Crystal instability in nanocrystalline materials Guang-Ping Zheng a,b , Mo Li a, * a School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245, USA b Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China Received 26 March 2007; received in revised form 27 March 2007; accepted 11 June 2007 Available online 7 August 2007 Abstract As the grain size in nanocrystalline materials is made ever smaller, the questions of what the smallest grain size could be and what factors influence it become highly relevant to material synthesis and application. Using extensive atomistic simulation and theoretical analysis, this paper shows that the crystalline phase instability sets the ultimate limit for grain size reduction below which amorphization occurs. The instability is caused by the combined effect of structural disorder present at grain boundaries and the internal inhomogeneous strain fields associated with solutes or impurities. A phase diagram describing the instability or crystal-to-glass transition is constructed from a Ginzburg–Landau theory based on the effects of the two types of disorders and their interactions. The mean critical grain size is shown to range from several nanometers to tens or hundreds of nanometers, depending on the impurity or solute concentration. Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanocrystalline materials; Amorphous materials; Amorphization; MD-simulations; Ginzburg–Landau theory 1. Introduction In contrast to other types of nanoscale materials such as nanoparticles or nanoporous matter, nanocrystalline (nc) materials consist of an ensemble of single crystallites of nanometer dimensions separated by grain boundaries or interface boundaries. In past decades, a variety of nc mate- rials have been synthesized successfully by using different methods [1,2]. These nc materials exhibit a wide range of new and exceptional properties from high yield strength to fascinating magnetic properties [3,4], making them one of the most promising nanoscale materials with wide appli- cations. Since the most significant property change takes place at small grain sizes (1–100 nm), it is desirable to make nanocrystals with smaller and smaller grain sizes. Natu- rally, one would like to ask how small the grain size could ever be made, or is there a limit to the grain size reduction? Reducing the grain size is tantamount to introducing more grain or interface boundaries. For instance, the frac- tion of the number of atoms in the grain boundaries could change from a few per cent in polycrystals of micron-sized grains to more than 50% in nanocrystals with the mean grain size of a few nanometers. In general, the majority of the grain boundaries or interfaces in nanocrystals are incoherent random boundaries characterized by structural disorder [1–4]. That is, the atoms have large static mean displacements from their equilibrium positions in the defect-free crystals. By continuously injecting grain bound- aries, one would expect to get smaller and smaller grains. However, there are many processes that could disrupt the nc phase stability at the decreasing grain size. The first is grain growth and coarsening at temperatures well below the bulk melting point. The grain growth could lead to unwanted property changes [3,5,6]. The second is related to structural transitions at small dimensions to new crystal- line phases that can significantly alter the desired physical properties [7,8]. If these interruptions do not happen or the nc systems remain in the same phase, the smallest grain size that can be reached should be on the order of several atomic diameters. At this scale, the nanocrystallites in nc materials more closely resemble clusters with short- or medium-range crystalline order embedded in the disor- dered grain boundary phase. Further reduction of the grain 1359-6454/$30.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.06.013 * Corresponding author. E-mail address: mo.li@mse.gatech.edu (M. Li). www.elsevier.com/locate/actamat Acta Materialia 55 (2007) 5464–5472