- Email: [email protected]
Remarks on the elastic constants and temperatures of martensitic transformation in the Li-Mg alloys
ACTA
986
Such a result is reasonable
for known and assumed
Therefore,
values of yal and b,.
METALLURGICA,
our model(i)
is in
VOL.
10,
1962
one would expect t’hat as the anisotropy change
of Mg content
agreement with the fact that stacking fault rings have
structure
should
been observed in aluminium, which could not be explained in previous models(2). G. SAAD.4
transform
at progressively
University
2c44
Division
c,,
Berkeley 4, California
April 2, 1962.
and especially alloys
dependence
recently
by Trivisonno
unstable
and
Metals
and
of these alloys becomes
via a martensitic
(110)
anisotropy, (li0)
instability manifest
crystal
reaction. structure
indicative
having
a high
of a low value of the
shear modulus, exhibit a tendency at low temperatures.
by transformation
ture, generally by a nucleation
preclude
interpolated
transformation
In the last two columns
temperatures from
as a function
curves
by
currently
of annealed Li-Mg alloys (M, temperacolumn
at which the transformation
with mechanical
deformation
(M, tempera-
(c
c,,
11
8.7s 8.91 9.03 9.12 9.24
pure Li 1.09 2.26 3.01 4.28
2C,,
_ c _)
M,, “K 71 77 82 86 91
8.55 8.59 8.58 8.62 8.i3
1.027 I .037 1.053 1.058 1.0.58
is
from the composition
dependence
2c44
although the alloy containing 2.26 a/o c,, - C,, ’ Mg is not in good agreement. It is not’eworthy that of
the curves of M, and M, vs a/o Mg by Barrett Trautz exhibit a maximum
then decrease rapidly with This decrease is so pronounced
character
because
that no transformation
could be induced at 78°K in an
the diffusion
required
This phenom-
M,
temperatures
alloy containing severely
24.2 a/o Mg even if the sample were
cold-worked,
although
M, temperatures
be of interest to see whether a corresponding is observed
Cu-Be(‘)
The writertg) has noted that the major
and beta Au-Cd,
unit cell which occurs during
at least in the case of beta Ag-Cd
is a glide of alternate
(110) planes
along the [llO] direction with respect to the interleaving (110) planes.
Low resistance to such a shear is in
these alloys by Zirinskyo”)
2c44
measured in c11 - C,, in beta Au-Cd, Lazarusoi)
accord with the high value of
and
the M,
increasing Mg content.
crystal
and
around 12 a/o Mg;
binary systems Cu-Zn,(4) Ag-Cd,c5) Au-Cd,(s)
this transformation,
97 105 111 116 121
As can be seen, the trend of both M, and M, is as would be expected
Li,@) Li-Mg allays(3) and the b.c.c. beta phases of the
of the b.c.c.
M,, “K
I” (Cl, - Cl,)
high as 165°K are noted at the maximum.
distortion
and the
occurs con-
in the pure metals Na and
and Cu-Al.@)
and
t’he t’emperatures of spontaneous
tures) are listed in the penultimate temperatures
of Mg
Barrett
struc-
and growth mechanism.
enon has been observed
toward
This instability
to another
one of martensitic
the low temperatures
as well as the ratio
of Li-Mg
b.c.c. structure
elastic
from their data.
Trautzc3) are given;
and Smith(l) at which the
alloys with a b.c.c.
below,
.__
can be correlated with the temperatures transforms
content
of the elastic constants
that of the elastic anisotropy
reported
The
which is a measure of the elastic anisotropy,
Composition at. y,‘, Mg
constants and temperatures of martensitic transformation in the Li-Mg alloys*
The composition
therefore
ture) in the last.
on the elastic
Remarks
and
’
c,,
calculated
1. G. &ADA, Acta IWet. 2. D. KUHLMAN-WILSDORF, Phil. &fag. 3, 125 (19.58). 3. R. M. J. COTTERILL, cited by M. J. WHELAN, Conference, Electro?z Microsco-py and Strength of Crystals, Berkeley, (1961). 4. F. VINCOTTE, M.D. Thesis, University of California, Berkeley (1962). * Received
-
stable
higher temperatures.
C,,) and C,, reported by Trivisonno
the transformation
References 10, 551 (1962).
less
and Smith are tabulated
of California
Inorganic Materials
become
values of $(C,, -
increased with
in the alloy series, the b.c.c.
in the elastic anisotropy
as
It would maximum
of these alloys
around 12 a/o Mg. If such a composition dependence exists it might suggest a CIA of c44 and &G greater contribution of the Fermi energy to the elastic constants
of the Li-Mg
alloys
than Trivisonno
and
Smith imply. The magnitude
2c44
of the ratio CI,
-
reported
for
c,,
the Li-Mg alloys is of the order of magnitude
of those
measured by Zirinsky for beta Au-Cd (11.6 and 14.1, depending on the composition) and by Lazarus in
in beta Cu-Zn and now Trivisonno and Smith in Li and the Li-Mg alloys. If this elastic anisotropy criterion for mart,ensitic
beta Cu-Zn (8.47), both of which alloys undergo martensitic reactions at low temperatures. The relation-
transformation
ship between the M, temperature
from the b.c.c. structure
is accepted,
and valence electron
LETTERS
density is under study in this laboratory, that the two can be related through stants.
A study
contemplated,
of the alloys
however,
in the hope
the elastic
con-
of Li and Mg is not
since there are alloy systems
where the effect of the Fermi constants
TO
energy on the elastic
THE
ways
which
definition location
lead to opposite
results.
We prefer a
which assigns to a right-handed
screw dis-
direction as does the definition of Peach and Koehler.(2) According
a Burgers vector in the positive
to this definition location
is better understood.
987
EDITOR
the Burgers vector
with the extra
half-plane
of an edge disbelow
the glide
plane points to the right when the observer looks in
D. B. MASSON Department of Metallurgy
the positive direction along the dislocation.
Metals Research Xection Washington State University
shown.
In Fig. l(a) two left-handed
screw dislocations
are
Their positive directions are given by the unit
vectors L, and L,, their Burgers vectors by b, and b,.
References 1. J. TRIVISONNO and C. S. S~XITH,Acta Met. 9, 1064 (1961). 2. C. S. BARRETT,Acta Cry&, 9, 671 (1956). 3. C. S. BARRETT and 0. R. TRAUTZ, Trans. Amer. Inst. Min. (Metall.) Engrs. 175, 579 (1948). Metals TechnoZog?/,TP 23463 (April, 1948). 4. A. B. GRENINGERand V. G. MOORADIAN,Trans. Aww. Inst. Min. (Metdl.) Engrs. 122, 337 (1938). 5. D. B. MAS~ONand C. S. BARRETT,Trans. Amer. Inst. Min. (Metall.) Engrs. 212, 260 (1958). 6. 1,. CRANG and T. A. READ, Trans. Amer. Inst. Min. (MetaZl.) Engrs. 189, 47 (1951). 7. R. J. BLOCK and G. H. KEHL, Trans. Amer. Inst. Min. (Metall.) Engrs. 215, 878 (1959). 8. R. HAYNES, Amer. Sot. Met& 82, 493 (1953). 9. D. B. MASSON,Tmns. Amer.Inst. Min. (MetaZZ.)&grs.218, 94 (1960). 10. S. ZIRINSKY, Actrc Met. 4, 164 (1956). 11. D. LAZARUS, Phys. Rev. 74, 1726 (1948); ‘46, 547 (1949).
L, moves
Dislocation
given by m,.
to the right in the direction
It is unnecessary
to define this vector
* Received Spril 2, 1962.
On the type of point defects formed after crossing of dislocations* When two dislocations cut through
both dislocations.
Especially
are screw dislocations, motion
with intersecting glide planes
each other, generally,
a jog is formed in
when both dislocations
the jogs will hinder
further
because they can only keep up with the dis-
location by the emission of point defects, vacancies interstitial atoms. defect is formed locations.
after the crossing of two given dis-
Saadao)
when vacancies
or
The problem is which type of point gave an expression
be positive when interstitials
which should
are formed and negative
more precisely. cut through Fig. l(b).
it contains only the Burgers vector of the stationary and not the positive
direction
of it.
But
L, has
The situation after dislocation
the stationary
dislocation
Now both dislocations
jog in L, has the length Whether it is +b,
are formed.
This expression, however, cannot be correct because dislocation
Fm. 1. Two left-handed screw dislocations before crossing (a) and after crossing (b). The lattice planes perpendicular to the di&oation form a helicoidal surface. One turn of it is shown which sots as glide plane for the other dislocation. The hatched extra half-plane of the edge-type jog links the helicoidal lattice planes of the two parts of the screw dislocation.
or -b,
L, is given in
contain a jog.
and the direction is determined
The
of -b,.
by the direc-
tion in which L, pierces the glide plane determined
by
L, A m,. The sign is positive if, before crossing, L, and L, are related to each other as the direction of an
the sign of the Burgers vector can only be determined
electric current and the direction of the magnetic field
after a positive direction along the dislocation
has been
around it and negative in the opposite case, as in Fig.
changes sign when this The reason for this mis-
(Llm,L2)/j (L1m1L2) I, which contains the scalar triple
defined. The Burgers vector positive direction is reversed. understanding importance textbooks.
may
be that
and, remarkably,
this point
is rarely
of
is not stressed in most
After a positive direction has been chosen along the dislocation the Burgers vector can be defined in two 6
l(a).
Hence this sign is determined
by the expression
vector product of the three relevant vectors by its absolute value. When the jog with length and direction
divided -b,
and
Burgers vector b, moves a distance c1 it will emit interstitials (Fig. l(b)) because the extra half-plane has
986
Such a result is reasonable
for known and assumed
Therefore,
values of yal and b,.
METALLURGICA,
our model(i)
is in
VOL.
10,
1962
one would expect t’hat as the anisotropy change
of Mg content
agreement with the fact that stacking fault rings have
structure
should
been observed in aluminium, which could not be explained in previous models(2). G. SAAD.4
transform
at progressively
University
2c44
Division
c,,
Berkeley 4, California
April 2, 1962.
and especially alloys
dependence
recently
by Trivisonno
unstable
and
Metals
and
of these alloys becomes
via a martensitic
(110)
anisotropy, (li0)
instability manifest
crystal
reaction. structure
indicative
having
a high
of a low value of the
shear modulus, exhibit a tendency at low temperatures.
by transformation
ture, generally by a nucleation
preclude
interpolated
transformation
In the last two columns
temperatures from
as a function
curves
by
currently
of annealed Li-Mg alloys (M, temperacolumn
at which the transformation
with mechanical
deformation
(M, tempera-
(c
c,,
11
8.7s 8.91 9.03 9.12 9.24
pure Li 1.09 2.26 3.01 4.28
2C,,
_ c _)
M,, “K 71 77 82 86 91
8.55 8.59 8.58 8.62 8.i3
1.027 I .037 1.053 1.058 1.0.58
is
from the composition
dependence
2c44
although the alloy containing 2.26 a/o c,, - C,, ’ Mg is not in good agreement. It is not’eworthy that of
the curves of M, and M, vs a/o Mg by Barrett Trautz exhibit a maximum
then decrease rapidly with This decrease is so pronounced
character
because
that no transformation
could be induced at 78°K in an
the diffusion
required
This phenom-
M,
temperatures
alloy containing severely
24.2 a/o Mg even if the sample were
cold-worked,
although
M, temperatures
be of interest to see whether a corresponding is observed
Cu-Be(‘)
The writertg) has noted that the major
and beta Au-Cd,
unit cell which occurs during
at least in the case of beta Ag-Cd
is a glide of alternate
(110) planes
along the [llO] direction with respect to the interleaving (110) planes.
Low resistance to such a shear is in
these alloys by Zirinskyo”)
2c44
measured in c11 - C,, in beta Au-Cd, Lazarusoi)
accord with the high value of
and
the M,
increasing Mg content.
crystal
and
around 12 a/o Mg;
binary systems Cu-Zn,(4) Ag-Cd,c5) Au-Cd,(s)
this transformation,
97 105 111 116 121
As can be seen, the trend of both M, and M, is as would be expected
Li,@) Li-Mg allays(3) and the b.c.c. beta phases of the
of the b.c.c.
M,, “K
I” (Cl, - Cl,)
high as 165°K are noted at the maximum.
distortion
and the
occurs con-
in the pure metals Na and
and Cu-Al.@)
and
t’he t’emperatures of spontaneous
tures) are listed in the penultimate temperatures
of Mg
Barrett
struc-
and growth mechanism.
enon has been observed
toward
This instability
to another
one of martensitic
the low temperatures
as well as the ratio
of Li-Mg
b.c.c. structure
elastic
from their data.
Trautzc3) are given;
and Smith(l) at which the
alloys with a b.c.c.
below,
.__
can be correlated with the temperatures transforms
content
of the elastic constants
that of the elastic anisotropy
reported
The
which is a measure of the elastic anisotropy,
Composition at. y,‘, Mg
constants and temperatures of martensitic transformation in the Li-Mg alloys*
The composition
therefore
ture) in the last.
on the elastic
Remarks
and
’
c,,
calculated
1. G. &ADA, Acta IWet. 2. D. KUHLMAN-WILSDORF, Phil. &fag. 3, 125 (19.58). 3. R. M. J. COTTERILL, cited by M. J. WHELAN, Conference, Electro?z Microsco-py and Strength of Crystals, Berkeley, (1961). 4. F. VINCOTTE, M.D. Thesis, University of California, Berkeley (1962). * Received
-
stable
higher temperatures.
C,,) and C,, reported by Trivisonno
the transformation
References 10, 551 (1962).
less
and Smith are tabulated
of California
Inorganic Materials
become
values of $(C,, -
increased with
in the alloy series, the b.c.c.
in the elastic anisotropy
as
It would maximum
of these alloys
around 12 a/o Mg. If such a composition dependence exists it might suggest a CIA of c44 and &G greater contribution of the Fermi energy to the elastic constants
of the Li-Mg
alloys
than Trivisonno
and
Smith imply. The magnitude
2c44
of the ratio CI,
-
reported
for
c,,
the Li-Mg alloys is of the order of magnitude
of those
measured by Zirinsky for beta Au-Cd (11.6 and 14.1, depending on the composition) and by Lazarus in
in beta Cu-Zn and now Trivisonno and Smith in Li and the Li-Mg alloys. If this elastic anisotropy criterion for mart,ensitic
beta Cu-Zn (8.47), both of which alloys undergo martensitic reactions at low temperatures. The relation-
transformation
ship between the M, temperature
from the b.c.c. structure
is accepted,
and valence electron
LETTERS
density is under study in this laboratory, that the two can be related through stants.
A study
contemplated,
of the alloys
however,
in the hope
the elastic
con-
of Li and Mg is not
since there are alloy systems
where the effect of the Fermi constants
TO
energy on the elastic
THE
ways
which
definition location
lead to opposite
results.
We prefer a
which assigns to a right-handed
screw dis-
direction as does the definition of Peach and Koehler.(2) According
a Burgers vector in the positive
to this definition location
is better understood.
987
EDITOR
the Burgers vector
with the extra
half-plane
of an edge disbelow
the glide
plane points to the right when the observer looks in
D. B. MASSON Department of Metallurgy
the positive direction along the dislocation.
Metals Research Xection Washington State University
shown.
In Fig. l(a) two left-handed
screw dislocations
are
Their positive directions are given by the unit
vectors L, and L,, their Burgers vectors by b, and b,.
References 1. J. TRIVISONNO and C. S. S~XITH,Acta Met. 9, 1064 (1961). 2. C. S. BARRETT,Acta Cry&, 9, 671 (1956). 3. C. S. BARRETT and 0. R. TRAUTZ, Trans. Amer. Inst. Min. (Metall.) Engrs. 175, 579 (1948). Metals TechnoZog?/,TP 23463 (April, 1948). 4. A. B. GRENINGERand V. G. MOORADIAN,Trans. Aww. Inst. Min. (Metdl.) Engrs. 122, 337 (1938). 5. D. B. MAS~ONand C. S. BARRETT,Trans. Amer. Inst. Min. (Metall.) Engrs. 212, 260 (1958). 6. 1,. CRANG and T. A. READ, Trans. Amer. Inst. Min. (MetaZl.) Engrs. 189, 47 (1951). 7. R. J. BLOCK and G. H. KEHL, Trans. Amer. Inst. Min. (Metall.) Engrs. 215, 878 (1959). 8. R. HAYNES, Amer. Sot. Met& 82, 493 (1953). 9. D. B. MASSON,Tmns. Amer.Inst. Min. (MetaZZ.)&grs.218, 94 (1960). 10. S. ZIRINSKY, Actrc Met. 4, 164 (1956). 11. D. LAZARUS, Phys. Rev. 74, 1726 (1948); ‘46, 547 (1949).
L, moves
Dislocation
given by m,.
to the right in the direction
It is unnecessary
to define this vector
* Received Spril 2, 1962.
On the type of point defects formed after crossing of dislocations* When two dislocations cut through
both dislocations.
Especially
are screw dislocations, motion
with intersecting glide planes
each other, generally,
a jog is formed in
when both dislocations
the jogs will hinder
further
because they can only keep up with the dis-
location by the emission of point defects, vacancies interstitial atoms. defect is formed locations.
after the crossing of two given dis-
Saadao)
when vacancies
or
The problem is which type of point gave an expression
be positive when interstitials
which should
are formed and negative
more precisely. cut through Fig. l(b).
it contains only the Burgers vector of the stationary and not the positive
direction
of it.
But
L, has
The situation after dislocation
the stationary
dislocation
Now both dislocations
jog in L, has the length Whether it is +b,
are formed.
This expression, however, cannot be correct because dislocation
Fm. 1. Two left-handed screw dislocations before crossing (a) and after crossing (b). The lattice planes perpendicular to the di&oation form a helicoidal surface. One turn of it is shown which sots as glide plane for the other dislocation. The hatched extra half-plane of the edge-type jog links the helicoidal lattice planes of the two parts of the screw dislocation.
or -b,
L, is given in
contain a jog.
and the direction is determined
The
of -b,.
by the direc-
tion in which L, pierces the glide plane determined
by
L, A m,. The sign is positive if, before crossing, L, and L, are related to each other as the direction of an
the sign of the Burgers vector can only be determined
electric current and the direction of the magnetic field
after a positive direction along the dislocation
has been
around it and negative in the opposite case, as in Fig.
changes sign when this The reason for this mis-
(Llm,L2)/j (L1m1L2) I, which contains the scalar triple
defined. The Burgers vector positive direction is reversed. understanding importance textbooks.
may
be that
and, remarkably,
this point
is rarely
of
is not stressed in most
After a positive direction has been chosen along the dislocation the Burgers vector can be defined in two 6
l(a).
Hence this sign is determined
by the expression
vector product of the three relevant vectors by its absolute value. When the jog with length and direction
divided -b,
and
Burgers vector b, moves a distance c1 it will emit interstitials (Fig. l(b)) because the extra half-plane has