Parabolic Time Dependence Research Articles

Kinetics of interstitial uptake during gaseous carbo-oxidizing of titanium foils

Foils of titanium grade 2 were carbo-oxidized in CO at temperatures ranging from 600 to 1100°C in steps of 50°C. Carbo-oxidation was performed for up to 130 hours in a thermogravimetric setup, enabling the investigation of the kinetics of carbon and oxygen uptake from the gas mixture. The carbo-oxidized specimens were characterized with transmission X-ray diffraction, light optical microscopy, scanning electron microscopy, electron probe microanalysis and nanoindentation to investigate the microstructural evolution along with the uptake of oxygen and carbon. At the surfaces of the foils TiCx developed, while the core remained h.c.p. titanium. The interstitial content in h.c.p. titanium increased with temperature and first reached its maximum solubility at 1000°C and above. TiO developed within the core for high interstitial contents. The TiCxOy phase developed in-between TiCx and the oxygen containing h.c.p. titanium core for temperatures above 800°C. For temperatures up to 850°C, the uptake of C and O in the titanium foils (initially) obeys a parabolic time dependence. Arrhenius analysis of the thermogravimetry results indicates that volume diffusion of oxygen in h.c.p. titanium is (initially) the rate determining step. For temperatures above 850°C, the activation energy is reduced by a factor 3, suggesting that short-circuit diffusion of species in TiCx controls mass increase. The hardness of h.c.p. titanium determined with nanoindentation scales with the interstitial content and the associated c/a ratio of the h.c.p. unit cell. The evolution of the microstructure with time and temperature are discussed in relation to the observed kinetics of mass uptake.

High-temperature oxidation performance of wire-arc additively manufactured Inconel 718 superalloys

This work investigated the high-temperature oxidation kinetics and evolution of oxide phases of as-fabricated (AF) and heat-treated (HT) Inconel 718 alloys in air fabricated by the wire-arc additive manufacturing process. The results showed that the oxidation kinetics of all samples followed the parabolic time dependence. The microstructural study revealed the formation of very similar oxide scales in both AF and HT conditions. The oxide surface was found to be a mixture of complex spinel-MnCr2O4 and rutile-TiO2 phases. The cross-sectional view yielded an outer layer of protective Cr2O3 scale, an inner layer of Nb-rich Ti0.67Nb1.33O4 oxide and discretely formed internal Al2O3 oxides. The mechanism of scale formation is suggested on the basis of thermodynamic and kinetic abilities of cationic species.

Improvement of isothermal oxidation resistance of a γ′-strengthened Co–Al–W–Mo–Ta–B alloy at 800 °C via doping Ce

Isothermal oxidation resistance, oxide scale evolution and failure mechanism of Ce-doped Co–Al–W–Mo–Ta–B alloy (0.01 at%, 0.05 at%, 0.10 at% and 0.20 at% Ce) exposed at 800 °C were compared. The 0.01Ce and 0.05Ce alloys were consisted of γ/γ′ coherent microstructure, while the κ-Co3W compound precipitated at the grain boundary of the 0.10Ce and 0.20Ce alloys in addition to the γ/γ′ microstructure. The oxidation kinetics curves of the Ce-doped alloys exhibited a parabolic time dependence on the weight gain. With an increasing nominal Ce content, the weight gain of the Co–Al–W–Mo–Ta–B alloys monotonically decreased. An oxide scale composed of a dense and uniform outer Co3O4 + CoO layer, a middle CoAl2O4 and CoWO4 compound layer and an inner Al2O3 layer. The excellent oxidation resistance of 0.2Ce alloy was mainly attributed to a shorter incubation stage for the formation of the continuous and protective Al2O3 layer and the thickest Al2O3 layer during entire oxidation process.

Current-ramp assisted sintering of 3YSZ: Electrochemical and microstructural comparison to flash and thermal sintering

Flash sintering features an unoptimized and uncontrolled rise in current density and sample conductivity. By using a controlled current-ramp technique with a predetermined ramp function, microstructure and electrochemical properties can be improved. This current-ramp method is investigated through use of test functions that follow square-root, linear, and parabolic time dependence with comparison to conventional flash sintering and thermal sintering. Steeper ramp functions during the sintering result in higher activation energy, suggesting a change in the vacancy concentration for both the bulk and grain boundary regions. Estimation of the grain boundary domain width suggests a grain size dependence of the unique space charge contribution to conduction independent of sintering method. Contrary to conventional wisdom, flash sintering can actually result in enhanced grain growth compared to controlled current-ramps and conventional sintering, implying that uncontrolled rise in current to a set cutoff may not be the optimal method for densification.

Improvement of “Pest” Resistance of MoSi2 Intermetallic Compound at 500 °C and 600 °C via Addition of B Fabricated by Spark Plasma Sintering

Mo–Si–B alloys were obtained by spark plasma sintering (SPS) using fine Mo–Si–B alloy powders with a particle size of 2.5 μm. The SPS Mo–Si–B alloys consisted of fine MoSi2/Mo2Bi5(Mo5Si3)/MoB/SiO2 phases. Under isothermal conditions, the weight-gain kinetics of the Mo–Si–B alloys obtained by SPS exhibited parabolic time dependence and these Mo–Si–B alloys showed better oxidation resistance at moderate temperatures of 500 °C and 600 °C with no “pest” failure. The oxide scale on the sample surface consisted of MoO3, amorphous borosilicate and crystalloid SiO2 phases. An increase in the oxidation temperature from 500 to 600 °C caused a significantly higher fluidity and a shorter incubation stage for the formation of a continuously protective borosilicate layer, so that the mass gain was smaller than 1 mg/cm2 for oxidation at 600 °C for 100 h, which corresponds to the excellent oxidation resistance.

Microstructural evolution and oxidation behaviour of Mo-Si-B coatings on an Nb-16Si-22Ti-7Cr-2Al-2Hf alloy at 1250 °C prepared by spark plasma sintering

Mo-Si-(5, 10, 15)B ternary coatings were firstly coated on an Nb-Si based alloy using the spark plasma sintering technique. The Mo-Si-B coatings consisted of an outer MoSi2/MoB/SiO2/Mo2B5 (Mo5Si3) layer and an inter-diffusion zone, while SiO2 was formed during SPS. The oxidation kinetics curves exhibited parabolic time dependence and 5B coating had the lowest mass gain of approximately 0.41 mg/cm2 after oxidation at 1250 °C for 100 h. The good oxidation resistance results from a dense and protective borosilicate layer formed on coatings and the low growth rate of the inter-diffusion zone beneath the Mo-Si-B coatings.

Isothermal and cyclic oxidation behaviours of MoSi2 with additions of B at 1250 °C prepared by spark plasma sintering

Mo-Si-B alloys were obtained by spark plasma sintering (SPS) using Mo-57Si-10B and Mo-52Si-15B alloy powders, and the effects of the B content and powder size on the isothermal and cyclic oxidation behaviours of the Mo-Si-B alloys at 1250 °C were investigated. A SiO2 phase was introduced during the SPS process and the Mo-Si-B alloys consisted of a fine MoSi2/Mo2B5/MoB/SiO2 microstructure. Under isothermal and cyclic oxidation conditions, the kinetic curves of the SPS Mo-Si-B alloys exhibited parabolic time dependence on the weight gain. The increase in the nominal B caused a decrease in the incubation stage of the formation of continuously protective borosilicate layer but increased the mass gain due to the higher fluidity of the borosilicate layer. The SiO2 phase was found to supply the borosilicate layer with a “Mechanical locking” mechanism through the spilling of the SiO2 phase in the SPS samples, especially under the cyclic oxidation condition.

Acceleration of the growth of Cu3Sn voids in solder joints

Soldering to Cu surface finishes usually leads to the formation of a bi-layer intermetallic structure, Cu3Sn/Cu6Sn5, that provides a more robust bond than common alternatives. Occasionally, and so far unpredictably, voids may however grow within the Cu3Sn over time and allow for premature failure of microelectronics products in service. A quantitative assessment of the reliability risk of voids observed after accelerated aging requires the knowledge of the variation of void growth with temperature and time. It is argued that in the case of realistic solder joints diffusion controlled void growth kinetics are unlikely to follow simple Arrhenius and parabolic dependencies, respectively. Nevertheless, three very different sets of samples were all shown to exhibit void growth that could be well approximated by a parabolic time dependence and an effective activation energy of 0.65–0.80eV.

Physical origin of thickness-controlled sequential phase formation during reactive diffusion: Atomistic modeling

Experimental studies of reactive diffusion during annealing of a film deposited on a substrate reveal that the phase formation proceeds either simultaneously or sequentially depending on the film thickness and that its time dependence exhibits a linear-to-parabolic time-dependence transition. This surprising behavior is investigated here theoretically at the atomistic scale via kinetic Monte Carlo simulations based on an Ising energetic model that preserves the main thermodynamic properties of the model system under study, namely, a $B$ substrate with an fcc structure on which a thicker or thinner $A$ film is deposited and annealed at a given temperature. We show that the phase growth linear time dependence is related neither to an interface effect nor to diffusion asymmetry but results from the first stage of phase formation in a local composition close to the phase stoichiometry, whereas the following parabolic time dependence is due to the need for atom transport before phase nucleation. In addition, the thickness-controlled sequential phase formation is attributed to the existence of an asymmetric interdiffusion profile that results, even in the case of symmetric diffusion kinetics, from the respective finite and semi-infinite nature of the film and of the substrate.

Modelling of Zry-4 cladding oxidation by air, under severe accident conditions using the MAAP4 code

In a nuclear power plant, a potential risk in some low probability situations in severe accidents is air ingress into the vessel. Air is a highly oxidizing atmosphere that can lead to an enhanced core oxidation and degradation affecting the release of Fission Products (FP), especially increasing that of ruthenium. This FP is of particular importance because of its high radio-toxicity and its ability to form highly volatile oxides. Oxygen affinity is decreasing between Zircaloy cladding, fuel and ruthenium inclusions in the fuel. It is consequently of great need to understand the phenomena governing cladding oxidation by air as a prerequisite for the source term issues. A review of existing data in the field of Zircaloy-4 oxidation in air-containing atmosphere shows that this phenomenon is quantitatively well understood. The cladding oxidation process can be divided into two kinetic regimes separated by a breakaway transition. Before transition, a protective dense zirconia scale grows following a solid state diffusion-limited regime for which experimental data are well fitted by a parabolic time dependence. For a given thickness, which depends mainly on temperature and the extent of pre-oxidation in steam, the dense scale can potentially breakdown. In case of breakaway combined with oxygen starvation, cladding oxidation can then be much faster because of the combined action of oxygen and nitrogen through a complex self sustaining nitriding-oxidation process. A review of the pre-existing correlations used to simulate zirconia scale growth under air atmospheres shows a high degree of variation from parabolic to accelerated time dependence. Variations also exist in the choice of the breakaway parameter based on zirconia phase change or oxide thickness. Several correlations and breakaway parameters found in the literature were implemented in the MAAP4.07 Severe Accident code. They were assessed by simulation of the QUENCH-10 test, which is a semi-integral test designed to study fuel bundle exposure to steam first and then to air. This paper deals with the main results obtained with MAAP4.07 when simulating QUENCH-10.

Dynamic sorting of lipids and proteins in membrane tubes with a moving phase boundary

Cellular organelle membranes maintain their integrity, global shape, and composition despite vigorous exchange among compartments of lipids and proteins during trafficking and signaling. Organelle homeostasis involves dynamic molecular sorting mechanisms that are far from being understood. In contrast, equilibrium thermodynamics of membrane mixing and sorting, particularly the phase behavior of binary and ternary model membrane mixtures and its coupling to membrane mechanics, is relatively well characterized. Elucidating the continuous turnover of live cell membranes, however, calls for experimental and theoretical membrane models enabling manipulation and investigation of directional mass transport. Here we introduce the phenomenon of curvature-induced domain nucleation and growth in membrane mixtures with fluid phase coexistence. Membrane domains were consistently observed to nucleate precisely at the junction between a strongly curved cylindrical (tube) membrane and a pipette-aspirated giant unilamellar vesicle. This experimental geometry mimics intracellular sorting compartments, because they often show tubular-vesicular membrane regions. Nucleated domains at tube necks were observed to present diffusion barriers to the transport of lipids and proteins. We find that curvature-nucleated domains grow with characteristic parabolic time dependence that is strongly curvature-dependent. We derive an analytical model that reflects the observed growth dynamics. Numerically calculated membrane shapes furthermore allow us to elucidate mechanical details underlying curvature-dependent directed lipid transport. Our observations suggest a novel dynamic membrane sorting principle that may contribute to intracellular protein and lipid sorting and trafficking.

Comparison of the High-Temperature Steam Oxidation Kinetics of Advanced Cladding Materials

Isothermal and transient steam oxidation kinetics of the fuel rod cladding materials Duplex, M5™, E110, and Zircaloy-4 (Zry-4) were determined in separate-effect tests at various temperatures between 1073 and 1673K. All materials show parabolic time dependence at all temperatures, at least at the beginning of the oxidation. The temperature dependence of the oxidation rate is Arrhenius-like. All materials investigated show changes in the activation energy of the steam oxidation connected with the tetragonal-monoclinic phase transformation in the oxide. The temperatures of these changes differ between the Zr-Sn (Zry-4, Duplex: 1223 to 1273 K) and the Zr-Nb alloys (M5™, E110: 1273 to 1323 K). At temperatures below this phase transition, parts of the oxide layer can spall after longer oxidation times. It is known as the so-called “breakaway effect.” This effect occurs in Zry-4 and E110, whereas it was not detected in Duplex and M5™. The breakaway effect results in nearly linear oxidation kinetics. The width of the temperature range and the morphology of the spalled oxide parts differ significantly between Zry-4 and E110. For Zry-4, the breakaway effect was found only at temperatures between 1233 and 1313 K. The spalling of the oxide layer at E110 was detected between 1073 and 1313 K. This wide temperature range also affects the transient steam oxidation behavior. For heating rates below 0.1 K/s, a stronger oxidation was found than expected for parabolic oxidation behavior. The oxide parts spalled from E110 specimens are much finer than the particles after breakaway from Zry-4.

Intermetallic growth in gold ball bonds aged at 175°C: comparison between two 4N wires of different chemistry

Gold wires of different chemistry (denoted as Types A and B) are ballbonded on identical metallization and isothermally aged at 175°C. In both wire types the same intermetallic compounds Au4Al and Au8Al3 grow with parabolic time dependence as long as there is a supply of Al from the bondpad. After Al is completely reacted, composition of intermetallics in Type A wire remains unchanged but in Type B wire, the Au8Al3 compound undergoes a phase transformation into a second layer of Au Al. The phase transformation does not affect mechanical reliability of the ballbonds. Intermetallic growth kinetics, growth sequence and the possible origins of the phase transformation are discussed.

異なる組成のFe-Alペレットを用いたべーパーアルミナイズコーティングの成長挙動

Growth behavior of coatings formed by AlF3 activated vapor phase aluminizing on a Ni-base superalloy substrate was investigated at 1223-1353 K for up to 4 h using FeAl, FeAl2, Fe2Al5, and FeAl3 pellets as aluminum donors, with an aim at understanding the kinetics under different aluminum activities. The coatings consist of an outer δ-Ni2Al3 layer, a middle β-NiAl layer, and an inner diffusion layer of γ′-Ni3Al. The amount of aluminum deposition w shows parabolic time dependence at 1353 K, and the parabolic rate constant increases with an increase of the aluminum content of the pellet. The linear relationship is approved between ln (w2) and reciprocal of absolute temperature, 1/T. This implies that aluminum deposition is a thermally activated process. When the Fe2Al5 or FeAl3 pellet is used, the activation energy is similar to those of the aluminum diffusion in the binary Ni-Al alloys. Therefore, the rate of aluminum deposition might be dominantly controlled by the aluminum diffusion in the coating. When the FeAl pellet is used, the activation energy is much smaller. It is supposed that the aluminum supply from the gas phase to the coating surface is smaller than the aluminum diffusion in the coating. In this case, the processes other than the aluminum diffusion in the coating might contribute to the rate-controlling step. The rate falling occurs in the last stage owing to the phase transformations of FeAl3 → Fe2Al5 → FeAl2 → FeAl caused by the depletion of aluminum in the pellet. When the pellet surface is completely covered by FeAl, the rate-controlling step might change.

Growth Behavior of Coatings Formed by Vapor Phase Aluminizing Using Fe-Al Pellets of Varying Composition

Growth behavior of coatings formed by AlF3 activated vapor phase aluminizing on an Ni-base superalloy substrate was investigated at 1353 K for up to 4 h using FeAl, FeAl2 ,F e 2Al5, and FeAl3 pellets as aluminum donors, with an aim of understanding the kinetics under the different aluminum activities. The coatings consist of an outer � -Ni2Al3 layer, a middle � -NiAl layer, and an inner diffusion layer of � 0 -Ni3Al. The thickness of the � -Ni2Al3 layer remarkably increases with an increase of the coating time and of the aluminum content of the donor pellet. Contrarily, the aluminum concentration at the coating surface increases only a little, which might be due to the strong dependence of the aluminum activity on composition of solid Ni-Al alloys. The amount of aluminum deposition shows parabolic time dependence in all the cases, and the deposition rate becomes higher for the donor pellet of higher aluminum content. Except for the case of the FeAl pellet, the parabolic rate constants are similar to the reported value calculated from the diffusion rate of aluminum in solid Ni-Al alloys. This suggests that the rate of aluminum deposition is dominantly controlled by solid diffusion in the coating. However, the rate falling occurs in the last stage due to the phase transformations of FeAl3 ! Fe2Al5 ! FeAl2 ! FeAl caused by the depletion of aluminum in the pellet. It is supposed that the gaseous diffusion of aluminum or the other process might contribute to the rate-controlling when a sufficiently thick FeAl layer covers the pellet surface. [doi:10.2320/matertrans.47.2341]

Interlayer growth at interfaces of Ti/Al–1%Mn, Ti/Al–4·6%Mg and Ti/pure Al friction weld joints by post-weld heat treatment

The interlayer growth at interfaces of Ti/Al–1%Mn and Ti/Al–4·6%Mg weld joints was studied by postweld heat treatment. The heating temperatures ranged from 676 to 873 K (400–600°C) and maximum heating time was 360 ks (100 h). The basic mechanism of interlayer growth for pure Ti/pure Al friction weld joint was also estimated. The interlayer growth rate of Ti/Al–4·6%Mg joint was much faster than for the Ti/ Al–1%Mn joint. The interlayer mainly consisted of (Al,Si)3Ti for the Ti/Al–1%Mn joint, and Al18Mg3Ti2 for the Ti/Al–4·6%Mg joint. While the interlayer grew from Al alloy substrate to the Ti side for the Ti/Al–1%Mn joint, it grew from the Ti substrate to the Al alloy side for the Ti/Al–4·6%Mg joint. The interlayer growth stopped for several hours on heating for 36 ks (10 h). Neither linear nor parabolic time-dependence relations could be exactly fit to the interlayer growth rate for both joints. The interlayer growth of Ti/Al–1%Mn was proportional to heating time raised to approximately 0·85. The crystal direction of Al3Ti interlayer growth of the Ti/Al joint was close to 〈001〉 and 〈111〉 directions obtained by OIM method. Nucleation and nuclei growth were observed at the interface of the Ti/Al joint. The nucleation and the nuclei growth are the reason for the phenomena (time dependence) described above.

In situ observation of interlayer growth during heat treatment of friction weld joint between pure titanium and pure aluminium

The growth of an intermediate layer, consisting of an intermetallic compound phase, in a friction welded joint between pure Ti and pure Al heated at 853 K for up to 173 ks (580°C, 48 h) was elucidated via an in situ (direct) and continuous observation method using a high temperature optical microscope. The following conclusions were reached. The layer grew from the Al substrate to the Ti substrate, and neither a linear nor a parabolic time dependence could be used to describe the rate of layer growth. The layer growth stopped for some time (i.e. several hours) after every heating interval of approximately 36 ks (10 h). That is, several plateaus appeared during heat treatment. It is thought that nucleation, and growth of such nuclei, of the Al- Ti binary intermetallic phase are necessary for layer growth. The interlayer growth rate for joints between pure Ti and highly pure Al was higher than that for joints between pure Ti and commercially pure Al. This is due to the Si content in the Al base metal. There was a slight variation of the layer growth rate with location along the radius of the joint and with friction time.

Aluminizing Behaviors of Vacuum Plasma Sprayed MCrAlY Coatings

AbstractThe objective of this study is aluminide overlay coatings of MCrAlY sprayed by a vacuum plasma spraying (VPS) process for the protection against high-temperature corrosion and oxidation of gas turbine components. Diffusion coating processes have been applied for many years to improve similarly the environmental resistance by enriching the surface of nickel-based superalloys with chromium, aluminum, or silicon element. Recently, aluminizing of MCrAlY coatings is used for improving further the high-temperature oxidation resistance. However, the aluminizing properties of plasma-sprayed MCrAlY coatings, which have an important effect on the coating performance, have not been clarified. In this study, five kinds of plasma-sprayed MCrAlY (CoCrAlY, CoNiCrAlY, CoNiCrAlY+Ta, NiCrAlY, and NiCoCrAlY) coating were selected for pack-aluminizing tests. The as sprayed and the heat-treated (1393 K, 2 h, argon cooled and 1116 K, 24 h, argon cooled) MCrAlY specimens were Al-Cr-Al2O3-NH4Cl pack-aluminized at 1173, 1223, and 1273 K for 5, 10, and 20 h, respectively. The experimental results showed that the aluminizing process formed the aluminum rich layers of NiAl or CoAl phase. It also indicated that the thickness of the aluminum rich layer showed a parabolic time-dependence in all MCrAlY coatings. The order of reaction diffusion rate was NiCoCrAlY=NiCrAlY>CoNiCrAlY>CoNiCrAlY+Ta>CoCrAlY. There was a tendency that the reaction diffusion rate by aluminizing increased with increasing nickel content in the MCrAlY coatings and the reaction diffusion rate of as sprayed MCrAlY coatings is faster than that of the heat-treated MCrAlY coatings.

On the formation mechanism of γ-AgI thin films

Programmed iodization of silver foils at ambient temperature and pressure leads to the formation of γ-AgI films with zinc-blende structure. Gravimetric experiments show that the AgI film formation follows a parabolic time dependence. X-ray diffraction monitoring of the film formation on unannealed, annealed and etched silver foils reveals that the absence of intrinsic stacking faults is a necessary condition for the formation of γ-AgI thin films and that the presence of such faults invariably results in the formation of β-AgI thin films. Optical absorption studies indicate eventual saturation of the direct optical band gap with increase in iodination time, which corroborates X-ray diffraction and gravimetry results.

Origin of the time dependence of wet oxidation of AlGaAs

The time dependence of the wet oxidation of high-Al-content AlGaAs can be either linear, indicating reaction-rate limitation, or parabolic, indicating diffusion-limited rates. The transition from linear to parabolic time dependence can be explained by the increased rate of the formation of intermediate As2O3 versus its reduction to elemental As. A steadily increasing thickness of the As2O3-containing region at the oxidation front will shift the process from the linear to the parabolic regime. This shift from reaction-rate limited (linear) to diffusion-limited (parabolic) time dependence is favored by increasing temperature or increasing Al mole fraction.