•A method for AFCR prediction of ternary system has been proposed.•The ΔG of Zr–Fe–Al has been calculated with the different grain sizes.•The results suggest that the alloys with higher Fe–Zr content have higher AFA.Mechanical alloying (MA), as one of the main methods of solid state amorphization (SSA), has been intensively used to prepare amorphous alloys. The composition of alloys and processing conditions of MA is very sensitive for the amorphous forming ability (AFA) or/and amorphous forming composition range (AFCR). During the MA processing, the powder was severely plastically deformed and broken into tiny grains with sub-micro or even nano scale size. In this work, a method for AFCR prediction of ternary system has been proposed based on a thermodynamic point of view and including the size-dependent grain boundary energy. The Gibbs free energy (ΔG) of Zr–Fe–Al system has been calculated with the different grain sizes. Compared with the experimental data, the present calculations are reasonable. The present calculations indicate that the smaller the grain size, the wider AFCR for Zr–Fe–Al system is. The present results also indicate that the higher Fe–Zr content alloys have higher AFA, and grain refinement benefits on extending the AFCR.

•The thermodynamic, electronic and lattice dynamic properties of CaX2Si2 have been investigated.•The CaZn2Si2 phase is dynamically instable at the ground state.•The electronic structure of CaX2Si2 shows a strong covalent character of the Si–Si bond.The thermophysical and electronic properties as well as the lattice dynamics of ThCr2Si2-type CaX2Si2 (X = Ni, Zn, Cu, Ag, Au) are investigated by using first-principles calculations based on the density functional theory (DFT). The lattice constants and formation enthalpies of CaX2Si2 are elaborately calculated. All of calculated results are in good agreement with the experimental data. The mechanical properties, including single crystal elastic constants, polycrystalline elastic moduli and orientation dependence of Young’s moduli and shear moduli of CaX2Si2, and electronic properties such as the electronic density of states (DOS) and charge density distribution of CaX2Si2 are predicted in this work. The calculated charge density indicates the presence of covalent bonding between Si–Si atoms in CaX2Si2 compounds. The calculations of phonon spectrum and phonon density of states for CaX2Si2 are also completed. The imaginary frequency of CaZn2Si2 in the vicinity of Γ point indicates that the CaZn2Si2 phase is dynamically instable at the ground state. Based on the phonon spectrum calculation, the predictions of heat capacity and entropy for CaX2Si2 are accomplished with quasi-harmonic approximation.

A method based on the semi-empirical Miedema model and a geometrical model was used to study the glass forming abilities (GFA) and the amorphous forming ranges of Al-Fe-Nd-Zr system and its constituent ternary systems. The amorphous forming composition ranges were analyzed based on different criteria such as ΔGam-ss and PHSS (PHSS=ΔHchem (ΔSC/R)(ΔSs/R)) for Al-Fe-Nd system. The predicted amorphous forming range was in good agreement with the experimental results. The results showed that the criterion of ΔGam-ss was more accurate, and agreed well with the experiment results. The Gibbs free energy difference ΔGam-ss and parameter PHSS were then used to predict the amorphous forming composition range for the rest of the constitutive ternary systems of Al-Fe-Nd-Zr. In addition, the amorphous forming composition ranges of the (Al-Fe-Zr)100-xNdx (x=50, 60, 70) systems were predicted by ΔGam-ss and the modified parameter PHSS. The Gibbs free energy of Al10(Fe1−xZrx)30Nd60 were also calculated. The GFA parameter PHSS indicated that the composition with the highest GFA was Al33.5Fe13.5Zr3Nd50 for the (Al-Fe-Zr)50Nd50 system, Al28.8Fe10Zr1.2Nd60 for the (Al-Fe-Zr)40Nd60 system and Al22.8Fe6.9Zr0.3Nd70 for the (Al-Fe-Zr)30Nd70 system, and the results suggested that those alloys with high content of Al had higher GFA. The appropriate content of neodymium and zirconium resulted in the lower value of PHSS and increased the GFA obviously.Amorphous forming ranges obtained by different methods for Al-Fe-Nd (The isometric contours indicate the calculated results of PHSS (kJ/mol), the contour maps indicate the results of ΔGam-ss (kJ/mol))

The equilibrium geometries, relative stabilities, both vertical and adiabatic of ionization potentials and electron affinities as well electronic properties of Aln and Aln−1Mg (n = 2–17) clusters have been systematically investigated by using B3LYP/6-311G(d). In general, the ground state structures of Aln−1Mg clusters have similar geometries as the host Aln clusters, except for Al4Mg. Starting from n = 7, the Mg atom prefers to stay away from the center of Aln clusters and locate on the site of the corresponding Aln clusters surface. The dissociation energy of the Aln−1Mg clusters dissociate into Aln−1 clusters with one Mg atom are lower than those dissociate into Aln−2Mg clusters with one Al atom, which suggests that the Aln−1Mg clusters are likely to break into Aln−1 clusters with one Mg atom. The results of AEA and VEA, AIP and VIP and second-order difference energy indicate that the Aln−1Mg (n = 3, 5, 7, 9, 11, 13, 15, and 17) clusters are more stable than others, which reveals that the chemical activity of Aln−1Mg clusters are diminished. The electronic structure has been discussed and the results of natural charge population analysis shows that there is a charge transfer from 3s states of Mg atom to 3p states of Al atoms resulting in the strong s-p hybridization.Graphical abstractThe deformation map of electron density of Al6Mg cluster.Highlights► Aln−1Mg cluster have been investigated firstly at B3LYP/6-311G(d) level. ► The charge transfer from 3s of Mg to 3p states of Al and lead to s-p hybridization. ► The Mg atom prefers to stay away from the center of Aln−1Mg clusters from n = 7.

The mechanical, electronic and thermodynamic properties of Al12X (X = Mo, W, Re) compounds are investigated by means of density functional theory (DFT) based calculations. The calculated lattice constants of the compounds are in good agreement with the experimental data. Compared with the other theoretical data, the calculated formation enthalpy of Al12Mo is very accurate. The elastic constants of the three compounds have been calculated, and the bulk modulus, shear modulus, and Young’s modulus have been evaluated. The calculated results indicated that all three compounds show brittle behavior. The electronic density of states (DOS) and the bonding charge density have also been calculated to elucidate the bonding mechanism in these compounds and the results indicate that bonding characteristic is mostly of covalent nature. Finally, using a quasiharmonic Debye model, the Debye temperature, the heat capacity, the coefficient of thermal expansion and the Grüneisen parameter have also been obtained in the present work. The present calculations show that the Al12X (Mo, W and Re) intermetallics can enhance mechanical properties of the Al-matrix dramatically.Highlights► The mechanical properties of Al12X (X = Mo, W and Re) have been studied. ► The bonding characteristic of Al12X (X = Mo, W and Re) is mostly of covalent nature. ► The Al12X (X = Mo, W and Re) phases can be used to enhance the Al-matrix.

The comprehensive investigation to cohesive properties of 344 intermetallic compounds in 17 Mg–RE (RE = Sc, Y, and Lanthanide elements) binary system has been carried out systematically in the framework of density-functional theory (DFT) type first-principles with the generalized gradient approximation (GGA). The calculated properties at present work; including total energy, enthalpy of formation, equilibrium volume, bulk modulus, and electronic structure, was consistent with the experimental data. It was convinced that both D03-Mg3RE and B2-MgRE were stable compounds in Mg–RE systems except Mg3Eu, Mg3Yb and Mg3Lu in Mg3RE series and MgYb for B2-MgRE branch extracting from calculated results.

We present a study of the energetics, elastic properties and electronic structures of the Laves C15-Mg2RE (RE = La, Ce, Pr, Nd, Pm, Sm, and Gd) through density functional theory (DFT). The calculated lattice constants are in good agreement with available experimental data and previously theoretical predictions. The formation enthalpies, elastic constants, bulk moduli, and pressure derivatives of the C15-type Mg2RE are predicted. Young’s moduli, shear moduli, and anisotropic ratios of the C15-type Mg2RE are further estimated from the calculated single-crystal elastic constants. The present results indicate that the Young’s modulus and anisotropic ratio of C15-Mg2RE are all less than those of B2-MgRE and D03-Mg3RE. The electronic densities of states and bonding charge densities have been discussed in details. The characteristic of mechanical properties has been explained from the point view of electronic structure. The present calculation indicates that C15-Mg2RE might be more ductile than B2-MgRE and D03-Mg3RE.

The ground states of the 3d-metal aluminides AlSc, AlTi, AlV, AlCr, AlMn, AlFe, AlCo, AlNi, AlCu and AlZn along with their singly negatively and positively charged ions are assigned based on the results of calculations employing B3LYP density functional method. Bond lengths re, harmonic vibrational frequencies ωe, dissociation energies D0, electron affinities EA, ionization energies IE and dipole moments μ of these species are obtained. The calculated spectroscopic constants (re, ωe and D0) and ionization energies are in good agreement with the available experimental and other theoretical data except for the dissociation energies of AlCr and AlCr−. The ground state spin multiplicities of all the ions are found to differ from the spin multiplicities of the corresponding neutral parents by one. The dissociation energy of channel AlX+ → X + Al+ is lower than that of channel AlX+ → Al + X+. As for AlX−, channel AlX− → X + Al− is preferred for X = Sc, Ti, V, Cr, Mn and Zn, and channel AlX− → Al + X− is favor for X = Fe, Co, Ni and Cu. The ionization energy increases monotonically from AlSc to AlCu, while the electron affinity varies erratically across the transition metal series. The bonding patterns are also discussed.

The crystallization behavior and thermal stability of Al82Fe5Ni5Ce8 amorphous alloy, obtained by mechanical alloying, were investigated by using X-ray diffraction (XRD), differential thermal analyzer (DTA) at constant heating rate. One exothermic peak was observed from the continuous heating DTA curves, implying the crystallization process undergoes only one stage. The product phases of crystallization are intermetallic compounds Al11Ce3 and Al3(Fe, Ni). The crystallization kinetic parameters, including activation energy (Ea), Avrami exponent (n) were determined with isothermal and isochronal analysis method based on the DTA data. The results suggest that the crystallization mechanism is governed dominantly by a three-dimensional diffusion-controlled growth.

Ab initio calculations for the total energy and elastic properties of the C15-type Al2RE (RE = Sc, Y, Lanthanide) at T = 0 K have been performed by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). The lattice constants, formation enthalpies, elastic constants, bulk modulus and its pressure derivatives of the C15-type Al2RE are obtained. Poisson’s ratios, Young’s modulus, shear modulus and the ratios of elastic anisotropy are also estimated in the present work. By using the Debye–Grüneisen model, the Debye temperatures, Grüneisen constants and the coefficients of thermal expansion at T = 300 K are obtained for the C15-type Al2RE. The present calculated results are in good agreement with reported experimental values and with other theoretical calculations available as well.

The electronic structure, the total energy and elastic properties of the Mn3AlN with anti-peroviskite structure have been calculated at T = 0 K by using the projector augmented-wave (PAW) method within LDA and GGA. The lattice constants, elastic constants, bulk modulus and its pressure derivatives of Mn3AlN are obtained. The Gibbs energies of different magnetic states are estimated by using quasi-harmonic Debye–Grüneisen model. The changes of volume resulted from the magnetic transformation are discussed according to the present calculations. The transformation from ferromagnetic to paramagnetic phase for Mn3AlN happens at 250 K.

Amorphous Al65Fe20Zr15 alloy has been prepared by mechanical alloying. The as-milled powders were analyzed by XRD and DTA. The fully amorphous alloy was identified by the hallo rings of XRD pattern. The effective activation energy of crystallization was estimated with modified Kissinger’s plot and it is 321.0 kJ/mol evaluated from the peak temperature of crystallization. The product phases of crystallization composed of Al3Zr, Al82Fe18, AlFeZr and an unidentified phase. The crystallization kinetics was also discussed by using the isochronal DTA scans and the values of corresponding kinetic parameters were determined.

The elastic properties of B2-MgRE (RE=Sc, Y, La–Lu) intermetallic compounds have been calculated at T=0K by using first principles within the generalized gradient approximation (GGA). The calculated equilibrium lattice constants and bulk modulus are in agreement with the available experimental values. And the polycrystalline shear moduli, Young’s moduli, the ratio of bulk to shear modulus B/G are also estimated to insight the brittle/ductile behaviors of the B2-MgRE. The calculated results indicated that MgEu is the most brittle, and MgEr is the most ductile among the B2-MgRE alloys. The calculated polycrystalline shear modulus and Young’s modulus shown that the RE additions can improve the elastic properties of B2-MgRE compounds. The density of states and charge densities distribution of the B2-MgRE under deformation are calculated. The characteristic of elastic constants of B2-MgRE are explained by the insight of electronic structures under deformation.

The ground states of alkali-Al dimers (AlLi, AlNa, AlK, AlRb and AlCs) and alkaline earth-Al dimers (AlBe, AlMg, AlCa, AlSr and AlBa) along with their monovalent anions and cations were assigned based on the results of calculations. Bond lengths re, harmonic vibrational frequencies ωe and dissociation energies D0 of these species were obtained. For neutral dimers, we also calculated adiabatic electron affinities (EA) and adiabatic ionization energies (IE). The present results are in agreement with the available experimental and other theoretical data. The ground state symmetry of AlLi, AlNa, AlK, AlRb and AlCs is 1 Σ+. The ground state symmetry of AlBe+, AlMg+, AlCa+, AlSr+ and AlBa+ is also 1Σ+. The ground state of AlLi−, AlNa−, AlK−, AlRb− and AlCs− is 2Π, and is the same as in the isoelectronic neutral Al-alkaline-earth dimers. For both the alkali-Al and alkaline earth-Al neutral AlX species, the bond length increases monotonously with increasing atomic number of X. For the alkali-Al ions, energies of dissociation via the channels AlX− → Al + X− and AlX+ → Al + X+ are smaller than the energies of dissociation via the channel AlX− → X + Al− andAlX+ → X + Al+, respectively. While the opposite dissociation manner is found for alkaline earth-Al anions.

A method to estimate the thermodynamic properties of ternary alloys from those of constitutive binary alloys was proposed. The thermodynamic data of binaries were calculated by Miedema's theory. The asymmetry of constitutive binary alloys in the ternary system was considered in the present extrapolating procedure. The dependence of asymmetric constituent on the choice in Toop's model was overcome. The present method was used to calculate the formation enthalpies of Fe–Ni–V alloys. The agreement between the calculation and experiment is reasonable. So the formation enthalpies of Fe–Al–RE (RE = lanthanide metal) ternary alloys were calculated with the present method. The relative stability of RE(Fe1−xAlx)13, RE2(Fe1−xAlx)17 and RE5(Fe1−xAlx)17 were also studied with the present method.

Nano-amorphous (FeAl)1−xZrx (x = 20, 33.3) alloys have been prepared by mechanical alloying. The microstructure, morphology and thermal stability of as-milled powders were analyzed by XRD, TEM and DTA, respectively. The size of milled powders was smaller than 50 nm. The thermal stability of as-milled powders decreased with increment of Zr. The products of crystallization for milled powders annealed at temperature over the crystallization temperature were also investigated. The effective activation energies for crystallization are evaluated according Kissinger's plot. The composition range of amorphous (FeAl)1−xZrx was predicted from Miedema's theory and a geometric model.