Mixed Dumbbell Research Articles

First-principles study of Re in BCC-Mo: Diffusion behavior and interaction with point defects

Due to their some beneficial properties, molybdenum-based alloys, such as Mo-Re alloys, are recognized as potential structural materials for nuclear power reactors. Irradiation induced precipitation of rhenium (Re) atoms causes hardening and embrittlement of Mo-Re alloys, restricting their application. The interaction of rhenium (Re) atoms with point defects (PDs), as well as the diffusion behavior of Re atoms in BCC-Mo (Body Center Cubic-molybdenum), were investigated using first-principles methods. The results revealed that Re atoms exhibited high binding energies with both vacancy (Vac) and interstitial dumbbells. Furthermore, the binding energies increased with the number of Re atoms. The binding energies of Re with self-interstitial dumbbell (SIA, ie., Mo-Mo) and mixed interstitial dumbbell (Mo-Re) were quite close to. Due to the high exchange barrier between Vac and Re, the diffusion of rhenium through the vacancy-drag mechanism was difficult. Due to the low migration and rotation barrier of Mo-Re mixed interstitial dumbbell, the diffusion of Re atoms in Mo was dominated by the interstitial-mediated mechanism. From the perspective of diffusion dynamics, only interstitial dumbbells can promote the aggregation of Re atoms. By comparing the binding energy of interstitial dumbbell with interstitial dumbbell and interstitial dumbbell with Re atoms, pairs of Mo-Re interstitial dumbbell was suggested to be the nucleation sites to attract more interstitial dumbbells, thereby promoting the precipitation of Re clusters. It was because they had high binding energy and were difficult to decompose once combined.

The evolutionary process of W-V mixed dumbbell in tungsten crystals: A study about W-V alloy as a plasma-facing material in fusion devices

Alloying is widely used to improve the radiation resistance of plasma-facing materials. The first-principles method based on density function theory was used in this work to study the stability and mobility properties of the W-V mixed dumbbell pair. The diffusion of monovacancy and recovery of mixed dumbbell pairs were also studied. The rotations and diffusion results indicated that the W-V mixed dumbbell pair diffusions are favored in two/three-dimensional motion because of low energy barriers. And the results are also suggested the mixed dumbbell lowers the diffusion energy barriers of the monovacancy. New vacancy diffusion modes were also observed along the 〈110〉 direction during the simulation. Besides, the addition of V may also moderate the diffusion of W SIA in 〈111〉 direction.

First-principles calculations to investigate thermodynamic and mechanical behaviors of molybdenum-lanthanum alloy

ABSTRACT Using first-principles calculations, we have performed the detailed researches on La behavior in Mo including structure, thermodynamic stability, interaction with vacancy, and mechanical properties of Mo-La alloy. La prefers to stay at substitution site with the solution energy of 2.86 eV. The <111> mixed dumbbell is more stable than both <100> and <110> mixed dumbbells. The La-La interaction displays attraction and repulsion in short- and long-distance range, respectively. Both 1nn and 2nn shells are most likely to form the La-La clusters since there are relatively larger binding energies, which are 0.43 and 0.33 eV, respectively. The La-vacancy interaction is much local and limited within the 2nn shell range. At 1nn and 2nn shells, the binding energies of La-vacancy are 1.33 and 0.26 eV, respectively. Also, the mechanical properties of Mo1-xLax (0 < x < 0.1) binary alloys have been analyzed in detail. The mechanical quantities of single crystal are the elastic constants, Young’s modulus and shear modulus, while the mechanical quantities of poly-crystal include bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio v, Anisotropy factor A and B/G. These results can provide a much valuable reference for Mo-alloy application in nuclear fusion field.

Influence of titanium on the clustering of vacancy, rhenium and osmium in tungsten-titanium alloys: First-principles study

The formation of point defects including vacancies and interstitials and transmutation elements rhenium (Re), osmium (Os), tantalum (Ta), etc., has been reported to seriously degrade the mechanical properties of tungsten in a fusion environment. In this work, the aggregation behavior of between vacancy and rhenium or osmium, and the effect of Ti as the interstitial atoms on the transmutation element (Re or Os) are studied using first-principles calculation. We demonstrate that the addition of Ti or Re/Os will promotes the clusters of vacancy in the W-Ti alloys. Here, the concentration balance of the vacancy and Ti plays an important role in the aggregation of Re/Os atoms in W-Ti alloys. Furthermore, we found that doping of Ti induced vacancy migration, this plays a positive role in the recovery of the interstitial with the vacancies. Interestingly, the presence of Re/Os similarly promote the migration of vacancy to Ti sites, but Ti makes the migration of vacancy to Re/Os harder. Besides, we found the most stable configuration with <11h> mixed dumbbell in W-Ti (h∼0.50), Ti-Os (h∼0.34) and Ti-Re (h∼0.50) interstitial, in which The Ti-Re/Os interstitial with most stable <11h> dumbbell has a strong attractive to Re/Os atoms. Consequently, the formation of the Ti-Re/Os interstitial greatly promotes the Os/Re to clustering, and further increase the probability of radiation-induced precipitation in W-Ti alloys.

Interactions of solute atoms with self-interstitial atoms/clusters in vanadium: A first-principles study

The interactions of solute atoms with self-interstitial atoms (SIA)/clusters and their effect on stability of single SIAs and small SIA clusters in vanadium (V) were investigated using first-principles calculations. We calculated the binding energies of 16 substitutional solute elements (Cr, Ti, Al, Fe, Mo, Y, Nb, Cu, Mn, Ni, Ta, Zr, W, Si, S and P) with SIAs and found that the solute Cr/Fe/Mn/P/S prefers to form solute-V<111> mixed interstitial dumbbell. The interaction between solute Ti/Si/Y/Nb/Ta and <111> SIA dumbbell is attractive, while most of other solutes repel with the <111> SIA. The stable Cr- < 111> mixed interstitials and the Ti- < 111> SIA can attract five metal solutes (Ti, Y, Zr, Nb, and Ta), further stabilizing the SIA. The stability of small SIA clusters are determined and the parallel <111> SIA dumbbell clusters are the most stable configurations, followed by the parallel <110> SIA configurations. The small SIA clusters can attract three metallic solutes (Ti, Y and Zr) and two impurities (P and S), but will repel most solute atoms. The presence of solute atoms does not change the relative stability order among SIA clusters. The present calculations provide the basic data for understanding the influence solutes on the stability of SIAs/SIA clusters in V alloys under irradiation.

Interatomic potentials and defect properties of Fe–Cr–Al alloys

Fe–Cr–Al alloys have the potential to form a crucial class of enhanced accident tolerant fuel cladding materials in light water reactor due to their excellent oxidation resistance in high temperature steam environments. The irradiation resistant performance is also significant for the development and application of fission and fusion reactor materials. In this work, we developed a Fe–Cr–Al interatomic potential based on the Finnis–Sinclair (F–S) formulism, which can be used to describe the defect properties in Fe–Cr–Al alloys. The potential parameters for Fe–Cr–Al alloys were determined by fitting to a set of experimental results and density functional theory (DFT) calculations. Specifically, the formation energies of self–interstitial atoms and the stacking fault energy obtained from the present Al potential are consistent with the DFT results. The point–defect properties of Fe–Cr and Fe–Al alloys determined with the DFT calculations, such as the mixed (both Fe–Cr and Fe–Al) or pure (both Cr–Cr and Al–Al) dumbbells and the substitutions (both Cr and Al atoms) in the body–centered cubic (bcc) Fe matrix, are well reproduced by our atomistic simulations. Consequently, this parameterized potential is expected to be capable for atomistic simulations of irradiation defects and defect evolution in Fe–Cr–Al ternary systems.

Solute diffusion by self-interstitial defects and radiation-induced segregation in ferritic Fe–X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys

This work investigates solute transport due to self-interstitial defects and radiation induced segregation tendencies in dilute ferritic alloys, by computing the transport coefficients of each system based on ab initio calculations of binding energies, migration rates, as well as formation and migration vibrational entropies. The implementation of the self-consistent mean field method in the KineCluE code allows for the calculation of transport coefficients extended to arbitrary interaction ranges, crystal structures, and diffusion mechanisms. In addition, the code gives access to the diffusion and dissociation rates of small solute-defect clusters – in this case, vacancy- and dumbbell-solute pairs. The results show that the diffusivity of P, Mn, and Cr solute atoms is dominated by the dumbbell mechanism, that of Cu by vacancies, while the two mechanisms might be in competition for Ni and Si, despite the fact that the corresponding mixed dumbbells are not stable. Systematic positive radiation-induced segregation (RIS) at defect sinks is expected for P and Mn solutes due to dumbbell diffusion, and for Si due mainly to vacancy drag. Vacancy drag is also responsible for Cu and Ni enrichment at sinks below 1085 K. The RIS behavior of Cr is the outcome of a fine balance between enrichment due to the dumbbell diffusion mechanism and depletion due to the vacancy one. Therefore, for dilute Cr concentrations global enrichment occurs below 540 K, and depletion above. This threshold temperature grows with solute concentration. The findings are in qualitative agreement with experimental observations of RIS and clustering phenomena, and confirm that solute-defect kinetic coupling plays an important role in the formation of solute clusters in reactor pressure vessel steels and other alloys.

Atomistic simulations of the interaction between transmutation-produced Re and grain boundaries in tungsten

High energy neutron irradiation not only causes the transmutation of tungsten (W), but also induces transmutation elements to segregate and precipitate at grain boundaries. In this work, the segregation of transmutation-produced rhenium (Re) and their clusters at a Σ5(130) grain boundary (GB) in bulk W has been investigated by using both molecular dynamics and molecular statics methods. It is found that, for single interstitial, Re atom diffuses from the bulk to the GB region via a three-dimensional rotation and migration in the form of an interstitial 〈1 1 1〉 Re-W mixed dumbbell, because the rotation and migration barriers of a Re-W dumbbell are both small. When Re atoms are absorbed by the GB, it is noteworthy that Re atoms tend to occupy the substitutional sites near the GB. The segregation energy of interstitial Re is ranged from −7.67 to −6.12 eV, and the effective interaction distance between the GB and Re interstitials is about 7 Å, which increases with increasing the cluster size. By modeling the uniaxial tensile test of W-GB structure containing Re substitution clusters, the fracture strength and elongation of the GB are significantly reduced. The present results provide important insights into the detailed mechanisms of Re segregation at GBs and its possible effects on the mechanical properties of W-based materials.

Effect of Grain Boundary on Diffusion of P in Alpha-Fe: A Molecular Dynamics Study

In this study, we have investigated the effect of the grain boundary (GB) on the diffusion of a Phosphorus (P) atom in alpha-Fe using molecular dynamics simulations. A Fe-P mixed dumbbell is created in the six symmetric tilt grain boundary (STGB) models. The dumbbells are allowed to migrate at different temperatures from 400 K to 1000 K, with starting positions between 5 Å to 10 Å away from the GB core. The trajectories and mean square displacements (MSD) have been recorded to analyze the diffusion details. The Nudged Elastic Band (NEB) method has been used to study the energy barrier at different positions around the GBs. Our simulation results demonstrate that the GB structure affects the diffusion mechanisms of Fe-P dumbbell. The two low Σ favored GBs display significantly weak trapping effect, which is consistent with the formation energy distribution. The reduction in the migration barrier has been observed due to the decrease of distance from the GB center. Furthermore, the barriers of migration towards the GB are lower than the barriers of migration away from the GB. As evident by NEB calculation, absorption sink effect of GB has been observed. This effect saturates as the distance reaches 8 Å or more. Our simulation results provide an insight into the GB trapping effect in alpha-Fe.

The interactions between rhenium and interstitial-type defects in bulk tungsten: A combined study by molecular dynamics and molecular statics simulations

Tungsten (W) and W-based alloys are the leading candidates for plasma-facing materials (PFMs) in future fusion reactors. However, the high energy neutrons generated in fusion reactions not only result in cascade damages but also cause W transmutation. Both the irradiation defects and transmutation products, mainly rhenium (Re), have serious effects on the service behaviors of W PFMs. In this work, we have systematically investigated the interaction between Re and the self-interstitial atoms, self-interstitial clusters and 1/2<111> interstitial dislocation loops in bulk W using molecular dynamics and statics simulations. It is found that there is a strong attractive interaction between an interstitial W atom and a substitutional Re atom, forming a Re–W dumbbell that migrates 3-dimentionally due to the low migration and rotation energies. The small SIA clusters strongly bind with both the substitutional Re atoms and an interstitial Re atom (Re–W mixed dumbbell), thus decreasing the mobility of these clusters. The strong attractive interaction between a Re atom and a 1/2<111> interstitial dislocation loop occurs when the Re atom is located at the core of the loop, and also, their interaction distance along <111> direction is large. The mobility of the 1/2<111> interstitial dislocation loop decreases progressively with increasing Re concentration.

Solute Diffusion by Self-Interstitial Defects and Radiation-Induced Segregation in Ferritic Fe- &lt;i&gt;X&lt;/i&gt; ( &lt;i&gt;X&lt;/i&gt;=Cr, Cu, Mn, Ni, P, Si) Dilute Alloys

This work investigates solute transport due to self-interstitial defects and radiation induced segregation tendencies in dilute ferritic alloys, by computing the transport coefficients of each system based on ab initio calculations of binding energies and migration rates. The implementation of the self-consistent mean field method in the KineCluE code allows to extend the calculation of transport coefficients to arbitrary interaction ranges, crystal structures, and diffusion mechanisms. The results show that the diffusivity of P, Mn, and Cr solute atoms is dominated by the dumbbell mechanism, that of Cu by vacancies, while the two mechanisms might be in competition for Ni and Si, despite the fact that the corresponding mixed dumbbells are not stable. Systematic enrichment at defect sinks is expected for P and Mn solutes due to dumbbell diffusion, and for Si due mainly to vacancy drag. Vacancy drag is also responsible for Cu and Ni enrichment below 1085 K. The RIS behavior of Cr is the outcome of a fine balance between dumbbell enrichment and vacancy depletion. Therefore, for dilute Cr concentrations global enrichment occurs below 540 K, and depletion above. This threshold temperature grows with solute concentration. The findings are in agreement with experimental observations of RIS and clustering phenomena, and confirm that solute-defect kinetic coupling plays an important role in the formation of solute clusters in reactor pressure vessel steels and other alloys.

Interplay of solute-mixed self-interstitial atoms and substitutional solutes with interstitial and substitutional helium atoms in tungsten-transition metal alloys

In a fusion reactor environment, the irradiation of neutrons and helium (He) plasma produces a great number of self-interstitial atoms and vacancies in tungsten (W), which inevitably interact with alloying solutes to form mixed self-interstitial atoms and substitutional solutes. The interactions of solutes with He atoms affect the behaviors of both, and ultimately cause the formation of solute precipitates and He bubbles; however, the micro-mechanisms of this are still mysterious. In this work, we perform systematic ab initio calculations to study the mutual influence of solutes and He atoms on their behaviors. It is found that most of the considered solutes bind tightly with the most stable dumbbells forming mixed or dumbbells. Solute-mixed dumbbells can act as trapping centers for He atoms. Mixed dumbbells bind very tightly with interstitial He atoms and all the binding energies are larger than 1.0 eV. Compared with the energy for the formation of a W Frenkel pair with the presence of He, the energies needed for the formation of most solute-mixed Frenkel pairs are decreased while titanium, zirconium, niobium, hafnium, and tantalum-mixed Frenkel pairs are exceptions. Similarly, substitutional solutes can also trap interstitial and substitutional He atoms, and solutes bind stronger with interstitial He followed by and solutes while it is the opposite for interactions of substitutional solutes with substitutional He atoms. The underlying reasons controlling the interactions of mixed dumbbells and substitutional solutes with interstitial and substitutional He atoms are analyzed.

Atomistic simulation of phosphorus segregation to Σ3 (111) symmetrical tilt grain boundary in α-iron

Irradiation-induced grain boundary (GB) phosphorus segregation is an important factor for estimating the embrittlement of nuclear reactor pressure vessel steels, but the physical process of phosphorus migration to grain boundaries is still unclear. We numerically studied phosphorus migration toward a Σ3(111) symmetrical tilt GB in α-iron using molecular dynamics. We found that, in the vicinity of the GB within ∼1 nm distance, an iron–phosphorus mixed dumbbell and an octahedral interstitial phosphorus atom push a self-interstitial atom into the GB, and the phosphorus atom becomes a substitutional atom. A phosphorus-vacancy complex in the region also becomes dissociated, and the vacancy is absorbed in the GB without dragging phosphorus. The results claim that a novel view of the segregation process is required.

First-principles study of solvent-solute mixed dumbbells in body-centered-cubic tungsten crystals

Tungsten (W) is considered as a promising candidate for plasma-facing materials for future nuclear fusion devices, and selecting optimal alloying constituents is a critical issue to improve radiation resistance of the W alloys as well as to improve their mechanical properties. We conducted in the current study a series of first-principles calculations for investigating solvent-solute mixed dumbbells in W crystals. The results suggested that titanium (Ti), vanadium (V), and chromium (Cr) are favorable as solutes for W alloys from irradiation-effect perspectives because these elements are expected to promote vacancy-interstitial recombination without causing radiation-induced precipitation that reduces ductility of irradiated materials.

Towards understanding the mechanism of rhenium and osmium precipitation in tungsten and its implication for tungsten-based alloys

Using a first-principles method in combination with thermodynamic models, we investigate the interaction between rhenium/osmium (Re/Os) and defects to explore the mechanism of radiation-induced Re/Os precipitation in tungsten (W). We demonstrate that radiation-induced defects play a key role in the solute precipitation in W, especially for self-interstitial atoms (SIAs). The presence of SIAs can significantly reduce the total nucleation free energy change of Re/Os, and thus facilitate the nucleation of Re/Os in W. Further, SIA is shown to be easily trapped by Re/Os once overcoming a low energy barrier, forming a W-Re/Os mixed dumbbell. Such W-Re/Os dumbbell forms a high stable Re/Os-Re/Os dumbbell structure with the substitutional Re/Os atoms, which can serve as a trapping centre for subsequent interstitial-Re/Os, leading to the growth of Re/Os-rich clusters. Consequently, an interstitial-mediated migration and aggregation mechanism for Re/Os precipitation in W has been proposed. Our results reveale that the alloying elements-defects interaction has significantly effect on their behaviors under irradiation, which should be considered in the design of W-based alloys for future fusion devices.

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 material 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 W-2Re alloys. We use a generalized Hamiltonian for crystals containing point defects parametrized entirely with electronic structure calculations. Our model incorporates recently gained mechanistic information of mixed-interstitial solute transport, which is seen to control cluster nucleation and growth by forming quasispherical nuclei after an average incubation time of 13.5($\ifmmode\pm\else\textpm\fi{}8.5$) s at 1800 K. These nuclei are seen to grow by attracting more mixed interstitials bringing solute atoms, which in turn attracts vacancies leading to recombination and solute agglomeration. Owing to the arrival of both Re and W atoms from the mixed dumbbells, the clusters are not fully dense in Re, which amounts to no more than 50% of the atomic concentration of the cluster near the center. Our simulations are in qualitative agreement with recent atom probe examinations of ion-irradiated W-2Re systems at 773 K.

Stability of β″ nano-phases in Al-Mg-Si(-Cu) alloy under high dose ion irradiation

The microstructure of a 6061-T6 Al alloy subjected to ion irradiation at 95 and 165 displacements per atom (dpa) has been evaluated by transmission electron microscopy and atom-probe tomography. The initial microstructure of the alloy is dominated by needle-shaped β″ precipitates. After 95 dpa irradiation, the β″ precipitates display a slight lattice distortion and are partially dissolved, together with the formation of a new phase. After 165 dpa irradiation, the β″ precipitates are completely dissolved, the new phase has grown and a high density of clusters rich in Mg, Si, Cu and Cr is observed. The determination of ballistic versus radiation enhanced diffusion coefficients shows that enhanced diffusion is predominant for β” dissolution. The formation and growth of the new particles may be caused by radiation induced segregation. Solute drag by vacancies or mixed dumbbell interstitials migration could explain the diffusion of some elements as Si or Cr towards the new particles.

Interaction between solute atoms and radiation defects in Fe-Ni-Si and Fe-Mn-Si alloys under irradiation with proton ions at low-temperature

Isochronal annealing followed by residual resistivity measurements at 12 K was performed in Fe-0.6Ni-0.6Si and Fe-1.5Mn-0.6Si alloys irradiated with 1 MeV proton ions below 70 K, and recovery stages were compared with those of Fe–0.6Ni and Fe–1.5Mn. The effects of silicon addition in the Fe-Ni alloy was observed as the appearance of a new recovery stage at 282–372 K, presumably corresponding to clustering of solute atoms in matrix, and as a change in mixed dumbbell migration at 122–142 K. Silicon addition mitigated the manganese effect in Fe–Mn alloy that is obstructing the recovery of radiation defects. Reduction of resistivity in Fe-Mn-Si alloy also suggested formation of small solute atom clusters.

Migration of rhenium and osmium interstitials in tungsten

Tungsten is expected to be a promising plasma-facing material for future fusion devices, but radiation-induced precipitation (RIP), which leads the material to hardening, is a concern at their practical use. One of the keys to accurate prediction of the emergence of RIP is migration of solute atoms, rhenium and osmium, that are produced by nuclear transmutation through irradiation. We conduct a series of numerical simulations using an atomic kinetic Monte Carlo method and investigate the migration of these solute atoms in the form of tungsten–rhenium and tungsten–osmium mixed dumbbells, considered to be the most efficient ”carriers” of the solute atoms. We find that the low rotation energy barrier of these mixed dumbbells leading to three-dimensional migration greatly influences their diffusivities. The result also suggests that, although these dumbbells have three-dimensional motion, one cannot simply reduce their migration behavior to that of vacancy-like spherical objects.

Uranium mobility in face-centered cubic aluminium driven by interstitial migration

We characterize the solute mobility behavior driven by interstitial mechanism in FCC diluted alloys using a classical molecular static technique (CMS). In the same line of ideas as the multi-frequency model, we calculate the tracer self- and solute diffusion coefficients. Specifically, we perform our calculations for the Al –U diluted alloy. We verify that in the Al –U system, mixed dumb-bells are observed to be unstable and U mobility is driven by crowdions. From previous results of diffusion in same alloys containing only vacancies, qualitatively we conclude that, experimental data are in perfect agreement with previous calculations of solute U diffusion driven by a vacancy mechanism. Also we give a possible migration path for solute U atoms through interstitial migration, where we have found that U enhances the Al mobility in the alloy.