- Email: [email protected]
Grain boundary phase transformation in Cu–Co solid solutions
Journal of Alloys and Compounds 536S (2012) S554–S558
Contents lists available at SciVerse ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Grain boundary phase transformation in Cu–Co solid solutions S.N. Zhevnenko ∗ , E.I. Gershman Department of Physical Chemistry, National University of Science and Technology “MISIS”, 4, Leninsky pr., Moscow 119049, Russia
a r t i c l e
i n f o
Article history: Received 2 July 2011 Received in revised form 8 December 2011 Accepted 9 December 2011 Available online 19 December 2011 Keywords: Copper Cobalt Grain boundary Interface controlled diffusional creep
a b s t r a c t The present work examined the creep behavior of copper based solid solutions with cobalt at temperatures between 980 ◦ C and 1080 ◦ C and stresses lower than 0.2 MPa. The samples were made from 18 m foil and were formed into cylinders. After the pre-annealing at 1000 ◦ C during about 30 h the samples had a parquet structure. The experiments were performed in the hydrogen atmosphere. New equipment was designed for these measurements. The activation energy of pure copper creep was close to the activation energy of copper volume selfdiffusion. Cu–Co solid solution creep rate was always lower than that of pure copper. It was shown that the creep activation energy in the relatively low temperature region was higher than in the high temperature region. The same behavior was typical for all studied solid solutions. The transition temperature was about 1030 ◦ C. It was proposed that such creep behavior was connected with grain boundary phase transformation and explanation was made in terms of interface controlled diffusional creep. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Alloys exhibiting high mechanical strength together with high electrical and thermal conductivity at elevated temperatures are in increasing demand. Copper has one of the best electrical and thermal conductivity. However, its strength must be increased in order to meet design requirements for high-temperature applications. The high-temperature mechanical strength of metallic alloys can be increased by adding a small fraction of dispersoids [1]. Probably there is another way. Particles could be formed during the deformation because in this case the conditions are nonequilibrium. At high homologous temperatures and low stresses polycrystals deform by diffusional creep. Diffusional creep theory is well developed and able to predict the deformation rate theoretically. The theory was developed independently by Nabarro [2] and Herring [3], for lattice diffusion of vacancies from grain boundaries under tension to those under compression, predicts linear stress dependence of the deformation rate. If so, activation energy of the creep is close to the activation energy of the volume diffusion. The kinetics of diffusional creep has been examined in many studies and there is good agreement for pure materials [4]. The deformation rate can be significantly less for multicomponent and multi-phase systems because the continuing steady state creep requires two processes: vacancy generations at source (flowing from a sink) and vacancy diffusion between source and sink. These processes operate sequentially and the slowest
process must control the overall creep rate. The main question is how a grain boundary acts as a sink or source. Ashby [5] considered the process of vacancy creation and annihilation occurs by the climb and glide of grain boundary dislocations. If such dislocations migrate by climb along the boundary, then vacancies will be emitted or absorbed depending on the climb direction. The entire grain boundary surface is a perfect sink or source for vacancies. So the diffusion from source to sink is rate controlling in case of pure materials. Situation can be more complicated for multi-component materials. The grain boundaries could not be perfect sink and source due to adsorption or second phase formation. If grain boundaries act as a perfect sink and source so that creep is diffusion controlled, then the deformation rate is given by Nabarro–Herring creep equation ε˙ N–H =
0925-8388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2011.12.027
(1)
where ε˙ N–H is creep rate, is applied stress, ˝ is atomic volume, D is lattice selfdiffusivity, d is average distance between source and sink (assume to be equal to grain size), B is a constant equal to 12, k is Boltzmann’s constant and T is temperature. Creep rate is proportional to the stress and viscosity is equal to N–H = d2 kT/B˝D. If grain boundaries are not a perfect sink and source then deformation rate is controlled by grain boundary dislocation moving and given by [6] ε˙ dis =
∗ Corresponding author. Tel.: +7 9262100790. E-mail address: [email protected] (S.N. Zhevnenko).
B˝D d2 kT
b2n M d
(2)
where bn is component of Burger’s vector perpendicular to grain boundary, is grain boundary dislocation density and M is
S.N. Zhevnenko, E.I. Gershman / Journal of Alloys and Compounds 536S (2012) S554–S558
S555
electrolytically and the sample is homogenized for about 50 h. The foils were placed into massive copper cylinder and investigated “in situ” by modified zero creep method at high temperatures. The experimental scheme is described in [9] and you can see it in Fig. 1. All annealing was performed in atmosphere of dry hydrogen. After preannealing the grain size of stabilized parquet structure was approximately 170 m. The method allows getting the time dependence of load on the cylindrical sample (Fig. 2). Non-zero equilibrium value is due to surface tension action. The experimental dependences are approximated by [9]
P = P0 + (Pinitial − P0 )exp
t A
(3)
where P is load, P0 is zero creep load (it corresponds to surface tension), Pinitial is initial load, t is time and A is a constant (A = −1.89 × 10−9 m2 /N). So the best approximation gives us viscosity . Eq. (3) can be used when the strain rate dependence of stress is linear as it was obtained in our experiments. Fig. 1. Experimental scheme. The elastic beam is rigidly connected to the foil. The sample bends the elastic beam due to surface tension.
3. Results and discussion dislocation’s mobility. According to [4] M ∼ Ds /kT, so viscosity of interface controlled creep is dis = dkT/B1 b2n Ds , where Ds is a coefficient characterizing diffusional climb of grain boundary dislocations and B1 is a constant. It is supposed that grain boundary dislocations move by climb. Ds can be close to the diffusion coefficient for the solute in case of formation of Cottrell clouds around grain boundary dislocations. Ds may be equal to the grain boundary diffusion coefficient of impurity if it is located in the dislocation core. And finally Ds can be effective diffusion coefficient if grain boundary dislocations need to overcome the grain boundary particles. Anyway the temperature dependence of viscosity is the same for all cases when the grain structure is stabilized: ∼ T/D and D = D0 exp(−E/RT). Thus if we measure the viscosity at different temperatures we can determine the activation energy of diffusional creep by linearization in ln(T/) ∼ 1/RT coordinates. The present work examined the creep behavior of pure copper foil and foils of solid solutions Cu–0.45 at.% Co; Cu–0.7 at.% Co; Cu–1.4 at.% Co; Cu–2.8 at.% Co. Cobalt in copper has positive deviation from ideality and tends to precipitate formation in volume and grain boundaries [7,8]. This caused the interest to Cu–Co system. Creep is a structurally sensitive property. So the creep experiments can help to understand phase formation in the system. 2. Experimental procedure For preparing the samples polycrystalline copper foils were used. Purity of copper was 99.995 wt.% Cu and foil thickness was 18 m. The foils were formed into cylinders with about 7 mm diameter and 150 mm length. Cobalt was introduced
First of all experiment on pure copper was performed. Temperature range was from 909 ◦ C to 1070 ◦ C and linearized temperature dependence of viscosity is shown in Fig. 3. The slope of the line is −E and it is equal to 203 kJ/mol. This activation energy is close to the volume self diffusion activation energy for pure copper. Direct radiotracer experiments give the activation energy is 211 kJ/mol [10], 209 kJ/mol [10]. It is also possible to estimate the average distance between source and sink of vacancies using the intercept on the ln(T/) axis. It equals to ln(B˝D0 /Rd2 ). Taking into account the pre-exponential factors D0 from [10,11] we calculated d ≈ 40 m. The value is between foil thickness (18 m) and average grain size (170 m). Thus the method is correct and the result is in good agreement with data obtained by direct methods. The next creep experiment was performed on Cu–20 at.% Ni solid solution. Cu–Ni system is close to ideality at high temperature so there is no sense to obtain a large difference from creep behavior of pure copper. Ni was electrolytic deposited on pure copper cylindrical foil and the sample was annealed for about 100 h at 1020 ◦ C. We assumed that the homogenization was done at these conditions. The results of viscosity measurements are shown in Fig. 3. Activation energy of Cu–20 at.% Ni solid solution is higher than that for pure copper and equals approximately 275 kJ/mol. Creep experiments on Cu–2 wt.% Ni were performed in work [12]. Authors have obtained the creep activation energy (approximately 200 kJ/mol) which is close to the creep activation energy for pure copper. So the creep activation energy of Cu–Ni alloys grows with Ni concentration increasing.
Fig. 2. (a) The experimental sample. The arrow points to the copper foil. (b) Time dependence of load on the sample. Dotted line in (a) is an approximation by Eq. (3).
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where xCu , xNi are atomic fractions, DCu , DNi are volume selfdiffusion coefficients for Cu and Ni respectively and DCuNi , DNiCu are coefficients which take into account the influence of one component flux to other. Assuming that a gradient in the chemical potential of one element does not produce flux of the second element if the chemical potential of that second element is uniform, i.e. DCuNi = DNiCu = 0, then:
Dalloy =
Fig. 3. Linearized temperature dependence of the viscosity: diamonds – for pure copper; squares – for Cu–20 at.% Ni solid solution. Slope is equal to −E.
Creep behavior of Cu–20 at.% Ni can be explained in terms of effective volume diffusivity. Effective diffusion coefficient in alloy is given by [3]:
Dalloy =
2 −2·D 2 DCu · xNi CuNi xCu xNi + DNi · xCu 2 DCu DNi − DCuNi
−1 (4)
2 xCu
DCu
+
2 xNi
−1 (5)
DNi
Ni concentration is high in our alloy so we must take into account DCuNi , DNiCu . It can explain increasing of the creep activation energy of Cu–20 at.% Ni. The temperature dependencies of the viscosity for Co–Cu solid solutions were obtained (Fig. 4). Character of these dependencies is more complicated. They have the viscosity gap (Fig. 4). The temperature of the gap is about 1030 ◦ C. Two different parts of the dependence can be noted. At relatively low temperatures the activation energy increases with Co concentration increasing by straight line (Fig. 5a). At high temperatures the activation energy also increases except Cu–2.8 at.% Co sample. The concentration dependence of the activation energy at high temperatures can be described by a parabolic curve (Fig. 5a). The value of the gap can also be described by a parabola (Fig. 5b). Volume diffusion coefficient of Co in Cu is close to that for Cu in Co: DCo in Cu = 1.93·10−4 ·exp(−226,500 J mol−1 /R·T) m2 s−1 [13] and 2 /D ] concentration of Co is low. Therefore Dalloy ≈ [xCu Cu
−1
= 1.06 ·
Fig. 4. Linearized temperature dependence of the viscosity for cobalt solid solutions in copper: (a) Cu–0.45 at.% Co; (b) Cu–0.7 at.% Co; (c) Cu–1.4 at.% Co; (d) Cu–2.8 at.% Co. Slope is equal to −E. Dotted line shows the same dependence for pure copper.
S.N. Zhevnenko, E.I. Gershman / Journal of Alloys and Compounds 536S (2012) S554–S558
S557
Fig. 5. Concentration dependence of creep activation energy (a) at relatively low temperatures (ETlow ) and high temperatures (EThigh ); (b) is the concentration dependence of viscosity gap.
DCu is practically equal to the copper selfdiffusion coefficient. Diffusion controlled creep would be just several percents slower than that for pure copper. We assume that there is interface controlled diffusional creep in case of Cu–Co solid solutions. The activation energy of Cu–2.8 at.% Co sample is about 105 kJ/mol at relatively high temperatures and 480 kJ/mol at relatively low temperatures. The magnitude of the gap is low /high ≈ 2. The high temperature activation energy is very large. Such activation energies are typical for the diffusional creep of materials containing dispersed particles. For instance the creep activation energy of Cu containing Al2 O3 particles is about 500 kJ/mol as obtained by Burton [14]. Diffusion rates are not affected by a small volume fraction of inert particles. The reason of large reduction of deformation rate and high activation energies may be the necessity of grain boundary dislocations to overcome grain boundary obstacles. It can be assumed that in our case grain boundary precipitates form under the experimental conditions. The concentration of Co is about two times less than the solubility at the temperature of the
gap but there are no equilibrium conditions. The sample is under stress and vacancy flux can lead to the cobalt redistribution (just as the denudation zone formation [15]). The high temperature activation energy is about two times lower than that of pure copper. The value 105 kJ/mol is close to the typical for the solute grain boundary diffusion. There is no reliable data but article [16] presents data on Co grain boundary diffusion in Cu. The activation energy is 95 kJ/mol. We can assume that at high temperature Co inhibits the movement of dislocation by segregating into dislocation core. As a result the creep activation energy is close to Co grain boundary activation energy. Scanning electron microscopy was made on the Cu–2.8 at.% Co sample after creep test. The foil was embrittled as it was described in [17]. Grain boundary microstructure is shown in Fig. 6. There were Co-rich particles on the grain boundary brittle fracture. It would be a confirmation of the particles formation assumption but the question is how fast it is necessary to quench? In our case the rate of quenching was about 100 ◦ C/min at high temperatures and time of quenching was about 30 min. In addition there were not
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S.N. Zhevnenko, E.I. Gershman / Journal of Alloys and Compounds 536S (2012) S554–S558
Fig. 6. Scanning electron microscopy of grain boundary of Cu–2.8 at.% Co sample after creep test. The bright spots are Co-rich particles.
2. Creep activation energy of Cu–20 at.% Ni foil was measured. The creep behavior was similar to the pure copper and creep activation energy was approximately 275 kJ/mol. 3. Creep behavior of Cu–0.45 at.% Co, Cu–0.7 at.% Co, Cu–1.4 at.% Co and Cu–2.8 at.% Co solid solutions was investigated. There were the gaps on temperature dependence of viscosity and the deformation rates were lower than the rates for pure copper. These features can be attributed to the interface controlled diffusional creep. 4. Activation energy at relatively low temperatures (T < 1030 ◦ C) increases with Co concentration increasing from 235 kJ/mol for Cu–0.45 at.% Co solid solution to 485 kJ/mol for Cu–2.8 at.% Co solid solution by straight line. Activation energy at relatively high temperatures (1030 ◦ C < T < Tm) depends nonlinearly on Co concentration. 5. The gap on the temperature dependence of viscosity and significant difference in activation energies at different temperatures gives us the evidences of grain boundary transformation in Cu–Co solid solutions. Acknowledgments
any particles of such size on grain boundaries after quenching with about 500 ◦ C/min rate without creep testing. So the particle formation can be the result of Co redistribution during creep process. The samples containing less concentration of Co (Cu–0.45 at.% Co, Cu–0.7 at.% Co and Cu–1.4 at.% Co) can be transient from cobalt solid solution in grain boundaries and interaction of Co with moved grain boundary dislocations to grain boundary particles formation. The temperature of the gap can be interpreted as the temperature of phase transformation from grain boundary solution to the two-phase grain boundary system in case of Cu–2.8 at.% Co sample. For more dilute solid solutions the temperature of the gap is also grain boundary phase transition temperature but interpretation requires further research. 4. Conclusions 1. Creep activation energy of pure copper (99.995 Cu) was obtained at 960–1070 ◦ C, stresses lower than 0.25 MPa. The creep test shows good agreement with Nabarro–Herring creep theory. Creep activation energy was approximately 203 kJ/mol which is close to the volume self diffusion activation energy.
The research is carried out with financial support of the Programme of Creation and Development of the National University of Science and Technology “MISiS”. References [1] O.D. Sherby, P.M. Burke, Prog. Mater. Sci. 13 (1967) 325. [2] F.N.R. Nabarro, Report of a Conference on the Strength of the Solids. The Physical Society of London, London, 1948, pp. 75. [3] C. Herring, J. Appl. Phys. 21 (1950) 437. [4] H. Jones, Mater. Sci. Eng. 4 (1969) 106. [5] M.F. Ashby, Scr. Metall. 3 (1969) 837. [6] E. Arzt, M.F. Ashby, R.A. Verrall, Acta Metall. 31 (1983) 1977. [7] R. Monzen, T. Echigo, Scr. Mater. 40 (1999) 963. [8] D. Watanabe, C. Watanabe, R. Monzen, Acta Mater. 57 (2009) 1899. [9] E.I. Gershman, S.N. Zhevnenko, J. Phys. Met. Metall. 110 (2010) 102. [10] S.J. Rothman, N.L. Peterson, Phys. Status Solidi 35 (1969) 305. [11] G. Krautheim, A. Neidhardt, U. Reinhold, A. Zehe, Krist. Tech. 14 (1979) 1491. [12] P.A. Thorsen, J.B. Bilde-Sorensen, Mater. Sci. Eng. A 265 (1999) 140. [13] C.A. Mackliet, Phys. Rev. 109 (1958) 1964. [14] B. Burton, Metal Sci. J. 5 (1971) 11. [15] J. Wadsworth, O. Ruano, O. Sherby, Met. Mater. Trans. 33A (2002) 219. [16] R.S. Mishra, H. Jones, G.W. Greenwood, J. Mater. Sci. Lett. 7 (1988) 728. [17] S.N. Zhevnenko, D.V. Vaganov, E.I. Gershman, J. Mater. Sci. 46 (12) (2011) 4248.
Contents lists available at SciVerse ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Grain boundary phase transformation in Cu–Co solid solutions S.N. Zhevnenko ∗ , E.I. Gershman Department of Physical Chemistry, National University of Science and Technology “MISIS”, 4, Leninsky pr., Moscow 119049, Russia
a r t i c l e
i n f o
Article history: Received 2 July 2011 Received in revised form 8 December 2011 Accepted 9 December 2011 Available online 19 December 2011 Keywords: Copper Cobalt Grain boundary Interface controlled diffusional creep
a b s t r a c t The present work examined the creep behavior of copper based solid solutions with cobalt at temperatures between 980 ◦ C and 1080 ◦ C and stresses lower than 0.2 MPa. The samples were made from 18 m foil and were formed into cylinders. After the pre-annealing at 1000 ◦ C during about 30 h the samples had a parquet structure. The experiments were performed in the hydrogen atmosphere. New equipment was designed for these measurements. The activation energy of pure copper creep was close to the activation energy of copper volume selfdiffusion. Cu–Co solid solution creep rate was always lower than that of pure copper. It was shown that the creep activation energy in the relatively low temperature region was higher than in the high temperature region. The same behavior was typical for all studied solid solutions. The transition temperature was about 1030 ◦ C. It was proposed that such creep behavior was connected with grain boundary phase transformation and explanation was made in terms of interface controlled diffusional creep. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Alloys exhibiting high mechanical strength together with high electrical and thermal conductivity at elevated temperatures are in increasing demand. Copper has one of the best electrical and thermal conductivity. However, its strength must be increased in order to meet design requirements for high-temperature applications. The high-temperature mechanical strength of metallic alloys can be increased by adding a small fraction of dispersoids [1]. Probably there is another way. Particles could be formed during the deformation because in this case the conditions are nonequilibrium. At high homologous temperatures and low stresses polycrystals deform by diffusional creep. Diffusional creep theory is well developed and able to predict the deformation rate theoretically. The theory was developed independently by Nabarro [2] and Herring [3], for lattice diffusion of vacancies from grain boundaries under tension to those under compression, predicts linear stress dependence of the deformation rate. If so, activation energy of the creep is close to the activation energy of the volume diffusion. The kinetics of diffusional creep has been examined in many studies and there is good agreement for pure materials [4]. The deformation rate can be significantly less for multicomponent and multi-phase systems because the continuing steady state creep requires two processes: vacancy generations at source (flowing from a sink) and vacancy diffusion between source and sink. These processes operate sequentially and the slowest
process must control the overall creep rate. The main question is how a grain boundary acts as a sink or source. Ashby [5] considered the process of vacancy creation and annihilation occurs by the climb and glide of grain boundary dislocations. If such dislocations migrate by climb along the boundary, then vacancies will be emitted or absorbed depending on the climb direction. The entire grain boundary surface is a perfect sink or source for vacancies. So the diffusion from source to sink is rate controlling in case of pure materials. Situation can be more complicated for multi-component materials. The grain boundaries could not be perfect sink and source due to adsorption or second phase formation. If grain boundaries act as a perfect sink and source so that creep is diffusion controlled, then the deformation rate is given by Nabarro–Herring creep equation ε˙ N–H =
0925-8388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2011.12.027
(1)
where ε˙ N–H is creep rate, is applied stress, ˝ is atomic volume, D is lattice selfdiffusivity, d is average distance between source and sink (assume to be equal to grain size), B is a constant equal to 12, k is Boltzmann’s constant and T is temperature. Creep rate is proportional to the stress and viscosity is equal to N–H = d2 kT/B˝D. If grain boundaries are not a perfect sink and source then deformation rate is controlled by grain boundary dislocation moving and given by [6] ε˙ dis =
∗ Corresponding author. Tel.: +7 9262100790. E-mail address: [email protected] (S.N. Zhevnenko).
B˝D d2 kT
b2n M d
(2)
where bn is component of Burger’s vector perpendicular to grain boundary, is grain boundary dislocation density and M is
S.N. Zhevnenko, E.I. Gershman / Journal of Alloys and Compounds 536S (2012) S554–S558
S555
electrolytically and the sample is homogenized for about 50 h. The foils were placed into massive copper cylinder and investigated “in situ” by modified zero creep method at high temperatures. The experimental scheme is described in [9] and you can see it in Fig. 1. All annealing was performed in atmosphere of dry hydrogen. After preannealing the grain size of stabilized parquet structure was approximately 170 m. The method allows getting the time dependence of load on the cylindrical sample (Fig. 2). Non-zero equilibrium value is due to surface tension action. The experimental dependences are approximated by [9]
P = P0 + (Pinitial − P0 )exp
t A
(3)
where P is load, P0 is zero creep load (it corresponds to surface tension), Pinitial is initial load, t is time and A is a constant (A = −1.89 × 10−9 m2 /N). So the best approximation gives us viscosity . Eq. (3) can be used when the strain rate dependence of stress is linear as it was obtained in our experiments. Fig. 1. Experimental scheme. The elastic beam is rigidly connected to the foil. The sample bends the elastic beam due to surface tension.
3. Results and discussion dislocation’s mobility. According to [4] M ∼ Ds /kT, so viscosity of interface controlled creep is dis = dkT/B1 b2n Ds , where Ds is a coefficient characterizing diffusional climb of grain boundary dislocations and B1 is a constant. It is supposed that grain boundary dislocations move by climb. Ds can be close to the diffusion coefficient for the solute in case of formation of Cottrell clouds around grain boundary dislocations. Ds may be equal to the grain boundary diffusion coefficient of impurity if it is located in the dislocation core. And finally Ds can be effective diffusion coefficient if grain boundary dislocations need to overcome the grain boundary particles. Anyway the temperature dependence of viscosity is the same for all cases when the grain structure is stabilized: ∼ T/D and D = D0 exp(−E/RT). Thus if we measure the viscosity at different temperatures we can determine the activation energy of diffusional creep by linearization in ln(T/) ∼ 1/RT coordinates. The present work examined the creep behavior of pure copper foil and foils of solid solutions Cu–0.45 at.% Co; Cu–0.7 at.% Co; Cu–1.4 at.% Co; Cu–2.8 at.% Co. Cobalt in copper has positive deviation from ideality and tends to precipitate formation in volume and grain boundaries [7,8]. This caused the interest to Cu–Co system. Creep is a structurally sensitive property. So the creep experiments can help to understand phase formation in the system. 2. Experimental procedure For preparing the samples polycrystalline copper foils were used. Purity of copper was 99.995 wt.% Cu and foil thickness was 18 m. The foils were formed into cylinders with about 7 mm diameter and 150 mm length. Cobalt was introduced
First of all experiment on pure copper was performed. Temperature range was from 909 ◦ C to 1070 ◦ C and linearized temperature dependence of viscosity is shown in Fig. 3. The slope of the line is −E and it is equal to 203 kJ/mol. This activation energy is close to the volume self diffusion activation energy for pure copper. Direct radiotracer experiments give the activation energy is 211 kJ/mol [10], 209 kJ/mol [10]. It is also possible to estimate the average distance between source and sink of vacancies using the intercept on the ln(T/) axis. It equals to ln(B˝D0 /Rd2 ). Taking into account the pre-exponential factors D0 from [10,11] we calculated d ≈ 40 m. The value is between foil thickness (18 m) and average grain size (170 m). Thus the method is correct and the result is in good agreement with data obtained by direct methods. The next creep experiment was performed on Cu–20 at.% Ni solid solution. Cu–Ni system is close to ideality at high temperature so there is no sense to obtain a large difference from creep behavior of pure copper. Ni was electrolytic deposited on pure copper cylindrical foil and the sample was annealed for about 100 h at 1020 ◦ C. We assumed that the homogenization was done at these conditions. The results of viscosity measurements are shown in Fig. 3. Activation energy of Cu–20 at.% Ni solid solution is higher than that for pure copper and equals approximately 275 kJ/mol. Creep experiments on Cu–2 wt.% Ni were performed in work [12]. Authors have obtained the creep activation energy (approximately 200 kJ/mol) which is close to the creep activation energy for pure copper. So the creep activation energy of Cu–Ni alloys grows with Ni concentration increasing.
Fig. 2. (a) The experimental sample. The arrow points to the copper foil. (b) Time dependence of load on the sample. Dotted line in (a) is an approximation by Eq. (3).
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where xCu , xNi are atomic fractions, DCu , DNi are volume selfdiffusion coefficients for Cu and Ni respectively and DCuNi , DNiCu are coefficients which take into account the influence of one component flux to other. Assuming that a gradient in the chemical potential of one element does not produce flux of the second element if the chemical potential of that second element is uniform, i.e. DCuNi = DNiCu = 0, then:
Dalloy =
Fig. 3. Linearized temperature dependence of the viscosity: diamonds – for pure copper; squares – for Cu–20 at.% Ni solid solution. Slope is equal to −E.
Creep behavior of Cu–20 at.% Ni can be explained in terms of effective volume diffusivity. Effective diffusion coefficient in alloy is given by [3]:
Dalloy =
2 −2·D 2 DCu · xNi CuNi xCu xNi + DNi · xCu 2 DCu DNi − DCuNi
−1 (4)
2 xCu
DCu
+
2 xNi
−1 (5)
DNi
Ni concentration is high in our alloy so we must take into account DCuNi , DNiCu . It can explain increasing of the creep activation energy of Cu–20 at.% Ni. The temperature dependencies of the viscosity for Co–Cu solid solutions were obtained (Fig. 4). Character of these dependencies is more complicated. They have the viscosity gap (Fig. 4). The temperature of the gap is about 1030 ◦ C. Two different parts of the dependence can be noted. At relatively low temperatures the activation energy increases with Co concentration increasing by straight line (Fig. 5a). At high temperatures the activation energy also increases except Cu–2.8 at.% Co sample. The concentration dependence of the activation energy at high temperatures can be described by a parabolic curve (Fig. 5a). The value of the gap can also be described by a parabola (Fig. 5b). Volume diffusion coefficient of Co in Cu is close to that for Cu in Co: DCo in Cu = 1.93·10−4 ·exp(−226,500 J mol−1 /R·T) m2 s−1 [13] and 2 /D ] concentration of Co is low. Therefore Dalloy ≈ [xCu Cu
−1
= 1.06 ·
Fig. 4. Linearized temperature dependence of the viscosity for cobalt solid solutions in copper: (a) Cu–0.45 at.% Co; (b) Cu–0.7 at.% Co; (c) Cu–1.4 at.% Co; (d) Cu–2.8 at.% Co. Slope is equal to −E. Dotted line shows the same dependence for pure copper.
S.N. Zhevnenko, E.I. Gershman / Journal of Alloys and Compounds 536S (2012) S554–S558
S557
Fig. 5. Concentration dependence of creep activation energy (a) at relatively low temperatures (ETlow ) and high temperatures (EThigh ); (b) is the concentration dependence of viscosity gap.
DCu is practically equal to the copper selfdiffusion coefficient. Diffusion controlled creep would be just several percents slower than that for pure copper. We assume that there is interface controlled diffusional creep in case of Cu–Co solid solutions. The activation energy of Cu–2.8 at.% Co sample is about 105 kJ/mol at relatively high temperatures and 480 kJ/mol at relatively low temperatures. The magnitude of the gap is low /high ≈ 2. The high temperature activation energy is very large. Such activation energies are typical for the diffusional creep of materials containing dispersed particles. For instance the creep activation energy of Cu containing Al2 O3 particles is about 500 kJ/mol as obtained by Burton [14]. Diffusion rates are not affected by a small volume fraction of inert particles. The reason of large reduction of deformation rate and high activation energies may be the necessity of grain boundary dislocations to overcome grain boundary obstacles. It can be assumed that in our case grain boundary precipitates form under the experimental conditions. The concentration of Co is about two times less than the solubility at the temperature of the
gap but there are no equilibrium conditions. The sample is under stress and vacancy flux can lead to the cobalt redistribution (just as the denudation zone formation [15]). The high temperature activation energy is about two times lower than that of pure copper. The value 105 kJ/mol is close to the typical for the solute grain boundary diffusion. There is no reliable data but article [16] presents data on Co grain boundary diffusion in Cu. The activation energy is 95 kJ/mol. We can assume that at high temperature Co inhibits the movement of dislocation by segregating into dislocation core. As a result the creep activation energy is close to Co grain boundary activation energy. Scanning electron microscopy was made on the Cu–2.8 at.% Co sample after creep test. The foil was embrittled as it was described in [17]. Grain boundary microstructure is shown in Fig. 6. There were Co-rich particles on the grain boundary brittle fracture. It would be a confirmation of the particles formation assumption but the question is how fast it is necessary to quench? In our case the rate of quenching was about 100 ◦ C/min at high temperatures and time of quenching was about 30 min. In addition there were not
S558
S.N. Zhevnenko, E.I. Gershman / Journal of Alloys and Compounds 536S (2012) S554–S558
Fig. 6. Scanning electron microscopy of grain boundary of Cu–2.8 at.% Co sample after creep test. The bright spots are Co-rich particles.
2. Creep activation energy of Cu–20 at.% Ni foil was measured. The creep behavior was similar to the pure copper and creep activation energy was approximately 275 kJ/mol. 3. Creep behavior of Cu–0.45 at.% Co, Cu–0.7 at.% Co, Cu–1.4 at.% Co and Cu–2.8 at.% Co solid solutions was investigated. There were the gaps on temperature dependence of viscosity and the deformation rates were lower than the rates for pure copper. These features can be attributed to the interface controlled diffusional creep. 4. Activation energy at relatively low temperatures (T < 1030 ◦ C) increases with Co concentration increasing from 235 kJ/mol for Cu–0.45 at.% Co solid solution to 485 kJ/mol for Cu–2.8 at.% Co solid solution by straight line. Activation energy at relatively high temperatures (1030 ◦ C < T < Tm) depends nonlinearly on Co concentration. 5. The gap on the temperature dependence of viscosity and significant difference in activation energies at different temperatures gives us the evidences of grain boundary transformation in Cu–Co solid solutions. Acknowledgments
any particles of such size on grain boundaries after quenching with about 500 ◦ C/min rate without creep testing. So the particle formation can be the result of Co redistribution during creep process. The samples containing less concentration of Co (Cu–0.45 at.% Co, Cu–0.7 at.% Co and Cu–1.4 at.% Co) can be transient from cobalt solid solution in grain boundaries and interaction of Co with moved grain boundary dislocations to grain boundary particles formation. The temperature of the gap can be interpreted as the temperature of phase transformation from grain boundary solution to the two-phase grain boundary system in case of Cu–2.8 at.% Co sample. For more dilute solid solutions the temperature of the gap is also grain boundary phase transition temperature but interpretation requires further research. 4. Conclusions 1. Creep activation energy of pure copper (99.995 Cu) was obtained at 960–1070 ◦ C, stresses lower than 0.25 MPa. The creep test shows good agreement with Nabarro–Herring creep theory. Creep activation energy was approximately 203 kJ/mol which is close to the volume self diffusion activation energy.
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