Classical Theory

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Crystallization requires the presence of nucleus (nucleation) on which the crystal will subsequently grow (crystal growth) to detectable size. If no Nuclei are present  crystal growth cannot occur and the material will form glass. Even if some nuclei are present, but   no growth has occurs, the solid is , for all practical purposes, still a glass.</div> <div> <IMG SRC="0c1af7e0.gif" border=0 width="431" height="382" ALT="Corel Presentations 8 Drawing" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> The figure shows the nucleation and crystal growth rates of glass. As long as the melt is held at a temperature above melting temperature there will be no nucleation. As the melt cools down the changes in the <A HREF="id56.htm" TARGET="_top" TITLE="_"><U>free energy</U></A>  is such that  a nucleus can become stable. At higher temperature the free energy is very low and the required radius of the nuclei is so big, making it impossible to  form nuclei. But as temperature decreases the free energy goes up, making it possible to form nuclei. So as you see in the curve nucleation rate goes up. Oh!, but the is a <A HREF="id56.htm" TARGET="_top" TITLE="_"><U>kinetic energy barrier</U></A> which make it harder, because as the melt cools down it becomes more solid so the atoms cannot jump around to form nuclei. So the nucleation rate goes down.  We can explain the curve for the crystal growth rate in a similar way. (<FONT SIZE="3" COLOR="#0000FF" FACE="Comic Sans MS" ><A HREF="id42.htm" TARGET="_top" TITLE="References"><U>Ref.3</U></A></FONT>)</div> <div> Now let's look in to the <A HREF="id56.htm" TARGET="_top" TITLE="_"><U>classical theory</U></A>.</div> </td> </tr></table></body>