Heat treatment — annealing, normalising, quenching, tempering; precipitation hardening: Foundations

This page assumes you know nothing about metals. We build every word the parent note throws at you, one brick at a time, so that when it says "quench to trap BCT martensite and block dislocation motion" you can see every piece.

Brick 0 — What a crystal even is

Look at the left panel of the figure below. The lavender dots are atoms; the thin slate lines are just guides showing the repeating box (the unit cell) — they are not physical bonds, they help your eye see the pattern. The red arrow points to one atom so you can pick a single grid point out of the crowd.

Figure — Heat treatment — annealing, normalising, quenching, tempering; precipitation hardening

Why the topic needs this: heat treatment is entirely about which grid pattern the iron atoms choose, and whether carbon atoms fit into the gaps. No lattice, no story.

In the right panel of s01, the coral atom is the body-centre of the BCC cell; the butter-yellow atoms are the face-centres of the FCC cell. Look at how the FCC (right box) has more atoms crowding the faces yet leaves fatter open gaps in the middle — that open room is the entire reason austenite swallows carbon and ferrite spits it out.

Brick 1 — Phase, grain, microstructure

In this figure each coloured patch is one grain; the dark slate seams tracing between colours are the grain boundaries (follow the coral arrow to one). The short slate bar labelled "size $d$ " measures the diameter of a single grain — that length is the $d$ you will meet in the Hall–Petch formula.

Why the topic needs this: the parent note's headline claim — "cooling rate decides which phase you trap" — only makes sense once phase and grain are real objects in your head. See Iron-Carbon Phase Diagram for which phases appear at which composition and temperature.

Brick 2 — Symbols for temperature and time

The special temperature the parent calls "~723 °C" is the line below which austenite (FCC) is no longer stable and wants to become ferrite + cementite. Above it, heat; below it, freeze the result.

Brick 3 — Diffusion (the star of the whole topic)

Read this figure left to right as time passing. In the left frame the coral atoms are bunched at the centre; in the middle frame a few have hopped outward; in the right frame they have spread evenly across the faint slate lattice sites. The arrow beneath labelled "time" is your reminder that spreading costs time — and (from Brick 2) enough heat to hop at all.

The single most important consequence, drilled into the parent note:

Deeper treatment lives in Diffusion in Solids.

Brick 4 — Dislocations (why "hardness" has a mechanism)

Follow the three frames left to right. The coral atoms mark the wrinkle (the extra half-plane). In frame 1 it sits at one column; in frame 2 it has glided one column over; by frame 3 the top of the crystal has shifted sideways by exactly one atom spacing — the little arrow labelled $b$ measures that shift. Moving a wrinkle one step at a time is cheap; that cheapness is exactly what makes metals soft.

Two symbols enter here for later formulas:

$b$ = Burgers vector, the length of one glide step (roughly one atom spacing, the arrow in s04). It measures "how much slip one dislocation delivers".
$G$ = shear modulus, the metal's stiffness against sliding one layer of atoms over the next. Big $G$ = stiff, resists shear. (Do not confuse $G$ , a fixed material property, with $τ$ below, which is the stress you apply.)

Full story: Dislocations and Plastic Deformation.

Brick 5 — The Greek letters and formula symbols

Now the parent's equations are readable. Each symbol below is earned by the bricks above.

Intuition Why

$1/ d$ and not $1/ d$ — the pile-up picture Look at s05. Inside a grain of size $d$ , applied shear $τ$ pushes dislocations until they jam against a boundary in a pile-up (the stacked coral marks). Two facts combine:

How many pile up? The number $n$ that fit scales with grain size: $n \propto d τ$ . A bigger grain holds a longer queue.
The queue amplifies stress. A pile-up of $n$ dislocations presses on the boundary with a concentrated stress $\approx n τ$ . The next grain yields when this reaches a fixed critical value $τ_{c}$ : so $n τ \approx τ_{c}$ .

Substitute $n \propto d τ$ into $n τ \approx τ_{c}$ : that gives $d τ^{2} \approx const$ , so $τ \propto 1/ d$ . The square root falls straight out of "stress² × grain size = constant". That is why halving $d$ does not double the bonus — it multiplies it by $2$ . See Hall-Petch Strengthening.

Brick 6 — Precipitates and the Orowan idea

Formula Orowan bowing — where

$G b / L$ comes from $Δ τ = \frac{G b}{L}$ Study s06. A dislocation line is pinned on two precipitates a gap $L$ apart and must bow into an arc to squeeze between them (coral curve). A line resists bending because it has a line tension $T_{ℓ} \approx G b^{2}$ (energy per unit length — think of it as a stretched elastic string of stiffness set by $G$ and step $b$ ). The applied shear $τ$ pushes the line forward with a force $τ b$ per unit length. Balancing that push against the string's pull-back, the sideways force the two pinning points must supply is $2 T_{ℓ} sin θ$ ; the tightest arc (a half-circle of radius $L /2$ ) is reached when $τ b L \approx 2 T_{ℓ} = 2 G b^{2} \Rightarrow Δ τ \approx \frac{G b}{L} .$ WHY smaller $L$ is harder: a smaller gap forces a tighter arc, and a tighter arc needs more push to hold — exactly like blowing a smaller soap bubble needs higher pressure. Over-ageing grows the studs apart ( $L$ up), so $Δ τ$ falls and the metal softens.

Alloys that live by this rather than martensite: Aluminium Alloys (Duralumin) and Nickel Superalloys.

A pattern of atoms repeating in 3D on a fixed grid.

Difference between BCC and FCC, and which dissolves more carbon?

BCC = corners + centre (ferrite, soft); FCC = corners + face-centres (austenite), packs tighter with bigger gaps so it dissolves more carbon.

What is a grain and a grain boundary?

A grain is one small crystal region; the boundary is the mismatched wall where two grains meet.

Why does heat let atoms move?

Heat = jiggling energy; hotter atoms more often gain enough energy to hop to a new site.

Why do rates use kelvin not °C?

The Arrhenius factor

e^{- Q / R T}

needs

T

measured from absolute zero;

T (K) = T (°C) + 273

The two things diffusion needs?

Temperature (energy to jump) and time (many jumps).

Slow cooling gives ___; fast cooling gives ___?

Slow → soft equilibrium phases; fast → trapped hard out-of-equilibrium phase.

What is a dislocation and why does it matter?

A line fault (extra half-plane) whose easy gliding lets metals bend; blocking it = hardness.

Difference between

G

and

τ

G

is a fixed material stiffness (shear modulus);

τ

is the shear stress you apply.

What does

σ_{y}

mean?

Yield stress — the stress at which permanent bending begins; bigger = stronger.

In Hall–Petch

σ_{y} = σ_{0} + k / d

, why the square root?

Pile-up length

n \propto d τ

and boundary yields at

n τ =

const give

d τ^{2} =

const, so

τ \propto 1/ d

In Orowan

Δ τ = G b / L

, what are

G

b

L

and why smaller

L

is harder?

G

= shear modulus,

b

= Burgers vector,

L

= precipitate spacing; smaller

L

forces a tighter bow, needing more stress.

Why does over-ageing soften a metal?

Precipitates coarsen and

L

grows, so

Δ τ = G b / L

falls — fewer, wider studs block dislocations less.

Foundations — Heat treatment — annealing, normalising, quenching, tempering; precipitation hardening

Brick 0 — What a crystal even is

Brick 1 — Phase, grain, microstructure

Brick 2 — Symbols for temperature and time

Brick 3 — Diffusion (the star of the whole topic)

Brick 4 — Dislocations (why "hardness" has a mechanism)

Brick 5 — The Greek letters and formula symbols

Brick 6 — Precipitates and the Orowan idea

How the bricks feed the topic

Worked check — Hall–Petch with the new symbols

Equipment checklist