parabolic kinetics
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2021 ◽  
Author(s):  
Mei Yang ◽  
Haoxing You ◽  
Richard D. Sisson

Abstract A physics-based software model is being developed to predict the nitriding and ferritic nitrocarburizing (FNC) performance of quenched and tempered steels with tempered martensitic microstructure. The microstructure of the nitrided and FNC steels is comprised of a white compound layer of nitrides (ε and γ’) and carbides below the surface with a hardened diffusion zone (i.e., case) that is rich in nitrogen and carbon. The composition of the compound layer is predicted using computational thermodynamics to develop alloy specific nitriding potential KN and carburizing potential KC phase diagrams. The thickness of the compound layer is predicted using parabolic kinetics. The diffusion in the tempered martensite case is modeled using diffusion with a reaction. Diffusion paths are also developed on these potential diagrams. These model predictions are compared with experimental results.


2019 ◽  
Vol 37 (1) ◽  
pp. 36-45
Author(s):  
Christopher Breach

Purpose The purpose of this study is to demonstrate that isothermal intermetallic growth data for gold ball bonds can be non-parabolic with explanations of why deviation from parabolic kinetics may occur. Design/methodology/approach Intermetallic thickness measurements were made at the centre of cross-sectioned ball bonds that were isothermally annealed at 175°C. Intermetallic growth kinetics were modelled with a power law expression(x(t) − x0)2 = α1tα2. The parameters of the power law model were obtained by transformation of the response and explanatory variables followed by data fitting using simple linear regression (SLR). Findings Ball bonds made with 4 N (99.99%Au) and 3 N (99.9%Au) gold wires exhibited two consecutive time regimes of intermetallic growth denoted Regime I and Regime II. Regime I was characterised by reactive diffusion between the gold wire and the aluminium alloy bond pad, during which Al was completely consumed in the formation of Au–Al intermetallics with non-parabolic kinetics. In Regime II, the absence of a free supply of Al to sustain intermetallic growth led to the conclusion that thickening of intermetallics was caused by phase transformation of Au8Al3 to Au4Al. Ball bonds made with 2 N (99%Au) wire also exhibited non-parabolic kinetics in Regime I and negligible intermetallic thickening in Regime II. Research limitations/implications The analysis of intermetallic growth is limited to total intermetallic growth at a single temperature (175°C). Originality/value The value of this study lies in showing that the assumption that only parabolic intermetallic growth is observed in isothermally aged gold ball bonds is incorrect. Furthermore there is no need to assume parabolic growth kinetics because with an appropriate data transformation, followed by fitting the data to a power law model using SLR and with the use of statistical diagnostics, both the suitability of the kinetic model and the nature of the growth kinetics (parabolic or non-parabolic) can be determined.


Materials ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3120 ◽  
Author(s):  
Zifu Li ◽  
Panos Tsakiropoulos

In this paper, we report research about the isothermal oxidation in air at 800 and 1200 °C for 100 h of the as-cast alloys (at.%) Nb-18Si-5Ge (ZF1), Nb-18Si-10Ge (ZF2), Nb-24Ti-18Si-5Ge (ZF3), Nb-24Ti-18Si-5Cr (ZF4), Nb-24Ti-18Si-5Al (ZF5), Nb-24Ti-18Si-5Al-5Cr-5Ge (ZF6), and Nb-24Ti-18Si-5Al-5Cr-5Ge-5Hf (ZF9), the microstructures of which were reported in previous publications. Only the alloys ZF1, ZF2, and ZF3 suffered from pest oxidation at 800 °C. The Ge addition substantially improved the oxidation resistance of the other alloys both at 800 °C and 1200 °C, which followed parabolic kinetics at 800 °C and in the early stages at 1200 °C and linear kinetics at longer times, where there was spallation of the scales. The Nb2O5 and TiNb2O7 oxides were formed in the scales of the alloys ZF4, ZF5, ZF6, and ZF9 at 800 °C and 1200 °C, the GeO2 was observed in all scales and the SiO2 in the scales of the alloys ZF4 and ZF5, the CrNbO4 in the scales of the alloys ZF4, ZF6, and ZF9 and the AlNbO4 in the scales of the alloys ZF5, ZF6, and ZF9. Diffusion zones were formed below the scale/substrate interface only in the alloys ZF4 and ZF5 where the Nbss and Nb5Si3 were contaminated by oxygen. However, these phases were not contaminated by oxygen in the bulk of the alloys ZF4, ZF5, ZF6, and ZF9. The alloys ZF9 and ZF6 exhibited the best oxidation behaviour at 800 °C and 1200 °C, respectively. The alloys were compared with Nb-silicide based alloys of similar compositions without Ge and Hf additions and the alloy ZF9 with refractory metal High Entropy Alloys. Compared with the former alloys, the addition of Ge reduced the vol % of the Nbss. Compared with the latter alloys, the superior oxidation behaviour of the alloy ZF9 was attributed to its higher and lower values respectively of the parameters δ and VEC.


2019 ◽  
Vol 144 ◽  
pp. 209-216 ◽  
Author(s):  
Hannah Aris ◽  
Shayan Borhani ◽  
Devorah Cahn ◽  
Colleen O'Donnell ◽  
Elizabeth Tan ◽  
...  

2015 ◽  
Author(s):  
Alexander Vasiliev

During postulated design-basis or beyond-design-basis accident at nuclear power plant with PWR or BWR, the high temperature oxidation of Zr-based fuel claddings in H2O-O2-N2 gas atmosphere could take place. Recent experimental observations showed that the oxidation of those claddings in the air (or, more generally, in oxygen-nitrogen and steam-nitrogen mixtures) behaves in much more aggressive way (linear or enhanced parabolic kinetics) compared to oxidation in pure steam (standard parabolic kinetics). This is why an advanced model of Zr-based cladding oxidation was developed. For calculations of cladding oxidation in oxygen-nitrogen and steam-nitrogen mixtures, the effective oxygen diffusion coefficient in ZrO2+ZrN layer formed in cladding is used. The diffusion coefficient enhancement factor depends on ZrN content in ZrO2+ZrN layer. A numerical scheme was realized to determine ZrO2+ZrN/α-Zr(O) and α-Zr(O)/β-Zr layers boundaries relocation and layers transformations in claddings. The model was implemented to the SOCRAT best estimate computer modeling code. The SOCRAT code with advanced model of oxidation was successfully used for calculations of separate effects tests and air ingress integral experiments QUENCH-10, QUENCH-16 and PARAMETER-SF4.


2013 ◽  
Vol 75 ◽  
pp. 58-66 ◽  
Author(s):  
S. Cruchley ◽  
H.E. Evans ◽  
M.P. Taylor ◽  
M.C. Hardy ◽  
S. Stekovic

2012 ◽  
Vol 715-716 ◽  
pp. 599-604 ◽  
Author(s):  
Stephen M. Foiles

Grain growth in nanocrystalline Ni has been simulated by molecular dynamics. The simulations show the creation of a high density of twin boundaries during the growth as well as the formation of vacancies consistent with recent experimental observations. The growth follows parabolic kinetics with the diameter increasing with the square root of time consistent with behavior of conventional scale metals but in disagreement with prior simulation results.


2011 ◽  
Vol 696 ◽  
pp. 1-11 ◽  
Author(s):  
David J. Young

Wagner’s 1959 diffusion model of the internal oxidation process provided a method of predicting the rate at which a binary alloy was penetrated by dissolved oxygen as it precipitated the more reactive (but dilute) alloy component. Parabolic kinetics were predicted to depend on oxygen permeability in the unreacted alloy solvent and also, in cases where the reactive component was sufficiently mobile, the diffusion coefficient of the latter. The model has proven very successful, but is restricted to single oxidant-binary alloy systems, in which the precipitated oxide has extremely low solubility. This paper reviews recent results on a number of internal precipitation processes which cannot be described with the Wagner theory. These include formation of low stability carbides and nitrades; internal precipitation driven by multiple oxidants; the templating effects of prior precipitates on subsequently formed corrosion products; cellular precipitation morphologies; internal interface diffusion effects; volume changes in the reaction zone and the effects upon them of simultaneous external scaling.


2011 ◽  
Vol 312-315 ◽  
pp. 283-288
Author(s):  
Zbigniew Grzesik ◽  
Monika Migdalska ◽  
Stanisław Mrowec

The corrosion behavior of X33CrNiMn23-8, X50CrMnNiNbN21-9 and X53CrMnNiN20-8 steels utilized in automobile industry has been studied in oxidizing atmosphere, containing water vapor and acetic acid, usually present in combustion gases of biofuels in car engines. It has been found that the mechanism of corrosion under these conditions is rather complex. After early stages of the reaction, not exceeding 40 hours, the process follows approximately parabolic kinetics, being thus diffusion controlled. It has been shown that the presence of acetic acid highly increases corrosion rate of X33CrNiMn23-8 steel, containing highest chromium content, but has virtually no influence on the corrosion rate of X50CrMnNiNbN21-9 steel with lowest chromium concentration. These differences have been explained in terms of phase and chemical composition of corrosion products.


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