Production of hollow hemisphere shells by pure Kirkendall porosity formation in Au/Ag system

Abstract

Interdiffusion has been studied in Ag/Au hemispherical core-shell structures on sapphire substrate. In isothermal heat treatments first a relatively fast growth of nanovoids was observed, which was followed by a slower shrinkage process. The void formation is interpreted by pure Kirkendall-porosity formation since Ag-50%Au solid solution has been formed in the shell. In contrary, in all previous publications on hollow nanoshell formation a chemical reaction took place and the shell consisted of the reaction product ͑i.e., of sulphide or oxide͒. Furthermore, in these cases the shrinkage was observed at temperatures higher than the formation temperature. © 2010 American Institute of Physics. ͓doi:10.1063/1.3490675͔It is well-known that voids can be formed during interdiffusion in binary systems ͑Kirkendall porosity formation 1 or Frenkel effect 2,3 ͒. The origin of this effect is the resultant vacancy flow ͑caused by the inequality of the intrinsic atomic fluxes in the lattice frame of reference͒ oriented toward the faster component. In fact this resultant volume flow is responsible for the development of stress free strain in the diffusion zone: one side tends to shrink and the other one to expand. Additional stress free strains can also develop due to the difference of the atomic volumes and/or to the formation of intermetallic compounds in which the specific volumes of the constituents can be considerably different than in the parent phases. 4 The partial or full relaxation of these diffusional stresses can lead to the well-known Kirkendall shift: in case of vacancy mechanism, if the efficiency of the vacancy sources and sinks ͑at dislocations͒ is high enough, atomic planes will be removed/inserted at the corresponding fast/slow component of the diffusion couple. If this process is fast and complete then the stresses will be relaxed and the pure Darkenregime is realized. Thus the overall intermixing in the laboratory frame of reference is controlled by the larger diffusion coefficient. In real systems, however, more complex time evolution is expected. It can happen that the restricted efficiency of vacancy sinks leads to vacancy super saturation and porosity formation on the side of the faster component. These pores then can also sink vacancies and thus this will be a competing process with the vacancy annihilation at dislocations, i.e., with the Kirkendall shift. 2 Furthermore, the additional diffusional stresses can enhance or suppress the porosity formation. This complex interplay of the above effects is a delicate theoretical problem and it is expected that simple analytical solutions can work only at very special simple cases. In addition, if the sample geometry is closed ͑cylindrical, spherical samples͒, since the stress free strain fields are long range fields, the stress development and relaxation will certainly depend on the shape and size of the sample and for example a radius dependence of the processes are also expected. 4,5 In extreme circumstances even a switching between the Darken and Nernst-Pla...

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

“…An example of the results obtained using this approach is the growth of a void in a rod [72,73,74,75]. The above equations were solved using a central difference scheme in space and an implicit time scheme (see Appendix G).…”

The Kirkendall effect and nanoscience: hollow nanospheres and nanotubes

“…In this same study, the authors show that a similar effect occurs during oxidation or selenization of Co nanocrystals. Since this first report, the nanoscale Kirkendall effect has become very popular and been adopted by many research groups for the synthesis of hollow nanoparticles covering a wide range of materials including sulfides [8,[26][27][28][29][30], oxides [9][10][11], selenides [30,42,53], telurides [14,30], fluorides [53,54], phosphides [17,55] and metals [56][57][58][59]. Through these studies, two conversion mechanisms were identified: symmetrical and asymmetrical.…”

Evolution of Pores in Nanoshells — a Competition of Direct and Inverse Kirkendall Effects, Frenkel and Gibbs–Thomson Effects: the Phenomenological Description and Computer Simulation

“…Отметим, что целью моделирования являлось исследование лишь общих качественных закономерностей для понимания природы процесса и проверки теоретических моделей. Тем не менее, некоторые из наших модельных результатов стали причиной и стимулом для постановки эксперимента группой Беке [51,52] (см. п.…”

“…Идея «единого жизненного цикла» нанооболочки с переходом через точку кроссовера, возникшая в процессе теоретических исследований, была экспериментально реализована для бинарной металлической системы Ag/Au и Ag/Pd [51,52].…”

“…На самом деле, в большинстве ре-альных экспериментов с образованием халькогенидов твёрдым является только ядро (внутренний реагент) и образующаяся фаза, а внешний реагент находится либо в газовой фазе [4,6,[8][9][10][11][12][13], либо входит в какое-то химическое соединение [3,5,7]. И только в недавних исследованиях [51,52] получена бинарная интерметаллидная оболочка в результате реакции двух чистых металлов. Кроме того, в работе [12] продемонстрировано влияние внешних условий (в частности вакуума) на особенности процесса стягивания бинарной оболочки.…”