Lecture 4: Diffusion: Fick’s cond law
Today’s topics
• Learn how to deduce the Fick’s cond law, and understand the basic meaning, in
comparison to the first law.
• Learn how to apply the cond law in veral practical cas, including
热爱生命作文homogenization, interdiffusion in carburization of steel, where diffusion plays dominant
role.
Continued from last lecture, we will learn how to deduce the Fick童年的吉他谱’s cond law, and
understand the meanings when applied to some practical cas.
小学生唐诗三百首Let’s consider a ca like this
We can define the local concentration and diffusion flux (through a unit area) at position “x”
as:
So, Fick’s first law can be considered as a specific (simplified) format of the cond law when
applied to a steady state.
Now, let’s consider two real practical cas, and e how to solve the Fick’s cond law in
秋天的况味
the specific cas.去外婆家
Ca 1. Homogenization: (non-uniform →uniform)
Consider a composition profile as superimpod sinusoidal variation as shown below, where
舞蹈创编the solid line reprents the initial concentration profile (at t=0), and the dashed line
reprents the profile after time τ.
以学教育
It is an exponential decay, the longer the wavelength (l), the longer the relaxation time (τ),
then the slower decay. Short wavelength dies fast. That’s why shaking always helps speed up
the dispersion, becau it enables wide spreading (smaller l) of the stuff (like particles) you
try to disper
Ca 2. Interdiffusion (the carburization of steel):doping of steel with carbon
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Situation a): Doping with fixed amount of dopant
Consider a thin layer of B deposited onto A, through annealing at high temperature, we will
be able to get the concentration profile at different times, from there then we can determine
