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An interatomic potential for the Al–Tb alloy around the composition of Al90Tb10 is developed using the deep neural network (DNN) learning method. The atomic configurations and the corresponding total potential energies and forces on each atom obtained from ab initio molecular dynamics (AIMD) simulations are collected to train a DNN model to construct the interatomic potential for the Al–Tb alloy. We show that the obtained DNN model can well reproduce the energies and forces calculated by AIMD simulations. Molecular dynamics (MD) simulations using the DNN interatomic potential also accurately describe the structural properties of the Al90Tb10 liquid, such as partial pair correlation functions (PPCFs) and bond angle distributions, in comparison with the results from AIMD simulations. Furthermore, the developed DNN interatomic potential predicts the formation energies of the crystalline phases of the Al–Tb system with an accuracy comparable to ab initio calculations. The structure factors of the Al90Tb10 metallic liquid and glass obtained by MD simulations using the developed DNN interatomic potential are also in good agreement with the experimental X-ray diffraction data. The development of short-range order (SRO) in the Al90Tb10 liquid and the undercooled liquid is also analyzed and three dominant SROs, i.e., Al-centered distorted icosahedron (DISICO) and Tb-centered ‘3661’ and ‘15551’ clusters, respectively, are identified.

The elastic properties and structural evolution of (Ti0.5V0.5)n+1GeCn (n = 1–4) are studied under pressure from first principles. Many general evolution trends are concluded for the six structures, including the lattice parameters (a, c), elastic constants (cij) and the degree of the isotropy (A, A1, A2), and the axial shrinkage tendency. The (Ti0.5V0.5)2GeC behaves the largest compressive anisotropy in (c/a)/(c0/a0) but (Ti0.5V0.5)5GeC4 behaves opposite compressive anisotropy which shows a value below 1 between 0 and 40 GPa, whereas (Ti0.5V0.5)4GeC3 exists a softening behavior between 20 and 40 GPa. The lowest volume contraction of (Ti0.5V0.5)4GeC3 is confirmed by the density of states, together with the observation of its minimum c12 and c13 among the same type of compounds. The density of states analysis observed the smaller contribution of Ti at Fermi level with respect to that of V. A common phenomenon is observed from the six structures, namely, for any considered heavy atoms including Ti or V, once the heavy atom is surrounded by one C layer and one Ge layer, its density of states contribution at Fermi level is larger than that of atom surrounded by two C layers originating mainly from the electronegativity difference of C and Ge. The bond length of C/Ge Ti is always slightly longer than that of C/Ge V except for (Ti0.5V0.5)2GeC which shows totally equivalent length. A smaller shear modulus of (Ti0.5V0.5)2GeC is observed relative to its two end members. The electron density difference analysis reveals the diverse charge transfer directions and bonding features in these compounds.

The structural inheritance and difference between Ti2AlC, Ti3AlC2 and Ti5Al2C3 under pressure from first principles are studied. The results indicate that the lattice parameter a are almost the same within Ti2AlC, Ti3AlC2 and Ti5Al2C3, and the value of c in Ti5Al2C3 is the sum of Ti2AlC and Ti3AlC2 which is revealed by the covalently bonded chain in the electron density difference: Al–Ti–C–Ti–Al for Ti2AlC, Al–Ti2–C–Ti1–C–Ti2–Al for Ti3AlC2 and Al–Ti3–C2–Ti3–Al–Ti2–C1–Ti1–C1–Ti2–Al for Ti5Al2C3. The calculated axial compressibilities, volumetric shrinkage, elastic constant [Formula: see text], [Formula: see text] ratio, bulk modulus, shear modulus, and Young’s modulus of Ti5Al2C3 are within the range of the end members (Ti2AlC and Ti3AlC2) in a wide pressure range of 0–100 GPa. Only Ti2AlC is isotropic crystal at about 50 GPa within the Ti–Al–C compounds. All of the Ti 3d density of states curves of the three compounds move from lower energy to higher energy level with pressure increasing. The similarities of respective bond length, bond overlap population (Ti–C, Ti–Al and Ti–Ti), atom Mulliken charges under pressure as well as the electron density difference for the three compounds are discovered. Among the Ti–Al–C ternary compounds, Ti–Ti bond behaves least compressibility, whereas the Ti–Al bond is softer than that of Ti–C bonds, which can also been confirmed by the density of states and electron density difference. Bond overlap populations of Ti–Ti, Ti–C and Ti–Al indicate that the ionicity interaction becomes more and more stronger in the three structures as the pressure increasing. Mulliken charges of Ti1, Ti2, Ti3, C and Al are 0.65, 0.42, 0.39, −0.73, −0.04 at 0 GPa, respectively, which are consistent with the Pauling scale.