Self-diffusion Mechanism Research Articles

Self-Diffusion in Sr-Containing Iron-Polyphosphate Glasses by Molecular Dynamics Simulations

Among the many possible applications of iron phosphate glasses, one of them is that they are promising materials in waste vitrification, particularly for radioactive waste. In vitrified form, waste elements should be permanently immobilized in a glass network as they are susceptible to harsh environmental conditions. The self-diffusion of the vitrified material species may limit the potential usefulness of the glasses. This paper presents the possibility of using molecular dynamics simulations to study this process and the substitution of SrO into an iron phosphate glass network. It was evidenced that the self-diffusion mechanism differed significantly depending on whether the glass was in a solid or liquid state. The proposed method also offered a relatively easy prediction of glass characteristic temperatures, such as transformation and flow. We also observed, and here describe, an aggregation process of the glass elements that may drive their crystallization. The obtained results are discussed in light of the experimental and theoretical structural feature literature data.

Internal structure of metal vacancies in cubic carbides

A combinatorial approach is employed to investigate the atomic and electronic structures of a metal vacancy in titanium carbide. It turns out that the usual relaxed geometry of the vacancy is just a metastable state representing a local energy minimum. Using calculations and by systematically searching through the configurational space of a Ti monovacancy, we identify a multitude of local minima with reconstructed geometry that are lower in energy. Among them, there is a planar configuration with two displaced carbons forming a dimer inside the vacancy. This structure has the optimal number and order of C–C bonds making it the global minimum. Further calculations show that this reconstructed geometry is also the ground state of metal vacancies in other carbides such as ZrC, HfC, and VC. The reconstructed metal vacancies are characterized by localized electron states due to the relatively short C–C bonds. The defect states lie just below the upper and lower valence bands. The existence of reconstructed vacancy configurations is essential for understanding the mechanism of metal self-diffusion in transition-metal carbides. Published by the American Physical Society 2024

Disentangling the self-diffusional dynamics of H2 adsorbed in micro- and mesoporous carbide-derived carbon by wide temporal range quasi-elastic neutron scattering

Understanding the processes guiding the confinement of adsorbed H2 in different porous structures is vital for the development of adsorbents for effective cryo-adsorptive H2 storage systems. Quasi-elastic neutron scattering (QENS) is applied over a wide range of timescales (0.2 ps – 150 ps) to determine different self-diffusion mechanisms of H2 adsorbed in a carbide (synthesized from TiC via the sol-gel method) derived carbon (sol-gel TiC-CDC) adsorbent with hierarchical porous structure. The bulk and porous structure is characterized by gas adsorption, Raman spectroscopy, and wide-angle X-ray scattering methods. Sol-gel TiC-CDC belongs to a series of CDCs that have been previously characterized and where the self-diffusion of adsorbed H2 has been investigated with QENS. Sol-gel TiC-CDC is very mesoporous, has relatively high stacking (2.76 graphenic layers per stack), and small interlayer spacing of graphenic sheets (3.43 Å) in comparison to other CDCs in the series, thus, being a well-ordered highly porous CDC. Restricted rotational self-diffusion of adsorbed H2 is determined in ultramicropores (pore width, w, < 7 Å) and translationally self-diffusing H2 adsorbed in multilayers across multiple timescales are determined in micro- and mesopores (7 Å < w < 500 Å). The microporous and graphenic structure of the CDC does not remarkably affect the self-diffusion of H2 at high surface coverages. The simultaneous determination of adsorbed H2 motions across different timescales allows to analyze the influence of micro- and mesopores under H2 loading conditions, which are close to the ones used in technical applications and are vital for adsorbent optimization.

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix.

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

MD Simulation and Transport Property Analysis of Silicon in High-Temperature Molten Fluoride Salts Electrolyte

Silicon is the dominant solar material because of its abundance, low cost, and high solar efficiency. But manufacturing high-purity silicon required for solar energy is very complex, hard to scale, and unsafe since it involves dealing with toxic flammable gases. Therefore, a new solar silicon production technology based on molten salt electrolysis has been proposed. To comprehensively study the self-diffusion and deposition mechanism of silicon ions in high-temperature molten salt electrolyte and their composition and temperature dependence, both interatomic potential molecular dynamics (IPMD) and ab-initio molecular dynamics (AIMD) are introduced. Thermodynamics and transport properties of molten salt electrolyte such as density, heat capacity, viscosity etc. are investigated and compared to the existed experimental results. Also, local structural information and coordination number analysis are obtained and discussed.

Structural transformation and anomalous diffusion in network forming liquid GeO2

In this study, we simulated the structural transformation and self-diffusion mechanism in liquid GeO2 oxide system. Under compression, structure of liquid GeO2 model tends to transform gradually from low-density phase to high-density phase. Concentration of basic structural units can be determined via density of material model. The average Ge–O bond distance in GeO4 tetrahedra is smaller than the ones in GeO5 pentahedra and GeO6 octahedra. Each GeOx polyhedron always exists a Ge–O bond with the longest length (the weakest bond). The diffusion mechanism in liquid GeO2 oxide system is via breaking the weakest bonds that accompany the change local coordination environment of Ge cations. The longest Ge–O bond in a GeO5 pentahedron is very weak in comparison to the one in other polyhedra. The diffusivity is significantly dependent on the number of GeO5 pentahedra. The increase of GeO5 under compression is the origin of anomalous diffusion in liquid GeO2 oxide. The increase of average Ge–O bond distance under compression is also clarified in this work.

Structural and dynamic heterogeneity in associative networks formed by artificially engineered protein polymers.

This work investigates static gel structure and cooperative multi-chain motion in associative networks using a well-defined model system composed of artificial coiled-coil proteins. The combination of small-angle and ultra-small-angle neutron scattering provides evidence for three static length scales irrespective of protein gel design which are attributed to correlations arising from the blob length, inter-junction spacing, and multi-chain density fluctuations. Self-diffusion measurements using forced Rayleigh scattering demonstrate an apparent superdiffusive regime in all gels studied, reflecting a transition between distinct "slow" and "fast" diffusive species. The interconversion between the two diffusive modes occurs on a length scale on the order of the largest correlation length observed by neutron scattering, suggesting a possible caging effect. Comparison of the self-diffusive behavior with characteristic molecular length scales and the single-sticker dissociation time inferred from tracer diffusion measurements supports the primarily single-chain mechanisms of self-diffusion as previously conceptualized. The step size of the slow mode is comparable to the root-mean-square length of the midblock strands, consistent with a single-chain walking mode rather than collective motion of multi-chain aggregates. The transition to the fast mode occurs on a timescale 10-1000 times the single-sticker dissociation time, which is consistent with the onset of single-molecule hopping. Finally, the terminal diffusivity depends exponentially on the number of stickers per chain, further suggesting that long-range diffusion occurs by molecular hopping rather than sticky Rouse motion of larger assemblies. Collectively, the results suggest that diffusion of multi-chain clusters is dominated by the single-chain pictures proposed in previous coarse-grained modeling.

Atomic mechanisms of self-diffusion in amorphous silicon

Based on recent calculations of the self-diffusion (SD) coefficient in amorphous silicon (a-Si) by classical Molecular Dynamics simulation [Posselt et al., J. Appl. Phys. 131, 035102 (2022)], detailed investigations on atomic mechanisms are performed. For this purpose, two Stillinger–Weber-type potentials are used, one strongly overestimates the SD coefficient, while the other leads to values much closer to the experimental data. By taking into account the individual squared displacements (or diffusion lengths) of atoms, the diffusional and vibrational contributions to the total mean squared displacement can be determined separately. It is shown that the diffusional part is not directly correlated with the concentration of coordination defects. The time-dependent distribution of squared displacements of atoms indicates that in a-Si, a well-defined elemental diffusion length does not exist, in contrast to SD in the crystalline Si. The analysis of atoms with large squared displacements reveals that the mechanisms of SD in a-Si are characterized by complex rearrangements of bonds or exchanges of neighbors. These are mono- and bi-directional exchanges of neighbors and neighbor replacements. Exchanges or replacements may concern up to three neighbors and may occur in relatively short periods of some ps. Bi- or mono-directional exchange or replacement of one neighbor atom happens more frequently than processes including more neighbors. A comparison of results for the two interatomic potentials shows that an increased three-body parameter only slows down the migration but does not change the migration mechanisms fundamentally.

Pore wall corrugation effect on the dynamics of adsorbed H2 studied by in situ quasi-elastic neutron scattering: Observation of two timescaled diffusion

The self-diffusion mechanisms for adsorbed H2 in different porous structures are investigated with in situ quasi-elastic neutron scattering method at a temperature range from 50 K to 100 K and at various H2 loadings. The porous structures of the carbon materials have been characterized by sorption analysis with four different gases and the results are correlated with previous in-depth analysis with small-angle neutron scattering method. Thus, an investigation discussing the effect of pore shape and size on the nature of adsorbed H2 self-diffusion is performed. It is shown that H2 adsorbed in nanometer-scale pores is self-diffusing in two distinguishable timescales. The effect of the pore, pore wall shape and corrugation on the fraction of confined and more mobile H2 is determined and analyzed. The increased corrugation of the pore walls is shown to have a stronger confining effect on the H2 motions. The difference of self-diffusional properties of the two H2 components are shown to be smaller when adsorbed in smoother-walled pores. This is attributed to the pore wall corrugation effect on the homogeneity of formed adsorbed layers.

Diffusion of guest molecules in coal: Insights from simulation

The ever-rising consumption of fossil fuels has led to dramatically increased CO2 emissions and notably global warming. Investigations of diffusion behaviors of small guest molecules such as CH4, CO2, N2, H2O, and O2 were critical for the relief the global warming, effective implementation of the injection of CO2 and N2 to enhance the CBM (coalbed methane) recovery (CO2-ECBM, N2-ECBM), as well as the prediction and prevention of coal spontaneous combustion. Herein, using the self-created coal vitrinite macromolecular representation, the self-diffusion coefficients and transport diffusion coefficients of CH4, CO2, N2, H2O, and O2 were clarified via MM (molecular mechanics), GCMC (grand canonical Monte Carlo), and MD (molecular dynamics) to clarify the impacts from different ensembles, as well as the pressure and temperature dependence. The self-diffusion mechanism was also discussed with the aid from the trajectory analysis. For the identified gas species and temperature, the self-diffusion coefficients (Ds) and transport diffusion coefficients (Dt) were higher for NPH (constant parameter: particle number, system pressure, thermodynamic enthalpy) and NPT (constant parameter: particle number, system pressure, temperature) ensemble than NVE (constant parameter: particle number, system volume, system energy) and NVT (constant parameter: particle number, system volume, temperature). For all ensembles, the DsH2O has always jumped up with the increasing temperature independent of the ensembles. The DtH2O were higher than CH4 and CO2 for NPH, NVE, and NVT ensembles. DtCH4 has steep increase points for NPT and NPH ensemble at high temperatures, resulting in the higher DtCH4 than DtCO2. However, DtCH4 was overall lower than DtCO2 for NVE and NVT ensemble at 298 ∼ 358 K. The diffusion activation energy increases with the increasing pressure, indicating that the diffusion barrier rises as the pressure increases. Also, the higher swelling deformation of H2O suggested that the water injection during the drainage and depressurization process should be reduced to achieve the successful ECBM engineering. The results in this paper verify the feasibility of ECBM and provides the innovative theory and technology for “carbon neutralization and carbon peak” target.

High Temperature Mechanical Properties and Microstructure Evolution of Ti-6Al-4V Alloy Linear Friction Welding Joints

The combination of linear friction welding (LFW) and hot forming processes is limited due to a lack of research on the high-temperature flow behavior and microstructure evolution of welded joints. In this paper, an electric-assisted high-temperature uniaxial tensile test platform based on digital image correlation (DIC) is built, and uniaxial tensile tests of Ti-6Al-4V alloy with LFW joints are performed at different temperatures (923–1023 K) and different strain rates (0.001 s−1–0.01 s−1). Then the microstructure of the LFW joints under different hot deformation conditions have been analyzed by scanning electron microscope (SEM), electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The results indicate that the high-temperature flow behavior of LFW joints shows an obvious correlation between temperature and strain rate: the yield stress decreases from 203 MPa at 923 K to 105 MPa at 1023 K, and increases from 85 MPa to 130 MPa when the strain rate increases from 0.001 s−1 to 0.01 s−1 at 973 K. The hot deformation mechanisms with deformation conditions have been characterized, which changes from the mechanism of dislocation creep to the mechanism of self-diffusion as the deformation temperature increases from 923 to 1023 K. Especially, the fraction of high angle boundaries (HABs) rapidly rise from 49.2% to 64.1% with the increasing temperatures, the discontinuous dynamic recrystallization (DDRX) become the primary mechanism of nucleation during high-temperature deformation of LFW joints.

Mechanisms of Self-Diffusion of Linear Associative Polymers Studied by Brownian Dynamics Simulation

Mechanisms of Self-Diffusion of Linear Associative Polymers Studied by Brownian Dynamics Simulation

Self-diffusion mechanisms based defect complexes in MoSi2

MoSi2 is widely concerned due to excellent electrical conductivity, oxidation resistance as a typical transition metal silicide. The high-temperature diffusion behavior is one of the important factors for the degradation of MoSi2 coatings. However, the diffusion mechanism in MoSi2 is still unclear. Prior theoretical work mostly focused on defect formation energy, but these are not consistent with the self-diffusion experiments because the migration behaviors were not considered. Therefore, the purpose of this work was to investigate the microscopic diffusion mechanisms of Mo and Si atoms in MoSi2 using density functional theory and the CI-NEB method. We confirmed that the temperature-dependent vibrational contribution has a significant impact on the defect formation free energy. The isolated point defects in MoSi2 will tend to aggregate to form defect complexes, which participate in the atomic diffusion as mediators. The defect migration behaviors of atoms for vacancy mediated, vacancy complex mediated, and antisite assisted jumps were obtained based on electronic structures analysis. The results show that Si diffusion is mediated by intrasublattice jumps of the nearest neighbor Si vacancies. Moreover, the destroyed covalent Mo–Si bonds by Si vacancies and the non-directional weak metal bonds formed by the Mo antisites and Mo atoms could improve the mobility of the Mo atom which results in the low migration barrier. The agreement between our calculations and the reported experimental results indicates that the dominant diffusion mechanism for Mo atoms is mediated by vacancy complex mediated jumps and antisite assisted jumps. It is concluded that the Si vacancy-based defect complexes are likely the diffusion mediators for Mo atom self-diffusion in MoSi2. This work provides a deeper insight into the connection between the atomic mechanism and the macroscopic behavior for the diffusion in the MoSi2, and establishes the basis for further optimizing high-temperature coating materials.

Nuclear Magnetic Resonance Diffusometry of Linear and Branched Wormlike Micelles.

Diffusion studies using nuclear magnetic resonance (NMR) spectroscopy were conducted on two model surfactant solutions of cetyltrimethylammonium bromide/sodium salicylate (CTAB/NaSal) and cetylpyridinium chloride/sodium salicylate (CPCl/NaSal). By increasing the salt-to-surfactant concentration ratio, these systems display two peaks in the zero-shear viscosity and relaxation time, which are indicative of transitions from linear to branched micellar networks. The goal of this work is to assess the sensitivity of NMR diffusometry to different types of micellar microstructures and identify the mechanism(s) of surfactant self-diffusion in micellar solutions. At low salt-to-surfactant concentration ratios, for which wormlike micelles are linear, the surfactant self-diffusion is best described by a mean squared displacement, Z2, that varies as Z2 ∝ Tdiff0.5, where Tdiff is the diffusion time. As the salt concentration increases to establish branched micelles, Z2 ∝ Tdiff, indicating a Brownian-like self-diffusion of surfactant molecules in branched micelles. This result indicates that NMR diffusometry is capable of differentiating various types of micellar microstructures. In addition, the self-diffusion coefficient of the surfactant molecules in linear and branched micelles are determined, for the first time, by comparing the existing restricted diffusion models and are shown to be much slower than the diffusion of proton molecules in the bulk. Moreover, in linear and moderately branched wormlike micelles, the dominant mechanism of surfactant self-diffusion is through the curvilinear diffusion of the surfactant molecules along the contour length of the micelles, whereas in the branched micelles, before the second viscosity maxima, the surfactant self-diffusion could arise from a combination of micellar breakage, exchange between micelles and/or the bulk.

Dendrite-tolerant all-solid-state sodium batteries and an important mechanism of metal self-diffusion

Inhibition of dendrite growth in all-solid-state lithium batteries (ASSLBs) has long been a challenge to the field. In the present study, the conditions for dendrite growth for a similar but less mature technology, all-solid-state sodium batteries (ASSNBs), are investigated. By simply sticking sodium metal to Na3.4Zr2(SiO4)2.4(PO4)0.6 (NZSP) ceramic pellets and without applying external pressure during operation, the critical current density of Na/NZSP/Na symmetric ASSNBs reaches 9 mA cm−2 at 25 °C. The cells can be stably operated at an areal capacity of 5 mAh cm−2 (per half cycle, with 1.0 mA cm−2) at 25 °C for 300 h in a galvanostatic cycling measurement without any dendrite formation. The results outperform the existing ASSLBs and ASSNBs, and also go beyond satisfying the requirements for practical applications. The influence of the high metal self-diffusion coefficient on the dendritic plating/stripping is regarded as the most likely reason for the high dendrite tolerance of ASSNBs. A mathematical model based on Fick's second law was applied as a first approximation to illustrate this influence. Full ASSNBs were fabricated with infiltrated Na3V2(PO4)3 (NVP) as the cathode and can be stably operated with a capacity of 0.60 mAh cm−2 at high rate of 0.5 mA cm−2 at room temperature.

Vacancy- and interstitial-mediated self-diffusion coefficients determined from the analysis of observed self-diffusion coefficients in silicon crystals

We clarify the mechanisms of self-diffusion mediated by both vacancies and interstitials in silicon crystals. Südkamp and Bracht published carefully measured self-diffusion data for silicon and determined the vacancy-mediated diffusion coefficients from the difference between their new data and previous data of metal diffusion under consideration of a correlation factor. Instead, we analyzed their data using the vacancy properties: the formation energy was obtained from quenching experiments of silicon crystals in a hydrogen atmosphere, and the migration energy determined from low-temperature electron irradiation. The self-diffusion coefficient is given by the sum of the diffusion coefficients of the vacancy mechanism, 0.90 exp (−4.30 eV/kBT), and the interstitial mechanism, 6.9 × 102 exp (−4.8 eV/kBT) cm2 s−1.

Kinetics of radiation defect formation in iron under high displacement rate irradiation

In this study, the kinetics of vacancy and interstitial formation has been simulated in iron at a temperature of 600 K under irradiation at high radiation defect production rate 6.5·10-3,3.25·10-3,1.63·10-3dpa/s and displacement energies of 10 keV, 15 keV, 20 keV. The reaction-diffusion equations and molecular dynamics simulation of displacement cascades have been combined to calculate the kinetics of radiation defect formation. We have introduced the criterion to estimate homogeneity of distribution of radiation defects in the system. The kinetics of radiation defect formation has been calculated up to doses of ~5·10−5 dpa, whereas stationary values of their concentration are achieved at ~10−5 dpa. It has been shown, that high defect production rate of irradiation causes inhomogeneous distribution of the radiation defects with a finite life-time. Also, we consider the effect of high defect production rate and displacement energy on kinetics of radiation defect formation and the self-diffusion mechanism in iron at the considered temperature.

Atomic diffusion mediated by vacancy defects in L12-Zr3Al: A first-principles study

Systematic first-principles calculations based on density functional theory have been performed to determine the self-diffusion mechanism of Zr3Al. The formation energies of four intrinsic point defects were calculated and the relationship between concentration of different point defects and temperature was determined. Then, the effect of defect types on the stability of the system was explored after analyzing the electronic density of different supercells. In addition, the minimum energy pathways (MEPs) and the saddle point configurations during Zr or Al atom migration were calculated using the climbing image nudged elastic band method (CI-NEB). The energetic results show that the VZr-mediated nearest neighbor (NN) jump mechanism is the feasible migration mechanism for Zr atom and dominant Al atom diffusion mechanism is the antisite assisted (AS) mechanism because of the lowest diffusion activation energy barrier. The present study lays the foundation for further investigation, including solute-diffusion in Zr3Al and quantitative calculation of diffusion coefficients, and provides theoretical guideline for further design and improvement of the crucial diffusion-mediated properties of Zr3Al.

First-principles study of pressure and SiO-incorporation effect on dynamical properties of silicon oxide

The pressure and SiO-incorporation effect on the temperature dependence of dynamical properties for silicon oxide (SiO2)1−x(SiO)x is theoretically studied by first-principles molecular dynamics. It is found that the incorporation of SiO enhances the selfdiffusions even under high pressure. The SiO effect on Si selfdiffusion is however reduced by the pressure at temperature lower than 4000 K, and the amount of reduction is larger for lower temperature, while the effect on O selfdiffusion is hardly reduced, being independent of the temperature. Such a difference is thought to come from the difference in selfdiffusion mechanisms between Si and O. It is indicated that the incorporated SiO acts as combined SiO interstitials rather than separate Si interstitials or O vacancies. This also suggests that the oxide viscous flow mechanism is a promising candidate for the origin of the Si missing in oxidizing Si nanopillars.

DFT study of Au self-diffusion on Au(001) in the presence of a Cl adlayer

The atomic-scale mechanism of self-diffusion on coinage metal surfaces has been investigated by density functional theory calculations before. However, the detailed role of the co-adsorbed anions and of the electrochemical interface is not yet fully understood. We present diffusion paths of a Au adatom on c(2 × 2)-Cl and c(2×22)R45◦-Cl Au(001) surfaces. In the case of the fully Cl covered Au(001) surfaces, the diffusion energy barriers are ≥0.44 eV. In the presence of a neighboring Cl vacancy, the diffusion barriers are drastically reduced to about half of the value for the fully Cl covered surface. Thus, Au self-diffusion is promoted by Cl vacancies. A first estimate for the effect of water on the diffusion energy barrier of the Cl vacancy is derived by calculating the interaction of configurations along the diffusion path with a water layer.