Computer simulation of solute-enhanced diffusion kinetics in dilute fcc alloys

This paper describes a Monte Carlo study of the linear enhancement factor for the solvent tracer diffusivity in dilute fcc alloys. The model used is the well-known five-frequency model with isolated solute atoms. It is shown that the analytical treatments by Howard and Manning and by Ishioka and Koiwa have major shortcomings in their handling of correlation effects for certain combinations of the atom-vacancy exchange frequencies. Many of the values of the exchange frequency ratios that have been determined from experiment by way of these treatments are probably in some error.     

Interdiffusion and thermotransport in Ni–Al liquid alloys

In this paper, we present extensive self-consistent results of molecular dynamics (MD) simulations of diffusion and thermotransport properties of Ni–Al liquid alloys. We develop a new formalism that allows easy connection between results of the MD simulations and the real experiments. In addition, this formalism can be extended to the case of ternary and higher component liquid alloys. We focus on the temperature and composition dependence of the self-diffusion coefficients, interdiffusion coefficients, thermodynamic factor, Manning factor and the reduced heat of transport. The two latter quantities both represent measures of the off-diagonal Onsager phenomenological coefficients. The Manning factor and the reduced heat of transport can be related to experimentally obtainable quantities provided the thermodynamic factor is available. The simulation results for the reduced heat of transport show that for all compositions, in the presence of a temperature gradient, Ni tends to migrate to the cold end. This is in agreement with an available experimental study for a Ni_21.5Al_78.5 melt (only qualitative result is available so far).     

Simultaneous tracer diffusion and interdiffusion in a sandwich-type configuration to provide the composition dependence of the tracer diffusion coefficients

In this paper, a new formalism of a combined tracer and interdiffusion experiment for a binary interdiffusion couple is developed. The analysis requires an interdiffusion couple that initially contains a thin layer of tracers of one or both of the constituent elements at the original interface of the couple (sandwich interdiffusion experiment). This type of interdiffusion experiment was first performed in 1958 by J.R. Manning. The theoretical analysis presented in this paper is based on a newly developed phenomenological theory of isotopic interdiffusion combined with the Boltzmann–Matano formalism. This new analysis now provides the means to obtain the composition dependent interdiffusion coefficient and tracer diffusion coefficients simultaneously from analysis of the interdiffusion and tracer profiles in a single sandwich interdiffusion experiment. The new analysis is successfully applied to the results of Manning’s original ‘sandwich interdiffusion’ experiment in the Ag–Cd system (six couples in total) and is validated with an independent determination of the Ag and Cd tracer diffusion coefficients by Schoen using the conventional thin film technique. Suggestions for further development of the sandwich interdiffusion experiment and analysis to the case of multicomponent alloys are provided.     

Pseudo-binary and pseudo-ternary diffusion couple methods for estimation of the diffusion coefficients in multicomponent systems and high entropy alloys

The benefits of using the pseudo-binary and pseudo-ternary diffusion couple methods in multicomponent inhomogeneous systems are demonstrated by estimating different types of composition-dependent diffusion coefficients. These are important for understanding the basic atomic mechanism of diffusion and complex compositional evolutions. These were otherwise considered impossible during the last many decades. Without any options previously, sometimes the average values over a composition range of random choice were estimated, which are not the material constants but depend on the composition range and also the end member compositions. The steps and analyses for utilising the pseudo-binary and pseudo-ternary methods are first described in the Ni-Co-Fe-Mo system by producing the ideal diffusion profiles fulfilling the concepts behind these methods. Following, the discussion is extended to the systems related to medium (Ni-Co-Cr) and high (Ni-Co-Fe-Mn-Al) entropy alloys. In fact, this is the first report showing a correct experimental method that should be followed for the estimation of the interdiffusion and intrinsic diffusion coefficients in inhomogeneous high entropy alloys. In the end, the limitations of following these methods because of the generation of non-ideal diffusion profiles are discussed based on experimental results. The steps are also suggested to avoid such complications. These methods are easy to adopt for research engineers. Most importantly, these give an opportunity to validate the data estimated following newly proposed numerical methods by different groups with experimentally estimated diffusion coefficients, which were not possible earlier.     

Random alloy diffusion kinetics for the application to multicomponent alloy systems

In this paper, extensive Monte Carlo simulation results are reported on tracer and collective diffusion correlation effects in the random ternary alloy, as an example of a multicomponent alloy system. The problem of analytically describing both collective and tracer diffusion kinetics is also addressed for the random multicomponent alloy by application of a combination of the Manning theory and Holdsworth and Elliott theory. It is found that the overall results from the combined theory agree reasonably well with Monte Carlo results. This combined approach is much more accurate than Manning’s approach itself and much more manageable than the almost exact, but unfortunately difficult to use, self-consistent theory of Moleko, Allnatt and Allnatt. Some relations between the Onsager phenomenological coefficients and tracer diffusion coefficients are derived and are tested with our Monte Carlo data. Good agreement is found.     

Interdiffusion in strongly ionic insulating compounds: The Nernst–Planck equation

In strongly ionic insulating materials, the Nernst–Planck Equation relates the interdiffusion coefficient of the cations (having the same charge) with the corresponding tracer diffusivities and the thermodynamic factor. In this paper, we explore the Nernst–Planck Equation for ionic ternary (quasi-binary) and ionic quaternary (quasi-ternary) systems using the diffusion kinetics formalisms of Darken [Trans. Am. Inst. Min. (Metall.) Eng. 175 184 (1948)], Manning [Phys. Rev. B 4 1111 (1971)] and Moleko, Allnatt and Allnatt [Phil. Mag. A 59 141 (1989)]. It is shown that for the binary system, the Darken and Manning formalisms both give the usual form of the Nernst–Planck Equation. However, the almost exact Moleko, Allnatt and Allnatt formalism (for randomly mixed systems) provides an additional correction factor analogous to the vacancy-wind factor in the well-known Darken–Manning Equation used in binary alloy systems. Nernst–Planck-type equations are also derived for strongly ionic insulating ternary systems and are found to behave similar to the binary case.     

Relating tracer and chemical diffusion coefficients in intermetallic compounds taking the DO3 and A15 structures

In this article we employ computer simulation to explore the validity of the Darken/Manning relation between the chemical diffusion coefficient and the tracer diffusion coefficients of the components in stoichiometric intermetallic compounds A₃B taking the DO₃ and A15 structures at vanishingly small vacancy contents. The analysis centres on the validity of Manning’s random alloy expression for the vacancy wind factor. The models for both the DO₃ and A15 structures use eight atom-vacancy exchange frequencies. For the DO₃ structure it is found that the actual vacancy wind factor is usually somewhat larger than that predicted by Manning but overall the agreement is good. At worst the use of Manning’s expression would underestimate this factor by about 30 or 40%. For the A15 structure a similar result is found except when diffusion along the chains in the structure is rapid. Then Manning’s expression fails badly when a constant geometrical tracer correlation factor is employed. In both the structures if the geometrical correlation factor is varied to reflect the structure actually explored by the atoms (mainly the majority atoms A) the agreement is improved very dramatically.     

Invar合金的电子化学势均衡判据

用二元团簇作为描述Invar合金的基本结构单元,运用"团簇共振"结构模型,建立起以某一已知二元团簇与连接原子按1:x比例连接,描述Invar合金的电子化学势均衡判据.给出了Invar合金成分的经验分子式,即Invar合金成分=[团簇]1(连接原子)x.运用此判据,解析了部分Invar合金成分.发现典型的Invar合金实验成分与经验分子式相符合,说明基于"团簇共振"模型的Invar合金的电子化学势判据很好地解释了Invar合金成分的形成规律.     

Correlated tracer diffusion in an ordered interface structure

In this paper, we postulate a simple two-dimensional structure that attempts to capture the character of many of the qualitative findings from computer simulations of diffusion paths in grain boundaries. We postulate two types of mechanism: those where single atom jumps occur and those where multiple atom jumps occur. We derive analytical expressions for the tracer correlation factors, including those correlation factors that appear in the analysis of the diffusion isotope effect. We also carry out Monte Carlo simulations of these correlation factors. We find very good agreement between the derived expressions for the correlation factors and the simulation results. We are able to show that, in the absence of knowledge about the kinetic energy factor ΔK, isotope effect experiments cannot differentiate between a simple atom-jump mechanism and multiple-atom-jump mechanism.     

Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu,FeMn, FeNi,and FeCr

The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ? 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.     

A high accuracy diffusion kinetics formalism for random multicomponent alloys: application to high entropy alloys

In this paper, a new, lighter, version of the highly accurate Moleko, Allnatt and Allnatt formalism for describing both tracer (self) and collective diffusion kinetics in multicomponent random alloys is presented. Verification of the resulting expressions is performed by means of kinetic Monte Carlo simulation. The accuracy of the new formalism is much higher than that of the combined Manning and Holdsworth and Elliott formalism discussed recently. Using this formalism the possible range of the tracer diffusion ratio of the highest to the lowest atomic component is examined for equiatomic (or near equiatomic) binary, ternary, quaternary and quinary alloys. It is shown that in the random alloy model, the correlation effect is the highest with a reduction of the fastest tracer diffusion by 40–55%, when moving from two pure metals to their equiatomic binary alloy. By adding the third component (with an intermediate mobility) this effect can be further increased with a possible total reduction of the fastest tracer diffusion by up to 70% (depending on the combinations of mobilities), while adding the fourth component brings this reduction up to 80% and with a possible maximum of up to 85% reduction for the 5-component alloy (again depending on the combinations of mobilities). But the slowest diffusing components are not affected by this. This suggests that kinetics arguments alone are not enough for explaining the sluggish diffusion observed of all atomic components in (equiatomic) high-entropy alloys.     

Mass and thermal transport in liquid Cu-Ag alloys

In this paper, the diffusion, thermodynamic and thermotransport properties in Cu–Ag liquid alloys are extensively investigated with molecular dynamics over a wide composition and temperature range. The simulations are performed with the most reliable EAM potential. The Green-Kubo formalism is employed for calculating transport properties. It is found that the reduced heat of transport in Cu–Ag is very small (about 0.10?eV in absolute value) and almost temperature independent. Further it is found that the interdiffusion coefficient together with both self-diffusion coefficients are almost composition independent. In Cu–Ag, the thermodynamic factor is found to be less than unity whereas the Manning factor is greater than unity (with significant composition and temperature dependence) and their product is very close to 1.     

X-ray photoelectron spectroscopy and magnetism of Mn1−x Al x alloys

X-ray photoelectron spectroscopy (XPS), magnetization and magnetic susceptibility of Mn_1−x Al _x (x = 0.0, 0.2, 0.4, 0.5, 0.6, 0.7) alloys are reported. X-ray diffraction measurements showed that all investigated samples have the same crystallographic structure as the parent compound (AuCu₃-structure type). The alloys are disordered for x ≤ 0.5, but become almost crystallographically ordered for higher Al concentration. This change in the crystallographic order is reflected both in the magnetization and Curie temperature values. The exchange interaction is ferromagnetic between the pairs of the near-neighbour Mn-Ni and Ni-Ni magnetic moments and antiferromagnetic for Mn-Mn pairs. The last one is present only in the disordered alloys, which leads to smaller values of the magnetization of these alloys in comparison with the ordered ones. The Mn magnetic moment has the fully ordered value of 3.2 μB in all investigated alloys. The decrease of the Ni magnetic moment as the Al concentration increases may be explained by the hybridization of the Ni 3d and Al 3sp states, which leads to a partial filling of the Ni 3d band. The magnetic susceptibility measurements pointed out the existence of spin fluctuations on Ni sites.      

Fractal study of Ni–Cr–Mo alloy for dental applications: effect of beryllium

Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving “diffusion towards electrode surface”. The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.     

Autodiffusion dans les alliages concentres fer-palladium

Measurements of the diffusion coefficients of ³⁹Fe and ¹⁰³Pd in various iron-palladium alloys (between 0 and 100at.% iron) between 1100 and 1250°C, have shown that the activation energies for selfdiffusion for the two tracers are practically equal, independent of composition.The values obtained are very close to those corresponding to the activation energy of chemical diffusion. This result is in good agreement with the fact that the thermodynamic activities of iron and palladium have small temperature dependance and that the vacancy flow, as calculated with the model of Manning, is rather small.In spite of a strong ordering tendency in the solid solution of Fe-Pd, as indicated by a thermodynamic calculation, this model allows to calculate, with the aid of the measured self-diffusion coefficients, various parameters, such as the correlation factors for both iron and palladium, the vacancy correlation factors, and the atomic jump frequencies.     

Growth of tertiary dendritic arms during the transient directional solidification of hypoeutectic Pb–Sb alloys

Despite the importance of a complete characterization of dendritic patterns in castings, the availability of studies on the development of tertiary dendrite arms is scarce in the literature. In the present study, the tip cooling rate, local solidification time, primary and tertiary dendrite arm spacings have been determined in Pb–Sb alloys castings directionally solidified under unsteady-state heat flow conditions. The alloys compositions experimentally examined are widely used in the as-cast condition for the manufacture of positive and negative grids of lead-acid batteries. The initial growth of tertiary dendritic arms from the secondary branches was found to occur only for a Pb–3.5 wt% Sb alloy at cooling rates in the range 0.4–0.2?K/s, with no evidence of this spacing pattern for Pb–Sb alloys having lower solute content. Tertiary dendritic branches have been observed along the entire casting lengths for alloys of the Pb–Sb hypoeutectic range having compositions higher than 4.0 wt% Sb. It is shown that a power function experimental law with a characteristic ?0.55 exponent is able to characterize the tertiary spacing evolution with the solidification cooling rate for alloys compositions ≥4.0 wt% Sb. The only exception was the Pb–3.5 wt% Sb alloy for which λ ₃ exhibited significant lower values when compared with the experimental values obtained for the other Pb–Sb alloys for a same solidification cooling rate.     

Statistical calculations of tracer and intrinsic diffusion coefficients in concentrated alloys and estimates of microscopic parameters of diffusion from experimental data

The earlier-developed statistical theory of diffusion in concentrated alloys based on the master equation approach is generalized to treat tracer diffusion in binary alloys. The theory developed is used to describe concentration dependencies of both tracer and intrinsic diffusion coefficients and to estimate microscopic parameters of diffusion in alloys CuNi, CuZn and AgCd for which necessary experimental data are available. We show that all main features of strong and peculiar concentration dependencies of diffusion coefficients observed in these alloys are naturally explained by the theory. Signs and scales of interatomic interactions important for diffusion in these alloys are found to strongly depend on the ratio of atomic sizes of alloy components, and types of these dependencies agree with simple physical considerations. We also discuss physical reasons for sharp concentration dependencies of diffusion coefficients characteristic of real alloys.     

Composition dependence of the electrical transport properties of amorphous transition metal alloys

Summary A quadratic composition dependence of the electrical resistivity of amorphous transition metal alloys has been investigated at room temperature. A very good agreement between the theoretical and the observed values has been obtained in the case of Ni_xZr_1−x and Cu_xZr_1−x for all compositions. The thermoelectric power was then correlated with the electrical resistivity satisfactorily for the Cu_xZr_1−x and Ni_xZr_1−x To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Determination of the surface composition of palladium-nickel alloy film catalysts using Auger electron spectroscopy

Palladium-nickel films evaporated in UHV on room temperature substrates form alloys of good bulk homogeneity as indicated by X-ray diffraction. The average composition of the outermost 3 to 5 atom layers has been determined from the intensities of the high energy 848 eV nickel and 330 eV palladium Auger electrons. This average composition is in close agreement with the bulk composition determined by X-ray diffraction, X-ray fluorescence and atomic absorption spectrophotometry. If the nickel concentration is determined from the intensity of the low energy 61 eV nickel Auger electrons, when the analysis refers more critically to the first 1 to 3 atom layers, then a surface enrichment of palladium is indicated for all alloy compositions. From the decrease in the relative intensities of the low energy and high energy nickel Auger electrons with increasing palladium concentration it may be deduced that the enrichment of palladium in the first atom layer is higher than in the second and third layers and that a complete monolayer of palladium is formed for bulk concentrations of 65 at% or more. The experimental observations are in qualitative agreement with theoretical predictions of surface composition from bulk thermodynamic data. The palladium-nickel alloys form a range of surface compositions which can be controlled by changing the bulk composition and which are useful for studying catalytic activity as a function of composition. The alloy films are stable under electron irradiation in the AES analysis in UHV but air exposed films analysed in a residual pressure of 1.3 microPa water vapour show a decrease in palladium surface concentration on irradiation indicating a diffusion of nickel to the surface to form an overlayer of nickel oxide.     

Ni-X-In(X=Mn,Fe和Co)合金的缺陷稳定性和磁性能的第一性原理研究

Ni-Mn-In是一种新型的磁控形状记忆合金, 它通过磁场诱导逆马氏体相变实现形状记忆效应. 实验中常围绕化学计量比Ni₂MnIn合金进行成分调整, 以获得适宜的马氏体相变温度与居里温度, 在这个过程中必然会产生多种点缺陷. 本文使用量子力学计算软件包VASP, 在密度泛函理论的框架下通过第一原理计算, 系统地研究了非化学计量比Ni-X-In(X=Mn, Fe 和Co)合金的缺陷形成能和磁性能. 反位缺陷中, In和Ni在X亚晶格的反位缺陷(In_X和Ni_X)的形成能最低, Ni和X反位于Y的亚晶格(Ni_Y和X_Y)得到较高的形成能. 因此, In原子可以稳定立方母相的结构, 而X原子对母相结构稳定性的影响则相反; 空位缺陷中最高的形成能出现在In空位缺陷, 再次肯定了In原子对稳定母相结构的作用. 此外, 详细研究了点缺陷周围原子的磁性能以及电荷分布. 本文的计算结果在指导实验中的成分设计和开发新型磁控形状记忆合金方面具有重要意义.