Tungsten Single Crystals Research Articles

Experiments and/or crystal plasticity finite element modeling of the mechanical properties of pristine and irradiated tungsten single crystal

Tungsten is used for vital applications in nuclear industry, particularly in experimental fusion reactors like ITER. Experimental evaluation of the irradiation-induced hardening is usually carried out by indentation tests. However, accurate prediction of irradiation hardening by indentation simulations faces two challenges: (1) compression data of single-crystal tungsten for indentation model calibration are lacking, since most available data are from tension tests, but tungsten exhibits a tension-compression asymmetry; (2) the irradiation hardening model for tungsten needs to be improved by incorporating more accurate irradiation defect strengthening mechanisms and defect density evolution laws that are quantitatively extracted from the lower scale modeling such as dislocation dynamics (DD) and molecular dynamics (MD). In this work, we present a comprehensive solution for the neutron irradiation hardening prediction of tungsten based on the experiments on pristine single-crystal tungsten and lower scale simulations. First, we conduct compression and Vickers indentation experiments to calibrate and validate the model for indentation simulations, and extend the model with the irradiation defect hardening law and the defect density evolution law informed by DD and MD simulations. Then, we use the irradiation hardening results from the literature to benchmark the model for its effectiveness, and find that the predicted hardness increases match well with the experimental results for different doses. Moreover, we discuss the drawback to the widely-used conventional hardening models, and find that these models tend to overestimate the defect strengthening coefficients.

INTENSIFICATION OF THE PROCESS OF PLASMA-INDUCTION GROWING OF LARGE PROFILED TUNGSTEN SINGLE CRYSTALS

The structure of a profiled tungsten single crystal obtained by plasma-induction layer-by-layer growth on a single crystal seed crystal at different deposition rates is investigated. Investigated – microhardness, size of the subgrain structure, angles of misorientation of subgrains, the nature of the distribution of dislocations, etc. A complex of experimental methods of modern physical materials science was used, including light, scanning and transmission microdiffraction electron microscopy. It was found that the ingot is a single crystal body with a crystallographic orientation given by the seed crystal. An increase in the growth rate to 70 mm/min leads to an insignificant decrease in microhardness, refinement of the substructure with a uniform distribution of the dislocation density, which makes it possible to obtain tungsten single crystals with a single crystal structure at disorientation angles not exceeding 3°.

Shock response of He bubble in single crystal tungsten: molecular dynamics simulation study

Nonequilibrium molecular dynamics simulations are performed to study the shock response of He bubble with various He-vacancy ratios in single crystal W. Simulation results show that the plastic deformation mode of He bubble is realized by emission of a [100] vacancy type of prismatic dislocation loop, which is formed by reaction of 1/2<111> type of edge dislocations. He bubble with high He-vacancy ratio is more stable than that with low He-vacancy ratio. Finally, the plastic deformation mode and stability of the He bubble are discussed in term of elasticity theory. It is found that the distribution character of resolved shear stresses on the bubble surface is the underlying cause to control the formation of the vacancy type prismatic dislocation loop; and that the resolved shear stress on the He bubble surface decreases with increase of He-vacancy ratio is the reason why He bubble can be stabilized by increase of its He-vacancy ratio.

Hardness-Deformation Energy Relationship in Metals and Alloys: A Comparative Evaluation Based on Nanoindentation Testing and Thermodynamic Consideration.

Nanoindentation testing using a Berkovich indenter was conducted to explore the relationships among indentation hardness (H), elastic work energy (We), plastic work energy (Wp), and total energy (Wt = We + Wp) for deformation among a wide range of pure metal and alloy samples with different hardness, including iron, steel, austenitic stainless steel (H ≈ 2600–9000 MPa), high purity copper, single-crystal tungsten, and 55Ni–45Ti (mass%) alloy. Similar to previous studies, We/Wt and Wp/Wt showed positive and negative linear relationships with elastic strain resistance (H/Er), respectively, where Er is the reduced Young’s modulus obtained by using the nanoindentation. It is typically considered that Wp has no relationship with We; however, we found that Wp/We correlated well with H/Er for all the studied materials. With increasing H/Er, the curve converged toward Wp/We = 1, because the Gibbs free energy should not become negative when indents remain after the indentation. Moreover, H/Er must be less than or equal to 0.08. Thermodynamic analyses emphasized the physical meaning of hardness obtained by nanoindentation; that is, when Er is identical, harder materials show smaller values of Wp/We than those of softer ones during nanoindentation under the same applied load. This fundamental knowledge will be useful for identifying and developing metallic materials with an adequate balance of elastic and plastic energies depending on the application (such as construction or medical equipment).

Pressure Dependence of Structural and Mechanical Properties of Single-Crystal Tungsten: A Molecular Dynamics Study

In the current study, molecular dynamics (MD) simulations were performed to study the pressure dependence of the structural and mechanical properties of single-crystal tungsten. The results show that single-crystal tungsten possesses noteworthy high-pressure stability and exhibits linear lattice contraction with increasing external pressure. Consistent with the results of the performed experiments, the predicted elastic moduli, including Young’s modulus, shear modulus, and bulk modulus, as well as Poisson’s ratio and Pugh’s modulus ratio, show a clear increasing trend with the increase in pressure. Under uniaxial tensile loading, the single-crystal tungsten at high pressures experiences a phase transition from BCC to FCC and other disordered structures, which results in a stripe-like morphology in the tungsten crystal. These results are expected to deepen our understanding of the high-pressure structural and mechanical behaviors of tungsten materials.

A stochastic solver based on the residence time algorithm for crystal plasticity models

The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

The role of shear deformation in pure tungsten: Mechanical properties and micro-mechanism

The effects of shear deformation at 1173 K on the mechanical properties and deformation mechanism of pure tungsten are investigated by molecular dynamics (MD). The results show that the shear deformation of pure tungsten is dominated by dislocation multiplication and slip band deformation. The shear angle has a significant effect on the mechanical properties of pure tungsten. The yield strength is 4.21 Gpa at a shear angle of 11[Formula: see text], and it increases significantly to 11.84 Gpa while the shear angle increasing to 27[Formula: see text]. In the plastic deformation stage, the stress–strain curve shows obvious oscillation due to the interaction of dislocations in the single-crystal tungsten and the effect of strain strengthening. In addition, the evolution of dislocation and twining in the compression system against shear angle indicates the variation of deformation behavior. When the shear angle is 11[Formula: see text], the lengths of dislocation 1/2[Formula: see text] and [Formula: see text] increase to a peak rapidly, which illustrates dislocation strengthening. However, when the shear angle is more than 11[Formula: see text], the decrease of dislocation length and the appearance of twins along [Formula: see text] direction demonstrate the twining accompanied with dislocation tangling, resulting in the additional increase of strength.

Effect of irradiation damage and indenter radius on pop-in and indentation stress-strain relations: Crystal plasticity finite element simulation

In this work, a crystal plasticity finite element model is developed to simulate the spherical nano-indentation of ion-irradiated metallic materials. Two critical features are addressed by the proposed theoretical framework, which include the pop-in event observed in the loading force-indentation depth (P−h) relations and irradiation hardening characterized by the transformed indentation stress-strain (ISS) curves. For the former, the pop-in event is dominated by the dislocation nucleation mechanisms, which are affected by both the density of irradiation-induced dislocation nucleation sites and indenter radii. For the latter, irradiation hardening is closely related to the heterogeneously distributed irradiation-induced defects within the irradiated layer with a limited depth. By applying the developed model to the spherical nano-indentation of helium-irradiated single crystal tungsten, it is informed that the simulated results can match well with corresponding experimental data, which include the unirradiated and irradiated P−h and ISS relations at different indenter radii. Moreover, the evolution of different hardening mechanisms during the indentation process is systematically analyzed, which can help comprehend the fundamental deformation mechanisms of ion-irradiated materials under spherical nano-indentation.

Mechanical properties of neutron-irradiated single crystal tungsten W(100) studied by indentation and FEM modelling

The aim of this work is to investigate the effect of high-temperature neutron irradiation on the mechanical properties of single-crystal tungsten W(100) studied by mechanical testing and modelling. Neutron irradiation up to 0.12 displacements per atom was performed at 600, 800, 900 and 1200 °C in the Belgium material test reactor BR2 at SCK•CEN in Mol. The mechanical properties of the irradiated tungsten were assessed by impulse excitation and depth-sensing indentation measurements. The values of Young's modulus, shear modulus and Poisson ratio are not affected by the irradiation. The mean hardness of the irradiated tungsten increases by 48, 45, 46, and 34% after irradiation at 600, 800, 900 and 1200 °C, respectively. The results obtained by the instrumented hardness tests were used as input for the finite element method model, applied to deduce the contributions coming from the neutron irradiation defects to the plastic deformation upon the indentation process, which include the impediment of gliding dislocations by sessile defects and modification of surface morphology due to the inhibited strain hardening ability through the dislocation-defect interaction. The validation of the fitted constitutive laws was realized by the crystal plasticity finite element method (CP-FEM) model which was applied to simulate the indentation load-depth curves, with certain assumptions on the irradiation-induced microstructure, and to calculate the distribution of stress under the indenter to investigate the extension of the plastic zone in the process of the indentation.

Anisotropy in the hardness of single crystal tungsten before and after neutron irradiation

In this work, the hardness of single crystal tungsten (W) after low, medium and high temperature neutron irradiation, reaching up to 1200°C, is studied. Micro-hardness tests with Vickers pyramid indenter are performed on reference and neutron irradiated samples by varying the orientation of the indenter on the single crystal tungsten contact surface. Due to the availability of multiple slip systems, the anisotropy of the hardness is characterized to allow the construction of uncertainty bands as well as dependence of the absolute value of the hardness on the orientation of the indenter wedges and principal crystallographic axes of the crystal. The applied neutron fluence and flux is representative for the ITER reactor, where tungsten is selected as armour material for plasma facing components. The neutron irradiation is performed in the BR2 reactor with mixed neutron spectrum up to 1 dpa (end of life fluence for ITER) but with appropriate measures to reduce the thermal neutron flux, such that the spurious transmutation into rhenium is reduced. The hardness study is accompanied with a detailed microscale examination to deduce the true indenter surface area. As a result, the true values of the hardness accounting for the pile-up effects are obtained as a function rotation angle of the indenter. The variation of the hardness as a function of indenter orientation before and after irradiation is discussed based on the indenter-slip system geometry. A simple but efficient methodology is proposed to deduce the true hardness and its angle-dependent variation for single crystal tungsten.

Numerical simulations of thermal conductivity in void-containing tungsten: Topological feature of voids

Tungsten, as a promising candidate for plasma-facing material in the advanced fusion reactors, has to suffer heat loading and high-energy particle irradiation. Since numerous voids form in the grain interior and on the grain boundary during irradiation, the thermal transfer capacity of tungsten would face a grand challenge. Herein, we systematically investigate the thermal conductivity of void-containing tungsten using finite element method. To understand the relation between the topological features of void and the corresponding thermal response within a wide temperature range, we analyze the thermal conductivity of tungsten by considering the arrangements, shapes and rotation angles of voids. The effects of intra- and inter-granular voids on the heat transmission are examined. The numerical results show how the thermal conductivity of single-crystal tungsten can be independent of void distribution pattern and how the void shape can lead to an anisotropic effective thermal conductivity. The predicted thermal conductivities are compared with those of well-known models and experimental data. Apart from voids, the proportion of grain boundary is also considered to analyze its effect on the thermal resistivity. Finally, we show how the spatial distribution of voids influences the heat flow inside the crystalline phase and across the grain boundary.

Quantitative investigation of surface structure and interatomic potential with impact-collision ion scattering spectroscopy

Helium ion beam interactions with materials have important implications for magnetic confinement fusion, material modification, and helium ion microscopy. These interactions depend on the precise physics of how helium ions channel into the materials, which can vary greatly based on the local crystalline orientation. In this work, we performed a dedicated experiment to investigate helium ion channeling in a well-characterized tungsten single crystal. Time-of-flight impact-collision ion scattering spectroscopy was used to obtain multi-angle maps of the backscattering intensity for 3 keV He+ → W(111). We found that the backscattering intensity profile arising from helium ion channeling could be well described by a shadow cone analysis. This analysis revealed that subsurface W atoms as deep as the ninth monolayer contributed to the backscattering intensity profile. Binary collision approximation simulations were performed with MARLOWE to model the experimental maps with sufficient accuracy to allow for quantitative comparisons using reliability factors. These quantitative comparisons were applied to investigate how the W lattice structure and He–W interatomic potential affect the multi-angle maps.

Repulsion leads to coupled dislocation motion and extended work hardening in bcc metals

Work hardening in bcc single crystals at low homologous temperature shows a strong orientation-dependent hardening for high symmetry loading, which is not captured by classical dislocation density based models. We demonstrate here that the high activation barrier for screw dislocation glide motion in tungsten results in repulsive interactions between screw dislocations, and triggers dislocation motion at applied loading conditions where it is not expected. In situ transmission electron microscopy and atomistically informed discrete dislocation dynamics simulations confirm coupled dislocation motion and vanishing obstacle strength for repulsive screw dislocations, compatible with the kink pair mechanism of dislocation motion in the thermally activated (low temperature) regime. We implement this additional contribution to plastic strain in a modified crystal plasticity framework and show that it can explain the extended work hardening regime observed for [100] oriented tungsten single crystal. This may contribute to better understanding the increase in ductility of highly deformed bcc metals.

An atom probe tomography and inventory calculation examination of second phase precipitates in neutron irradiated single crystal tungsten

Tungsten is the prime candidate material for the plasma facing divertor system and first wall armor of future nuclear fusion reactors. However, the understanding of the microstructural and chemical evolution of pure tungsten under neutron irradiation is relatively unknown, in part due to a lack of experimental data on this topic. Here, single crystal tungsten has been irradiated in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory at a nominal temperature of 700–800 °C to damage levels of 0.1 and 1.8 displacements per atom (dpa). Inventory calculations of the neutron irradiation experiments have been used to track isotope generation and decay to inform atom probe tomography (APT) results in the determination of the transmutation-induced precipitate compositions. Furthermore, APT crystallography has been used to show the relationship between precipitates and matrix. The composition of the precipitates is shown to progress towards that of the σ-phase at the highest dose studied, with those precipitates lying along crystallographic planes similar to those of displacement-induced dislocations. This work also sets the framework for APT studies of materials that contain isotopic ratios far from those observed in the natural state.

3D HR-EBSD Characterization of the plastic zone around crack tips in tungsten single crystals at the micron scale

High angular resolution electron backscatter diffraction (HR-EBSD) was coupled with focused ion beam (FIB) slicing to characterize the shape of the plastic zone in terms of geometrically necessary dislocations (GNDs) in W single crystal in 3 dimensions. Cantilevers of similar size with a notch were fabricated by FIB and were deformed inside a scanning electron microscope at different temperatures (21 ∘C, 100 ∘C and 200 ∘C) just above the micro-scale brittle-to-ductile transition (BDT). J-integral testing was performed to analyse crack growth and determine the fracture toughness. At all three temperatures the plastic zone was found to be larger close to the free surface than inside the specimen, similar to macro-scale tension tests. However, at higher temperature, the 3D shape of the plastic zone changes from being localized in front of the crack tip to a butterfly-like distribution, shielding more efficiently the crack tip and inhibiting crack propagation. A comparison was made between two identically deformed samples, which were FIB-sliced from two different directions, to evaluate the reliability of the GND density estimation by HR-EBSD. The analysis of the distribution of the Nye tensor components was used to differentiate between the types of GNDs nucleated in the sample. The role of different types of dislocations in the plastic zone is discussed and we confirm earlier findings that the micro-scale BDT of W is mainly controlled by the nucleation of screw dislocations in front of the crack tip.

Trends in vacancy distribution and hardness of high temperature neutron irradiated single crystal tungsten

The aim of the present study is to extend the knowledge about the formation and thermal stability of vacancy-type defects in tungsten under neutron irradiation, thereby mimicking the temperature and neutron flux expected in the ITER divertor. Neutron irradiation of single crystal tungsten, W(100), in the temperature range 600-1200 °C is performed up to 0.12 dpa. Positron annihilation spectroscopy is employed to detect the presence of open volume defects, while hardness tests are applied to relate the irradiation-induced defects with the modification of mechanical properties. Rationalization of the experimental results is enhanced by the application of a kinetic Monte Carlo simulation tool, applied to model the microstructural evolution under the neutron irradiation process. The relation between radiation microstructure and hardness is explained via a dispersed barrier model.

Deformation and fracture of crystalline tungsten and fabrication of composite STM probes

Fracturing microscale constrictions in metallic wires, such as tungsten, platinum, or platinum-iridium, is a common fabrication method used to produce atomically sharp tips for scanning tunneling microscopy (STM), field-emission microscopy and field ion microscopy. Typically, a commercial polycrystalline drawn wire is locally thinned and then fractured by means of a dislocation slip inside the constriction. We examine a special case where a dislocation-free microscale constriction is created and fractured in a single crystal tungsten rod with a long side parallel to the [100] direction. In the absence of dislocations, vacancies become the main defects in the constriction which breaks under the tensile stress of approximately 10 GPa, which is close to the theoretical fracture strength for an ideal monocrystalline tungsten. We propose that the vacancies are removed early in the tensile test by means of deformation annealing, creating a defect-free tungsten constriction which cleaves along the W(100) plane. This approach enables fabrication of new composite STM probes which demonstrate excellent stability, atomic resolution and magnetic contrast that cannot be attained using conventional methods.

Characteristic Regularities in Condensation of Nickel Layers on the Surface of a Tungsten Single Crystal

Condensation and adsorption of Ni with a thickness from several tenths of a monoatomic layer to several hundred layers on the surface of a single-crystal W tip has been studied by field emission microscopy in a wide range of surface temperature T. In contrast to adsorption of Si on W, adsorption of Ni on W does not induce any W surface reconstruction in the entire range of substrate temperatures T. Phenomena of bulk diffusion and field reconstruction of the surface are not observed as well. At multilayer Ni coatings, Ni crystallites with peculiar structure and faceting grow on the W surface (on close-packed and loose W faces at small and large T values, respectively). The presence of a strong external electric field makes it possible to retain crystallites on the W surface at temperatures much higher than their dissolution temperature in the absence of an external field.

D retention and depth profile behavior for single crystal tungsten with high temperature neutron irradiation

Single crystalline W (tungsten) samples irradiated at 633, 963 and 1073 K by neutrons to a damage level of 0.1 dpa were exposed to a high-flux D (deuterium) plasma at 673, 873 and 973 K, respectively, in TPE (Tritium Plasma Experiment) at INL (Idaho National Laboratory). Deuterium desorption was analyzed by TDS (Thermal Desorption Spectroscopy), and D depth profiles were determined by NRA (Nuclear Reaction Analysis) at SNL (Sandia National Laboratories). HIDT (Hydrogen Isotope Diffusion and Trapping) simulation code was applied to evaluate D behavior for neutron-damaged W at higher temperature.The D retention at depths up to 3 μm for the neutron-damaged sample at 673 K was two orders of magnitude larger than that for undamaged tungsten, and its D desorption spectrum had a single broad stage at around 900 K. As the neutron irradiation/plasma exposure temperature increased, D retention was largely reduced, and the desorption temperature was shifted to higher temperatures above 1100 K. The D depth profiles by NRA also showed D migration toward bulk by higher temperature irradiation, compared to undamaged W.The HIDT simulation indicated that the major binding energy of D was changed from 1.43 eV to 2.07 eV at higher neutron irradiation and plasma exposure temperatures, suggesting that some vacancies and small vacancy clusters would aggregate to form larger voids, or depopulation of weak traps at high D plasma exposure temperatures. It can be said that more stable trapping sites played dominant roles in the D retention at higher neutron irradiation and plasma exposure temperature. The binding energy by HIDT simulation was almost consistent with the reported value by TMAP, but the consideration of not only total D retention measured by TDS but also D depth profile by NRA led to the more accurate D behavior in neutron-damaged W.

Molecular dynamics study of tensile behaviour for cold and linear friction welded single crystal tungsten

In the present paper, single crystal tungsten model has been established by using molecular dynamics simulation. The joining of two single-crystal tungsten has been shown using two different welding techniques namely Cold welding and Linear Friction Welding (LFW) at room temperature. The tungsten atom interactions have been developed using the Embedded Atom Method potential. The Radial Distribution Function (RDF) simulation has been performed for two different layer thickness around the welded region for structural analysis. It has been found that as the layer thickness increases the probability of getting perfect structure atoms in long range order decreases. It has also been observed that few dislocations are generated during welding. The tensile properties have also been investigated for the sample joined by two processes for 50 ps, 100 ps and 150 ps at a strain rate of 1.5 × 109 sec−1. The results show that the joint developed by cold welding process at 100 ps resulted in a yield strength of 3588 MPa and ultimate strength of 6678 MPa. During LFW yield strength (5152 MPa) and ultimate strength (7172 MPa) is achieved in less welding time i.e. 50 ps.