Direct observation of sintering mechanics of a single grain boundary F. Wakai a,⇑ , H. Fukutome a , N. Kobayashi a , T. Misaki a , Y. Shinoda a , T. Akatsu a , M. Sone b , Y. Higo b a Secure Materials Center, Materials and Structures Laboratory, Tokyo Institute of Technology, R3-23 4259 Nagatsuta, Midori, Yokohama 226-8503, Japan b Precision and Intelligence Laboratory, Tokyo Institute of Technology, R2-35 4259 Nagatsuta, Midori, Yokohama 226-8503, Japan Received 9 August 2011; received in revised form 16 September 2011; accepted 3 October 2011 Available online 22 November 2011 Abstract A method to analyze the mechanics of sintering of a single grain boundary was developed by using specimens fabricated by focused ion beam micro-machining. The translational motion and rotation of particles in sintering are influenced by the grain boundary diffusion coefficient and grain boundary energy; both are dependent on crystallographic orientation. Three-dimensional computer simulation was used to analyze the shrinkage and rotation as a response to sintering force and torque, respectively. The model experiments on gold were compared with the simulation results to determine the depth of the cusps on the plot of grain boundary energy vs. misorientation angle, the grain boundary diffusion coefficients, and the surface diffusion coefficient. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Sintering; Simulation; Micromechanical modeling 1. Introduction The macroscopic shrinkage in sintering depends on the microscopic structure on the particle scale. Shrinkage is the result of the motion of many particles, which interact with their neighbors. The translational motion and rota- tion of crystalline particles are influenced by grain bound- ary diffusion coefficient and grain boundary energy, both of which are dependent on crystallographic orientation [1,2]. The anisotropic grain boundary diffusion coefficient will be one of the origins of anisotropic shrinkage when particles are arranged in a preferred orientation in powder processing. Particle rotation often occurs during sintering, and influences texture formation and microstructural evo- lution [3]. In the mechanics of sintering, the translational motion, or shrinkage, is driven by the sintering force, and the rota- tion is driven by torques arising from anisotropic grain boundary energy [4,5] and asymmetric neck shape [6–8]. The sintering force is originally defined for equilibrium states [9–11], and is measured by mechanical force [12,13] that must be applied to stop the shrinkage. Beere [14] iden- tified the sintering force that arose from the difference between the stress on the neck surface and the average compressive stress on the grain boundary. This definition of sintering force is applicable not only to equilibrium states [15,16], but also to non-equilibrium processes [17]. Shewmon [4] proposed the torque that drives particle rota- tion by the lowering of the free energy of the tilt boundary for the first time. Exner and Bross [7] analyzed the torque induced by asymmetric neck shape. The particle motion was directly observed experimen- tally in sintering of row of particles to measure diffusion coefficients [18–20]. The particle rotation in sintering of spheres on a plate was analyzed in order to study the grain boundary energy as a function of misfit angle [5,21–23]. The particle rearrangement occurs due to asymmetric neck geometry [6]. The importance of the crystallographic orien- tation on the sintering of nano-particles is also demon- strated by in situ observation under transmission electron microscopy [24,25] and molecular dynamics simulations 1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.10.003 ⇑ Corresponding author. Tel.: +81 45 924 5361; fax: +81 45 924 5390. E-mail address: wakai.f.aa@m.titech.ac.jp (F. Wakai). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 60 (2012) 507–516