Diffusion Of Interstitial Impurities Research Articles

Effect of Temperature on the Kinetics of Localized Plasticity Autowaves in Lüders Deformation

The paper analyzes the elastoplastic transition in Fe–0.025 wt. % C at a temperature of 296–503 K and strain rate of 6.67·10−6–3.33·10−3 s−1. The analysis shows that the lower yield stress increases by a power law with increasing the strain rate, and that its rate sensitivity decreases linearly with increasing the test temperature. At temperatures lower than 393 K, the rate sensitivity of the lower yield stress is normal, and at 393–503 K, it is zero. In the range 393–503 K, the kinetics of the Lüders bands is changed from steady to discrete, and the higher the strain rate, the higher the temperature of this transition. Using the available data on the dynamics of dislocations and diffusion of interstitial impurities in the test alloy, it is demonstrated that the kinetics of Lüders bands are controlled by the effect of dynamic strain aging. If the arrest time of mobile dislocations tw at barriers which are overcome via thermal activation is comparable with the precipitation time of interstitial atoms ta at these dislocations, the motion of a Lüders band is discrete, and the band represents an excitation wave of localized plasticity; its refractory period is determined by the time of dynamic strain aging. If ta >> tw, the band moves monotonically and represents a switching autowave. The results of the analysis suggest that the effect of serrated yielding at the lower temperature boundary of blue brittleness can be suppressed by increasing the strain rate. When the arrest time of dislocations tw decreases, the comparability of tw and ta is broken, and no excitation autowave is formed. The data reported in the paper can be used to develop warm rolling technologies for materials with a sharp elastoplastic transition.

Reaction synthesis of gradient coatings by annealing of three-layer Ti–Ni–Ti nanolaminate magnetron sputtered on the TiNi substrate

In this work, Ti-Ni-Ti nanolaminate was deposited on a TiNi substrate by magnetron sputtering. Subsequent synthesis in Ar at temperatures of 500, 700 and 900 °C was carried out. To investigate the effect of the reaction synthesis temperature for obtaining a dense thin intermetallic biofunctional coating, a comparative analysis of the morphology, structure, phase composition, mechanical properties and wettability of the coatings was carried out. It was found that crystallization processes have a different impact on the amorphous Ti and Ni layers depending on temperature. In all cases, multilayer gradient crystalline coatings were formed that bound to the substrate by the diffusion zone. The reaction synthesis temperatures of 500 and 700 °C are insufficient for reaction completion and complete transformation; therefore, the obtained thin loose layers are unstable under stresses caused by the substrate. Reaction synthesis in Ti – Ni – Ti nanolaminate at 900 °С formed a dense two-layer gradient coating 2 µm thick, which reliably protects the matrix from further diffusion of interstitial impurities and segregation of Ni atoms onto the surface. An analysis of the nano-indentation deformation diagrams showed that the coatings do not prevent the viscoelastic deformation of the TiNi substrate.

Kinetics of segregation formation in the vicinity of edge dislocation in fcc metals

We use new equations for the interstitial impurity diffusion fluxes under strain to study impurity atom redistribution in the vicinity of dislocations taking into account the strain generated by mentioned defects. Two levels of simulation are applied. First one is evaluation of coefficients that determine the influence of strain tensor components on interstitial diffusion fluxes in fcc structures for different kinds of atom jumps. For this purpose we have developed a model into the framework of molecular static method taking into account an atom environment as near the interstitial site as for the saddle-point configuration. The second level is modeling of interstitial segregation formation based on nonlinear diffusion equations taking strains generated by defects. The results show, that the distributions of the interstitials near the dislocations have quite complicated characters and the vacancy distribution has qualitatively different character as compared with carbon distribution.

Ab initio approach to the effect of Fe on the diffusion in hcp Zr II: The energy barriers

Using density functional theory calculations together with the Monomer method for the search of saddle points (combined for the first time with an ab initio algorithm), we obtain the vacancy formation energies and the migration barriers for α-Zr self-diffusion and for the diffusion of interstitial impurities, including the ultra-fast diffuser Fe. Good agreement with measured diffusion coefficients is obtained, as a much lower energy barrier for the ultra-fast diffuser is found. We also suggest a possible mechanism for the increase in self-diffusion due to the Fe impurity, always present in the experimental samples.

Activation energy of hydrogen, oxygen, and nitrogen diffusion in metals

Significant progress has recently been made in experimental studies of the diffusion of atoms of light elements in metals. In particular, for a number of metals, the diffusion coefficients of tracer atoms of hydrogen (tritium), oxygen, nitrogen, and boron were measured. Previously, such data were available only for carbon. New experimental data enabled us in this work to formulate the problem of developing a theoretical criterion for the reliability of experimental results on the activation energy Q for the interstitial diffusion mechanism. The necessity of formulating such a problem is primarily caused by the fact that the scatter of experimental data on the diffusion of interstitial impurities in metals is often very wide. For example, experimental values of the activation energy Q of hydrogen diffusion in α -Ti are within the range 24‐62 kJ/mol [1]. In this context, in this work, we analyzed experimental data on the diffusion of interstitial atoms in metals that were obtained by reliable methods. It was found that all such data on the activation energy of hydrogen, oxygen, and nitrogen diffusion are consistent with a calculation model [2, 3] based on the theory of elasticity. The calculation accuracy corresponds to the level of a modern precision experiment (on the order of 1%). The corresponding data for carbon and boron were excluded from the analysis. This is because the adequacy of the elastic model of the potential barrier for carbon was not confirmed by the results of measuring the anisotropy of the diffusion coefficients in α -Ti [4, 5]. Data on the diffusion of tracer boron atoms in metals are extremely meager and did not allow us to analyze relationships for boron. Elastic model of the potential barrier. The currently dominant concept of the nature of Q and procedures for calculating Q was formulated in the midtwentieth century [2, 3]. Within this concept, the activation energy Q for the interstitial diffusion mechanism is determined by the elastic energy of crystal strain when an impurity atom is placed at a saddle point; i.e., the larger the diffusant atom, the higher the activation energy Q . The expression for Q has the form [2]

Diffusion of interstitial impurities through a cylindrical shell with residual stresses

Diffusion of interstitial impurities through a cylindrical shell with residual stresses

Kinetics of static strain aging in polycrystalline NiAl-based alloys

The kinetics of yield point return have been studied in two NiAl-based alloys as a function of aging time at temperatures between 300 and 700 K. The results indicate that the upper yield stress increment, Delta sigma(sub u) (i.e., stress difference between the upper yield point and the final flow stress achieved during prestraining), in conventional purity (CP-NiAl) and in high purity carbon-doped (NiAl-C) material first increased with a t(exp 2/3) relationship before reaching a plateau. This behavior suggests that a Cottrell locking mechanism is the cause for yield points in NiAl. In addition, positive y-axis intercepts were observed in plots of Delta sigma(sub u) versus t(exp 2/3) suggesting the operation of a Snoek mechanism. Analysis according to the Cottrell Bilby model of atmosphere formation around dislocations yields an activation energy for yield point return in the range 70 to 76 kJ/mol which is comparable to the activation energy for diffusion of interstitial impurities in bcc metals. It is, thus, concluded that the kinetics of static strain aging in NiAl are controlled by the locking of dislocations by Cottrell atmospheres of carbon atoms around dislocations.

Motion of oxygen in vanadium and niobium studied by nuclear magnetic resonance

The motion of oxygen in solid vanadium and niobium, containing different amounts of oxygen (0.26-3.40 at.%), was studied by means of 51V and 93Nb nuclear spin relaxation (NSR) measurements at 300 K < T < 1400 K. In the entire temperature range the Zeeman NSR rate 1/ T 1 is determined by fluctuations of the conduction electron-nucleus interaction. The rotating frame NSR rates 1/ T 1 ϱ , however, exhibit three distinct maxima at elevated temperatures, in addition to the conduction electron induced contribution. These NSR peaks are shown to be caused by fluctuations of the nuclear quadrupole interaction of the probe nuclei due to migration of interstitial oxygen atoms. From the experimental data the corresponding activation energies E a and pre-exponential factors τ 0 for the respective oxygen jump rates have been determined. We found that the atomic jump rates differ in τ 0 basically, while the activation energies are nearly identical for all three relaxation mechanisms (≈ 1eV). The results are discussed in the framework of three existing models for the diffusion of interstitial impurities in metals.

Distribution of interstitial impurities in titanium-vanadium alloys after holding in liquid lithium

The distribution of interstitial impurities between liquid lithium and solid titanium-alloyed vanadium is investigated. It is shown that titanium alloying of vandium intensifies nitrogen and carbon transport from lithium into the solid metal. At the same time, the concentration of oxygen in the surface layers of the specimens increases as a result of penetration of lithium and formation of complex oxides of the Me x Li y O z type. Increase in the titanium content leads to an increase in the carbon concentration on the surface and to the formation of protective carbon films that inhibit the diffusion of interstitial impurities into deep-seated layers.

Strain aging embrittlement of the ordered intermetallic compound NiAl

The deformation behavior and fracture toughness of single crystals of the ordered intermetallic compound NiAl were investigated as functions of relatively low temperature thermal treatments. A strain aging embrittlement phenonenon, similar to that observed in mild steels, was identified. In the non-embrittled condition, tensile ductilities on the order of 7%–8% and fracture toughness values of 15–17 MPa m 1 2 were obtained for crystals with a 〈110〉 axis tested at room temperature. Additional observations of serrated yielding during compression testing at temperatures between 100 and 200 °C are consistent with strain aging induced by the low temperature diffusion of interstitial impurities or constitutional vacancies to dislocations, thus rendering them immobile at room temperature.

Interstitial Impurities in Wurtzite Vs. Zincblende Semiconductors: The Case of H In SiC

ABSTRACTMost compound semiconductors crystallize in the zincblende or the wurtzite structures. In both cases, all the host atoms are tetrahedrally coordinated. However, the two lattices have no high symmetry interstitial sites in common. As a result, the stability, lowest-energy configuration, electronic structures, and barriers for diffusion of interstitial impurities are in general very different. This situation is illustrated here in the case of interstitial H in 3C (zincblende) and 2H (wurtzite) SiC. The results can be used to obtain the properties of H in other hexagonal polytypes, in particular 6H-SiC.

A Study of Interstitial Impurity Diffusion by the Linear Response Theory

AbstractThe diffusion of interstitial impurities is studied within the linear response theory using Hamiltonian describing localized and quasi‐free states of impurity particles, as well as their interaction with lattice vibrations. The diffusion coefficient for light impurity atoms is shown to deviate from the Arrhenius‐type linear dependence ln D ∼ 1/T at high temperatures.

Note on the origin of intrinsic stresses in films deposited via evaporation and sputtering

An attempt is made to provide a broad and brief review (with a sufficient number of references) of the question of intrinsic stresses in films deposited via evaporation and sputtering. Films deposited via evaporation are usually found initially in a disordered state, at the limit in an amorphous condition. Very broad thermodynamic principles imply that disorder is usually accompanied by an increase in volume (with few exceptions, e.g. water). Any relaxation from a disordered state to a more ordered state will, therefore, be accompanied by a decrease in volume and the formation of tensile stresses. The situation is modified in films deposited in the presence of impurities. Then one often finds the formation of compressive stresses. Several mechanisms may account for this result: (a) direct diffusion of interstitial impurities in the bulk of the underlying film: (b) surface and grain boundary diffusion of the impurities leading to compound formation (and swelling) in the grain boundaries, and at low temperatures in intergranular voids; (c) some attention is paid to a third model where compressive stresses could result from impurity adsorption not at the top surface of the growing films, but one monolayer below. The presence of compressive stresses in films deposited via sputtering is briefly reviewed in terms of the atomic peening mechanism. An experiment exploring the interrelationship between the purification effect of ion bombardment, thus causing tensile stresses, and the more normal formation of compressive stresses is discussed.

Anomalous diffusion in nonmetals (origin and effects of internal electric fields)

When electrically active impurities or defects diffuse in a material with a band gap ≳ 10kT, the changing concentration of these ions may result in internal electric fields which will significantly alter the diffusion process, and result in gross misinterpretation of diffusion experiments. Equations are derived which describe the diffusion of interstitial impurities in such a system, and which take proper account of compensating immobile impurities. A technique for numerical solution of these equations is described and the results of calculations for the case of H+ in TiO2 are presented. These calculations predict a large enhancement of the over−all diffusion rate and a very distinctive concentration profile. The latter is of critical importance in identifying this effect, since our calculations show that a measurement of total impurity content vs time will appear to agree fairly well with Fick’s law; however, the apparent diffusion coefficient obtained in this way can be in error by a factor of 100 or more. Experimental results for the H+−TiO2 system are presented, which agree quantitatively with our calculations.

Diffusion in non-uniform crystals

The statistical-kinetic theiry of diffusion, based on random walk analysis and the statistical theory of atomic jumps, is applied to non-uniform crystals. The non-uniformity may arise from field gradients or temperature gradients. For field gradients alone, the results are consistent with thermodynamics and with previous studies of specific fields. Centrifugal forces and strain fields are treated explicitly as special cases. For thermal gradients, an inherent inconsistency arises that leads to the conclusion that the quasi-equilibrium statistical-kinetic theory cannot rigorously describe the irreversibility introduced by heat flow. It is suggested that this inconsistency can be removed by referring the thermodynamic functions of the system to a second phase that acts as a source of diffusing species. Several experiments are suggested to test this approach. The diffusion flux equations are explicitly given for diffusion of interstitial impurities, vacancies, tracers and substitutional impurities.

Simplified Experiment Demonstrating Interstitial Diffusion in Alpha Iron

An experiment is described which demonstrates the diffusion of interstitial impurities in alpha iron. It consists in the measurement of the logarithmic decrement of the oscillatory motion of a torsional pendulum utilizing a commercially available iron suspension wire of high purity. From the results obtained over a conveniently small temperature range, the activation energy for diffusion of the predominant impurity—nitrogen—can be found. This energy agrees favorably with earlier determinations made over a much wider temperature range using iron wire with specially introduced impurities.

Dislocation interstitial interactions in single crystal Tungsten

Dislocation interstitial interactions have been investigated in zone melted single crystal tungsten by means of internal friction measurements. A Marx piezoelectric composite oscillator resonating at 50 kc/s was used to measure the log decrement as a function of time, temperature and strain amplitude. Measurements on slightly cold worked single crystal tungsten show that at temperatures above ~300°C the amplitude independent damping decreases with time and the strain amplitude necessary for breakaway increases. These effects have been explained in terms of the diffusion of interstitial impurities, according to the t 2 3 law of Cottrell and Bilby, to the dislocation lines pinning them and rendering them immobile. An activation energy for the process has been found to be 47,000 ± 5,000 cal/mole. The interstitial has not been definitely identified, however, evidence tends to indicate inter-stitial carbon as the pinning agent.

Ratio of Interstitial to Substitutional Zinc in GaAs and its Relation to Zinc Diffusion

An order-of-magnitude estimate of the ratio of singly charged interstitial to substitutional zinc in GaAs is made by combining experimental data for copper in GaAs with theories of solubility and diffusion of interstitial impurities. Calculations of the diffusion constant on the basis of a substitutional-interstitial mechanism yield values which agree to within one or two orders of magnitude with experimental values in the temperature range 750° to 1000°C.

Semiempirical Approach to the Theory of Thermal Diffusion in Crystals

The theory of thermal diffusion is developed by defining two isothermal systems: one at a temperature such that the jump frequency is equal to that in the direction along the temperature gradient in the nonisothermal system, and another at a temperature such that the jump frequency is equal to that in the direction against the gradient. The difference between these two defined temperatures, and the existing temperature gradient, are used to define a distance parameter ${x}_{c}$. The flux equations in a temperature gradient are then developed in a formal way using ${x}_{c}$ as an expansion parameter for interstitial impurity diffusion, substitutional impurity diffusion by a vacancy mechanism for the two extreme cases of weak binding and tight binding of the vacancy-impurity complex, and for the flux of vacancies in pure metals. ${x}_{c}$ is interpreted in such a way that it defines the region in which the maximum energy is localized in the critical configuration for a jump, and is, therefore, a measure of the spatial distribution of activation energy. The analysis is applied to existing experimental data.

Theory of Diffusion and Equilibrium Position of Interstitial Impurities in the Diamond Lattice

A theory is developed for diffusion of interstitial impurities in the diamond lattice. For ionized impurities the theory is based on a model in which the interaction of the ion with the host atoms is given by an attractive potential produced by the polarization of the host atoms, and a repulsive potential due to overlap of nonbonding electrons. The interaction energy is calculated at two interstitial positions of symmetry, and the activation energy for diffusion is taken as the difference between the two. Good agreement with experiment is found for lithium, copper, and silver. The theory predicts an optimum impurity size for diffusion, and thus explains the great diffusivity of copper. It also claims that the interstitial position of lithium and copper is not one of tetrahedral symmetry.