Gibbs energy functions with the vacancy complexes in the Al-Cu binary system

The Gibbs energy functions of the phases in the Al-Cu binary system are taken from the CALPHAD-type thermodynamic assessment (Witusiewicz et al., 2004; Ansara et al., 1998) [1], [2], where the effect of the monovacancy (Va), divacancy (VaVa) and Va-solute atom pair are taken into account based on the formulation (Abe et al., In press). The divacancy is modeled as an associate, VaVa, in the FCC solid solution. The contributions from the Va-solute pair are included through the ternary excess Gibbs energy term. Using the Gibbs energy functions provided in this data article, the fractions of the monovacancies and divacancies, even in various metastable conditions, can be calculated. Since the Gibbs energy functions and phase descriptions are written in the TDB (Thermodynamic DataBase) format, one can use this file with various thermodynamic software packages, such as OpenCalphad [3] etc.


Specifications
Even in metastable states, such as higher vacancy fractions after heavy deformation or irradiation, it is possible to estimate the properties of the monovacancy and the vacancy complexes.

Data
This includes experimentally measured thermodynamic properties of vacancies (Section 2) and Gibbs energies of phase with vacancies for thermodynamic calculations on software packages [1,2,3] in the TDB format (Section 3). Thermodynamic models and descriptions [4] are briefly explained in Section 1.

Monovacancy
The monovacancy (Va) was introduced to a substitutional solution model as a non-preserved quantity [5], where the Gibbs energy of the monovacancy formation was described in the regular term, L ð0Þ A;Va ¼ f H Va A À f S Va A T À G Va m , and the Gibbs energy of the empty endmember, G Va m , was set þ 10RT to avoid an unwilling miscibility gap at very high temperatures. The vacancy formation entropy, f S Va A , and enthalpy, f H Va A , in the regular term were optimized so as to reproduce experimental data with reasonable accuracy.

Divacancy
The divacancy, which is defined as a pair of vacancies in the nearest neighbor distance, was treated as an associate, VaVa, using the associate solution model [3,[6][7][8] where the Gibbs energy of the divacancy formation in matrix A was described in the regular term, L ð0Þ A;VaVa , and the Gibbs energy of the empty associate, G VaVa m , was set þ 10RT. Using the binding entropy, S BindÀVaVa A , and enthalpy, H BindÀVaVa A , and monovacancy formation entropy and enthalpy defined above, the divacancy formation entropy and enthalpy in the FCC lattice can be given as f S Associate Table 1 Properties of vacancies in pure Al where symbols denote as Cp: specific heat, DD: differential dilatometry, PA: positron annihilation, RR: resistivity measurements, *: divacancy binding enthalpy, **: divacancy formation entropy, and ***: calculated value in this work.

Method
in the regular term, and were optimized so as to reproduce experimental data with reasonable accuracy.

Vacancy-solute atom pair
The effect of the vacancy-solute atom pair, which is defined as a pair of a monovacancy and a solute atom within the nearest neighbor distance, was considered using the ternary excess Gibbs energy term as 0 L A;B;Va ¼ 12H BÀVa_Bind A where H BÀVa_Bind A is the binding enthalpy between the monovacancy and a solute atom B in matrix A. This relation was obtained from the comparison between parameters in the Lomer model [9] where the binding energy is considered and in the substitutional solution model using the Redlich-Kister polynomial [10].

Pure Al
The properties of vacancies in Al in literature are summarized in Table 1. The calculated vacancy fractions in pure Al are presented in Fig. 1 with experimental data [13,14,16,21].

Pure Cu
The properties of vacancies in Cu in literature are summarized in Table 2. The calculated vacancy fractions in pure Cu are presented in Fig. 2 with experimental data [21,49,50,53,65].

Al-Cu FCC solid solution
The calculated vacancy fraction in an FCC solid solution in the Al-Cu binary system is presented in Ref. [4]. The properties of the vacancies in the FCC solid solution phase are listed in Table 3.  Table 4.

TDB file for the thermodynamic calculations
The TDB file for the FCC phase with vacancies are listed in Table 4 where the parameters of vacancies in Table 2 of Ref. [3] are written in the TDB format [80]. This TDB file can be used with various software packages [5]. The full TDB file for the Al-Cu binary system is given as a supplement.  Table 4.

Acknowledgements
This work was partly supported by Council for Science, Technology and Innovation (CSTI), Crossministerial Strategic Innovation Promotion Program (SIP), "Structural Materials for Innovation" (Funding agency: JST).

Transparency document. Supporting information
Transparency data associated with this article can be found in the online version at https://doi.org/ 10.1016/j.dib.2018.09.092.

Appendix A. Supporting information
Supplementary data associated with this article can be found in the online version at https://doi. org/10.1016/j.dib.2018.09.092. Table 4 The TDB file for the parameters listed in Table 2 of Ref. [3]. The full TDB file for the Al-Cu binary system is provided as a supplement.