2.2: Diffusion
- Last updated
- Jul 28, 2022
- Save as PDF
\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }
\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}
\newcommand{\id}{\mathrm{id}} \newcommand{\Span}{\mathrm{span}}
( \newcommand{\kernel}{\mathrm{null}\,}\) \newcommand{\range}{\mathrm{range}\,}
\newcommand{\RealPart}{\mathrm{Re}} \newcommand{\ImaginaryPart}{\mathrm{Im}}
\newcommand{\Argument}{\mathrm{Arg}} \newcommand{\norm}[1]{\| #1 \|}
\newcommand{\inner}[2]{\langle #1, #2 \rangle}
\newcommand{\Span}{\mathrm{span}}
\newcommand{\id}{\mathrm{id}}
\newcommand{\Span}{\mathrm{span}}
\newcommand{\kernel}{\mathrm{null}\,}
\newcommand{\range}{\mathrm{range}\,}
\newcommand{\RealPart}{\mathrm{Re}}
\newcommand{\ImaginaryPart}{\mathrm{Im}}
\newcommand{\Argument}{\mathrm{Arg}}
\newcommand{\norm}[1]{\| #1 \|}
\newcommand{\inner}[2]{\langle #1, #2 \rangle}
\newcommand{\Span}{\mathrm{span}} \newcommand{\AA}{\unicode[.8,0]{x212B}}
\newcommand{\vectorA}[1]{\vec{#1}} % arrow
\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow
\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }
\newcommand{\vectorC}[1]{\textbf{#1}}
\newcommand{\vectorD}[1]{\overrightarrow{#1}}
\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}
\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}
\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }
\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}
\newcommand{\avec}{\mathbf a} \newcommand{\bvec}{\mathbf b} \newcommand{\cvec}{\mathbf c} \newcommand{\dvec}{\mathbf d} \newcommand{\dtil}{\widetilde{\mathbf d}} \newcommand{\evec}{\mathbf e} \newcommand{\fvec}{\mathbf f} \newcommand{\nvec}{\mathbf n} \newcommand{\pvec}{\mathbf p} \newcommand{\qvec}{\mathbf q} \newcommand{\svec}{\mathbf s} \newcommand{\tvec}{\mathbf t} \newcommand{\uvec}{\mathbf u} \newcommand{\vvec}{\mathbf v} \newcommand{\wvec}{\mathbf w} \newcommand{\xvec}{\mathbf x} \newcommand{\yvec}{\mathbf y} \newcommand{\zvec}{\mathbf z} \newcommand{\rvec}{\mathbf r} \newcommand{\mvec}{\mathbf m} \newcommand{\zerovec}{\mathbf 0} \newcommand{\onevec}{\mathbf 1} \newcommand{\real}{\mathbb R} \newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]} \newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]} \newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]} \newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]} \newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]} \newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]} \newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]} \newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]} \newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]} \newcommand{\laspan}[1]{\text{Span}\{#1\}} \newcommand{\bcal}{\cal B} \newcommand{\ccal}{\cal C} \newcommand{\scal}{\cal S} \newcommand{\wcal}{\cal W} \newcommand{\ecal}{\cal E} \newcommand{\coords}[2]{\left\{#1\right\}_{#2}} \newcommand{\gray}[1]{\color{gray}{#1}} \newcommand{\lgray}[1]{\color{lightgray}{#1}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\row}{\text{Row}} \newcommand{\col}{\text{Col}} \renewcommand{\row}{\text{Row}} \newcommand{\nul}{\text{Nul}} \newcommand{\var}{\text{Var}} \newcommand{\corr}{\text{corr}} \newcommand{\len}[1]{\left|#1\right|} \newcommand{\bbar}{\overline{\bvec}} \newcommand{\bhat}{\widehat{\bvec}} \newcommand{\bperp}{\bvec^\perp} \newcommand{\xhat}{\widehat{\xvec}} \newcommand{\vhat}{\widehat{\vvec}} \newcommand{\uhat}{\widehat{\uvec}} \newcommand{\what}{\widehat{\wvec}} \newcommand{\Sighat}{\widehat{\Sigma}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9}https://www.doitpoms.ac.uk/tlplib/diffusion/index.php
- 2.2.1: Solids and Liquids
- What distinguishes solids, liquids, and gases– the three major states of matter— from each other? The pages present an overview of the condensed states of matter. Although there is more detail than can be found in standard textbooks, the level is still suitable for first-year college and advanced high school courses. These pages should also be helpful as review material for students in more advanced courses in chemistry, geology, and materials science.
- 2.2.2: Fick's First Law of Diffusion
- The fact that a concentration difference causes diffusion should be familiar to everyone, particularly in the case of liquids and gases. Consider adding a drop of ink to a bowl of water. The ink will diffuse through the water until the concentration is the same everywhere. There is no force causing the ink particles to diffuse through the water. It is in fact a statistical result of the random motion of the particles.
- 2.2.3: Fick's Second Law of Diffusion
- Fick’s second law is concerned with concentration gradient changes with time.
- 2.2.4: Applications of Diffusion
- Carburisation is the process by which carbon is diffused into the surface of steel in order to increase its hardness. The carbon forms carbide precipitates (particularly if the steel contains carbide forming elements such as manganese or molybdenum) which pin dislocations and prevent slip, thus making the material harder. However, the increased carbon content reduces the toughness of the material.
