*Article* **First-Principles Investigation of the Diffusion of TM and the Nucleation and Growth of L12 Al3TM Particles in Al Alloys**

**Te Hu 1,2, Zixiong Ruan 3, Touwen Fan 1,3,\*, Kai Wang 4,\*, Kuanfang He <sup>4</sup> and Yuanzhi Wu <sup>3</sup>**


**Abstract:** The key parameters of growth and nucleation of Al3TM particles (TM = Sc-Zn, Y-Cd and Hf-Hg) have been calculated using the combination of the first principles calculations with the quasi-harmonic approximation (QHA). Herein, the diffusion rate *Ds* of TM elements in Al is calculated using the diffusion activation energy *Q*, and the results show that the *Ds* of all impurity atoms increases logarithmically with the increase in temperature. With the increase in atomic number of TM, the *Ds* of 3–5d TM elements decreases linearly from Sc, Y and Hf to Mn, Ru and Ir, and then increases to Zn, Ag and Au, respectively. The interface energy *γα/β*, strain energy Δ*Ecs*, chemical formation energy variation Δ*GV* and surface energy *Eave sur* were further computed from the based interface and slab models, respectively. It was found that, with the increase in the atomic number of TM, the interface energies *γα/<sup>β</sup>* of Al/Al3TM (TM = (Sc-Zn, Y-Cd)) decreased from Sc and Y to Mn and Tc and then increased to Zn and Cd, respectively (except for the (001) plane of Al/Al3(Fe-Co), the (111) plane of Al/Al3Pd and the (110) and (111) planes of Al/Al3Cd). The strain energies Δ*Ecs* of Al/Al3TM (TM = (Sc-Zn)) increased at first, and then decreased for all cycles. The chemical formation energy Δ*GV* of all Al3TM changed slightly in the temperature range of 0~1000 K, except that the Δ*GV* of Al3Sc, Al3Cu, Al3(Y-Zr), Al3Cd, Al3Hf and Al3Hg increased nonlinearly. With the increase in atomic number at both 300 and 600 K, the Δ*GV* of 3–5d TM elements increased from Sc, Y and Hf to Mn, Tc and Re at first, and then decreased to Co, Rh and Ir, respectively, and slightly changes at the end. With the increase in atomic number of TM, the variation trends of the surface energies of Al3TM intermetallic compounds present similar changes for all cycles, and the (111) surface always has the lowest values.

**Keywords:** DFT framework; nucleation and growth; diffusion behavior; L12 Al3TM
