Piezoelectric crystals crystal becomes polarized under mechanical stress

Piezoelectric crystals: crystal becomes polarized under mechanical stress Quartz, barium titanate s + + +++ - - V e. W W

Piezoelectric crystals Piezoelectric crystal: no centerof symmetry Applications of piezoelectric crystals: -e • frequency stabilizer (quartz watch 8 has stability 1/10 ) s=0 polarization=0 +3 e -e • Ultrasonic transducers: ultrasonic 7 10 waves in liquids (f~10 -10 Hz) -e • Scanning tunnelling microscope, atomic force microscope: -e precise movement of STM and AFM tips -e +3 e -e s¹ 0 polarization¹ 0

Polar and pyroelectric crystals Polar crystal: centroids of positive and negative charges in a unit cell do not coincide. As a result non-zero polarization P of the crystal occurs. Crystals lack centre of symmetry Ba 2+ Ti 4+ O 2 - Simplified picture of Ba. Ti. O 3 d Side view of Ba. Ti. O 3 at T <120 o C Polarized charges are neutralized by free external and internal charges

Polar and pyroelectric crystals Pyroelectric crystal: polarization P of the crystal changes with temperature. This is result of a structure changes with temperature. Tourmaline: (Na, Ca)(Li, Mg, Al)(Al, Fe, Mn)6(BO 3)3(Si 6 O 18)(OH 4) class 3 m. P decreases as T decreases Pyroelectricity is only possible in crystals lacking a centre of symmetry plus having a unique polar axis: 1, 2, m, 2 mm, 3, 3 mm, 4, 4 mm, 6, 6 mm Twenty-one classes lacking a centre of symmetry : 1, 2, m, 2 mm, 222, 3, 3 mm, 32, 4, 4, 4 mm, 422, 6, 6, 6 mm, 622, 23, 43 m, 432

Pyroelectric crystal: Ba. Ti. O 3

Ferroelectric crystals: formation of microscopic electric domains in crystal with a particular polarization Electric domains Ba 2+ Ti 4+ O 2 - d c 550 V/cm Ba. Ti. O 3 at T >120 O C cubic 705 V/cm 980 V/cm Polarization a Ba. Ti. O 3 at T <120 O C a=b=3. 98Å, c=4. 03Å Electric field

Mechanical properties: elasticity L DL e mg compression tension s elastic region

Elasticity L 2 L 1 + D L 1 L 2 + D L 2 DL 2<0

Compressibility and shear F 1 F 2 L 1 F 3 L 2 L 3

Compressibility and shear F a Metal E, (10 Mpa) n Elastic limit (10 Mpa) Aluminium 6900 0. 33 1. 22 Copper 12800 0. 36 34 Iron 12000 0. 17 26 lead 1400 0. 4 0. 6

Elasticity and atomic structure Interaction between two ions For a small change of a the displacement is proportional to the force. Atoms return to equilibrium position when the force is removed: elastic region. -1/4 elastic region