Temperature gradient → Electrical work
Temperature gradientThermoacoustic effectAcoustic waveAcoustoelectric effectCharge carriersElectrical work
Epistemic state of the route
- known constituent relations
- 3 / 5 established or replicated · weakest constituent demonstrated
- constituent maturity floor
- K4 · experimentally observed
- search for this exact route
- Exact composition search: reviewed 2026-09-21 — partial; No demonstration known: the second reader's web search found no experiment in which a thermoacoustic engine, Rijke tube or Sondhauss tube drove classical Weinreich carrier drag, and each of its five nearest works fails the composition for a stated reason — the thermoacoustic-to-electric device that exists (Zheng 2022) is piezoelectric, and the acoustoelectric currents that exist (Weinreich 1959, Atashbar 2026) come from electrically launched waves. The physics review changed the route's spelling: Weinreich drag needs a travelling wave, so the candidate is now the travelling-wave spelling (handoff token acoustic:travelling-wave) and the generic-sound spelling is incomplete-handoff. Both conversion steps now carry a constitutive relation (Swift's critical gradient; the Weinreich relation), so the route is the atlas's first bounded candidate; the second reader's order-of-magnitude estimate — of order 10⁻³ of a 700 W engine's acoustic power crossing a bare helium–germanium interface, nanoamp-to-microamp acoustoelectric currents, femtowatt-to-sub-picowatt matched-load power — lives in the pass log, not here. Inconclusive as a route search until the engine runs exist. OpenAlex (pass 27) adds nothing that qualifies: the mechanism-pair form's single hit is the biomedical acoustoelectric effect, the whole-chain and precision forms return nothing, and the driver-mechanism list is thermoacoustic-engine engineering whose electrical converters are alternators, piezoelectric membranes (Smoker 2012 the earliest) or triboelectric generators — never Weinreich drag. Scholar and Semantic Scholar remain outstanding.
- recorded-pathway overlap
- none recorded
- route-level evidence
- 0 sources for the complete composition · 9 cited by the constituent steps
- boundaries and interfaces
- BOUNDARY unresolved · 1 theoretical interface
- thermoacoustic-acoustoelectric-gas-solid · gas–solid acoustic boundary · theoretical · resonator-gas → acoustoelectric-solid · carries Acoustic wave · preserves acoustic:travelling-wave · between thermoacoustic-produces-travelling-sound and acoustic-wave-drives-acoustoelectricI₂ = T_I I₁; T_I = 4 Z₁ Z₂ / (Z₁ + Z₂)^2 — ideal plane boundary at normal incidence; Z₁ and Z₂ are the characteristic acoustic impedances of the gas and the solid; matching layers, finite geometry and dissipative losses neglectedthe travelling gas-borne acoustic wave mechanically loads the acoustoelectric solid directly; an electrically driven piezoelectric or IDT launcher would instead create a longer-chain implementationZheng 2022 physically demonstrates direct thermoacoustic gas-wave coupling into a solid piezoelectric membrane, establishing that an active intermediate launcher is not required. No experiment is recorded in which this boundary directly drives a Weinreich-type semiconductor; the ideal transmission relation is a model for the candidate interface, not a measured datum — for 30-bar helium (Z ≈ 4.9 × 10³ Pa·s/m) on germanium (≈ 2.9 × 10⁷ Pa·s/m) it gives T_I ≈ 7 × 10⁻⁴, an illustration only.
- thermoacoustic-acoustoelectric-gas-solid · gas–solid acoustic boundary · theoretical · resonator-gas → acoustoelectric-solid · carries Acoustic wave · preserves acoustic:travelling-wave · between thermoacoustic-produces-travelling-sound and acoustic-wave-drives-acoustoelectric
Explorematrix context · physics checks · steps · route evidence · constituent evidence · cite
Matrix context
D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.
D.01 × C.03 · Temperature gradient × Thermoacousticfamily: ThermoacousticD.01 × C.35 · Temperature gradient × Acoustoelectricfamily: Acoustoelectric
Literature search for this exact composition
No demonstration known: the second reader's web search found no experiment in which a thermoacoustic engine, Rijke tube or Sondhauss tube drove classical Weinreich carrier drag, and each of its five nearest works fails the composition for a stated reason — the thermoacoustic-to-electric device that exists (Zheng 2022) is piezoelectric, and the acoustoelectric currents that exist (Weinreich 1959, Atashbar 2026) come from electrically launched waves. The physics review changed the route's spelling: Weinreich drag needs a travelling wave, so the candidate is now the travelling-wave spelling (handoff token acoustic:travelling-wave) and the generic-sound spelling is incomplete-handoff. Both conversion steps now carry a constitutive relation (Swift's critical gradient; the Weinreich relation), so the route is the atlas's first bounded candidate; the second reader's order-of-magnitude estimate — of order 10⁻³ of a 700 W engine's acoustic power crossing a bare helium–germanium interface, nanoamp-to-microamp acoustoelectric currents, femtowatt-to-sub-picowatt matched-load power — lives in the pass log, not here. Inconclusive as a route search until the engine runs exist. OpenAlex (pass 27) adds nothing that qualifies: the mechanism-pair form's single hit is the biomedical acoustoelectric effect, the whole-chain and precision forms return nothing, and the driver-mechanism list is thermoacoustic-engine engineering whose electrical converters are alternators, piezoelectric membranes (Smoker 2012 the earliest) or triboelectric generators — never Weinreich drag. Scholar and Semantic Scholar remain outstanding.
- Thermoacoustic energy harvesting using thermally-stabilized polyacrylonitrile nanofibers (2022) · wrong coupling · Zheng et al. 2022 (Nano Energy): a mini thermoacoustic engine's sound converted to electricity in situ by a thermally stabilised PAN nanofibre membrane (102 V and 10 μA peak, 30 LEDs, a battery charged) — the thermoacoustic source is the route's, but the abstract names the mechanism piezoelectric conversion; the authors' 'acoustoelectric' is not Weinreich carrier drag. Recorded instead as the demonstrated pathway thermoacoustic-piezoelectric-harvester and kept here as the negative control for the alias set.
- Acoustoelectric Effect in n-Type Germanium (1959) · constituent only · Weinreich, Sanders & White 1959: a travelling ultrasonic wave from an external transducer drags electrons in arsenic-doped n-type germanium — the downstream mechanism demonstrated and the Weinreich relation validated, with no thermoacoustic source (metadata on Crossref; the reviewer's summary of the experiment).
- Observation of giant acoustoelectric currents in graphene on lead magnesium niobate–lead titanate (2026) · source variant · Atashbar et al. 2026 (Nature Communications, open access): RF-driven interdigitated transducers on (111)-cut PMN–PT launch a surface acoustic wave through monolayer graphene; acoustoelectric current up to 90.39 μA and voltage 341.72 mV at 20 dBm with a 50 V gate (17 μA and 225 mV ungated). A travelling solid-state wave does yield substantial carrier-drag current when coupling and mobility are engineered, but the wave is launched electrically — the route's acoustoelectric stage with a different source.
- A thermoacoustic-Stirling heat engine: Detailed study (2000) · constituent only · Backhaus & Swift 2000: the travelling-wave (Stirling-cycle) thermoacoustic engine in detail — the driver, the first mechanism and the travelling acoustic carrier demonstrated, no acoustoelectric element.
- Traveling Wave Thermoacoustic Engine in a Looped Tube (1998) · constituent only · Yazaki, Iwata, Maekawa & Tominaga 1998: the first travelling-wave thermoacoustic engine (a looped tube) — the same role as Backhaus & Swift 2000, earlier.
- Wideband frequency-dependent dielectric properties of rat tissues exposed to low-intensity focused ultrasound in the microwave frequency range (2023) · wrong coupling · The mechanism-pair query's only hit (Chinese Physics B 32, 034305): the biomedical acoustoelectric effect — focused ultrasound modulating the conductivity and permittivity of rat tissues — with no thermoacoustic driver and no carrier drag; the query matched 'thermoacoustic imaging' and 'acoustoelectric' in one abstract.
- Energy harvesting from a standing wave thermoacoustic-piezoelectric resonator (2012) · wrong coupling · Smoker, Nouh, Aldraihem & Baz 2012 (J. Appl. Phys. 111, 104901): a standing-wave thermoacoustic resonator whose pressure oscillation excites a piezoelectric diaphragm at the far end, validated on a small prototype with infrared, PIV and microphone measurements — the thermoacoustic source is the route's, the conversion is piezoelectric. The earlier demonstration of the atlas's thermoacoustic piezoelectric harvester; recorded there as evidence.
- Performance Enhancement of an Acoustic Energy Harvester with a Flexible Polyvinylidene Fluoride-Based Piezoelectric Nanogenerator via the Thermoacoustic Effect (2026) · wrong coupling · Liu & Chen 2026 (Nanomaterials 16, 848): a loudspeaker-driven acoustic harvester with a PVDF piezoelectric nanogenerator whose oscillation a thermoacoustic stack amplifies (pressure amplification up to 3.73 at a 101.5 °C stack temperature difference) — piezoelectric conversion, and the thermoacoustic effect here modifies an externally driven wave rather than sourcing it.
- Modelling and analysis of a thermoacoustic-piezoelectric energy harvester (2019) · wrong coupling · Chen, Tang & Mace 2019 (Applied Thermal Engineering 150, 532–544): a model of the thermoacoustic-piezoelectric harvester; the piezoelectric family, by title.
- High-temperature energy harvesting via thermoacoustic-triboelectric hybridization: Design, modelling, and application demonstration (2026) · wrong coupling · Li et al. 2026 (Nano Energy 155, 112082; abstract read on the publisher's page): a piston-assisted thermoacoustic engine drives a honeycomb-structured freestanding contact-separation triboelectric nanogenerator — stable oscillations at heating temperatures around 150 °C, a peak power of 0.49 mW at 80 MΩ, four stacked units charging 1 μF to 17.05 V in 10 s, a wireless temperature sensor powered. A third conversion family after the alternator and the piezoelectric membrane, not carrier drag; a sibling composition the atlas does not yet spell (with the 2025 liquid-metal triboelectric paper, Energy 137745, in the same list), put to the second reader.
- Development of a 5 kW traveling-wave thermoacoustic electric generator (2017) · constituent only · Bi et al. 2017 (Applied Energy 185, 1355–1361): a 5 kW travelling-wave thermoacoustic engine with a linear alternator — the driver, the first mechanism and the travelling carrier at engineering scale, the atlas's recorded thermoacoustic generator; no acoustoelectric element.
1503 indexed works reported across the queries, 151 unique retrieved; nobody has read them for a qualifying demonstration. A person can screen this frozen list and promote it to a reviewed record without re-running the query.
- OAdriver-mechanism:1751 reported · 100 retrieved
- OAdriver-mechanism:1751 reported · 50 retrieved
- OAmechanism-pair:1-21 reported · 1 retrieved
- OAwhole-chain0 reported · 0 retrieved
- OAdemonstration-precision0 reported · 0 retrieved
- OAdemonstration-precision0 reported · 0 retrieved
Planned runs NOT run in this bundle (engine unavailable): search:2026-09-21-p-231472e45e/s2-dm1 (semantic-scholar); search:2026-09-21-p-231472e45e/s2-mp12 (semantic-scholar); search:2026-09-21-p-231472e45e/s2-wc (semantic-scholar); search:2026-09-21-p-231472e45e/s2-dp (semantic-scholar).
Protocol route-search-v1: a frozen index run changes only the search state; only a reviewed record can say that a demonstration was or was not found.
Typed bounds on this route
Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).
- Carnot limit · formula-bound · hard, applies to this routeη ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c
Steps
- 01thermal → acoustic · loss to thermal|∇T_crit| = β T_m ω |p₁| / (ρ_m c_p |u₁|); prime-mover onset requires |∇T| > |∇T_crit| · critical-gradient factor β T_m ω/(ρ_m c_p u₁) [K/(Pa·m)]p₁ and u₁ are the local first-order acoustic pressure and particle-velocity amplitudes; β is the volumetric thermal expansion coefficient (β T_m ≈ 1 for an ideal gas); this is the linear short-stack / standing-wave criterion of Swift 1988 — above the critical gradient the stack amplifies the wave, below it the same interaction pumps heat — not a closed-form performance law for every travelling-wave regenerator.
- temperature gradient along the stack steeper than the critical gradient set by the acoustic pressure and displacement amplitudes
- a resonant gas column
gas · temperature gradient requiredrefs [1] - 02acoustic → acoustic
- travelling-wave thermoacoustic regime with a non-zero time-averaged acoustic power flux; pressure and particle velocity have the phase relation required for directed acoustic power (a looped tube or a travelling-wave regenerator), unlike the standing wave of a straight resonator
gasrefs [2] [3] - 03acoustic → electrical · loss to thermal|j_AE| = μ |Γ| I_s / v_s · Weinreich acoustoelectric responsivity μ Γ / v_s [A/W]I_s is positive along the acoustic wavevector and Γ > 0 is the intensity attenuation coefficient due to the carriers; momentum transfer is along propagation, so electron drift gives conventional current opposite to propagation while hole current is along it — the magnitude form keeps the carrier sign out of μ.
- a travelling longitudinal bulk acoustic wave propagates through a semiconductor, or a travelling surface acoustic wave is coupled to mobile carriers
- net DC Weinreich drag requires directed acoustic momentum; a pure standing wave does not by itself supply the required net momentum
- a gas-borne acoustic wave may couple mechanically into the solid at a gas–solid boundary; an active piezoelectric launcher is an optional implementation, not part of the acoustoelectric effect
solid · semiconductor requiredrefs [4] [5] [6] [7] [8] - 04electrical → electricalrefs [4] [5]
- 05electrical → electrical · loss to thermal
- carriers driven through an external load at the potential difference the source maintains
refs [9]
Evidence for the complete composition · 0
No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.
Evidence for the constituent relations · 9
- [1]G. W. Swift. Thermoacoustic engines (1988)
- [2]T. Yazaki et al.. Traveling Wave Thermoacoustic Engine in a Looped Tube (1998)
- [3]S. Backhaus, G. W. Swift. A thermoacoustic-Stirling heat engine: Detailed study (2000)
- [4]G. Weinreich, H. G. White. Observation of the Acoustoelectric Effect (1957)
- [5]R. H. Parmenter. The Acousto-Electric Effect (1953)
- [6]G. Weinreich. Ultrasonic Attenuation by Free Carriers in Germanium (1957)
- [7]G. Weinreich, T. M. Sanders, H. G. White. Acoustoelectric Effect in n-Type Germanium (1959)
- [8]M. Atashbar et al.. Observation of giant acoustoelectric currents in graphene on lead magnesium niobate–lead titanate (2026)
- [9]N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)
Cite this route
Physical Transformation Atlas (2026). route p-231472e45e: Temperature gradient → Thermoacoustic effect → Acoustic wave → Acoustoelectric effect → Charge carriers → Electrical work. Dataset revision rbfbfcbb70e57 (hash of the canonical data). https://physical-transformation-atlas.wldud5192.workers.dev/path/231472e45e
Ids and matrix addresses are stable across revisions; the revision hash identifies the exact canonical files the record was compiled from and is meta.data_hash in every /api export. Reuse terms: see the license field in any export.