Number Density Of Clusters Research Articles

Dust in brown dwarfs and extra-solar planets

Context. Modelling the formation of cloud condensation nuclei (CCNs) is key for predicting cloud properties in planet and brown dwarf atmospheres. The large diversity of exoplanets (rocky planets, mini-Neptunes, giant gas planets) requires a fundamental approach to cloud formation modelling in order to allow a full analysis of observational data contributing to exoplanet characterisation. Aims. We aim to understand the onset of cloud formation and study the formation of TiO2-CCNs. The formation of (TiO2)N clusters as precursors to extrasolar cloud formation is modelled by two different methods in order to understand their potential, identify underlying shortcomings, and to validate our methods. We propose potential spectral tracers for TiO2-CCN formation. Methods. We applied three-dimensional Monte Carlo (3D MC) simulations to model the collision-induced growth of TiO2-molecules to (TiO2)N-clusters in the free molecular flow regime of an atmospheric gas. We derived individual, time-dependent (TiO2)N cluster number densities. For T = 1000 K, the results are compared to a kinetic approach that utilises thermodynamic data for individual (TiO2)N clusters. Results. The (TiO2)N cluster size distribution is temperature dependent and evolves in time until a steady state is reached. For T = 1000 K, the 3D MC and the kinetic approach agree well regarding the cluster number densities for N = 1 … 10, the vivid onset of cluster formation, and the long transition into a steady state. Collision-induced growth and evaporation simulated using a 3D MC approach enables a faster onset of cluster growth through nucleation bursts. Different size distributions develop for monomer-cluster and for cluster-cluster growth, with the largest clusters appearing for cluster-cluster growth. Conclusions. The (TiO2)N cluster growth efficiency has a sweet-spot temperature at ≈1000 K at which CCN formation is triggered. The combination of local thermodynamic conditions and chemical processes therefore determines CCN formation efficiency. The onset of cloud formation may be observable through the (TiO2)4, (TiO2)5, and (TiO2)6 vibrational lines, which may be detectable with the Mid-Infrared Instrument on the James Webb Space Telescope or the Extremely Large Telescope’s mid-IR imager, but more complete line-list data are desirable.

An Object Kinetic Monte Carlo Simulation for Defect Evolution of Neutron‐Irradiated Reactor Pressure Vessel Steels: Carbon Sensitive Study

Herein, the defect evolution in the FeCMnNi model alloy is investigated by the gray‐alloy method in an object kinetic Monte Carlo (OKMC) model. Based on the parameters of the Fe–C system, the influence of Mn and Ni is implicitly considered, and the migration energy of mobile defects is modified. The number density of interstitial clusters and vacancy clusters in simulation has a good agreement with experimental results. The defect evolution features versus carbon and solutes concentration are also studied. The simulation results show that the number density of defect clusters increases with increasing carbon or solutes concentration. The average size of interstitial clusters decreases, while the average size of vacancy clusters is hardly affected by increasing impurity/solutes concentration. The defect features do not show a saturation tendency with increasing carbon/solutes concentrations. It also seems the influence of solutes concentration is more sensitive on defect features than carbon concentration in this FeCMnNi alloy.

Migration energy of a self-interstitial atom in α-iron estimated by in situ observation of interstitial clusters at low temperatures using high-voltage electron microscopy

ABSTRACT Modeling cluster dynamics or rate theory to describe the microstructural evolution of irradiated materials requires a precise knowledge of the migration energy of a self-interstitial atom (SIA), a product of energetic particle radiation. We measured the evolution of the number density of SIA clusters in electron-irradiated α-iron at low temperatures (110–320 K) by in situ observation using high-voltage electron microscopy. We identified temperature-dependent physical quantities, including (1) the peak density of SIA clusters and (2) the critical defect-free zone thickness in a thin foil specimen, associated with interstitial mobility. By fitting these quantities to the Arrhenius relations derived by rate theory analysis, we obtained estimated interstitial migration energy values of and eV for (1) and (2), respectively.

Microstructural evolution at the initial stage of two-step aging in an Al-Mg-Si alloy characterized by a three dimensional atom probe

Microstructural evolution at the initial stage of two-step aging in an Al-0.9 Mg-1.0 Si (mass%) alloy was studied using 3DAP. The chemical composition, cluster size, number density, and volume fraction change were analyzed through the maximum separation method. This study confirmed that the clusters with Si-rich and Balanced compositions accounted for 97% of the total, and the larger the size, the more similar to the composition of the alloy. At two-step aging at 170 °C for 0.6 ks, the smaller and lower number density clusters were formed compared with the clusters formed after natural aging for 2419.2 ks. Thus, we found that the dissolution of the nanocluster predominantly occurred at the initial stage of two-step aging at 170 °C after natural aging for 2419.2 ks. Then, the cluster size was increased and the formation of pre-β" was dominant during two-step aging for 1.2 ks. The pre-β″, nuclei of β″, formed is considered to be similar to the Mg:Si ratio of β″. In order to investigate the internal structure change of clusters at the initial stage of two-step aging, the atomic number density of clusters with an average size of 2 nm or more was analyzed. The atomic number density for the two-step aging at 170 °C for 1.2 ks was higher than 30 nm-3, while the atomic density of natural aging for 2419.2 ks was lower than 30 nm-3. In Al-Mg-Si alloys, we propose for the first time that a nanocluster can act as the nucleus of precipitate, pre-β ", with a size and an atomic density of more than 2 nm and 30 nm-3. In addition, the relationship was analyzed between the hardness change, the volume fraction, and the number density in the initial stage of two-step aging.

Neutron irradiation induced defects and clustering in NF616 and T91

NF616 is a third-generation ferritic martensitic steel, developed to have better creep resistance than the prior generation T91. Unlike relatively numerous studies of T91, there is a lack of understanding of the irradiation effect on the microstructural evolution and mechanical response of NF616. This work evaluated the microstructures and radiation hardening of NF616 irradiated up to 8.2 displacement per atom (dpa) at 292 °C – 431 °C, compared with T91 from two heats. Dislocation loops were observed in all investigated samples. NF616 exhibited comparable loop size but slightly lower loop density than those in the general T91 heat at 430 °C. Cavities were only observed in NF616 at 431 °C but absent at lower irradiation temperatures (292 °C and 359 °C). Ni-rich clusters were also observed in NF616 at 431 °C, while only weak Ni-clustering were observed at lower irradiation temperatures. Compared to the general T91 heat, NF616 demonstrated better swelling resistance (e.g., one third of swelling in the general T91 heat at 430 °C), a slightly higher number density of Ni-rich clusters, and slightly lower radiation hardening. The low-carbon T91 showed the greatest hardening with the largest swelling and loop sizes, despite its lowest irradiation temperature and intermediate dose. The calculated hardening from loops, cavities and Ni-rich clusters using the classic dispersed barrier-hardening model had reasonable agreement with the experiment-derived results, with the primary hardening contribution attributed to dislocation loops.

Grouping Methods of Cluster Dynamics Model for Precipitation Kinetics

Due to its simplicity and efficiency, cluster dynamics modeling has been widely used to simulate microstructure evolution in materials, such as defect formation in metals. However, its computation cost becomes prohibitive when the clusters grow too large, so a particle-size-grouping method is often required. In this paper, three different size-grouping methods are compared with the exact solution of the ungrouped cluster dynamics model for Al3Sc precipitation in an Al-0.18 at.% Sc alloy. A new assumption of logarithmically-linear distribution of cluster number densities inside each size group is shown to be the most efficient way to match with all results of the ungrouped model. Finally, the calculated results are compared with the measured sizes and distributions of Al3Sc precipitates at different aging temperatures. The new size-grouping method is shown to have better accuracy for the chosen discretization and time-stepping method evaluated. This will enable significant computational savings, and the extension of time scales and cluster sizes to the ranges of realistic metallurgical systems, while preserving reasonable accuracy.

Full-sky photon simulation of clusters and active galactic nuclei in the soft X-rays for eROSITA

The eROSITA X-ray telescope on board the Spectrum-Roentgen-Gamma (SRG) mission will measure the position and properties of about 100,000 clusters of galaxies and 3 million active galactic nuclei over the full sky. To study the statistical properties of this ongoing survey, it is key to estimate the selection function accurately. We create a set of full sky light-cones using the MultiDark and UNIT dark matter only N-body simulations. We present a novel method to predict the X-ray emission of galaxy clusters. Given a set of dark matter halo properties (mass, redshift, ellipticity, offset parameter), we construct an X-ray emissivity profile and image for each halo in the light-cone. We follow the eROSITA scanning strategy to produce a list of X-ray photons on the full sky. We predict scaling relations for the model clusters, which are in good agreement with the literature. The predicted number density of clusters as a function of flux also agrees with previous measurements. Finally, we obtain a scatter of 0.21 (0.07, 0.25) for the X-ray luminosity -- mass (temperature -- mass, luminosity -- temperature) model scaling relations. We provide catalogues with the model photons emitted by clusters and active galactic nuclei. These catalogues will aid the eROSITA end to end simulation flow analysis and in particular the source detection process and cataloguing methods.

Chemical analysis and field emission study of electropolished niobium surface containing synthesized niobium oxide particles

We conducted electropolishing (EP) of a Nb superconducting RF coupon cavity containing coupons at various positions of the cavity, and laboratory EP of Nb samples. The surface of the electropolished coupons was studied by using XPS, SEM, AFM, and EDX. The XPS analysis revealed that the atomic compositions and Nb 3d peak shapes (intensity ratio of the Nb5+ and Nb0 peaks) varied for the different coupons, indicating that the chemical state was not the same over the entire cavity surface. These differences might originate from the particle clusters observed on the coupon surfaces, which mainly existed as Nb2O5 and its hydrated form in different number densities. An individual particle cluster was isolated from the surface for EDX analysis, revealing the presence of C and F impurities, where F existed mostly as CFx with traces of niobium fluoride. These particle clusters were possibly synthesized during the post-EP water rinsing process by the hydrolysis of the niobium fluoride species (H2NbOF5) that were produced in the EP process and existing in the acid viscous layer on the surface. The post-EP water rinsing conditions affected the number density of particle clusters, and strong agitation of the acid reduced the particle content on the laboratory electropolished samples. An individual particle cluster emitted electrons at a DC field of 64 MV/m after being activated at a high field of ~150 MV/m, possibly limiting the performance of the SRF cavity. An optimized post-EP water rinsing followed by HF rinsing or prolonged ultrasonic rinsing of the cavity was effective at removing undesired particles from the surface.

Characterisation of nano-scale precipitates in BOR60 irradiated T91 steel using atom probe tomography

Atom probe tomography has characterised the microstructural changes in T91 steel after BOR60 reactor irradiation at five temperatures between 376 °C and 524 °C to doses between 14.6 dpa and 35.1 dpa. Irradiation-induced precipitation and segregation to carbide/matrix interface induced by neutron irradiation has been characterised. Atom probe tomography characterisation shows that Mn, Ni, Si -rich (MNS-rich) clusters form in T91 steel irradiated in BOR60 reactor at temperatures between 376 °C and 415 °C, which is not observed at higher temperatures 460 °C and 524 °C. The number density, volume fraction and composition of MNS-rich clusters have been characterised. Ni, Mn, Si and P is found to segregate at carbide matrix interface after irradiation at lower temperature and only P segregation is observed at 524 °C.

Degeneracy effects and Bose condensation in warm nuclear matter with light and heavy clusters

We have investigated the composition of nuclear matter under thermodynamic conditions relevant for the core-collapse of massive stars, with a focus on quantum-statistical effects for light clusters. We find that deviations in the number densities of light clusters between Boltzmann and quantum statistics are small at sub-nuclear densities and temperatures 1–3 MeV, ≈0.2% at most. The formation of heavy clusters in stellar matter leads to a reduction in the number densities of light clusters. As a result, quantum-statistical effects such as the Bose–Einstein condensation of deuterons and α-particles are suppressed. The condensation of α-particles in iso-symmetric nuclear matter is predicted under the assumptions that it is composed solely of nucleons and light clusters and that no heavy clusters are present. We also find that Coulomb screening hardly affects the critical baryon densities for alpha condensation, although it modifies the masses and chemical potentials of the α-particles.

Vacancy-solute clustering in Fe–Cr alloys after neutron irradiation

Vacancy-solute clustering in neutron irradiated Fe–Cr alloys with various concentrations of Cr and minor solutes (Ni, Si and P) were studied by using coincidence Doppler broadening spectroscopy and small angle neutron scattering techniques. The results from both experiments, supported by an object kinetic Monte Carlo model, show in a very consistent way the existence and formation of vacancy-CrNiSiP clusters that play detrimental role in irradiation hardening. Similar solute cluster number density of about 30–50 ×1016cm−3 and an average diameter of about 1 nm were estimated for all alloys containing minor solutes, irrespectively of the chromium content. In Fe9Cr ferritic and Fe9Cr ferritic/martensitic alloys, with significantly reduced concentration of minor solute elements, the main defects are vacancy clusters, with an average cluster size of about 10 and 2 vacancies, respectively. Large concentration of α’-precipitates was observed in Fe14Cr(NiSiP). However, both vacancy clusters and α’-precipitates provide significantly less impact to hardening in comparison to vacancy-CrNiSiP clusters. The fact that vacancy clustering in Fe9Cr ferritic alloy resembles that of pure iron suggests that Cr solutes may play lesser role in irradiation hardening of ferritic alloys and steels than previously believed.

The effect of molybdenum on interphase precipitation at 700 °C in a strip-cast low-carbon niobium steel

The effect of Mo on the clustering and interphase precipitation occurring during phase transformation has been investigated in a strip-cast low-carbon steel containing Nb. In this work, isothermal coiling treatments were performed at 700 °C for various times to form interphase precipitates. Transmission electron microscopy (TEM), small-angle neutron scattering (SANS) and atom probe tomography (APT) results show that the addition of Mo increases the number density and volume fraction of clusters and interphase precipitates but has a negligible effect on their size, and overall provides for greater strengthening in the Mo-containing alloy. APT analysis shows that the interphase precipitates are composed of Nb, C and N in both alloys. The segregation of Mo is also observed in the interphase precipitates in the Mo-containing alloy, which is believed to relieve the lattice misfit between the precipitate and the matrix. It is proposed that the reduced lattice misfit allows for precipitate nucleation to occur more easily in the Mo-containing alloy.

Selective variant growth of precipitates in an as-extruded Mg-Gd-Zn-Mn alloy

Selective variant growth of precipitates was found in an as-extruded Mg-13.7Gd-1.7Zn-0.5Mn (wt.%) alloy. In the coarse-deformed grains, β' phases and hexagonal clusters mainly precipitate along the [101-0]Mg orientation. While in the fine dynamic recrystallized (DRXed) grains, the β' phases and a few of the hexagonal clusters are relatively uniform distributed along the three < 101-0>Mg directions. This phenomenon is attributed to the coupling of dislocation strain field and residual stress component in the as-extruded alloy. Moreover, dislocations in the deformed grains result in a significant increase in the number density of hexagonal clusters comparing to those in the DRXed grains. This selective variant growth of precipitates is expected to change the deformation behavior and modify the mechanical properties in Mg-RE (rare earth) alloys.

Development of Fe-based high Bs nanocrystalline alloy powder

We developed nanocrystalline powders with high Fe contents through methodological and compositional innovations. The Fe-Cr-Cu-Si-B-Sn powders exhibit high Bs of 1.55 T–1.60 T and core losses of 4800–8000 kW/m3 at 2 MHz under 30 mT, P0.2/3M. The Cu clusters provide a high number density of nucleation sites, leading to the formation of powders with nanocrystalline structures. It is found that high number density of Cu clusters are realized by distribution of sub-nanometer Sn clusters, especially near the surface. The addition of Sn enables the maintenance of a stable supply of nucleation sites regardless of powder diameters i.e., a wide variety of quenching rates is accepted.

Effects of pre-aging and natural aging on the clusters, strength and hemming performance of AA6014 alloys

In this study, the effects of pre-aging and natural aging on the clusters, strength and hemming performance of AA6014 Al–Mg–Si alloys with different Mg/Si ratios were investigated through three-dimensional atom probe (3DAP) in combination with tensile test and three-point bend test. Samples are subjected to natural aging (room temperature, ~25 °C) or pre-aging (elevated temperature, 75 °C) treatments in order to generate different types of clusters. The number density, size and compositions of clusters are analyzed by 3DAP. The increased strength and deteriorated hemming performance are found in natural aged alloys, especially for Si-rich alloy. The hemmability is sensitive to the strength, and an increased strength leads to inferior hemmability. The formation of Mg1Si1 type cluster is encouraged during pre-aging treatment regardless of the alloy composition. Natural aging following directly water quenching promotes the formation of a large number density of small-sized Si-rich clusters in Si-rich alloy, whereas relatively low density of clusters with scattered Mg/Si ratios distribution in Mg-rich alloy. The concentration of the excess vacancies and the binding energy between vacancy and Mg and Si atoms plays an important role in the precipitation kinetics of cluster during different aging processes. Finally, the clusters and solid solution atoms statistics are utilized to predict the yield strength of the alloys in different aging conditions.

Using alpha hulls to automatically and reproducibly detect edge clusters in atom probe tomography datasets

An automated way to accurately and reproducibly identify edge clusters within atom probe tomography datasets has been developed. The alpha-hull algorithm is used to generate a concave alpha-shape around an atom probe dataset. Information from core-linkage cluster searches is used, in combination with the calculated alpha-shape, to determine which clusters are on the edge of the dataset.The potential effects that not removing edge clusters may have on calculated cluster sizes, number densities and compositions is discussed. The viability of the methodology is demonstrated via application to real datasets, one of which was a non-standard shape.The sensitivity of the method to user parameter selection is explored. Sampling fractions >0.1% and an alpha value, used to make the alpha shape, greater than twice the maximum measured nearest neighbour distance were found to be suitable.

Tuning of ionic mobility to improve the resistive switching behavior of Zn-doped CeO2

Correlation between the resistive switching characteristics of Au/Zn-doped CeO2/Au devices and ionic mobility of CeO2 altered by the dopant concentration were explored. It was found that the ionic mobility of CeO2 has a profound effect on the operating voltages of the devices. The magnitude of operating voltage was observed to decrease when the doping concentration of Zn was increased up to 14%. After further increasing the doping level to 24%, the device hardly exhibits any resistive switching. At a low doping concentration, only isolated Vo existed in the CeO2 lattice. At an intermediate doping concentration, the association between dopant and Vo formed (Zn, Vo)× defect clusters. Low number density of these defect clusters initially favored the formation of Vo filament and led to a reduction in operating voltage. As the size and number density of (Zn, Vo)× defect clusters increased at a higher doping concentration, the ionic conductivity was limited with the trapping of isolated Vo by these defect clusters, which resulted in the diminishing of resistive switching. This research work provides a strategy for tuning the mobility of Vo to modulate resistive switching characteristics for non-volatile memory applications.

Enhancing the bake-hardening responses of a pre-aged Al-Mg-Si alloy by trace Sn additions

Effects of additions of trace Sn on the bake-hardening responses of a pre-aged Al-0.85Mg-0.85Si (in wt%) alloy were investigated through mechanical tests, differential scanning calorimetry, electrical resistivity and transmission electron microscopy. Results indicate that trace Sn additions reduced the number density of pre-aging clusters by inhibiting the formation of unstable counterpart during pre-aging treatment, leading to low strength and high supersaturation of solute atoms. In a subsequent paint-bake treatment, the presence of highly supersaturated solute atoms and high concentrated free vacancies moderated the activation energy barrier of βʺ phase and thus kinetically accelerated the formation of βʺ. Consequently, the trace Sn additions enhanced the bake-hardening responses of the pre-aged alloys significantly. The Sn-containing pre-aged Al-Mg-Si alloys with low strength and great bake-hardening responses hold promising potential for automotive body skin applications.

Effects of one-dimensional migration of self-interstitial atom clusters on the decreasing behaviour of their number density in electron-irradiated α-iron

ABSTRACTAn in- situ observation using high-voltage electron microscopy (HVEM) showed that the number density of stationary self-interstitial atom (SIA) clusters in electron-irradiated α-iron at room temperature seems to reach its peak value at an early stage of irradiation and continuously decreases at the prolonged irradiation. A thin foil specimen is used in the in situ HVEM experiments; hence, the SIA clusters can annihilate because of their escape to the specimen surfaces and their mutual coalescence through one-dimensional (1D) migration. In this study, we derive analytical models associated with the experimentally revealed 1D migration mechanisms to examine the decreasing behaviour of the cluster number density: (1) trapping of one-dimensionally migrating SIA clusters by impurity atoms within the specimen surfaces and (2) detrapping of stationary SIA clusters from a bounded impurity atom caused by impact with incident electrons. By introducing a simple cluster evolution model that accounts for only the trapping and detrapping processes, the model calculation indicates that the detrapping of the stationary SIA clusters causes the surface annihilation of the liberated SIA clusters, leading to the decrease in their number density. The decreasing behaviour is in closer accordance with the experimental data when setting the impurity concentration in the same order as the estimation from the previous in situ HVEM experiment. This result suggests that the trapping and detrapping of the SIA clusters are the possible underlying processes for the decreasing behaviour.

Effect of Low-Temperature Ion Irradiation on the Nanostructure of 12% Chromium ChS-139 Steel

Specimens of ChS-139 steel (0.2 С–12 Cr–Ni–Mo–W–Nb–V–N–B) were irradiated up to 6 displacements per atom (dpa) with Fe ions at 250, 300, and 400°C. The radiation-induced clusters and Cottrell atmospheres enriched in Ni, Si, and Mn were revealed in irradiated samples by atom probe tomography. The typical sizes of the radiation-induced clusters were about 2–7 nm, and their number density was about (2–20) × 1023 m–3. It was shown that the highest irradiation temperature (400°C) is compliant with the lowest enrichment of clusters in Ni, Si, and Mn as well as with the largest average size of clusters (~5 nm) and the least number density (~2 × 1023 m–3). A noticeable decrease in the number density of radiation-induced clusters with an increase in the damage dose to 4 dpa at 300°C was found. At the same time, it was shown that the Cr–V–Nb–N clusters found in the initial state dissolve with the increase in the irradiation dose at all considered temperatures. The value of detected radiation-induced effects is indicative of their significant role in the low temperature radiation embrittlement of ChS-139 steel.