Intuition The one core ideaAn aerospace metal is chosen by asking "how much strength do I get per kilogram I have to fly, at the temperature this part will see?" Everything else on the parent page — dislocations, precipitates, grains, phases — is just the machinery that explains where that strength comes from and why it fades when things get hot .
This page assumes you have seen nothing . Every letter, ratio, and picture the parent note (parent topic ) throws at you is built here, in order, each one earning the next.
Definition Crystal latticeA crystal lattice is a pattern of atoms stacked in a regular, repeating 3-D grid — like oranges packed in a crate, row on row on row. A pure metal is just billions of identical atoms sitting on this grid.
Look at the figure below. The black dots are atoms; each sits at a fixed spot, and the whole pattern repeats forever. That regularity is the reason metals conduct, shine, and — crucially for us — deform in a predictable way .
Intuition WHY the topic needs thisEvery strengthening trick in the parent note is really "mess up this perfect grid on purpose so it's harder to slide." You cannot understand strength without first seeing the grid it disturbs.
Definition Stress, symbolσ Stress is force spread over the area it acts on :
σ = A F F A
Intuition WHY divide by area — the picturePull a thin wire and a thick bar with the same force. The wire snaps, the bar shrugs. Same force, different area → different intensity of pull per unit area . That intensity, not the raw force, decides whether the metal survives. Dividing by A
The unit is the pascal : 1 Pa = 1 N/m 2 megapascal , 1 MPa = 1 0 6 Pa
Definition Yield strengthσ y
Yield strength σ y stops springing back and starts to deform permanently. Below it, let go and it returns to shape; above it, it stays bent.UTS (ultimate tensile strength) = the maximum stress the metal holds before it starts to fail.
Both are just special values of σ
Definition Density, symbolρ Density is how much mass is crammed into a given volume :
ρ = V m m V g/cm 3
Two blocks of the exact same size: one aluminium, one steel. The steel one is far heavier to lift. Same volume, more mass → higher ρ ρ ≈ 7.9 ρ ≈ 4.5
ratio answers the real question
A flying part has two enemies at once: it must not break (wants high σ ρ two competing demands into a single score you can rank . That is exactly the trade the parent note opens with.
Common mistake "Higher absolute strength always wins."Why it feels right: bigger σ The fix: steel can have higher σ lose because its huge ρ σ / ρ ratio , never the raw strength. (This is why the parent's table ranks Ti above steel.)
Recall Why doesg σ / ( ρ g ) g g compare two metals it cancels — engineers just write σ / ρ
A dislocation is a line defect : one row of atoms in the crystal grid is out of place, like a wrinkle running through a carpet. Metal deforms permanently when this wrinkle glides across the grid, one atomic step at a time.
Look at the figure. The extra half-row of atoms (the accent line) is the dislocation. To slide the whole top of the crystal over, you don't shove every atom at once — you just walk the wrinkle across, exactly like moving a heavy rug by pushing a ripple along it instead of dragging the whole thing.
Intuition The ONE sentence that unlocks the whole topicStrength = how hard it is to move dislocations. Every method in the parent note — solid solution, precipitates, grain boundaries, work hardening — is just "put obstacles in the wrinkle's way." See Dislocations and Slip for the full mechanics.
Definition Burgers vectorb Burgers vector b how far and in which direction one glide step shifts the crystal — essentially the size of the wrinkle. It appears in the Orowan formula as the step size a dislocation takes. Think of it as "the length of one atomic footstep."
Definition Grain and grain boundaryA real metal is not one perfect crystal. It is a patchwork of many small crystals called grains , each with its grid pointing a different way. Where two grains meet is a grain boundary — a mismatched seam. d diameter (the size of one patch).
Intuition The picture and why it mattersImagine a tiled floor where each tile's pattern faces a random direction. A dislocation gliding smoothly inside one tile hits the seam and stops — the next tile's grid doesn't line up. So boundaries block sliding → smaller grains (more seams per distance) → stronger. This is Hall–Petch Strengthening , where σ y = σ 0 + k d − 1/2 d d − 1/2
Common mistake "So more grain boundaries arealways good."
Why it feels right: at room temperature, more seams = stronger.
The fix: when very hot, boundaries slide and open up (creep), becoming the weak spot — which is why the hottest turbine parts are single crystals with no boundaries at all. The rule flips with temperature (Creep and High-Temperature Deformation ).
A phase is a region with one specific way of stacking the atoms . The very same element can stack two ways depending on temperature/alloying:
==α HCP (hexagonal close-packed) → strong, less bendable.
==β BCC (body-centred cubic) → more bendable.
Intuition WHY two stackings matterTi-6Al-4V mixes both. By heat-treating, engineers change how much α β phase diagram .
A precipitate is a tiny second-phase particle that forms inside the grid (e.g. CuAl₂ in Al, or γ ′ Precipitation Hardening .
Intuition The picture — why1/ L L L τ L 1/ L
Definition Service temperatureMax service temperature = the hottest a part can run and still keep its strength . Above it, the metal softens, creeps, or oxidises and the part fails.
Intuition Why it's the second axis of everythingStrength is not a fixed label — it melts away as T . That is why the parent's whole family ladder (Al → Ti → Stainless → Ni) is ordered by temperature, not weight. A rough danger line is 0.7 × Corrosion and Passivation (hot oxidation) and Fatigue and Fracture Toughness (repeated-load failure).
Strength equals resistance to dislocation motion
Specific strength sigma over rho
Pick the right metal family
Test yourself — cover the right side and answer before revealing.
What does σ Stress = force over area, σ = F / A
What does ρ Density = mass over volume, ρ = m / V
Why do we use σ / ρ σ It scores strength AND lightness together — the two competing demands of flight.
What physically IS strength, in one sentence? How hard it is to move dislocations through the crystal.
What is a dislocation and how does it move? A line-defect "wrinkle" in the grid; it glides one atomic step at a time to deform the metal.
What is the Burgers vector b The size/direction of one dislocation glide step.
Why do smaller grains (smaller d More grain-boundary seams block the wrinkle; Hall–Petch gives σ y = σ 0 + k d − 1/2
When do grain boundaries become a WEAKNESS instead? At high temperature they slide/crack (creep), so hot parts go single-crystal.
What are α β Two atomic stackings — α β
In τ = G b / L G L 1/ L G L L 1/ L
What does "max service temperature" tell you? The hottest a part stays strong; above it, softening/creep/oxidation cause failure.
Recall Feynman self-checkExplain to a friend why titanium can beat steel even when steel is "stronger." ::: Steel may have higher σ ρ σ / ρ