Phenomenon · phenomenon:piezoelectric-effect

Direct piezoelectric effect

Mechanical stress on a non-centrosymmetric crystal displaces its charge centres and produces a surface charge proportional to stress, D = d·σ.

Condensed matterfirst reported 1880

Atlas record: 19 claims reference this phenomenon — 14 established and 5 demonstrated.

Explorerelations · matrix context · routes · sources · cite

conditions: solid · non-centrosymmetric crystal required

19claims47enumerated routes6routes with complete-composition evidence7candidate routes not searched11cited sources

Relations

drives · 4

Mechanical stress or strain—drives→Direct piezoelectric effectestablished

a non-centrosymmetric crystal or a poled ferroelectric ceramic or polymer
stress below the depoling and fracture limits

D = d · σ · piezoelectric charge coefficient d [C/N]

Elastic stress—drives→Direct piezoelectric effectestablished

stress transmitted into a piezoelectric element

Acoustic field—drives→Direct piezoelectric effectestablished

an acoustic pressure field stressing a piezoelectric element; the working principle of piezoelectric microphones and many piezoelectric ultrasonic receivers

Acoustic wave—drives→Direct piezoelectric effectdemonstrated

sound pressure strains a compliant piezoelectric membrane or plate; standing and travelling waves both serve, the response following the pressure oscillation

produces · 1

Direct piezoelectric effect—produces→Separated surface chargeestablished

couples to · 1

Joule magnetostriction—couples to→Direct piezoelectric effectestablished

strain transferred across a bonded interface in a laminate composite

member of · 1

Direct piezoelectric effect—member of→Piezoelectricestablished

implemented by · 6

Direct piezoelectric effect—implemented by→Piezoelectric vibration harvesterestablished

Direct piezoelectric effect—implemented by→Magnetoelectric laminateestablished

the piezoelectric layer of a magnetoelectric laminate
strained by the bonded magnetostrictive layer

Direct piezoelectric effect—implemented by→Bimetallic-strip piezoelectric harvesterdemonstrated

the piezoelectric element struck by the snapping strip

Direct piezoelectric effect—implemented by→Pneumatic pressure piezoelectric harvesterdemonstrated

Direct piezoelectric effect—implemented by→Wave-impact piezoelectric harvesterdemonstrated

Direct piezoelectric effect—implemented by→Thermoacoustic piezoelectric harvesterdemonstrated

bounded by · 1

Direct piezoelectric effect—bounded by→Electromechanical coupling factorestablished

requires · 1

Direct piezoelectric effect—requires→Lead zirconate titanate (PZT)established

any non-centrosymmetric material; PZT is the reference

observed in · 4

Direct piezoelectric effect—observed in→Quartz (α-SiO₂)established

Direct piezoelectric effect—observed in→Lead zirconate titanate (PZT)established

Direct piezoelectric effect—observed in→Polyvinylidene fluoride (PVDF)established

Direct piezoelectric effect—observed in→Zinc oxide (ZnO) nanowiresestablished

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.08 × C.10 · Mechanical stress or strain × Piezoelectric · Established D.23 × C.10 · Acoustic field × Piezoelectric · Established

family: Piezoelectric (C.10)

Enumerated routes through this · 47 (showing 24)

Thermoacoustic piezoelectric harvester4/5 est · demonstrated
Bimetallic-strip piezoelectric harvester5/5 est · demonstrated
Pneumatic pressure piezoelectric harvester5/5 est · demonstrated
Piezoelectric vibration harvester5/5 est · demonstrated
Flow-induced-vibration piezoelectric harvester7/7 est · demonstrated
Wave-impact piezoelectric harvester7/7 est · demonstrated
Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work3/3 est · extends a recorded pathway
Acoustic field → Direct piezoelectric effect → Separated surface charge → Electrical work3/3 est · candidate
Changing magnetic flux → Joule magnetostriction → Direct piezoelectric effect → Separated surface charge → Electrical work4/4 est · candidate
Temperature gradient → Thermoacoustic effect → Acoustic wave → Direct piezoelectric effect → Separated surface charge → Electrical work4/5 est · extends a recorded pathway
Pressure gradient → Elastic deformation → Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Electric potential difference → Converse piezoelectric effect → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · same energy form
Changing magnetic flux → Joule magnetostriction → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · candidate
Mechanical stress or strain → Elastic deformation → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Mechanical vibration → Elastic deformation → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Mechanical vibration → Elastic deformation → Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Incident radiation flux → Photostriction → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work3/5 est · weakly supported
Thermocapillary piezoelectric micro heat engine6/7 est · weakly supported
Temperature gradient → Marangoni effect → Pressure gradient → Elastic deformation → Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work6/7 est · weakly supported
Temperature gradient → Thermal expansion → Mechanical stress or strain → Elastic deformation → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work7/7 est · candidate
Chemical potential difference → Combustion → Temperature gradient → Thermoacoustic effect → Acoustic wave → Direct piezoelectric effect → Separated surface charge → Electrical work6/7 est · extends a recorded pathway
Chemical potential difference → Combustion → Temperature gradient → Thermoacoustic effect → Acoustic wave → Direct piezoelectric effect → Separated surface charge → Electrical work6/7 est · extends a recorded pathway
Chemical potential difference → Combustion → Temperature gradient → Thermal expansion → Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work7/7 est · extends a recorded pathway
Electric potential difference → Peltier effect → Temperature gradient → Thermoacoustic effect → Acoustic wave → Direct piezoelectric effect → Separated surface charge → Electrical work6/7 est · same energy form

Cited sources · 11

[1]
J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)
Oxford University Press · book, no DOI · record
[2]
A. Erturk, D. J. Inman. Piezoelectric Energy Harvesting (2011)
Wiley · doi:10.1002/9781119991151 · crossref ✓ 2026-09-19 · record
[3]
J. Curie, P. Curie. Développement par compression de l'électricité polaire dans les cristaux hémièdres à faces inclinées (1880)
Bulletin de la Société minéralogique de France 3, 90–93 · doi:10.3406/bulmi.1880.1564 · crossref ✓ 2026-09-19 · record
[4]
S. R. Anton, H. A. Sodano. A review of power harvesting using piezoelectric materials (2003–2006) (2007)
Smart Materials and Structures 16, R1–R21 · doi:10.1088/0964-1726/16/3/R01 · crossref ✓ 2026-09-19 · record
[5]
Z. L. Wang, J. Song. Piezoelectric nanogenerators based on zinc oxide nanowire arrays (2006)
Science 312, 242–246 · doi:10.1126/science.1124005 · crossref ✓ 2026-09-19 · record
[6]
C.-W. Nan et al.. Multiferroic magnetoelectric composites: Historical perspective, status, and future directions (2008)
Journal of Applied Physics 103, 031101 · doi:10.1063/1.2836410 · crossref ✓ 2026-09-19 · record
[7]
J. Boughaleb et al.. Coupling of a bimetallic strip heat engine with a piezoelectric transducer for thermal energy harvesting (2016)
Molecular Crystals and Liquid Crystals 628, 15–22 · doi:10.1080/15421406.2015.1137390 · crossref ✓ 2026-09-20 · record
[8]
C. Yang et al.. Design and Experimental Investigation of a Novel Piezoelectric Energy Harvester in Pneumatic System (2022)
Energy Technology 10, 2200096 · doi:10.1002/ente.202200096 · record
[9]
I. Mozumder, S. C. Banik. Design and Experimental Validation of a Piezoelectric Impact-Based Energy Harvester for Low-Frequency Oceanic Waves (2026)
SciEn Conference Series: Engineering 4, 684–687 · doi:10.38032/scse.2026.4.309 · record
[10]
Y. Zheng et al.. Thermoacoustic energy harvesting using thermally-stabilized polyacrylonitrile nanofibers (2022)
Nano Energy 95, 106995 · doi:10.1016/j.nanoen.2022.106995 · record
[11]
J. Smoker et al.. Energy harvesting from a standing wave thermoacoustic-piezoelectric resonator (2012)
Journal of Applied Physics 111, 104901 · doi:10.1063/1.4712630 · record

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