Central-force Many-body Potentials Research Articles

Influence of non-glide stresses on plastic flow: from atomistic to continuum modeling

The Schmid law, which is accurate for face-centered-cubic (fcc) metals, assumes that only the shear stress acting in the slip plane in the slip direction controls the plastic deformation. Hence, it is implicitly assumed that the critical resolved shear stress (CRSS) for the slip is not affected by any other components of the applied stress tensor. This rule is almost ubiquitously utilized in large-scale continuum computations of plastically deforming single and polycrystals. On the other hand, in materials with more complex structures and for some orientations of the dislocation line the cores can spread onto several non-parallel planes. The most widely-known example is the screw dislocation in bcc metals, though this phenomenon is quite universal in structures that are not close packed. Signatures of such core configurations commonly include unexpected deformation modes and slip geometries, strong and unusual dependence of flow stresses on temperature and strain rate, a high Peierls stress, and, in general, a breakdown of the Schmid law. In this paper, we first summarize results of atomistic computer simulations of the response of 1/2〈1 1 1〉 screw dislocations to the applied shear stresses. The calculations have been made using central-force many-body potentials and tight-binding based bond-order potentials for molybdenum. While the core structure found is not the same for the two descriptions of atomic interactions, both lead to a very similar orientation dependence of the critical resolved shear stress for the dislocation motion which takes place along the most highly stressed {1 1 0} plane. This dependence reveals the break down of the Schmid law invoked by the effect of shear stresses acting in another {1 1 0} plane, which are called non-glide stresses. These results are then transferred to macroscopic level by formulating single crystal yield criteria that include the effects of non-glide components of the stress tensor. These criteria form a basis for multislip yield criteria and flow relations for continuum analyses. Using this approach we demonstrate that the effects of non-glide stresses that have their origin at the level of individual dislocations also have significant effect on polycrystalline response, including a significant tension-compression asymmetry.

An Atomistic Study of Interfacial Diffusion in Lamellar TiAl Alloys

In this paper we investigate self-diffusion of Ti and Al along interfaces present in the lamellar L10 TiAl by atomistic computer modeling. The interactions between the atoms are described by central-force many-body potentials. The approach adopted is similar to that used in earlier atomistic modeling of bulk diffusion in TiAl [1, 2]. Both the formation and migration of vacancies is examined. The interfaces studied are the three types of γ–γinterfaces: ordinary twin, pseudotwin and 120° rotational fault. For the latter two interfaces the diffusion was investigated not only for the stoichiometric case but also when the interfaces possess a surplus of titanium in the form of a layer with the composition and structure of Ti3Al, as was found in an earlier Monte Carlo study of titanium segregation to these interfaces. The calculations suggest that the diffusivity along γ–γinterfaces is higher than in the bulk. However, the difference between bulk and interfacial diffusivity is not as drastic as it may be encountered in grain boundaries. At the same time the above mentioned surplus of Ti appears to affect the interfacial diffusion only marginally.

A study of the applicability of many-body central force potentials in NiAl and TiAl

The applicability and characteristics of the central force many-body potentials of Finnis-Sinclair-type for NiAl and TiAl are investigated by studying the variation of the energy of these compounds with structural transformations that correspond to three distinct paths: tetragonal (B2L10), trigonal (B2L11) and hexagonal (B2B19). The energy was computed using both the central force potentials and the full potential linearized augmented plane waves (FLAPW) ab initio method. Comparison of these two calculations provides a means for the analysis of the efficacy of the potentials. The central force many-body potentials reproduce the results of ab initio calculations very satisfactorily for NiAl. This propounds that they are sufficient in atomistic modelling of lattice defects in this compound. For TiAl the central force potentials mimic the results of ab initio calculations qualitatively but are unable to differentiate adequately between structures with practically the same separations of the first and second neighbours. However, the present study provides a justification for the use of these potentials when investigating extended defects in which separations of the first and second nearest neighbours differ significantly from those in the L10 structure.

Application of Surface Ab Initio Methods to Studies of Electronic Structure and Atomic Configuration of Interfaces in Metallic Materials

Surface ab initio electronic structure methods are reviewed and their application to studies of electronic and atomic structure of interfaces in metallic materials is discussed. Examples presented here are electronic structure of the Σ = 5(210)/[001] tilt grain boundary in tungsten, magnetic moments at the Σ = 5(310)/[001] tilt grain boundary in iron, and magnetic behaviour of Ru and Rh overlayers at the Ag(001) substrate. Versatility and generalization of the Green's function method to include also compositionally disordered systems is emphasized. At the same time it is argued that, depending on the character of the problem, simpler methods such as central force many-body potentials may be sufficient for description and understanding of many phenomena in metallic systems but they have to be linked synergistically with first-principles methods and with experiments.

An atomistic study of segregation to lamellar interfaces in non-stoichiometric TiAl alloys

Segregation to γ/ γ interfaces in non-stoichiometric L1 0 TiAl is analyzed on the atomic level using a Monte Carlo method and central force many-body potentials of the Finnis–Sinclair type to describe atomic interactions. While these alloys are Ti-rich and thus segregation of Ti is of principal interest, the calculations have also been made for Al-rich bulk in order to investigate the generality of structural features revealed in this study. No segregation takes place to ordered twins but both Ti and Al, depending on which of them is in surplus in the bulk, segregate to the 120° rotational faults, pseudotwins and ordered twins with the APB. The segregation of Ti to 120° rotational faults and pseudotwins leads to an apparent formation of a thin layer of the DO 19 Ti 3Al at these interfaces. However, an analogous DO 19 type structure, but with stoichiometry Al 3Ti, is also obtained when Al segregates to these interfaces. Hence, the segregation propensity cannot be associated with a thermodynamically favored formation of the DO 19 phase at γ/ γ interfaces. Rather, the distribution of Al sites that are favored for segregation is such that their filling by Ti leads to the formation of the structure which is the same as that of the basal plane in Ti 3Al. Consequently, the conspicuous formation of the DO 19 Ti 3Al at 120° rotational faults and pseudotwins results from the topology of the nearest neighbors of the atoms at these interfaces. Segregation is also favored to the ordered twin with the APB but it invokes dissociation of this interface into the 120° rotational fault and the pseudotwin which then possess the same structure as the corresponding isolated interfaces.

Effect of Non-Glide Components of the Stress Tensor on Deformation Behavior of Bcc Transition Metals

AbstractIn this paper we demonstrate by atomic computer simulation that the non-Schmid slip behavior in bcc metals is a direct consequence of the non-planar core structure of 1/2<111> screw dislocations and their response to the applied stress tensor. The analysis has been carried out in detail for tantalum using the Finnis-Sinclair type central force many-body potentials. Two distinct non-Schmid effects have been discerned. The first is twinning-antitwinning slip asymmetry on {112} planes. This is an intrinsic property of the bcc structure and depends on the sense of the applied glide stress. The second non-Schmid effect is extrinsic and is controlled by the non-glide shear stresses perpendicular to the total Burgers vector on {110} planes into which the stress-free core of screw dislocations spread.

Many-body potentials for Cu-Ti intermetallic alloys and a molecular dynamics study of vitrification and amorphization

The authors present central force many-body potentials for the Cu-Ti system which were constructed so as to reproduce a number of properties of the CuTi2 compound (tetragonal structure). The authors fitted the potentials not only to the available experimental data (equilibrium lattice parameters and enthalpy of mixing) but employed an ab initio method to determine additional data, in particular the bulk modulus. It is shown that these potentials ensure the stability of the CuTi2 crystal structure against alternate structures and changes in the c/a ratio and closely reproduce the melting temperature of CuTi2. The authors then employ these potentials in simulations of the glass transition and amorphization by irradiation and use the concept of atomic level stresses to interpret the results.

A Comparative Atomistic Study of the Structure of Grain Boundaries in Tungsten

ABSTRACTMost atomistic studies of grain boundaries have been carried out using central forces to describe atomic interactions. However, in transition metals with unfilled d-bands the angular dependence of interatomic forces may be important. The purpose of this paper is to investigate the significance of angular forces in the case of Tungsten. The calculations have been performed for the Σ5(210) symmetrical tilt grain boundary using two alternate approaches. First are the central-force many-body potentials of the Finnis-Sinclair type. The second are the angular dependent potentials obtained via a moment analysis of the electronic density of states. The results of these two approaches are compared by analyzing the boundary structures, the relative displacements of the adjoining grains and the expansion. Differences in structural characteristics are discussed in terms of the effect of angular forces.