Interstitial Diffusion Coefficient Research Articles

A novel methodology for mapping interstitial fluid dynamics in murine brain tumors using DCE-MRI

We present a comprehensive methodology for measuring heterogeneous interstitial fluid flow in murine brain tumors using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) coupled with the computational tool, Lymph4D. This four-part protocol encompasses glioma cell preparation, tumor inoculation, MRI imaging protocol, and histological verification using Evans Blue. While conventional DCE-MRI analysis primarily focuses on vascular perfusion, our methods reveal untapped potential to extract crucial information about interstitial fluid dynamics, including directions, velocities, and diffusion coefficients. This methodology extends beyond glioma research, with applicability to conditions routinely imaged with DCE-MRI, thereby offering a versatile tool for investigating interstitial fluid dynamics across a wide range of diseases and conditions. Our methodology holds promise for accelerating discoveries and advancements in biomedical research, ultimately enhancing diagnostic and therapeutic strategies for a wide range of diseases and conditions.

Thermal expansion, lattice vibration, and isotope effect on hydrogen diffusion in BCC Fe, Cr, and W from first-principles calculations.

Fe, Cr, and W are important elements in the alloys of in-reactor materials and operate in high-temperature environments with thermal expansion. Their tritium-impeding abilities are crucial to the radiation safety of various nuclear reactors. In this study, first-principles density functional theory is combined with quasi-harmonic approximation to evaluate factors that can affect the interstitial formation energy and diffusion coefficient of hydrogen isotopes in body-centered cubic (BCC) Fe, Cr, and W, including thermal expansion, metal host lattice vibrations, phonon density-of-states (pDOS) coupling diffusing atoms, and isotope effects. Calculation results indicate that the interstitial formation energy decreases as lattice expansion increases, whereas the jump barriers remain almost constant. Thermal expansion, host lattice vibration, and pDOS coupling minimally affect the diffusion coefficients of hydrogen isotopes in Fe, Cr, and W. The diffusion coefficient ratios between hydrogen isotopes are higher than the inverse ratio of the square root of the isotope mass at low temperatures. However, they decrease to the inverse ratio of the square root of the isotope mass at temperatures exceeding 800K. This study comprehensively investigates factors that affect the diffusion coefficients of hydrogen isotopes in BCC Fe, Cr, and W, thus providing a firm theoretical foundation for predicting the diffusion coefficients of tritium at different temperatures using protium/deuterium diffusion coefficients.

Study of helium diffusion in yttria: A multiscale approach based on the density functional theory and kinetic Monte Carlo, with transmission electron microscopy and thermo-desorption spectroscopy

A known issue for future nuclear reactors is helium accumulation inside the steel structure materials, responsible for structural issues such as embrittlement and cracking. One possible solution is using new types of reinforced steel, such as oxide dispersion strengthened (ODS) steel. It consists of adding oxide nanoparticles to the Fe-based material, especially yttrium oxide (yttria, Y2O3), improving its properties. Therefore, one first step is understanding the helium diffusion inside this system. Very little is known about helium inside yttria, with most studies being theoretical ones. Based on this context, this work proposes a combined theoretical and experimental multiscale approach to investigate helium diffusion inside yttria.The theoretical approach starts with the density functional theory, used to model the atomic yttria cell and determine helium insertion sites. The transitions between the sites were described using the Nudged Elastic Bond (NEB) method. Kinetic Monte Carlo was then employed to obtain the interstitial diffusion coefficient expression for the first time for this material. It showed a limited diffusion at temperatures below 600 K, which may indicate a tendency for He to be blocked in the oxide. Then, the charged vacancies were explored. It showed that the vacancy further reduces helium diffusion. Finally, it was demonstrated that helium spreads across different vacancies and interstitial sites.The experimental part involved implanting helium ions at 50 keV in samples with nanometric or micrometric grains. Then, the specimens were characterised with transmission electron microscopy (TEM) and thermo-desorption spectroscopy (TDS) techniques. TEM did not evidence detectable bubbles even at the highest studied fluence (1 × 1016 cm−2). The TDS highlighted different mechanisms for helium diffusion and the grain size's role, providing a novel model for diffusion coefficient calculation based on interstitial diffusion.

Understanding helium diffusion in iron: a multiscale modelling method based on the DFT and kinetic Monte Carlo, coupled to TEM and thermo-desorption spectroscopy experiments

Helium (He) is known to accumulate in vacancies of the steel structure materials of nuclear reactors, forming bubbles that increase in size and eventually cause structural problems, such as embrittlement. Several studies provided insights into the interstitial diffusion of this gas inside the iron matrix. However, much is still unknown about its behaviour. Based on this context, this study proposes a new combined theoretical and experimental multiscale approach made by the same team in a complementary way. It helps to have a global view of the helium diffusion in iron as a function of He content, temperature and structural defect concentration.Firstly, density functional theory has been used to identify the possible helium insertion sites in iron and the possible transitions between them. Then, the kinetic Monte Carlo method was applied to calculate its interstitial diffusion coefficient. It showed that helium swiftly diffuses interstitially in iron. It also tends to be trapped in iron vacancies and accumulate. The chromium and vacancy effects were also investigated.Experimentally, He was ion-implanted in several pure iron and high-purity Fe10wt%Cr samples. An analysis of He behaviour and its diffusion was carried out with transmission electron microscopy (TEM) and thermo-desorption spectroscopy (TDS) techniques. TEM shows the presence of small (∼0.7 nm radius) He bubbles and no significant difference with the presence of Cr. TDS evidences sequential “burst-type” He releases as T is sequentially increased. Based on these observations and inferred from the literature, we propose that He is detrapped and released from the studied materials as a consequence of the decrease in maximum He capacity of the trapping aggregates as T increases.

Concentrations and diffusion coefficients of thermal equilibrium point defects in silicon crystals

The dependencies of concentrations of thermal equilibrium vacancies and interstitials on temperatures in Si crystals are determined directly, which has been a long-standing issue since the 1950s. They are evaluated by combining the formation energies and self-diffusion entropies deduced from the analyses of self-diffusion coefficients, and migration entropies deduced from diffusion coefficients of point defects. The concentrations as the number density of thermal equilibrium vacancies and interstitials at temperature T (K) are determined to be 5 × 1022exp(6.5)exp(–3.85 eV/k B T) and 5 × 1022exp(10.6)exp(–4.3 eV/k B T) cm−3, respectively. The diffusion coefficients of vacancies and interstitials are determined to be 2.7 × 10−3exp(–0.45 eV/k B T) and 2.5 × 10−2 exp(–0.49 eV/k B T) cm2 s−1, respectively. The results are discussed in comparison with those reported experimentally.

Dislocation loop evolution in Kr‐irradiated ThO2

AbstractThe early stage of microstructural evolution of ThO2, under krypton irradiation at 600, 800, and 1000°C, was investigated using in situ transmission electron microscopy (TEM). Dislocation loops grew faster, whereas their number density decreased with increasing irradiation temperature. Loop density was found to decrease with ion dose. Interstitial dislocation loops, including Frank loops with Burgers vector of a/3〈111〉 and perfect loops with Burgers vector of a/2〈110〉, were determined by traditional TEM and atomic resolution–scanning TEM techniques. Atomistic and mesoscale level modeling are performed to interpret experimental observations. The migration energy barriers of defects in ThO2 were calculated using density‐functional theory. The energetics of different dislocation loop types were studied using molecular dynamics simulations. Loop density and diameter were analyzed using a kinetic rate theory model that considers stoichiometric loop evolution. This analysis reveals that loop growth is governed by the mobility of cation interstitials, whereas loop nucleation is determined by the mobility of anion defects. Lastly, a rate theory model was used to extract the diffusion coefficients of thorium interstitials, oxygen interstitials, and vacancies.

Phase and defect evolution in uranium-nitrogen-oxygen system under irradiation

Uranium mononitride (UN) with 5 wt.% uranium dioxide (UO2) is used as a model system to study the phase and defect evolution under proton irradiation in nitride-oxide composite. Phase composition, crystallographic orientation relationships (ORs) and dislocation loops were characterized using X-ray diffraction, transmission electron microscopy, and energy dispersive X-ray spectroscopy techniques. Proton-irradiation at elevated temperatures promoted the transformation of UN into uranium sesquinitride (U2N3) and UO2 phases. U2N3 and UO2 formed a fully coherent structure with two ORs: {002}U2N3‖{002}UO2 and [001]U2N3‖[001]UO2; U2N3{101}‖UO2{101} and U2N3[101]‖UO2[101] due to low lattice misfit (2.3%) and low interfacial energy (127 mJ/m2). Observed oxidation of UN and coherent interface are consistent with density-functional theory calculations which suggest lower energy for oxidized configuration and low energy of the interface. The dislocation loops grew while their number density decreased with the temperature and dose. The loop size was over three times larger in two nitride phases than that in UO2, while the number density was one order of magnitude higher in UO2 than in nitride phases. Loop density and diameter were analyzed using a kinetic rate theory that considers stoichiometric loop evolution. This analysis led to the conclusion in all compounds loop growth is governed by mobility of uranium interstitials, and enabled measurement of diffusion coefficients of uranium interstitials and non-metal interstitials and vacancies. This analysis provided a comparative study of early stage of microstructure evolution under irradiation which has implications for use of this mixture as advanced fuel in nuclear energy systems.

Numerical simulation of the influence of electron injections on the short-term annealing in pulse-neutron-irradiated p-type Si

The physical reason behind the much more rapid short-term annealing progress in the presence of electrons in P-type silicon irradiated by pulse neutrons is investigated. Continuum equations coupled with defect reactions are used for the numerical simulation on the temporary evolutions of defects at different electron injection ratios. It is indicated that electron injections can significantly accelerate the creations of boron and carbon interstitials, but may have little influence on the creation of the vacancy-oxygen complex. The calculations on the relative concentrations of interstitials and vacancies in different charge states via the electron injection ratio show that more and more interstitials in the doubly positive charge state change into neutral ones, and neutral vacancies are always dominant with an increase in the electron concentration. The thermal diffusion coefficient of neutral interstitials is much larger than the ones of interstitials in other charge states. As a consequence, normal ionization enhanced diffusion for interstitials in the presence of electrons can significantly accelerate the short-term annealing progress in P-type silicon. Ionization enhanced diffusion coefficients for interstitials due to athermal diffusion are further estimated using the Bourgoin mechanism, and results indicate that the diffusion coefficients of positively charged interstitials are improved by several orders of magnitude when compared to their corresponding thermal diffusion coefficients. However, the production of boron and carbon interstitials is only accelerated by about one order of magnitude, which would be ascribed into such large thermal diffusion coefficients of neutral interstitials.

First-principles calculations of solute transport in zirconium: Vacancy-mediated diffusion with metastable states and interstitial diffusion

Zirconium alloys are the most widely used nuclear fuel cladding materials for light water power reactors where irradiation damage causes solute redistribution, leading to degradation of alloy properties such as corrosion resistance. Designing radiation-tolerant zirconium alloys requires a thorough understanding of the atomic-scale transport behavior of the alloying elements in Zr. We perform density function theory calculations to investigate the diffusion of Sn, Cr, Fe, Be, Al, and Ni in the hexagonal close-packed (HCP) Zr matrix. We develop a methodology to accurately model the metastable vacancy states along the basal migration path, known to occur in group IV metals. We compute the vacancy-mediated solute diffusion coefficients and drag ratios using the kinetic Monte Carlo method and an analytic Green's function method---the agreement between the two validates our methodology. The computed diffusion coefficients of Sn and Al show good agreement with the experimental data and we expect these solutes to diffuse via the vacancy-mediated mechanism. We use a Green's function approach, parameterized with data from density functional theory calculations, to compute the interstitial diffusion coefficients of Cr, Fe, Be, and Ni in the HCP Zr lattice. The computed diffusion coefficients of Cr, Ni, and Be agree with the experimental measurements within one order of magnitude, while those of Fe are within two orders of magnitude of the experimental measurements. The drag ratios for Cr, Fe, Be, and Ni are positive up to 1235 K, which suggests that nonequilibrium vacancy fluxes could drag these solutes toward sinks such as dislocation loops and grain boundaries. We also compute the transport coefficients without including the metastable states, and using the eight- and thirteen-frequency model. Our results show significant differences in drag ratio for the eight- and thirteen-frequency model predictions compared with the Green's function methodology, but smaller errors in the solute diffusivity. Combining interstitial and vacancy-mediated diffusivities, we predict the unusual result that increased vacancy concentration slows down solute diffusivity, while a sufficiently high vacancy concentration can change the dominant mechanism to an accelerated vacancy-mediated diffusion.

Inferring diameters of spheres and cylinders using interstitial water.

Most early methods to infer axon diameter distributions using magnetic resonance imaging (MRI) used single diffusion encoding sequences such as pulsed gradient spin echo (SE) and are thus sensitive to axons of diameters > 5 μm. We previously simulated oscillating gradient (OG) SE sequences for diffusion spectroscopy to study smaller axons including the majority constituting cortical connections. That study suggested the model of constant extra-axonal diffusion breaks down at OG accessible frequencies. In this study we present data from phantoms to test a time-varying interstitial apparent diffusion coefficient. Diffusion spectra were measured in four samples from water packed around beads of diameters 3, 6 and 10 μm; and 151 μm diameter tubes. Surface-to-volume ratios, and diameters were inferred. The bead pore radii estimates were 0.60±0.08 μm, 0.54±0.06 μm and 1.0±0.1 μm corresponding to bead diameters ranging from 2.9±0.4 μm to 5.3±0.7 μm, 2.6±0.3 μm to 4.8±0.6 μm, and 4.9±0.7 μm to 9±1 μm. The tube surface-to-volume ratio estimate was 0.06±0.02 μm-1 corresponding to a tube diameter of 180±70 μm. Interstitial models with OG inferred 3-10 μm bead diameters from 0.54±0.06 μm to 1.0±0.1 μm pore radii and 151 μm tube diameters from 0.06±0.02 μm-1 surface-to-volume ratios.

Rate Theory for Dislocation Loops Evolution in AL-6XN Austenitic Stainless Steel under Proton Irradiation

The average size and density evolution of dislocation loops in AL-6XN austenitic stainless steel, a candidate fuel cladding material for supercritical water-cooled reactor, under proton irradiation were simulated through a rate theory model. The simulation results exhibit relatively good agreement with the experimental results at 563 K. The size and density of defect clusters are calculated under irradiation temperature between 550 K and 900 K and irradiation doses up to 15 dpa which satisfies the working condition in supercritical water-cooled reactor. The fast nucleation between self-interstitials happens at the initial stage of irradiation. The average size of dislocation loops increases while the average density of these loops reduces with the increasing temperature, and the average density approaches to a constant when irradiated at higher irradiation doses. The mechanism is discussed based on the variation of rate constants of defect reactions and the variation of the diffusion coefficients of interstitials and dislocation loops with dose and temperature.

Modelling of point defect complex formation and its application to H+ ion implanted silicon

The diffusion and interaction of impurity atoms in semiconductors play an important role in modelling of the technological processes for device fabrication. Being mobile, impurity atoms, vacancies and interstitials can recombine and/or precipitate in the form of stable complexes which leads to the modification of target material properties. Here, we present an analytic model that predicts the concentrations of such complexes as a function of point defect concentrations using the probabilities for point defects to encounter and the probabilities for the formation of specific complexes dependent on their formation energies. This approach is general and can be used in different systems. We applied this model to the formation of different complexes after H+ implantation in silicon at room temperature. The formation energies of the complexes were calculated using the density functional theory. We linked the macroscopic strain measured in the implanted crystal to the individual deformation fields generated by the different complexes and to their concentrations. Such model calibration allowed determining the diffusion coefficients of silicon vacancies and interstitials at room temperature, the time required for the formation of all the complexes, the concentrations of complexes as a function of H concentration and the specific role of some complexes in generating strain. The model can be extended to the case of the systems co-implanted with different ions and can be applied for developing the SmartCut® technology used for creating innovative substrates.

First-principles multiple-barrier diffusion theory: The case study of interstitial diffusion in CdTe

The diffusion of particles in solid-state materials generally involves several sequential thermal-activation processes. However, presently, diffusion coefficient theory only deals with a single barrier, i.e., it lacks an accurate description to deal with multiple-barrier diffusion. Here, we develop a general diffusion coefficient theory for multiple-barrier diffusion. Using our diffusion theory and first-principles calculated hopping rates for each barrier, we calculate the diffusion coefficients of Cd, Cu, Te, and Cl interstitials in CdTe for their full multiple-barrier diffusion pathways. As a result, we found that the calculated diffusivity agrees well with the experimental measurement, thus justifying our theory, which is general for many other systems.

Copper diffusion in germanium: connecting point defect parameters with bulk properties

Copper diffusion in germanium is fundamentally and technologically important as it has a very low activation energy and influences the precipitation and gettering of copper respectively. These constitute the understanding of copper’s diffusion properties in germanium over a range of temperatures and pressures important. In the present study we use the cBΩ model in which the defect Gibbs energy is proportional to the isothermal bulk modulus (B) and the mean volume per atom (Ω). The elastic and expansivity data is used in the description of the cBΩ model to derive the copper interstitial diffusion coefficient in germanium in the temperature range 827–1,176 K. The calculated results are discussed in view of the available experimental data.

Calculation of diffusion coefficients of defects and ions in UO2

This paper has presented molecular dynamics calculations of the diffusion coefficients of interstitials, vacancies, and vacancy complexes of oxygen and uranium in UO2, as well as the coefficients of ion diffusion provided by these defects. The interatomic potentials have been chosen by comparing the defect formation energies with data of the DFT + U calculations. The results of the calculations have been compared with experimental data on the annealing of defects and the measurements of self-diffusion coefficients of ions. The limitations of the model of point defects for the description of the self-diffusion in nominally stoichiometric UO2 have been discussed.

Diffusion coefficients of vacancies and interstitials along tilt grain boundaries in molybdenum

The diffusion coefficients of vacancies and interstitials along symmetrical tilt grain boundaries in molybdenum have been calculated using the molecular dynamics method. The migration energies of defects have been obtained. The activation energy and coefficients of grain boundary self-diffusion have been deter-mined. A comparison of the obtained results with the studies of other authors indicates that boundaries formed between particles in the powder in sintering experiments have a higher diffusion activity as compared to stable grain boundaries in polycrystals.

Measuring Interstitial Diffusion, Convection, and Binding Parameters in Mouse Tumors

Noninvasive techniques have been developed for the assessment of various parameters in normal and diseased tissues of mice. This protocol describes the measurement of extravascular parameters, including interstitial diffusion, convection, and binding parameters, in mouse tumors. A fluorescently labeled molecule of interest is infused into the tumor interstitium, followed by imaging using single-photon microscopy or multiphoton laser-scanning microscopy (MPLSM). Fluorescence recovery after photobleaching (FRAP) with spatial Fourier analysis is performed. To measure interstitial diffusion coefficients, multiphoton FRAP is performed.

Carbon diffusion and reactivity in Mn5Ge3 thin films

AbstractThe Curie temperature of Mn5Ge3 has been successfully enhanced by carbon doping. In this context the diffusion of a carbon thin film in Mn5Ge3 has been studied at room temperature. A value of the diffusivity of about D = 2.4 × 10‐23 ± 0.5 × 10‐23 m2 s‐1 is reported. This value is in the typical range of interstitial diffusion coefficients. Moreover Auger Ge and Mn peaks shifts and Ge3d core level have been investigated to get some details on the reactivity of carbon atoms in Mn5Ge3.Mn Auger transitions display a shift of 4 eV whereas Ge transitions do not. Similarly Ge3d core level does not contain C related contribution but presents a Mn one. These observations confirmed the fact that carbon atoms are not inert species for Mn. It suggests that a ternary Ge‐Mn‐C alloy could occur and should be taken into account when doping the Mn5Ge3 with carbon. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Application of the inverse Kirkendall model of radiation-induced segregation to ferritic–martensitic alloys

The inverse Kirkendall (IK) model was applied to the binary Fe–Cr b.c.c. system, to determine whether observations of Cr in ferritic–martensitic (F–M) alloys can be explained by the IK mechanism. Irradiations were conducted on alloys T91, HCM12A, and HT9 using energetic protons and Fe++ ions and Cr RIS at prior austenite grain boundaries was measured using STEM-EDS. An input data set relevant to b.c.c. Fe–Cr was assembled and model results were compared to experimental results. It was found that unlike austenitic alloys, in b.c.c. Fe–Cr alloys, interstitials played a strong role in Cr RIS. The IK model reproduced the temperature dependence of proton and Fe++ ion irradiations, as well as the composition dependence of proton irradiations. The temperature dependence of Cr RIS is attributed to the dominance of Cr depletion by the vacancy mechanism at high temperatures, and Cr enrichment by interstitials at low temperatures. Cr enrichment changes to Cr depletion at the temperature where the Cr:Fe vacancy and interstitial diffusion coefficient ratios cross one another. Model results also showed a decrease in grain boundary Cr enrichment with bulk Cr concentration, in agreement with experimental results from T91, HCM12A, and HT9 following proton irradiation at 400°C. The IK model did not account for the experimentally observed dose dependence. This dose dependence of RIS was attributed to the complex microstructural evolution, which is not accounted for in the IK model.

Oxygen Diffusion in an Nb-Ta Alloy Measured by Mechanical Spectroscopy

When metals that present bcc crystalline structure receive the addition of interstitial atoms as oxygen, nitrogen, hydrogen and carbon, they undergo significant changes in their physical properties because they are able to dissolve great amounts of those interstitial elements, and thus form solid solutions. Niobium and most of its alloys possess a bcc crystalline structure and, because Brazil is the largest world exporter of this metal, it is fundamental to understand the interaction mechanisms between interstitial elements and niobium or its alloys. In this study, mechanical spectroscopy (internal friction) measurements were performed on Nb-8.9wt%Ta alloys containing oxygen in solid solution. The experimental results presented complex internal friction spectra. With the addition of substitutional solute, interactions between the two types of solutes (substitutional and interstitial) were observed, considering that the random distribution of the interstitial atoms was affected by the presence of substitutional atoms. Interstitial diffusion coefficients, pre-exponential factors and activation energies were calculated for oxygen in this alloy.