deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index b97cb65..9aa8620 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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\subsection{Motivations}  The unique properties of metals are enabling numerous state-of-art technologies.  They are essential in applications ranging from catalysis \cite{astruc2008nanoparticles,Astruc_2006} to photovoltaics \cite{Atwater_2010}, photonics, information storage, electronics, energy storage, environmental protection, and cancer therapeutics \cite{Jain_2010,Kim_2010}.  Nanoparticles are clusters of atoms or molecules with the size of 1 to 100 nanometers. Nanocrystals are nanoparticles with a single crystalline lattice.  Numerous properties of nanoparticles nanocrystals  are found to depend on their size \cite{Roduner_2006} and shape \cite{Xia_2008}. The ability to control the size and shape of nanoparticles nanocrystals  allows their properties to be tailored towards applications such as catalysis \cite{astruc2008nanoparticles,Astruc_2006}, solar cell \cite{Atwater_2010}, and cancer therapeutics \cite{Jain_2010,Kim_2010}. For instance, tetrahedral Pt nanoparticles nanocrystals  are more active than spherical and cubic Pt nanoparticles as the catalyst for electron-transfer reactions \cite{Narayanan_2005}. Higher proportion of surface atoms of tetrahedrals nanoparticles are on edges and corners, which accounts for the higher catalytic activity. Drug delivery shape. 
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\subsection{Research objective}  \subsection{Significance}