Analysis of β´(Cu4Ti) Precipitation During Isothermal Aging of a Cu-4wt.%Ti Alloy

This work analyzed experimentally and numerically the growth kinetics of β′ precipitation of a Cu–4 wt%Ti alloy after aging at 400, 500, and 600 °C for times from 0.0166 to 200 h. Results indicated that the precipitation process is almost controlled by nucleation and growth during aging at 400 °C, originating a slow growth kinetics of precipitation. In contrast, the coarsening of precipitates dominates the precipitation process during aging at 500 and 600 °C. The interfacial energy of interface between the α matrix phase and β′ precipitates was determined to be about 0.1135, 0.0980, and 0.0725 Jm−2 for aging at 400, 500, and 600 °C, respectively. These values suggest a coherent interface, which is in agreement with the flat faces of β′ cuboid precipitates. Calculated Time–Temperature–Precipitation diagram for the β′ precipitation indicated good agreement with experimental results. Precipitation hardening was higher for the slower growth kinetics of precipitation.


Introduction
Cu-Ti alloys are prone to have precipitation hardening after isothermal aging for alloy compositions of about 1-5wt.% Ti [1][2][3][4] . Age-hardenable Cu-Ti alloys have high tensile strength and good formability and they are used as connector materials in electronic and electrical components 5,6 ; nevertheless, its conductivity is less than the half of that corresponding to Cu-Be alloys. Therefore, the application of Cu-Ti alloys has been focused on mechanical properties. In order to obtain good mechanical properties, Cu-Ti alloys are solution treated above 800 ºC and then quenched and the aging process is carried out at temperatures of 400-500 ºC. As a result of aging, the fcc Cu-rich supersaturated solid solution decomposes spinodally to form a disordered fcc Ti-rich phase and then become order to form the metastable tetragonal β´Cu 4 Ti phase which is responsible for the good mechanical properties of these alloys 1,7,8 . After prolonged aging, the cellular precipitation of the stable orthorhombic β Cu 4 Ti phase takes place by nucleation and growth on grain boundaries which is the main cause for the decrease in the mechanical strength in the later stage of aging 1 . The mechanical strength of Cu-Ti alloys has been improved either by the addition of a third alloying element such as Chromium, zirconium, carbon, nitrogen or hydrogen 9-11 or by using cold work previously to the aging treatment 12,13 . In the former case, the precipitation sequence was similar to that observed in the binary alloy; however, the presence of a different precipitates such as titanium chromide, nitride, carbide or hydride was also reported to occur during aging [9][10][11] . In the latter case, the cold work, used after solution treatment and quenching, has been reported 12,14 to promote the precipitation of titanium on dislocations and to inhibit the precipitation of the β´ Cu 4 Ti and β Cu 4 Ti phases during aging.
Recently, TC-PRISMA software has been used to analyze the precipitation process of different aged alloys 15 . This software is based on the solution of the Langer-Schwartz (LS) and modified LS (MLS) theories and the Kampmann and Wagner numerical model (N model) 16 , and it has been used to analyze the precipitation kinetics of different phases during aging in steels and nonferrous alloys [16][17][18] . This software permits, for example, to determine the size, distribution size, density number and composition of precipitated phases, as well as the Time-Temperature-Precipitation (TTP) diagram in multiparticles, multiphases and multicomponents alloy systems. Besides, the nucleation site can be selected among grain boundaries, bulk and dislocations. Thus, the use of Thermo-Calc PRISMA would be a good alternative to complement the precipitation analysis of β´phase in the aged Cu-Ti alloys.
Thus, the purpose of this work is to study experimental and numerically the growth kinetics of β´phase precipitation in an isothermally aged Cu-4wt. % Ti alloy in order to obtain the Time-Temperature-Precipitation (TTP) diagrams, as well as the determination of the interfacial energy between the α matrix and β´precipitates.

Experimental Method
A Cu-4wt.% Ti alloy was melted with an electric furnace using 99.99 % purity titanium and 99.999 % purity copper in an alumina crucible under an argon gas atmosphere. and subsequently cold rolled to obtain plate specimens of about 30 x 10 x 5 mm. These specimens were encapsulated in air-evacuated and Ar gas filled quartz tube and then solution treated at 900 ºC for 1 h in an electrical resistance furnace, and subsequently quenched in ice-water in order to obtain solution treated specimens. These specimen were aged at temperatures of 400, 500 and 600 ºC for times up to 200 h. The Transmission Electron Microscope (TEM) disc specimens of approximately 3 mm were thinned using the twin-jet electropolishing technique in a solution of 75 vol. % methanol and 25 vol. % nitric acid at -60 ºC. TEM specimens were mounted on a Be-specimen holder and observed with a TEM JEM-2000FX-II at 200 kV, equipped with a Noran EDXS. Vickers hardness test was determined in all the heat treated specimens using 10 determinations with 500 g and 12 s.

Numerical Method
Thermo-Calc software was used to analyze the stability of phases and the coarsening constant and interfacial energy γ between matrix and precipitates. Likewise, the analysis of precipitation was pursued in the aged Cu-4wt. % Ti alloy employing the Thermo-Calc (TC) PRISMA software. The kinetic and thermodynamic data was determined from the Thermo-Calc databases for CUDEMO and MCUDEMO 15 . A homogeneous nucleation was assumed for the precipitation simulation in the austenite matrix, named bulk nucleation in TC-PRISMA. The precipitate shape was considered to be cuboid considering a cube elastic-strain energy for the α phase matrix and precipitate with the following elastic constants: c 11 = 168.4 GPa, C 12 =121.4 GPa and c 44 =75.4 GPa.

a) Temporal Evolution of Precipitation
The temporal evolution of precipitation of β´ phase in the Cu-rich α phase matrix is illustrated in the Bright-Field (BF) Transmission Electron Micrographs corresponding to the Cu-4wt.%Ti alloy aged at 400, 500 and ºC for different times, as shown in Figs. 1-3, respectively. The β´ precipitates has a cuboid morphology and they are aligned on the <100> direction of the α phase matrix for all aging temperatures because of its low value of elastic-strain energy 7,19 . As aging progresses, the morphology changes to plates also aligned with respect to the matrix phase, Figs. 1(d), 2(d) and 3 (c). The electron diffraction pattern, shown in Fig. 1 (c), indicates clearly the presence of supereflections spots between those corresponding to the matrix phase which confirms that the β´phase has a Cu 4 Ti crystalline structure. Table 1 shows the average equivalent radius and its corresponding dispersion error determined for the β´precipitates after aging at 400, 500 and 600 ºC for different times. An increase in precipitate  radius can be noted with aging time and temperature. The discontinuous or cellular precipitation of the β´phase can be noted clearly for the alloy specimen aged at 600 ºC, Fig. 3 (d). This type of precipitation was also observed to be present after aging at 400, 500 and 600 ºC for 100, 0.5 and 0.166 h, respectively

b) Thermo-Calc analysis of precipitation
The Thermo-Calc calculated amount of all phases versus temperature is shown in Fig. 4. This plot indicates clearly that the α and β´phases are present at temperatures between 500 and 840 ºC. This figure also suggests that the precipitation reaction: (1) It may occur after aging at those temperatures. The volume fraction of β´precipitates increases with the decrease in temperature. Table 2 shows the Thermo-Calc calculated values of interfacial energy for the interface of α matrix and β´ precipitate. This value decreases with the increase in temperatures, as expected in the case of free energy due to the increase in entropy 16 . The magnitude order, 0.03 Jm -2 , suggests a coherent interface 20 . This table also indicates the values of coarsening constant k for 400, 500 and 600 ºC. Unsurprisingly, this parameter increases with temperature because of the increase in atomic diffusion 16 .

c) Thermo-Calc PRISMA analysis of precipitation
The experimental and calculated variation of equivalent radius for β´ precipitates with time are shown in Figs. 5 (a-c) for the Cu-4wt. % Ti alloy aged at 400, 500 and 600 ºC. The continuous line and triangle points correspond to the calculated and experimental values, respectively. The error bar of radius measurements is also shown in Figs. 5 (a-c) which indicates, in general, a good agreement between calculated and experimental values. This plot of shows clearly three characteristic stages: a continuous and slow increase in precipitate radius for short aging times, Fig. 5(a), because of the rise of nucleation rate with time. The number density   of precipitates also increases with aging time, as shown in Fig. 6(a). Then, the radius increases more rapidly after 1 h of aging time, following a parabolic law of t 1/2 which can be attributable to the growth stage. The nucleation rate subsequently becomes zero because either the solute sss " a a b + l supersaturation turns into zero or all nucleation sites are used 16,21 . As a result of this, the number density and the precipitate radius remain constant, as shown in Fig. 6(a-c) and 5 (a), respectively. As aging progresses, the number density starts decreasing with time, following a t -1 power law, and the growth kinetics of precipitate radius with time follows a slope of 1/3, t 1/3 . That is, the growth kinetics corresponds to the coarsening stage of precipitates and it follows the Lifshitz-Slyozov-Wagner theory for diffusioncontrolled theory 16 . According to the previously mentioned explanation, most of the experimental points for the growth kinetics of precipitates at 400 ºC are located in the nucleation and growth stage, while the experimental points at 500 and 600 ºC corresponds to the coarsening stage. It is important to mention that the interfacial free energy γ was changed in order to find the best fit of experimental values with the calculated curves. They are shown in Table 2 and decrease as aging temperature increases. These values are higher than the Thermo-Calc determined ones. The low values calculated by Thermo-Calc can be attributed to the fact that the calculation of interfacial energy uses thermodynamic data and assumes a complete coherent interface; however, the interfacial energy is also dependent on several factors such as crystallographic misorientation, elastic misfit strains, degree of coherency, and solute segregation 21 , which may cause higher energy values. These values between 0.07 and 0.11 Jm -2 show are in good agreement with the values of 0.1-0.2 Jm -2 reported for coherent β´ precipitates in the literature 7,17,22 , and it suggests that the interface between matrix and precipitates should be coherent 20 , which is in agreement with the cuboid morphology of β´ precipitates, as shown in Figs. 1-3. The TC-PRISMA calculated Time-Temperature-Precipitation TTP diagram of the Cu-4wt. % Ti alloy is shown in Fig. 7. This was calculated using an average value of 0.0946 Jm -2 determined from the experimental ones shown in Table 2. This figure shows that the fastest precipitation kinetics corresponds to an aging at about 500 ºC for 0.01 h. This figure also includes the TEM micrographs for the alloy specimens aged at 400 ºC for 5 h, and 500 and 600 ºC for 0.166 and 1 h. These TEM images suggests that the start of β´ precipitation is very similar for aging at 500 and 600 ºC which is in good agreement with the growth kinetics of precipitation shown in the calculated TTP diagram. Nevertheless, the growth kinetics of precipitation at 400 ºC is much faster than that detected experimentally, Fig. 1. This can be attributable to the constant value of interfacial energy, 0.0946 Jm -2 , used for the present calculation. That is, the energy value should be higher at 400 ºC which might cause a higher activation energy for nucleation and consequently the nucleation rate would be expected to be slower 20 than that of the TTP diagram. Figure 8 shows the aging curves, plot of hardness as a function of aging time, for the Cu-4wt. % Ti alloy aged at 400, 500 and 600 ºC. The aging curves corresponding to 500 and 600 ºC show an increase in hardness, then the hardness peak is reached and finally this decreases as a result of the discontinuous precipitation and coarsening process   of precipitates. In contrast, aging at 400 ºC presents a slow increase in hardness and the hardness peak, 370 VHN, is obtained after aging for 200 h, not shown in Fig. 8. The highest and lowest hardness peaks correspond to the alloy specimens aged at 400 ºC and 600 ºC. The hardness peaks of aging at 500 and 600 ºC were reached more rapidly than that at 400 ºC which agrees very well with the faster growth kinetics of precipitation, as shown in the calculated TTP diagram.

Conclusions
The numerical and experimental analysis of β´ precipitation during aging at 400, 500 and 600 ºC permitted to state the following conclusions: 1. The numerical analysis of precipitation indicated that the nucleation and growth stage is dominant during aging at 400 ºC, while the precipitation during aging at 500 and 600 ºC is mainly controlled by the coarsening stage.

The interfacial energy between matrix and precipitates
was determined to be about 0.1135, 0.0980 and 0.0725 Jm -2 for aging at 400, 500 and 600 ºC, respectively, which is agreement with the coherent interface of cuboid β´ precipitates. 3. Calculated TTP diagram showed a good concordance with the experimental results. The slowest growth kinetics at 400 ºC promoted the highest precipitation hardening, while the fastest kinetics causes the lowest hardness.

Miyazaki T. A New Evaluation Method of Phase Decomposition by Utilizing the Macroscopic Composition Gradient in Alloys.
In: Proceedings of the International Conference on Solid-Solid Phase Transformations ´99; 1999 May 24-28; Kyoto, Japan. p. 15-22.