Add notes on diffusion

mechanical/mmme1029_materials.md

@@ -1065,3 +1065,68 @@ $$\sigma_{yield} = \sigma_0 + k_yd^{-0.5}$$
 where $d$ is the grain size and $\sigma_0$ and $k_y$ are material constants.
 
 Therefore a plot of $\sigma_{yield}$ against $d^{-0.5}$ would results in a straight line.
+
+# Diffusion
+
+Diffusion is atomic or ionic movement down a concentration gradient.
+
+## Solid State Diffusion
+
+![](./images/vimscrot-2021-12-22T13:54:09,340198890+00:00.png)
+
+Solid state diffusion is the stepwise migration (*march*) of atoms or ions through a lattice, from
+site to site.
+
+In order for this to happen, there must an adjacent vacant site.
+The diffusion particle must also have sufficient thermal energy to 'jump' to the new site.
+
+### Vacancy Diffusion (Diffusion of Metal Ions)
+
+![](./images/vimscrot-2021-12-22T13:59:03,553059517+00:00.png)
+
+### Interstitial DIffusion (Diffusion of Small, Non-Metallic Particles)
+
+![](./images/vimscrot-2021-12-22T13:59:53,080635889+00:00.png)
+
+## The Math(s) of Diffusion
+
+Diffusion is time dependent.
+
+For steady state diffusion, Fick's 1st Law holds:
+
+$$J = -D \frac{\mathrm{d}C}{\mathrm{d}x}$$
+
+where $J$ is the *flux*, $\frac{\mathrm{d}C}{\mathrm dx}$ is the concentration gradient, and $D$ is
+the constant of proportionality known as the *diffusion coefficient*.
+
+$D$ is constant for a particular metal at a particular temperature.
+The *flux*is the number of atoms or ions moving per second through a cross sectional area.
+
+### Things that Affect the Speed of Diffusion
+
+- size of the diffusion species --- smaller species results in faster diffusion
+- temperature --- more thermal energy allows more particles to have enough energy to make the 'jump'
+- host lattice
+
+  - simple cubic --- 52% occupancy of ions
+  - body centered cubic --- 68% occupancy of ions
+  - face centered cubic --- 74% occupancy of ions
+
+  Diffusion is faster in a BCC host than in an FCC host for iron ions in an iron host and also for
+  carbon atoms diffusing into an iron host.
+  However this is not always the case.
+
+### Influence of Temperature on Diffusion (Arrhenius Equation)
+
+You can apply the Arrhenius equation for all thermally activated diffusion:
+
+$$D = D_0 \exp{\left( - \frac{Q}{RT} \right)}$$
+
+where $Q$ is the activation energy and $R$ is the ideal gas constant (8.31 J k$^{-1}$ mol$^{-1}$).
+
+# Glossary
+
+- liquidus - for a system of more than one component, the liquidus is the lowest temperature at
+  which the whole system is all in the liquid state.
+- solidus - for a system of more than one component, the solidus is the highest temperature at which
+  the whole system is still in the solid state