France

(2)

Institut für

_{Festkörperphysik,}

Universität Wien, A-1090

Boltzmanngasse

5, Vienna, Austria

(Reçu

le 17 mars 1989,

_accepté

sous

_{forme définitive}

le 3 mai

₁₉₈₉₎

Résumé. 2014 Les

configurations

des dislocations résiduelles, observées

_{après l’intégration}

dans le

joint

de

_grains

des dislocations

glissiles,

sont

_expliquées

par

analogie

avec le

_glissement

dévié dans

le massif. Les dissociations,

cristallographiquement possibles,

des dislocations du

_grain

en

dislocations

_parfaites

ou

_imparfaites

du réseau DSC sont discutées. Les

_{configurations}

les

_plus

favorables

_{énergétiquement}

servent

_d’étapes

intermédiaires lors de l’activation

_{thermique qui}

fait intervenir à la fois le

_glissement

et la montée. L’activation

_{thermique bloque}

au

_joint

les dislocations à 60°, alors

_qu’elle

aide les dislocations vis à le traverser.

Abstract. 2014

Experimentally

observed

_{configurations}

of the

_integration

of

_glide

dislocations into a

03A3 = 9

_boundary

are

_explained

in

_analogy

to

_cross-slip

in the bulk.

_{Crystallographically possible}

dissociations of the bulk dislocations into

_complete

or

_imperfect

dislocations of the DSC lattice are discussed. The

_{energetically}

most favorable

_{configurations}

serve as activated

_intermediary

steps in thermal activation

_involving

both

_glide

and climb. Thermal activation blocks 60° dislocations at the

_boundary,

but

helps

screw dislocations to traverse it.

Classification

Physics

Abstracts

61.70G, J, L, N, P, Y

1. Transmission of

_slip

across

_grain

boundaries.

1.1 THE PROBLEM. - Hirth

_[1]

was the first to consider the

_necessity

and

_possibility

of

_slip

across

_{grain-boundaries.}

Before a dislocation

_gliding

in one

_grain

can

_glide

into the other

grain,

it has to cross the

_boundary

between. The

_problem

of transmission of

_slip

is thus a

twofold one : first the

_glide

dislocation has to enter the

_boundary,

then it has to leave it

_again.

Since Hirth’s paper the

subject

has advanced

_{considerably, mainly}

because of the work on

crystallographically

well defined boundaries. In

_particular,

conventional electron

_microscopy

[2],

synchrotron topography,

1 MeV in situ

_experiments

_{[3, 4]}

and

_high

resolution electron

microscopy

[5, 6]

on -Y = 9 silicon

_{bicrystals greatly improved}

the

_{understanding}

of the behaviour of

_glide

dislocations near or « at » the

boundary

(for

a review see

_[7]).

_Though

discussed

_[8]

but still unsolved is the

_problem

of actual

_{incorporation}

into and transmission

across the

_boundary

of the dissociated dislocations.

_Apparently

this process does not

_happen

spontaneously,

and

_{although macroscopically}

_{necessary and}

_observed,

still eludes

understand-ing

on a

_{crystallographic}

and

_energetic

level.

In this paper we _propose two new ideas :

_firstly

we invoke

(and

_give

evidence

for)

the

existence of

_{grain-boundary partials,}

and

_secondly,

we invoke thermal activation of

three-dimensional critical

_{configurations.}

When dissociation of the

_in-coming

dislocation occurs

within the

_boundary,

transmission of

_slip

is

_impeded.

When dissociation occurs

_only

on the

glide planes

of the other

_{grain, slip}

into the other

_grain

_{is easy.} 1.2 EXPERIMENTAL DETAILS.

- £

= 9

bicrystals

were obtained

_by

the Czochralski method. Both the

_grains

and the GB

_plane

were dislocation-free. The GB

_plane

was

(122 )I

or

(122 )II

(subscripts

1 and II are for

_crystal

1 and

_crystal

II

_{respectively),}

the common tilt axis

was

_[011]

and the tilt

_angle

was 38.94°.

The stress

_experiments

were

_performed

_{by Jacques}

and

_George

at the Ecole des Mines de

Nancy,

France,

the deformation conditions

_being

as described in an earlier

_paper

_[9].

The

compression

stress was

applied along

the

[26, 7, 20 ]I

axis,

_equivalent

to the

_{[26, 20,}

_7]11

axis and was contained in the GB

_plane.

The deformation condition was a

_{single slip}

condition in both

_crystals.

The deformation was

_stopped

in the

_{yield region}

and

_samples

cooled down under load in order to freeze-in the dislocation-GB

_{configurations.}

In the traction tests the

stress axis was

[411]1’

_equivalent

to

_[411

_]II.

The deformation conditions are summarized in

table I.

Table I. - The

deformation

conditions

_{o f}

the observed

_samples

are summarized in this table.

T :

_{temperature in K, s :}

strain in

_{9,,, é :}

strain rate in

s-1.

The

_compression

tests and the tension tests are indicated

_{by (c)}

and

(t) respectively.

After deformation the

_samples

were

_mechanically

cut and

_polished

to a thickness of 70 _wm.

Discs 3 mm in diameter were then extracted

by

ultrasonic

grinding,

and ion-thinned. A final

chemical

_polishing

at 0 °C revealed the

_grains

and GB dislocations.

_{Rapid ion-thinning}

(15 mn)

and chemical

_polishing

were then undertaken between successive observations in

order to

_explore

a maximum

_length

of GB.

The

_samples

were observed with a JEOL 200 CX electron

microscope equipped

with an

ultra-high-resolution pole-piece

(Cs

= 1.05

mm ).

The _common

[011

axis

of the

bicrystal

_was

parallel

to the electron beam.

The

_only

dislocations studied were those

_{lying along}

the

[01 ]

axis.

They

were viewed

end-on in the

_microscope.

Owing

to the choice of deformation axis in the

_compression

tests, the activated

_slip

_system

with the

_highest

Schmid factor

_(s

=

0.467)

_was the most favourable _one for HREM

observations :

_{(111)1, [110]1}

or

(111)n,

[101]11.

_{Consequently,}

on these

_{primary planes,}

60°

dislocations were observed

_edge-on.

Another

_slip

_system

_(s

=

0.382)

was detected on the same

_planes,

which led to screw dislocations observed

_edge-on

too :

(111 )I,

_{[011 ]I}

or

(111)11’

[011]n.

An additional

_slip

_system

_{(s = 0.217 )}

could also be observed :

_(111)1,

[101 ]I

or

(111 )jj, [110 ]jp

In the tension _tests, the Schmid factor of the

_slip

_system

_inducing

60°

dislocations

_{(line 011)}

on the

_{primary planes}

is

0.408,

whereas it is 0.226 on the additional

planes.

The

_slip

_systems

_inducing

screw dislocations

_{aligned along}

011 are not activated in tension.

2.

_{Grain-boundary partial}

dislocations. 2.1 DSC LATTICE. - A

grain-boundary

dislocation

_(GBD)

in a coincidence

_{grain boundary}

(GB)

has a

_Burgers

vector

_belonging

to the associated DSC lattice

_[10].

The

_sign

for the

Burgers

vector is

_{given by}

the SF/RH convention on the open circuit around the dislocation

pointing

into the paper as

_{given by}

Hirth and Lothe

[11].

The

_Burgers

vector of a GBD and

the

_height

of the associated GB

_step

are measured

following

the method described

by King

and Smith

_[12].

It has to be noticed that the GB

_step

connected with a

_given

GBD

Burgers

vector has a

_precisely

determined

_height

even if several values can exit. The characterization

of the defects in the

_grain

and in the

_boundary

is based on the fact that the

Burgers

vectors

and the associated

_step

_heights

are conservative.

Every

point

of the f.c.c. Bravais lattice of silicon is a

_point

of the DSC

_lattice,

but not vice

versa. The DSC lattice associated with the 1 = 9 is a

_body

centered one with a Cartesian basis

consisting

of :

and

The

_elementary

dislocations within this lattice are

_bc,

_b

_g and

_{b 30}

2

_(bc

+

_{b 9}

+

_{2 s ) (Fig. la).}

2 B

bc

and -

_&c

are not associated with a GB

_step

unlike the other GBD’s. The GB

_step

_heights

associated

_respectively

with

_bg

and -

_bg

are -

_ho

and +

_{ho (ho}

=

a/3 ) [5].

There are 4 distinct

projections

of the 30° GBD

_Burgers

vector :

b3o,

b3o, b50’

bjo.

Each

_{b3o is}

found associated with

a

_step

of two

_{possible heights :}

b 1

with h = 1.75

_ho

or - 2.75

_ho,

_{b 2}

with h = -1.75

_ho

or

2.75

_ho,

_b3o

with - 1.75

_ho

or + 2.75

ho

and

b 4

with h = 1.75

ho

_{or -} 2.75

ho.

Due _to the GB

symmetry,

only

four different structures exist :

_b50

with h = 1.75

_ho

and - 2.75

_ho

and

b3o

with h = -1.75

_ho

and 2.75

_ho,

the others can be deduced

_by

a mirror

_symmetry

with

respect

to the GB

_plane.

The screw

_component

of the

_Burgers

vector will not be

_given

in the

following owing

to the fact that

_by

_HREM,

which

_{only gives}

the

_projection,

it is not

observable.

However,

at least in the

_compression

tests, the stress conditions would

_permit

us

to deduce the

_sign

of the screw

_component

of the observed dislocations. On both sides of a

DSC dislocation the GB structure is

_unchanged.

Within the

_{grain-boundary}

a network of the three

_elementary

dislocations can be formed.

2.2 DSC PARTIAL DISLOCATIONS. - In

our

observations,

two other

_types

of GB dislocations

were detected that we will define as «

_{imperfect »}

or «

partial »

dislocations.

i)

The first

_type

is a dislocation located in the GB but connected with another

_grain

_partial

Fig.

1.

_{- a) Z}

= 9 DSC lattice

projection along

[011].

Definition of the

terminology

used in the _text

(.)

lattice

_point

at level z = 0, and ₊ lattice

point

at level z =

± a

[11 ].

Grain 1 is on the left hand side of

the vertical axis,

grain

II on the

_right

hand side.

_b)

_{Projection along}

the

_{[011 ] axis}

of the two lattices GBPL1 and GBPL2 that define the

_partial

vectors of the DSC lattice :

_{2 pÎ = a/18}

_[211]1’

Pl 2

=

a /9 [III ]1’ 2 plI

=

a / 18 [21 l ]11’ P fI

=

a /9 [III ]11.

If the

_stacking

fault

_(SF)

lies on the

_{primary plane,}

we observed an «

imperfect

» GBD whose

_Burgers

vector is a DSC vector.

_However,

the structure of the GB dislocattion bonded

to a

_grain

SF is not the same as the one of the isolated GBD : see for instance in

_figure

2a the

bc

dislocation

_resulting

from the

_{decomposition}

of the 90°

_{partial incoming}

on the

_primary

planes

(DSC vector)

into a

_{glissile perfect}

_bg

GBD

_{(DSC vector)}

and an

_imperfect

bc

dislocation. Futhermore this

_{bc imperfect}

GB defect

_{(DSC vector)}

has an associated

_step

whose

_height

is h = 1.5

ho,

(ho

=

a/3 ),

whereas the isolated

perfect

GB bc

is characterized

by

a well defined structural unit

(a boat-shaped

six-atom

_ring

called T

_by

Bourret and Bacmann

[13]

and has no associated

_step

(Fig. 2b).

If the SF lies on the additional

_planes,

we observed an «

imperfect »

dislocation whose

Burgers

vector does not

_belong

to the DSCL : see in

_figure

2c the observation of the

plI.

ii)

The second

_type

is a dislocation located in the GB but connected with another GB

dislocation

_through

a «

grain-boundary

SF »

(GBSF) (Fig. 2d).

The total

Burgers

vector of the

_{global configuration}

is a DSCL vector _{like any GBD}

_Burgers

vector. These defects could be defined as «

partial »

GB dislocations. In the case of

the £

= 9

GB,

this GBSF _can be

described as a combination of

_boat-shaped

six atom

_rings

on the additional

_plane

close to the

five-seven atom

_rings

structural units of

the 1

= 9 GB. This GBSF _never extends _{over more}

than one

_period

of the GB

_leading

to the idea that this structure is of

_high

_energy. The

_{previous configurations}

were described in terms of dissociation in

_analogy

to the

Fig.

2. -

a)

Observation of the

_{« imperfect » bc}

GBD connected with a GBSF in

_grain

I. The

bc

vector is a DSC

perfect

vector

_(micrograph

M.

_Elkajbaji)

however the step

height

is h = ₊ 1.5

ho

whereas the

_perfect

_bc

GBD

_(b)

is isolated in the GB and characterized

by

the T

boat-shaped

six-atom

ring

(h

=

0). c)

Observation of the

pÎ +

grain-boundary

partial

dislocation. Because of the

projection,

only

the

_edge

_{component pÎ =}

1 a

_{[211 )}

can be seen, the screw _component ± s

= a

_{[0 11}

_]

remains

36 4

invisible. The

partial

pÎ +

(or pl-)

borders an intrinsic

stacking

fault that extends into

grain

I.

d)

Observation of a

p Î

_{grain-boundary partial}

dislocation. The

partial

borders a

_y’

«

stacking

fault » of the Z = 9

_{grain boundary,}

terminated on the other side

_by

a

(p2 + 2 p Î)

_imperfect

dislocation. The total

Burgers

vector is

_{b 90}

This

_{configuration}

has to be

_compared

with the non dissociated

_{configuration}

_(e)

of the same

b 90 1

(micrographs

with black atoms and 0 on the seven atom

_rings).

this idea and its structural and

_energetical

_{consequences have} to be

_clarified,

but will not be detailed in this _paper.

The

_concept

of DSC

_partials

was

_already

introduced to describe the defects

_separating

two

structurally

distinct

_(but

_{energetically}

_equivalent)

_parts

of the

same X

GB or to define the linear

_jonctions

between facets

_{[14, 15, 16].}

In our _case, the

_concept

of «

_partials

» is

_slightly

different : as _{mentioned the energy of the GBSF}

_might

_be

_{certainly higher}

_{than the energy of}

the initial 1 = 9 and futhermore the _structure of the GBSF is

completely coupled

_{to one or}

the other

_{adjacent grain,}

via the boat six-atom

_rings.

The «

partial »

GBD

_Burgers

vector could be described with the

_help

of the two

_orthogonal

bases

_consisting

of

and

2 s,

both

_being

centered on the faces with

normal p2

(i.e.

_they

have additional

_points

at

(p 1 + s ),

see

Fig.1b).

_Physically

realized are the

_partial

dislocations

pl - = P 1 + s,

p 1 + = p 1 _ s and p 2.

In our

_images,

which are

_projections

in the

_s-direction,

_only

the

components pl

and

_p2

are

observable,

and have

_actually

been observed

(Fig. 2c, d).

3. Thermal activation.

Although

our observations are restricted to two-dimensional

_{configurations,}

the

_possibility

that the actual mechanism of

absorption

of the dislocations

_by

the

_{grain-boundary}

is not a

two-dimensional but a three-dimensional process, cannot be excluded. On the

_contrary,

it

seems even

_probable

that similar to cross

_slip

or climb in the

bulk,

_thermally

activated

configurations

are involved.

_However,

the activated

_{configurations}

in the

_boundary

are

substantially

different from the ones

envisaged

for bulk cross

_slip.

In the cross

_slip

model of Schoeck et al.

_{[17, 18]}

a

_totally

constricted

configuration

over a finite

_length

is invoked which

moves off into the

_{cross-slip plane by dissociating.}

In the

_{analogous grain-boundary}

cases,

some residue must be left behind where the constricted dislocation was, because the

slip

vectors in

_grain

1 and in the

_boundary

are not the same. In the cross

_slip

model of Friedel and

Escaig

[19, 20]

no total constriction exists over _{any finite}

_length,

but a constricted

_point

dissociates into the

_{cross-slip plane.}

A model of

_cross-slip

from a

_{single partial,}

without constriction was

_proposed

first

_by

Fleischer

_[21].

In the

_{analogous grain boundary}

case the

dislocation rests on its

_{slip plane,}

but a

_point

of the

_{leading partial expands}

into a faulted

_loop

in the

_{grain boundary plane.}

Unlike in

_cross-slip,

the fact that the

_possible

_Burgers

vectors of the

_{grain-boundary}

dislocations can do work not

_{only by glide,}

but also

_by

climb

_[22],

influences

_merely

the work term in the

exponent

of the Arrhenius

_expression

_[23].

3.1 INTEGRATION OF 60’ DISLOCATIONS.

3.1.1. Tension with

_glide

on the

_{primary plane.}

- The 600 dislocation arrives

on the

(111 )I

plane

in

_grain

_I,

the 30°

_partial

in front and the 90°

_partial

_trailing

behind. The

integration

of the

_complete

60°D in the GB would have left a GB defect characterized

_by

a

total

_Burgers

vector

b 3

with an associated

_height

h = - 0.75

_ho.

The

_applied

stress,

possibly

even

_augmented

because the dislocation under consideration

might

be the first one of a

pile-up, presses the

leading

30°

_partial

_(though

_{b 3}

= DSC

vector)

against

the

_boundary.

If the activation follows the upper

path

of

_figure

_3,

a

_loop

of a

_complete

GBD -

_{bg (h}

_{= - ho ),}

is emitted in the

_{boundary plane, leaving}

a

b3o = a

₃₀

[Il2]n

imperfect

GBD at the intersection

6

with an associated

_step

whose

_height

is h = - 0.75

ho,

whereas the

perfect

bjo

GBD has an

associated

step

whose

_height

is either 1.75

_ho

or - 2.75

_{ho [5].}

Since -

_bg

is

_glissile

in the

Fig.

3. - The

integration

into the

_{grain boundary plane}

_(GBP)

of a 60° dislocation in tension,

glide

on

the

primary plane

(PGP)

of

_grain

I, which is

_{(III )1.}

In the small

_rectangular

insert the various

decompositions

of the

_Burgers

vectors are shown with respect to

_grain

_{I. The upper}

_path

illustrates the

thermally

actived

_(TA)

_glide

model of Friedel and

_Escaig,

the middle

_path

shows the

_thermally

activated

glide

model of

Seeger

and Schoeck. Both lead to the

_br

constricted

_{configuration.}

In the lower

path,

supersaturation

of

point

defects allows climb

_(C)

of the

_{leading partial}

_(which

in this favorable case

belongs

to the DSC

_lattice)

in the

grain boundary.

The

_integration

and

_{decomposition}

of the

_trailing

partial

follows

_{spontaneously.}

This

_path

leads to a

br decomposed

into

b 30 3

and -

_b,.

whereas the

_applied

stress is

_inactive,

its traction

_being

zero in the

_boundary.

We take this to

be the

_{configuration}

of

_highest

_{energy, i.e. the activated} one. The

bjo

GBD and the 90°

_partial

are almost

perpendicular ;

then,

the

stacking

fault in between and the

pile-up

stress

_pull

them

together

into a « constricted »

_{br (h}

= - 1.75

_{ho), (Fig. 4a).}

Because _{of the energy}

_gain

the

b3 r

line

gets

spontaneously longer.

Either it remains constricted or it

_{decomposes by}

climb into DSC dislocations : -

_bc

= a

_[122]j

_(h

=

0 )

plus

bjo

= a

[112]j (h

= - 1.75

_{h o ), (Fig. 4b).}

9 30 6

Under another thermal activation the

_b3(h

= - 1.75

_{h o )}

can form a

b 4(h

= - 2.75

_{h o )}

_by

splitting

off another -

_bg

_(or

_receiving

a +

_bg

_already

_present

in the

boundary).

Under our

experimental

conditions

_(deformation

at 1020

_K)

the

_completely

constricted

b3(h

= - 1.75

_{h o )}

or

b 4(h

= - 2.75

_{h o )}

have never been observed. Instead we found

closely

dissociated forms :

_figure

4a shows the dissociated form of

_{b r 3}

into -

_{(p 2 + 2 p 1 + p 1 ± )II}

_plus

-

(2 pl + p2)U. The b 4

is dissociated into -

4 p Î

plus

(- p 2 - 2 p 1 - p 1-

sexe

figure

4c. If climb is

available,

the

_{b 4}

can

_decompose

further into a

b30 (h

= - 2.75

h o ) plus - bc,

see

figure

4d. The measurement of each

_partial

_Burgers

vector,

using

the

_King

and Smith

_[12]

Fig.

4. - Residues left

by

a 60° dislocation in tension

₍₁₀₂₀

K,

1.3 %). (a)

and

_c)

show the

br and b4

residual dislocations left after

_integration

of the 60° dislocation

_(upper

and middle

_paths

in

Fig. 3). They

are

_slightly

dissociated into DSC

partials

(lower scheme).

The necessary

stacking

fault appears as a bulk

_stacking

fault

_(units)

attached to the

_{grain boundary}

on one or the other additional

(111)

plane.

(b)

and

_(d)

Elementary

DSC dislocations left after the

_{decomposition}

_{of br}

and

b 4

respectively :

the

_b3

_(h

= - 1.75

_{h o )}

and -

_bc(h

=

0 ) in

(b),

and the

bio(h

= - 2.75

h o )

and

deduced a

_posteriori

_{by comparing}

the structural models of the dissociated

br

and

b 4

proposed

in

_figure

4a and c. If the activation follows the middle

_path

of

_figure

_3,

the

_trailing

90°

_partial

_b9o

= 1

_[211]1

follows

_{spontaneously}

to

_produce

a constriction at one

_point.

This

6

constriction is extended and this

_complete

60° dislocation

_{(h = -}

0.75

_{h o )}

_decomposes

spontaneously

into -

_{bg (h}

=

ho )

plus

b r 3(h

= - 1.75

_{h o )}

_reaching

the

_{configuration}

discussed before.

In

_principle,

if one allows climb

_(the

existence of which has been shown

_{experimentally}

in the

_grains

_[24])

_during

the last

_stages

_{of the upper and middle}

_paths

of

_figure

_3,

one has to

allow for the

_possibility

that the

_leading

_{b 3}

climbs

_immediately

in the

_boundary,

until the

b9o

partial

is

_pulled

into the

_{boundary by}

the

_stacking

fault. The result of the

_spontaneous

decomposition

of the

_{b 3}

into -

_b,,

_{plus -}

_bg

leads to the same

_{configuration}

as before.

3.1.2

Compression

with

_glide

on the

_primary

_plane.

- The 60° dislocation arrives

_again

on the

( 111 )I

plane

of

_grain

_I,

with the 90°

_partial

in front and the 30°

_{partial trailing}

behind. The

integration

of the

_complete

60 °D would have left a GB defect characterized

_by

a

_Burgers

vector

_{b 1}

associated with a GB

_step

whose

_height

is h = ₊ 0.75

ho.

The

b90

decomposes

into

the

_perfect

GBD

_{bg (h}

_{= - ho )}

_plus

the «

_{imperfect »}

GBD

_b,,(h

= 1.5

ho),

the former

doing

work under internal stresses

_{by gliding}

in the

_boundary.

_{If the upper}

_path

of

_figure

5 is

followed,

a

_loop

of

_bg

is formed

(doing work),

_leaving

a

b 2

_{imperfect edge}

behind. This GBD

Fig.

5. - The

integration

of a 60° dislocation in

_{compression, glide}

on

_{primary planes}

_(PGP)

of

_grain

1

which is

_{(III )1.}

In the small

_rectangular

inserts the various

_{decompositions}

of the

_Burgers

vector are

shown with _respect to

_grain

I. As in

_figure

3, three

_{possible paths}

are

_presented.

_{The upper and middle} ones show

_thermally

activated

_(TA)

_glide

mechanisms. The lower one takes

_place

when

_climb(C)

is almost

_{perpendicular}

to the 30°

_{partial left}

behind and the

_stacking

fault combines them to a

constricted

_br.

Either this one remains or, if climb is

possible, decomposes

into

b 2

+

_b,.

If the middle

_path

of

_figure

5 is

followed,

the 30°

_{trailing approaches}

the

b,

by

thermal activation to

_give

a constricted

_b’.

The

_completely

constricted or

_slightly

dissociated

_{configurations}

of

_{br and b,2}

have never been detected even at 970 K.

_They

were

always

found

_{decomposed by}

climb in either :

or

On the other h and

Fig.

6. - The

integration

of a 60° dislocation in

compession, glide

on

_{primary planes.}

_(a)

and

_(b)

correspond

to the

_bj

in two different

decomposed

core

_{configurations}

where the DSC dislocations

bJo

and

_b2

are

_{recognizable.}

In

_(a)

_bJo

is in a _compact form unlike in

(b)

where it is dissociated

(micrograph

M.

_{Elkajbaji). (c)}

and

_(d)

show the

_{complete decomposition}

_{of bj and br}

into

b + b,

and

_{b 2 + b,.}

Deformation conditions

_(a)

and

_(c)

T =1120 K, s = 1.7 %,

(b)

and

(d)

These final results all involved climb. In the reaction

_[1],

the

_bjo

DSC GBD is sometimes found in a

_slightly

dissociated form :

The lower

_path

of

_figure

5 illustrates the direct climb

_integration

of the

_b,

DSC GBD into the

boundary.

This mechanism leaves an «

_imperfect

» _pure

_step

(h

= 1.5

ho)

in the GB. The 30°

trailing partial

could then enter

_{spontaneously.}

3.1.3 Tension with

_glide

on the additional

plane.

- The 600 dislocation arrives

on the

(111 )I

plane

of

_grain

I,

with the 30°

_partial

_{b3o (I ) in}

front and the 90°

_{partial trailing}

behind. These

_partials

do not

_belong

to the DSC lattice. The

_integration

of the

_complete

60 °D would have left a GBD whose

Burgers

vector would have been the initial 60 °D

_Burgers

vector and whose associated

step

height

would have been h = ₊ 0.25

ho.

By

thermal activation the 30°

partial

b’ (1)

(pÎ 1 + p 2)

decomposes

into -

_bg

_plus

a

partial

pÎ

+

(Fig.

7 upper

path).

The

loop

of the -

_6g

_expands.

Recombination of

_{the p 1 +}

with the

_trailing

_{b9o (1)}

=

(- 2 pÎ - 4 pÎ )

is

_{energetically}

favourable to form a

bp(h

= - 0.75

ho)

constricted dislocation

belonging

to

the DSCL. This one

_decomposes

_{spontaneously}

into another -

_bg

_plus

a

_remaining

b2 (h

= -1.75

_{h o ).}

However,

like in the other cases,

spontaneous

constriction over a certain

Fig.

7. - The

integration

of a 60° dislocation in tension,

glide

on additional

planes(AGP)

of

_grain

1

which is

_{(111 )I.}

In the small

_rectangular

inserts the

_{decompositions}

of the

_Burgers

yector are shown with

respect to

_grain

I. As in the other cases three

_paths

are

_given.

The two _upper ones

_{require glide only,}

but

the lower one

_requires

climb

_(C).

In this case the

_{leading partial}

must dissociate into a DSC

_partial

-

2 p Î plus b ô.

In order to have a more

legible

pattern, the

angle

between the additional

plane

and the

length

cannot be

excluded,

and the

_resulting

_{b6ü(I) (never observed)}

could

_decompose

into either one of the

previous configurations.

Unlike in the

_previous

case

_(lower

_path

of

_3.1.2),

the

_{leading partial}

cannot climb on its whole in the

_boundary.

_Moreover,

a further climb

decomposition

could lead to

_{b 2}

_plus

_{(- 2 pl).}

The

_stacking

fault then

_repels

the

_trailing

partial spontaneously.

The

_boundary

residual is - 2

bg

and can

_{immediately glide}

off in the

boundary.

The three

_paths

lead to the same

b 2 (h

= - 1.75

_{h o )}

residual dislocation. As shown

in table

I,

only

one series of

_samples

deformed in tension was studied and

_furthermore,

as

mentioned in §

1.2,

the Schmid factor of this

_slip

_system

is

_relatively

low and

_consequently

the number of dislocations

_gliding

on the additional

_planes

is

_extremely

low. Thus we found

_only

one GB defect

_{unambiguously}

related to the above described mechanism : this GBD is

completely

isolated on a wide

_length

of

_perfect

_GB,

its

_Burgers

vector is

_{b 1 (h}

= - 2.75

_{ho )}

and this defect results from the interaction of the initial

_{b 2(h}

= -1.75

_ho)

with a

_glissile

bg (h

= - ho )

GBD. This

_b3o

arises

_unlikely

from the direct

_{decomposition}

_{(b3o -}

3

_{bg )}

of the initial 60 °D

_(h

= 0.25

ho)

coming

_on the additional

plane.

Fig.

8. - The final results of the different

paths

of the

integration

of a 60 °D in tension on additional

planes

are the same :

_only

one

b 2 (h

= -1.75

_{ho )}

has to be found in the

_boundary

or one

b3o (h

= - 2.75

_{h o )}

which is shown in the

_picture

and which results from the interaction between

b2

and another

_glissile

_{bg (T}

= 1020 K, £

= 1.3 % ).

3.1.4

Compression

with

_glide

on the additional

_plane.

- The 90°

partial

arrives first and

decomposes

by

thermal activation into two -

_bg

dislocations

_plus

a

_{remaining partial}

(- 2 pÎ )

(Fig. 9).

Since the two -

_bg

do work in the

_{boundary by glide,}

and since the two

reaction

_products

are almost

_{perpendicular}

to each

other,

this process

might actually proceed

without thermal activation.

_Subsequently

the

_(-

_{2 pl)}

and the 30°

_trailing

attract each other

spontaneously

to form a

b 4(h

= 1.75

ho)

_as observed in

figure

10. The _same result

might

be

reached

_{by thermally}

_activating

a total constriction into a

_{ba (1) (h = - 0.25 ho) =}

2 bg

+ b1o(h = 1.75 ho).

The

_{leading partial}

cannot climb on its whole in the GB. A

combination of

_bg

emission and of climb

_{decomposition}

into

_partials

_(lower

_{path Fig.}

₉₎

leads

Fig.

9. - The

integration

of a 60° dislocation in

_{compression, glide}

on additional

_planes(AGP)

of

_grain

I. In the small

_rectangular

inserts the

_Burgers

vector

_{decompositions}

are shown with respect to

_grain

I.

Three

_{paths analogous}

to the three

paths

of

_figure

7 are drawn.

They

all

_give

the same

b4

residue under

_glide

or climb

_integration

_(the

remark in

_Fig.

7 about the

_angle

between the additional

planes

and the GB

_plane

is valid here as

_well).

Fig.

10. - The

integration

of a 60° dislocation in

_{compression, glide}

on additional

planes.

The

bjo

is found

completely

isolated and can

_only

be the result of the

_{decomposition}

shown in

_figure

9. The

3.2 A SCREW DISLOCATION ON ANY PLANE UNDER TENSION OR COMPRESSION. - This is the

simplest

case. Like in

_cross-slip

in the

bulk,

the two

_{Shockley partials}

could recombine to

form a constricted screw

_by

thermal

_activation,

and dissociate

_again

on one or the other

_glide

plane

of the other

_grain.

Dissociation of the constricted screw that

_produces

_bg

_glissile

dislocations in the

_boundary

is

_highly

_improbable,

nor is it

_{probable by using}

the

_partials

of section 2. If the screw remains

_dissociated,

the emission of a

_bg

from the

_leading

30°

_partial

like in the case

_figure

3

(upper path)

would lead to an even more

_{unlikely configuration}

where the

_{trailing partial}

would be

_repelled

at a

_higher

distance than before. If climb is

available,

the constricted screw dislocation could dissociate and

_consequently

be

_stopped

at the

_boundary.

Figure

11 shows a

_{configuration}

without any

_global

_Burgers

vector which

_might

be the

projection

of a screw dislocation dissociated in the GB

_plane.

As the screw

_component

is

invisible two structures could be

_proposed

_{(Fig.11b, c).}

In the first case the core of two 30°

GB dislocations is

_{recognizable :}

the screw is

_{decomposed by}

climb

_absorbing

two

interstitials. In the second case

(c)

a

_completely

reconstructed defect could be

_{imagined using}

T units : this

residue,

which also consumed two

_{interstitials,}

_might

be left in the GB after the reemission of the screw dislocation from the

_{previous rearranged}

_compact

_{configuration.}

Owing

to the

_stability

of the initial 4 = 9 GB _a direct

absorption

of interstitials

_inducing

a

structural

_change

could be dismissed. We could not decide in favour of either one or the other model.

Nevertheless,

it remains valid that if

large

climb occurs, the two initial

_b30

would climb

over a

_larger

distance

_impeding

the transmission of the screw. If climb is not

available,

having

no other

_choice,

the screw dislocation traverses the

_{boundary, presumably}

with an activation

energy very similar to cross

_slip

in the bulk. Baillin et al.

[3]

have indeed seen

_{by in}

situ

HVEM electron

_microscopy

screws

_traversing

the

_boundary.

At low

_temperature

(T

lower

than 970

_K),

_{using high}

resolution

_microscopy,

we never observed any GB residue

stemming

from screws. This seems to confirm their

_findings.

Fig.

11. - Observation of _{a screw} dislocation

completely integrated

in the GB but

decomposed

into two

30° DSC dislocations. The total

_Burgers

vector is null in

_projection

whereas the core of both 30° DSC dislocations can be

_recognized

_(micrograph

M.

_{Elkajbaji). Compression}

1.7 %, T = 1120 K

₍₀

on the

seven atom

_rings).

4. Discussion.

The reader

_might

be

_disappointed

that we offer no

_preference

for the upper or lower

_path

of

figures

3, 5, 7, 9 (in

3.1.1,

in

3.1.2,

in

3.2.1,

in

_3.2.2).

The upper

path,

is in fact a mechanism

that a

_point

of the

_{leading partial decomposes}

into a

_{perfect loop}

in the GB

_plane.

The lower

path

is a modified version of the

_{Seeger-Schoeck}

mechanism in the bulk. For the

_bulk,

Bonneville,

Escaig

and Martin

_[25]

offered

_experimental

evidence for the

_{Friedel-Escaig}

mechanism. In the case of

_thermally

activated

_integration

of a

_gliding

dislocation in the

boundary,

we feel that our

_experiments

are insufficient to decide in favour of one or the other

reaction

_path.

Since the activated

_{configuration}

_is,

in

_{principle, directly}

not

_observable,

a

distinction between one or the other

_path

can be made

_only

from their

_{macroscopically}

observable consequences, or from

_thorough

and

_precise

calculations of the

_type

made

_by

Püschl and Schoeck

_[26].

The activation rates

_{depend explicitly}

on

_temperature

and

_applied

and internal stresses, therefore one or the other mechanism

_might

be

_preferred.

Furthermore,

the observed «

_{partial »}

DSC

dislocations,

leads to the idea that the structure of the core of the intermediate

_{configurations plays certainly}

a

_major

role and

_might

_{determine the ways of}

éntrance.

Besides these

subtleties,

the idea of

_thermally

activated

_entry

is a

_simple

one.

Crystallog-raphically

the 60° dislocation cannot cross over

_{directly by glide}

into the other

grain.

Nevertheless work can be done

_by

_splitting

off a dislocation

_glissile

in the

_boundary,

and this work facilitates

_entry.

_{Crystallographically}

the screw dislocation cannot dissociate

_by

_glide

in the

_boundary,

but work can

_only

be done in

grain

II,

which favours

cross-slip.

If climb is available even more

configurations

within the

boundary

become

available,

and

transmission becomes even less

_likely.

Although

thermal activation makes

_slip

into the

_{boundary likely}

and

_slip

into

_grain

II

unlikely,

the latter is not

_{totally impossible.}

Whenever a

_totally

constricted

_segment

exists in the

_boundary,

one can force its

_{decomposition}

into a

_{glide loop}

in

_grain

II

_plus

some residue

in the

_{boundary by}

_very

_{high applied}

stresses - if thermal activation is available : this

explanation might

account for transmission of non screw dislocations as observed

_{by Jacques,}

Baillin and

George

[27].

5. Conclusion.

This 60° dislocation can, and the screw dislocation cannot emit a

_bg

dislocation

_glissile

in the

boundary. Only

under very

high

stresses the 60° dislocation can

_split

off a dislocation

_glissile

in

_grain

II.

_{Only by}

climb the screw dislocation

_partials

can move in the

_boundary.

Therefore the 60° dislocation is

_integrated

in the

_boundary

_(but

transmitted

_only

under

_high

_stresses),

and the screw dislocation traverses into

_grain

II

_(but

is

_integrated

into the

_boundary

under climb

_conditions).

Thus thermal activation blocks 60° dislocations at the

_boundary,

but

_helps

screw dislocations to transverse it.

Acknowledgment.

The work was

_{supported by}

the C.N.R.S. in France and the Austrian

_Academy

of Sciences. H.O.K.K.

_acknowledges

support

by

the Wiener

_{Hochschuljubilâumsstiftung.}

References

[1]

HIRTH J. _P., Metall. Trans. A 3

₍₁₉₇₂₎

3047.

[2]

MARTINEZ-HERNANDEZ M., KIRCHNER H. O. K., KORNER A., GEORGE A. and MICHEL J. P.,

Philos.

_Mag.

A 56

₍₁₉₈₇₎

641.

[3]

BAILLIN X., PELISSIER J., BACMAN J. J., JACQUES A. and GEORGE A., Philos.

_Mag.

A. 55

₍₁₉₈₇₎

143.

[5]

ELKAJBAJI M. and THIBAULT-DESSEAUX J., Philos.

_Mag.

A 58

₍₁₉₈₈₎

325.

[6]

THIBAULT-DESSEAUX J., PUTAUX J. L., JACQUES A., ELKAJBAJI M., Interfacial Structure,

Properties

and

_Design,

MRS Ser. 122

(1988)

293.

[7]

GEORGE A., Rev.

_{Phys. Appl.}

23

₍₁₉₈₈₎

479.

[8]

KING A. H., CHEN F., Mat. Sci.

_Eng.

66

₍₁₉₈₄₎

227.

[9]

ELKAJBAJI M., THIBAULT-DESSEAUX J., MARTINEZ-HERNANDEZ, JACQUES A., GEORGE A., Rev.

Phys.

Appl.

22

₍₁₉₈₇₎

569.

[10]

BOLLMANN W.,

Crystal

defects and

_crystalline

interface

_{(Springer Verlag)}

1970.

[11]

HIRTH _J., LOTHE J.,

Theory

of Dislocations

_{(McGraw-Hill)}

1968,

p. 21.

[12]

KING A. H., SMITH D. A., Acta

_Cryst.

A 36

₍₁₉₈₀₎

335.

[13]

BOURRET A., BACMANN J. J., Rev.

_Phys.

_Appl.

22

₍₁₉₈₇₎

563.

[14]

SCHOBER T., BALLUFFI R., Philos.

_Mag.

21

₍₁₉₇₀₎

109.

[15]

POND R., Proc. R. Soc. London A 357

₍₁₉₇₇₎

471.

[16]

BACMANN J. J., SYLVESTRE G., PETIT M., BOLMANN W., Philos.

_Mag.

A 43

₍₁₉₈₁₎

189.

[17]

SCHOECK G., and SEEGER A., Phil. Soc. London, 340

_{(1955a) ;}

_Report

of the Bristol Conference

on Defects in

_{Crystalline Solids,}

London,

Physical Society

(1955b)

p. 340.

[18]

WOLF _H., Z.

_{Naturforschung}

A 15

₍₁₉₆₀₎

180.

[19] FRIEDEL

J., Dislocations and Mechanical

_Properties

of

_Crystals,

J. C. Fisher et al. Eds.

(New

York :

_Wiley)

1957, p. 330.

[20]

ESCAIG _B.,

_Phys.

Stat. sol. 28

_(1968a)

463 ; J.

_Phys.

29

_(1968b)

255 ; Dislocation

_Dynamics,

Rosenfield, Hahn, Bemont, Jaffee Eds.

_(New

York : McGraw

_Hill)

1968c p. 665 ; Thèse de

Doctorat d’Etat, université de Paris, Centre

_d’Orsay,

No A 382

_(1968d).

[21]

FLEISCHER R., Acta Met. 7

₍₁₉₅₉₎

134.

[22]

THIBAULT J., ELKAJBAJI M., J.

_Phys.

_Colloq.

France 49

₍₁₉₈₈₎

C5-283.

[23]

POIRIER J. _P., Rev.

_Phys.

_Appl.

11

₍₁₉₇₆₎

731.

[24]

THIBAULT-DESSEAUX

J., PUTAUX J. L., KIRCHNER H. O. K., Philos.

_Mag

_(accepted).

[25]

BONNEVILLE _J., ESCAIG B. and MARTIN J. L., Acta metall. 36

₍₁₉₈₈₎

1989.

[26]

PUSCHL W. and SCHOECK G.,

Strength

of Metals and

_Alloys,

Kettunen,

Lepisto,

Lehtonen Eds.

(Pergamon Press)

vol. I

₍₁₉₈₈₎

_{p. 239.}

[27]

JACQUES A., BAILLAIN _X., GEORGE A.,

Strength

of Metals and

_Alloys,

Kettunen,

Lepisto,