From d1b06d44defb472c2080d6bb1250bc8da502bbce Mon Sep 17 00:00:00 2001
From: Alvie Rahman <alvierahman90@gmail.com>
Date: Tue, 21 Dec 2021 22:54:38 +0000
Subject: [PATCH] mmme1029 Notes on the crystallisation of materials

---
 mechanical/mmme1029_materials.md | 131 +++++++++++++++++++++++++++++++
 1 file changed, 131 insertions(+)

diff --git a/mechanical/mmme1029_materials.md b/mechanical/mmme1029_materials.md
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+++ b/mechanical/mmme1029_materials.md
@@ -771,3 +771,134 @@ of heat and electricity (they are insulators).
 Polymer foams are even better insulators because they have holes which lowers their density.
 
 </details>
+
+# Chemical Bonding of Materials
+
+Chemical bonds are what holds a material together in solid state.
+There are 5 main types of bonds:
+
+Type     | Dissociation energy
+-------- | -------------------
+Ionic    | 600   to 1500
+Covalent | 300   to 1200
+Metallic | 100   to  800
+Hydrogen |   4   to   23
+vdw      |   0.4 to    4
+
+The dissociation energy is the energy required to break the bond, or the strength of the bond.
+
+## Materials and their Properties and Bonding
+
+### Ceramics and Glasses
+
+Ceramics and glasses are composed of mixed ionic and covalent bonding.
+Their strong and rigid bonds have no ability to slide past each other.
+This makes the materials brittle.
+
+### Metals
+
+Metals are based on metallic bonding (woah).
+This type of bonding *does* allow for ions to slide past each other, making metals ductile.
+
+### Polymers
+
+Polymer chains made of C-C covalent bonds are strong, like those found in ceramics.
+
+However, in thermoplastics polymers, the materials can yield by having the chains untangle and
+then align, as the chains slide past each other.
+This means that **stronger bonds between polymer chains means a higher yield stress in thermoplastic
+polymers**.
+
+# Crystallisation of Materials
+
+## Atomic Arrangement
+
+- No order
+- Short range order
+
+  Silica glasses have short range order on the atomic scale.
+  They are composed of regular SiO$_4$ units which all have the same bond length and bond angles.
+
+  However, these units bond together irregularly, which results in different length chemical bonds
+  and angles between the units, meaning they do not have any long range order.
+
+- Long range order
+
+## Cubic Unit Cells
+
+- Lattice Parameter --- One side of a unit cell
+
+  The lattice parameter can be different for each side of a cell.
+
+- Simple cubic unit (SC):
+
+  ![](./images/vimscrot-2021-12-21T21:28:34,863875469+00:00.png)
+
+  Lattice Parameter = 2r
+
+- Face centred cubic (FCC)
+
+  ![](./images/vimscrot-2021-12-21T21:44:21,618384089+00:00.png)
+
+- Body centred cubic (BCC)
+
+  ![](./images/vimscrot-2021-12-21T21:44:40,816535537+00:00.png)
+
+### Packing Factor
+
+$$\text{packing factor} = \frac{\text{ions per unit cell} \times V_{ion}}{V_{cell}}$$
+
+### Theoretical Density
+
+$$\text{theoretical density} = \frac{\text{ions per unit cell} \times m_{ion}}{V_{cell}}$$
+
+### Polymorphism
+
+Example of a polymorphic solid-state phase transfomration of iron at 1185 K and 1 atm:
+
+$$\text{Fe}_{\text{BCC}} \longleftrightarrow \text{Fe}_{\text{FCC}}$$
+
+Below 1185 K and at 1 atm, only BCC exists. Above 1185 K and at 1 atm, only FCC exists.
+
+### Points, Directions, Planes in a Cubic Unit Cell
+
+![](./images/vimscrot-2021-12-21T22:33:35,491930818+00:00.png)
+
+### Slip Systems in Metals
+
+Metal ions lying in close-packed planes and directions move more easily, increasing ductility.
+The combination of a close packed plane and direction is called a *slip system*.
+
+A close packed direction is where ions touch all the way along the direction.
+
+A close packed plane is where ions touch all the way on a plane.
+
+FCC metal ductility is mainly controlled by the *(111) slip plane*
+
+![](./images/vimscrot-2021-12-21T22:40:37,978916142+00:00.png)
+
+
+## X-Ray Diffraction (Bragg's Law)
+
+The wavelength of x-rays, $\lambda$, is roughly equal to the distance, $d$, between atom/ion layers.
+This allows x-rays to probe for $d$ via Bragg's Equation:
+
+![](./images/vimscrot-2021-12-21T22:44:15,147729727+00:00.png)
+
+Requirements for the x-rays:
+
+- Monochromatic
+- Coherent (phase difference of $2\pi n$ where n is any integer)
+- Parallel with each other
+
+
+The incoming x-rays 1 and 2 strike the rows of ions in the crystal and are diffracted, which can be
+considered reflection at the atomic level.
+The angle of incidence equals the angle of reflection.
+
+The outgoing x-rays 1 and 2 are coherent only if the extra path travelled by ray 2, $2d\sin\theta$
+is any multiple, $n$, of $\lambda$. Or:
+
+$$n\lambda = 2d\sin\theta$$
+
+This is Bragg's Law.