Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles

Diffusion coefficients of alloying elements in Mg are critical for the development of new Mg alloys for lightweight applications. Here we present the data set of the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp) Mg calculated from first-principles calculations based on density functional theory (DFT) by combining transition state theory and an 8-frequency model. Benchmark for the DFT calculations and systematic comparison with experimental diffusion data are also presented. The data set refers to “Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study” by Zhou et al. [1].

The calculated diffusion data can be used to develop CALPHAD-type diffusion mobility databases for multi-component Mg alloys.
The solute diffusion data in Mg can be used as the input for the microstructure level simulations such as phase-field simulations and finite element modeling.

Computational methods
We used first-principles calculations based on DFT coupled with transition state theory and the 8frequency model to calculate the dilute solute tracer diffusion coefficients in hcp Mg. Forty-seven substitutional alloying elements have been considered herein, namely Ag, Al, As, Au, Be, Bi, Ca, Cd, Co, Cr, Cu, Fe, Ga, Ge, Hf, Hg, In, Ir, Li, Mn, Mo, Na, Nb, Ni, Os, Pb, Pd, Pt, Re, Rh, Ru, Sb, Sc, Se, Si, Sn, Sr, Ta, Tc, Te, Ti, Tl, V, W, Y, Zn, and Zr.
First-principles calculations based on DFT were employed to calculate the free energies needed in the diffusion equations and the 8-frequency model. The finite temperature vibrational contributions to the free energies were calculated using the quasi-harmonic approximations from phonon or Debye model. The ion-electron interaction was described by the projector augmented plane-wave (PAW) method [2] and the X-C functional was described by an improved GGA of PBEsol [3], as implemented in the VASP 5.3.2 code [4]. The PAW potentials (POTCAR files) used in the present work were released by VASP on April 19, 2012. The recommended core configurations by VASP were adopted for each element in the present work. Due to the magnetic nature of V, Cr, Mn, Fe, Co, and Ni, first-principles calculations containing these elements were performed with the spin polarization approach. An energy cut-off of 350 eV was used for the plane-wave expansion of the electronic wave functions. For the complete description of the diffusion theory used in the present work and more computational details, the reader can refer to the main article [1].

Supercell size convergence test
Solute-vacancy binding energies were calculated for Zn and Y in different supercell sizes of 36 (3 Â 3 Â 2 conventional hcp unit cells), 64 (4 Â 4 Â 2), 96 (4 Â 4 Â 3) and 150 (5 Â 5 Â 3) atoms in order to test the convergence of supercell size. ΔV X is the volume difference induced by placing a single solute into pure Mg, which is a quantitative measure of the atomic size of each solute. Zn and Y represent solutes with negative and positive ΔV X , respectively. From the test results as shown in Table 1, we can conclude that the supercell size of Zn converges at 64 atoms and the supercell size of Y converges at 96 atoms. Therefore, for elements with large ΔV X (Ba, Bi, Ca, K, Pb, Sr, and Y), 96-atom supercell was used. 64-atom supercell was adopted in calculations for all the rest of the elements.

K-point convergence test
An 8 Â 8 Â 9 Γ-centered k-point mesh was used for the 64-atom supercell for the electronic integration in the Brillouin zone. For calculations using 96-atom supercells, a 5 Â 5 Â 4 Γ-centered k-point mesh was used in structural relaxation and a 7 Â 7 Â 7 Γ-centered k-point mesh in subsequent static calculations. Fig. 1 shows the energy convergence test as a function of KPOINTS in VASP for both supercells used in the calculations.

Thermodynamic properties of pure hcp Mg
In order to validate the applicability of quasi-harmonic Debye model, thermodynamic properties (heat capacity Cp and entropy S) were predicted using both quasi-harmonic Debye and phonon model and were compared with experimental data, as shown in Fig. 2. Excellent agreement was achieved between computation and experiments.

Vacancy formation in pure hcp Mg
The thermodynamic properties of vacancy formation in pure hcp Mg were predicted using the quasi-harmonic Debye model and were compared with experimental data, as shown in Fig. 3.

Plots of the calculated diffusion coefficients compared with experiments
Figs. 4-13 show the plots of the calculated diffusion coefficients of solutes compared with available experimental data besides Al, Zn, and Sn shown in the main article [1].

Plots of the calculated diffusion coefficients with strong correlation effects
Figs. 14-18 show the plots of the calculated diffusion coefficients with strong correlation effects, i.e. diffusion coefficients of Na, Se, Sr, Te, and Y in Mg (Ca in Mg in the main article [1]).

Diffusion data file
All the diffusion plots shown in the present work were plotted using the calculated data directly from first-principles, not the fitted Arrhenius equation. The original calculated diffusion data sets and  other physical properties for each element can be found in the Excel worksheet file in the Supplementary data associated with this article.
In the diffusion data Excel worksheet file , there are the following six parts:              [13]. Note that f Ab and f Az almost overlap with each other.