By extrapolating the mean grain size of nanocrystal to an infinitesimal value, an amorphous phase has been obtained from the Voronoi construction. The molecular dynamics simulations indicated that for nanocrystal, the grain size variation of melting temperature exhibits two characteristic regions. As mean grain size above about 4 nm for Ag, the melting temperatures decrease with decreasing grain size. However, with grain size further shrinking, the melting temperatures almost keep a constant. This is because the dominant factor on the melting temperature of nanocrystal shifts from grain phase to grain boundary. As a result of fundamental difference in structure, the amorphous phase has a much lower solid-to-liquid transformation temperature than that of nanocrystal.

The thermodynamic data, such as the formation enthalpies of disordered solid solutions and intermetallic compounds, and the lattice parameters in the RE–Au (RE = Sc, Y, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er) systems are calculated with the modified analytical embedded atom method (EAM). This work has been undertaken to investigate systemically in RE–Au alloying energies, and to augment available calorimetric data for enthalpies of formation in support of the development of accurate multicomponent thermodynamics databases for these technologically interesting systems. The accuracy of our calculations is assessed through comparisons with the experimental measurements and the theoretical results from the first-principles VASP as well as Miedema’s theory. The composition dependence of the heats of formation for these 10 binary systems is similar, and there is a minimum at 50 at.% Au for REAu (CsCl-type) ordered phase. In all 10 binary systems, the calculated zero-temperature intermetallic formation energies generally agree well with the calorimetric data obtained by the direct reaction synthesis and/or VASP results except for REAu2 (MoSi2type) phase. For the intermetallic phase, the calculated EAM and VASP zero-temperature lattice parameters agree well with the experimental data at ambient temperature. The largest discrepancy between the EAM calculated lattice parameters and experimental data [K. Fitzner,W.G. Jung, O.J. Kleppa, Metall. Trans. A 22 (1991) 1103 [16]; K. Fitzner, O.J. Kleppa, Metall. Trans. A 24 (1993) 1827 [17]; K. Fitzner, O.J. Kleppa, Metall. Trans. A 25 (1994) 1495 [18]; R. Ferro, G. Borzone, N. Parodi, J. Alloys. Compd. 321 (2001) 248 [19]] is approximately 10-18% for some intermediate phases, such as REAu (CrB-type) and RE3Au4 (Pu3Pd4-type).

Analytic modified embedded atom method (AMEAM) type many-body potentials have been constructed for ten hcp metals: Be, Co, Hf, Mg, Re, Ru, Sc, Ti, Y and Zr. The potentials are parametrized using analytic functions and fitted to the cohesive energy, unrelaxed vacancy formation energy, five independent second-order elastic constants and two equilibrium conditions. Hence, each of the constructed potentials represents a stable hexagonal close-packed lattice with a particular non-ideal c/a ratio. In order to treat the metals with negative Cauchy pressure, a modified term has been added to the total energy. For all the metals considered, the hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure and the hcp lattice with ideal c/a. The activation energy for vacancy diffusion in these metals has been calculated. They agree well with experimental data available and those calculated by other authors for both monovacancy and divacancy mechanisms and the most possible diffusion paths are predicted. Stacking fault and surface energy have also been calculated and their values are lower than typical experimental data. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the basal split or crowdion is the most stable configuration for metals with a rather large deviation from the ideal c/a value and the non-basal dumbbell (C or S) is the most stable configuration for metals with c/a near ideal. The relationship between SIA formation energy and melting temperature roughly obeys a linear relation for most metals except Ru and Re.

In the atomic scale, the melting behaviors of nanocrystalline Ag with mean grain size ranging from 3.03 to 12.12 nm have been investigated with molecular dynamics simulations, and a method to determine the melting temperatures of the infinite polycrystalline nanostructured materials is presented. It is found that the melting in nanostructured polycrystals starts from their grain boundaries, and the relative numbers of the three typical bonded pairs, (1551), (1431), and (1541), existing in the liquid phase, increase rapidly with the evolvement of melting. The melting temperatures of nanocrystalline Ag decrease with decreasing mean grain size, and it can be estimated from the size-dependent melting temperature of the corresponding nanoparticles.

Using the modified analytic embedded atom method and molecular dynamics, the binding energies and their second order finite differences stability functionsd of icosahedral Ni clusters with shell and subshell periodicity are studied in detail via atomic evolution. The results exhibit shell and sub shell structures of the clusters with atoms from 147 to 250 000, and the atomic numbers corresponding to shell or subshell structures are in good agreement with the experimental magic numbers obtained in time-of-flight mass spectra of threshold photoionization, and Martin’s theoretical proposition of progressive formation of atomic umbrellas. Clusters with size from 147 to 561 atoms are energetically investigated via one-by-one atomic evolution and their magic numbers are theoretically proved. For medium-size Ni clusters with 561 to 2057 atoms, the prediction of magic numbers with atomic numbers is performed on the basis of umbrellalike subshell growth in near face-edge-vertex order. The similarity of the energy curves makes it possible to extend the prediction to even larger Ni nanoclusters in hierarchical Mackay icosahedral configurations.