Tight-binding Second Moment Approximation Research Articles

Theoretical Modelling of Equations of States for Aluminum to Pressure up to 10 TPa and Temperature to 10 eV

Response of materials to extreme temperature (T) and/or Pressure (P) conditions can be studied through, e.g., equations of states (EOS), which link between macroscopic observations to the microscopic consequences. Accurate knowledge of EOS is therefore always desirable, and plethora of different forms of EOS is proposed in literature. Of which, the most frequently used Mie-Grüneisen EOS coupled either with Debye-Model or Einstein-model within the quasiharmonic approximation requires prior knowledge of Grüneisen parameter (γ), characteristic temperature (θ) and their volume variation. At the pair-potential level, the Einstein characteristic temperature (θE) is derived through second-order potential derivatives. Although, many potential-energy-functional (PEF) are proposed for metallic systems, all including many-body effects, however, in order to compute θE effective pair-potential has to be deduced from PEF. But this procedure relies on some unavoidable approximations and fitting procedure. In this context, we have used energy-functional based definition of effective θE and for its volume dependence. We have employed tight-binding second-moment approximation (TB-SMA) to deduce cold energy curve to deduce θE and γ. Further, anharmonicity associated in bonding is parameterized; and it is shown that the parameter describing it is related to the thermodynamic Grüneisen parameter. Thus, the present scheme also circumvents additional empirical relation for γ (V). The present proposal is then employed to deduce equations of states and related thermo-physical properties; taking aluminum as a prototype. Results so generated to pressures more than 10 TPa and temperatures as high as 110 kK are compared and discussed in light of other simulated and experimental findings.

Modification of Pt/Co/Pt film properties by ion irradiation

We studied the structural modifications of a Pt/Co/Pt trilayer epitaxial film under ${\mathrm{Ga}}^{+}$ 30-keV ion irradiation by means of classical molecular dynamics and Monte Carlo simulations. The semiclassical tight-binding second-moment approximation potential was adjusted to reproduce the enthalpies of formation, the lattice constants, and the order-disorder transition temperatures for Co-Pt alloys. We found that during irradiation, the sandwich-type Pt(fcc)/Co(hcp)/Pt(fcc) film structure underwent a transition to the new solid solution $\ensuremath{\alpha}\ensuremath{-}\mathrm{Co}/\mathrm{Pt}(\mathrm{fcc})$ phase. Our analysis of the short-range order indicates the formation, within a nanosecond time scale, of a homogeneous chemically disordered solution. The longer time-scale simulations employing a Monte Carlo algorithm demonstrated that the transition from the disordered phase to the ordered $L{1}_{0}$ and $L{1}_{2}$ phases was also possible but not significant for the changes in perpendicular magnetic anisotropy (PMA) observed experimentally. The strain analysis showed that the Co layer was under tensile strain in the lateral direction at the fluences of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{14}--3.5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.28em}{0ex}}{\mathrm{ions}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}}^{\ensuremath{-}2}$; this range of fluences corresponds to the appearance of PMA. This strain was induced in the initially relaxed hcp Co layer due to its partial transformation to the fcc phase and to the influence of atomic layers with larger lattice constants at upper/lower interfaces.

Thermal Properties of Divalent Metal Oxides: CaO as a Prototype

Commonly employed quasiharmonic approximation (QHA) is inadequate to account for intrinsic anharmonism such as phonon-phonon interaction, vacancy contribution, etc. Though anharmonic contributions are important at high temperatures and low pressure, complete ab initio calculations are scanty due largely to laborious computational requirements. Nevertheless, some simple semi-empirical schemes can be used effectively to incorporate the anharmonism. In this regards, in the present study we have proposed a simple computational scheme to include the effect of vacancy directly into the description within the mean-field potential approach, which calculates vibrational free energy of ions. Validity of the scheme is verified by taking calcium oxide as a test case. Equilibrium properties at (T,P) = (0,0) condition is obtained within the tight-binding second-moment approximation (TB-SMA), whose parameters were determined through first principles density functional theory. Kohn-Sham equations for core electrons were solved using ultrasoft plane-wave pseudopotential employing the generalized gradient approximation for exchange and correlation. Present findings for thermal expansion and high-T EOS clearly show perceptible improvement over the case when vacancy contribution was not included. Some related thermodynamic properties are also calculated and compared with the available experimental and theoretical data.

Effects of incident cluster size, substrate temperature, and incident energy on bombardment of Ni clusters onto Cu (0 0 1) surface studied using molecular dynamics simulation

The bombardment process of a Ni cluster onto a Cu (001) surface is studied using molecular dynamics (MD) simulations based on the tight-binding second-moment approximation (TB-SMA) many-body potential. The effects of incident cluster size, substrate temperature, and incident energy are evaluated in terms of molecular trajectories, kinetic energy, stress, self-diffusion coefficient, and sputtering yield. The simulation results clearly show that the penetration depth and Cu surface damage increase with increasing incident cluster size for a given incident energy per atom. The self-diffusion coefficient and the penetration depth of a cluster significantly increase with increasing substrate temperature. An incident cluster can be scattered into molecules or atoms that become embedded in the surface after incidence. When the incident energy is increased, the number of volcano-like defects and the penetration depth increase. A high sputtering yield can be obtained by increasing the incident energy at high temperature. The sputtering yield significantly increases with cluster size when the incident energy is above 5eV/atom.

Effect of thermal annealing on the stress and morphology of deposited nanofilms analyzed using molecular dynamics

Molecular dynamics (MD) simulations are used to investigate the surface roughness and intermixing of grown films and to calculate the atomic-level stress before and after the annealing process. The tight-binding second-moment approximation (TB-SMA) many-body potential is employed to model the interaction. The results reveal that the morphology of the film becomes smoother after 900K annealing due to the substrate temperature being lower for the as-deposited film. The results indicate that the annealing decreases the number of vacancies and voids for all thin films. More Al atoms penetrate into the substrate after the annealing process. The interface mixing of annealed film is thus better than that of as-deposited film. The first peak of the radial distribution function (RDF) becomes higher and narrower when the Al–Cu film is cooled from 700 to 300K. This indicates that new grains nucleate and grow to replace those deformed by internal stresses and that recrystallization may occur for the Al–Cu film. In the atomic-level stress analysis, the average normal stress along the thickness direction and the average mean biaxial stress are considered. Both residual stresses decrease for all layers after the annealing process. This implies that internal stress is relieved within the Al–Cu film during the cooling phase.

Influence of the Cluster Orientation on the Epitaxy: Deposition of Co Nanoclusters on Cu(001) Surfaces

Deposition at low energy of 147-atom icosahedral Co nanoclusters on Cu(001) substrates is studied by molecular-dynamics simulations. Atomic interactions were mimicked by a many-body potential based on the tight-binding second-moment approximation. Clusters were rotated by using the two first Euler angles, in the so-called "x-convention," and subsequently, they were deposited on the substrate. The dependence of the degree of epitaxy on these angles has been obtained. Epitaxy is also related to the initial number of (001)-oriented atoms, especially for extreme values of this latter quantity. A better epitaxial matching is connected with a larger spreading index. The explanation of the epitaxial behavior of the supported clusters resides mainly in the dynamical interaction between grains during approximately the first 40 ps. Whenever the newly-formed (001)-oriented grain competes against a large number of grains after the collision, a very low epitaxial matching is obtained.

Molecular dynamics of contact behavior of self-assembled monolayers on gold using nanoindentation

Molecular dynamics simulation is used to study nanoindentation of the self-assembled monolayers (SAMs) on an Au surface. The interaction of SAM atoms is described by a general universal force field (UFF), the tight-binding second-moment approximation (TB-SMA) is used for Au substrate, and the Lennard-Jones potential function is employed to describe interaction among the indenter, the SAMs, and the Au substrate atoms. The model consists of a planar Au substrate with n-hexadecanethiol SAM chemisorbed to the substrate. The simulation results show that the contact pressure increases as the SAMs temperature increases. In addition, the contact pressure also increases as the depth and velocity of indentation increase.

Properties of the liquid-vapour interface of fcc metals calculated using the tight-binding potential

The second-moment approximation (SMA) of the tight-binding (TB) scheme was used to calculate the molar volume, volume expansion, internal energy and pair correlation function for bulk liquids of the fee metals at several temperatures both above and below the melting point. The calculated values were found to be in generally good agreement with experiments, although the volume expansion upon melting does differ by 55% from the expected result for some of the elements studied. The total energy of a liquid system with surfaces was calculated, and the results were compared with the bulk liquid results to determine the enthalpy and width of the liquid-vapour interface. The TB SMA values for surface enthalpy were found to be lower than experimental values by by about 10-40%.

The effect of the nature of the interaction potential on cluster reaction rates

The effect of two different interaction potentials, a two-body and a many-body potential, on thermal cluster reaction rates was studied for 2–13 atom nickel clusters using the classical trajectory method. The reaction rates were computed for cluster–monomer and cluster–cluster collisions at T=1200 K, using the bulk and dimer parametrized Lennard-Jones (LJ) potentials and were compared with the rates previously obtained for these collisional events by using a more realistic many-body tight-binding second moment approximation (TB-SMA) potential. For cluster–monomer collisions, close agreement exists between the reaction cross section results for dimer fitted LJ (LJD) potential and TB-SMA potential suggesting that the cluster–monomer collisions may be dominated by pairwise interactions. The bulk fitted LJ potential (LJB) underestimates the sticking cross section results of the other two potentials for most cluster sizes. This discrepancy however appears to be due to the relatively smaller cluster binding energies obtained for this potential as a result of which a larger cross section for dissociation is observed. For cluster–cluster collisions, for most cluster sizes, no agreement exists between the reaction cross section results for the three potentials. The discrepancy between the cross section results for the LJ potentials and the TB-SMA potential appears to lie in the difference in the scaling of cluster energy with cluster coordination for these two types of potentials (i.e., linear for LJ vs square root dependence for TB-SMA). Some characteristics of the cross section results of both LJB and LJD potentials correlate with the relative cluster stability pattern for the LJ clusters. For TB-SMA case, no such correlation exists, which however is consistent with the smooth and featureless size distributions observed experimentally for nickel and other transition metals. The cut-off used in the TB-SMA potential appears to lead to a significant underestimation of the total reaction cross section for N=13, in the case of the cluster–cluster collisions. The results of this study indicate that the rate calculations may be sensitive to both the nature and parametrization of the simulation potential depending on the temperature range considered and cluster growth process simulated.

Computer simulation of Au(001)/Ni multilayers: comparison with experiments

The structure of thin Ni film on Au(001) and Au(001)/Ni multilayers is studied as a function of the thickness of Ni using a semiempirical potential based on the tight-binding second-moment approximation. It is shown that the stable structure is pseudomorphic for a thickness less than five monolayers and (2 1 1 0) HCP or 4H for a greater thickness with close-packed planes perpendicular to the interfaces. Moreover, we show that a thin Ni film grown on Au(001) substrate is covered by at least one monolayer of Au. We compare our results with high-resolution electronic microscopy (HREM) and X-ray diffraction.