M. I. Baskes

The embedded-atom method: a review of theory and applications

Abstract The embedded-atom method is a semi-empirical method for performing calculations of defects in metals. The EAM incorporates a picture of metallic bonding, for which there is some fundamental basis. The limitations of the EAM are fairly well characterized: it works best for purely metallic systems with no directional bonding; it does not treat covalency or significant charge transfer; and it does not handle Fermi-surface effects. The main physical property incorporated in the EAM is the moderation of bond strength by other bonds (coordination-dependent bond strength). Within these constraints, the EAM provides a very useful and robust means of calculating approximate structure and energetics, from which many interesting properties of metals can be obtained. We believe that atomistic calculations will continue to play an important role in the development of materials theory. Where the EAM can be useful, there is a tremendous number of interesting projects that have yet to be carried out. The understanding of mechanical properties on an atomistic level has only just begun. For materials where the EAM is not expected to work well, there are recent developments which may allow calculations similar to those presented here. We have mentioned already the problem of treating directional bonding in semiconductors and elements from the transition series. One approach which promises to be useful for treating directional bonding is reviewed by Carlsson [70]; the interested reader is encouraged to start there.

The dependence of polycrystal work hardening on grain size

Abstract Existing rationales for the effect of grain size on work hardening do not explain the behavior of copper and aluminum. A new analytical approach to polycrystal work hardening was devised to understand and describe these data, together with data on 70-30 brass. The physical model was novel in its emphasis on the importance of regions of the grains in which either statistically stored or geometrically necessary dislocations are accumulated. One prediction of the model, that large-strain cell size in copper ought to depend on grain size, was verified by direct measurement. A number of other details computed from the model, including slip lengths and dislocation density variation with strain, were consistent with the results of other workers.

LENGTH SCALE AND TIME SCALE EFFECTS ON THE PLASTIC FLOW OF FCC METALS

We examine size scale and strain rate effects on single-crystal face-centered cubic (fcc) metals. To study yield and work hardening, we perform simple shear molecular dynamics simulations using the embedded atom method (EAM) on single-crystal nickel ranging from 100 atoms to 100 million atoms and at strain rates ranging from 107 to 1012 s−1. We compare our atomistic simulation results with experimental data obtained from interfacial force microscopy (IFM), nano-indentation, micro-indentation and small-scale torsion. The data are found to scale with a geometric length scale parameter defined by the ratio of volume to surface area of the samples. The atomistic simulations reveal that dislocations nucleating at free surfaces are critical to causing micro-yield and macro-yield in pristine material. The increase of flow stress at increasing strain rates results from phonon drag, and a simple model is developed to demonstrate this effect. Another important aspect of this study reveals that plasticity as reflected by the global averaged stress–strain behavior is characterized by four different length scales: (1) below 104 atoms, (2) between 104 and 106 atoms (2 μm), (3) between 2 μm and 300 μm, and (4) above 300 μm.

Modified embedded atom potentials for HCP metals

The modified embedded atom method (MEAM) is an empirical extension of embedded atom method (EAM) that includes angular forces. The MEAM, which has previously been applied to the atoms in the FCC, BCC, and diamond cubic crystal systems, has been extended to the HCP crystal structure. Parameters have been determined for HCP metals that have c/a ratios less than ideal. The model is fitted to the lattice constants, elastic constants, cohesive energy, vacancy formation energy, and the BCC-HCP structural energy difference of these metals and is able to reproduce this extensive data base quite well. Structural energies and lattice constants of the HCP metals in a number of cubic structures are predicted. The divacancy is found to be unbound in all of the metals considered except for Be. Stacking fault and surface energies are found to be in reasonable agreement with experiment.

A calculation of the surface recombination rate constant for hydrogen isotopes on metals

Abstract The surface recombination rate constant for hydrogen isotopes on a metal has been calculated using a simple model whose parameters may be determined by direct experimental measurements. Using the experimental values for hydrogen diffusivity, solubility, and sticking coefficient at zero surface coverage a reasonable prediction of the surface recombination constant may be made. The calculated recombination constant is in excellent agreement with experiment for bcc iron. A heuristic argument is developed which, along with the rate constant calculation, shows that surface recombination is important in those metals in which hydrogen has an exothermic heat of solution.

Interpretations of Indentation Size Effects

For very shallow indentations in W, Al, Au, and Fe-3wt%Si single crystals, hardness decreased with increasing depth irrespective of increasing or decreasing strain gradients. As such, strain gradient theory appears insufficient to explain the indentation size effect (ISE) at depths less than several hundred nanometers. Present research links the ISE to a ratio between the energy of newly created surface and plastic strain energy dissipation. Also, the contact surface to plastic volume ratio was nearly constant for a range of shallow depths. Based on the above, an analytical model of hardness versus depth provides a satisfactory fit to the experimental data and correlates well with embedded atom simulations. @DOI: 10.1115/1.1469004#

Trapping of hydrogen to lattice defects in nickel

This paper addresses the energy associated with the trapping of hydrogen to defects in a nickel lattice. Several dislocations and grain boundaries which occur in nickel are studied. The dislocations include an edge, a screw, and a Lomer dislocation in the locked configuration, i.e. a Lomer-Cottrell lock (LCL). For both the edge and screw dislocations, the maximum trap site energy is approximately 0.1 eV occurring in the region where the lattice is in tension approximately 3-4 angstroms from the dislocation core. For the Lomer-Cottrell lock, the maximum binding energy is 0.33 eV and is located at the core of the a/6(110) dislocation. Several low-index coincident site lattice grain boundaries are investigated, specifically the Sigma 3(112), Sigma 9(221) and Sigma 11(113) tilt boundaries. The boundaries all show a maximum binding energy of approximately 0.25 eV at the tilt boundary. Relaxation of the boundary structures produces an asymmetric atomic structure for both the Sigma 3 and Sigma 9 boundaries and a symmetric structure for the Sigma 11 tilt boundary. The results of this study can be compared to recent experimental studies showing that the activation energy for hydrogen-initiated failure is approximately 0.3-0.4 eV in the Fe-based superalloy IN903. From the results of this comparison it can be concluded that the embrittlement process is likely associated with the trapping of hydrogen to grain boundaries and Lomer-Cottrell locks.

Superhard silicon nanospheres

Abstract Successful deposition and mechanical probing of nearly spherical, defect-free silicon nanospheres has been accomplished. The results show silicon at this length scale to be up to four times harder than bulk silicon. Detailed measurements of plasticity evolution and the corresponding hardening response in normally brittle silicon is possible in these small volumes. Based upon a proposed length scale related to the size of nanospheres in the 20– 50 nm radii range, a prediction of observed hardnesses in the range of 20– 50 GPa is made. The ramifications of this to computational materials science studies on identical volumes are discussed.

Determination of modified embedded atom method parameters for nickel

The modified embedded atom method (MEAM) is an empirical extension of the embedded atom method that includes angular forces. A detailed study is presented to show the effect of various MEAM parameters on the calculated properties of a model material, nickel. Over 50 physical properties of nickel are calculated for four MEAM potentials. It is found that, in general, the predicted material properties are extremely insensitive to the parameter variations examined. In a few cases: interstitial migration; the (110) surface reconstruction; and the coefficient of thermal expansion, significant effects of potential were found. Minor differences were also found for the vacancy migration energy, the interstitial formation energy, and the stability of the b.c.c. structure. These results point out the appropriate experimental measurements or first principles calculations that need to be performed to obtain a reliable MEAM parameter set. This work results in a MEAM potential that reproduces all of the experimental data examined.

Deuterium trapping in irradiated 316 stainless steel

Abstract Linear ramp thermal desorption measurements were conducted on 316 stainless steel samples implanted at 296 K with 1–10 keV D + to fluences of 10 17 –10 19 D + /cm 2 . Samples were held 1–100 h at 296 K prior to desorbing. The desorption data were shown to arise from two dominant mechanisms: bulk migration of mobile deuterium atoms with ~0.6 eV migration energy, and release from near surface traps with a net detrapping energy of ~0.9 eV. After 10 keV D + bombardment, more complex desorption spectra were observed. Samples pre-damaged with 300 keV He + exhibited a significant increase in the deuterium trapping compared to samples without pre-bombardment. Based on the data and modelling, estimates of tritium retention in TFTR were made.