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

The part is the anode (it is oxidised to grow $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ — "anodising"). At the cathode only hydrogen ($H_2$) is released. WHAT this checks: you can name the electrode from the process name, not from the "metal = cathode" reflex.

Thickest → thinnest:

1. Plasma spraying — $100\text{–}500\mu \mathrm{m}$.
2. Anodising — $5\text{–}25\mu \mathrm{m}$.
3. Vapour deposition — $0.5\text{–}10\mu \mathrm{m}$. WHY: plasma spraying stacks molten splats (bulk-like build-up), anodising grows oxide from the metal, and vapour deposition adds one atom at a time (slowest, thinnest).

Reaction. In CVD a gas precursor chemically reacts/decomposes on the hot surface; in PVD the material is only physically evaporated or sputtered — no chemical change.

WHAT: plug straight into $d=\frac{MIt\eta }{6F\rho A}$. $d=\frac{(0.10196)(10)(600)(0.5)}{6(96485)(3000)(0.02)}$ Numerator $=0.10196\times 10\times 600\times 0.5=305.88$. Denominator $=6\times 96485\times 3000\times 0.02=3.4735\times 10^7$. $d=\frac{305.88}{3.4735\times 10^7}=8.81\times 10^{-6}\mathrm{m}\approx 8.8\mu \mathrm{m}.$ WHY the 6: the half-reaction releases 6 electrons per mole of $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$, so 6 mol of charge (per $F$) builds only 1 mol of oxide.

$r=\frac{\Phi M}{N_A\rho }=\frac{(2\times 10^{19})(0.0479)}{(6.022\times 10^{23})(4500)}$ Numerator $=9.58\times 10^{17}$. Denominator $=2.7099\times 10^{27}$. $r=3.535\times 10^{-10}m/s.$ Convert: $3.535\times 10^{-10}\times 3600\times 10^6=1.27\mu m/hr$. WHY divide by $N_A\rho$: $\Phi M/N_A$ is mass arriving per area per second; dividing by density $\rho$ turns mass-per-area into thickness.

Two terms — first heat, then melt. $Q=c_p(T_m-T_0)+L_f=880(2050-25)+1.09\times 10^6.$ Heating: $880\times 2025=1.782\times 10^{6}J/kg$. Fusion: $1.09\times 10^{6}J/kg$. $Q=1.782\times 10^6+1.09\times 10^6=2.872\times 10^{6}J/kg.$ WHY per kg: so we can compare against plasma enthalpy flux ($\sim 10^{7}J/kg$) without knowing particle size.

$Q_A=20\times 300=6000\mathrm{C}$; $Q_B=5\times 1200=6000\mathrm{C}$. Since $d\propto Q$ (with all else equal), the formula predicts identical thickness. WHAT the formula hides: $\eta$ is not truly constant. High current density ($20\mathrm{A}$) heats the bath and dissolves oxide, lowering $\eta$; low current for long may passivate cleanly with higher $\eta$. So in reality Run B often gives a slightly thicker, better-quality film despite equal charge. Lesson: the equation is exact only in charge; real efficiency depends on current density and temperature.

Bonding is mostly mechanical interlocking (with minor local fusion), not a metallurgical weld. The skipped step is grit-blasting to roughen the surface. See Adhesion and Surface Roughness. WHY roughness matters: interlocking needs peaks and valleys for splats to hook into. A smooth surface gives no anchor points, so splats solidify and shrink, then pop off. More surface roughness → more contact area and mechanical keying → stronger adhesion.

• PVD for thin hard films: atom-by-atom deposition gives a smooth, dense, defect-free layer — ideal for a thin wear/diffusion barrier. Plasma spraying can't make a clean sub-10 µm layer because splats are tens of µm across (too coarse).
• Plasma spray for thick heat shields: yttria-stabilised zirconia melts at ~2700 °C; only a plasma jet ($10,000\text{–}15,000\mathrm{K}$) can melt it and lay down $100\text{–}500\mu \mathrm{m}$ fast. PVD at ~$1\mu m/hr$ would take hundreds of hours for the same thickness — utterly impractical. See Thermal Barrier Coatings. Rule: thickness need decides the process; PVD wins thin-and-smooth, plasma wins thick-and-refractory.

(a) Rearrange for time: $t=\frac{6F\rho Ad}{MI\eta }$. Use $\rho =3000$, $M=0.10196$, $d=15\times 10^{-6}$. Numerator $=6\times 96485\times 3000\times 0.015\times 15\times 10^{-6}$. $=6\times 96485=578910$; $\times 3000=1.7367\times 10^9$; $\times 0.015=2.6051\times 10^7$; $\times 15\times 10^{-6}=390.76$. Denominator $=0.10196\times 12\times 0.55=0.67294$. $t=\frac{390.76}{0.67294}=580.7\mathrm{s}\approx 9.7\text{min}.$ (b) $t_{\text{PVD}}=\frac{2\mu \mathrm{m}}{1.27\mu m/hr}=1.575\mathrm{hr}\approx 94.5\min$. (c) PVD (~95 min) dwarfs anodising (~10 min). Lesson: atom-by-atom PVD is the bottleneck; combine processes so each does what it's fastest at — thick protection by anodising, only the very thinnest ultra-hard skin by PVD.

(a) Per kg: $Q/m=c_p(T_m-T_0)+L_f=580(2675)+7\times 10^5$. $=1.5515\times 10^6+0.7\times 10^6=2.2515\times 10^{6}J/kg$. Times mass: $Q=2.2515\times 10^6\times 3\times 10^{-11}=6.7545\times 10^{-5}\mathrm{J}$. (b) $t=Q/P=\frac{6.7545\times 10^{-5}}{8\times 10^{-4}}=0.0844\mathrm{s}\approx 84\mathrm{ms}$. WHY the latent term dominates the danger: during melting the temperature stops rising while $L_f$ is absorbed (a phase-change plateau). If residence time is shorter than $84\mathrm{ms}$, the particle arrives partly solid and won't splat properly.

(a) $t=\frac{6F\rho Ad}{MI\eta }$. Numerator $=6\times 96485\times 3000\times 0.03\times 25\times 10^{-6}$. $578910\times 3000=1.7367\times 10^9$; $\times 0.03=5.2102\times 10^7$; $\times 25\times 10^{-6}=1302.55$. Denominator $=0.10196\times 18\times 0.5=0.91764$. $t=\frac{1302.55}{0.91764}=1419.4\mathrm{s}\approx 23.7\text{min}.$ (b) $Q=It=18\times 1419.4=25,549\mathrm{C}$. (c) Effective charge building oxide $=\eta Q=0.5\times 25549=12,775\mathrm{C}$. Moles of oxide $=\frac{\eta Q}{6F}=\frac{12775}{6\times 96485}=0.02207\mathrm{mol}$. (d) Anodic oxide is porous before sealing. Dye soaks into the open pores; sealing (hot water/steam hydrates the $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ to boehmite, closing pores). So you must dye first, then seal — seal first and the dye can't get in, and the sealed passive layer is what resists corrosion. See Corrosion and Passivation.

Anodising (20 µm): from Ex 4.1a a 15 µm layer took $580.7\mathrm{s}$; thickness $\propto t$, so $20\mu \mathrm{m}$ takes $580.7\times \frac{20}{15}=774.3\mathrm{s}\approx 12.9\text{min}$. Plasma spray (300 µm at 50 µm/min): $300/50=6\text{min}$. PVD (3 µm at 1.27 µm/hr): $3/1.27=2.362\mathrm{hr}\approx 141.7\text{min}$. Total $\approx 12.9+6+141.7=160.6\text{min}\approx 2.68\text{hr}$. Which to speed up: PVD dominates (~142 of ~161 min). It is the atom-by-atom step — increasing flux $\Phi$ (higher sputter power) is the biggest lever. Insight: thickness-per-time varies by four orders of magnitude across these processes, so the thinnest layer can still cost the most time.

Which process is fastest per micron? ::: Plasma spraying (tens of µm per minute) Which is slowest per micron? ::: PVD / vapour deposition (~µm per hour) In anodising, thickness depends on charge divided by what factor times F? ::: 6 (electrons per mole of oxide) Why dye before sealing? ::: sealing closes the pores the dye needs to enter