Diffusion Of Impurity Atoms Research Articles

Constitutive modelling of thermomechanical abnormalities due to dynamic strain aging in commercially pure titanium

Dynamic Strain Aging (DSA) is the irregular increase in metal strength that results from the diffusion of impurity atoms and their interactions with dislocations during plastic deformation at specific strain rates and temperatures. Commercially Pure Titanium (CP–Ti) has been reported to exhibit DSA over a broad range of temperature and strain rates during plastic deformation owing to the impurity atoms diffusion. The current work focuses on the modification of the physical-based Voyiadjis Abed (VA) model by introducing an additional term, based on the concentration and diffusion kinetics of different impurities, to capture DSA in CP-Ti. The analysis of diffusion parameters indicates that the hydrogen impurity diffuse into the dislocation core and interact with the mobile dislocations, thus defining the temperature range for the activation of DSA at low and high strain rates. The results show that the modified VA model could capture DSA in CP-Ti over a wide range of strain rates and temperatures when the recommended novel modification based on physical and microstructural parameters was introduced.

Metastable Antimony‐Doped SnO2 Quantum Wires for Ultrasensitive Gas Sensors

AbstractDoping is fundamental to controlling the properties of bulk semiconductors. Although the antimony (SbV)‐doping strategy is widely employed in the design of practical tin oxide (SnO2) semiconductor gas sensors for higher signal‐to‐noise ratio, challenges remain to dope semiconductor nanocrystals since the diffusion of impurity atoms may be far from realized at the synthesis temperatures used. Herein, a metastable Sb‐doping strategy is proposed to overcome the serious receptor‐versus‐transducer mismatch in SnO2 quantum wires (QWs). The solvothermal synthesis of colloidal SbIII‐doped SnO2 QWs has been conducted at 180 °C, whereby the antimony amount is varied to optimize the structural and morphological properties for higher surface activity and electrical conductivity. A unique n‐type doping mechanism arising from the stable presence of SbIII on SnO2 (101) facets via SnII‐O‐SbIII is demonstrated. Further, the use of sensitive (down to 4 ppb, the lowest detection limit ever reported), fast (response and recovery time of 43 s and 96 s toward 10 ppm of H2S) gas sensors for H2S detection at near room temperature (40 °C) is showcased. The metastable Sb‐doping strategy may pave the way to ultrasensitive gas sensor possessing low power consumption and excellent integration compatibility to satisfy the increasing demand for ubiquitous and reliable gas detection.

Statistical Model of Impurity Atoms Diffusion in the Crystal Lattice of Metals and Its Application for Calculating the Diffusion Coefficients of Hydrogen and Carbon Atoms in Iron

A simple statistical model of the diffusion of impurity atoms in the crystal lattice of metals has been developed. The relationship between the diffusion flux of atoms and the gradient of their chemical potential is obtained from the basic principles of statistical thermodynamics. For an ideal solid solution of a substance atoms in a metal, an expression is found for the zero diffusion coefficient, which depends on the square of the temperature. The calculated diffusion coefficients of hydrogen and carbon atoms in iron are in a fairly good agreement with the known experimental data.

SIMULATION OF BORON DIFFUSION IN THE NEAR-SURFACE REGION OF SILICON SUBSTRATE

The mechanism of boron-enhanced diffusion from a thin boron layer deposited on the surface in the case of silicon crystal doping is proposed and investigated. It was supposed that lattice contraction occurs in the vicinity of the surface due to the difference between the atomic radii of boron and silicon. This lattice contraction provides a stress-mediated diffusion of silicon self-interstitials from the near-surface region to the bulk of a semiconductor. Due to the stress-mediated diffusion, the near-surface region is depleted of silicon self-interstitials, and simultaneous oversaturation of this species occurs in the bulk. In this way, a strong nonuniform distribution of silicon self-interstitials in the vicinity of the surface is formed without regard to the large migration length of this species. The oversaturation of the bulk of a semiconductor with nonequilibrium self-interstitials allows one to explain the boron-enhanced diffusion of impurity atoms. The strong nonuniform distribution of these point defects also results in a specific form of boron concentration profile in the vicinity of the surface. Good agreement of the calculated boron profile with the experimental data for the entire doped region was obtained within the limit of the proposed model.

Surface-Kinetics-Limited Ostwald Ripening of Spherical Precipitates at Grain Boundaries

Ostwald ripening of sufficiently large (usually macroscopic) precipitates is the late stage of the diffusion decomposition of a supersaturated solid solution, occurring through the formation of fluctuations and subsequent growth of centers (nuclei) of a new phase. The paper describes a theoretical study of the Ostwald ripening of spherical precipitates of a newly formed phase at the grain boundary of finite thickness with the diffusion of impurity atoms from the grain interior to the grain boundary considered. The precipitate growth is assumed to be limited by the kinetics of impurity atom imbedding into the precipitate rather than by the impurity atom diffusion inside the grain boundary. The speed of diffusion growth of spherical precipitate located on the grain boundary is found. A system of equations which describes surface-kinetics-limited growth of Oswald ripening of spherical precipitates on the grain boundary is formulated. This system consists of the equation of growth rate of the precipitate, the kinetic equation for the precipitates size distribution function which is normalized by the precipitates density, and the equation of the balance of matter in the system (the law of conservation of matter). The law of conservation of matter takes into account the atoms of impurities which are in solid solutions of the grain boundary and the body of the grain as well as in the precipitates which is the specifics of our problem. The asymptotic time dependences are found for the average and critical precipitate radius, supersaturation of solid solution of impurity atoms in the grain boundary, precipitate size distribution function, precipitate density, and for the factor of grain boundary filling with precipitates (the area covered by the precipitates per unit area of the grain boundary) and the total number of impurity atoms in precipitates. The factor of grain boundary filling with precipitates is a characteristic of the two-dimensional Ostwald ripening problem. A discussion of the limits of validity of obtained results is given.

Effect of Charged Clusters on the Diffusion of Impurity Atoms in Silicon Crystals

An equation of diffusion of impurity atoms in silicon crystals has been obtained, based on which the influence of charged clusters in a silicon crystal on the process of impurity transfer can be determined. It is shown that a characteristic feature of this effect is the appearance of an additional flux of impurity atoms, which is capable of leading to impurity segregation.

Analysis of coupled diffusion and stress of nanowire using diffusion equation with a chemo-mechanical potential

Nanowire is a cylindrical object with nano-order diameter. Because of its low number of defects such as dislocations and twins, nanowire has very high strength. However, its relatively large surface volume fraction compared to bulk materials, enhances its corrosion. This problem inhibits its application. Corrosion of nanowire can be treated as a diffusion of impurity atoms into a base material. This phenomenon is modeled by a diffusion equation. When impurity atoms intrude into the base material, volume expansion occurs. The volume expansion induces internal stress. This stress effects on the diffusion. To count this effect into the diffusion equation, we defined chemo-mechanical potential, which includes internal stress (mechanical effect) to a chemical stress (mechanical effect). A very large volume expansion may causes yielding. Because the stress and the diffusion are coupled, the yielding causes a non-contiguous effect on the diffusion. So we considered the effect of yielding. And we also considered blocking effect, decrease of apparent diffusion coefficient induced by high impurity concentration. We modeled hydrogen diffusion in nickel nanowire counting these effects. We numerically solved the diffusion equation. The obtained results tell that yielding delays the diffusion and it suggests the possibility of diffusion control by external stress.

Microscopic mechanism responsible for radiation-enhanced diffusion of impurity atoms

Modelling of radiation-enhanced diffusion (RED) of boron and phosphorus atoms during irradiation of silicon substrates respectively with high- and low-energy protons was carried out. The results obtained confirm the previously arrived conclusion that impurity diffusion occurs by means of the ‘impurity atom – intrinsic point defect’ pairs and that the condition of the local thermodynamic equilibrium between substitutional impurity atoms, nonequilibrium point defects created by irradiation, and the pairs is valid. It is shown that using RED, one can form a special impurity distribution in the semiconductor substrate including retrograde profiles with increasing impurity concentration in the bulk of the semiconductor. In addition, modelling of radiation-induced segregation of nitrogen implanted in stainless steel modified by titanium is carried out. It is shown that vacancy-impurity complexes are responsible for nitrogen diffusion in an implanted layer excluding the ‘tail’ region. The calculations performed give clear evidence in favour of further investigation of various doping processes based on RED, especially the processes of plasma doping, to develop a cheap method for forming specific impurity distributions in the near surface region.

Correlation factors for impurity diffusion on the sublattice of dodecahedral sites in garnet

The method of Koiwa and Ishioka (Philos Mag A 47:927–938, 1983) is used, with slight modification, to evaluate the correlation factor for vacancy-mediated diffusion of impurity atoms on the sublattice of dodecahedral sites in garnet, as a function of the relevant vacancy-jump frequencies. The required values of the lattice Green’s function were obtained from multiple Monte Carlo simulations in lattices of progressively larger size, extrapolated to an infinite lattice using a model that linearizes the dependence of the functional value on lattice size. As Online Resources, codes are provided that permit evaluation of the correlation factor for any chosen set of vacancy-jump frequencies, for implementation in either Mathematica® or Matlab®.

Gyrosolitons and helical surfing diffusion of impurity atoms in reactor fuel materials

Fundamentally new gyrosolitons with helical trajectories of motion have been revealed in UO2 and PuO2 reactor fuel materials by the computer simulation of the microdynamics of high-amplitude atomic vibrations. The phonon spectra of nanostructures, as well as of gyrotropic materials, include quasioptical branches with different-sign linear dispersion. The corresponding branches of gyrosolitons have been revealed on the phase plane in the spectral density of vibrations. The main dynamic event of the kinetic process of helical surfing diffusion of impurity atoms on gyrosolitons has been observed.

ChemInform Abstract: Impurity Diffusion in Highly‐Ordered Intermetallic Compounds Studied by Nuclear Quadrupole Interactions

AbstractReview: 30 refs.

Impurity Diffusion in Highly-Ordered Intermetallic Compounds Studied by Nuclear Quadrupole Interactions

Diffusion of impurity atoms depends on the sublattices occupied, active diffusion mechanisms, and jump frequencies to neighboring sites. The method of perturbed angular correlation of gamma rays (PAC) has been applied over the past decade to study impurity diffusion through measurement of nuclear quadrupole interactions (NQI) at nuclei of 111In/Cd probe atoms. Extensive measurements have been made on highly-ordered compounds having the L12 crystal structure, including In3R, Sn3R, Ga3R, Al3R and Pd3R phases (R= rare-earth element). Measurements in thermal equilibrium at high temperature served to determine lattice locations of 111In parent probe-atoms, through characteristic NQIs, and to measure diffusional jump-frequencies of 111Cd daughter probe-atoms, through relaxation of the NQI. This paper summarizes results of the jump-frequency measurements and relates them to the conventional diffusivity that can be determined, for example, from penetration profiles of tracer species. In spite of chemical similarities of the series of rare-earth phases studied, remarkably large variations in jump frequencies have been observed especially along series of In3R and Pd3R phases. Most phases appear as “line compounds” in binary phase diagrams, but large differences in site-preferences and jump-frequencies were observed for samples prepared to have the opposing limiting phase boundary compositions. Comparisons of jump-frequencies measured at opposing boundary compositions can give insight into the predominant microscopic diffusional mechanisms of the impurity. A change in diffusion mechanism was proposed in 2009 to explain jump-frequency systematics for In3R phases. An alternative explanation is proposed in the present paper based on site-preferences of 111Cd daughter probes newly observed along the parallel Pd3R series. The diffusivity can be expressed as the product of a jump-frequency such as measured in these studies and a correlation factor for diffusion that depends on the diffusion mechanism. The correlation factor can be modeled for the L12 structure and diffusion sublattice of interest using a five-frequency model originally proposed for metals. Although the correlation factor is an essential parameter for the diffusion of impurities, it has never been measured. It is suggested that values of the correlation factor can be determined feasibly by combining results of jump-frequency measurements such as the present ones with diffusivity measurements made for the same host-impurity systems.

Density functional theory calculations of stability and diffusion mechanisms of impurity atoms in Ge crystals

Ge-based substrates are being developed for applications in advanced nano-electronic devices because of their higher intrinsic carrier mobility than Si. The stability and diffusion mechanism of impurity atoms in Ge are not well known in contrast to those of Si. Systematic studies of the stable sites of 2nd to 6th row element impurity atoms in Ge crystal were undertaken with density functional theory (DFT) and compared with those in Si crystal. It was found that most of the impurity atoms in Ge were stable at substitutional sites, while transition metals in Si were stable at interstitial sites and the other impurity atoms in Si were stable at substitutional sites. Furthermore, DFT calculations were carried out to clarify the mechanism responsible for the diffusion of impurity atoms in Ge crystals. The diffusion mechanism for 3d transition metals in Ge was found to be an interstitial-substitutional diffusion mechanism, while in Si this was an interstitial diffusion mechanism. The diffusion barriers in the proposed diffusion mechanisms in Ge and Si were quantitatively verified by comparing them to the experimental values in the literature.

Percolation mechanism of the diffusion of impurity atoms in dense surface layers

The molecular dynamics method is used to study the migration of an impurity atom on an unfilled square lattice. The calculations are performed on a lattice containing 212 × 214 sites at various values of the ratio p of the frequencies of jumps impurity and lattice atoms and various relative concentrations of vacancies ϑV. In the limit of vanishingly small concentrations of vacancies, ϑV ≪ 1, the present simulation results are in agreement with our previous analytical results. With increasing ϑV, the diffusion coefficient of impurity atoms predicted by the simulations exceeds the result of the analytical theory, a behavior that can be explained by the growing influence of vacancy clusters, voids on the surface, in which the impurity atom can travel long distances. This is most clearly seen in the case of highly mobile impurity atoms (p ≫ 1), where within the characteristic time of displacement of impurity atoms, lattice atoms remain practically immobile, and the problem appears to be closely related to the percolation problem. In this case, up to ϑV ≈ 0.3, the diffusion coefficient is independent of p; then, such a dependence appears, and the diffusion coefficient increases sharply with ϑV.

Generation and suppression of misfit dislocations at the seed/crystal interface in Si bulk crystal growth

AbstractMechanism of generation and suppression of misfit dislocations in Si bulk crystal growth at the seed/crystal interface is studied. Misfit dislocations in B‐doped CZ‐Si crystal growth are suppressed when the difference in B concentration between a seed and the grown crystal is at least 9 × 1018 cm–3, corresponding to 4.5 × 10–5 of misfit strain. Similar misfit strain of 3.4 × 10–5 was obtained in Ge‐doped CZ‐Si crystal growth. In the CZ‐Si crystal growth, a transition region of impurity concentration with about 40 μm in width is formed at the seed/crystal interface in both dislocation‐free and dislocated crystals by diffusion of impurity atoms from the seed. From a macroscopic viewpoint at the seed/crystal interface, the critical misfit strain in Si bulk crystal growth is larger than that in epitaxial growth model in a consideration that the width of the transition region is the critical thickness of the grown layer. We propose a preliminary new mechanism of generation and suppression of misfit dislocations dependent on the local misfit strain at the interface during the growth from a microscopic viewpoint. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phenomenological model of the diffusion of impurity atoms in ultrathin silicon layers with a nonuniform distribution of temperatures

The influence of fluxes of intrinsic nonequilibrium semiconductor defects on impurity diffusion in a nonuniform temperature field is considered in the framework of the phenomenological theory of irreversible processes. The mass transfer coefficient defined as the ratio of the concentrations of nonequilibrium and equilibrium defects is introduced to take the excessive concentration of nonequilibrium defects into account. The introduction of this coefficient into equations for matter and heat fluxes makes it possible to express the parameters of the process of thermal diffusion (the diffusion coefficient and the heat of transport) as a time-dependent function of the excessive concentration of intrinsic nonequilibrium semiconductor defects.

Migration kinetics of ion-implanted beryllium in glassy carbon

Migration kinetics of low-concentration implanted 7Be in glassy carbon has been studied by the modified radiotracer technique at temperatures 1285 °C and 1340 °C. The annealed sample concentration profiles show two distinctive components: (i) Main profile broadening assigned to beryllium trapping in defects during annealing. (ii) Tail parts on both sides of the profile maximum related to faster migration. Of the latter the profile representing bulk diffusion lies on the region free of defect influence and is well described by concentration-independent diffusivity. The features of the concentration profile broadening towards the sample surface indicate partial Be trapping in defects upon annealing. Diffusion coefficients for Be migration in the damaged and defect-free material are provided. It is concluded that light impurity atom diffusion in glassy carbon is of the same order of magnitude as diffusion in diamond.

Diffusion in Nanoporous Phases: Size Dependence and Levitation Effect

Self-diffusivity, D, of diffusants in widely differing mediums such as liquids (e.g., solution), porous solids (e.g., guests in zeolites), or ions in polar solvents exhibit strong size dependence. We discuss the nature of the size dependence observed in these systems. Altogether, different theoretical approaches have been proposed to understand the nature of size dependence of D not only across these widely differing systems but even in just one medium or class of systems such as, for example, ions in polar solvents. But molecular dynamics investigations in the past decade have shown that the size dependence of self-diffusion in guest-porous solids could have origins in the mutual cancellation of forces that occurs when the size of the diffusant is comparable to the size of the void. The effect leading to the maximum in D is known as the levitation effect (LE). Such a cancellation is a consequence of symmetry. This effect exists in all porous solids irrespective of the geometrical and topological details of the pore network provided by the solid. Recent studies show that the levitation effect and size-dependent diffusivity maximum exists for uncharged solutes in solvents. One of the consequences of this is the breakdown in the Stokes-Einstein relationship over a certain range of solute-solvent size ratio. Experimental measurements of ionic conductivity over the past hundred years have found the existence of a size-dependent diffusivity maximum leading to violation of the Walden's rule for ions in polar solvents. Molecular dynamics simulations and experimental data suggest that even this maximum has its origin in LE. Simulation studies of impurity atom diffusion in close-packed solids as well as ions in superionic and other solids suggest the existence of a size-dependent diffusivity maximum in these materials as well. The levitation effect is a universal effect leading to a maximum in diffusivity of a diffusant in a variety of condensed matter phases. The only condition for its existence appears to be the presence of van der Waals or electrostatic interactions.

Diffusion of Xe in Ta, Zr, and Pt

The diffusion-limited release of radioactive 120Xe ( T 1 / 2 = 40 m ) from several thin metal foils abruptly heated to temperatures of order 1000 °C while in a vacuum is characterized and interpreted in terms of impurity atom diffusion coefficients. The 120Xe impurities were produced in situ from the decay of 120Cs implanted into Ta, Pt, and Zr foils from a 30 keV mass-separated ion beam. The temperature dependence of the diffusion coefficients extracted from our data is well described by Arrhenius relations, for which best-fit parameters are presented. The fastest release of 120Xe for a given set of implantation conditions and temperature is observed for Zr, although its reactivity may prove problematic for its use as a catcher foil. A number of convenient analytic formulae for the diffusion-limited release of impurity atoms are presented.

Simulation of Coupled Diffusion of Impurity Atoms and Point Defects under Nonequilibrium Conditions in Local Domain

A two-dimensional model of doping of the active regions in semiconductor devices by means of ion implantation and thermal annealing is stated and analyzed. Radiation enhanced diffusion of impurity atoms during high temperature implantation of hydrogen ions is also considered. An economic finite difference method for solving the obtained system of diffusion equations is developed and numerical computations of the diffusion processes are carried out.