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S. Ulam, “Random Processes and Transformations,” Proceedings of International Congress of Mathematicians, Cambridge, 30 August-6 September 1950, pp. 264-275.

has been cited by the following article:

• TITLE: Cellular Automata Simulation of Gap-Filler Dissolution during Transient Liquid Phase Bonding of Single Crystal Materials

  AUTHORS: Adam Ghoneim, Olanrewaju Akanbi Ojo

  KEYWORDS: Cellular Automata; Transient Liquid Phase Bonding; Single Crystal; Powder Dissolution

  JOURNAL NAME: Modeling and Numerical Simulation of Material Science, Vol.2 No.2, April 16, 2012

  ABSTRACT: A new numerical model is developed using a Cellular Automata (CA) method to study the liquid-phase dissolution behavior of gap-filler powder particles in interlayer powder mixture during transient liquid phase (TLP) bonding process. The model prediction of microstructural evolution in TLP joint between single crystal substrates show that formation of misoriented stray-grains results from incomplete liquation of the gap-filler powder particles. In contrast to what is generally assumed and reported, numerical calculations coupled with experimental verification show that under properly selected process parameters, complete melting of the gap-filler powder particles is possible. This is imperative to prevent the formation of misoriented stray-grains and maintain single crystallinity during TLP bonding of single crystal materials. The dependence of complete melting of the gap-filler particles on salient TLP bonding parameters are analyzed and discussed.