Dielectric Properties of Solids

Electric polarization In an insulator the electrons are so tightly bound that at ordinary temperatures they cannot be dislodged either by thermal vibrations or with ordinary electric fields. However, when an electric field is applied the centres of positive and negative charge distributions separate and electric dipoles are formed througout the medium. This is called electric polarization. Materials Physics MT-0.2101 2

E Dipole -q q Dipole moment a -------------- Electric dipole Whenever the centres of positive and negative charges are displaced from one another an electric dipole is borne. Dipole moment is defined p E p qa torque Materials Physics MT-0.2101 4

Electric polarization -------------- E - - - - - - - - - There are two types of media: permanent electric dipoles no electric dipoles A medium that can be polarized by an electric field E is called a dielectric. Polarization p P dipole moment/m V 3 Materials Physics MT-0.2101 5

d -Q -------------- E - - - - - - - - - Q Positive surface charge Negative surface charge Electric polarization Polarization gives rise to net (immobile) charges on the surfaces. Note: the internal electric field is opposite to the external one field inside is less than outside P p V Qd V Qd Ad Q A 6

A Field inside C 2 is less than in C 1 C 1 C 2 Electric polarization Two parallel plate capacitors. One empty, the other filled with dielectric material. Ratio of capacitances is d r C C 2 e 1 C 1 0 A d C 2 A d e r 0 e is called dielectric constant of the material Is also called relative permittivity ε r 7

Electric polarization The change in total charge is e Q P 1 1 1 e A E E 0 0 e 0 e is called electric susceptibility. A C 1 C 2 d C 1 0 A d C 2 A d 8

Electric polarization Generally polarization P is proportional to the external electric field E: Q P P e 0E 1 1 e e A E E so that e is constant. For most materials e is a positive (dimensionless) number. is vacuum permittivity. 0 0 9

Polarisability α Materials polarise differently a) Charge cloud around the atom is deformed in electric field electronic polarisability b) Chaged ions are displaced ionic polarisability c) Molecules can have permanent dipoles orientational polarisability d) Mobile charges (electrons, holes etc.) space charge polarisability 10

Clausius-Mossoti relations Polarisability α Polarisability of a material in relation to relative permittivity ε r : where N is number of atoms (or formula units of the structure) per unit volume α polarisability of isotropic material E local E local E local E local E local E local Local field is uniform in isotropic materials 3 Where 1 11

Polarisability 12

Ferroelectricity In certain materials the orientation of polarization remains after removal of E. These are called ferroelectric materials. Examples: PZT (Pb[ZrO 3 ][TiO 3 ], lead zirconate titanate) BaTiO 3 (barium titanate) Applications: capacitors, sensors, actuators 13

Remnant polarization or remanence P Hysteresis polarization may take place in domains. At saturation the sample is like one big domain. E As the electric field is reversed, some of the domains remain in their original polarizations. Coercive field 14

-F ------------- F V Piezoelectricity Some materials generate surface charges when pressed. These are called piezoelectric materials. Examples: crystalline quartz titanates, zirconates 15

-F Piezoelectricity Explanation - - schematically: - - turning of the dipoles. - - - - Application: vibration sensors acoustic emitters - - -------------- F 16

Electric polarization Dielectric properties of solids are determined by the number and orientation of electric dipole moments an external electric E field tends to turn the dipoles (parallel or antiparallel) to E in certain materials the orientation remains (ferroelectric materials) after removal of E 17

Lead zirconate titanate 19

Porous polypropylene 21

Effect of tension 22

Piezoelectric effect 23

Polyvinylidene fluoride 24

Activating Exercises Explain by schematics 1) The difference between: (a) ferroelectricity and piezoelectricity (b) Electronic and ionic polarisablity of a material 2) What is poling? 28