Question bank — Refractory metals — W, Mo, Ta, Re for rocket nozzles

False — highest $T_m$ only wins the temperature contest; pure W is brittle below its ductile–brittle transition (~250–450 °C, so at any warm-but-not-hot handling temperature) and forms volatile $W{O}_3$ in oxidising exhaust, so it needs alloying and coating to be usable.

False — thermal stability (holding the lattice together) and chemical inertness (resisting reaction) are separate properties; W and Mo are thermally superb yet oxidise readily into smoke-like volatile oxides.

False — it peaks near the half-filled d-band (Groups 5–7, near W/Re) and then falls toward filled-d metals; mercury is a filled-d relative that is liquid at room temperature. This is exactly the hump in Figure 1.

True — a stronger bond (bigger $E_{coh}$) means atoms need more thermal energy $k_{B}T$ to shake loose, so $T_m$ scales up with cohesive energy for a given constant $c$.

False (wrong mechanism) — the rhenium effect lowers the ductile–brittle transition and raises the recrystallisation temperature (toughness and creep resistance), not primarily $T_m$; it stops W from cracking on thermal shock.

False — PBR 1–2 gives a dense adherent oxide, but if that oxide is volatile (like $W{O}_3$, $Mo{O}_3$) it simply evaporates, so a "good" PBR still fails. See Oxidation kinetics and the Pilling–Bedworth ratio.

Often true — Ta's oxide is far less volatile and it is more corrosion-resistant, so in oxidising conditions Ta (or Ta–10W) survives where bare W erodes; W still wins on peak temperature in reducing burns.

False — light and cheap are advantages; Mo is chosen deliberately when peak temperature is lower or weight matters, usually with a protective coating.

The factor is roughly indicative but not exact — $T_m\propto E_{coh}$ holds only within the same $c$; different crystal structures and vibrational behaviour shift $c$, so you cannot read exact bond-energy ratios straight off melting-point ratios.

Above ~500 °C W forms $W{O}_3$, which sublimes away, continuously exposing fresh metal — so an uncoated W surface in oxidising flow erodes, it does not survive indefinitely.

$A{l}_2{O}_3$ is a dense, adherent, non-volatile skin that seals the surface; $W{O}_3$ is volatile and boils/sublimes off, so it never forms a protective layer — opposite behaviour despite both being oxides.

Re is denser (21.0 g/cm³) than W, so it does not lighten anything; it is added to toughen W (lower ductile–brittle transition) against thermal-shock cracking.

It does not have the highest $T_m$ (W does); it is chosen for ductility and fabricability — you can form intricate cooling channels — while the 10% W boosts strength and $T_m$ enough. See Rocket nozzle thermal management — radiation vs regen cooling.

PBR < 1 means the oxide occupies less volume than the metal it replaced, so it cannot cover the surface and cracks/fissures, giving no protection — thin here means porous, not good.

Near a half-filled d-band the maximum number of bonding d-orbitals are occupied while anti-bonding ones stay empty, maximising cohesive energy — the peak of Figure 1 and the middle of Figure 2; filling anti-bonding states toward the right weakens bonding and lowers $T_m$.

Melting destroys the lattice's long-range order, and $E_{coh}$ is exactly the energy holding each atom in its lattice site — so the thermal energy $k_{B}T$ must reach a critical fraction $c$ of that well depth for atoms to escape their cages. Ties to Metallic bonding and the electron sea model.

Reducing exhaust has little free O₂, so almost no $W{O}_3$ forms; short duration also limits total oxide loss, letting bare or thinly coated W survive without eroding.

More W does nothing against oxidation — the problem is chemical, not thickness; a non-volatile barrier (Ir, silicide, $Zr{B}_2$) blocks oxygen from reaching the W surface. See Thermal barrier coatings and ablatives.

Long before $T_m$, atoms can slowly slide and rearrange under stress at high temperature, deforming the part; Re resists this best, which is why creep and recrystallisation govern life, not the melting number. See Creep and recrystallisation in metals.

Ceramics resist oxidation far better and can exceed metal service temperatures, trading away toughness — worthwhile when the environment is strongly oxidising or the burn is long. See Ceramic-matrix composites — alternatives to refractory metals (ZrB2, HfC).

Brittle — it sits below its ductile–brittle transition (~250–450 °C), so it snaps and cracks on thermal shock unless alloyed with Re.

The transition depends on grain size, impurity content, prior working, and how fast the load is applied — coarse grains and dirty boundaries push it up, fine clean grains push it down — so different W samples cross from snapping to bending at different temperatures within that band.

This is the threshold where $W{O}_3$ begins to form and sublime — below it W is essentially stable in air, above it it steadily loses mass, so it is a genuine boundary the designer must respect.

$k_B{T}_m\approx c\cdot 0=0$, i.e. $T_m=0$ K — with no bonding there is no solid to melt, the degenerate limit that confirms the model's logic.

Mo (2896 K) is lowest of the four, but it is far from useless — its low density and cost make it ideal for lower-temperature, weight-sensitive parts, usually coated.

The non-volatile one — PBR only judges volume fit; if the oxide evaporates it cannot stay on the surface to shield the metal, so volatility overrides a good PBR.