Impurity Diffusion Research Articles

Impurity convection reversal caused by edge localized turbulence for generating a stationary edge radiative layer in the HL-2A tokamak

Abstract Effect of impurity on edge turbulence was investigated on the HL-2A tokamak by using Neon supersonic molecular beam injection (SMBI). For the first time, a stationary radiative layer accompanied by edge localized turbulence lasting more than 100ms is observed at the edge region ρ=0.7-0.9. This duration is much longer than the SMBI pulse length (1.2ms), indicating that the impurity diffusion is on the whole cancelled out by the impurity convection without spreading of the localized turbulence during this period. This implies that the impurity convection is reversed from positive to negative impurity density gradient region. This reversal could be explained by the parallel impurity compression mechanism. The observed turbulence is a broadband electrostatic turbulence (25-70 kHz) propagating in the electron diamagnetic drift direction with normalized poloidal wavenumber of 0.1≤ kθρs≤0.4. It has been found that the excitation of the edge localized turbulence strongly depends on the local collisionality. This feature is qualitatively predicted by the spectral multiscale gyrokinetic turbulence simulation, which suggests that the turbulence could be a dissipative trapped electron mode (DTEM). This experiment demonstrates that mutual interaction between externally injected impurity ions and edge turbulence can generate a stationary edge radiative layer and avoid impurity core accumulation. These results could provide a potential approach for the formation of a stable impurity radiative layer by impurity injection in tokamaks.

Elemental diffusion coefficient prediction in conventional alloys using machine learning

This paper presents the Machine Learned Diffusion Coefficient Estimator, a comprehensive machine learning framework designed to predict diffusion coefficients in impure metallic (IM) and multi-component alloy (MCA) media. The framework incorporates five machine learning models, each tailored to specific diffusion modes: (1) impurity and (2) self-diffusion in IM media, and (3) self, (4) impurity, and (5) chemical diffusion in MCA media. These models use statistical aggregations of atomic descriptors for both the diffusing elements and the diffusion media, along with the temperature of the diffusion process, as features. Models are trained using the random forest and deep neural network algorithms, with performance evaluated through the coefficient of determination (R2), mean squared error (MSE), and uncertainty estimates. The models within this framework achieve an impressive R2 score above 0.90 with MSE less than 10−16 m2/s, demonstrating high predictive accuracy and reliability for diffusion coefficient.

Finding Diffusivity and Solubility of Impurities inside ILs By MD

Ionic liquids (ILs) are promising candidates for use in the semiconductor industry due to their unique and tunable physicochemical properties. One possible application is to use ILs as a barrier or protective liquid film that does not evaporate in low-pressure conditions. For this application, we need a better understanding of the molecular scale of the behavior of the ILs at different temperature ranges. To develop such a new process, the knowledge of absorbing/desorbing impurities (such as O2, CO2, and H2O, including their mixtures and other organic materials) in the ILs and their transport properties (diffusion coefficients) inside the ILs at different temperatures is essential from the surface protection film point of view. This work seeks to answer these essential questions at the nanometer scale by showing the results from molecular dynamics (MD) simulations of the diffusivity and solubility of impurities inside ILs.

Development and morphological analysis of the zone refining process for high purity germanium

A highly efficient purification process has been developed to enhance the purity of germanium (Ge) up to 13 N from an initial 4N purity. Hall effect measurements demonstrated that part of the zone refined Ge (ZRGe) bars exhibited p-type conductivity and high purity with a net charge carrier concentration of around 4–9 × 1010 cm−3. Noteworthy observations include a rise in carrier concentration (1011 to 1012 cm−3) at a very low zone refining (ZR) velocity of 1 mm/min, which is attributed to the diffusion of impurities from the container into the Ge melt. The purification efficiency was enhanced by optimizing the ZR velocity to around 4–5 mm/min. Purification was carried out at different process steps using graphite and quartz containers. Subsequent microstructural examinations, conducted in conjunction with wet-chemical etching of the sample unveiled the presence of various grains, grain boundaries (GBs), and low & high-density of dislocation clusters: These observations were made in samples that had undergone zone refining under various gas atmospheres including argon, nitrogen and hydrogen. Electron back scattered diffraction (EBSD) analysis reveals the characteristics of multiple grains and grain boundaries (GBs) of Ge refined in argon and nitrogen atmosphere, including low-angle GBs, high-angle GBs with coincide site lattice (CSL) Σ3, Σ9, Σ27a, and random angle GBs. In contrast, the EBSD results of Ge refined in hydrogen atmosphere shows larger grains with only a few low-angle grain boundaries. The materials refined in argon and nitrogen show a lower carrier lifetime (10–30 μs) owing to the presence of various high angle grains boundaries as well as low purity. Conversely, zone refining in hydrogen resulted in the carrier lifetime of around 50 μs in polycrystalline Ge wafers with larger grains.

Nanosecond laser annealing processed surface-structured hyperdoped silicon for efficient near-infrared detection

Surface-structured engineering of hyperdoped silicon can effectively facilitate the absorption of sub-bandgap photons in pristine single-crystal silicon (sc-Si). Here, we conducted different annealing approaches of ordinary thermal annealing (OTA) and nanosecond laser annealing (NLA) on modification of titanium-hyperdoped silicon (Si:Ti) surface structure, to achieve efficient near-infrared detection. It is presented that both OTA and NLA processes can improve the crystallinity of Si:Ti samples. In detail, atomic-resolved STEM characterization illustrates that NLA treatment will further eliminate the amorphous phase on Si:Ti surface to varying degrees. While one-dimensional periodic stacking fault structure of 9R-Si phase is formed at the surface of sc-Si and embedded in the Si matrix during the OTA process, which reveals the seamless interface of 9R-Si/sc-Si along with [11¯0] direction. Due to the high sub-bandgap light absorption and good crystal structure, the Si:Ti photodetector after NLA treatment with an energy density of 2.6 J cm-2exhibited the highest responsivity, reaching 151 mA W-1at 1550 nm even at a low operating voltage of 1 V. We assume the performance enhancement of NLA processed Si:Ti photodetectors can be attributed to two aspects, the one is NLA can reduce the recombination of photo-generated charge carriers in amorphous surface layer by improving crystallization, and the other is that NLA process can weaken the diffusion of titanium impurities due to the extremely rapid heating and cooling rates. This study presents prospects towards surface-structured silicon in infrared light detection.

Effect of TiN coating on suppressing Ce-Fe interaction under irradiation

Advanced cladding is critical for fast reactors with the adequate thermal conductivity, mechanical stability and radiation tolerance of the cladding base material, corrosion resistance and high temperature coolant compatibility of the cladding surface, and chemical stability of the cladding inner wall against fuel cladding chemical interaction (FCCI). The preliminary results of recent ion irradiation studies of two diffusion-couple samples of cerium (Ce)/oxide-dispersion strengthened steel (ODS) and Ce/TiN/ODS, irradiated with 80 MeV xenon (Xe) ions to 100 displacements per atom (dpa) at 500°C, are summarized. Significant Ce-Fe interaction occurred in the Ce/ODS sample, and no noticeable Ce-Fe interaction was found in the Ce/TiN/ODS sample. It shows the effectiveness of 1-µm TiN diffusion barrier coated by the pulsed laser deposition on suppressing Ce-Fe interaction, a major contributor to FCCI in cladding. Density function theory (DFT) calculations of the impurity diffusivities of Ce and Fe within the Ti sublattice of TiN were performed to assist a mechanistic understanding of the experimental results.

Influence of crystallite size and impurity density on the grain structure evolution of electroplated copper films during thermal and laser annealing

In this paper, the changes in microstructure and conductivity of the films before and after thermal and laser annealing are observed, which corresponds to various combinations of crystallite sizes and impurity densities. The results show that the impurities promote grain boundary migration at larger initial crystallite sizes, which contradicts previous reports. This is because the rate of grain growth is determined by the driving force and resistance to grain growth, the former provided by the energy of grain boundaries and the impurities outside the nanograin boundaries, and the latter by the impurities enriched within the boundaries. Additionally, laser annealing is more effective than thermal annealing in stimulating impurity diffusion, resulting in a reduced influence of impurities on grain growth.

Diffusion of iron in zinc selenide during hot isostatic pressing

The diffusion of iron impurities in zinc selenide (ZnSe) during hot isostatic pressing (HIP) in the temperature range T = 1000–1300 °C and pressures P = 100–190 MPa has been investigated. The iron concentration and its distribution over the sample volume with a step from 20 to 50 μm was determined by IR spectroscopy in combination with an IR microscope. The diffusion coefficients of Fe in ZnSe at various temperatures and pressures were determined. The diffusion coefficients of Fe in ZnSe at P = 100 MPa and T = 1000 °C were (5.3 ± 0.6)x10−10 cm2/s, T = 1300 °C were (9.4 ± 0.9)x10−9 cm2/s. It is shown that the temperature dependences are described by the Arrhenius equation, and the isostatic pressure does not affect the value of the diffusion coefficients.

Nanocrystalline copper for direct copper-to-copper bonding with improved cross-interface formation at low thermal budget

Direct copper-to-copper (Cu-Cu) bonding is a promising technology for advanced electronic packaging. Nanocrystalline (NC) Cu receives increasing attention due to its unique ability to promote grain growth across the bonding interface. However, achieving sufficient grain growth still requires a high thermal budget. This study explores how reducing grain size and controlling impurity concentration in NC Cu leads to substantial grain growth at low temperatures. The fabricated NC Cu has a uniform nanograin size of around 50 nm and a low impurity level of 300 ppm. To prevent ungrown NC and void formation caused by impurity aggregation, we propose a double-layer (DL) structure comprising a normal coarse-grained (CG) layer underneath the NC layer. The CG layer, with a grain size of 1 μm and an impurity level of 3 ppm, acts as a sink, facilitating impurity diffusion from the NC layer to the CG layer. Thanks to sufficient grain growth throughout the entire NC layer, cross-interface Cu-Cu bonding becomes possible under a low thermal budget, either at 100 °C for 60 min or at 200 °C for only 5 min.

Impurity transport study based on measurement of visible wavelength high-n charge exchange transitions at W7-X

A recently installed high-speed charge exchange diagnostic at the W7-X stellarator has been used to identify several high-n Rydberg emission lines near 500 nm following impurity injections. The wavelengths of observed high-n Rydberg transitions are independent of the impurity species and originate from ions with ionization states ranging from 14+ to 45+ suggesting that this approach can be applied to a variety of heavy impurities. Moreover, little to no passive signal is observed since the high-n energy levels are unlikely to be populated by electron impact excitation. The combination of the newly developed diagnostic and the observation of high-n Rydberg states provides spatially resolved, high-speed measurements of multiple charge states which are analyzed in a Bayesian inference framework to determine both impurity diffusion and convection profiles. Measurements from the 2023 experimental campaign conclusively show high diffusion and an inward pinch in the core, well above predictions by neoclassical theory.

Theoretical study of kinetic isotope effects for vacancy diffusion of impurity in solids

Theoretical study of kinetic isotope effects for vacancy diffusion of impurity in solids

Introducing concepts of estimating tracer and intrinsic diffusion coefficients in a ternary system: a case study in the FCC Fe-Mn-Cr solid solution

ABSTRACT Estimating tracer and intrinsic diffusion coefficients following the diffusion couple method with systematic composition variation can be challenging because of the diffusion paths’ serpentine or double serpentine nature on the Gibbs triangle. Moreover, the possibility of estimating these diffusion coefficients from a single diffusion profile can have immense benefits. We have demonstrated four ways of estimating tracer and impurity diffusion coefficients in the FCC Fe-Mn-Cr solid solution: (i) We have shown that these can be estimated directly at the Kirkendall marker plane from a single conventional ternary diffusion profile. (ii) We have, for the first time, demonstrated that the estimation at the intersection of a conventional ternary and constrained pseudo-binary diffusion path is helpful for systematically generating composition-dependent tracer diffusion coefficients. (iii) We have followed the Kirkaldy-Lane method for estimating these diffusion coefficients at the intersection of two conventional ternary diffusion couples (for comparison of the data measured by new methods), although for data generation at random compositions. This was proposed a long time ago but practised occasionally. It helps to compare with the estimated data following other methods. (iv) Additionally, we have estimated the impurity diffusion coefficients of Cr and Mn in Fe following the Hall method, which helps in understanding the variation of the diffusion coefficients in Fe-Mn-Cr alloys compared to pure Fe. The sensitivity of data estimation following different methods, i.e. different equation schemes, is discussed, explaining the strategic design of diffusion couple for a small error range.

Measurement of Diffusion Coefficients and Assessment of Atomic Mobilities in HCP Mg-Ag-Sn Alloys

Reliable thermodynamic and kinetic databases are essential for designing and developing novel magnesium (Mg) alloys for elevated-temperature applications in the automotive and aerospace industries. This study investigated diffusion behaviors of HCP Mg-Ag-Sn alloys by four sets of three diffusion couples annealed at 450, 500, and 550 °C, respectively. Interdiffusion and impurity diffusion coefficients at the three annealing temperatures were extracted using the forward-simulation method. The determined diffusion coefficients, combined with prior results in the literature, were then used to assess atomic mobilities for the HCP phase of the Mg-Ag-Sn system. This assessment was conducted using the DICTRA and the TCMG5 thermodynamic database within the Thermo-Calc software. Comprehensive comparisons between calculated and experimental diffusion coefficients yielded an excellent agreement. The atomic mobilities were also further validated by appropriate predictions of concentration profiles and diffusion paths observed in independent diffusion couple experiments performed at 525 °C for 18 hrs. It has been found that the addition of Sn and Ag both increase the diffusivity of Ag in HCP Mg and Sn in HCP Mg in the stable temperature range of HCP Mg, respectively. This improved understanding of the kinetics in the Mg-Ag-Sn ternary system is essential for controlling diffusion-dependent properties such as coarsening and, therefore, the mechanical properties of Mg-Ag-Sn alloys at elevated temperatures.

High efficiency solar-grade silicon producing by directional solidification through controlling diffusion of impurity

The precise distribution of impurity of the whole silicon ingot is investigated through a theoretical model and the experiments. This model solves the problem of inaccurate prediction of impurity distribution in the final solidification region. The model was used to calculate the distribution of iron impurity in polycrystalline silicon ingots after directional solidification and compared with experiments. The calculation accuracy was significantly improved compared to the traditional Scheil equation. This paper investigates the influence of cooling rate, silicon ingot height and solidification rate on the yield of purified products after directional solidification. For the experimental equipment and raw materials in this paper, the optimal cooling rate of silicon ingots after directional solidification is 0.33 °C/s, the optimal height of silicon ingots is 0.34 m, and the yield of silicon purification increases with the decrease of directional solidification rate. Based on the research results, a standard for removing the top skin of silicon ingots after directional solidification and a method for improving the purification yield by suppressing impurity diffusion during the cooling stage were obtained. This model can provide theoretical guidance for the development of low-cost and high-efficiency methods for removing impurities from polycrystalline silicon, and is of great significance for the development of the photovoltaic industry. In addition, the theoretical model proposed in this paper can also be applied to the directional solidification purification process of other materials, such as the preparation of high-purity aluminum and high-purity titanium, and can predict the impurity migration behavior and distribution pattern throughout the purification process.

An experimental estimation method of diffusion coefficients in ternary and multicomponent systems from a single diffusion profile

Until recently, it was textbook knowledge that the diffusion coefficients could not be estimated in a multi-component system following the widely practised diffusion couple method. The recently proposed constrained diffusion couple method largely solved the problems. The need to produce two intersecting diffusion paths in a multi-component space with very well-controlled compositions of the diffusion couple end members may be tricky in certain situations, depending on the complications of diffusion paths. In this study, we have shown the estimation of all types of diffusion coefficients from a single diffusion profile without neglecting Onsager's cross terms in concentrated ternary Ni-Co-Fe, Fe-rich quaternary Fe-Ni-Co-Cr and concentrated Ni-Co-Fe-Cr-Al quinary alloys. This is applicable in ternary and multicomponent component systems (n≥3) at a stable Kirkendall marker plane position. One can even estimate the impurity diffusion coefficients utilizing the composition profiles at the ends of the diffusion couples following the Hall method, which has been rarely practised in multicomponent systems until now. We have further demonstrated the importance of estimating the tracer and intrinsic diffusion coefficients in a concentrated or multi-principal element alloy in which interdiffusion coefficients can be vague and misleading for understanding the elements' diffusional interactions and relative mobilities. We have also shown the importance of considering the vacancy wind effect in concentrated alloys. The method proposed in this study will help to generate a mobility database with relative ease in various multicomponent systems important for various applications, which was considered impossible until recently.

Diffusivities and Atomic Mobilities in BCC Ti-Fe-Cr Alloys.

In this research, the diffusion behaviors within the Ti-Fe-Cr ternary system were examined at the temperatures of 1273 K and 1373 K through the diffusion couple technique. This study led to the determination of both ternary inter-diffusion and impurity diffusion coefficients in the body-centered cubic (bcc) phase for the Ti-Fe-Cr alloy, utilizing the Whittle-Green and Hall methods. The statistics show that the average diffusion coefficients D˜FeFeTi and D˜CrCrTi measured at 1273 K were 1.34 × 10-12 and 3.66 × 10-13, respectively. At 1373 K, the average values of D˜FeFeTi and D˜CrCrTi were 4.89 × 10-12 and 1.43 × 10-12. By adopting the CALPHAD method, a self-consistent database for atomic mobility in the bcc phase of the Ti-Fe-Cr system was established. This database underwent refinement by comparing the newly acquired diffusion coefficients with data from the existing literature. Diffusion simulations for the diffusion couples were performed, drawing on the established database. The error between the simulated diffusion coefficient and the experimental measurement data is within 15%, and the simulated data of the component distance distribution and diffusion path are in good agreement with the experimental data. The simulations generated results that aligned well with the observed experimental diffusion characteristics, thereby affirming the reliability and accuracy of the database.

Evaluation of diffusion behavior and mechanical characteristics in the ZrC-NbC pseudo-binary system

Accurate information on diffusion kinetics and mechanical characteristics for the ZrC-NbC pseudo-binary system is essential for developing high-performance ZrC-based alloys. At present work, we have employed the diffusion couple method to investigate systematically the diffusion kinetics of the ZrC-NbC pseudo-binary system in the temperature range of 1373–1673 K. The mechanical characteristics of the diffusion region have been studied by the nanoindentation technique. Evaluations have been conducted on the impurity diffusion and inter-diffusion coefficients of the ZrC-NbC pseudo-binary system. As Nb concentration increases, the inter-diffusion coefficients of the ZrC-NbC pseudo-binary system decline. The inter-diffusion activation energies of the ZrC-NbC pseudo-binary system increase as Nb concentration increases, with the largest value of 395.3 kJ/mol at 55 at. % Nb concentration. The impurity diffusion activation energies of C in ZrC, C in NbC, Nb in ZrC, and Zr in NbC are 242.4 kJ/mol, 167.9 kJ/mol, 388.3 kJ/mol, and 288.0 kJ/mol, respectively. The Vickers hardness and Young's modulus of Zr1-xNbxC have also been measured, with the highest values of 29.4 ± 2.7 GPa and 650.7 ± 12.9 GPa, respectively. With an increase of Nb concentration, Young's modulus of Zr1-xNbxC increases, while its Vickers hardness first increases and subsequently declines. The results of this study could be advantageous to develop ZrC-based alloys and improve their properties.

Simultaneous reproduction of experimental profiles, fluxes, transport coefficients, and turbulence characteristics via nonlinear gyrokinetic profile predictions in a DIII-D ITER similar shape plasma

Experimental conditions obtained on the DIII-D tokamak in the ITER Similar Shape (ISS) have been compared extensively with nonlinear gyrokinetic simulation using the CGYRO code [Candy et al., J. Comput. Phys. 324, 73–93 (2016)] with comparisons spanning ion and electron heat fluxes, electron and impurity particle transport, and turbulent fluctuation levels and characteristics. Bayesian optimization techniques [Rodriguez-Fernandez et al., Nucl. Fusion 62(7), 076036 (2022)], combined with nonlinear gyrokinetics, have been used to obtain simultaneously Qi, Qe, and Γe flux-matched profiles that are found to be in good agreement with experimental profile measurements. Synthetic diagnostics were used to compare measured beam emission spectroscopy and correlation electron cyclotron emission turbulent fluctuations with nonlinear simulation. Although some disagreements exist, nonlinear simulations are found to be in generally good agreement with measured fluctuation levels, spectral shapes, and measured radial trends in low-k δne/ne and δTe/Te. Low (Li and C) and mid-Z (Ca) impurity transport was also compared with these flux-matched simulations. Fully stripped, low-Z impurities are well reproduced by the gyrokinetic modeling while clear disagreement exists in comparisons with mid-Z impurities. Nonlinear gyrokinetic investigation into the Z dependence of impurity transport in the ISS conditions is also performed, demonstrating clear trends of impurity diffusion with impurity Z (both D∝Z and D∝1/Z) that vary with the radial location studied. These trends are shown to result from the local dominance of ion temperature gradient or ∇n driven trapped electron mode turbulence and may contribute to the disagreement between simulation and experiment in mid-Z impurity transport. The results of this work represent one of the most complete validation studies of the gyrokinetic model performed to date and provide an example of new capabilities for predicting performance in future fusion devices.

ON THE THEORY OF EVAPORATION REFINING

The theory of sublimation and distillation refining, which takes into account the diffusion of impurities, is considered. The conceptual nature of the theory is noted due to the large number of parameters whose values are unknown.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed. Mass sources of various power are uniformly distributed in a certain internal interval of the body. Statistics of random sources are given. The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources. The solution is averaged over both certain internal subinterval and the entire body region. Simulation units are designed for modeling of the behavior of the averaged concentration function with acting system of point mass sources of various power. On this basis, the averaged concentration field is investigated depending on the internal interval length, power and number of sources in the system as well as the concentration values at the layer boundaries.