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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.

We investigate the elastic and thermodynamic properties of nanolaminate V2AlC by using the ab initio pseudopotential total energy method. The axial compressibility shows that the c axis is always stiffer than a axis. The elastic constants revealed the structural instability at about 500 and 732 GPa. Furthermore, elastic constants C44 reached its maximum at about 550 GPa, differing with the other four C11, C12, C13 and C33 constants. The Poisson’s ratio investigations demonstrated that a higher ionic or weaker covalent contribution in intra-atomic bonding and the degree of ionicity increases with pressure. The G/B and B/C44 investigations revealed that V2AlC is brittle and the brittleness decreases with pressure. Also, we found that V2AlC is elastic anisotropic materials and the degree of anisotropy rapidly rises with pressure. Study on Debye temperature and Gruneisen parameter observed weak temperature and strong pressure responses, whereas the sensitive dependence in the thermal expansion coefficient and Helmholtz free energy are clearly seen.

The structural B1–B2 (B1 is the NaCl phase and B2 is the CsCl phase) phase transition of MgS and the elastic properties of the B1 and B2 phases of MgS are investigated by ab initio plane-wave pseudopotential density functional theory method. The dependences of the elastic constants c ij , the aggregate elastic modulus B S , G , and the Debye temperature Θ D on pressure are successfully discussed. From the usual condition of equal enthalpies, we find that the structure B1–B2 phase transition of MgS occurs at 255.5 GPa. Moreover, the dependences of the aggregate elastic modulus and the Debye temperature on the pressure P have been investigated for the first time.

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.

The systematical trends of the equation of state and electronic properties of Cr2GeC, (Cr0.5V0.5)2GeC and V2GeC have been extensively studied using ab initio pseudopotential density functional theory. A stiffer c-axis within the three nanolaminates has been observed and confirmed by the electronic structure investigations. The regular variations of B/C 44, σ, C 44, G, Y, C 11, C 12 have been revealed unambiguously for the first time with the three exceptions of C 33, C 13, and B only. The bonding nature, Poisson’s ratio, and brittleness-ductility relationships are also studied systematically.

The structural properties of Mo2Ga2C are simulated by first-principles under pressure. At 40 GPa, the axial compressibilities of [Formula: see text]- and [Formula: see text]-axes are 0.9763 and 0.9264, respectively, which are the known largest and smallest values in the [Formula: see text] compounds. A phase transition at 48 GPa is observed with an abrupt increase of [Formula: see text]-axis and a rapid decrease of [Formula: see text]-axis. The elastic properties and phonon imaginary frequencies confirmed the structural transition at 48 GPa, which probably should be the lowest-pressure transition in the [Formula: see text] ([Formula: see text], etc.) phases. The anti-expansion of Mo–Mo bond length is responsible for the [Formula: see text]-axis ultra-incompressibility as well as the structural transition at 48 GPa.

The elastic and structural properties of nanolaminate Zr2InC are studied by first-principles, and it is shown that, for any used modes, including the generalized gradient approximation (GGA) and localized density approximation, there always exists an ultraincompressibility along c axis between 70 GPa and 400 GPa. Such anomalous behavior is originated from the slowdown of core-valence charge transfer. The rapid shift of Zr atom along c axis also contributed much to the ultraincompressibility as it is greatly reduced once the Zr atom shift suspends along c axis above about 400 GPa. Both the elastic constants and the phononic vibrational frequencies investigations confirmed the structural unstable simultaneously. The Poisson's ratio investigations observed a higher ionic or weaker covalent contribution in interatomic bonding and the degree of ionicity increases with pressure.

Using Vanderbilt-type plane-wave ultrasoft pseudopotentials within the generalized gradient approximation (GGA) in the frame of density functional theory (DFT), we have investigated the crystal structures, elastic, and thermodynamic properties for Ti2SC under high temperature and high pressure. The calculated pressure dependence of the lattice volume is in excellent agreement with the experimental results. The calculated structural parameter of the Ti atom experienced a subtle increase with applied pressures and the increase suspended under higher pressures. The elastic constants calculations demonstrated that the crystal lattice is still stable up to 200 GPa. Investigations on the elastic properties show that the c axis is stiffer than the a axis, which is consistent with the larger longitudinal elastic constants (C33, C11) relative to transverse ones (C44, C12, C13). Study on Poisson's ratio confirmed that the higher ionic or weaker covalent contribution in intra-atomic bonding for Ti2SC should be assumed and the nature of ionic increased with pressure. The ratio (B/G) of bulk (B) and shear (G) moduli as well as B/C44 demonstrated the brittleness of Ti2SC at ambient conditions and the brittleness decreased with pressure. Moreover, the isothermal and adiabatic bulk moduli displayed opposite temperature dependence under different pressures. Again, we observed that the Debye temperature and Gruneisen parameter show weak temperature dependence relative to the thermal expansion coefficient, entropy, and heat capacity, from which the pressure effects are clearly seen.

We investigate the elastic and the thermodynamic properties of nanolaminate V2GeC by using the ab initio pseudopotential total energy method. The axial compressibility shows that the c axis is always stiffer than the a axis. The elastic constant calculations demonstrate that the structural stability is within 0–800 GPa. The calculations of Young's and shear moduli reveal the softening behaviour at about 300 GPa. The Possion ratio makes a higher ionic or a weaker covalent contribution to intra-atomic bonding and the degree of ionicity increases with pressure. The relationship between brittleness and ductility shows that V2GeC is brittle in ambient conditions and the brittleness decreases and ductility increases with pressure. Moveover, we find that V2GeC is largely isotropic in compression and in shear, and the degree of isotropy decreases with pressure. The Gruneisen parameter, the Debye temperature and the thermal expansion coefficient are also successfully obtained for the first time.

Orbital responses to methyl sites in CnH2n+2 (n = 1?6) are studied by B3LYP/TZVP based on the most stable geometries using the B3LYP/aug-cc-pVTZ method. Vertical ionization energies are produced using the SAOP/et-pVQZ model for the complete valence space. The highest occupied molecular orbital (HOMO) investigations indicate the p-electron profiles in methane, ethane, propane, and n-butane. By increasing the number of carbon?carbon bonds in lower momentum regions, the s, p-hybridized orbitals are built and display strong exchange and correlation interactions in lower momentum space (P ? 0.50 a.u.). Meanwhile, the relative intensities of the isomers in lower momentum space show the strong bonding number dependence of the carbon?carbon bonds, meaning that more electrons have contributed to orbital construction. The study of representative valence orbital momentum distribution further confirms that the structural changes lead to evident electronic rearrangement over the whole valence space. An analysis based on the isomers reveals that the valence orbitals are isomer-dependent and the valence ionization energy experiences an apparent shift in the inner valence space. However, such shifts are greatly reduced in the outer valence space. Meanwhile, the opposite energy shift trend is found in the intermediate valence space.

First-principles calculations of the crystal structures, phase transition, and elastic properties of B1-B2 phase calcium sulfide (CaS) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures and the phase transition) are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c(ij), the aggregate elastic modulus, the deviation from the Cauchy relation, and the elastic anisotropy on pressure have been investigated. The normalized elastic constants c(ij)' have been introduced to investigate the elasticity of CaS in detail. Moreover, the variation of the Poisson ratio, Debye temperature, and longitudinal and transverse elastic wave velocity with pressure P up to 70 GPa at 0 K have been investigated for the first time.