deletions | additions       diff --git a/Many_of_the_common_NW__.tex b/Many_of_the_common_NW__.tex  index 7c3a1b8..168913f 100644  --- a/Many_of_the_common_NW__.tex  +++ b/Many_of_the_common_NW__.tex 
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Many of the common NW synthesis techniques can be used for the III-V NW synthesis of GaAs, such as Vapor-Liquid-Solid (VLS),  molecular beam epitaxy (MBE), Metal Organic Phase epitaxy (MOVPE) and many techniques that improve on these earlier techniques such as laser ablation, and hydride vapor phase epitaxy (HVPE). Vapor-Liquid-Solid growth (VLS) is common for nanowire synthesis and has been used for GaAs nanowire growth.\cite{Hu_1999} A catalytic liquid phase droplet is formed (in the case of GaAs NW, the catalyst could be Cu, Ag or Au) on the solid surface of the substrate, the droplet quickly absorbs the vapor becoming supersaturated to the point that crystal growth begins.\cite{9781420067828} Historically it is known that the radius limit of nanowires grown this way depends on the formation and stability of the liquid catalyst cluster beads, for which the minimum radius ($r_{min}$) of the wire is given by equation \ref{eq:vls_limit} and is limited by equilibrium conditions ($T$ is growth temperature, $V_l$ is the liquid molar volume, $\sigma$ is the degree of vapor pressure saturation and $\sigma_{LV}$ is the liquid-vapor interfacial energy) .\cite{9781420067828}  \begin{equation}