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.     

Modeling of high entropy alloys of refractory elements

Reverting the traditional process of developing new alloys based on one or two single elements with minority additions, the study of high entropy alloys (HEA) (equimolar combinations of many elements) has become a relevant and interesting new field of research due to their tendency to form solid solutions with particular properties in the absence of intermetallic phases. Theoretical or modeling studies at the atomic level on specific HEA, describing the formation, structure, and properties of these alloys are limited due to the large number of constituents involved. In this work we focus on HEA with refractory elements showing atomistic modeling results for W–Nb–Mo–Ta and W–Nb–Mo–Ta–V HEA, for which experimental background exists. An atomistic modeling approach is applied for the determination of the role of each element and identification of the interactions and features responsible for the transition to the high entropy regime. Results for equimolar alloys of 4 and 5 refractory elements, for which experimental results exist, are shown. A straightforward algorithm is introduced to interpret the transition to the high entropy regime.     

Al_xCrFeNiTi系高熵合金成分和弹性性质关系

为了探索Al_xCrFeNiTi系高熵合金组成成分和弹性性质的关系,结合固溶体特征参数和第一性原理计算,研究Al元素含量对Al_xCrFeNiTi (x=0, 0.5, 1, 2, 3, 4)合金结构和弹性性质的影响,并分析合金固溶体特征参数与弹性性质之间的关系.结果表明:Al_xCrFeNiTi系合金的价电子浓度随着Al含量的增加逐渐减小,合金在体心立方结构下的形成焓均低于面心立方结构,说明研究的Al_xCrFeNiTi系合金会形成单一的体心立方结构固溶体;合金的晶格常数和形成能力强弱随着Al含量的增加而增大,但合金的结构稳定性略有下降;当合金元素按照等原子比进行成分配比时,合金的原子尺寸差异最大; Al_xCrFeNiTi系合金中不同原子之间除了金属键结合外,还表现出一定的共价和离子键结合特征;对于Al_xCrFeNiTi系合金而言,随着热力学熵焓比的增大,合金体弹模量和韧性随之增大;随着合金混合焓的增加,合金在压缩方向的各向异性程度明显降低.热力学熵焓比和混合焓可作为Al_xCrFeNiTi系高熵合金成分设计的重要参数.     

有序合金中的原子扩散与格点停留时间

到目前为止,有序合金扩散理论尚存在两个重要的问题有待突破.一是如何正确理解原子的热扩散运动与合金中原子有序排列之间的矛盾;二是能否将扩散系数以外的其它理论参量与原子跳跃迁移的相关实验测量联系起来.为了解决这些问题,作者建议使用原子在不同格点的停留时间差异来表达合金的有序度参量.当原子在反结构晶格位置的平均停留时间很短时,原子完全可能以最近邻跳跃的方式在有序合金中迁移而不破坏原子的长程有序排列.以B2-NiGa有序合金为例,根据Ni原子格点停留时间的赝弹性中子散射实验测定,作者计算了1403 K温度时B2-NiCa合金的有序度为78.9%.     

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.     

第一性原理计算Al元素含量对高熵合金AlxCoCrCuFeNi的影响

采用第一性原理密度泛函理论,结合平面波赝贽和广义梯度近似(GGA),用虚拟晶体近似(VCA)方法建模,计算了高熵合金Alx CoCrCuFeNi的结构性能、弹性性能及生成热.计算结果表明,高熵合金Alx CoCrCuFeNi的密度随Al元素摩尔含量的增大而减小,晶格常数在Al元素摩尔含量为1时最小.Al元素摩尔含量为2时,高熵合金Alx CoCrCuFeNi符合力学稳定性判据.生成热随Al元素摩尔含量增大而增大,皆为负值的生成热表明高熵合金在热力学条件下稳定.     

Phase equilibria of multicomponent mineral systems at high pressures and high temperatures

Abstract

The substance of the Earth's upper mantle was essentially differentiated in the course of deep-seated magmatic processes. It is for the most part formed by peridotitic as well as pyroxenitic and eclogitic The most deep-seated ones pertain to the garnet-peridotitic facies. Liquidus phase relations between the minerals of primary garnet lherzolite (compositional estimations are given in Refs. 1–3) account for the regularities of the formation, evolution, crystallization of multicomponent silicate magmatic melts and petrogenesis of garnet-peridotitic mantle rocks.     

Studies of diffusion coefficients in disordered porous matrices confined in a slit-pore

We present a series of molecular dynamics simulations to study the structure of porous matrices confined in a slit-pore. The matrices were prepared by two different methods. In the first method we used direct simulations of a fluid at a fixed density and the matrix was taken from the last configuration of its particles. In the second method we simulated a binary mixture where one of the components served as a template material and the final porous matrix configuration was obtained by removing template particles from the mixture. In both methods the matrices were confined by two parallel walls (slit-pore) modeled by continuous solid surfaces. The results show that the matrix structure and porosity were affected by the method of preparation of the porous matrices. Moreover, we found smaller void cavities in these matrices than in matrices prepared without walls. Finally, diffusion of a fluid inside the matrices was investigated and it was found that the diffusion coefficient did not decrease with the fluid density, and presented a maximum at certain values of the fluid density.     

Calculation of entropy of mixing of liquid metal alloys in a hard sphere system

A semi-empirical model, based on the hard sphere system, is used to determine the entropy of mixing of simple as well as compound-forming alloys. For the compound-forming liquid solutions, the method leads to fairly accurate results, showing thereby that the usual theory of hard spheres mixtures can be applied to compound forming alloys also. It has been shown that the compound formation is very sensitive to the temperature of the mixture. Numerical applications are attempted for NaHg and NaGa.     

Effect of Al doping on the martensitic transition and magnetic entropy change in Ni-Mn-Sn alloys

Effect of Al doping on the martensitic transition and magnetic entropy change in Mn₅₀Ni₄₀Sn_10−xAl_x was investigated. The experimental results show that the martensitic transition temperatures increase with the increase of Al content due to cell contraction, while the martensitic transition temperature range decreases rapidly. Mn₅₀Ni₄₀Sn₈Al₂ alloy has the largest value of  (3.14 J/kg K) for the magnetic field changing from 0 to 10 kOe, which is nearly twice as large as that of Mn₅₀Ni₄₀Sn₁₀ alloy. It is demonstrated that a larger can be obtained due to the sharper magnetization change around martensitic transition.     

The Kirkendall effect in single-phase multicomponent systems: dependence on drift and entropy distribution

This paper concerns interdiffusion in a diffusion couple and determination of the Kirkendall plane. The “entropy density” model is proposed in which the entropy is used to predict the position of the Kirkendall plane in a multicomponent system. It is shown that the marker position depends on the drift velocity and pressure field only. Application of the model is presented for ternary CoFeNi diffusion couples of three various initial compositions. The concentration profiles and entropy densities are calculated for each diffusion couple. The positions of the Kirkenadl planes are determined and compared with those obtained by velocity-curve and trajectory methods.     

Measure of irreversibility and entropy production in open quantum systems

A new concept of a measure of irreversibility for quantum dynamics in open systems is introduced as a suitably regularized substitute for the common notion of entropy production, which, unfortunately, yields infinite values for so many irreversible processes of physical relevance.     

A pseudobinary approach to study interdiffusion and the Kirkendall effect in multicomponent systems

Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.     

The influence of the ideal mixing entropy on concentration profiles and diffusion paths in ternary systems

The diffusion profiles and the reaction paths in ternary solid solutions are determined by both thermodynamics and kinetics. The matrix of the diffusion coefficient can be described as the product of the Hessian matrix for the thermodynamic influences and the Onsager matrix for kinetic influences.In this paper the interest is focused on the influence of the ideal part of the Hessian matrix, i.e. the ideal mixing entropy on interdiffusion. The ideal diffusion profiles are calculated by a computer simulation and they are compared with experimental results from the literature. These comparisons reveal that in most cases the qualitative shape of the diffusion profiles and of the reaction paths can be considered as caused by the ideal mixing entropy. Surprisingly, the shape of the diffusion profiles turns out to depend on the component that was chosen as the so-called solvent of the ternary mixture. This means that the ideal reaction paths do not show the triangular symmetry expected for an ideal ternary system. Especially, reaction paths between starting positions showing the same concentration of one of the three components do not run along straight lines.     

高熵合金短程有序现象的预测及其对结构的电子、磁性、力学性质的影响

如何有效预测高熵合金的稳态结构,是开展研究其物理及化学等性能的基础.以FeCuCrMnMo合金为例,在有限晶胞尺寸内,采用蒙特卡洛结合密度泛函理论杂化计算方法(Monte Carlo/density functional theory,MC/DFT)预测高熵合金的平衡态结构.与准随机近似方法(special quasirandom structures,SQS)不同,该方法不再追求高熵合金结构的理想随机状态,而是充分考虑合金中原子尺寸、混合焓、原子间相互作用等物理因素.通过第一性原理计算体系能量来实现,使得蒙特卡洛(Monte Carlo,MC)方法保证结构在原子交换过程中体系能量逐渐收敛于平衡态.最终预测得到的平衡态结构出现Cu原子的短程有序现象(short range order,SRO)与实验上合金中的Cu偏析现象相一致.相较于由SQS方法获得的随机状态,该SRO结构在能量上更加稳定.同时本文对稳态结构通过序参数及径向分布函数进行表征,并对SRO现象的出现进行物理解释,进一步揭示了SRO的出现对高熵合金结构性质的影响.     

Long-time integration methods for mesoscopic models of pattern-forming systems

Spectral methods for simulation of a mesoscopic diffusion model of surface pattern formation are evaluated for long simulation times. Backwards-differencing time-integration, coupled with an underlying Newton–Krylov nonlinear solver (SUNDIALS-CVODE), is found to substantially accelerate simulations, without the typical requirement of preconditioning. Quasi-equilibrium simulations of patterned phases predicted by the model are shown to agree well with linear stability analysis. Simulation results of the effect of repulsive particle–particle interactions on pattern relaxation time and short/long-range order are discussed.     

A Monte Carlo model for determination of binary diffusion coefficients in gases

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman–Enskog equation in the first and higher orders. We have selected two different cases, H₂ in H₂ and O in O₂, assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman–Enskog results in all the cases considered, the deviations being reduced using higher order approximations.     

Sc在Al-Zn-Mg-Cu超高强铝合金中作用机理的电子理论研究

通过晶胞平移获得Al-Zn-Mg-Cu合金中α-Al,Al₃Sc及η相原子集团模型,采用自编软件建立α-Al/液态Al界面、α-Al/Al₃Sc界面原子团模型.用递归法计算合金中各组织的态密度、结合能、费米能级,合金元素Sc与空位相互作用能等电子参数.依据电子参数解释合金晶粒细化、腐蚀的物理本质.研究表明： Al₃Sc从液态金属析出时释放的能量比α-Al从液态金属析出时所释放的能量少,可先于α-Al从液态金属中析出;且α-Al 关键词： 电子结构 腐蚀 超高强Al合金     

Lattice Boltzmann simulation for the energy and entropy of excitable systems

The internal energy and the spatiotemporal entropy of excitable systems are investigated with the lattice Boltzmann method.The numerical results show that the breakup of spiral wave is attributed to the inadequate supply of energy,i.e.,the internal energy of system is smaller than the energy of self-sustained spiral wave.It is observed that the average internal energy of a regular wave state reduces with its spatiotemporal entropy decreasing.Interestingly,although the energy difference between two regular wave states is very small,the different states can be distinguished obviously due to the large difference between their spatiotemporal entropies.In addition,when the unstable spiral wave converts into the spatiotemporal chaos,the internal energy of system decreases,while the spatiotemporal entropy increases,which behaves as the thermodynamic entropy in an isolated system.