Role of Kirkendall effect in diffusion processes in solids

In the 1940s, KIRKENDALL showed that diffusion in binary solid solutions cannot be described by only one diffusion coefficient. Rather, one has to consider the diffusivity of both species. His findings changed the treatment of diffusion data and the theory of diffusion itself. A diffusion-based framework was successfully employed to explain the behaviour of the Kirkendall plane. Nonetheless, the complexity of a multiphase diffusion zone and the morphological evolution during interdiffusion requires a physico-chemical approach. The interactions in binary and more complex systems are key issues from both the fundamental and technological points of view. This paper reviews the Kirkendall effect from the circumstances of its discovery to recent developments in its understanding, with broad applicability in materials science and engineering.

Kirkendall效应和空心纳米晶体的人工合成

在1946年被发现的Kirkendall效应,对科学技术引起很大的冲击,至今,仍在许多科学技术和工程领域受到关注。本文悦目瞭然地阐述Kirkendall效应和Darken分析,计算实例,空位风和反Kirkendall效应。最后,更为重要地指明,2004年发表的应用纳米尺度Kirkendall效应人工合成中空纳米球方法提供了人工合成无机化合物的空心纳米晶体和纳米管的通用途径。近年来,这种具有空心结构的纳米晶体愈来愈受到人们的青睐。

Sn基钎料/Cu焊点Kirkendall空洞抑制研究

无铅钎料Sn-3.5Ag/Cu焊点用于微电子封装电子器件的互连,随着电镀铜的使用,电镀铜中引入杂质,以及焊点尺寸减小,封装密度增大,产生的Kirkendall空洞会使焊点在服役过程中严重影响接头的可靠性。文章分析了Kirkendall空洞形成机制,研究了抑制Kirkendall空洞的措施。

一种研究Cu／Al界面原子扩散Kirkendall效应的新方法

利用铆钉法制备了Cu-Al扩散偶。借助光学显微镜和彩色金相技术,通过分析烧结过程中销钉及销孔直径尺寸的变化,研究了Cu／Al界面原子扩散的Kirkandall效应。结果表明,在烧结温度范围内铜向铝中的扩散强度大于铝向铜中的扩散强度。

Kirkendall效应和空心纳米晶体的人工合成

5反Kirkendall效应[9,28]经典的Kirkandall效应反映的是合金中组元元素在成分浓度梯度下引发空位的净流量,以一定的扩散速度越过扩散偶界面。或解释为：在退火的扩散偶条件下,在溶质原子的区域中诱发产生空位点缺陷的浓度改变。

利用Kirkendall效应制备Ce1-xTixO2中空纳米球

利用Kirkendall效应,在溶剂热条件下成功制备了复合氧化物Ce1-xTixO2的纳米空心球,并通过XRD,TEM和XPS等测试手段进行了表征.结果表明,Ce1-xTixO2纳米空心球的粒径为65 nm,小于初始状态的CeO2纳米球,并且Ce1-xTixO2纳米空心球的结构与前驱体CeO2晶体结构相同,均为面心立方结构.Ti/Ce摩尔比和温度是影响产物形貌和结构的重要因素,通过实验得出最佳反应条件为n(Ti)∶n(Ce)=8∶10,于190℃反应8 h.

Morphological evolution and growth kinetics of Kirkendall voids in binary alloy system during deformation process-Phase field crystal simulation study

The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.

Fabrication and Optical Property of Cu_7S_4 Hollow Nanoparticles Formed Through Kirkendall Effect

1 Introduction In recent years, there has been increasing interest in the controlled synthesis of hollow nanoparticles because of their widespread potential applications. The hollow nanoparticles can be used as catalysts, adsorbents, drug-delivery carriers, chemical reactors, and so on^[1-6]. Some nano and micro spheres are em- ployed as hard or soft templates to produce hollow structures＆[7-10].

Influence of Electric Current on Kirkendall Diffusion of Zn/Cu Couples

The influence of electric current on Kirkendall diffusion in Zn/Cu couples was investigated. Under the action of different electric currents, the Zn/Cu diffusion couples were annealed at 785℃ for different holding time. The experimental results show that the displacement of the Kirkendall plane increases with increasing holding time. However, the displacement of the Kirkendall plane with electric current is larger than that without electric current. The relationship between the displacement of the Kirkendall plane and the holding time is changed under the action of electric current. The likely reason for the electric current enhancing effect is the energy transfer from electron to jumping atom, increasing the integrated diffusion coefficient, which leads to the increase in the velocity of Kirkendall plane.

Kirkendall空洞生长抑制机理的晶体相场方法研究

采用晶体相场模型模拟研究了应力及温度对Kirkendall空洞生长的抑制作用。分析应力、温度等因素对Kirkendall空洞生长抑制的微观机理。结果表明:相同演化时间,增加应力和提升温度,Kirkendall空洞的尺寸对比无应力和无升温作用时尺寸减小;随着应力的增加,Kirkendall空洞的平均尺寸和生长指数呈现先增加后减小的变化规律,Kirkendall空洞的生长出现迟缓。研究表明应力和温度对Kirkendall空洞的生长有显著的抑制作用。

Controllable synthesis of one-dimensional silicon nanostructures based on the dual effects of electro-deoxidation and the Kirkendall effect

In this study,we successfully synthesized silicon nanotubes(Si-NTs)and silicon nanowires(Si-NWs)in a controllable manner using a catalyst-and template-free method through the direct electrolysis of SiO_(2)in a molten CaCl_(2)-CaO system,while also proposing a novel formation mechanism for Si-NTs.Si-NWs are formed through electro-deoxidation when the cell voltage is within the range of CaO decomposition voltage and SiO_(2)decomposition voltage.By subsequently adjusting the voltage to a value between the decomposition potentials of CaCl_(2)and CaO,in-situ electro-deoxidation of CaO takes place on the surface of the synthesized Si-NWs,leading to the formation of a Ca layer.The formation of Ca-Si diffusion couple leads to the creation of vacancies within the Si-NWs,as the outward diffusion rate of Si exceeds the inward diffusion rate of Ca.These differential diffusion rates between Si and Ca in a diffusion couple exhibit an analogy to the Kirkendall effect.These vacancies gradually accumulate and merge,forming large voids,which ultimately result in the formation of hollow SiCa-NTs.Through a subsequent dealloying process,the removal of the embedded calcium leads to the formation of Si-NTs.Following the application of a carbon coating,the Si-NTs@C composite showcases a high initial discharge capacity of 3211 mAh·g^(-1)at 1.5 A·g^(-1)and exhibits exceptional long-term cycling stability,maintaining a capacity of 977 mAh·g^(-1)after 2000 cycles at 3.0 A·g^(-1).

The Kirkendall effect on erosion resistance of chrome-coated 25Cr3Mo2WNiV and 30SiMn2MoV gun barrel steels

This study aimed to investigate the erosion behavior and mechanism of a newly developed 25Cr3Mo2WNiV steel with a chrome coating using promoted ignition combustion tests.The erosion threshold pressure and temperature of the chrome-coated 25Cr3Mo2WNiV steel were determined to be 0.2 MPa and 254.3 K higher than those of traditional chrome-coated 30SiMn2MoV steel.Furthermore,Kirkendall voids and inter-diffusion between the Cr coating and matrix were first observed before ero-sion.The improved erosion resistance of the chrome-coated 25Cr3Mo2WNiV steel was attributed to the suppression of the Kirkendall effect,which minimized heat generation at the Cr/matrix interface by pre-venting oxygen diffusion and reducing oxygen affinity.

Microfluidic synthesis of hollow CsPbBr_(3) perovskite nanocrystals through the nanoscale Kirkendall effect

All inorganic metal halide perovskite nanocrystals(NCs)have attracted much attention for their outstanding optoelectronic properties,which can be tuned by the composition,surface,size and morphology in nanoscale.Herein,we report the microfluidic synthesis of hollow CsPbBr_(3)perovskite NCs through the nanoscale Kirkendall effect.The formation mechanism of the hollow structure(Kirkendall void)controlled by the temperature,flow rate,ratios of precursors and ligands was investigated.Compared with the solid CsPbBr_(3)NCs of the same size,the hollow CsPbBr_(3)NCs exhibit blue shifts in ultraviolet-visible(UV-vis)absorption and photoluminescence(PL)spectra,and remarkably longer PL average lifetime(~98.2 ns).Quantum confinement effect,inner surface induced additional trap states and lattice strain of the hollow CsPbBr_(3)NCs were discussed in understanding their unique optoelectronic properties.The hollow CsPbBr_(3)NC based photodetector exhibits an outstanding negative photoconductivity(NPC)detectivity of 8.9×10^(12)Jones.They also show potentials in perovskite NC based photovoltaic and light emitting diodes(LEDs).

晶体相场法研究Kirkendall效应诱发的相界空洞的形成和演变

采用二元晶体相场模型研究了Kirkendall效应诱发的相界空洞的形成及扩展过程.模拟结果表明:对于取向差角较小的相界,空洞向原子迁移率高的一侧(a相)方向移动,空洞的形状由最初的平行四边形向六边形演化,空洞周围原子湮没速率大于产生速率,从而造成空洞扩大,空洞扩展过程中伴有相界的移动及相的长大和缩小.对于取向差角较大的相界,空洞还会沿相界方向扩展,使得空洞连通,将相界割裂开,割裂后的两侧相界呈现锯齿状.扩散过程中,体系的自由能逐渐降低.对于取向差角较小的相界,原子迁移率差值增大,自由能下降无明显差异.对于取向差角较大的相界,原子迁移率相差越大,自由能下降速率越快.随着相界取向差角的增大,自由能的下降速率逐渐增大.相界空洞的模拟结果与实验观察一致.

Sn/Cu互连体系界面和金属间化合物层Kirkendall空洞演化和生长动力学的晶体相场法模拟

采用二元合金晶体相场模型模拟研究了Sn/Cu互连体系Cu/Cu3Sn界面及金属间化合物层中Kirkendall空洞形成和形貌演化及长大过程,对Kirkendall空洞生长的微观机制进行了剖析,同时还模拟和分析了界面Cu3Sn层厚度和杂质含量对Kirkendall空洞形貌和生长动力学的影响.研究表明,Kirkendall空洞的生长过程由4个阶段组成:Cu/Cu3Sn界面形成大量原子错配区,原子错配区迅速成长为空洞,空洞的长大及随后的空洞合并生长.Kirkendall空洞优先在Cu/Cu3Sn界面处形核,其尺寸随时效时间的延长而增大,并在时效后期空洞的生长伴随有空洞的合并.Cu3Sn层厚度增加和杂质含量增多均使得Kirkendall空洞数量和生长指数增加以及尺寸增大,并且2种情况下空洞数量随时间的变化均呈现先增后减的规律.

Porous FeS nanofibers with numerous nanovoids obtained by Kirkendall diffusion effect for use as anode materials for sodium-ion batteries

Porous FeS nanofibers with numerous nanovoids for use as anode materials for sodium-ion batteries were prepared by electrospinning and subsequent sulfidation. The post-treatment of the as-spun Fe（acac）3-polyacrylonitrile composite nanofibers in an air atmosphere yielded hollow Fe2O3 nanofibers due to Ostwald ripening. The ultrafine Fe2O3 nanocrystals formed at the center of the fiber diffused toward the outside of the fiber via Ostwald ripening. On sulfidation, the Fe2O3 hollow nanofibers were transformed into porous FeS nanofibers, which contained numerous nanovoids. The formation of porosity in the FeS nanofibers was driven by nanoscale Kirkendall diffusion. The porous FeS nanofibers were very structurally stable and had superior sodium-ion storage properties compared with the hollow Fe2O3 nanofibers. The discharge capacities of the porous FeS nanofibers for the Ist and 150th cycles at a current density of 500 mA.g-1 were 561 and 592 mA.h-g-1, respectively. The FeS nanofibers had final discharge capacities of 456, 437, 413, 394, 380, and 353 mA-h.g-1 at current densities of 0.2, 0.5, 1.0, 2.0, 3.0, and 5.0 A.g-1, respectively.

Facile synthesis of yolk-shell Ni@void@SnO2（Ni3Sn2） ternary composites via galvanic replacement/Kirkendall effect and their enhanced microwave absorption properties

Yolk-shell ternary composites composed of a Ni sphere core and a SnO2（Ni3Sn2） shell were successfully prepared by a facile two-step method. The size, morphology, microstructure, and phase purity of the resulting composites were characterized by scanning electron microscopy, energy dispersive X-ray spectroscopy, transmission electron microscopy （TEM）, high-resolution TEM, selected-area electron diffraction, and powder X-ray diffraction. The core sizes, interstitial void volumes, and constituents of the yolk-shell structures varied by varying the reaction time. A mechanism based on the time-dependent experiments was proposed for the formation of the yolk-shell structures. The yolk-shell structures were formed by a synergistic combination of an etching reaction, a galvanic replacement reaction, and the Kirkendall effect. The yolk-shell ternary SnO2 （Ni3Sn2）@Ni composites synthesized at a reaction time of 15 h showed excellent microwave absorption properties. The reflection loss was found to be as low as -43 dB at 6.1 GHz. The enhanced microwave absorption properties may be attributed to the good impedance match, multiple reflections, the scattering owing to the voids between the core and the shell, and the effective complementarities between the dielectric loss and the magnetic loss. Thus, the yolk-shell ternary composites are expected to be promising candidates for microwave absorption applications, lithium ion batteries, and photocatalysis.

Engineered porous Ni2P-nanoparticle/Ni2P-nanosheet arrays via the Kirkendall effect and Ostwald ripening towards efficient overall water splitting

Transitional metal phosphides with array-like structure grown on conductive support materials are promising bifunctional catalysts for the oxygen evolution reaction(OER)and hydrogen evolution reaction(HER).In this study,a method was developed to synthesize directly porous Ni2P nanosheet arrays and Ni2P nanoparticles onto nickel foam via a hydrothermal reaction followed by a phosphorization process.Mechanistic studies revealed that the allomorphs of Ni2P nanosheets and Ni2P nanoparticles in the array-like structure were formed via the Kirkendall effect and Ostwald ripening.A fully functional water electrolyzer containing Ni2P as electrodes for the OER and HER exhibited promising activity and stability.At 10 mA·cm^−2,a Ni2P cell voltage of 1.63 V was obtained,which was only 0.05 V smaller than that found for Pt/C/NF||RuO2/NF cell.The enhanced electrocatalytic performance resulted from the favorable porosity of the Ni2P arrays and the synergistic effect between Ni2P nanosheets and Ni2P nanoparticles.

Atomic level understanding of the nanoscale Kirkendall effect

Exactly 70 years after Kirkendall’s revolutionary experiments established the vacancy diffusion mechanism and the resultant Kirkendall effect and Kirkendall pores[1],Sun et al.[2]advanced the understanding of the Kirkendall effect to near atomic level with the real-time tracking three-dimensional(3D)evolution of colloidal nanoparticles under real reaction conditions.Smigelskas and Kirkendall[1]in 1947 reported an experiment on the interdiffusion between copper and zinc in a

Unexpected Kirkendall effect in twinned icosahedral nanocrystals driven by strain gradient

Nanoscale Kirkendall effect has been widely used for rationally fabricating high-quality hollow nanocrystals, but often requires the intrinsic diffusion coefficient of out-diffusion materials higher than that of in-diffusion components. Here we demonstrate an unexpected Kirkendall effect that occurs in diffusing intrinsically faster Cu atoms into Pd icosahedra, leading to the formation of PdCu alloyed hollow nanocrystals. The control experiment with Pd octahedra replacing icosahedra indicates the critical role of twin boundaries in facilitating such unexpected Kirkendall effect. In addition, geometric phase analysis and density functional theory calculation show that out-diffusion of Pd atoms in the icosahedra is faster than in-diffusion of Cu atoms, particularly through the twin boundaries, upon the strain gradient with an inward distribution from tensile to compressive strains. The unexpected Kirkendall effect is also found in the interdiffusion of Ag and Pd atoms in Pd icosahedra. Our finds break the limitation of the intrinsic diffusion coefficient for the synthesis of hollow nanocrystals through Kirkendall effect and are expected to enormously enrich the family of hollow nanocrystals which have shown great potential in broad areas, such as fine chemical production, energy storage and conversion, and environmental protection. This work also provides a deep understanding in the diffusion behavior of atoms upon the strain gradient.