Abstract:The ability to predict the morphology of crystals formed by chemical reactions is of fundamental importance for the shape-controlled synthesis of nanostructures.Based on the atomistic mechanism for crystal growth under different driving forces, we have developed morphology diagrams to predict regimes for the growth of two-dimensional crystals. By using controlled reactions for crystal growth in the absence of surfactants/capping agents, we demonstrate the validity of this approach for the formation of 2-D structures of Au, Ag, Pt, Pd andhydroxyapatite.An understanding of the external morphology of crystals and its relation to internal structure has been a topic of active study since the times of Kepler. It is well-recognised that the morphology of nanostructures affects their properties profoundly [1][2][3][4][5][6][7][8] . Twodimensional nanostructures in the form of platelets/sheets, nanoprisms and belts exhibit intriguing properties that have several potential applications [1][2][3][4]6,7,[9][10][11] . In spite of the availability of a number of methods [2][3][4][5][6][7][8][12][13][14][15] , the mechanism of formation of such structures remains elusive. Mechanisms based on preferential adsorption of surfactants 8,16 , oriented attachment 16 , soft templates 17,18 , aggregation of spherical particles 4 and kinetic control [6][7][8]18,19 have been proposed in the literature but do not satisfactorily explain the shape control. Here, we show for the first time that this problem can be analysed based on classical crystal growth concepts. Based on the atomistic mechanism for crystal growth under different driving forces 20,21 , we have developed morphology diagrams to predict conditions under which two-dimensional crystals form. By using controlled reactions for crystal growth in the absence of reducing and capping agents or by precipitation under controlled conditions coupled with detailed microstructural evidence, we demonstrate the validity of this approach for the formation of 2-D nanostructures of Au, Ag, Pt, Pd and hydroxyapatite. The analysis and experiments have important consequences for rational synthesis of two-dimensional nanostructures and answer some long-standing questions related to their growth. The generality of the analysis implies that it can be used to predict regimes of two-dimensional growth in a variety of systems ranging from crystals synthesized from a solution phase, from the vapor phase and inorganic phases formed by biomineralization.The formation of crystals from vapor or in a liquid phase proceeds by nucleation and growth mechanism with the driving force given by the associated volume free energy change. Based on the driving force, two distinct growth regimes can be identified. At large driving forces, the interface can move normal to itself leading to a continuous growth (Fig. 1A). At low driving forces, however, growth has to rely on the formation of steps and a lateral motion of steps on the surface [20][21][22] . It has been proposed that screw dislocations enable crysta...