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Concentration dependence of diffusion of cobalt in nickel-cobalt alloys
CONCENTRATION
DEPENDENCE OF DIFFUSION IN NICKEL-COBALT ALLOYS* B.
OF COBALT
MILLION? and J. KU;ERAt
In the present paper the results of measuring the self-diffusion cotffi4mts for Co in Ni-Co alloy in the composition interval 20-100 at.% Co, and in the temperature range 1057-1306°C are given. The measurements were carried out by the Gruzin method using the radioisotope Co-60. On the curves indicating the concentration dependence of the diffusion coefficient and of the diffusion characteristics log D, and AH, extrema appear in the neighbourhood of the compositions 70 at.% Co and 25 at.% Co. The existence of these extrema is discussed from the point of view of the equilibrium diagram Ni-Co, the extremum near 25 at.% Co is explained by means of the Cohen-Fine model for short range order. INFLUENCE
DE
LA
CONCENTRATION LES
SUR
ALLIAGES
LA
DIFFUSION
DU
COBALT
DANS
NICKEL-COBALT
Les auteurs donnent ici les resultats de mesures des coefficients d’auto-diffusion pour le cobalt dans l’alliage Ni-Co pour l’intervalle de concentrations allant de 20 a 100% at. Co et dans le domaine ds temperatures ds 1057-1306°C. Les mesures ont Bti: effect&es par la methode de Gruzin utilisant le radioisotope Co-60. Sur les courbes dormant la variation du coefficient ds diffusion et des oaracteristiques de diffusion log D, et AH en fonction de la concentration, 13s maxima se situent au voisinage des concentrations de 700/6 at. Co et de 25% at. Co. Les auteurs discutent l’existence de ces maxima Q partir du diamme grad’equilibre Ni-Co et interpretent le maximum sit& au voisinage de 25”/;, at. Co au moyen du modele de Cohen-Fine pour l’ordre a courte distance. KONZENTRATIONSABHANGIGKEIT
DER
DIFFUSION
VON
KOBALT
IN
NICKEL-KOBALT-LEGIERUNGEN Die vorliegende Arbeit berichtet tibar Messungen des Selbstdiffusionskoeffizienten von Kobalt in Nickel-Kobalt-Legierungen der Zusammensetzung 20-100 At% Co und im Temperaturbereich 10571306°C. Die Messungen wurden mit Hilfe der Gruzin-Methode mit dem Radioisotop Co-60 durchgefiihrt. Die Konzentrationsabhiingigkeit der Diffusionskoeffizienten und der charakteristischen Diffusionswerte Die log D, und AH zeigen in der N&he dsr Zusammensetzung 70 At% Co und 25 At% Co Extrema. Extremwerte werden an Hand des Phasendiagramms van Ni-Co diskutiert. Der Extremwert bei 25 At% Co wird mit dem Cohen-Fine-Model1 der Nahordnung erklart.
1. INTRODUCTION At present there exist very few papers dealing with the experimental study of concentration dependence of self-diffusion characteristics of single binary alloy components in a large concentration range. It is also difficult to interpret these results because of no theory has yet been worked out that would fully explain the self-diffusion in these alloys. One of the systems suitable for the study of the above mentioned type is the Ni-Co alloy, because of its very simple equilibrium diagram.(l) Many authors have been investigating the self-diffusion of Co, or Ni respectively, in this system. Gruzin and Noskov(2) determined the self-diffusion coefficients for Co-60 in alloys with 70 and 95.2 at.% Co, Hirano and his coworkers(3) measured the self-diffusion coefficients for Co-60 and Ni-63 in alloys containing 49, 70,80 and 89 at. y. Co close to the Curie temperature. Especially the paper by Hassner and Langec4) is very detailed giving the results of measuring the self-diffusion coefficients for Co and Ni in eleven different Ni-Co alloys in the temperature range 1050-1410°C. Where* Received
July 8, 1968. t Institute of Metallurgy, Sciences, Brno, CSSR. ACTA
METALLURGICA,
VOL.
Czechoslovak 17, MARCH
Academy 1969
of 339
as results obtained by different authors are in a very good agreement in the case of alloys containing about 50 at. y. Co, they substantially differ in Co-rich alloys. So e.g. Gruzin and Noskov found the maximum value of activation enthalpy for Co-self-diffusion in the alloy with 95.2 at.% Co, Hirano et al. found the maximum of concentration dependence of the activation enthalpy Co and Ni at 75 at.% Co, Hassner and Lange at 90-94 at.% Co. In a more recent paper 15) the Ni-Co system was investigated from the point of view of thermodynamic properties. It was shown that at high temperatures this system approaches an ideal solution, at lower temperatures results were obtained indicating the possibility of short range order at Ni,Co.@) In the equilibrium diagram Ni-Co, the possible existence of an ordered structure at this composition is mentioned and has also been claimed in(‘) on the basis of the results obtained by measuring the specific heat and by thermal analysis in the temperature range 50~800°C. In none of the above mentioned papers special attention was given to the determination of self-diffusion characteristics of the Ni-Co alloy near the composition Ni,Co. For these reasons, the concentration dependence of
ACTA
340
METALLURGICA,
the self-diffusion coefllcients of Co in the Ni-Co system in the composition interval 20-100 at.% Co has been investigated again in the present paper. 2.
EXPERIMENTAL
VOL.
1969
point x and in time 7 is proportional to the concentration of the radioactive isotope in the specimen c(x, 7) and is given by the relation
e, 4
PROCEDURE
The self-diffusion coeficients for Co were determined in pure cobalt and different Ni-Co alloys that were kindly delivered by the Centre National de Recherches Metallurgiques in Liege, Belgium. The composition of the alloys is summarized in Table 1. The cobalt used in this alloys contained following impurities : 0.016 wt. y0 Fe, 0.014 wt. y0 Cu, 0.01 wt. y0 Mn. Other elements were present in much lower concentrations. For diffusion measurements specimens of 12 mm dia. and 2.5 mm thickness were machined. They were subjected to homogenization anneal at 1200°C for 24 or 48 hr. Annealed specimens were ground on metallographic papers, electrolytically or chemically polished. The mean grain size was 14 mm. The radioisotope Co-60 was deposited electrolytically onto the polished surface of the specimens according to the instructions mentioned in reference 8 ; the thickness of the deposited layer was
17,
=
$0
exp
22/(rrD7)
--.
(2)
In the relation (2) i, is the initial activity in units of cpm per cm2 proportional to the surface concentration of the radioactive isotope at the time r = 0 on the surface of the specimen. By substituting from relation (2) into (1) and integrating we get I,(5) = : exp (,&) exp (~‘07) X erfc
[
&
+ 11d(D7)
1*
(3)
From this equation by the least square method the self-diffusion coefficient D was calculated using the computer MINSK-22. 3.
RESULTS
OF
MEASUREMENTS
The diffusion coefficients D found in our investigations are shown in Table 2 ; each of the given values represents the mean value of two measurements. The obtained diffusion coefficient values fit the Arrhenius equation D = Do exp (-AHIRT). The frequency factors Do and the activation enthalpy AH were calculated by the least square method and are summarized with their mean errors in Table 3. The concentration dependence of diffusion characteristics Do and AH is given in Fig. 1. The diffusion characteristics for cobalt in pure nickel Do = 1.11 cm2/sec and AH = 64.9 kcal/mol were taken from the paper.c4) These values are in good agreement with those given in paper,(s) Do = 0.75 cm2/sec and AH = 64.7 kcal/mol. 4. DISCUSSION
By means of diffusion characteristics shown in Table 3 the values of diffusion coefficients for temperatures 1450°C, 13OO”C, 115O’C and 1000°C were calculated and they are given in Fig. 2a. From this m i(z, 7) exp [-& - 81 dz, I,(5) = (1) figure it can be seen that the Ni-Co solid solution sc behaves at high temperatures as an ideal solution where ,u is the absorption coeficient determined by characterized by the fact that log Do and AH are using the data given in,(la) 7 is the annealing time, ,$ linear functions of the concentration.(ll) The ideal is the distance from the initial surface to the surface behavior of the Ni-Co solution at high temperatures of counting. The activity concentration i(x, 7) in the was also proved by using the Birchenall model@) in the TABLE 1. Composition No. of alloy At.%
Co
of the N&Co alloy
1
2
3
4
5
6
7
8
9
100
96.3
92.9
89.7
70.0
60.7
30.3
26.3
19.9
-
MILLION TABLE
AND
KUCERA:
DIFFUSION
OF
Co IN
2. Self-diffusion coefficients for Co in the Ni-Co system 92.9% co
96.3% Co
100% co WC)
D(cms/sec)
WC)
D(cmz/sec)
WC)
1067 1106 1131 1176 1306 -
6.14 * IO-‘* 1.32. lo-” 2.16 * lo-” 5.76. lo-” 3.79 * 10-10 -
1067 1116 1141 1186 1255 1306
1.19. lo-” 3.00. lo-” 3.47 * lo-“* 7.37. lo-” 2.59. 10-10 6.74 * 10-10
1076 1125 1150 1195 1255 1306
1093 1142 1167 1214 1254 1304
26.3% Co
30.3% co 1082 1131 1166 1202 1248 1297
4.46. lo-” 1.21. 10-10 1.73. 10-10 3.87 * IO-“’ 4.40 f 10-10 1.03 * IO-@
1092 1141 1166 1213 1262 1301
3.21 * lo-” 8.04 * IO-” 8.98 - lo-” 2.55. 10-l“ 3.05. 10-10 6.63. lo-lo
1089 1138 1163 1210 1254 1304
2.66. lo-” 5.53. IO-” 6.05. lo-” 1.66 * lo-“’ 2.72. 10-I” 6.80. 10-10
1086 1134 1159 1205 1265 1305
D (cma/sec) 1.77. lo-” 4.42 ’ lo-” 4.08. lo-” 1.20 * IO-‘0 2.68 * 1O-‘o 6.96. 10-l” 50.7% co
70.0% co
89.7% Co
--
341
Ni-Co
4.10 * lo-” 9.81. lo-” 1.20. 10-10 3.01. 10-10 4.02. lo-lo 8.23. lo-lo 19.9% co
4.21 - lo-” 1.12. 10-10 1.72. lo-10 4.16 * 10-l” 4.43 * lo-‘0 8.43 * lo-10
1070 1119 1144 1190 1242 1291
3.16 * lo-” 7.60 * lo-” 1.62 * 10-10 3.27. lo-lo 4.12. 1O-10 8.00. lo-“’
* The self-diffusion coefficient measured only once.
paper by Vse%al and Kucere@). With decreasing temperature, increasing deviations from the ideal behavior appear being dependent on the concentration. At the temperature t = lOOO”C,these deviations show two maxima near 70 and 25 at.% Co. It may be worth noting that at 70 at.% Co the transition a -+ E exists at room temperature, and that at this concentration the investigated system has zero stacking fault energy.(is) Present knowledge concerning self-diffusion in substitutional solid solutions does not enable us to explain in an explicit way the existence of this maximum. In agreement with the results given in Fig. 2a, a minimum in the
1
r------T
TABLE 3. Self-diffusion frequency factors and activation enthalpies for Co-60 in Ni-Co alloys D0 (cme/sec)
AH (kcal/mol)
2.20 + 2.41 - 1.13
70.5 f 2.1
96.3
1.23 f ;*;;
67.7 6 2.0
92.9
1.12 2 ;$
66.9 & 3.4
89.7
0.43 2 i.5;
63.9 & 3.0
70.0
0.10 2 8.;;
58.9 f 2.7
60.7
0.18 + ;‘;;
60.2 & 2.1
30.3
0.40 + i.1;
61.8 f
26.3
o.og + 0.29_ + -
57.4 & 3.8
At.% Co 100
19.9
0:26 0.07 OJx 0.16
2.8
59.9 & 3.6
Fro. 1. Concentmtion dependence of the activation enthalpy AH, and of the frequency factor D,.
342
ACTA
METALLURGTCA,
-8 I
b--O_ OL
t= 1450 ‘c
----o-@a_
24
0
O-o-
o-
t= 1300
‘c O\O
O-4
Ii \
_-o--o
t= 1150 ‘C
-10
o-o\o.\ 4
_,,Dm:
0
100
50 -
Ni
at 7 co
CO
FIG. 2a. Concentration dependence of log D at 1450°C, 13OO”C,1150°C and 1000°C in Ni-Co alloys.
__o,%<;r
cl b
9
l
-11
O-
[ -12 o_
-13
--
-
P
_/O
1
/
\\\
c
P
/”
t = 924 %
/’
cr’
-14
I 0 Ni
I
10
I
I
20
-
I
30 40 uf. 2 Fe
50
Fro. 2b. Concentration dependence of log D at 1076’C, 924”C, and 814°C in Ni-Fe alloys (these data were taken from paper.‘18’)
17,
1969
concentration dependence of the activation enthalpy and of the frequency factor respectively, appears in Fig. 1 near the concentration 70 at.% Co. This minimum was not found in papers.‘3*4) However, a maximum in the concentration dependence of the activation enthalpy was found near 75 at.% Co in paper.c3J In paperc4) a less sharp maximum in the concentration dependence of the activation enthalpy and of the frequency factor respectively, was found near 95 at.% Co. We assume that the differences between the results of the above mentioned authors and the present investigation are caused by different impurity content in the specimens, and in case of paperc3) also by a very low activation enthalpy of the self-diffusion for Co. The second maximum appears in Fig. 2a near the composition Ni,Co where, according to(1,5*7)an ordered structure could exist at temperatures t < 800°C. In agreement with the appearance of this maximum, minima of the concentration dependence curve for AH or for log Do are shown in Fig. 1 near the concentration Ni,Co. These extreme values can be explained on the basis of the Cohen-Fine assumptionso3) concerning the alloy structure in which short range order exists, and on the basis of well known results on diffusion in ordered alloys.(14,15) According to Cohen and Fine a short range order can be considered as a formation of ordered zones separated by a disordered matrix. The diffusion coefficient in ordered zones changes with temperature according to the Arrhenius equation the characteristics DOtord,and AHcord) of which are measured at temperatures t < t,, t, being the critical temperature of the order-disorder transformation. In the disordered matrix the temperature dependence of the diffusion coefficient is described by the Arrhenius equation using the characteristics DOcdis, and AHfdis) which can be obtained by linear interpolation between the values which belong to the components A or B resp. The accuracy of these values can be checked by measuring the concentration dependence of the diffusion coefficient D at sufficiently high temperatures for which the log D represents the linear function of concentration (see Fig. 2a). At these temperatures D(dis) = D. In the temperature range between t, and the temperature at which only a disordered structure exists, the measured effective values of D fit the Arrhenius dependence as well. An example of the temperature dependence of Dcord,, D,,,, and D for the Cu,Au alloy is given in Fig. 3. The relation between the quantities D, Dford, and D(dis) can be obtained by using the first Fick law under the assumption that in an arbitrary specimen
8’4 WC?
O\,
VOL.
MILLIOX
AND
I
I
I
I
DIFFUSION
KUCERA:
I
OF
Co
I
I
IN
I
343
Ni-Co
I
I i
FIG. 3. Temperature
dependence
of self-diffusion
coefficients
for gold in Cu,Au
alloy.
D = 0.0065 exp ( -3S250/RT).“6’ &rd) = 3.15 exp ( -46400/RT).“6’ D
section flux,
perpendicular
the ratio
ordered
to the
of areas belonging
or disordered
stant.
direction
structure
of diffusion
to regions
with
Stord,/Stdis, is conac
(ord) =
. %a
-&mu
similarly
the
effective
diffusion
(5)
coetllcient
is
The
(6)
8X
cross section
of the specimen
S (,,rdj + StdisJ. From the equations
S * D = &mu . D(ord) + Stdis) * D(dis). equation
(7) in terms of volumes
and
disordered
DE-
Vbrd)
phase
S =
(4-6) we get
temperature is given
VcordJ and
of the
VcdisJ we
get
relation
critical
temperature
is based
on results
coefficients
in
we get
%is,
dependence
in Fig. 4.
(9)
of
u for
The value
is given
by
of measuring
an ordered
and
the
CusAu
o = 1 at the
the
assumption
This assumption the self-diffusion disordered
p-brass
solid solution.04) With the results obtained in this work, the temperature dependence
(7)
the
D (ord)- D(dis)
D = Dtordi at this temperature.
S.&-SD& where the total
D -
a=
alloy
given by the equation
ordered
by
Vcoral/V w h’ic h is ’ q m‘t e analogous to the relation
(4)
* Fx
ac ax
Expressing
u =
= VtordJ+ Vfdk,.
for the short range order parameter,
Then S (ord) *I
And
where the total specimen volume V Introducing an order parameter
culated
by using
of o for the NisCo alloy the very
simplifying
was cal-
assumption
that AHford) = AH(dis), and under the condition This result is quoted in Fig. 4. On the basis of the mentioned suppositions we are
t, = 76O”C.(‘)
able to explain the existence of the second maximum
V
v . - Dcdis, * %xd~+ 7
(8)
near l&Co
on the concentration dependence of log D as follows : if we measure the temperature dependence
344
ACTA
METALLURGICA,
VOL.
17, 1969
21.1-43.3 at.% Co. However, the existence of extremes on concentration dependences log D, log Do and AaH was found in paper. The behavior of these dependences near the composition N&Fe was quite analogous to that one found in the present paper (Fig. 2b). The existence of an ordered structure at Ni,Fe was already experimentally verified.(l)
The authors wish to express their thanks to Professor Dr. Ing. Habil. K. Giesen, Dipl. Ing. H. Hallerberg and to the Centre National de Recherches Metallurgiques for kindly supplying the Ni-Co alloy specimens, to Ing. J. Tougek CSc. for carrying out the analyses of these specimens, and to Ing. K. Ciha for the metallographic examination of samples. REFERENCES 1. M. BUNSEN and K. ANDERXO, Cork?titutionof Binmy
-
k-6
FIO. 4. Temperature dependences of the order parameter celculat&d from diffusion characteristics for Cu,Au and Ni,Co alloys.
of the set-effusion ~oe~~ie~t at the concentration corresponding to the composition N&Co, then the diffusion coefCicient decreases with decreasing temperature slower than at any other concentration near NisCo. Therefore, at temperatures getting sufficiently close to t,, a maximum on the oon~ntration dependence of log I) must appear at 25 at.% Co. The physical reason of this phenomenon consists in the maximum increase of the short range order parameter with decreasing temperature at this ooncentration. The appearance of a minimum in the concentration dependence of the activation enthalpy AH, or of the frequency factor log De, is naturally caused by the existence of a maximum in the concentration dependence of log D. In the paper(“) the appearance of extreme values near the concentration 25 at. o/OCo was not found because the authors did not oarry out any measurements of D in the concentration interval
R2Zo.p. McGraw-Hill (1958). 2. P. L. GRUZIN and B. M. Nosxov, Pro@. ~~~~~v~. i Fiz. Met.&. 4, 609 (1955). 3. K. HIRANO, R. P. AQARWALA, B. L. AVER~~ACRand M. COHEN,J. appl. Phy8. Ss, 3049 (1962). 4. A. HHSSNER and W. LANGE, Phya. Status Solidi 8, 77 (lQS~Lvy 5. J. VREST~~L and J. K&RA, to be submitted for publicstion. 6. C. E. BIKCHENALL,Tram. Am. Imat. M&s. Engr&171,166
(1947). 7. J. VEL&SEKand J. V&&L, Czech. J. Phy8. Bl6, (1966). 8. J. STEPHEN,i?zccE.ilnstrum. Met. ii%, 269 (1964).
937
9. P. L. GRUZIN, DOLE.Akad. Nauk SSSR 86,269 (1962). 10. Beta- and Gamarrama-Ray Spectroscopy, edited by K. &EC+BAHN. North-Holland (1966). 11, W. C. MALLARD,A. B. GARDNER,R. V. 3~s 8nd L. NC. SLIFEIN, Phga. Rev. IZS, 617 (1963). 12, S. MADER, Elwtron &ficroacopy and Strength of Cr@uk?, edited by G. TEOMASand J. WASHBURN, p. 183. Wiley (1963). 13. J. B. COHENand M. E. FINE, J. Phya. Radium, Pa& 28, 749 (1962). 14. A. B. KUPER, D. IXZABUS, J. R. MANNING and C. T. TOM~ZUKA,Whys. Rev. 104, 1636 {1956). 15. S. BENCI and G. CASPARRINI, J. Phye. C%m. S&L& 27, 1035 (1906). 16. S. BENCI, G. GASPARRINI, G. GERMA~NOLI and G. SCHIANCHI,J. Phya. Chem. Sotids &8, 687 (1965). 17. A. B. M&TIN. R. D. JOHNSONand F. ASARO. J. am% ..
Phya 25, 364 (19.54).
18. A. D. KURTZ, B. L. A~ERBACHand M. COHEN, Acta Met.
8, 442 (1955). 19. E. WAL&E DE RECA and C. PAMPZLO, Acta Met. 15, 1263 (1967).
DEPENDENCE OF DIFFUSION IN NICKEL-COBALT ALLOYS* B.
OF COBALT
MILLION? and J. KU;ERAt
In the present paper the results of measuring the self-diffusion cotffi4mts for Co in Ni-Co alloy in the composition interval 20-100 at.% Co, and in the temperature range 1057-1306°C are given. The measurements were carried out by the Gruzin method using the radioisotope Co-60. On the curves indicating the concentration dependence of the diffusion coefficient and of the diffusion characteristics log D, and AH, extrema appear in the neighbourhood of the compositions 70 at.% Co and 25 at.% Co. The existence of these extrema is discussed from the point of view of the equilibrium diagram Ni-Co, the extremum near 25 at.% Co is explained by means of the Cohen-Fine model for short range order. INFLUENCE
DE
LA
CONCENTRATION LES
SUR
ALLIAGES
LA
DIFFUSION
DU
COBALT
DANS
NICKEL-COBALT
Les auteurs donnent ici les resultats de mesures des coefficients d’auto-diffusion pour le cobalt dans l’alliage Ni-Co pour l’intervalle de concentrations allant de 20 a 100% at. Co et dans le domaine ds temperatures ds 1057-1306°C. Les mesures ont Bti: effect&es par la methode de Gruzin utilisant le radioisotope Co-60. Sur les courbes dormant la variation du coefficient ds diffusion et des oaracteristiques de diffusion log D, et AH en fonction de la concentration, 13s maxima se situent au voisinage des concentrations de 700/6 at. Co et de 25% at. Co. Les auteurs discutent l’existence de ces maxima Q partir du diamme grad’equilibre Ni-Co et interpretent le maximum sit& au voisinage de 25”/;, at. Co au moyen du modele de Cohen-Fine pour l’ordre a courte distance. KONZENTRATIONSABHANGIGKEIT
DER
DIFFUSION
VON
KOBALT
IN
NICKEL-KOBALT-LEGIERUNGEN Die vorliegende Arbeit berichtet tibar Messungen des Selbstdiffusionskoeffizienten von Kobalt in Nickel-Kobalt-Legierungen der Zusammensetzung 20-100 At% Co und im Temperaturbereich 10571306°C. Die Messungen wurden mit Hilfe der Gruzin-Methode mit dem Radioisotop Co-60 durchgefiihrt. Die Konzentrationsabhiingigkeit der Diffusionskoeffizienten und der charakteristischen Diffusionswerte Die log D, und AH zeigen in der N&he dsr Zusammensetzung 70 At% Co und 25 At% Co Extrema. Extremwerte werden an Hand des Phasendiagramms van Ni-Co diskutiert. Der Extremwert bei 25 At% Co wird mit dem Cohen-Fine-Model1 der Nahordnung erklart.
1. INTRODUCTION At present there exist very few papers dealing with the experimental study of concentration dependence of self-diffusion characteristics of single binary alloy components in a large concentration range. It is also difficult to interpret these results because of no theory has yet been worked out that would fully explain the self-diffusion in these alloys. One of the systems suitable for the study of the above mentioned type is the Ni-Co alloy, because of its very simple equilibrium diagram.(l) Many authors have been investigating the self-diffusion of Co, or Ni respectively, in this system. Gruzin and Noskov(2) determined the self-diffusion coefficients for Co-60 in alloys with 70 and 95.2 at.% Co, Hirano and his coworkers(3) measured the self-diffusion coefficients for Co-60 and Ni-63 in alloys containing 49, 70,80 and 89 at. y. Co close to the Curie temperature. Especially the paper by Hassner and Langec4) is very detailed giving the results of measuring the self-diffusion coefficients for Co and Ni in eleven different Ni-Co alloys in the temperature range 1050-1410°C. Where* Received
July 8, 1968. t Institute of Metallurgy, Sciences, Brno, CSSR. ACTA
METALLURGICA,
VOL.
Czechoslovak 17, MARCH
Academy 1969
of 339
as results obtained by different authors are in a very good agreement in the case of alloys containing about 50 at. y. Co, they substantially differ in Co-rich alloys. So e.g. Gruzin and Noskov found the maximum value of activation enthalpy for Co-self-diffusion in the alloy with 95.2 at.% Co, Hirano et al. found the maximum of concentration dependence of the activation enthalpy Co and Ni at 75 at.% Co, Hassner and Lange at 90-94 at.% Co. In a more recent paper 15) the Ni-Co system was investigated from the point of view of thermodynamic properties. It was shown that at high temperatures this system approaches an ideal solution, at lower temperatures results were obtained indicating the possibility of short range order at Ni,Co.@) In the equilibrium diagram Ni-Co, the possible existence of an ordered structure at this composition is mentioned and has also been claimed in(‘) on the basis of the results obtained by measuring the specific heat and by thermal analysis in the temperature range 50~800°C. In none of the above mentioned papers special attention was given to the determination of self-diffusion characteristics of the Ni-Co alloy near the composition Ni,Co. For these reasons, the concentration dependence of
ACTA
340
METALLURGICA,
the self-diffusion coefllcients of Co in the Ni-Co system in the composition interval 20-100 at.% Co has been investigated again in the present paper. 2.
EXPERIMENTAL
VOL.
1969
point x and in time 7 is proportional to the concentration of the radioactive isotope in the specimen c(x, 7) and is given by the relation
e, 4
PROCEDURE
The self-diffusion coeficients for Co were determined in pure cobalt and different Ni-Co alloys that were kindly delivered by the Centre National de Recherches Metallurgiques in Liege, Belgium. The composition of the alloys is summarized in Table 1. The cobalt used in this alloys contained following impurities : 0.016 wt. y0 Fe, 0.014 wt. y0 Cu, 0.01 wt. y0 Mn. Other elements were present in much lower concentrations. For diffusion measurements specimens of 12 mm dia. and 2.5 mm thickness were machined. They were subjected to homogenization anneal at 1200°C for 24 or 48 hr. Annealed specimens were ground on metallographic papers, electrolytically or chemically polished. The mean grain size was 14 mm. The radioisotope Co-60 was deposited electrolytically onto the polished surface of the specimens according to the instructions mentioned in reference 8 ; the thickness of the deposited layer was
17,
=
$0
exp
22/(rrD7)
--.
(2)
In the relation (2) i, is the initial activity in units of cpm per cm2 proportional to the surface concentration of the radioactive isotope at the time r = 0 on the surface of the specimen. By substituting from relation (2) into (1) and integrating we get I,(5) = : exp (,&) exp (~‘07) X erfc
[
&
+ 11d(D7)
1*
(3)
From this equation by the least square method the self-diffusion coefficient D was calculated using the computer MINSK-22. 3.
RESULTS
OF
MEASUREMENTS
The diffusion coefficients D found in our investigations are shown in Table 2 ; each of the given values represents the mean value of two measurements. The obtained diffusion coefficient values fit the Arrhenius equation D = Do exp (-AHIRT). The frequency factors Do and the activation enthalpy AH were calculated by the least square method and are summarized with their mean errors in Table 3. The concentration dependence of diffusion characteristics Do and AH is given in Fig. 1. The diffusion characteristics for cobalt in pure nickel Do = 1.11 cm2/sec and AH = 64.9 kcal/mol were taken from the paper.c4) These values are in good agreement with those given in paper,(s) Do = 0.75 cm2/sec and AH = 64.7 kcal/mol. 4. DISCUSSION
By means of diffusion characteristics shown in Table 3 the values of diffusion coefficients for temperatures 1450°C, 13OO”C, 115O’C and 1000°C were calculated and they are given in Fig. 2a. From this m i(z, 7) exp [-& - 81 dz, I,(5) = (1) figure it can be seen that the Ni-Co solid solution sc behaves at high temperatures as an ideal solution where ,u is the absorption coeficient determined by characterized by the fact that log Do and AH are using the data given in,(la) 7 is the annealing time, ,$ linear functions of the concentration.(ll) The ideal is the distance from the initial surface to the surface behavior of the Ni-Co solution at high temperatures of counting. The activity concentration i(x, 7) in the was also proved by using the Birchenall model@) in the TABLE 1. Composition No. of alloy At.%
Co
of the N&Co alloy
1
2
3
4
5
6
7
8
9
100
96.3
92.9
89.7
70.0
60.7
30.3
26.3
19.9
-
MILLION TABLE
AND
KUCERA:
DIFFUSION
OF
Co IN
2. Self-diffusion coefficients for Co in the Ni-Co system 92.9% co
96.3% Co
100% co WC)
D(cms/sec)
WC)
D(cmz/sec)
WC)
1067 1106 1131 1176 1306 -
6.14 * IO-‘* 1.32. lo-” 2.16 * lo-” 5.76. lo-” 3.79 * 10-10 -
1067 1116 1141 1186 1255 1306
1.19. lo-” 3.00. lo-” 3.47 * lo-“* 7.37. lo-” 2.59. 10-10 6.74 * 10-10
1076 1125 1150 1195 1255 1306
1093 1142 1167 1214 1254 1304
26.3% Co
30.3% co 1082 1131 1166 1202 1248 1297
4.46. lo-” 1.21. 10-10 1.73. 10-10 3.87 * IO-“’ 4.40 f 10-10 1.03 * IO-@
1092 1141 1166 1213 1262 1301
3.21 * lo-” 8.04 * IO-” 8.98 - lo-” 2.55. 10-l“ 3.05. 10-10 6.63. lo-lo
1089 1138 1163 1210 1254 1304
2.66. lo-” 5.53. IO-” 6.05. lo-” 1.66 * lo-“’ 2.72. 10-I” 6.80. 10-10
1086 1134 1159 1205 1265 1305
D (cma/sec) 1.77. lo-” 4.42 ’ lo-” 4.08. lo-” 1.20 * IO-‘0 2.68 * 1O-‘o 6.96. 10-l” 50.7% co
70.0% co
89.7% Co
--
341
Ni-Co
4.10 * lo-” 9.81. lo-” 1.20. 10-10 3.01. 10-10 4.02. lo-lo 8.23. lo-lo 19.9% co
4.21 - lo-” 1.12. 10-10 1.72. lo-10 4.16 * 10-l” 4.43 * lo-‘0 8.43 * lo-10
1070 1119 1144 1190 1242 1291
3.16 * lo-” 7.60 * lo-” 1.62 * 10-10 3.27. lo-lo 4.12. 1O-10 8.00. lo-“’
* The self-diffusion coefficient measured only once.
paper by Vse%al and Kucere@). With decreasing temperature, increasing deviations from the ideal behavior appear being dependent on the concentration. At the temperature t = lOOO”C,these deviations show two maxima near 70 and 25 at.% Co. It may be worth noting that at 70 at.% Co the transition a -+ E exists at room temperature, and that at this concentration the investigated system has zero stacking fault energy.(is) Present knowledge concerning self-diffusion in substitutional solid solutions does not enable us to explain in an explicit way the existence of this maximum. In agreement with the results given in Fig. 2a, a minimum in the
1
r------T
TABLE 3. Self-diffusion frequency factors and activation enthalpies for Co-60 in Ni-Co alloys D0 (cme/sec)
AH (kcal/mol)
2.20 + 2.41 - 1.13
70.5 f 2.1
96.3
1.23 f ;*;;
67.7 6 2.0
92.9
1.12 2 ;$
66.9 & 3.4
89.7
0.43 2 i.5;
63.9 & 3.0
70.0
0.10 2 8.;;
58.9 f 2.7
60.7
0.18 + ;‘;;
60.2 & 2.1
30.3
0.40 + i.1;
61.8 f
26.3
o.og + 0.29_ + -
57.4 & 3.8
At.% Co 100
19.9
0:26 0.07 OJx 0.16
2.8
59.9 & 3.6
Fro. 1. Concentmtion dependence of the activation enthalpy AH, and of the frequency factor D,.
342
ACTA
METALLURGTCA,
-8 I
b--O_ OL
t= 1450 ‘c
----o-@a_
24
0
O-o-
o-
t= 1300
‘c O\O
O-4
Ii \
_-o--o
t= 1150 ‘C
-10
o-o\o.\ 4
_,,Dm:
0
100
50 -
Ni
at 7 co
CO
FIG. 2a. Concentration dependence of log D at 1450°C, 13OO”C,1150°C and 1000°C in Ni-Co alloys.
__o,%<;r
cl b
9
l
-11
O-
[ -12 o_
-13
--
-
P
_/O
1
/
\\\
c
P
/”
t = 924 %
/’
cr’
-14
I 0 Ni
I
10
I
I
20
-
I
30 40 uf. 2 Fe
50
Fro. 2b. Concentration dependence of log D at 1076’C, 924”C, and 814°C in Ni-Fe alloys (these data were taken from paper.‘18’)
17,
1969
concentration dependence of the activation enthalpy and of the frequency factor respectively, appears in Fig. 1 near the concentration 70 at.% Co. This minimum was not found in papers.‘3*4) However, a maximum in the concentration dependence of the activation enthalpy was found near 75 at.% Co in paper.c3J In paperc4) a less sharp maximum in the concentration dependence of the activation enthalpy and of the frequency factor respectively, was found near 95 at.% Co. We assume that the differences between the results of the above mentioned authors and the present investigation are caused by different impurity content in the specimens, and in case of paperc3) also by a very low activation enthalpy of the self-diffusion for Co. The second maximum appears in Fig. 2a near the composition Ni,Co where, according to(1,5*7)an ordered structure could exist at temperatures t < 800°C. In agreement with the appearance of this maximum, minima of the concentration dependence curve for AH or for log Do are shown in Fig. 1 near the concentration Ni,Co. These extreme values can be explained on the basis of the Cohen-Fine assumptionso3) concerning the alloy structure in which short range order exists, and on the basis of well known results on diffusion in ordered alloys.(14,15) According to Cohen and Fine a short range order can be considered as a formation of ordered zones separated by a disordered matrix. The diffusion coefficient in ordered zones changes with temperature according to the Arrhenius equation the characteristics DOtord,and AHcord) of which are measured at temperatures t < t,, t, being the critical temperature of the order-disorder transformation. In the disordered matrix the temperature dependence of the diffusion coefficient is described by the Arrhenius equation using the characteristics DOcdis, and AHfdis) which can be obtained by linear interpolation between the values which belong to the components A or B resp. The accuracy of these values can be checked by measuring the concentration dependence of the diffusion coefficient D at sufficiently high temperatures for which the log D represents the linear function of concentration (see Fig. 2a). At these temperatures D(dis) = D. In the temperature range between t, and the temperature at which only a disordered structure exists, the measured effective values of D fit the Arrhenius dependence as well. An example of the temperature dependence of Dcord,, D,,,, and D for the Cu,Au alloy is given in Fig. 3. The relation between the quantities D, Dford, and D(dis) can be obtained by using the first Fick law under the assumption that in an arbitrary specimen
8’4 WC?
O\,
VOL.
MILLIOX
AND
I
I
I
I
DIFFUSION
KUCERA:
I
OF
Co
I
I
IN
I
343
Ni-Co
I
I i
FIG. 3. Temperature
dependence
of self-diffusion
coefficients
for gold in Cu,Au
alloy.
D = 0.0065 exp ( -3S250/RT).“6’ &rd) = 3.15 exp ( -46400/RT).“6’ D
section flux,
perpendicular
the ratio
ordered
to the
of areas belonging
or disordered
stant.
direction
structure
of diffusion
to regions
with
Stord,/Stdis, is conac
(ord) =
. %a
-&mu
similarly
the
effective
diffusion
(5)
coetllcient
is
The
(6)
8X
cross section
of the specimen
S (,,rdj + StdisJ. From the equations
S * D = &mu . D(ord) + Stdis) * D(dis). equation
(7) in terms of volumes
and
disordered
DE-
Vbrd)
phase
S =
(4-6) we get
temperature is given
VcordJ and
of the
VcdisJ we
get
relation
critical
temperature
is based
on results
coefficients
in
we get
%is,
dependence
in Fig. 4.
(9)
of
u for
The value
is given
by
of measuring
an ordered
and
the
CusAu
o = 1 at the
the
assumption
This assumption the self-diffusion disordered
p-brass
solid solution.04) With the results obtained in this work, the temperature dependence
(7)
the
D (ord)- D(dis)
D = Dtordi at this temperature.
S.&-SD& where the total
D -
a=
alloy
given by the equation
ordered
by
Vcoral/V w h’ic h is ’ q m‘t e analogous to the relation
(4)
* Fx
ac ax
Expressing
u =
= VtordJ+ Vfdk,.
for the short range order parameter,
Then S (ord) *I
And
where the total specimen volume V Introducing an order parameter
culated
by using
of o for the NisCo alloy the very
simplifying
was cal-
assumption
that AHford) = AH(dis), and under the condition This result is quoted in Fig. 4. On the basis of the mentioned suppositions we are
t, = 76O”C.(‘)
able to explain the existence of the second maximum
V
v . - Dcdis, * %xd~+ 7
(8)
near l&Co
on the concentration dependence of log D as follows : if we measure the temperature dependence
344
ACTA
METALLURGICA,
VOL.
17, 1969
21.1-43.3 at.% Co. However, the existence of extremes on concentration dependences log D, log Do and AaH was found in paper. The behavior of these dependences near the composition N&Fe was quite analogous to that one found in the present paper (Fig. 2b). The existence of an ordered structure at Ni,Fe was already experimentally verified.(l)
The authors wish to express their thanks to Professor Dr. Ing. Habil. K. Giesen, Dipl. Ing. H. Hallerberg and to the Centre National de Recherches Metallurgiques for kindly supplying the Ni-Co alloy specimens, to Ing. J. Tougek CSc. for carrying out the analyses of these specimens, and to Ing. K. Ciha for the metallographic examination of samples. REFERENCES 1. M. BUNSEN and K. ANDERXO, Cork?titutionof Binmy
-
k-6
FIO. 4. Temperature dependences of the order parameter celculat&d from diffusion characteristics for Cu,Au and Ni,Co alloys.
of the set-effusion ~oe~~ie~t at the concentration corresponding to the composition N&Co, then the diffusion coefCicient decreases with decreasing temperature slower than at any other concentration near NisCo. Therefore, at temperatures getting sufficiently close to t,, a maximum on the oon~ntration dependence of log I) must appear at 25 at.% Co. The physical reason of this phenomenon consists in the maximum increase of the short range order parameter with decreasing temperature at this ooncentration. The appearance of a minimum in the concentration dependence of the activation enthalpy AH, or of the frequency factor log De, is naturally caused by the existence of a maximum in the concentration dependence of log D. In the paper(“) the appearance of extreme values near the concentration 25 at. o/OCo was not found because the authors did not oarry out any measurements of D in the concentration interval
R2Zo.p. McGraw-Hill (1958). 2. P. L. GRUZIN and B. M. Nosxov, Pro@. ~~~~~v~. i Fiz. Met.&. 4, 609 (1955). 3. K. HIRANO, R. P. AQARWALA, B. L. AVER~~ACRand M. COHEN,J. appl. Phy8. Ss, 3049 (1962). 4. A. HHSSNER and W. LANGE, Phya. Status Solidi 8, 77 (lQS~Lvy 5. J. VREST~~L and J. K&RA, to be submitted for publicstion. 6. C. E. BIKCHENALL,Tram. Am. Imat. M&s. Engr&171,166
(1947). 7. J. VEL&SEKand J. V&&L, Czech. J. Phy8. Bl6, (1966). 8. J. STEPHEN,i?zccE.ilnstrum. Met. ii%, 269 (1964).
937
9. P. L. GRUZIN, DOLE.Akad. Nauk SSSR 86,269 (1962). 10. Beta- and Gamarrama-Ray Spectroscopy, edited by K. &EC+BAHN. North-Holland (1966). 11, W. C. MALLARD,A. B. GARDNER,R. V. 3~s 8nd L. NC. SLIFEIN, Phga. Rev. IZS, 617 (1963). 12, S. MADER, Elwtron &ficroacopy and Strength of Cr@uk?, edited by G. TEOMASand J. WASHBURN, p. 183. Wiley (1963). 13. J. B. COHENand M. E. FINE, J. Phya. Radium, Pa& 28, 749 (1962). 14. A. B. KUPER, D. IXZABUS, J. R. MANNING and C. T. TOM~ZUKA,Whys. Rev. 104, 1636 {1956). 15. S. BENCI and G. CASPARRINI, J. Phye. C%m. S&L& 27, 1035 (1906). 16. S. BENCI, G. GASPARRINI, G. GERMA~NOLI and G. SCHIANCHI,J. Phya. Chem. Sotids &8, 687 (1965). 17. A. B. M&TIN. R. D. JOHNSONand F. ASARO. J. am% ..
Phya 25, 364 (19.54).
18. A. D. KURTZ, B. L. A~ERBACHand M. COHEN, Acta Met.
8, 442 (1955). 19. E. WAL&E DE RECA and C. PAMPZLO, Acta Met. 15, 1263 (1967).