Foundations — Surface treatments — anodising, plasma spraying, vapour deposition

This page assumes you have seen none of the notation in the parent note. We build every symbol from the ground up, in an order where each one leans only on the ones before it.

1. Counting stuff: the mole and Avogadro's number

Atoms are absurdly tiny, so chemists count them in giant packs.

Picture: imagine a box labelled "1 mole." Whatever you put in it — Al atoms, water molecules, electrons — there are always $6.022\times 10^{23}$ individual pieces inside.

Why the topic needs it: vapour deposition literally counts atoms arriving, but we weigh coatings in grams. $N_A$ is the bridge that turns "number of atoms" into "amount you can weigh."

2. Molar mass $M$ and density $\rho$: weight and packing

Why the topic needs both: a coating is a layer of material spread over an area. To turn "how much mass did I make" into "how thick is the layer", you divide mass by density (mass → volume) and then by area (volume → thickness). Look at the third block in the figure: the same mass, spread over the same area, becomes a thinner layer when the material is denser.

$\text{thickness}=\frac{\text{mass}}{\rho \times \text{area}}$

Every one of the three master formulas ends with this same "spread it out" step.

3. Area $A$ and thickness $d$: the geometry of a coating

Picture: think of pouring a fixed amount of paint on a table. Cover a bigger table ($A$ large) and the paint film is thinner ($d$ small). Same paint, spread thin. That inverse relationship is exactly why $A$ sits in the denominator of the thickness formulas.

4. Electric charge $Q$, current $I$, time $t$ — the electricity of anodising

Anodising runs on electricity. We need to count how much electricity flowed.

Picture: a water hose. $I$ is the flow rate (litres per second); $t$ is how long you leave it on; $Q$ is the total water that came out. A gentle flow for a long time can deliver the same total as a strong flow for a short time.

Why the topic needs it: in anodising, the coating grows in proportion to total charge, not just current. This is why the parent formula contains the product $It$, not $I$ alone.

5. The electron, and Faraday's constant $F$

Why the topic needs it: we measure charge $Q$ in coulombs, but reactions are bookkept in moles of electrons. $F$ converts between them: $\text{moles of electrons}=\frac{Q}{F}$ Divide by 6 more (because 6 electrons make each oxide unit) and you have moles of oxide. This whole chain is Faraday's Laws of Electrolysis.

6. Efficiency $\eta$ — not all charge does useful work

Picture: you throw 10 darts; 6 hit the board. Your efficiency is $0.6$. Same idea — some charge misses the target reaction.

Why the topic needs it: without $\eta$, the formula would over-predict thickness by assuming every electron built oxide. Multiplying by $\eta$ discounts the wasted fraction.

7. Anode vs cathode — which side are we on?

Why the topic needs it: "Anodising" literally means "make it the anode." The aluminium part loses electrons and grows oxide. This is the single fact the parent's [!mistake] callout warns about — connect it to Corrosion and Passivation, where controlled oxidation is a good thing.

8. Temperature $T$, heat capacity $c_p$, latent heat $L_f$ — the heat of plasma spraying

Plasma spraying is about melting, so we count heat, measured in joules $\mathrm{J}$.

Why two terms? Look at the heating graph: the sloped part is $c_p(T_m-T_0)$ — temperature climbing. The flat shelf is $L_f$ — energy pouring in while temperature stalls, because bonds are being broken to turn solid into liquid. Total melting energy is the sum: $Q_{\text{melt}}=m{c}_p(T_m-T_0)+m{L}_f$ This is the physics of Latent Heat and Phase Change, and it decides whether a ceramic particle melts mid-flight for a thermal barrier coating.

9. Flux $\Phi$ — the rain of atoms in vapour deposition

Picture: rain on a roof. Flux is "how many drops per square metre per second." A gentle drizzle is low flux; a downpour is high flux. In vapour deposition, atoms are the raindrops and the part is the roof.

Why the topic needs it: growth rate $r$ (thickness per second) is just flux converted to thickness: $r=\frac{\Phi M}{N_A\rho }$ Read it left to right using the tools we built: $\Phi$ counts atoms per area per second → divide by $N_A$ to get moles → times $M$ gives mass per area per second → divide by $\rho$ turns mass-per-area into thickness per second. Every symbol was earned in sections 1–3.

The prerequisite map

Equipment checklist

Cover the answers and test yourself. If you can state each one, you are ready for the parent note.

Connections

• Parent topic
• Faraday's Laws of Electrolysis — where $Q$, $F$ and the electron count come from
• Latent Heat and Phase Change — the physics behind $c_p$ and $L_f$
• Corrosion and Passivation — why controlled oxidation at the anode matters
• Thermal Barrier Coatings — the melting energy feeds this
• Adhesion and Surface Roughness — surface prep before coating
• Aluminium Alloys in Aerospace — the substrate being armoured