root/trunk/matml/transport/problems/fen/fen.tex

\documentclass{article}
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\begin{document}
\begin{enumerate}
\item Nitriding of an iron thin film
  
  An iron film is vapor-deposited on a silicon wafer with a thickness of 10
  $\mu$m (=10$^{-3}$ cm).  The film is then exposed (at time $t=0$, naturally)
  to a nitriding atmosphere which fixes the nitrogen concentration in the iron
  on the exposed surface at $C=C_s$.  You would like to know the nitrogen
  concentration in the iron film as a function of position and time.

  \begin{center}
    \input{fesin}
  \end{center}

  You may assume:
  \begin{itemize}
  \item $C_s$ is much higher than the nitrogen solubility in the silicon, that
    is, there is no nitrogen in the silicon, and the flux of nitrogen from the
    iron into the silicon is zero.

  \item $C_s$ is sufficiently low that there are no phase transformations here,
    and no significant volume change, just nitrogen diffusing into iron.
  \end{itemize}

  Datum: $D_{\rm N-Fe} = 10^{-8}\frac{\rm cm^2}{\rm s}$

  \begin{enumerate}
  \item Sketch the concentration profile of nitrogen at the start of the
    process (with no nitrogen), and for several times leading to
    steady-state.

  \item \label{whichsol} Write the simple (one-term) solution of the diffusion
    equation which is valid for a short time after the nitriding atmosphere is
    introduced.

  \item What is the thickness of the sublayer in which nitrogen concentration
    is at least half of the surface concentration at 1 second, and at four
    seconds?

  \item At what time $t$ does your solution in part \ref{whichsol} cease to be
    valid?

  \item Write the simple (one-term) solution of the diffusion equation which is
    valid a long time after the nitriding atmosphere is introduced.

  \item At what time $t$ does the nitrogen concentration on the iron side of
    the iron-silicon interface reach 0.9$C_s$?
  \end{enumerate}
\end{enumerate}
\end{document}