Activation Energy For Grain Boundary Diffusion Research Articles

Impact of crystalline orientation on Cu–Cu solid-state bonding behavior by molecular dynamics simulations

High-density electronics are hindered by the constraints of Sn-based solder joints, necessitating the exploration of Cu–Cu solid-state bonding. However, current bonding methods are expensive and time-consuming; therefore, understanding the Cu–Cu bonding mechanism is crucial for optimization. This study utilizes molecular dynamics (MD) simulation to elucidate the Cu–Cu solid-state bonding behavior, focusing on interfacial densification and diffusion phenomena. Furthermore, it highlights the influence of crystal orientation on the interfacial bonding behavior. To analyze the impact of crystal orientation, monocrystalline Cu slabs with a simplified periodic surface structure were employed to replicate surface roughness and subsequently bonded at a specific temperature. The results indicate the critical influence of crystalline orientations on the bonding process: identical orientations result in slower densification at the interface, whereas misoriented orientations significantly accelerate it. This effect, attributed to the grain boundary (GB) structures formed owing to misorientation, suggests a central role for GB diffusion in bonding progression. Diffusion coefficients calculated using the mean square displacement (MSD) confirmed these findings and exhibited significantly larger values for misoriented joints. Additionally, the simulations reveal an activation energy for GB diffusion that is lower than conventional values, highlighting the impact of the crystallographic orientation and voids at the bonding interface. Our research elucidates the role of crystalline orientation in diffusion phenomena at bonding interfaces, offering valuable implications for optimizing bonding-based manufacturing processes.

A Study of the Impact of Graphite on the Kinetics of SPS in Nano- and Submicron WC-10%Co Powder Compositions

This study investigates the impact of carbon on the kinetics of the spark plasma sintering (SPS) of nano- and submicron powders WC-10 wt.%Co. Carbon, in the form of graphite, was introduced into powders by mixing. The activation energy of solid-phase sintering was determined for the conditions of isothermal and continuous heating. It has been demonstrated that increasing the carbon content leads to a decrease in the fraction of η-phase particles and a shift of the shrinkage curve towards lower heating temperatures. It has been established that increasing the graphite content in nano- and submicron powders has no significant effect on the SPS activation energy for “mid-range” heating temperatures, QS(I). The value of QS(I) is close to the activation energy of grain-boundary diffusion in cobalt. It has been demonstrated that increasing the content of graphite leads to a significant decrease in the SPS activation energy, QS(II), for “higher-range” heating temperatures due to lower concentration of tungsten atoms in cobalt-based γ-phase. It has been established that the sintering kinetics of fine-grained WC-Co hard alloys is limited by the intensity of diffusion creep of cobalt (Coble creep).

Spark Plasma Sintering of fine-grained SrWO4 and NaNd(WO4)2 tungstates ceramics with the scheelite structure for nuclear waste immobilization

Spark Plasma Sintering has been used to obtain first ever fine-grained SrWO4 and NaNd(WO4)2 ceramics with the scheelite structure and high density (95.8–99%) that are promising as materials for nuclear waste immobilization. It has been demonstrated that the densification intensity in tungstates at the initial sintering stage is determined by the agglomeration degree of input powders. The activation energy of fine-grained ceramics with the scheelite structure has been established to correlate at high temperatures with the activation energy of grain-boundary diffusion. Rapid sintering of fine-grained NaNd(WO4)2 ceramic results in internal tensile stress fields that lead to lowered hardness and fracture toughness of the ceramic.

Impact of mechanical activation on sintering kinetics and mechanical properties of ultrafine-grained 95W-Ni-Fe tungsten heavy alloys

This paper is a study of sintering mechanisms, structure, and mechanical properties of ultrafine-grained 95W-Ni-Fe tungsten heavy alloys. Powder particle sizes were controlled by mechanical activation (MA) of original coarse-grained components and by addition of ultrafine particles. W-Ni-Fe alloys were obtained by sintering in hydrogen and Spark Plasma Sintering (SPS) in a vacuum. The dependence of ultrafine-grained (UFG) alloy density on sintering temperatures has been found to be non-monotonic with a maximum corresponding to the optimal sintering temperature. It has been demonstrated that the sintering activation energy of UFG alloys is significantly lower than that of coarse-grained alloys. It has been shown that the optimal SPS temperature for mechanically activated nanopowders goes down by 350–400 °C in comparison with the optimal sintering temperature in hydrogen for coarse-grained 95W-Ni-Fe powder composition. The reason for a lower optimal sintering temperature lies in a decreased activation energy of grain-boundary diffusion and formation of a non-equilibrium solid solution of nickel and iron in the surface layer of tungsten α-W particles during high-energy MA. High-energy MA and SPS were used to obtain samples of UFG tungsten alloys with high mechanical properties: macro-elastic limit – up to 2250 MPa, yield stress – up to 2500 MPa.

Effect of the severe plastic deformation temperature on the diffusion properties of the grain boundaries in ultrafine-grained metals

A model is proposed to explain the effect of the severe plastic deformation (SPD) temperature on the diffusion properties of the grain boundaries in ultrafine-grained (UFG) metals and alloys. It is shown that an increase in the SPD temperature in UFG metals leads to an increase in the activation energy of grainboundary diffusion from (3–5)k B T m, which corresponds to the diffusion parameters of nonequilibrium grain boundaries, to (8–10)k B T m, which corresponds to the diffusion parameters of equilibrium grain boundaries (k B is the Boltzmann constant, T m is the melting temperature). The dependence of the activation energy of grain-boundary diffusion on the SPD temperature is found to be determined by the kinetics of the competing processes of defect accumulation at grain boundaries and the diffusion accommodation of defects.

Effects of Alloying on Nanoscale Grain Growth in Substitutional Binary Alloy System: Thermodynamics and Kinetics

Applying the regular solution model, the Gibbs free energy of mixing for substitutional binary alloy system was constructed. Then, thermodynamic and kinetic parameters, e.g., driving force and solute drag force, controlling nanoscale grain growth of substitutional binary alloy systems were derived and compared to their generally accepted definitions and interpretations. It is suggested that for an actual grain growth process, the classical driving force P = γ/D (γ the grain boundary (GB) energy, D the grain size) should be replaced by a new expression, i.e., $$ P^{\prime} = \gamma /D - \Delta P $$ . ΔP represents the energy required to adjust nonequilibrium solute distribution to equilibrium solute distribution, which is equivalent to the generally accepted solute drag force impeding GB migration. By incorporating the derived new driving force for grain growth into the classical grain growth model, the reported grain growth behaviors of nanocrystalline Fe-4at. pct Zr and Pd-19at. pct Zr alloys were analyzed. On this basis, the effect of thermodynamic and kinetic parameters (i.e., P, ΔP and the GB mobility (M GB)) on nanoscale grain growth, were investigated. Upon grain growth, the decrease of P is caused by the reduction of γ as a result of solute segregation in GBs; the decrease of ΔP is, however, due to the decrease of grain growth velocity; whereas the decrease of M GB is attributed to the enhanced difference of solute molar fractions between the bulk and the GBs as well as the increased activation energy for GB diffusion.

Size dependence of the activation energy of diffusion in multilayer Cu-Ni films

The results of studying the effect of the characteristic size on the rate of diffusion processes in nanometer Cu-Ni film systems have been reported. The film system has been prepared by sequential vacuum deposition of the components, and the activation energy of diffusion has been determined from a change in the electrical resistance of the film system in a heating-cooling cycle. It has been shown that the activation energy of grain-boundary diffusion decreases with decreasing characteristic size of the system and amounts to 0.25 eV for the film system with a characteristic size of 5 nm, which corresponds to an increase in the grain-boundary diffusion coefficient by 10 orders of magnitude with respect to massive samples.

Activation energy of self-diffusion along symmetric tilt grain boundaries 〈111〉 in the Ni3Al intermetallic compound

Activation energy of self-diffusion along symmetric tilt grain boundaries 〈111〉 in the Ni3Al inter-metallic compound has been calculated depending on the temperature and misorientation angle. For comparison, two types of potentials of interatomic interaction have been used: pair Morse potentials and multi-particle Cleri-Rosato potentials. It has been shown that the activation energy of grain-boundary diffusion increases with temperature on applying the additional diffusion mechanisms. Three temperature ranges with various activation energies have been found.

Sintering of binderless tungsten carbide

The most widely used mold materials for optical glass molding processes are cemented tungsten carbide and silicon carbide. In this research, tungsten carbide with minor addition of TiC and TiN as the second phase has been studied. The powders were ball-milled and pre-formed under a temperature of 200 °C and a pressure of 130 MPa. The specimens were sintered in a graphite lined furnace at a temperature of 1600 °C. A density of 15.43 g/cm 3, a Vickers hardness number of 23.14 GPa, and a fracture toughness of 6.56 MPa m 1/2 was found for the sintered specimen fabricated by this process. The result of X-ray analysis revealed no trace of precipitated graphite during sintering, nor the brittle eta-phase as a result of decarburization. Through scanning electron microscopy, spherical air bubbles have been found to precipitate inside the grains, because the activation energy for grain-boundary diffusion is lower than that of the air inside the grains. Therefore it is advisable that the pre-form process is carried out in vacuum.

Impurity diffusion of 141Pr in LaMnO3, LaCoO3 and LaFeO3 materials

The impurity diffusion of Pr(3+) in dense polycrystalline LaMnO(3), LaCoO(3) and LaFeO(3) was studied at 1373-1673 K in air in order to investigate cation diffusion in these materials. Cation distribution profiles were measured by secondary-ion mass spectrometry and it was found that penetration profiles of Pr(3+) had two distinct regions with different slopes. The first, shallow region was used to evaluate the bulk diffusion coefficients. The activation energies for bulk diffusion of Pr(3+) in LaMnO(3), LaCoO(3) and LaFeO(3) were 126 +/- 6, 334 +/- 68 and 258 +/- 75 kJ mol(-1), respectively, which are significantly lower than previously predicted by atomistic simulations. The bulk diffusion of Pr(3+) in LaMnO(3) was enhanced compared to LaCoO(3) and LaFeO(3) due to higher concentrations of intrinsic point defects in LaMnO(3), especially La site vacancies. Grain-boundary diffusion coefficients of Pr(3+) in LaCoO(3) and LaFeO(3) materials were evaluated according to the Whipple-Le Claire equation. Activation energies for grain-boundary diffusion of Pr(3+) in LaCoO(3) and LaFeO(3) materials were 264 +/- 41 kJ mol(-1) and 290 +/- 36 kJ mol(-1) respectively. Finally, a correlation between activation energies for cation diffusion in bulk and along grain boundaries in pure and substituted LaBO(3) materials (B = Cr, Fe, Co) is discussed.

Diffusion of iron in Cr2O3: polycrystals and thin films

Chromia protective layers are formed on many industrial alloys to prevent corrosion by oxidation. The role of such layers is to limit the inward diffusion of oxygen and the outward diffusion of cations. A number of chromia-forming alloys contain iron as a major component, such as the stainless steels. To check if chromia is a barrier to the outward diffusion of iron in these alloys, iron diffusion in chromia was studied in both polycrystals and oxide films formed by oxidation of Ni–30Cr alloy in the temperature range 700–1100 ◦ C at an oxygen pressure equal to 10 −4 atm. An iron film of about 80 nm thick was deposited on the chromia surface, and after the diffusing treatment, iron depth profiles were established by secondary ion mass spectrometry (SIMS). Two diffusion domains appear whatever the nature of the chromia material, polycrystals or films. In the first domain, using a solution of the Fick’s second law for diffusion from a thick film, effective or bulk diffusion coefficients were determined. With the second domain, Le Claire’s and Hart’s models allowed both the bulk diffusion coefficient and the grain-boundary diffusion parameter (αDgbδ) to be obtained. Iron bulk and grain-boundary diffusion does not vary significantly according to the microstructure of chromia. The activation energy of grain-boundary diffusion is at least equal or even greater than the activation energy of bulk diffusion, probably on account of segregation phenomena. Iron diffusion was compared to cationic self-diffusion in the bulk and along grain boundaries and related to the protective character of chromia. © 2004 Elsevier B.V. All rights reserved.

Simulation of grain-boundary diffusion in ceramics by kinetic Monte Carlo

We show how methods based on an encounter model for diffusion can be used to simulate the grain-boundary diffusion coefficients in ceramics. Boundaries in NiO and ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ are used as examples of the method. The anisotropy of diffusion in boundaries (expected from the picture of a grain boundary as a dislocation array and seen in experiment) is well reproduced. The calculated activation energies for grain-boundary diffusion are inreasonable agreement with experiment. Problems in comparing the simulations with experiments on polycrystals are discussed.

Temperature and orientation dependences of the grain-boundary diffusion coefficient of antimony in copper bicrystals

An investigation is made of the diffusion of antimony through the bulk and along grain boundaries in copper bicrystals containing a symmetric 〈100〉 misorientation boundary with misorientation angles from 20 to 37.2°. The bicrystals are grown by the method of horizontal zone recrystallization. The temperature range for these studies is 480–580 °C, where the solubility of Sb in Cu is about 6 atomic % and practically temperature-independent. The concentration profiles are obtained by x-ray spectral microanalysis, and the grain-boundary diffusion parameters are computed by the method of Whipple and Suzuoka. The orientation dependence of the triple product P=sδD b (where s is the segregation coefficient, δ the width of the grain boundary, and D b the grain-boundary diffusion coefficient) is nonmonotonic, with a maximum for the special ∑5 misorientation boundary (36.9°). The effective activation energy for grain-boundary diffusion ranges from ∼70 kJ/mol for ∑5 to140 kJ/mol for general boundaries.

Segregation effect on grain-boundary diffusion in thin metallic films

The diffusion in AuCu and PtCu thin films has been studied by Rutherford backscattering sperctrometry (RBS) under the kinetic regimes B (within the temperature interval of 175–290 °C) and C (room temperature). The 1.5–2.0 MeV He + RBS spectra were taken using 14–18 keV resolution. The RBS spectra were changed to depth-concentration profiles for both bulk and grain boundary (GB) diffusion. Under kinetic regime C the absolute values of GB diffusion coefficients were obtained. Under kinetic regime B the triple products δKD b (δ is the GB width, D b is the GB diffusion coefficient, K is the enrichment ratio) were obtained using the Whipple and Gilmer-Farrell models. The activation energies for GB diffusion of Au into Cu films and Cu into Au films are close to 0.95–0.98 eV atom −1, whereas the activation energy for GB diffusion of Pt into Cu films is equal to 1.25 eV atom −1. The comparison between the data on the GB diffusion for kinetic regime B extrapolated to room temperature and the data on the GB diffusion for kinetic regime C enables one to derive the product δK and to separate the contribution of segregation to the parameters of GB diffusion for the systems under study.

Self-diffusion in α‒Al2O. IV. Oxygen grain-boundary self-diffusion in undoped and yttria-doped alumina polycrystals

Abstract Oxygen self-diffusion coefficients were determined in polycrystals of α-alumina either ‘undoped’ or doped with 500wt.ppm (225molppm) Y2O3 in the temperature range 1460-1720°C, with 18O2 and secondary-ion mass spectrometry. Oxygen grain-boundary diffusion coefficients obey the relations for ‘undoped’ alumina and for ‘yttrium-doped’ alumina. The comparison between the two materials indicates that yttrium addition decreases the oxygen grain-boundary diffusion. For both materials, it was observed that the activation energy of grain-boundary diffusion is greater than the activation energy of the bulk diffusion. Similar results were obtained in single crystals for diffusion in the bulk and in subboundaries. These results were interpreted as being due to impurity segregation along boundaries and led to a model.

Effect of composition on the enhanced microwave sintering of alumina-based ceramic composites

A series of comparative experiments were performed in which a number of alumina-zirconia compositions were sintered in both microwave and conventional furnaces, using identical heating profiles. Measurement of sample end-point densities showed an enhancement of the sintering process associated with the use of microwave heating for all compositions studied. The associated microstructures examined using scanning electron microscopy showed slightly larger grain sizes for the microwave-sintered compacts, as would be expected from their higher densities. The design of a high-temperature sintering dilatometer has allowed continuousin situ monitoring of the densification process in both the microwave and conventional environment. Data obtained in this way have shown that there is an effect of composition on microwave densification. This appears to be related to the increased lossiness of the composite, (increased zirconia content), rather than the effect of zirconia as a sintering aid. In addition the dilatometer results suggest that the microwave enhancement of the sintering process may be due to a reduction in the activation energy for grain-boundary diffusion.

On the possibility of Newtonian flow in the upper mantle

The possibility of a linear-creep (Newtonian-viscosity) upper mantle is reexamined on the basis of present knowledge on flow mechanisms in olivine, including differences between activation parameters for creep and for diffusion, and revised estimates of grain boundary width. Results of the comparison between linear superplastic creep and power-law creep are presented as crossover temperature between lattice and grain-boundary diffusion, and crossover stress between non-linear and linear creep, as a function of temperature (depth), grain size, grain-boundary width, grain-boundary diffusion activation energy, and rate-controlling species (silicon or oxygen). For the most realistic values of the parameters, linear creep is well within the range of possibilities. There is no major objection from rheology to the idea of a Newtonian-viscosity upper mantle. Viscosities for the two kinds of creep are compared for laboratory, upper mantle, and—tentatively—lower mantle conditions. This results in a prediction of the grain size at which Coble creep could be observed in olivine polycrystals in the laboratory (~ 10 μm or less). The upper mantle viscosity is in the 10 20–10 21 Pa s range. Minimum estimates for the viscosity of the lower mantle are of the same order. The pictures of the rheology of the mantle derived from microphysical models of flow and from geophysical observation can therefore be made compatible.

Oxygen self-diffusion in single and polycrystalline magnesio-ferrites

Self-diffusion coefficients of oxygen ion in polycrystalline and single-crystal magnesioferrites have been measured by a gas-solid isotopic exchange technique using18O as a tracer at temperature in the range 975 to 1465° C. A new method was considered for the oxygen volume diffusion in polycrystalline magnesio-ferrite, and its reliability is discussed. The volume diffusion coefficients of polycrystalline magnesio-ferrite (MgO/Fe2O3=0.95 in mole ratio) can be expressed asD=1.51×10−1exp (−78 600/RT) cm2 sec−1 (1135 to 1465° C) andD=1.2×10−7exp (−38 000/RT) cm2sec−1 (975 to 1135° C). The volume diffusion coefficients of the polycrystal in the high temperature range were very close to those of single crystal ferrite of the same composition as the polycrystal. The activation energy of grain-boundary diffusion in this polycrystal was expected to be greater than that of the volume diffusion. A possible interpretation of this unusual behaviour is given in terms of an increased enrichment of Fe2+ ion along the grain boundary with temperature elevation, by which oxygen vacancies increase.