Embedded atom potential for Fe-Cu interactions and simulations of precipitate-matrix interfaces (original) (raw)
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Thermodynamic and mechanical properties of copper precipitates inα-iron from atomistic simulations
Physical Review B, 2013
Precipitate hardening is commonly used in materials science to control strength by acting on the number density, size distribution, and shape of solute precipitates in the hardened matrix. The Fe-Cu system has attracted much attention over the last several decades due to its technological importance as a model alloy for Cu steels. In spite of these efforts several aspects of its phase diagram remain unexplained. Here we use atomistic simulations to characterize the polymorphic phase diagram of Cu precipitates in body-centered cubic (BCC) Fe and establish a consistent link between their thermodynamic and mechanical properties in terms of thermal stability, shape, and strength. The size at which Cu precipitates transform from BCC to a close-packed 9R structure is found to be strongly temperature dependent, ranging from approximately 4 nm in diameter (∼2700 atoms) at 200 K to about 8 nm (∼22 800 atoms) at 700 K. These numbers are in very good agreement with the interpretation of experimental data given Monzen et al. [Philos. Mag. A 80, 711 (2000)]. The strong temperature dependence originates from the entropic stabilization of BCC Cu, which is mechanically unstable as a bulk phase. While at high temperatures the transition exhibits first-order characteristics, the hysteresis, and thus the nucleation barrier, vanish at temperatures below approximately 300 K. This behavior is explained in terms of the mutual cancellation of the energy differences between core and shell (wetting layer) regions of BCC and 9R nanoprecipitates, respectively. The proposed mechanism is not specific for the Fe-Cu system but could generally be observed in immiscible systems, whenever the minority component is unstable in the lattice structure of the host matrix. Finally, we also study the interaction of precipitates with screw dislocations as a function of both structure and orientation. The results provide a coherent picture of precipitate strength that unifies previous calculations and experimental observations.
Interatomic potentials consistent with thermodynamics: The Fe–Cu system
Journal of Nuclear Materials, 2007
A methodology is developed to fit semi-empirical interatomic potentials aimed at obtaining a consistent thermodynamic behavior. The procedure is based on the cluster variation method theory which is seamlessly integrated to the other more standard equations of the fitting technique. A new interatomic potential for the Fe-Cu system is thus built within the framework of the embedded atom method, to be used in studies of the microstructure evolution of Fe-Cu alloys under irradiation. The potential is shown to reproduce very reasonably the Cu solubility curve in the Fe matrix as well as to lead to better description of the point defect kinetics with respect to previous interaction models. Limitations of the fitting technique and possible ways of improvement are discussed.
Development of modified embedded atom potentials for the Cu–Ag system
Superlattices and Microstructures, 2001
The modified embedded atom method is tested in the atomistic simulations of binary fcc metallic alloys. As an example the alloying behaviour of Cu-Ag is studied using the molecular dynamics (MD) method. The MD algorithms that we use are based on the extended Hamiltonian formalism and the ordinary experimental conditions are simulated using the constant-pressure, constant temperature (NPT) (MD) method. The enthalpy of mixing values of the random Ag-Cu binary alloys are obtained as functions of concentration after 20 000 steps.
Computational Materials Science, 2009
A new interatomic potential for copper-antimony (Cu-Sb) in low Sb concentration solid-solution alloys is proposed based upon the Lennard-Jones (LJ) pair formulation. Parameters for this new potential, r and e, are motivated by calculations of the Cu-Sb heat of solution (heat of mixing) and the strain field generated by a single substitutional impurity in single crystal copper, which is analyzed for impurity (dopant) atoms with various atomic radii. A well established embedded-atom method (EAM) potential is used to model the host copper. The e parameter is derived for a range of values of r by matching to the experimental value of the heat of solution. Then, the strain field around a single dopant atom is computed for each set of the calculated LJ parameters. Ultimately, the final parameters for the Cu-Sb interaction are selected to match the strain field corresponding to the atomic radius mismatch between Sb and Cu and are compared with the Eshelby solutions which are based on classical theory of elasticity. As an application of this new potential, it is shown using molecular dynamics simulations that the plastic deformation behavior of single crystal copper is affected by the characteristics of the strain field around the dopant atoms.
Revealing the atomistic nature of dislocation-precipitate interactions in Al-Cu alloys
Journal of Alloys and Compounds, 2019
Despite significant gains on understanding strengthening mechanisms in precipitate strengthened materials, such as aluminum alloys, there persists a sizeable gap in the atomistic understanding of how different precipitate types and their morphology along with dislocation character affects the hardening mechanisms. Toward this, the paper examines nature of precipitation strengthening behavior observed in the Al-Cu alloys using atomistic simulations. Specifically, the critical resolved shear stress is quantified across a wide range of dislocationprecipitate interactions scenarios for both θ' and θ phase of Al2Cu. Overall, the simulations reveal that the dislocation character (edge or screw) plays a key role in determining the predominant hardening mechanism (shearing vs. Orowan looping) employed to overcome the θ' Al2Cu precipitate. Furthermore, the critical shear stress and mechanism to overcome the precipitate is sensitivity to the position of the glide plane with respect to the precipitate and its orientation. Interestingly in our findings, the θ Al2Cu precipitate conventionally regarded as unshearable particle was overcome by shear cutting mechanism for small equivalent precipitate radius, which agrees with recent TEM observations. These findings provide necessary information for the development of atomistically informed precipitate hardening models for the traditional continuum scale modeling efforts.
Hardening due to copper precipitates in alpha-iron studied by atomic-scale modelling
J Nucl Mater, 2004
We present results of a large-scale atomic-level study of dislocation-precipitate interaction. We have considered a 1 2 AE1 1 1ae edge dislocation gliding in a-iron containing coherent copper precipitates of size from 0.7 to 6 nm over a temperature range from 0 to 450 K. The results demonstrate that some features are qualitatively consistent with earlier theoretical conclusions, e.g. the critical resolved shear stress (CRSS) is proportional to L À1 and lnðDÞ, where L and D are precipitate spacing and diameter. Other features, which are intrinsic to the atomic-level nature of the dislocationprecipitate interaction, include strong dependence of the CRSS on temperature, dislocation climb and precipitate phase transformation.
Hardening due to copper precipitates in α-iron studied by atomic-scale modelling
Journal of Nuclear Materials, 2004
We present results of a large-scale atomic-level study of dislocation-precipitate interaction. We have considered a 1 2 AE1 1 1ae edge dislocation gliding in a-iron containing coherent copper precipitates of size from 0.7 to 6 nm over a temperature range from 0 to 450 K. The results demonstrate that some features are qualitatively consistent with earlier theoretical conclusions, e.g. the critical resolved shear stress (CRSS) is proportional to L À1 and lnðDÞ, where L and D are precipitate spacing and diameter. Other features, which are intrinsic to the atomic-level nature of the dislocationprecipitate interaction, include strong dependence of the CRSS on temperature, dislocation climb and precipitate phase transformation.
Atomic scale modelling of edge dislocation movement in the alpha-Fe-Cu system
Modelling and Simulation in Materials Science and Engineering, 2000
The aim of the present work is to investigate by molecular dynamics (MD) calculations the interaction between a moving edge dislocation in an α-Fe crystal and a copper precipitate. In the absence of external stresses, two edge dislocations with the same slip plane and opposite Burgers vectors within a perfect α-Fe crystal lattice are investigated. In agreement with Frank's rule, the movement of the dislocations under mutual attraction is found and attention is focused on the interaction between one of the dislocations and the Cu precipitate. The critical resolved shear stress of the Fe was calculated and the influence of different sizes of Cu precipitates on the dislocation mobility was studied. The pinning of the dislocation line at the Cu inclusion as derived from the atomistic modelling agrees with previously published continuum theoretical behaviour of pinned dislocations. Therefore, nanosimulation as a way to model precipitation hardening could be established as a useful scientific tool. § On leave from
Philosophical Magazine, 2007
Liverpool L69 3GH, UK ‡Computer Science and Mathematics Division, ORNL, Oak Ridge, TN 37831-6138, USA Copper-rich precipitates can nucleate and grow in ferritic steels containing small amounts of copper in solution and this affects mechanical properties. Growth kinetics, composition and structure of precipitates under irradiation are different from those under thermal ageing, and also vary with type of radiation. This implies that the interaction between radiation defects, i.e. vacancies, self-interstitial atoms (SIAs) and their clusters, and precipitates is influential. It is studied here by atomic-scale computer simulation. The results are compared with those of elasticity theory based on the size misfit of precipitates and defects, and the modulus difference between bcc iron and bcc copper. It is found that SIA defects are repelled by precipitates at large distance but, like vacancies, attracted at small distance. Copper precipitates in iron can therefore be sinks for both vacancy and interstitial defects and hence can act as recombination centres under irradiation conditions. A tentative explanation for the mixed Cu-Fe structure of precipitates observed in experiment and the absence of precipitate growth under neutron irradiation is given. More generally, agreement between the simulations and elasticity theory suggests that the results are not artefacts of the atomic model:
Atomistic Simulation of Vacancy and Self-Interstitial Diffusion in Fe-Cu Alloys
MRS Proceedings, 2000
ABSTRACTNeutron hardening and embrittlement of pressure vessel steels is due to a high density of nanometer scale features, including Cu-rich precipitates which form as a result of radiation enhanced diffusion. High-energy displacement cascades generate large numbers of both isolated point defects and clusters of vacancies and interstitials. The subsequent clustering, diffusion and ultimate annihilation of primary damage is inherently coupled with solute transport and hence, the overall chemical and microstructural evolutions under irradiation. In this work, we present atomistic simulation results, based on many-body interatomic potentials, of the migration of vacancies, solute and self-interstitial atoms (SIA) in pure Fe and binary Fe-0.9 and 1.0 at.% Cu alloys. Cu diffusion occurs by a vacancy mechanism and the calculated Cu diffusivity is in good agreement with experimental data. Strain field interactions between the oversized substitutional Cu solute atoms and SIA and SIA cluste...