Activation Energy For Boundary Diffusion Research Articles

Spark plasma sintering for high-speed diffusion bonding of the ultrafine-grained near-α Ti–5Al–2V alloy with high strength and corrosion resistance for nuclear engineering

The paper demonstrates the prospects of spark plasma sintering (SPS) for the high-speed diffusion bonding of the high-strength ultrafine-grained (UFG) near-α Ti–5Al–2V alloy. The effect of increased diffusion bonding intensity in the UFG Ti alloys is discussed also. The bonding areas of the UFG near-α Ti–5Al–2V alloy obtained by SPS are featured by high density, strength, and corrosion resistance. The rate of bonding in the UFG alloys has been shown to depend on the heating rate non-monotonously (with a pronounced maximum). At the stage of continuous heating and isothermic holding, the bonding kinetics was found to be determined by the exponential creep rate, the intensity of which in the coarse-grained alloys is limited by the diffusion rate in the crystal lattice α-Ti. In the UFG alloy, the exponential creep processes associated with gliding and climb of dislocations, the activation energy of which corresponds to the diffusion activation energy in the lattice dislocation nuclei, may take place simultaneously with the grain boundary sliding and Coble creep, the activation energy of which corresponds to the grain boundary diffusion activation energy.

Structural transformations in (CoFeNi)/Ti nanocomposite systems during prolonged heating

A complex CoFeNi/Ti nanocomposite system with an average grain size of about 8 nm was fabricated on a Ti sheet under ball collisions. Heating experiments were performed at 400, 500, and 600 °C with hold times of up to 100 h at each temperature. The as-fabricated (CoFeNi)/Ti nanocomposite system demonstrated high thermal stability upon heating to 400 and 500 °C. Growth of the CoFeNi phases was retarded by closely spaced Ti particles. After heating to 600 °C, the system exhibited a bimodal nanograin structure due to coursing of the body-centered cubic (bcc) CoFeNi grains, which occurred more rapidly than with the face-centered cubic (fcc) CoFeNi grains. Upon heating, the diffusion that occurred between the phases tended to equilibrate the composition. Pairwise atomic interactions between the Co, Fe, and Ni components arose as chemical interactions in the corresponding binary alloy. The diffusive flux of elements in the system was outlined as Co from the fcc phase diffused into the bcc phase, Ni from the bcc phase diffused into the fcc phase, and Fe from the fcc phase diffused into the bcc phase. The activation energy for the reaction was calculated using time dependence curves of saturation magnetization. The activation energy coincided very closely with the value for the grain boundary diffusion activation energy for the Co, Fe, and Ni binary systems.

Deformation Behavior of Severely Deformed Al and Related Mechanisms Through Warm Tensile Test

Flow stress and ductility behaviors of the annealed and severely deformed Al were investigated at warm deformation temperatures. Constrained groove pressing (CGP) method as a severe plastic deformation process was used. The tensile test was carried out at the temperature range of the 298-573 K and strain rate range of 0.001-0.1 s−1 to present the elevated temperature deformation behavior utilizing hyperbolic sine constitutive equation. The flow stress of the CGPed sample is increased with the number of CGP passes and decreased with temperature. Dynamic recovery and strain softening are found as main restoration mechanisms. Flow stress amounts are not remarkably affected by the strain rate. Values of the elongation are decreased with the number of CGP passes. Values of the calculated strain rate sensitivity are utilized to justify the elongation behavior. Shear bands created by CGP remarkably decrease the fracture elongation values. Temperature interval of 298-473 K cannot remarkably affect the flow stress and ductility. The interval of 473-573 K is chosen as critical temperature interval in which the values of flow stress and elongation are remarkably decreased and increased, respectively. Increasing the temperature up to 573 K causes recrystallization in shear bands. Scanning electron microscope was used to study fracture surface which can truly predict the elongation behavior. With increasing the temperature, the shear decohesion area is gradually replaced with fully dimpled structures. Finally, hot deformation activation energy for CGPed samples was calculated about 85 kJ/mol which is close to the grain boundary diffusion activation energy in pure Al.

Creep properties and creep microstructure evolution of Mg-2.49Nd-1.82Gd-0.19Zn-0.4Zr alloy

The creep properties and creep microstructure evolution of Mg-2.49Nd-1.82Gd-0.19Zn-0.4Zr alloy were investigated as a function of creep stresses and creep temperatures. It was found that the creep strain and the creep rate increases but the creep life decreases with increasing creep temperatures and creep stresses. At a defined creep stress, the creep strain increases with increasing creep temperatures. At a defined creep temperature, the creep strain increases with increasing creep stresses. α(Mg), Mg12Nd phase and Mg5Gd phase are present in the microstructure after creep. Furthermore, the Mg12Nd phase appears to increase with increasing the creep stress, creep temperature and creep time, indicating that the creep stress, creep temperature and creep time may have a significant effect on the formation of the equilibrium Mg12Nd phase during the creep. At the temperature range less than 225℃, the calculated Qc value is about 74–98kJ/mol, which is very close to the grain boundary diffusion activation energy (80kJ/mol−1), indicating that the grain boundary sliding may be a dominant factor affecting creep properties. While, at the temperature range higher than 225℃, the calculated Qc value is about 227–289kJ/mol, which is much higher than the self - diffusion activation energy (135kJ/mol−1), indicating that the dislocation climbing may be a dominant factor affecting creep properties. The fracture was observed to occur along the grain boundaries. The initiation of the crack is from a trigeminal grain boundary, indicating that the Mg12Nd phase at the grain boundary has a significant effect on the initiation of the crack.

Hot deformation behaviour of as-extruded micrometre SiCp reinforced AZ91 composite

The 10 μm 10 vol.-% SiCp/AZ91 composite was fabricated by stir casting. After processing by forging and subsequent extrusion, the composite with 1∼2 μm grain size was obtained. Then the hot deformation behaviour of as-extruded composite was investigated at elevated temperatures (543–673 K). Results show that the existence of micrometre SiCp has obvious effect on stimulating dynamic recrystallization (DRX) nucleation and inhibiting the growth of DRXed grains. Both the flow stress and work hardening of as-extruded composite is lower than that of as-cast AZ91 alloy and composite, which means that the grain refinement strengthening mechanism is not fit for elevated temperatures, and the reasons were analysed. The calculated activation energy Q (∼90 KJ mol− 1) of as-extruded composite is very close to the grain boundary diffusion activation energy (∼92 KJ mol− 1) for Mg. Calculation analysis gives n = 5, which illustrates that the climb of dislocation is the main controlling mechanism of the as-extruded composite during hot deformation.

The Effects of Al Doping and Metallic-Cap Layers on Electromigration Transport Mechanisms in Copper Nanowires

We investigate electromigration transport mechanisms in Cu and Cu alloy damascene conductors. We show that the drift velocity exhibits a dependence on microstructure. We find that Cu-Al alloys exhibit a small increase in grain boundary diffusion activation energy compared to pure Cu and a reduction in the diffusion prefactor for Cu/cap interfacial transport. Cu-silicide- and CoWP-cap layers are both effective in reducing the interfacial component of electromigration primarily through increases in interface diffusion activation energy. The Cu silicide cap also impacts grain boundary electromigration as a result of silicon doping of grain boundaries during processing, while the CoWP cap has no measurable impact on grain boundary transport. The positive impact of Al doping and metallic-cap layers on electromigration is additive, suggesting the potential for impurity doping and metallic caps to be combined to optimize for reliability across the geometry ranges encountered in circuits.

Deformation Mechanisms in Nanocrystalline Materials

As a result of recent investigations on nanocrystalline (nc) materials, extensive experimental data on the deformation behavior of these materials have become available. In this article, an analysis of these data was performed to identify the requirements that a viable deformation mechanism should meet in terms of accounting for the mechanical characteristics and trends that are revealed by the data. The results of the analysis show that a viable deformation mechanism is required to account for the following: (1) an activation volume the value of which is in the range 10 to 40 b 3; (2) an activation energy that is close to the activation energy for boundary diffusion but that decreases with increasing applied stress; (3) the magnitudes of deformation rates that cover wide ranges of temperatures, stresses, and grain sizes; (4) inverse Hall–Petch behavior; and (5) limited ductility. The validity of available deformation mechanisms for nc materials is closely examined in the light of these requirements.

The Activation Energy of Superplastic Flow above the Critical Temperature for Steel CrWMn

By means of superplastic tensile test above the Ac1 temperature (γ→α transformation temperature), superplastic deformation activation energy of ultrafine-grained commercial die steel CrWMn is investigated on the basis of the Arrhenius theory equation, exp( / ) 1 ε& = Aσ m −Q RT , which indicates the resistance of the superplastic deformation. According to the Arrhenius equation, the activation energy is estimated from the log σt vs 1/T relationship at a constant of sensitivity index of strain rate. The results show that the strain rate sensitivity index is a constant and rather high at the conditions of superplastic deformation for the CrWMn steel, the activation energy for superplastic deformation of steel CrWMn above the critical temperature is 187KJ/mol, and the superplastic deformation activation energy is approached to the grain boundary diffusion activation energy of γ-Fe. This indicates that the grain boundary sliding (GBS) in superplastic deformation of CrWMn steel is controlled by grain boundary diffusion. The characters of superplastic deformation of the steel above the critical temperature, on the other hand, are also analyzed in this paper.

Thermal stability and mechanical behavior of ultra-fine bcc Ta and V coatings

Ultra-refined microstructures of both tantalum (Ta) and vanadium (V) are produced using electron-beam evaporation and magnetron sputtering deposition. The thermal stability of the micron-to-submicron grain size foils is examined to quantify the kinetics and activation energy of diffusion, as well as identify the temperature transition in dominant mechanism from grain boundary to lattice diffusion. The activation energies for boundary diffusion in Ta and V determined from grain growth are 0.3 and 0.2 eV atom − 1 , respectively, versus lattice diffusion values of 4.3 and 3.2 eV atom − 1 , respectively. The mechanical behavior, as characterized by strength and hardness, is found to inversely scale with square-root grain size according to the Hall–Petch relationship. The strength of Ta and V increases two-fold from 400 MPa, as the grain size decreases from 2 to 0.75 μm.

Transient nucleation of cavities under coupled lattice and boundary diffusion

A diffusive process is proposed and examined for the nucleation of a cavity above half the melting point of a material and under low applied tensile stresses at which stress assisted diffusion occurs. An equation is developed for the diffusion of N atoms at a time into a bimaterial boundary to begin the nucleation. The stability of the solution of the equation is examined for a copper-sapphire interface, resulting in an activation energy for boundary diffusion that is in excellent agreement with a range of values previously recorded for metals. A calculation of the time taken for diffusion to create a small cavity is also obtained from the equation developed for the nucleation process. A mechanism for a supersaturation of vacancies that could result in final cavity formation is also developed, with the amount of calculated supersaturation in the range found in other studies. An incubation time before final stable cavitation is calculated and is also found to agree very well with experimental data.

Experiment and Theory of Diffusion in Alumina

Despite all the work conducted over many decades, there remains a major problem in understanding diffusion in alumina. It is certain that all measurements of diffusion in alumina refer to extrinsic diffusion. However, the experimental activation energy is larger than any theoretical prediction by a factor of 2. The problem with grain boundary diffusion is, if anything, worse. The most complete set of experimental data suggests that the activation energy for boundary diffusion is 50% larger than for bulk diffusion. We discuss the problems involved in understanding the experimental data and in producing theoretical models and propose a strategy for resolving the problems.

Interface effects in superplastic deformation of alumina containing zirconia, titania or hafnia as a second phase

The superplastic properties of alumina can be changed in interesting ways by small additions of transition metals zirconium, hafnium, or titanium. All three introduce a “leaky” threshold stress of 5–20 MPa. Above the threshold the flow rate is linearly related to the applied stress. A similar threshold is observed in sinterforging experiments. The additions also have the effect of enhancing the superplastic ductility and the fracture strength, presumably by increasing interfacial cohesion. This higher interfacial cohesion appears to correlate to the higher activation energy for boundary diffusion and to a lower interfacial energy. The threshold is explained in terms of a roughening transition of interfaces that are faceted. Below the transition the flow rate is interface limited, while above it, it is diffusion limited. The stress for the roughening transition is obtained from a model that describes the transition in terms of a barrier for the nucleation of interface dislocations. The barrier is shown to depend on the change of the interface energy with misorientation. It is estimated that d γ/d θ = 1 mJ m −2/degree can give rise to a threshold stress of 10 MPa.

Estimate of the Activation Energies for Boundary Diffusion from Rate‐Controlled Sintering of Pure Alumina, and Alumina Doped with Zirconia or Titania

Sintering experiments at constant heating rates were employed to estimate the activation energy for sintering in alumina and in alumina containing 5 vol% zirconia or 5 vol% titania. Grain growth, which can complicate the analysis of sintering kinetics data, was suppressed by using uniformly and densely packed grain compacts prepared by colloidal processing. Grain‐boundary diffusion is believed to have been the dominant sintering mechanism. The activation energies were 440 ± 40 kJ/mol for pure alumina, 585 ± 40 kJ/mol for alumina (titania), and 730 ± 60 kJ/mol for alumina (zirconia). The alumina and alumina (titania) results are in agreement with the values reported in the literature. The possibility that the higher activation energies for doped alumina reflect a stronger bonding at alumina interfaces in the presence of zirconium and titanium is discussed.

Grain boundary diffusion activation energy derived from surface roughness measurements of aluminum thin films

Surface roughness measurements of 600-nm-thick aluminum thin films deposited on oxidized silicon substrates have been made by Verkerk and Raaymakers [Appl. Opt. 25, 3602 (1986)]. Here, their data are shown to yield an Arrhenius activation energy of 0.55±0.05 eV/atom. This activation energy is found for T>0.5 Tm, where T is the substrate temperature during deposition and Tm is the melting temperature of aluminum. The regime T>0.5Tm is known to correspond to zone 3 of the structure zone model (SZM) developed by Movchan and Demchishin [Fiz. Metal. Metalloved. 28, 653 (1969)]. The activation energy for grain growth within zone 3 is attributed primarily to bulk or grain boundary diffusion. The activation energy derived from the data of Verkerk and Raaymakers agrees well with the known activation energy for grain boundary diffusion in bulk aluminum, 0.56 eV/atom.

Electromigration measuring techniques for grain boundary diffusion activation energy in aluminum

The activation energy E g for electromigration along aluminum grain boundaries has been examined intensively by many authors and different methods. However, the common techniques yield very contradictory results, with E g ranging between 0.3 and 1.2 eV. For clarifying these contradictions, the present work examines the validity of the different test methods and their basic assumptions. It is shown that for most of these techniques the test quantity being measured is given by time dependent divergences which cause local stripe variations from scarcely detectable voids up to stripe interruptions. This means that constant conditions are not maintained during the test period, thus yielding more or less incorrect activation energies. A well defined measurement of the mass transport and the activation energy is practicable only if the divergence of the electromigration is both constant for a fixed test condition and proportional to the flux for different test conditions. Additionally, all other diffusion terms except electromigration must be negligible, especially the diffusion term based on pressure gradients. These preconditions are satisfied for the direct measurement of the drift velocity of an aluminum front on a TiN stripe, proper test conditions provided. That is why this technique is applied here extensively for clarifying several contradictions. Other techniques were performed for comparison yielding different results. The here obtained valid values of E g and their variation between 0.43 and 0.47 eV are smaller than generally reported, even for extremely different evaporation and sputtering conditions. In contrast to former results obtained by improper test methods, the activation energy is temperature independent in the examined temperature range between 140 and 280°C, and E g is not dependent on grain size even for most different fabrication conditions, yielding grain sizes from 0.3 up to 3 μm.

Mechanism of solid-state eutectoid transformation in an aluminium-zinc alloy

The growth rate of pearlite during isothermal transformation of an aluminium-zinc eutectoid has been determined experimentally. Different theoretical models, assuming either volume or boundary diffusion of zinc to be a rate controlling mechanism for the eutectoid transformation, have been applied. With volume diffusion models, the calculated growth rates were lower than the experimental growth rates by a factor of three orders of magnitude. Reasonable agreement between the calculated and experimental growth rates has been obtained on applying the boundary diffusion models. The activation energy for boundary diffusion of zinc in the aluminium-zinc alloy was estimated to be ≅11.6 kcals/mole.