Piezoelectric crystals

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Presentation transcript:

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

Piezoelectric crystals no centerof symmetry Applications of piezoelectric crystals: frequency stabilizer (quartz watch has stability 1/108) Ultrasonic transducers: ultrasonic waves in liquids (f~107-1010Hz) Scanning tunnelling microscope, atomic force microscope: precise movement of STM and AFM tips -e +3e s=0 polarization=0 -e -e +3e -e s¹0 polarization¹0

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 Ba2+ Ti4+ O2- Simplified picture of BaTiO3 d Side view of BaTiO3 at T <120o 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(BO3)3(Si6O18)(OH4) class 3m. 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, 2mm, 3, 3mm, 4, 4mm, 6, 6mm Twenty-one classes lacking a centre of symmetry : 1, 2, m, 2mm, 222, 3, 3mm, 32, 4, 4, 4mm, 42m, 422, 6, 6, 6mm, 62m, 622, 23, 43m, 432

Pyroelectric crystal:BaTiO3

Ferroelectric crystals Ferroelectric crystals: formation of microscopic electric domains in crystal with a particular polarization Electric domains d a c BaTiO3 at T <120O C a=b=3.98Å, c=4.03Å Ba2+ Ti4+ O2- BaTiO3 at T >120O C cubic 550V/cm 705V/cm 980V/cm Polarization Electric field

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

Elasticity L1 L1+DL1 L2 L2+DL2 DL2<0

Compressibility and shear F1 F2 L1 F3 L3 L2

Compressibility and shear F a Metal E, (10Mpa) n Elastic limit (10Mpa) 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