Nanostructured Thermoelectric: Phonon Glass, Electron Crystal (2D)

Nanostructuring

Grain size 60 nm

Smaller grains → more phonon-boundary scattering. Below ~20 nm the grains start scattering electrons too, so σ falls.

Rattler atoms (filled skutterudite) 4%

Heavy guest ions (e.g. La, Ce, Yb) rattling in CoSb₃ cages resonantly scatter low-frequency phonons.

Temperature 500 K

Higher T strengthens intrinsic phonon-phonon Umklapp scattering (mean free path ∝ 1/T).

Carrier density 2.0 ×10¹⁹ cm⁻³

Doping trade-off (Pisarenko relation): more carriers → higher σ but lower Seebeck S.

Live Readouts

Phonon λ (measured)— nm

Electron λ (measured)— nm

Lattice κ_l— W/m·K

Conductivity σ— S/m

Figure of merit ZT—

ZT vs. pristine baseline—

Legend

Phonon (heat carrier) — scatters often Electron (charge carrier) — scatters rarely Rattler guest atom Host lattice atom Grain boundary

How it works

A good thermoelectric wants to conduct electricity like a crystal but heat like a glass (Slack's "phonon-glass, electron-crystal" idea). This 2D engine actually simulates that decoupling instead of assuming it: phonons and electrons are independent random-walking particles that each get their own scattering probability per step, derived live from their own mean free path — so the on-screen bounce rate you see is the number the κ and ZT readouts are computed from, not a decorative overlay.

Matthiessen's rule (combine scattering mechanisms):
  1/Λ = 1/Λ_boundary + 1/Λ_rattler + 1/Λ_Umklapp(T)

Per-step scattering probability from the walked path:
  P_scatter = 1 − exp(−v·dt / Λ)

Kinetic theory of heat conduction:
  κ_l = (1/3)·C_v·v_s·Λ

Wiedemann-Franz law (electronic heat vs. charge):
  κ_e = L·σ·T           (L = 2.44×10⁻⁸ WΩ/K²)

Pisarenko relation (doping trade-off):
  S ∝ n^(-2/3)           σ = n·e·μ

Figure of merit:
  ZT = S²σT / (κ_l + κ_e)

Grain size — sets the boundary mean free path Λ_boundary directly; drag it down and watch phonons (orange) bounce off the vertical grain-boundary lines far more than electrons (cyan) do.
Rattler atoms — heavy guest ions vibrating loosely in cage voids (the mechanism behind filled skutterudites like La-CoSb₃, ZT≈1.7) resonantly scatter phonons without touching the electron gas.
Temperature — raises intrinsic Umklapp (phonon-phonon) scattering, which shortens Λ even with no nanostructuring at all.
Carrier density — the Pisarenko trade-off: more free carriers raise electrical conductivity σ but suppress the Seebeck coefficient S, so ZT peaks at an intermediate doping level, not at the extremes.
ZT vs. pristine baseline — recomputes ZT with grain size fixed at 300 nm (no boundaries) and 0% rattlers, everything else unchanged, so you can see exactly how much the nanostructuring you dialed in is buying you.

Real materials: bulk-nanostructured BiSbTe reaches κ_l ≈ 0.5 W/m·K via ~20 nm grains (Poudel et al.); filled skutterudites reach κ_l ≈ 1.5 W/m·K via rattling (vs. 10 W/m·K unfilled); record SnSe single crystals hit ZT = 2.6 through extreme lattice anharmonicity instead of nanostructuring at all.

🔥 HOT SIDE❄ COLD SIDE