Jaime Marian

Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations

Abstract We use a physically-based crystal plasticity model to predict the yield strength of body-centered cubic (bcc) tungsten single crystals subjected to uniaxial loading. Our model captures the thermally-activated character of screw dislocation motion and full non-Schmid effects, both of which are known to play critical roles in bcc plasticity. The model uses atomistic calculations as the sole source of constitutive information, with no parameter fitting of any kind to experimental data. Our results are in excellent agreement with experimental measurements of the yield stress as a function of temperature for a number of loading orientations. The validated methodology is employed to calculate the temperature and strain-rate dependence of the yield strength for 231 crystallographic orientations within the standard stereographic triangle. We extract the strain-rate sensitivity of W crystals at different temperatures, and finish with the calculation of yield surfaces under biaxial loading conditions that can be used to define effective yield criteria for engineering design models.

Energy spectra of primary knock-on atoms under neutron irradiation

Materials subjected to neutron irradiation will suffer from a build-up of damage caused by the displacement cascades initiated by nuclear reactions. Previously, the main “measure” of this damage accumulation has been through the displacements per atom (dpa) index, which has known limitations. This paper describes a rigorous methodology to calculate the primary atomic recoil events (often called the primary knock-on atoms or PKAs) that lead to cascade damage events as a function of energy and recoiling species. A new processing code SPECTRA-PKA combines a neutron irradiation spectrum with nuclear recoil data obtained from the latest nuclear data libraries to produce PKA spectra for any material composition. Via examples of fusion relevant materials, it is shown that these PKA spectra can be complex, involving many different recoiling species, potentially differing in both proton and neutron number from the original target nuclei, including high energy recoils of light emitted particles such as aparticles and protons. The variations in PKA spectra as a function of time, neutron field, and material are explored. The application of PKA spectra to the quantification of radiation damage is exemplified using two approaches: the binary collision approximation and stochastic cluster dynamics, and the results from these different models are discussed and compared.

Free Energy Generalization of the Peierls Potential in Iron

In body-centered-cubic (bcc) crystals, 1/2<111> screw dislocations exhibit high intrinsic lattice friction as a consequence of their nonplanar core structure, which results in a periodic energy landscape known as the Peierls potential U(P). The main features determining plastic flow, including its stress and temperature dependences, can be derived directly from this potential, hence its importance. In this Letter, we use thermodynamic integration to provide a full thermodynamic extension of U(P) for bcc Fe. We compute the Peierls free energy path as a function of stress and temperature and show that the critical stress vanishes at 700 K, supplying the qualitative elements that explain plastic behavior in the athermal limit.

Thermodynamic and mechanical properties of copper precipitates in alpha-iron from atomistic simulations

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 (similar to 2700 atoms) at 200 K to about 8 nm (similar to 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.

The atomistic representation of first strain-gradient elastic tensors

We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy–Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.

The role of interstitial binding in radiation induced segregation in W-Re alloys

Due to their high strength and advantageous high-temperature properties, tungsten-based alloys are being considered as plasma-facing candidate materials in fusion devices. Under neutron irradiation, rhenium, which is produced by nuclear transmutation, has been found to precipitate in elongated precipitates forming thermodynamic intermetallic phases at concentrations well below the solubility limit. Recent measurements have shown that Re precipitation can lead to substantial hardening, which may have a detrimental effect on the fracture toughness of W alloys. This puzzle of sub-solubility precipitation points to the role played by irradiation induced defects, specifically mixed solute-W interstitials. Here, using first-principles calculations based on density functional theory, we study the energetics of mixed interstitial defects in W-Re, W-V, and W-Ti alloys, as well as the heat of mixing for each substitutional solute. We find that mixed interstitials in all systems are strongly attracted to each other with binding energies of -2.4 to -3.2 eV and form interstitial pairs that are aligned along parallel first-neighbor strings. Low barriers for defect translation and rotation enable defect agglomeration and alignment even at moderate temperatures. We propose that these elongated agglomerates of mixed-interstitials may act as precursors for the formation of needle-shaped intermetallic precipitates. This interstitial-based mechanism is not limited to radiation induced segregation and precipitation in W-Re alloys but is also applicable to other body-centered cubic alloys.

Thermodynamic interpretation of reactive processes in Ni?Al nanolayers from atomistic simulations

Metals that can form intermetallic compounds by exothermic reactions constitute a class of reactive materials with multiple applications. Ni?Al laminates of thin alternating layers are being considered as model nanometric metallic multilayers for studying various reaction processes. However, the reaction kinetics at short timescales after mixing are not entirely understood. In this work, we calculate the free energies of Ni?Al alloys as a function of composition and temperature for different solid phases using thermodynamic integration based on state-of-the-art interatomic potentials. We use this information to interpret molecular dynamics (MD) simulations of bilayer systems at 800?K and zero pressure, both in isothermal and isenthalpic conditions. We find that a disordered phase always forms upon mixing as a precursor to a more stable nano crystalline B2 phase. We construe the reactions observed in terms of thermodynamic trajectories governed by the state variables computed. Simulated times of up to 30?ns were achieved, which provides a window to phenomena not previously observed in MD simulations. Our results provide insight into the early experimental reaction timescales and suggest that the path (segregated reactants)???(disordered phase)???(B2 structure) is always realized irrespective of the imposed boundary conditions.

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) 6 is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the ?-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe3+, He+ and H+) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

Mechanism of nucleation and incipient growth of Re clusters in irradiated W-Re alloys from kinetic Monte Carlo simulations

High-temperature, high-dose, neutron irradiation of W results in the formation of Re-rich clusters at concentrations one order of magnitude lower than the thermodynamic solubility limit. These clusters may eventually transform into brittle W-Re intermetallic phases, which can lead to high levels of hardening and thermal conductivity losses. Standard theories of radiation enhanced diffusion and precipitation cannot explain the formation of these precipitates and so understanding the mechanism by which nonequilibrium clusters form under irradiation is crucial to predict materials degradation and devise mitigation strategies. Here we carry out a thermodynamic study of W-Re alloys and conduct kinetic Monte Carlo simulations of Re cluster formation in irradiated W2Re alloys using a generalized Hamiltonian for crystals containing point defects parameterized entirely with electronic structure calculations. Our model incorporates recently-gained mechanistic information of mixedinterstitial solute transport, which is seen to control cluster nucleation and growth by forming quasi-spherical nuclei after an average incubation time of 20 s at 1800 K. These nuclei are seen to grow by attracting more mixed interstitials bringing solute atoms, which in turns attracts vacancies leading to recombination and solute agglomeration. The clusters grow to a maximum size of approximately 4-nm radius, and are not fully dense with Re, containing 50% or less near the center. Our simulations are in reasonable agreement with recent atom probe examinations of ion irradiated W-2Re systems at 773 K.

Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t)=FL(X,t)FP(X,t), an initial stress-free polycrystal is constructed by imposing FL to be a piecewise constant rotation field R0(X), and FP=R0(X)T, thereby having F(X,0)=I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.