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Comments on deformation twinning in silver- and copper-alloy crystals
Scripta METALLURGICA
Vol, 9, pp, 815-817, 1975 Printed in the United States
COMMENTS ON DEFORMATION
Pergamon
TWINNING IN SILVER- AND COPPER-ALLOY
Press,
Inc
CRYSTALS
S. Mahajan and G. Y. Chin Bell Laboratories Murray Hill, New Jersey 07974 [Received April
Recently, deformation
(i) have investigated
in detail the
twinning behavior of silver- and copper-alloy
temperatures (i)
Narita and Takamura
3, 1975)
down to 4.2°K.
Their principal
crystals at
results are summarized below:
Twinning takes place on the most active slip plane.
when the specimen
axis lies in the shaded triangle
observed on the primary and conjugate planes, o01 oc ~
in Fig.
i.e.,
B
Specifically, i, twinning
(ii[) and
(i[i).
is It has
A
OTO
010
oi~\
\
I /
/o~
ooi [100]
stereographic
projection
and the
Thompson n o t a t i o n .
The specimen axis lies in the shaded triangle been ascertained
that slip on the primary and conjugate planes is ac-
complished by dislocations whereas
the operative
with Burgers vectors BE and B~, respectively,
twinning vectors are B~ and B~.
In addition,
been shown that, as the tensile axis rotates towards the boundary,
(i).
coplanar
it has
[i00]-[iii]
slip with Burgers vector B~ is observed on the primary
plane. (ii)
The closer to
macroscopic
twinning
[iii] is the tensile axis, the lower is the
stress.
Narita and Takamura have attempted to rationalize in terms of a nucleation
model which they proposed 815
these observations
in 1968
(2).
It is
816
COMMENTS ON DEFORMATION TWINNING
Vol,
9, No. 8
envisaged that a primary dislocation at the head of a pile-up may react with a Lomer dislocation D~ to form a two-layer twin; the reaction is given by
To form the Lomer dislocation
(D~), the conjugate slip dislocations B5
must cross glide onto the cross plane,
i.e.,
(iii), and subsequently
react with the primary coplanar system B~; the resulting dislocation lies along the intersection of primary and cross planes.
The Lomer dislocation
C~, which is required for twinning on the conjugate plane, could likewise arise by the cross glide of CB dislocations
from the primary onto the cross
@lane and their reaction with B~ dislocations
lying on the conjugate plane;
the resulting Lomer lies along the intersection of conjugate and cross planes. mentally.
However,
D~ and C~ Lomer locks are not generally observed experi-
The ones that are seen lie along the directions of intersection
of the primary with the critical or conjugate plane highly stressed secondary slip planes.
(3,4).
The latter are
It is also emphasized that the
presence of slip traces on the cross plane do not necessarily imply the existence of D~ and C~ Lomers. not extensive,
Generally,
the slip on the cross plane is
and may be caused by the complex stress pattern that may
exist at the head of pile-ups on the primary and conjugate planes
(5).
We feel that the observations of Narita and Takamura can satisfactorily be accounted for in terms of a model which we have recently proposed
(6).
It is emphasized that the circumstantial evidence in support of the model has been developed by correlating the crystallographic
features of twins
and associated slip by transmission electron microscopy.
It is envisaged
'that a three-layer twin on the primary plane could evolve when the primary (B~) and coplanar
(B~) dislocations combine according to the following
reaction:
B~ + B~ + 3 B$
(B)
The twin thickens when the embryonic twins located at different levels within a slip band grow into each other.
Similarly,
the formation of twins
on the conjugate plane is likely to be governed by the following reaction:
B5 + B~ ÷ 3 B7
(C)
B~ dislocations on the conjugate plane could arise either from the B~ slip on the conjugate plane or from their cross glide from the primary pla~e. We do not foresee any difficulty for either of these processes because along the
[i00]-[iii] boundary the Schmid factors for the B ~ slip on the
primary and conjugate planes are the same.
Further,
it is evident from
the preceding discussion that the observed twin crystallography can be rationalized without invoking the existence of the unlikely Lomers D~ and
C~.
Vol.
9, No.
8
COMMENTS
Gallagher
ON DEFORMATION
(7) has shown that reactions
of fault-pairs w h i c h are e n v i s i o n e d embryonic twins
(6).
total d i s l o c a t i o n s
in reaction
pile-up is p r o b a b l y n e c e s s a r y Shockley partials,
interaction
one
the repulsive
(9).
The e v o l u t i o n a r y
with the experimental of pile-ups
observations
and
and e n h a n c e m e n t
[i00], respectively.
is farther
from
activation following twinning
a
to occur
rearrangement
(6,8).
of
can be locally changed into an
details thus developed
that fault-pairs
are consistent
can form in the absence
(7-9).
of the m a c r o s c o p i c
suppression
since the
(C) repel each other,
appropriate
N a r i t a and Takamura have a t t r i b u t e d dependence
to three-layer
for either of these reactions through
817
(C) govern the formation
and argued that,
(B) or
It has recently been shown that,
attractive
(B) and
to be p r e c u r s o r s
It has been suggested
involved
TWINNING
of cross
of coplanar
stress:
(BA).
stress-induced
slip in specimens o r i e n t e d near believe
primary
that if the specimen
slip
(BE) will precede
It is therefore
[iii] axis
the
reckoned that the
are likely to raise the observed m a c r o s c o p i c
(i)
(ii)
In summary,
slip
the o b s e r v e d o r i e n t a t i o n
stress to internal
We, however,
[iii], an extensive
two factors
structures;
twinning
the back stress exerted by the e x i s t i n g
propagating
slip
twins w o u l d encounter more obstacles.
it has been shown that the operative
o b s e r v e d by Narita
and Takamura
terms of our model
for twin formation
twinning
(i) can s a t i s f a c t o r i l y (6), without
systems
be r a t i o n a l i z e d
in
invoking the existence
of the unlikely Lomers D~ and C~. References i.
N. Narita and J. Takamura,
2.
S. Miura, J. Takamura and N. Narita, Proc. Inst. Conf. on the Strength of Metals and Alloys, Supplement to Trans. J.I.M. 9, 555
Phil.
Mag.
29, i001
(1968).
3.
S. Mader,
(1963).
4.
Z. S. Basinski,
5.
D. H. Avery and W. A. Backofen,
6.
S. M a h a j a n
7.
P. C. J. Gallagher,
8.
P. C. J. G a l l a g h e r
9.
S. Mahajan,
A. Seeger and H. M. Thieringer, cited in A d v a n c e s
Phys.
Stat.
Trans. AIME
Sol.
and J. Washburn,
submitted to Met.
J. Appl.
in Physics
and G. Y. Chin, Acta Met.
Trans.
(1974).
13, 206 227,
21, 1353 16, 95
835
34, 3368
(1964). (1963).
(1973).
(1966).
Phil. Mag. (1975).
Phys.
15, 969
(1967).
Vol, 9, pp, 815-817, 1975 Printed in the United States
COMMENTS ON DEFORMATION
Pergamon
TWINNING IN SILVER- AND COPPER-ALLOY
Press,
Inc
CRYSTALS
S. Mahajan and G. Y. Chin Bell Laboratories Murray Hill, New Jersey 07974 [Received April
Recently, deformation
(i) have investigated
in detail the
twinning behavior of silver- and copper-alloy
temperatures (i)
Narita and Takamura
3, 1975)
down to 4.2°K.
Their principal
crystals at
results are summarized below:
Twinning takes place on the most active slip plane.
when the specimen
axis lies in the shaded triangle
observed on the primary and conjugate planes, o01 oc ~
in Fig.
i.e.,
B
Specifically, i, twinning
(ii[) and
(i[i).
is It has
A
OTO
010
oi~\
\
I /
/o~
ooi [100]
stereographic
projection
and the
Thompson n o t a t i o n .
The specimen axis lies in the shaded triangle been ascertained
that slip on the primary and conjugate planes is ac-
complished by dislocations whereas
the operative
with Burgers vectors BE and B~, respectively,
twinning vectors are B~ and B~.
In addition,
been shown that, as the tensile axis rotates towards the boundary,
(i).
coplanar
it has
[i00]-[iii]
slip with Burgers vector B~ is observed on the primary
plane. (ii)
The closer to
macroscopic
twinning
[iii] is the tensile axis, the lower is the
stress.
Narita and Takamura have attempted to rationalize in terms of a nucleation
model which they proposed 815
these observations
in 1968
(2).
It is
816
COMMENTS ON DEFORMATION TWINNING
Vol,
9, No. 8
envisaged that a primary dislocation at the head of a pile-up may react with a Lomer dislocation D~ to form a two-layer twin; the reaction is given by
To form the Lomer dislocation
(D~), the conjugate slip dislocations B5
must cross glide onto the cross plane,
i.e.,
(iii), and subsequently
react with the primary coplanar system B~; the resulting dislocation lies along the intersection of primary and cross planes.
The Lomer dislocation
C~, which is required for twinning on the conjugate plane, could likewise arise by the cross glide of CB dislocations
from the primary onto the cross
@lane and their reaction with B~ dislocations
lying on the conjugate plane;
the resulting Lomer lies along the intersection of conjugate and cross planes. mentally.
However,
D~ and C~ Lomer locks are not generally observed experi-
The ones that are seen lie along the directions of intersection
of the primary with the critical or conjugate plane highly stressed secondary slip planes.
(3,4).
The latter are
It is also emphasized that the
presence of slip traces on the cross plane do not necessarily imply the existence of D~ and C~ Lomers. not extensive,
Generally,
the slip on the cross plane is
and may be caused by the complex stress pattern that may
exist at the head of pile-ups on the primary and conjugate planes
(5).
We feel that the observations of Narita and Takamura can satisfactorily be accounted for in terms of a model which we have recently proposed
(6).
It is emphasized that the circumstantial evidence in support of the model has been developed by correlating the crystallographic
features of twins
and associated slip by transmission electron microscopy.
It is envisaged
'that a three-layer twin on the primary plane could evolve when the primary (B~) and coplanar
(B~) dislocations combine according to the following
reaction:
B~ + B~ + 3 B$
(B)
The twin thickens when the embryonic twins located at different levels within a slip band grow into each other.
Similarly,
the formation of twins
on the conjugate plane is likely to be governed by the following reaction:
B5 + B~ ÷ 3 B7
(C)
B~ dislocations on the conjugate plane could arise either from the B~ slip on the conjugate plane or from their cross glide from the primary pla~e. We do not foresee any difficulty for either of these processes because along the
[i00]-[iii] boundary the Schmid factors for the B ~ slip on the
primary and conjugate planes are the same.
Further,
it is evident from
the preceding discussion that the observed twin crystallography can be rationalized without invoking the existence of the unlikely Lomers D~ and
C~.
Vol.
9, No.
8
COMMENTS
Gallagher
ON DEFORMATION
(7) has shown that reactions
of fault-pairs w h i c h are e n v i s i o n e d embryonic twins
(6).
total d i s l o c a t i o n s
in reaction
pile-up is p r o b a b l y n e c e s s a r y Shockley partials,
interaction
one
the repulsive
(9).
The e v o l u t i o n a r y
with the experimental of pile-ups
observations
and
and e n h a n c e m e n t
[i00], respectively.
is farther
from
activation following twinning
a
to occur
rearrangement
(6,8).
of
can be locally changed into an
details thus developed
that fault-pairs
are consistent
can form in the absence
(7-9).
of the m a c r o s c o p i c
suppression
since the
(C) repel each other,
appropriate
N a r i t a and Takamura have a t t r i b u t e d dependence
to three-layer
for either of these reactions through
817
(C) govern the formation
and argued that,
(B) or
It has recently been shown that,
attractive
(B) and
to be p r e c u r s o r s
It has been suggested
involved
TWINNING
of cross
of coplanar
stress:
(BA).
stress-induced
slip in specimens o r i e n t e d near believe
primary
that if the specimen
slip
(BE) will precede
It is therefore
[iii] axis
the
reckoned that the
are likely to raise the observed m a c r o s c o p i c
(i)
(ii)
In summary,
slip
the o b s e r v e d o r i e n t a t i o n
stress to internal
We, however,
[iii], an extensive
two factors
structures;
twinning
the back stress exerted by the e x i s t i n g
propagating
slip
twins w o u l d encounter more obstacles.
it has been shown that the operative
o b s e r v e d by Narita
and Takamura
terms of our model
for twin formation
twinning
(i) can s a t i s f a c t o r i l y (6), without
systems
be r a t i o n a l i z e d
in
invoking the existence
of the unlikely Lomers D~ and C~. References i.
N. Narita and J. Takamura,
2.
S. Miura, J. Takamura and N. Narita, Proc. Inst. Conf. on the Strength of Metals and Alloys, Supplement to Trans. J.I.M. 9, 555
Phil.
Mag.
29, i001
(1968).
3.
S. Mader,
(1963).
4.
Z. S. Basinski,
5.
D. H. Avery and W. A. Backofen,
6.
S. M a h a j a n
7.
P. C. J. Gallagher,
8.
P. C. J. G a l l a g h e r
9.
S. Mahajan,
A. Seeger and H. M. Thieringer, cited in A d v a n c e s
Phys.
Stat.
Trans. AIME
Sol.
and J. Washburn,
submitted to Met.
J. Appl.
in Physics
and G. Y. Chin, Acta Met.
Trans.
(1974).
13, 206 227,
21, 1353 16, 95
835
34, 3368
(1964). (1963).
(1973).
(1966).
Phil. Mag. (1975).
Phys.
15, 969
(1967).