diff --git a/mechanical/mmme1029_materials.md b/mechanical/mmme1029_materials.md index 15b17e3..288d47b 100755 --- a/mechanical/mmme1029_materials.md +++ 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. + +# 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.