Thermodynamic description of the Cu–Ni–Si system in the copper-rich corner above 700 ∘C

A1-L12 interfacial free energies from data on coarsening in five binary Ni alloys, informed by thermodynamic phase diagram assessments

“…They measured concentration profiles across interfaces using atom-probe tomography at aging times of 1, 4, and 4096 h. The maximum absolute values of the concentration gradients of Al and Ni, dX Al =dy j j max and dX Ni =dy j j max in the notation used in Appendix 2, at 1 h of aging are a factor of 1.5 to 1.6 larger than those at 4096 h of aging. Assuming that these gradients are proportional to the average gradients, hdX Al /dyi and hdX Ni /dyi, respectively (see Appendix 2), d must increase as the interfacial concentration gradients Table 8 Calculated values of the interfacial free energy of the Ni(Si)/Ni 3 Si interface using the thermodynamic models of Du and Schuster [24] and Miettinen [32] Model The interfacial free energies calculated using the TIDC theory are approximately 2/3 those calculated using the LSW theory, with the exception of the Ni-Si system where the ratio is *3/4. The reason for the smaller difference in Ni-Si alloys is that the data on the 2 longest aging times in the results of Cho and Ardell [55] were omitted in the TIDC analysis but used in the LSW analysis.…”

“…The model of Tokunaga et al [26], which has been used to calculate r in Table 7, overestimates the b 1 (c 0 -type) solvus, though it provides a better fit than the models of Lindholm and Sundman [25] or Du and Schuster [24]. The model of Miettinen [32] actually provides the best fit to the b 1 solvus. If the values of G 00 m from any of these other models are used to calculate r from the data on Table 5 Rate constants j À1=n T and k T used in the calculations of r assuming validity of the TIDC theory.…”

“…Thermodynamic models of the Ni-rich solid solutions have been published for all five binary alloy systems: Ni-Al [19][20][21], Ni-Ga [22], Ni-Ge [23], Ni-Si [24][25][26], and Ni-Ti [27]. There are also thermodynamic models of ternary Ni-rich solid solutions involving Al, Ga, Ge, Si, and Ti that are helpful in selecting data on G m [28][29][30][31][32][33]. As discussed recently by Costa e Silva et al [34], the deviation from ideality can have a significant effect on the values of r derived from data on coarsening, invariably increasing them because G 00 m increases as the departure from ideal solution behavior increases.…”

“…The capillary length, ' T , is also shown coarsening, the results are much smaller in magnitude. The results of calculations of r using the thermodynamic models of Du and Schuster [24] and Miettinen [32] are shown in Table 8. It is evident that the values of G 00 m are much smaller than those obtained from the model of Tokunaga et al [26] (see Table 4), yielding values of r that are about 1/2 to 2/3 those shown in Fig.…”

Coarsening of δ-Ni2Si precipitates in a Cu–Ni–Si alloy

“…The values of L CuNi , L CuSi , L NiSi and L CuNiSi were calculated from the literature [24]. For the later stage of aging where the coarsening of the precipitates only is taking place, Table 4.…”