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\subsection{Background}  The polyol synthesis is the most popular solution-phase synthesis of Ag nanocrystals \cite{Skrabalak_2007}.  In the polyol synthesis, ethylene glycol acts as both the solvent and the reducing agent.  The source of Ag is from AgNO_3 that is dissolved in ethylene glycol.  Structure-directing agents, typically polyvinylpyrrolidone (PVP), are added to prevent aggregation of nanocrystals and direct their shape.  The ratio of PVP to AgNO_3 is critical to the formation of different nanocrystal shapes.  The typical reaction temperature is $150^{\circ}$ C, although it can vary for different nanocrystal shapes with different protocols.  Slight modifications of the polyol synthesis protocol, such as introducing foreign species, enable different nanocrystal shapes to be produced.  In the synthesis of Ag nanocubes, trace amount of Na_2S can be added to increase the selectivity towards nanocubes \cite{Skrabalak_2007}.  The addition of Na_2S allows the formation of Ag_2S nanocrystals, which catalyzes the reduction of AgNO_3.  It is proposed that the faster reduction process can limit formation of twinned Ag seeds \cite{Wiley_2006}, thus favoring nanocube formations.  Comparatively, Ag nanowires can be synthesized by adding NaCl or KCl as a source of Cl$^-$ ions \cite{Tsuji_2008}.  Their experiments have shown that Cl$^-$ ions can accelerate dissolution of spherical nanoparticles, which promotes the growth of one-dimensional nanocrystals.  As a final example, Ag nanoplates can be formed by substituting PVP with polyacrylamide into the polyol synthesis \cite{Xiong_2007}.  It has been reported that the amino groups of polyacrylamide can form complexes with metal cations \cite{Sari_2006}, greatly reducing the potential of the Ag/Ag$^+$ pair, thus reduction rate of AgNO_3 is significantly reduced.  The reduced reduction rate favors the formation of nanoplates through kinetic control.  The growth of nanocrystals can be roughly divided into three stages \cite{Xia_2008}:  1) nucleation, where individual metal atoms cluster together to form nuclei;  2) evolution of nuclei into seeds;  3) growth of seeds into nanocrystals.  The difference between nuclei and seeds is the structure of nuclei can fluctuate but the seeds cannot.  In a thermodynamic-control growth, the seed shape is known to define the nanocrystal shape.  Although the process can be roughly defined, our current understanding of the evolution pathway is far from being able to visualize the atomistic details of how seeds nucleate and evolve into nanocrystals of specific shape.  \subsection{Goal and Objectives}  We aim to develop a fundamental understanding of how Ag nanocrystals are grown to specific shapes, such as nanocubes \cite{Im_2005}, nanoplates \cite{Lofton_2005} and nanowires \cite{Tsuji_2008}. 
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