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Solute segregation to stacking faults
ACTA
900
METALLURGICA,
References 1. P. M. KELLY und J. NUTTINU, J. Inst.Met. 87, 385 (1958-
59). 2. W. PITSCE und A. SCHRADER, Arch ~,~~~h~~e~u~, 29, 485 (1958). 3. E. C. BAIN, Truns Amer. In&. Min. (Metall.) Engng. 70, 25 (1924). 5. W. C. LESLIE, R.iV.Frs~~~und N. SEN,Acta Met. 7, 632 (1959). 5. K. W. ANDREWS, persijnliche Mitt&lung. 6. G. KUR~JQMOV und G.SACRS, 2. Ph‘ys.64,325 (1930). * Received
January 30, 1962.
Electrical resistivity recovery in cold-worked 60 per cent silver-40 per cent palladium alloy * investigations(1~2) on the effect of plastic deformation on resistivity in the two systems silverpalladium and gold-palladium indicate that both the magnitude and the sign of the change in resistivity due to deformation depend on the amount of strain and on the composition of the alloy. For alloys that show a decrease in resistivity with plastic deformation, Aarts and Houston-Macmillan(l) suggested that distortion of Brillouin zones in certain directions increases the number of electrons available for carrying current, thus ove~iding the usual increase in resistivity due to lattice defects. If this hypothesis is true, the electrical resistivities of such alloys should show a further decrease in resistivity at temperatures at which the point defects are annealed out. This effect was indeed found in an isochronal recovery study of plastically deformed (elongated at room temperature by 8 per cent) 60 per cent silver40 per cent palladium. The specimen was held at each temperature for a period of Recent
I
I
VOL.
10,
1962
30 min and all measurements were made at liquid nitrogen temperature. As shown in Fig. l? noticeable decreases in resistivity are observed between 80-120°C and again between 240-3OO’C. Sosin and Brinkman(3) have found that point defects anneal out in t’he same temperature ranges. Besides possible Brillouin zone effects, Logic et aZ.@) suggested that local static strains contribute a negative term to the resistivity at point,s where the density of states curve is concave downwards. A third tentative explanation is that the decrease in resisbivity due to cold working is the result of the possible existence of a miscibility gap in silver-palladium alloys. W. M. Reck oratory ojpEngineering Materials
K. KRISHNA
RAO
California. Institute of Technology Pasadena, California
References 1. W. H. AARTS and A. S.HOU~TON-M.~~~IL~~N,A~~~
52.5 (1957). 2. H. J. LOWE, J. JACKSON, I. C. ANDERSON NABARRO, ActaMet. 9, TO7 (1961). 3. A. SOSIN and T. 8. BRINKMAN. Act/rMet.
Xel. 5,
and F. R. N.
7, 478 (1959).
* Received February 16, 1962. Solute segregation
to stacking
faults*
As pointed out by Suzuki(l), a stacking fault in an alloy should have a composition differing from that of the matrix at equilibrium. The differences in composition between the fault and matrix is of considerable interest; previous treatments of this problem lead to an approximate result using ideal and regular solution treatments.‘lJ) The recent stacking fault energy measurements of Howie and Swarm@) on Cu and Ag alloys permit of a,more precise solut,iomto this problem. The stacking fault energy S per mole of fault is the difference between the molar free energies of the fault phase (Gf) and matrix (G) : S = G’ -
G.
(I)
Using the relation G = ZQG, + x$&,, where x1 and x2 are the atom fractions of components 1 and 2, resp., in the alloy then: s = xJ,f
TEMPERATURE
*C
FIG. 1. Isochronal recovery of resiativity in 60% Ag, 40% Pd alloy following an 8 per cent elongation at room temperature. Ap does not represent absolute change.
+ x&f
-
x,0
-
x.$7.
(2)
The 0’s are the chemical potentials of the two components in the two phases evaluated at the composition of the alloy. On substituting GI = RT In aI + GIO,etc., we obtain: S = RT(x, In a{ - gI In a, + x2 In u2f -
5Ina,)
+
x1&0
+
x@20
(3)
LETTERS
where uIr is the activity evaluated
of component
at a fault composition
composition,
ing with respect following
EDITOR
901
1 in the fault
difference between the fault and matrix decreases with increasing temperature which is to be expected in view
fault
1 and 2. On differentiat-
to xs and substituting
relations
THE
equal to the alloy
etc.! SrO and S,” are the stacking
energies of pure components Duhem
TO
the Gibbs-
x,d In a, + xsd In a2 = 0, etc.
the
relat)ion is obtained :
of the randomizing
influence of thermal motions.
Equation (7) combined with Suzuki’s equation(l) for the locking force in an extended dislocation, and Howie and Swann’d3) measured
stacking
fault ener-
gies for Ag and Cu alloys, yields interesting
results.
For example, in the Ag base Al system, the calculated
dS
~ = RT(ln a, dx,
In air -
locking force goes through a maximum at about 2 at. %
In a2
+ In a2f) -
S,” $- S,“.
(4)
Al since (dS/dx2j d ecreases sharply at this composition. This will be fully discussed in a later paper(*) which
Now the condition
for chemical equilibrium
between
the fault and matrix is the (?rf = fl, and 0s’ = o,, where the o’s are the chemical potentials and matrix
evaluated
at equilibrium.
activities of components
in the fault
Denoting
1 and 2 at equilibrium
$s, Alf and Azf, the following
considers
solid solution
The author gratefully bhe Atomic
relations are obtained:
A. A. HENDRICKSON Department of Metallurgical Engr. College of Mining
References
A2f
equations (5a) and (5b) into (4) taking
aI and A, E a2 (since the fault phase is present
in very small amounts, the matrix does not change in
:
z=RT[Ingj Equation solute);
(6)
(6) leads to a simple result in the special case (less than about 10 per cent
here we can take advantage
of Henry’s
law
for the solute and Raoult’s
law for the solvent with
very little loss in accuracy.
On substituting
and Raoult’s
laws and regarding component
solute, the following
x2f (1 -
=
Henry’s 2 as the
is obtained : &exp
1. H. SUZUKI, Sci. Rep. Tohoku Univ. 4A, 455 (1952). 2. P. A. FLINN, Acta Met. 6, 631 (1958). 3. A. HOWIE and P. R. SWANN, Phil. Msg. 6, 1215 (1961). 4. G. E. TARDI~F and A. A. HENDRICKSON, to be submitted for publication. 5. H. SUZUKI, J. Phys. Sot. Japan 17, 322 (1962). * Received
-In(y)]
of fairly dilute solutions
and
Nate added in proof: Suzuki I51has derived an equation similar to (7) using a different method.
8,” = RT In A2-
significantly)
the support of
Technology
and
composition
acknowledges
the
Xl0 = RT In 3 A,
A, s
in Ag
Energy Commission.
as A,, Michigan
On substituting
strengthening
base alloy systems.
(-z/RT)
February
20, 1962.
-
Etude quantitative des Plquilibres rkversibles striation de l’argent dans les atmosphkes faiblement sulfurantes* L’influence
de la composition
cette forme particuliere
de l’atmosphere
d’attaque
thermique,
(7)
sur qui a
&A d&rite par Benard et Moreau sous le nom de striation, semble avoir Bte Btablie d’une
X2f)
de
cutable
dans un certain nombre
argent
en
presence
maniere indis-
de cas particuliers:
d’oxygitne,(l)
alliages
nickel-
chrome,(2) alliages fer-chromec3) et fer pur(*) en pre-
where x2 is the atom fraction of the solute in the alloy
sence de melanges
and X2f is the atom fraction
Dans tous ces systemes,
le passage de la surface de
at equilibrium.
l’etat
strie s’opere
Equation (7) gives very reasonable results. First, a lowering of the stacking fault energy with solute con-
quasi-reversible pour une composition determinee de l’atmosphere variable en fonction de la temperature. Nous avons signale recemmenW que cette reversibi-
of the solute in the fault
tent yields X2f > x2, which is as it should be (note that Flinn’s(2) equation (13) does not always do this) ; further the faster the fault energy changes with composition, the larger is the compositional difference for a given solute content. Secondly, the compositional
speculaire
d’hydrogene
a l’etat
et de vapeur
d’eau.
d’une man&e
lite Btait Bgalement observable lorsqu’une surface d’argent Btait traitee dans une atmosphere d’hydrogene contenant des traces de sulfure d’hydrogene. L’etude dont nous donnons ici un bref compte rendu
900
METALLURGICA,
References 1. P. M. KELLY und J. NUTTINU, J. Inst.Met. 87, 385 (1958-
59). 2. W. PITSCE und A. SCHRADER, Arch ~,~~~h~~e~u~, 29, 485 (1958). 3. E. C. BAIN, Truns Amer. In&. Min. (Metall.) Engng. 70, 25 (1924). 5. W. C. LESLIE, R.iV.Frs~~~und N. SEN,Acta Met. 7, 632 (1959). 5. K. W. ANDREWS, persijnliche Mitt&lung. 6. G. KUR~JQMOV und G.SACRS, 2. Ph‘ys.64,325 (1930). * Received
January 30, 1962.
Electrical resistivity recovery in cold-worked 60 per cent silver-40 per cent palladium alloy * investigations(1~2) on the effect of plastic deformation on resistivity in the two systems silverpalladium and gold-palladium indicate that both the magnitude and the sign of the change in resistivity due to deformation depend on the amount of strain and on the composition of the alloy. For alloys that show a decrease in resistivity with plastic deformation, Aarts and Houston-Macmillan(l) suggested that distortion of Brillouin zones in certain directions increases the number of electrons available for carrying current, thus ove~iding the usual increase in resistivity due to lattice defects. If this hypothesis is true, the electrical resistivities of such alloys should show a further decrease in resistivity at temperatures at which the point defects are annealed out. This effect was indeed found in an isochronal recovery study of plastically deformed (elongated at room temperature by 8 per cent) 60 per cent silver40 per cent palladium. The specimen was held at each temperature for a period of Recent
I
I
VOL.
10,
1962
30 min and all measurements were made at liquid nitrogen temperature. As shown in Fig. l? noticeable decreases in resistivity are observed between 80-120°C and again between 240-3OO’C. Sosin and Brinkman(3) have found that point defects anneal out in t’he same temperature ranges. Besides possible Brillouin zone effects, Logic et aZ.@) suggested that local static strains contribute a negative term to the resistivity at point,s where the density of states curve is concave downwards. A third tentative explanation is that the decrease in resisbivity due to cold working is the result of the possible existence of a miscibility gap in silver-palladium alloys. W. M. Reck oratory ojpEngineering Materials
K. KRISHNA
RAO
California. Institute of Technology Pasadena, California
References 1. W. H. AARTS and A. S.HOU~TON-M.~~~IL~~N,A~~~
52.5 (1957). 2. H. J. LOWE, J. JACKSON, I. C. ANDERSON NABARRO, ActaMet. 9, TO7 (1961). 3. A. SOSIN and T. 8. BRINKMAN. Act/rMet.
Xel. 5,
and F. R. N.
7, 478 (1959).
* Received February 16, 1962. Solute segregation
to stacking
faults*
As pointed out by Suzuki(l), a stacking fault in an alloy should have a composition differing from that of the matrix at equilibrium. The differences in composition between the fault and matrix is of considerable interest; previous treatments of this problem lead to an approximate result using ideal and regular solution treatments.‘lJ) The recent stacking fault energy measurements of Howie and Swarm@) on Cu and Ag alloys permit of a,more precise solut,iomto this problem. The stacking fault energy S per mole of fault is the difference between the molar free energies of the fault phase (Gf) and matrix (G) : S = G’ -
G.
(I)
Using the relation G = ZQG, + x$&,, where x1 and x2 are the atom fractions of components 1 and 2, resp., in the alloy then: s = xJ,f
TEMPERATURE
*C
FIG. 1. Isochronal recovery of resiativity in 60% Ag, 40% Pd alloy following an 8 per cent elongation at room temperature. Ap does not represent absolute change.
+ x&f
-
x,0
-
x.$7.
(2)
The 0’s are the chemical potentials of the two components in the two phases evaluated at the composition of the alloy. On substituting GI = RT In aI + GIO,etc., we obtain: S = RT(x, In a{ - gI In a, + x2 In u2f -
5Ina,)
+
x1&0
+
x@20
(3)
LETTERS
where uIr is the activity evaluated
of component
at a fault composition
composition,
ing with respect following
EDITOR
901
1 in the fault
difference between the fault and matrix decreases with increasing temperature which is to be expected in view
fault
1 and 2. On differentiat-
to xs and substituting
relations
THE
equal to the alloy
etc.! SrO and S,” are the stacking
energies of pure components Duhem
TO
the Gibbs-
x,d In a, + xsd In a2 = 0, etc.
the
relat)ion is obtained :
of the randomizing
influence of thermal motions.
Equation (7) combined with Suzuki’s equation(l) for the locking force in an extended dislocation, and Howie and Swann’d3) measured
stacking
fault ener-
gies for Ag and Cu alloys, yields interesting
results.
For example, in the Ag base Al system, the calculated
dS
~ = RT(ln a, dx,
In air -
locking force goes through a maximum at about 2 at. %
In a2
+ In a2f) -
S,” $- S,“.
(4)
Al since (dS/dx2j d ecreases sharply at this composition. This will be fully discussed in a later paper(*) which
Now the condition
for chemical equilibrium
between
the fault and matrix is the (?rf = fl, and 0s’ = o,, where the o’s are the chemical potentials and matrix
evaluated
at equilibrium.
activities of components
in the fault
Denoting
1 and 2 at equilibrium
$s, Alf and Azf, the following
considers
solid solution
The author gratefully bhe Atomic
relations are obtained:
A. A. HENDRICKSON Department of Metallurgical Engr. College of Mining
References
A2f
equations (5a) and (5b) into (4) taking
aI and A, E a2 (since the fault phase is present
in very small amounts, the matrix does not change in
:
z=RT[Ingj Equation solute);
(6)
(6) leads to a simple result in the special case (less than about 10 per cent
here we can take advantage
of Henry’s
law
for the solute and Raoult’s
law for the solvent with
very little loss in accuracy.
On substituting
and Raoult’s
laws and regarding component
solute, the following
x2f (1 -
=
Henry’s 2 as the
is obtained : &exp
1. H. SUZUKI, Sci. Rep. Tohoku Univ. 4A, 455 (1952). 2. P. A. FLINN, Acta Met. 6, 631 (1958). 3. A. HOWIE and P. R. SWANN, Phil. Msg. 6, 1215 (1961). 4. G. E. TARDI~F and A. A. HENDRICKSON, to be submitted for publication. 5. H. SUZUKI, J. Phys. Sot. Japan 17, 322 (1962). * Received
-In(y)]
of fairly dilute solutions
and
Nate added in proof: Suzuki I51has derived an equation similar to (7) using a different method.
8,” = RT In A2-
significantly)
the support of
Technology
and
composition
acknowledges
the
Xl0 = RT In 3 A,
A, s
in Ag
Energy Commission.
as A,, Michigan
On substituting
strengthening
base alloy systems.
(-z/RT)
February
20, 1962.
-
Etude quantitative des Plquilibres rkversibles striation de l’argent dans les atmosphkes faiblement sulfurantes* L’influence
de la composition
cette forme particuliere
de l’atmosphere
d’attaque
thermique,
(7)
sur qui a
&A d&rite par Benard et Moreau sous le nom de striation, semble avoir Bte Btablie d’une
X2f)
de
cutable
dans un certain nombre
argent
en
presence
maniere indis-
de cas particuliers:
d’oxygitne,(l)
alliages
nickel-
chrome,(2) alliages fer-chromec3) et fer pur(*) en pre-
where x2 is the atom fraction of the solute in the alloy
sence de melanges
and X2f is the atom fraction
Dans tous ces systemes,
le passage de la surface de
at equilibrium.
l’etat
strie s’opere
Equation (7) gives very reasonable results. First, a lowering of the stacking fault energy with solute con-
quasi-reversible pour une composition determinee de l’atmosphere variable en fonction de la temperature. Nous avons signale recemmenW que cette reversibi-
of the solute in the fault
tent yields X2f > x2, which is as it should be (note that Flinn’s(2) equation (13) does not always do this) ; further the faster the fault energy changes with composition, the larger is the compositional difference for a given solute content. Secondly, the compositional
speculaire
d’hydrogene
a l’etat
et de vapeur
d’eau.
d’une man&e
lite Btait Bgalement observable lorsqu’une surface d’argent Btait traitee dans une atmosphere d’hydrogene contenant des traces de sulfure d’hydrogene. L’etude dont nous donnons ici un bref compte rendu