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Gibbs–Thomson relationship for the precipitation in Cu–Ti alloys
Materials Characterization 58 (2007) 303 – 306
Gibbs–Thomson relationship for the precipitation in Cu–Ti alloys Felipe Hernandez-Santiago, Victor M. Lopez-Hirata ⁎, Maribel L. Saucedo-Muñoz, Hector J. Dorantes-Rosales Instituto Politecnico Nacional Apartado Postal 188-556 07051 Mexico, D.F. Received 1 December 2005; received in revised form 18 May 2006; accepted 19 May 2006
Abstract A diffusion-couple Cu/Cu–Ti alloy was prepared in order to obtain a macroscopic composition gradient in the Cu–Ti alloy system. This couple was solution treated subsequently water quenched and aged at 837 K for 600 s. The precipitation process was analyzed with an EDS-TEM. The Gibbs–Thomson relation was used to analyze the precipitation of the metastable and semicoherent β′ phase in Cu–Ti alloys and this relationship enabled us to estimate the interfacial free energy between matrix and precipitates to be about 0.31 ± 0.02 J m− 2. © 2006 Elsevier Inc. All rights reserved. Keywords: Cu–Ti alloys; Precipitation; Macroscopic composition gradient method; Gibbs–Thomson relation
1. Introduction Cu–Ti alloys are susceptible to age-hardening. Besides, this type of alloys has shown to be a possible substitute for expensive and toxic age-hardenable Cu– Be alloys. Cu–Ti alloy have been also considered to be ultra-high strength conductive materials for applications such as conductive springs, interconnections, etc. [1]. The precipitation process and strengthening in Cu–Ti alloys have been a subject of continuous studying [1–7]. The phase decomposition in the early stage of aging has been shown to take place via the mechanism of spinodal decomposition [2]. Additionally, it has been reported [3–5] that an ordering reaction occurs to form metastable β′(Cu4Ti) precipitates, which contributes significantly to the maximum strengthening of Cu–Ti ⁎ Corresponding author. Tel.: +52 55 57548249; fax: +52 55 51191986. E-mail address: [email protected] (V.M. Lopez-Hirata). 1044-5803/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.matchar.2006.05.008
alloys. Prolonged aging or aging at high temperatures promoted the cellular or discontinuous precipitation with the formation of equilibrium β (Cu3Ti) precipitates [5–7]. A new experimental method was proposed by Miyazaki et al. [8,9] to study the precipitation process in binary alloys called macroscopic composition gradient method. This method enables to determine solubility limits and phase equilibria and it is based on the microstructural observation of different composition alloys formed by a continuous composition gradient. The macroscopic composition gradient can be created in a specimen by diffusion coupling, imperfect arc melting of sandwiched metals, imperfect homogenization of coarse precipitates, etc. The purpose of this work is to analyze the precipitation process with the Gibbs–Thomson relation in Cu–Ti alloys formed by the macroscopic composition gradient method using a diffusion couple between pure Cu and a Cu–4 at.% Ti alloy, after aging at 873 K.
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F. Hernandez-Santiago et al. / Materials Characterization 58 (2007) 303–306
2. Experimental procedure A Cu–4 wt.% Ti was produced by melting of 99.99% purity titanium and 99.999% purity copper in an alumina crucible under an argon gas atmosphere. The ingot was homogenized at 1223 K for 864 ks and then cold rolled to obtain specimens of 30× 10× 5 mm. The diffusion couple consisting of two specimens, Cu–4 wt.% Ti and pure Cu, with polished flat surfaces was placed in an austenitic stainless steel holder with screws. Specimens were pressed by the screw and diffusion welded by heating at 1173 K for 86.4 ks under an argon atmosphere. The diffusion-couple was sealed in an evacuated quartz tube and annealed at 1173 K for 777.6 ks in an electrical resistance furnace, controlled within ±2 K and subsequently quenched in icewater in order to obtain a solution treated specimen. After this heat treating procedure, specimens were aged at 873 K many times from 600 to 3600 s. The bulk heat treated diffusion-couples were cut and ground to cylinders with diameters of about 3 mm so that the interface could be included in the middle along the cylinder axis. Discs with about 0.15 mm were obtained by electroerosion of cylinders. These discs were thinned using the twin-jet electropolishing technique in a solution of 75 vol.% methanol and 25 vol.% nitric acid at 213 K. TEM specimens were mounted on a Bespecimen holder and observed with a TEM JEM2000FX-II at 200 kV, equipped with a Noran EDXS. 3. Results and discussion Fig. 1 illustrates a concentration profile determined on the surface of diffusion-couple after aging at 873 K
for 600 s. Several BF-TEM micrographs corresponding to different compositions are also shown in this figure. These micrographs indicate the precipitation evolution for different titanium compositions at the same aging condition. Three different zones can be noticed in the concentration profile. Precipitates were mainly cuboids in the case of compositions higher than 1.5 at.% Ti. These cuboids were aligned in the elastically softest 〈100〉 crystallographic direction of the Cu-rich matrix. The analysis of the corresponding electron diffraction pattern indicates that the precipitates correspond to the metastable β′ (Cu4Ti) phase. The dark and bright contrast of precipitates is due to the coherency strains and this suggests that the β′ precipitates are coherent with the matrix. The β′ precipitates show an elongated plate shape in the 〈100〉 direction of the matrix for the compositions about between 1.5 and 1.0 at.% Ti. The interface between matrix and precipitates seems to be semicoherent because it can be observed the coherency-strains in the longest side of plates. The details of morphology for these precipitates can be observed more clearly in Fig. 2. It can be noticed that these precipitates were elongated in the 〈100〉 direction of the Cu-rich matrix. In the case of titanium compositions lower than 1 at. %, the precipitates have an ellipsoidal shape showing no preferential orientation with the matrix. Besides, almost no contrast due to the coherency-strain can be seen, which suggests that the interface between precipitates and matrix seems to be incoherent. It is important to notice that the volume fraction of precipitates decreases with the decrease in titanium content, as expected according to the lever rule.
Fig. 1. Concentration profile of the diffusion-couple, after aging at 873 K for 600 s and BF-TEM micrographs corresponding to some compositions.
F. Hernandez-Santiago et al. / Materials Characterization 58 (2007) 303–306
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Fig. 2. BF-TEM micrographs of semicoherent β′ precipitates in Cu–Ti alloys.
Fig. 3 shows the plot of the equilibrium matrix composition Ce(r) as a function of the reciprocal value of the mean radius r of precipitates for the semicoherent precipitates in Cu–Ti alloys. There is a linear relationship, with an adjusted contribution ratio R2 of about
0.96116, between these two parameters. The empirical Ce(r) of the matrix phase seems to be inversely proportional to the particle radius r. In the limiting case of binary two-phase alloy with almost pure A, Cα→0, and pure B, Cβ→1, the Gibbs–
Fig. 3. Gibbs–Thomson relationship for the semicoherent β′ precipitates in Cu–Ti alloys.
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F. Hernandez-Santiago et al. / Materials Characterization 58 (2007) 303–306
Thomson equation predicts a variation of Ce(r) with r as follows [10]: Ce ðrÞ ¼ CðlÞdexp½1 þ ð2gVm =rRT Þ
ð1Þ
where γ is the interfacial energy between precipitates and matrix, Vm the molar volume of precipitate, R the gas constant, T the temperature and C(∞) the equilibrium composition at the precipitate with the infinite size. If the radius is larger than a few nanometers, Eq. (1) reduces to the more commonly quoted form of the Gibbs–Thomson equation: Ce ðrÞ ¼ CðlÞ½1 þ ð2gVm =rRT Þ
ð2Þ
If the two phases are not limiting solid solutions, one way that this effect can be introduced into the Gibbs– Thomson equation while retaining the form given in Eq. (2) is to define the molar volume, Vm, as the volume occupied by the Avogadro's number of solute atoms. Then, in a precipitate of atomic composition, AnB, Vm will be increased from the typical metallic value of 10− 5 m3 mol− 1 to about (n + 1) × 10− 5 m3 mol− 1. Ardell [11] used this form of the Gibbs–Thomson equation in the analysis of Ni–Ni3Al system. This analysis method was also employed in this work. Considering a Vm value of about 7.11 × 10− 6 m3 mol− 1 for the β′ precipitates, the interfacial energy γ can be determined using the slope value of the straight line shown in Fig. 3. The interfacial energy γ was determined to be about 0.31 ± 0.02 J m− 2, which is in good agreement with the reported values for semicoherent interfaces, γ > 0.25 J m− 2 [12]. Miyazaki et al. [9] reported an interfacial energy for the interface between the Cu-rich matrix and coherent β′ precipitates to be about 0.21 J m− 2. The equilibrium composition at the precipitate with the infinite size, C(∞), is about 1.054 ± 0.02 at.% Ti, which is close to the equilibrium value of about 1 at.% Ti at 873 K in the equilibrium phase diagram [13]. 4. Conclusions The macroscopic composition gradient method permitted to analyze the precipitation process in Cu–Ti
alloys. The precipitation process followed the Gibbs– Thomson relationship for the precipitation of the metastable and semicoherent (Cu4Ti) β′ phase. The interfacial energy between the Cu-rich matrix and β′ precipitates was determined to be about 0.31 ± 0.02 J m− 2. Acknowledgements The authors wish to thank the financial support from CGPI-COFAA-IPN and Fondo Sectorial para la Educacion-CONACYT 47151-Y. References [1] Soffa WA, Laughlin DE. High-strength age hardening copper– titanium alloys: redivivus. Prog Mater Sci 2004;49:347–66. [2] Laughlin DE, Cahn JW. Spinodal decomposition in age hardening copper–titanium alloys. Acta Metall 1975;23:329–39. [3] Datta A, Soffa WA. The structure and properties of age hardened Cu–Ti alloys. Acta Metall 1976;24:987–1001. [4] Dutkiewwicz J. Electron microscopy study of the effect of deformation on precipitation and recrystallization in copper– titanium alloys. Metall Trans 1977;8A:751–61. [5] Nagarjuna S, Balasubramanian K, Sarma DS. Effect of prior cold work on mechanical properties and structure of an aged-hardened Cu–1.5 wt% Ti alloy. J Mater Sci 1997;32:3375–85. [6] Nagarjuna S, Balasubramanian K, Sarma DS. Effect of cold work on precipitation hardening of Cu–4.5 mass% Ti alloy. Mater Trans JIM 1995;36:1058–66. [7] Hameda AA, Blaz L. Microstructure of hot-deformed Cu– 3.45 wt.% Ti alloy. Mater Sci Eng 1998;254A:83–9. [8] Miyazaki T, Koyama T, Kobayashi S. A new characterization method of the microstructure using the macroscopic composition gradient in alloys. Metall Mater Trans 1996;27A:945–9. [9] Miyazaki T, Kobayashi S, Koyama T. Determination of the critical nucleus size of precipitates using the macroscopic composition gradient. Metall Mater Trans 1999;30A:2783–9. [10] Martin JW, Doherty RD, Cantor B. Stability of microstructures in metallic systems. New York USA: Cambridge University Press; 1997. p. 243–8. [11] Ardell AJ. Observations of the effect of volume fraction on the coarsening of γ′ precipitates in binary Ni–Al alloys. Scr Metall Mater 1990;24:343–6. [12] Porter DA, Easterling KE. Phase transformations in metals and alloys. London, UK: Chapman and Hall; 1997. p. 145–8. [13] Baker H, editor. Alloy phase diagrams, vol. 3. Materials Park, OH, USA: ASM International; 1993. p. 173–5.
Gibbs–Thomson relationship for the precipitation in Cu–Ti alloys Felipe Hernandez-Santiago, Victor M. Lopez-Hirata ⁎, Maribel L. Saucedo-Muñoz, Hector J. Dorantes-Rosales Instituto Politecnico Nacional Apartado Postal 188-556 07051 Mexico, D.F. Received 1 December 2005; received in revised form 18 May 2006; accepted 19 May 2006
Abstract A diffusion-couple Cu/Cu–Ti alloy was prepared in order to obtain a macroscopic composition gradient in the Cu–Ti alloy system. This couple was solution treated subsequently water quenched and aged at 837 K for 600 s. The precipitation process was analyzed with an EDS-TEM. The Gibbs–Thomson relation was used to analyze the precipitation of the metastable and semicoherent β′ phase in Cu–Ti alloys and this relationship enabled us to estimate the interfacial free energy between matrix and precipitates to be about 0.31 ± 0.02 J m− 2. © 2006 Elsevier Inc. All rights reserved. Keywords: Cu–Ti alloys; Precipitation; Macroscopic composition gradient method; Gibbs–Thomson relation
1. Introduction Cu–Ti alloys are susceptible to age-hardening. Besides, this type of alloys has shown to be a possible substitute for expensive and toxic age-hardenable Cu– Be alloys. Cu–Ti alloy have been also considered to be ultra-high strength conductive materials for applications such as conductive springs, interconnections, etc. [1]. The precipitation process and strengthening in Cu–Ti alloys have been a subject of continuous studying [1–7]. The phase decomposition in the early stage of aging has been shown to take place via the mechanism of spinodal decomposition [2]. Additionally, it has been reported [3–5] that an ordering reaction occurs to form metastable β′(Cu4Ti) precipitates, which contributes significantly to the maximum strengthening of Cu–Ti ⁎ Corresponding author. Tel.: +52 55 57548249; fax: +52 55 51191986. E-mail address: [email protected] (V.M. Lopez-Hirata). 1044-5803/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.matchar.2006.05.008
alloys. Prolonged aging or aging at high temperatures promoted the cellular or discontinuous precipitation with the formation of equilibrium β (Cu3Ti) precipitates [5–7]. A new experimental method was proposed by Miyazaki et al. [8,9] to study the precipitation process in binary alloys called macroscopic composition gradient method. This method enables to determine solubility limits and phase equilibria and it is based on the microstructural observation of different composition alloys formed by a continuous composition gradient. The macroscopic composition gradient can be created in a specimen by diffusion coupling, imperfect arc melting of sandwiched metals, imperfect homogenization of coarse precipitates, etc. The purpose of this work is to analyze the precipitation process with the Gibbs–Thomson relation in Cu–Ti alloys formed by the macroscopic composition gradient method using a diffusion couple between pure Cu and a Cu–4 at.% Ti alloy, after aging at 873 K.
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F. Hernandez-Santiago et al. / Materials Characterization 58 (2007) 303–306
2. Experimental procedure A Cu–4 wt.% Ti was produced by melting of 99.99% purity titanium and 99.999% purity copper in an alumina crucible under an argon gas atmosphere. The ingot was homogenized at 1223 K for 864 ks and then cold rolled to obtain specimens of 30× 10× 5 mm. The diffusion couple consisting of two specimens, Cu–4 wt.% Ti and pure Cu, with polished flat surfaces was placed in an austenitic stainless steel holder with screws. Specimens were pressed by the screw and diffusion welded by heating at 1173 K for 86.4 ks under an argon atmosphere. The diffusion-couple was sealed in an evacuated quartz tube and annealed at 1173 K for 777.6 ks in an electrical resistance furnace, controlled within ±2 K and subsequently quenched in icewater in order to obtain a solution treated specimen. After this heat treating procedure, specimens were aged at 873 K many times from 600 to 3600 s. The bulk heat treated diffusion-couples were cut and ground to cylinders with diameters of about 3 mm so that the interface could be included in the middle along the cylinder axis. Discs with about 0.15 mm were obtained by electroerosion of cylinders. These discs were thinned using the twin-jet electropolishing technique in a solution of 75 vol.% methanol and 25 vol.% nitric acid at 213 K. TEM specimens were mounted on a Bespecimen holder and observed with a TEM JEM2000FX-II at 200 kV, equipped with a Noran EDXS. 3. Results and discussion Fig. 1 illustrates a concentration profile determined on the surface of diffusion-couple after aging at 873 K
for 600 s. Several BF-TEM micrographs corresponding to different compositions are also shown in this figure. These micrographs indicate the precipitation evolution for different titanium compositions at the same aging condition. Three different zones can be noticed in the concentration profile. Precipitates were mainly cuboids in the case of compositions higher than 1.5 at.% Ti. These cuboids were aligned in the elastically softest 〈100〉 crystallographic direction of the Cu-rich matrix. The analysis of the corresponding electron diffraction pattern indicates that the precipitates correspond to the metastable β′ (Cu4Ti) phase. The dark and bright contrast of precipitates is due to the coherency strains and this suggests that the β′ precipitates are coherent with the matrix. The β′ precipitates show an elongated plate shape in the 〈100〉 direction of the matrix for the compositions about between 1.5 and 1.0 at.% Ti. The interface between matrix and precipitates seems to be semicoherent because it can be observed the coherency-strains in the longest side of plates. The details of morphology for these precipitates can be observed more clearly in Fig. 2. It can be noticed that these precipitates were elongated in the 〈100〉 direction of the Cu-rich matrix. In the case of titanium compositions lower than 1 at. %, the precipitates have an ellipsoidal shape showing no preferential orientation with the matrix. Besides, almost no contrast due to the coherency-strain can be seen, which suggests that the interface between precipitates and matrix seems to be incoherent. It is important to notice that the volume fraction of precipitates decreases with the decrease in titanium content, as expected according to the lever rule.
Fig. 1. Concentration profile of the diffusion-couple, after aging at 873 K for 600 s and BF-TEM micrographs corresponding to some compositions.
F. Hernandez-Santiago et al. / Materials Characterization 58 (2007) 303–306
305
Fig. 2. BF-TEM micrographs of semicoherent β′ precipitates in Cu–Ti alloys.
Fig. 3 shows the plot of the equilibrium matrix composition Ce(r) as a function of the reciprocal value of the mean radius r of precipitates for the semicoherent precipitates in Cu–Ti alloys. There is a linear relationship, with an adjusted contribution ratio R2 of about
0.96116, between these two parameters. The empirical Ce(r) of the matrix phase seems to be inversely proportional to the particle radius r. In the limiting case of binary two-phase alloy with almost pure A, Cα→0, and pure B, Cβ→1, the Gibbs–
Fig. 3. Gibbs–Thomson relationship for the semicoherent β′ precipitates in Cu–Ti alloys.
306
F. Hernandez-Santiago et al. / Materials Characterization 58 (2007) 303–306
Thomson equation predicts a variation of Ce(r) with r as follows [10]: Ce ðrÞ ¼ CðlÞdexp½1 þ ð2gVm =rRT Þ
ð1Þ
where γ is the interfacial energy between precipitates and matrix, Vm the molar volume of precipitate, R the gas constant, T the temperature and C(∞) the equilibrium composition at the precipitate with the infinite size. If the radius is larger than a few nanometers, Eq. (1) reduces to the more commonly quoted form of the Gibbs–Thomson equation: Ce ðrÞ ¼ CðlÞ½1 þ ð2gVm =rRT Þ
ð2Þ
If the two phases are not limiting solid solutions, one way that this effect can be introduced into the Gibbs– Thomson equation while retaining the form given in Eq. (2) is to define the molar volume, Vm, as the volume occupied by the Avogadro's number of solute atoms. Then, in a precipitate of atomic composition, AnB, Vm will be increased from the typical metallic value of 10− 5 m3 mol− 1 to about (n + 1) × 10− 5 m3 mol− 1. Ardell [11] used this form of the Gibbs–Thomson equation in the analysis of Ni–Ni3Al system. This analysis method was also employed in this work. Considering a Vm value of about 7.11 × 10− 6 m3 mol− 1 for the β′ precipitates, the interfacial energy γ can be determined using the slope value of the straight line shown in Fig. 3. The interfacial energy γ was determined to be about 0.31 ± 0.02 J m− 2, which is in good agreement with the reported values for semicoherent interfaces, γ > 0.25 J m− 2 [12]. Miyazaki et al. [9] reported an interfacial energy for the interface between the Cu-rich matrix and coherent β′ precipitates to be about 0.21 J m− 2. The equilibrium composition at the precipitate with the infinite size, C(∞), is about 1.054 ± 0.02 at.% Ti, which is close to the equilibrium value of about 1 at.% Ti at 873 K in the equilibrium phase diagram [13]. 4. Conclusions The macroscopic composition gradient method permitted to analyze the precipitation process in Cu–Ti
alloys. The precipitation process followed the Gibbs– Thomson relationship for the precipitation of the metastable and semicoherent (Cu4Ti) β′ phase. The interfacial energy between the Cu-rich matrix and β′ precipitates was determined to be about 0.31 ± 0.02 J m− 2. Acknowledgements The authors wish to thank the financial support from CGPI-COFAA-IPN and Fondo Sectorial para la Educacion-CONACYT 47151-Y. References [1] Soffa WA, Laughlin DE. High-strength age hardening copper– titanium alloys: redivivus. Prog Mater Sci 2004;49:347–66. [2] Laughlin DE, Cahn JW. Spinodal decomposition in age hardening copper–titanium alloys. Acta Metall 1975;23:329–39. [3] Datta A, Soffa WA. The structure and properties of age hardened Cu–Ti alloys. Acta Metall 1976;24:987–1001. [4] Dutkiewwicz J. Electron microscopy study of the effect of deformation on precipitation and recrystallization in copper– titanium alloys. Metall Trans 1977;8A:751–61. [5] Nagarjuna S, Balasubramanian K, Sarma DS. Effect of prior cold work on mechanical properties and structure of an aged-hardened Cu–1.5 wt% Ti alloy. J Mater Sci 1997;32:3375–85. [6] Nagarjuna S, Balasubramanian K, Sarma DS. Effect of cold work on precipitation hardening of Cu–4.5 mass% Ti alloy. Mater Trans JIM 1995;36:1058–66. [7] Hameda AA, Blaz L. Microstructure of hot-deformed Cu– 3.45 wt.% Ti alloy. Mater Sci Eng 1998;254A:83–9. [8] Miyazaki T, Koyama T, Kobayashi S. A new characterization method of the microstructure using the macroscopic composition gradient in alloys. Metall Mater Trans 1996;27A:945–9. [9] Miyazaki T, Kobayashi S, Koyama T. Determination of the critical nucleus size of precipitates using the macroscopic composition gradient. Metall Mater Trans 1999;30A:2783–9. [10] Martin JW, Doherty RD, Cantor B. Stability of microstructures in metallic systems. New York USA: Cambridge University Press; 1997. p. 243–8. [11] Ardell AJ. Observations of the effect of volume fraction on the coarsening of γ′ precipitates in binary Ni–Al alloys. Scr Metall Mater 1990;24:343–6. [12] Porter DA, Easterling KE. Phase transformations in metals and alloys. London, UK: Chapman and Hall; 1997. p. 145–8. [13] Baker H, editor. Alloy phase diagrams, vol. 3. Materials Park, OH, USA: ASM International; 1993. p. 173–5.