Vacancy Flux Research Articles

A phase-field study to explore the nature of the morphological instability of Kirkendall voids in complex alloys

The present research explores theoretical and computational aspects of the morphological instability of Kirkendall voids induced by a directed flux of vacancies. A quantitative phase-field model is coupled with a multi-component diffusion model and CALPHAD-type thermodynamic and kinetic databases to obtain a meso-scale description of Kirkendall void morphologies under isothermal annealing. The material under investigation is a diffusion couple consisting of a multi-phase multi-component single-crystal Ni-based superalloy on one side and pure Ni on the other side. The flux of the fastest diffuser in the superalloy, Al, towards the pure Ni causes a strong flux of vacancies in the opposite direction. This directed flux of vacancies leads to morphologically instable growth of voids. Phase-field simulations are performed in two (2D) and three dimensions (3D) to understand these instabilities, and the results are compared with experimental observations obtained by synchrotron X-ray tomography. Finally, the simulation results are analyzed with respect to the Mullins–Sekerka linear stability criterion.

Improved passivation performance of selective laser melted Inconel 718 alloy via tempering treatment

The passivation performance of the selective laser melted Inconel 718 alloy after tempering treatments was investigated, and the underlying mechanism for the improved passivation film protectiveness was explored. The dislocation reversion and the mitigated segregation of Nb, Mo and Ti at Laves and δ phases decreased the storage energy of lattice distortion were critical factors for the formation of more protective passivation film in chloride-containing solutions. The film formation rate increased after tempering, presenting the increased electric field strength and the decreased dissolution rate accordingly, as well as for the point defect diffusion coefficient and the oxygen vacancy flux therein.

Effects of stress relief annealing in NGO steels

The effect of stress relief annealing (SRA) has been investigated on two classes of non-grain oriented (NGO) steels and with different sheet thickness. Magnetic properties were measured on mechanically sheared and water jet cut Epstein strips before and after SRA treatment at 800 °C in a nitrogen gas atmosphere. Significant improvement in power loss was achieved for the steel with lower aluminium content after SRA but the effect was much smaller for steel with the higher aluminium level, especially for thinner sheets where the SRA treatment was actually deleterious. No change in steel chemistry after SRA was found that could explain these differences. Microstructural examination showed residual dislocation substructures due to shearing before SRA and recrystallisation along the sheared edges together with recovery of the dislocation structures afterwards.A completely new finding was the presence of dislocation loops after SRA in the steel with higher aluminium content. These were not present previously but were created during the heat treatment. The presence of these dislocation loops is proposed as the reason for the weak or adverse effect of SRA on power loss. Detailed electron microscopy revealed that there are two families of dislocation loops having either Burgers’ vectors of a 〈100〉 lying on {100} planes or a√3/2 〈111〉 on {111 planes}. A model is presented whereby oxidation which occurs at the sheet surfaces causes a concentration gradient within which the Al atoms diffuse. This process necessitates a balancing flux of vacancies diffusing into the interior. When the content of vacancies exceeds the equilibrium content they agglomerate and ‘precipitate’ out as vacancy dislocation loops.

Effects of A-site potassium doping on oxygen permeability and intermediate-low temperature stability of Ba0.5Sr0.5Co0.8Fe0.2O3−δ membranes

Ba0.5Sr0.5Co0.8Fe0.2O3-δ (BSCF) perovskite membranes process excellent oxygen permeation flux at high temperature. However, the time-dependent flux degradation of BSCF restricts its industrial application at intermediate-low temperature. To address this issue, a series of K+ doped BSCF perovskite materials were prepared by EDTA-citric acid combined complexing method. The effect of K+ introduction on crystal structure, oxygen vacancy concentration, oxygen permeability and flux degradation of BSCF was systematically investigated. The results indicates that BSCF doped with K+ exhibits typical cubic perovskite structure and optimized oxygen permeability while the doping content of K+ is lower than 20%. Meanwhile, the oxygen permeability of BSCF can be significantly improved by introducing K+ ions, where the highest oxygen permeation flux of K0.05Ba0.45Sr0.5Co0.8Fe0.2O3-δ could reach up to 2.70 ml.min-1.cm-2. And a stable intermediate-low temperature oxygen permeation flux of 0.81 ml.min-1.cm-2 at 750 oC for 90 h can be realized for K0.1Ba0.4Sr0.5Co0.8Fe0.2O3-δ and no obvious flux degradation can be found.

Simulation of the atomic structure near spherical void in aluminum and the calculation of the anisotropy of the void growth rate

We simulate structure in the vicinity of different size nanovoids using a new variant of the Molecular Statics, wherein atomic structure in the vicinity of nanovoids and the parameters that define the displacements of atoms placed in elastic continuum around main computation cell are determined in a self-consistent manner. Then, the previously obtained kinetic equations are applied to calculate the shifting rate of the elements of the void surface in certain crystallographic directions. These equations take into account the dependence of the vacancy flux on the deformation fields. The displacement rates in different crystallographic directions for bcc and fcc metals are significantly different. The results show that the effects studied by computer simulation can lead to a change in the shape of initially spherical nanopores and cause their transformation into cuboidal pores in metals with a cubic structure under irradiation.

Effects of Carbon on Void Nucleation in Self-Ion–Irradiated Pure Iron

Impurities such as carbon atoms play a significant role in the void swelling of irradiated metals. The phenomenon is important to both materials designs in which impurities are intentionally introduced and accelerator-based ion irradiation testing in which impurities are introduced unintentionally as contaminants. Here, we report rate theory simulations of void nucleation in pure Fe, which are irradiated by 5-MeV Fe ions, as one typical irradiation condition used in nuclear material testing. Based on kinetics obtained previously from ab initio calculations, Multiphysics Object-Oriented Simulation Environment (MOOSE)–based numerical solvers were used to simulate defect distributions and void nucleation. Vacancy-carbon interactions increase the effective migration energies of carbon and decrease the diffusivity prefactors. The vacancy mobility reduction decreases both interstitial flux and vacancy flux. However, the vacancy flux reduction is more significant than that of interstitials, leading to reduced void nucleation in bulk. On the other hand, reduced vacancy flux toward the surface leads to local vacancy pileups, leading to locally enhanced void nucleation. These two combined effects make the void nucleation profile deviate from the displacements per atom (dpa) peak, and void swelling peaks shift to the near-surface region. The transition from deep swelling to near-surface swelling is plotted as a function of dpa rate, carbon concentration, and temperature. The study shows that the swelling peak shifting caused by the carbon effect can be avoided by either reducing dpa rates or increasing irradiation temperatures. The study is important to understand swelling behaviors and to optimize irradiation parameters for accelerator-based swelling testing.

Irradiation temperature and dose rate dependence of void swelling in RAFM steel during irradiation: Reaction rate theory analysis

Reaction rate theory analysis has performed to investigate the irradiation temperature and dose rate dependence of void swelling of RAFM steel under a wide range of irradiation temperatures and dose rates (250 to 620 °C and 10−7 to 10−3 dpa/s) with focusing on nucleation behavior of voids. In the rate theory analysis, an improved nucleation model is employed where the stable nucleus size of voids is estimated by the vacancy flux into/from voids which depends on irradiation condition and void size. The calculation says that the void swelling strongly depends on irradiation temperature and dose rate, and there is one unique peak temperature for each dose rate. As dose rate increases, the peak temperature shifts to higher temperatures and the peak swelling decreases; this results from the enhancement and suppression of void nucleation. The calculated stable nucleus size of voids remarkably depends on irradiation conditions and varies widely from 5 to about 50: the nucleus size drastically increases at higher temperatures, while it decreases at higher dose rates. For the dose rate dependence of the peak temperature of void swelling, the calculation provides a good agreement with the experiment more than a conventional model.

Effect of stacking order in cylindrical geometry on the growth of ZnAl2O4 spinel phase

Growth kinetics of ZnAl2O4 spinel phase was followed in double layered nanotubes (DLNTs), i.e. in cylindrical geometry in two different layer sequences. DLNTs were annealed at 700 °C in ambient atmosphere for different times. ZnAl2O4 phase formed due to solid-state reaction. To follow the growth kinetics of the spinel, thin lamellae were prepared from the cross sections of the tubes and studied in a transmission mode scanning electron microscope (TSEM). The phase grows parabolically with time, independently of the layer sequence. The growth rate was higher in the )ZnO)Al2O3) layer sequence, than for the reverse case. This can be explained by the competing vacancy fluxes induced by mechanical stress developing during the solid-state reaction and by the difference in the diffusion fluxes of the two constituents. This is the first case that the influence of closed geometry and layer sequence on spinel growth between two oxide layers has been experimentally investigated.

Localized corrosion and repassivation behaviors of additively manufactured titanium alloys in simulated biomedical solutions

The localized corrosion behavior of additively manufactured (AM) titanium alloys is studied based on the relation between pitting potentials, the flux of oxygen vacancies in a passive film, and the repassivation rate using potentiodynamic polarization, Mott–Schottky, and an abrading electrode techniques. The relationship between the localized corrosion resistance and the repassivation behaviors of AM titanium alloys was explained by the survival probability constant based upon the point defect model which describe the generated oxygen vacancies and accumulated cation vacancies affect the occurrence of the localized corrosion. Localized corrosion can be initiated by survival pits under sufficient conditions of the breakdown passive films. Survival probability is constant means a quantitative probability value of the transition from metastable pit to stable pit to occur localized corrosion. The higher the survival probability constant of AM titanium alloys, the more difficult repassivation and the easier occurrence of localized corrosion.

The electronic properties and surface chemistry of passive film on reinforcement: Effect of composition of simulated concrete pore solution

The effect of composition of simulated concrete pore solution on the electronic properties and surface chemistry is investigated. Compared to NaOH, Ca(OH)2 adsorption increases donor density and vacancy flux, decreases defects diffusion coefficient and accelerates the oxidation of FeⅡ, resulting in lower film resistance, and higher quasi-steady-state current density and roughness. Other elements, including Al, Si and S, make extracted cement pore solution (ECP) even more protective than NaOH. The FeII-rich inner layer causes the shallow donor density to increase at first and then stabilize, whereas the FeIII-rich outer layer causes the deep donor density to increase over time.

Understanding effects of chemical complexity on helium bubble formation in Ni-based concentrated solid solution alloys based on elemental segregation measurements

Helium bubble formation and swelling were systematically studied in Ni-based concentrated solid solution alloys containing different numbers and types of elements. Our microscopy analysis showed that although increasing the alloy chemical complexity helps suppress bubble formation in general, there is no monotonic relationship between the bubble growth rate and the number of alloying elements. Certain elements (e.g., Fe and Pd) are more effective in suppressing bubble growth than others (e.g., Cr and Mn). Atom probe tomography was applied to accurately measure elemental segregation around bubbles, revealing unique effects of certain alloying elements on vacancy migration towards bubbles. More specifically, the high vacancy mobility via Cr sites leads to a large vacancy flux and an increased bubble size, while the high degree of atomic size mismatch introduced by Pd helps deflect vacancy flow away from bubbles and decrease the amount of swelling. The effects identified in this study provide new strategies to design concentrated solid solutions with superior resistance to swelling.

Modelling the growth and filling of creep-induced grain-boundary cavities in self-healing alloys

A set of numerical and analytical models is presented to predict the growth and contraction of grain-boundary creep cavities in binary self-healing alloys. In such alloys, the healing is realised by preferential precipitation of supersaturated solutes at the free surface of the cavity. The cavity grows due to the diffusional flux of vacancies towards the cavity, which is driven by the stress gradient along the grain boundary. Upon deposition of healing solute atoms on the cavity wall, effectively vacancies are removed from the cavity due to the inverse Kirkendall effect. The competition between the inward and outward vacancy fluxes results in a time-dependent filling ratio (i.e. the fraction of the vacancies removed from the original cavity) of the creep cavity. It is found that for stress levels lower than a critical stress σcr, the filling ratio can proceed to unity, i.e. to complete filling and annihilation of the pore. For applied stresses higher than σcr, complete filling is not achieved and the open volume of the creep cavity will continue to grow once a maximum filling ratio is reached at the critical time tcr. The critical stress σcr, critical time tcr, and time for complete filling th (if fully filling is achievable) are derived from the models for different combinations of parameters. The results from the analytical model and from previous nanotomography experiments are compared and are found to be in good agreement.Graphical abstract

Metastable pitting corrosion behavior of laser powder bed fusion produced Ti-6Al-4V in Hank’s solution

The metastable pitting corrosion behavior of laser powder bed fusion (LPBF) produced Ti-6Al-4V is still unclear. Therefore, this work investigated the metastable pitting corrosion of LPBF-produced Ti-6Al-4V in Hank’s solution by electrochemical methods. The LPBF-produced sample (dominant by α′ phase in the microstructure) shows a higher frequency of pit nucleation than the annealed counterpart (composed by α + β dual phase). The passive films formed on the LPBF-produced sample exhibit a higher flux of oxygen vacancies, resulting in the absorption of more aggressive ions (e.g., Cl-) thereby producing more cation vacancies. The condensation of excessive cation vacancies contributes to the pit nucleation.

Onset of electronic conductivity in nanometer thick films of yttria stabilized zirconia (YSZ) at high electric fields

Electrochemical cells were prepared on a silicon wafer consisting of a 100 nm thick solid electrolyte of yttria stabilized zirconia (YSZ) prepared by atomic layer deposition (ALD), a bottom Ruthenium and an upper Gold electrode. Constant voltages were applied to the cells and currents were measured at temperatures between 120 °C and 170 °C. After an incubation time stationary currents were measured corresponding to conductivities well above the ionic one of the YSZ. After the polarization an open circuit voltage remained, which was reduced to zero by passing a constant depolarization current through the cell. All results were explained qualitatively and quantitatively assuming reactions with the electrodes and internal reactions within the YSZ. The latter lead to virtual electrodes with high electronic conductivity between which unreacted YSZ exists, i.e. a n/i/p junction forms. A stationary flux of single charged vacancies through the unreacted YSZ is assumed leading to the final stationary current. The calculated characteristic time for reaching this steady state is shown to be the incubation time, which in agreement with the experiment is inverse proportional to both the second power of electric field strength and the diffusion coefficient of oxygen vacancies.

Diffusion rates of hydrogen defect species associated with site-specific infrared spectral bands in natural olivine

We investigated hydrogen transport in naturally occurring, iron-bearing samples of San Carlos olivine that were hydrogenated at confining pressures of 200 or 300 MPa and 1173 to 1303 K or dehydrogenated at room pressure and 1191 to 1358 K. Chemical diffusion coefficients were determined from diffusion profiles for individual O-H-stretching bands from series of infrared spectra in orthogonal directions across each sample. Within experimental uncertainty, the diffusivities associated with all the individual bands are in good agreement with one another in both the hydrogenation and the dehydrogenation experiments. Hydrogenation proceeds by two diffusion mechanisms, as reported previously. The faster process involves interstitial diffusion of protons coupled with a counter-flux of polarons, with proton diffusion rate-limiting hydrogenation. For this mechanism, diffusion is faster along the olivine [100] direction than along [010] and [001], consistent with the anisotropy reported for proton diffusion and conductivity in olivine. The slower process involves interstitial proton diffusion coupled with a parallel flux of metal vacancies, with vacancy diffusion rate-limiting hydrogenation. For this mechanism, diffusion is faster along [001] than along [100] and [010], consistent with the anisotropy previously reported for the diffusion of metal cations in olivine. Diffusivities from our new dehydrogenation experiments are identical in both magnitude and anisotropy to those determined in our earlier hydrogenation experiments. This agreement demonstrates the validity of studies that used the results of our hydrogenation experiments to analyze dehydrogenation profiles in olivine xenocrysts and olivine in mantle xenoliths to determine rates of magma ascent from the source regions in Earth's interior.

МОДЕЛЮВАННЯ ПОРОУТВОРЕННЯ ПРИ РЕАКЦІЙНІЙ ДИФУЗІЇ У БІНАРНІЙ СИСТЕМІ

The proposed model of void formation takes into account existence two types of sinks/sources of non-equilibrium vacancies, depending on their location: in the phase volume and at the interfacial boundaries. At the interdiffusion and reaction diffusion which happens on the vacancy atomic diffusion mechanism, the inequality of atoms fluxes is caused by their differential mobility, give rise to a directional flux of vacancies. This flux of vacancies cause an appearance of areas in a diffusion zone with supersaturation and deficiency in vacancies, where sinks/sources of non-equilibrium vacancies act. It is believed that the voids arise with a certain periodicity near the interfacial boundary, where there is a vacancy supersaturation due to the different mobility of the components. The voids move in volume of growing phase, their sizes change. The void radius increases as long as void is in the region of the diffusion zone where there is a vacancy supersaturation. The void radius begins to decrease if the void is in the area of the diffusion zone, where there is a negative vacancy supersaturation (the concentration of vacancies is less than the equilibrium) until it disappears. The study of the influence on the kinetics of void formation during reaction diffusion in the binary system of sinks/sources of vacancies was carried out by computer simulation. In the case of efficient operation of vacancies sinks/sources only at the borders (vacancies sinks/sources do not work in the phase volume) we get a significant saturation of vacancies in the diffusion zone, which leads to rapid voids growth and the existence of significant pore size differences. If the vacancies sinks/sources in the volume work well (the efficiency of their work at the interfacial boundaries does not affect the result in this case), then almost everywhere in the system an equilibrium concentration of vacancies is established, as a result of which the vast majority of pores have the same (maximum) size. The pore sizes are much smaller than with the previous case.

Evolution mechanisms of irradiation-induced helium bubbles, C15 clusters and dislocation loops in ferrite/martensite steels: A cluster dynamics modeling study

• Evolution of helium bubbles , C15 clusters and dislocation loops is studied by a cluster dynamics model. • The model considers the formation of C15 clusters and followed transformation into loops. • Irradiation temperature and dose effects on the microstructural evolution are analyzed. • Helium bubble evolution upon irradiation is governed in sequence by three phases. • Loop growth driven by long-term defect migration follows a power law. Using a cluster dynamics model, we studied the evolution of helium bubbles, C15 clusters and dislocation loops produced by Fe 3+ /He + dual ion beam irradiation in reduced activation ferrite/martensite Eurofer97 steels. The model reasonably reproduced size distributions of experimentally detected helium bubbles and dislocation loops. We show that bubble evolution upon irradiation was governed by three phases in sequence: bubble nucleation dominated phase controlled by irradiation cascade, coupled phase of bubble nucleation and growth, and bubble growth dominated phase. As a first attempt, the model considers the formation of widely reported C15 clusters and develops a scheme for C15 clusters transformation into loops. We show that the loop growth driven by long-term defect migration follows a power law f(n) ~ a/n S . The increase of irradiation temperature from 603 K to 673 K promoted the growth of C15 clusters resulting in pronounced loop evolution. While at 773 K, the high flux of vacancies and low fluxes of single, di- and tri-interstitials suppressed loop nucleation and growth, leading to no loop formation confirmed by experiment. The effectiveness of the model developed in this study demonstrates its potential to be used in similar irradiation cases.

Simulation of TiN/HfO2/Pt memristor I–V curve for different conductive filament thickness

The operation of the TiN/HfO2/Pt bipolar memristor has been simulated by the finite elements method using the Maxwell steady state equations as a mathematical basis. The simulation provided knowledge of the effect of conductive filament thickness on the shape of the I-V curve. The conductive filament has been considered as the highly conductive Hf ion enriched HfOx phase (x < 2) whose structure is similar to a Magneli phase. In this work a mechanism has been developed describing the formation, growth and dissolution of the HfOx phase in bipolar mode of memristor operation which provides for oxygen vacancy flux control. The conductive filament has a cylindrical shape with the radius varying within 5–10 nm. An increase in the thickness of the conductive filament leads to an increase in the area of the hysteresis loop of the I-V curve due to an increase in the energy output during memristor operation. A model has been developed which allows quantitative calculations and hence can be used for the design of bipolar memristors and assessment of memristor heat loss during operation.

Simulation of TiN/HfO2/Pt memristor I–V curve for different conductive filament thickness

The operation of the TiN/HfO2/Pt bipolar memristor has been simulated by the finite elements method using the Maxwell steady state equations as a mathematical basis. The simulation provided knowledge of the effect of conductive filament thickness on the shape of the I–V curve. The conductive filament has been considered as the highly conductive Hf ion enriched HfOx phase (x < 2) whose structure is similar to a Magneli phase. In this work a mechanism has been developed describing the formation, growth and dissolution of the HfOx phase in bipolar mode of memristor operation which provides for oxygen vacancy flux control. The conductive filament has a cylindrical shape with the radius varying within 5–10 nm. An increase in the thickness of the conductive filament leads to an increase in the area of the hysteresis loop of the I–V curve due to an increase in the energy output during memristor operation. A model has been developed which allows quantitative calculations and hence can be used for the design of bipolar memristors and assessment of memristor heat loss during operation.

Irradiation-induced segregation at dislocation loops in CoCrFeMnNi high entropy alloy

To understand the redistribution of alloying elements in high entropy alloys under irradiation, a CoCrFeMnNi alloy was irradiated with 1 MeV Kr ions at room temperature and at 500°C, and characterized with atom probe tomography and transmission electron microscopy. At 500°C, Co and Ni were enriched around the interstitial, faulted and perfect, dislocation loops resulted from the ion irradiation. In contrast, no segregation was observed at room temperature. The inverse Kirkendall effect through vacancy flux, as opposed to the interstitial binding mechanism, was the primary underlying process attributing to the observed segregation. In addition, a ring-shaped segregation pattern was observed at the faulted dislocation loops, indicating a non-equilibrium nature of the defect clustering and solute segregation process in CoCrFeMnNi under irradiation at high temperature.