Computer simulation of monolayer growth kinetics of Fe2B phase during the paste-boriding process: Influence of the paste thickness

This paper deals with the effect of boron paste thickness on the study of the monolayer growth kinetics of Fe₂B phase forming on AISI 1045 steel by the paste-boriding process. A mathematical diffusion model based on the Fick's phenomenological equations was applied in order to estimate the growth rate constant at (Fe₂B/γ-Fe) interface, the layer thickness of iron boride as well as the associated mass gain depending on the boriding parameters such as time, temperature and surface boron concentration related to the boron paste thickness. The simulation results are found to be in a fairly good agreement with the experimental data derived from the literature.     

Simulation of the growth kinetics of the (FeB/Fe2B) bilayer obtained on a borided stainless steel

The present work is an attempt to simulate the growth kinetics of the (FeB/Fe₂B) bilayer grown on a substrate made of AISI 316 stainless steel by the application of the powder-pack boriding process, and using four different temperatures (1123, 1173, 1223 and 1273 K) and five exposure times (2, 4, 6, 8 and 10 h). The adopted diffusion model solves the mass balance equation at each growth front: (FeB/Fe₂B or FeB/substrate) under certain assumptions and without considering the diffusion zone. To consider the effect of the incubation times for the borides formation, the temperature-dependent function ?(T) was incorporated in the model. To validate this model, a computer code written in Matlab (version 6.5), was developed with the purpose of simulating the kinetics of the boride layers. This computer code uses the following parameters as input data: (the boriding temperature, the treatment time, the upper and lower limits of boron concentration in each iron boride, the diffusion coefficients of boron in the FeB and Fe₂B phases as well as the ?(T) parameter). The outputs of the computer code are the parabolic growth constant at each growth front and the thicknesses of the FeB and Fe₂B layers. A good agreement was obtained between the experimental parabolic growth constants taken from a reference work [I. Campos-Silva et al., Formation and kinetics of FeB/Fe₂B layers and diffusion zone at the surface of AISI 316 borided steels, Surf. Coat Technol., 205 (2010) 403-412] and the simulated values of the parabolic growth constants (k_FeB and k₁). The present model was also able to predict the thicknesses of the FeB and Fe₂B layers at a temperature of 1243 K during 3 and 5 h.In addition, the mass gain at the material surface was also estimated as a function of the time and the upper boron content in each iron boride phase. It was shown that the simulated values of the generated mass gain are very sensitive to the increase of both temperature and the upper boron contents in the FeB and Fe₂B phases.     

A model for studying the kinetics of the formation of Fe2B boride layers at the surface of a gray cast iron

The present work estimates, using a kinetic model, the growth kinetics of Fe₂B boride layers generated at the surface of a gray cast iron via the powder-pack boriding considering three different temperatures (1173, 1223 and 1273 K) and four treatment times (2, 4, 6 and 8 h). By the use of the mass balance equation at the (Fe₂B/substrate) interface under certain assumptions and considering the effect of the boride incubation time, it was possible to estimate the corresponding parabolic growth constant in terms of two parameters and β(T) depending on the boron content in the Fe₂B phase and on the process temperature, respectively. The mass gain at the material surface and the instantaneous velocity of the (Fe₂B/substrate) interface were also estimated. A fairly good agreement was observed between the experimental parabolic growth constants taken from a reference work (Campos-Silva et al., Characterization of boride layers formed at the surface of gray cast irons, Kovove Mater. 47 (2009) 1-7.) and the simulated values of the parabolic growth constants. Furthermore, the boride layer thicknesses were predicted and experimentally verified for three process temperatures and four treatment times.     

A simple model for the growth kinetics of Fe2B iron boride on pure iron substrate

The present work evaluates the growth kinetics of Fe₂B iron boride forming on iron substrate by means of a diffusion model in the temperature range 1223-1323 K. The model takes into account the effect of the boride incubation time during the formation of Fe₂B phase. The parabolic growth constant at the (Fe₂B/Fe) interface and the mass gain generated by this treatment were estimated. Likewise a simple relationship was proposed to describe the variation of the parabolic growth constant as a function of both the temperature and the boron content in the Fe₂B phase. Furthermore, the simulation results show a good agreement with our experimental results.     

Evaluation of boron mobility on the phases FeB, Fe2B and diffusion zone in AISI 1045 and M2 steels

The present study evaluates the growth kinetics of boride layers at the material surface on AISI 1045 and M2 steels during the paste boriding process. This surface hardening technique produces on the material two characteristic phases FeB, Fe₂B and a transition zone, denominated diffusion zone, in the layer/substrate interface. The thermochemical treatment was done at three different temperatures: 1193, 1223 and 1273 K with two treatment times: 2 and 6 h for the 1045 steel, and 1223, 1253 and 1273 K with the same treatment times for M2 steel, modifying the boron potentials in equilibrium at the substrates surfaces. Using the mass balance equation, and assuming a linear concentration profile at the interfaces, the mobility of boron was determined on both types of steels. The influence of boron potential, treatment time and temperatures is clearly observed on the growth kinetics of boride layers.     

Kinetics of the formation of Fe2B layers in gray cast iron: Effects of boron concentration and boride incubation time

The growth kinetics of Fe₂B layers formed at the surface of gray cast iron were evaluated in this study. The pack-boriding process was applied to produce the Fe₂B phase at the material surface, and the variables included three temperatures (1173, 1223 and 1273 K) and four exposure times (2, 4, 6 and 8 h). Taking into account the growth fronts obtained at the surface of the material and the mass balance equation at the Fe₂B/substrate interface, the boron diffusion coefficient on the borided phase was estimated for the range of treatment temperatures. Likewise the parabolic growth constant, the instantaneous velocity of the Fe₂B/substrate interface, and the weight gain in the borided samples were established as a function of the parameters τ(t) and α(C), which are related to the boride incubation time (t₀(T)) and boron concentration at the Fe₂B phase, respectively. Observation of the growth kinetics of the Fe₂B layers in gray cast irons suggest an optimum value of boron concentration that is in good agreement with the set of boriding experimental conditions used in this work.     

锗硅/硅异质结材料的化学气相淀积生长动力学模型

基于化学气相淀积(CVD)的Grove理论和Fick第一定律,提出并建立了锗硅(SiGe)/硅(Si)异质结材料减压化学气相淀积(RPCVD)生长动力学模型.与以前锗硅/硅异质结材料生长动力学模型仅考虑表面反应控制不同,本模型同时考虑了表面反应和气相传输两种控制机理,并给出了两种控制机理极限情况下的模型.本模型不仅适用于低温锗硅/硅应变异质结材料生长的表征,也适用于表征高温锗硅/硅弛豫异质结材料生长的表征.将模型计算值与实验结果进行了对比,无论是625℃低温下的应变SiGe的生长,还是900℃高温下的弛豫 关键词： SiGe/Si异质结材料 化学气相淀积生长动力学模型 Grove理论 Fick第一定律     

Temporary phase segregation processes during the oxidation of (Fe0.7Mn0.3)0.99O in N2---H2O atmosphere

A two-step thermochemical cycle with the ternary metal oxide system (Fe_{1 − x}Mn_x)₃O₄/(Fe_{1 − x}Mn_x)_{1 − y}O is applied to convert solar energy to chemical energy. Experimental investigations on the water splitting reaction of (Fe_{1 − x}Mn_x)_{1 − y}O revealed temporary formation of a manganese rich rock salt phase and an iron rich spinel phase due to phase segregation processes.     

UHV-MOCVD growth of TiO2 on SiOx/Si(1 1 1): Interfacial properties reflected in the Si 2p photoemission spectra

Metal–organic chemical vapour deposition growth of titanium oxide on moderately pre-oxidised Si(1 1 1) using the titanium(IV) isopropoxide precursor has been studied for two different growth modes, reaction-limited growth at 300 °C and flux-limited growth at 500 °C. The interfacial properties have been characterized by monitoring synchrotron radiation excited Si 2p photoemission spectra. The cross-linking from oxidised Si to bulk Si after TTIP exposure has been found to be very similar to that of SiO_x/Si(1 1 1). However, the results show that the additional oxidation of Si most probably causes a corrugation of the SiO_x/Si interface. Those conclusions are valid for both growth modes. A model is introduced in which the amorphous interface region is described as (TiO₂)_x(SiO₂)_y where x and y changes linearly and continuously over the interface. The model quantifies how (TiO₂)_x(SiO₂)_y mixing changes the relative intensities of the signals from silicon oxide and silicon. The method can be generalised and used for the analyses of other metal-oxides on silicon.     

A periodic model for the V2O5-TiO2 (anatase) catalyst. Stability of dimeric species

We present periodic DFT calculations to study the structure of the V₂O₅-TiO₂ (anatase) catalyst. Linear and cyclic dimeric V₂O₅ species represent the active phase. The support TiO₂ (anatase) is represented for the perfect (1 0 0) and (0 0 1) surfaces. The maximum interaction between the active phase and the support is favored, and low coverage is assumed. The most stable models allow the compensation of the surface dangling bonds, and can be understood as a continuation of the bulk anatase structure. The more suitable models for studying reactivity possess uncoordinated atoms available for reactivity, such as terminal oxygen atoms in V₂O₅. Relaxation plays an important role in the adsorption systems, and cannot be discarded when modeling the V₂O₅-anatase catalyst.     

Atomic force microscopy study of growth kinetics: Scaling in TiN-TiB2 nanocomposite films on Si(1 0 0)

We used the reactive unbalanced close-field dc-magnetron sputtering growth of TiN-TiB₂ on Si(1 0 0) at room temperature to determine if scaling theory provides insight into the kinetic mechanisms of two-phase nanocomposite thin films. Scaling analyses along with height-difference correlation functions of measured atomic force microscopy (AFM) images have shown that the TiN-TiB₂ nanocomposite films with thickness ranging from 70 to 950 nm exhibit a kinetic surface roughening with the roughness increasing with thickness exponentially. The roughness exponent α and growth exponent β are determined to be ∼0.93 and ∼0.25, respectively. The value of dynamic exponent z, calculated by measurement of the lateral correlation length ξ, is ∼3.70, agreeing well with the ratio of α to β. These results indicate that the surface growth behavior of sputter-deposited TiN-TiB₂ thin films follows the classical Family-Vicseck scaling and can be reasonably described by the noisy Mullins diffusion model, at which surface diffusion serves as the smoothing effect and shot noise as the roughening mechanism.     

水热法合成FeS2粉晶及其生长热动力学的研究

采用溶胶_凝胶水热法合成了单相黄铁矿结构的FeS2₂粉晶. 用x射线衍射、傅 氏变换红外光谱等分析手段对FeS2₂粉晶进行了表征，以简化的数学模型及相 变理论讨论了晶体 生长过程. 结果表明：FeS2₂晶粒的生长过程属于相变与扩散的混合机制，符 合经时间 指数修正的二次方动力学方程，是一个生长速率随时间变化的过程；水热晶化温度高于453 K、反应时间超过18 h且有适量的硫参与反应时，可得到单相的黄铁矿型的FeS2₂关键词： 溶胶_凝胶水热法 2粉晶')" href="#">FeS2₂粉晶 晶粒生长 热动力学     

温度对ZnO/Al2O3(0001)界面的吸附、扩散及生长初期模式的影响

构建了一个ZnO沉积在α-Al₂O₃(0001)表面生长初期的模型，采用基于密度泛函理论的平面波超软赝势法进行了动力学模拟.发现在400，600和800℃的条件下界面原子有不同的扩散能力，因此温度对ZnO/α-Al₂O₃(0001)表面界面结构以及ZnO薄膜生长初期模式有决定性的影响.在整个ZnO吸附生长过程中，O原子的扩散系数大于Zn原子的扩散系数，O原子的层间扩散对薄膜的均匀生长起着重要作用.进一步从理论计算上证实了ZnO在蓝宝石(0001)上两种生长模式的存在，400℃左右生长模式主要是Zn螺旋扭曲生长，具有Zn六角平面对称特征，且有利于Zn原子位于最外表面.600℃左右呈现为比较规则的层状生长，且有利于O原子位于最外表面.模拟观察到在ZnO薄膜临近Al₂O₃基片表面处，Zn的空位缺陷明显多于O的空位缺陷. 关键词： 扩散 薄膜生长 2O₃(0001)')" href="#">α-Al₂O₃(0001) ZnO     

A non-linear Rζ gauge condition for the electroweak SU(2) × U(1) model

A non-linear R_ζ gauge condition is presented and explicitly developed in the framework of the SU(2)×U(1) gauge model. We give the corresponding Feynman rules, which are simpler than in R_ζ gauges, because couplings involving unphysical Higgs and gauge bosons disappear or simplify. The Faddeev-Popov sector is more elegant, the ghosts coupling to neutral gauge bosons like in scalar electrodynamics. Finally, as a practical example, the transition Higgs→γγ is considered and compared with the usual calculation in linear gauges.     

Surface properties of rutile TiO2(1 1 0) from molecular dynamics and lattice dynamics at 300 K: Variable-charge model results

Geometric structure, atomic vibrations and atomic charges and their thermally induced fluctuations have been calculated as a function of depth in, and thickness of, rutile TiO₂(1 1 0) slabs, within the framework of the variable-charge potential of Swamy and Gale [V. Swamy, J.D. Gale, Phys. Rev. B 62 (2000) 5406] at 300 K. Molecular dynamics simulations and lattice dynamics calculations were performed with a 2D periodic slab model for slab thicknesses between 3 and 11 triple layers (approximately 9-35 Å). Odd-even oscillations with respect to the number of slab layers are found for the surface relaxation for very thin slabs, and for the (slowly converging) rumpling in the middle of the slab. The Ti and O atomic charges in the outermost three atomic layers differ from the rest of the slab (they are less ionic); the thermal vibrations do not alter this picture. The atomic mean-square amplitudes are some 50% larger (more for O, less for Ti) at the surface than in the middle of the slab and decay rather slowly to the bulk values. Comparisons with the results of a rigid-ion potential for titania [M. Matsui, M. Akaogi, Mol. Simul. 6 (1991) 238] are presented for non-electronic properties.     

A variable temperature EPR study of the manganites (La1/3Sm2/3)2/3SrxBa0.33−xMnO3 (x=0.0, 0.1, 0.2, 0.33): Small polaron hopping conductivity and Griffiths phase

Four manganite samples of the series, (La_1/3Sm_2/3)_2/3Sr_xBa_0.33−xMnO₃, with x=0.0, 0.1, 0.2 and 0.33, were investigated by X-band (∼9.5 GHz) electron paramagnetic resonance (EPR) in the temperature range 4-300 K. The temperature dependences of EPR lines and linewidths of the samples with x=0.0, 0.1 and 0.2, containing Ba²⁺ ions, exhibit similar behavior, all characterized by the transition temperatures (T_C) to ferromagnetic states in the 110-150 K range. However, the sample with x=0.33 (containing no Ba²⁺ ions) is characterized by a much higher T_C=205 K. This is due to significant structural changes effected by the substitution of Ba²⁺ ions by Sr²⁺ ions. There is an evidence of exchange narrowing of EPR lines near T_min, where the linewidth exhibits the minimum. Further, a correlation between the temperature dependence of the EPR linewidth and conductivity is observed in all samples, ascribed to the influence of small-polaron hopping conductivity in the paramagnetic state. The peak-to-peak EPR linewidth was fitted to ΔB_pp(T)=ΔB_pp,min+A/Texp(−E_a/k_BT), with E_a=0.09 eV for x=0.0, 0.1 and 0.2 and E_a=0.25 eV for x=0.33. From the published resistivity data, fitted here to σ(T)∝1/T exp(−E_σ/k_BT), the value of E_σ, the activation energy, was found to be E_σ=0.18 eV for samples with x=0.0, 0.1 and 0.2 and E_σ=0.25 eV for the sample with x=0.33. The differences in the values of E_a and E_σ in the samples with x= 0.0, 0.1and 0.2 and x=0.33 has been ascribed to the differences in the flip-flop and spin-hopping rates. The presence of Griffiths phase for the samples with x=0.1 and 0.2 is indicated; it is characterized by coexistence of ferromagnetic nanostructures (ferrons) and paramagnetic phase, attributed to electronic phase separation.     

Analysis of the kinetics of N2O-CO reaction on Pd(1 1 0)

Experimental studies indicate that the N₂O-CO reaction occurring on Pd(1 1 0) under UHV conditions exhibits a first-order kinetic phase transition in the steady-state case and also transient kinetics strongly dependent on the initial state of the system. We construct a mean-field kinetic model describing these phenomena. With a minimal number of the fitting parameters, the model reasonably reproduces the special features of the reaction kinetics.     

Adsorption and diffusion of H2O molecule on the Be(0001) surface: A density-functional theory study

Using first-principles calculations, we systematically study the adsorption behavior of a single molecular H₂O on the Be(0001) surface. We find that the favored molecular adsorption site is the top site with an adsorption energy of about 0.3 eV, together with the detailed electronic structure analysis, suggesting a weak binding strength of the H₂O/Be(0001) surface. The adsorption interaction is mainly contributed by the overlapping between the s and pz states of the top-layer Be atom and the molecular orbitals 1b₁ and 3a₁ of H₂O. The activation energy for H₂O diffusion on the surface is about 0.3 eV. Meanwhile, our study indicates that no dissociation state exists for the H₂O/Be(0001) surface.     

Ab initio chemical kinetics for the reactions of HNCN with O(P) and O2

The kinetics and mechanisms of the reactions of cyanomidyl radical (HNCN) with oxygen atoms and molecules have been investigated by ab initio calculations with rate constant prediction. The doublet and quartet state potential energy surfaces (PESs) of the two reactions have been calculated by single-point calculations at the CCSD(T)/6-311+G(3df, 2p) level based on geometries optimized at the CCSD/6-311++G(d, p) level. The rate constants for various product channels of the two reactions in the temperature range of 300-3000 K are predicted by variational transition state and RRKM theories. The predicted total rate constants of the O(³P) + HNCN reaction at 760 Torr Ar pressure can be represented by the expressions k_total (O + HNCN) = 3.12 × 10⁻¹⁰ × T^−0.05 exp (−37/T) cm³ molecule⁻¹ s⁻¹ at T = 300-3000 K. The branching ratios of primary channels of the O(³P) + HNCN are predicted: k₁ for producing the NO + CNH accounts for 0.72-0.64, k₂ + k₉ for producing the ³NH + NCO accounts for 0.27-0.32, and k₆ for producing the CN + HNO accounts for 0.01-0.07 in the temperature range studied. Meanwhile, the predicted total rate constants of the O₂ + HNCN reaction at 760 Torr Ar pressure can be represented by the expression, k_total(O₂ + HNCN) = 2.10 × 10⁻¹⁶ × T^1.28exp (−12200/T) cm³ molecule⁻¹ s⁻¹ at T = 300-3000 K. The predicted branching ratio for k₁₁ + k₁₃ producing HO₂ + ³NCN as the primary products accounts for 0.98-1.00 in the temperature range studied.