Activation Energy For Self-diffusion Research Articles

Evidence for dislocation glide controlled creep in niobium-base alloys

It was shown several years ago that a coarse-grained Nb-5.4Hf-2.0Ti alloy (known commercially as C103) could exhibit large tensile elongations of over 200%; the phenomenon was observed at intermediate homologous temperatures (about 0.7 T{sub m}, where T{sub m} is the absolute melting temperature) and at intermediate strain rates (of about 10{sup {minus}3} s{sup {minus}1}). The extended ductility in C103 was attributed to the fact that it is representative of a special group of alloys known as Class I solid solutions. This paper reports that based on these descriptions, Class I solid solutions are found in alloys that have relatively large atomic size mismatches for a given value of elastic modulus, although it has been pointed out that the solute concentration, stress level, and the ratio of climb to glide diffusivities are also important variables. Often there is little or no subgrain formation, and the deformation behavior of the alloys does not exhibit a direct dependence on the stacking fault energy. During creep, the alloys exhibit either little primary creep or an inversion of primary creep that often enters directly into tertiary, or accelerating, creep. The activation energy for creep in Class I solid solutions is for chemical interdiffusion and ismore » often below the activation energy for self-diffusion of the matrix metal.« less

Self-diffusion of magnesium in spinel and in equilibrium melts: Constraints on flash heating of silicates

We have measured Mg self-diffusion in spinel and coexisting melt at bulk chemical equilibrium using an isotopic tracer. The diffusion coefficients were calculated from the measured isotope profiles using a model that includes the complementary diffusion of 24Mg, 25Mg, and 26Mg in both phases with the constraint that the Mg content of each phase is constant. This model also permits the calculation of the diffusion coefficient in one phase from the measured data in a coexisting phase. The activation energy and pre-exponential factor for Mg self-diffusion in spinel are, respectively, 384 ± 7kJ and 74.6 ± 1.1 cm 2/s. These data indicate Mg diffusion in spinel is much slower than previous estimates, probably because earlier measurements included grain boundary transport. The activation energy for Mg self-diffusion in coexisting melt is 343 ± 25 kJ and the pre-exponential factor is 7791.9 ± 1.3 2cm/s. The results from this study were applied to evaluate cooling rates of Plagioclase-Olivine Inclusions (POI) in the Allende meteorite. Given a maximum melting temperature for POIs of ~ 1500°C, these results show that a 10 μ radius spinel would equilibrate isotopically with a melt within about 60 min. To preserve Mg isotopic heterogeneity, the POIs must have initially cooled faster than 15 to 250°C/h depending on the initial temperature of flash heating. The cooling rate must also be slow enough to generate the observed basaltic textures. The inferred cooling rate appears to be comparable or up to ten times greater than those inferred from experimental and textural studies of synthetic CAI systems. The nature of the heating process is thus required to be short with relatively rapid cooling, such as flash heating. However, the relatively rapid cooling cannot be due to radiation into a cold, ~400°K nebula but would require radiation into a rather stable hot environment.

Interaction of surface misfit and monatomic steps on unreconstructed {110} surfaces of anisotropic f.c.c. crystals I. Ledges parallel to rectangular surface unit cell axes

The difference between the bulk atomic spacings of a crystal and the spacings at and near the surface constitutes “surface misfit” and accordingly implies stressed surface layers. When an atomic step is formed on the surface, the stressed layers relax somewhat and induce stresses which act on the crystal “surface”. The surface stress distribution (needed to calculate the stress-strain fields generated within the crystal) resulting from the formation of a monatomic step on the {110} surface of an anisotropic f.c.c. crystal is derived. Both the tangential and normal components of the surface stresses are expressed in terms of the crystal parameters: the surface misfits (fx, fy, fz), the stiffness constants (c11, c12, c44), the anisotropy ratio A and the nearest-neighbour distance d. The monolayer atom-crystal interaction is modelled as a surface interaction potential V represented by a Fourier series truncated after six terms. The activation energies of surface self-diffusion are shown to be directly related to the Fourier coefficients Fi and to be anisotropic. This anisotropy is confirmed by empirical data for {110} surfaces of copper, nickel and rhodium. The results also imply the existence of upper and lower bounds for stiffness constants when activation energies are known, and vice versa.

Theory of Doping of Diamond

ABSTRACTElectronic applications of diamond require control over native defects as well as the ability to dope it p- and n-type. B is an excellent p-type dopant, but n-type doping has proven very difficult. Diamond films have also been very difficult to anneal, indicating a high activation energy for self-diffusion. We have investigated the properties of native defects and impurities through large-scale band structure and Car-Parrinello calculations. We indeed find that the activation energy for self-diffusion is very high in the intrinsic material, but it decreases by as much as 3 eV in either p- or n-type material. P, Li, and Na are shallow donors, but their solubilities are too low for incorporation into diamond through in-diffusion. It is energetically favorable for B and N to dissolve in diamond, which explains their prevalence in natural diamond. The calculations explain for the first time the reasons for the distortion of atoms around N from the fully tetrahedral site, as well as why N is a deep rather than a shallow donor. We also consider the effects of simultaneous doping with N and B on the thermodynamic equilibrium between diamond and graphite.

Polymer self-diffusion in Nal-poly(ethylene oxide) electrolytes

Using the technique of fluorescence recovery after photobleaching we have measured the self-diffusion coefficients ( D) of poly(ethylene oxide) (PEO) in NaI-PEO electrolytes. From the temperature dependence of the D values, the activation energy of self-diffusion was obtained. It has the same salt concentration dependence as the activation energy of ionic conductivity, suggesting that polymer segmental mobility is essential for ion transport in NaI-PEO electrolytes. The PEO diffusion rate was reduced significantly at low salt concentration, but raising the NaI concentration beyond 6 mol% resulted in only slight changes in D values. The concentration dependence of D was interpreted in terms of the interactions between PEO and sodium ions. From the response of D and the immobile fraction of PEO molecules to temperature and composition changes, several features in the NaI-PEO phase diagram were elucidated.

Theory of native defects, doping and diffusion in diamond and silicon carbide

The properties of native defects and impurities in diamond and SiC are investigated via large-scale band structure and Car-Parrinello calculations. In diamond, the activation energy for self-diffusion is very high in the intrinsic material (9 eV) but decreases by up to 3 eV in either p- or n-type material. Phosphorus, lithium and sodium are shallow donors, but their solubilities are very low, which makes them unsuitable for incorporation into diamond via in-diffusion. Instead, kinetic trapping during growth or ion implantation must be used. Considering the stability at the dopant site, substitutional phosphorus is expected to diffuse by the vacancy mechanism and to have a high activation energy by analogy to self-diffusion. Both lithium and sodium diffuse through the interstitial channel. Lithium is a relatively fast diffuser while sodium should be stable up to moderately high temperatures. For nitrogen in diamond, the well known (111) distortion is found to be due to the interaction of the fully occupied nitrogen lone pair with the dangling bond of the C(111) atom. The single electron associated with the center resides in an antibonding orbital formed from the dangling hybrid and the nitrogen lone pair. This orbital has most of its amplitude on the carbon atom. In SiC, the lowest energy defect in n-type and intrinsic material is the electrically inactive silicon antisite, while the lowest energy defect in p-type SiC is the doubly positive carbon vacancy. The electrons released by the vacancies compensate acceptor dopants, leading to strong self-compensation effects when doping occurs during crystal growth. In carbon-rich SiC, the dominant defect for all Fermi level positions is the electrically inactive carbon antisite. In boron-doped SiC, BC is preferred for silicon-rich material while, in carbon-rich SiC, BC and BSi have similar formation energies.

Activation parameters of high-temperature creep in polycrystalline nickel at ambient and high pressures

Polycrystalline specimens of pure nickel were deformed in uniaxial compression at temperatures of 1000–1550 K, strain rates of 1×10 −5-3×10 −3s −1 and pressures of 0.1–1500 MPa, in order to determine the activation parameters of high temperature creep. Experiments at 0.1 MPa were conducted in an MTS apparatus with the specimen immersed in a molten heat-treating salt to prevent oxidation. The data show a decreasing power-law stress exponent with decreasing normalized steady-state flow stress ( σ/ G), approaching the “natural law” value of n=3 at normalized stresses <10 −4. In contrast, the activation energy is constant over our range of temperatures ( T/ T m = 0.55−0.90), and is indistinguishable from the activation energy of self-diffusion (284 kJ/mol). High pressure experiments were conducted in a modified piston-cylinder apparatus using the same molten heat-treating salt for the confining medium. The small activation volume could not be resolved; however, the trend of the high pressure data parallels that of the 0.1 MPa data with a systematic offset, and is consistent with the measured activation volume of self diffusion. Specimens deformed at 0.1 MPa exhibited significant strain-enhanced grain growth; this effect is greatly reduced under hydrostatic pressure, whereas subgrain size was less affected.

Mechanical properties of the Zr-1% Nb alloy at elevated temperatures

The tensile deformation of the Zr-1% Nb alloy was investigated in the temperature interval 295 to 773 K. Elongation to fracture versus temperature curves exhibited a minimum. The elevated temperature yield and ultimate tensile strength, ductility, strain rate sensitivity and the strain hardening exponent were found to be strain rate dependent. The minimum in the strain rate sensitivity versus temperature curve is coincident with the elongation minimum temperature. The activation energy of 217.6 kj mol−1 was obtained from the shift of elongation minimum temperature. An empirical relationship between strength and test temperature at different strain rates was obtained from which the activation energy of the α-phase zirconium self-diffusion was evaluated. Electron microscopy revealed that sub-grains and β-Nb precipitates are present from 295 K to the temperature of the ductility minimum. An attempt based on the presence of β-Nb precipitates and oxygen content has been made to explain the ductility minimum and the stress plateau at elevated temperatures.

Microstructure and thermal stability of coated Si3N4 and SiC

Microstructure of coatings obtained by treating Si3N4 and SiC in Cr powders at 1273–1623 K has been studied employing XRD, SEM, AES and TEM. In accordance with thermodynamic calculations and kinetic consideration, the coatings have layered structures and contain metal-rich silicides and metal-rich nitrides or carbides. The microstructure of the coatings has been found to depend on the treatment conditions. The kinetics of the coatings growth obeys a parabolic growth law, the activation energies being close to the activation energies for self-diffusion of the corresponding metals. Thermal stability of the coated and uncoated Si3N4 and SiC in Fe-, Ni- and Co-based matrices has been studied and the coatings have been found to considerably improve the stability of Si3N4- and SiC-metal interfaces.

Grain Growth and Reaction in Nickel‐Silicon Thin‐Films

AbstractThin‐film reactions in nickel‐silicon bilayers were studied by differential scanning calorimetry and transmission electron microscopy. Interesting particularities of thin‐film reactions were observed: a small exothermic effect before the main peak of reaction is due to grain growth of polycrystalline nickel. The activation energy of the process ((220 ± 50) kJ/mol) is in the same order of magnitude as the activation energy of grain boundary self diffusion of nickel. A mean grain boundary enthalpy of nickel ((0.7 ± 0.3) J/m2) is calculated. The main exothermic peak is due to the formation of di‐nickel silicide; its molar enthalpy of formation (‐(155 ± 20) kJ/mol)) and the energy of activation of the reaction ((150 ± 30) kJ/mol) are in good agreement with literature values. The activation energy is comparable to the activation energy of grain boundary diffusion of nickel in δ‐Ni2Si.

Intercalation compounds: Some recent developments and future trends in mixed conductors

Abstract Intercalation compounds are formed by the injection of guest ions (e.g. Li+) and their charge compensating electrons into a solid host (e.g. TiS2). Such compounds are mixed, ionic and electronic conductors. Recent developments concerning three aspects of intercalation are discussed in this article. (1) Ionic diffusion. Results are presented for the self-difusion coefficient of Li+ in both layered and cubic titanium disulphide which permits comparison of Li+ diffusion in two and three dimensions within a chemically identical environment. In both cases the activation energy and pre-exponential factor for self-diffusion exhibit a dramatic variation with Li+ ion content. These variations and possible interpretations are discussed. (2) Thermodynamics of intercalation. The variation in the chemical potential of lithium in cubic TiS2 is presented and interpreted in terms of interactions between both the ions and electrons; the interactions follow a cube root dependence on composition. (3) New intercalat...

Effect of applied mechanical stress on the electromigration failure times of aluminum interconnects

Accelerated lifetime electromigration tests were performed on pure aluminum interconnect lines which were subjected to an applied mechanical bending stress. The median time to open failure (MTTF) was found to decrease with increasing applied tensile stress. The diminished failure times suggest a decrease in the activation energy for aluminum grain boundary self-diffusion on the order of 0.003 eV per 100 MPa of applied stress, resulting in a MTTF reduction of 10% at 210 °C for an increase in tensile stress of 100 MPa.

Investigation of grain boundary self-diffusion at low temperatures in polycrystalline aluminium by means of the dislocation spreading method

The dislocation spreading method was used to study grain boundary (GB) self-diffusion in polycrystalline aluminium. This made it possible to obtain information on GB self-diffusion in aluminium at temperatures as low as 0.31–0.43 Tm. The distributions of GB diffusivity were determined at temperatures: 293, 343, 373 and 403 K. On the basis of these results the distributions of Arrhenius parameters (activation energy of GB self-diffusion and pre-exponential factor) were obtained. Both distributions of GB diffusivity and distributions of Arrhenius parameters depend on the history of the material. The obtained values of GB self-diffusion activation energy are consistent with results obtained by other methods. Higher diffusional properties of GBs and greater uniformity of GB diffusivity in polycrystalline aluminium were observed in the case of a higher recrystallization temperature.

Vacancy diffusion along twist grain boundaries in copper

Vacancy diffusion along two different high-angle twist grain boundaries (Σ5 and Σ13) was studied using the Embedded Atom Method (EAM). Vacancy formation energies in all the possible sites were calculated and found to be directly related to the degree of coincidence with the neighboring crystal planes. Optimal migration paths and migration energies were determined and found to be very low. The activation energies for self-diffusion at the boundaries were found to be less than half of the bulk value.

High temperature creep of silicon carbide particulate reinforced aluminum

The effect of stress on the creep properties of 30 vol.% silicon carbide particulate reinforced 6061 aluminum (SiC p-6061 Al), produced by powder metallurgy, has been studied in the temperature range of 618–678 K. The experimental data, which extend over seven orders of magnitude of strain rate, show that the creep curve exhibits a very short steady-state stage; that the stress exponent, n, is high ( n > 7.4) and increases with decreasing the applied stress; and that the apparent activation energy for creep, Q a, is much higher than the activation energy for self-diffusion in aluminum. The above creep characteristics of SiC p-6061 Al are similar to those reported for dispersion strengthened (DS) alloys, where the high stress exponent for creep and its variation with stress are explained in terms of a threshold stress for creep that is introduced by the dispersoid particles. Analysis of the creep data of SiC p-6061 Al using the various threshold stress models proposed for DS alloys indicates that the threshold stresses introduced by the SiC particulates are too small to account for the observed creep behavior of the composite. By considering an alternate approach for the source of the threshold stress in SiC p-6061 Al, an explanation for the asymptotic behavior of the creep data of the composite is offered. The approach is based on the idea that the oxide particles present in the Al matrix, as a result of manufacturing the composite by powder metallurgy, serve as effective barriers to dislocation motion and give rise to the existence of a threshold stress for creep.

Grain growth in copper and alpha-brasses

The wires of 99.999% copper and alpha-brasses containing 12, 20, 30 and 35 at % Zn have been annealed in vacuum for 30 to 240 min at 873, 923, 973 and 1023 K. The grain-growth data obtained are well encompassed by the relationD 2, —D 0 2 , =Kt exp(-H/kT), whereD is the instantaneous mean grain diameter at the time,t, of isothermal anneal andD 0 refers to the initial mean grain diameter. In alpha-brasses the activation energy for grain-boundary self-diffusion,H, and the pre-exponential factor,K, depends on the zinc concentration,c, asH = (H 0 — 1.1c) eV andK =K 0 exp(-10.7c) cm2 sec−1. The values ofH 0 andK 0, referred to the base metal are respectively 0.87 eV and 3.0 × 10−4 cm2 sec−1, which are in good agreement with those (0.85 eV and 3.6 × 10−4 cm2 sec−1) found for copper.

Adsorption sites of111In and111mCd on Pd(111) surfaces characterized by the electric field gradient

PAC measurements of the electric field gradient at the nucleus of isolated probe atoms on Pd(111) surfaces lead to the identification of five adsorption sites successively occupied by the parents111In and111mCd during annealing between 80K and 600K. The data are consistent with an estimated activation energy for Pd surface self diffusion of Ea=0.76(8)eV.

Motions of Methylammonium Ions in (CH3NH3)2ZnBr4 Crystals Studied by 1H NMR and Thermal Measurements

Abstract Measurements of the 1H spin-lattice relaxation time T1, the linewidth parameter T*2 the second moment of 1H NMR absorption, differential thermal analysis, and differential scanning calorimetry were performed on methylammonium tetrabromozincate(II) crystals from 58 to above 500 K. A solid-solid phase transition was located at 456 K. In the room temperature phase, 120° reorientational jumps of CH3 and NH3 + groups in the cation about its C -N bond axis were detected. In the high-temperature phase, the cations undergo overall reorientation as well as translational self-diffusion. The activation energy for the cationic self-diffusion was evaluated to be 18 kJ mol-1 .

Creep of Pb–2·5Sb–0·2Sn alloy at low stresses

The creep of a Pb–2·5Sb–0·2Sn alloy has been studied at stresses up to 6·5 MN m−2 in the temperature range 318–348 K (0·53–0·58Tm) using helical specimens. At 333 K, a transition in the stress exponent from ~1 to 3 occurred at ~3 MN m−2. The observed good agreements below the transition stress, both for experimental dE/do and predictions for Coble diffusional creep of lead, and for measured activation energy for creep and the activation energy for grain boundary self-diffusion in lead, suggest that grain boundary diffusional creep is the dominant mechanism. at low stresses. The presence of antimony does not seem to affect the magnitude of dE/do appreciably, and the results suggest that the grain boundary self-diffusivity of lead is not influenced by the presence of segregated antimony on the grain boundaries. The diffusional creep occurred above a threshold stress of magnitude ~0·5 MN m−2, and its temperature dependence was characterised by an activation energy of ~20 kJ mol−1, similar to the value of 23 ± 7 kJ mol−1 typical of pure metals in the temperature range investigated. The stress exponent of ~3 observed for the power law regime suggests control by viscous glide of dislocations constrained by dragging of solute atmospheres. Preliminary tests on sagging beam specimens of as-worked material at an applied stress of 2·5 MN m−2 and a test temperature of 333 K has provided the first direct evidence that anisotropic grain shape affects Coble creep. The specimen with the longest grain dimension along the stress axis underwent slower creep than the specimen with the longest grain dimension perpendicular to the stress axis. This observation is in qualitative agreement with theoretical predictions.MST/1139

Creep of Pb–2·5Sb–0·2Sn alloy at low stresses

AbstractThe creep of a Pb–2·5Sb–0·2Sn alloy has been studied at stresses up to 6·5 MN m−2 in the temperature range 318–348 K (0·53–0·58Tm) using helical specimens. At 333 K, a transition in the stress exponent from ~1 to 3 occurred at ~3 MN m−2. The observed good agreements below the transition stress, both for experimental dE/do and predictions for Coble diffusional creep of lead, and for measured activation energy for creep and the activation energy for grain boundary self-diffusion in lead, suggest that grain boundary diffusional creep is the dominant mechanism. at low stresses. The presence of antimony does not seem to affect the magnitude of dE/do appreciably, and the results suggest that the grain boundary self-diffusivity of lead is not influenced by the presence of segregated antimony on the grain boundaries. The diffusional creep occurred above a threshold stress of magnitude ~0·5 MN m−2, and its temperature dependence was characterised by an activation energy of ~20 kJ mol−1, similar to the valu...