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

2. Piezoelectric crystals
no centerof symmetry
Applications of piezoelectric crystals:
frequency stabilizer (quartz watch
has stability 1/108)
Ultrasonic transducers: ultrasonic
waves in liquids (f~ Hz)
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

3. 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

4. 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

5. Pyroelectric crystal:BaTiO3

6. 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

7. Mechanical properties: elasticityDL mg e s
tension
compression
elastic
region

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

9. Compressibility and shearF1 F2 L1 F3 L3 L2

10. Compressibility and shearF 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

11. 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