1 APPLIED PHYSICS CODE : 07A1BS05 CODE : 07A1BS05 I B.TECH I B.TECH CSE, IT, ECE & EEE CSE, IT, ECE & EEE UNIT-4 UNIT-4 CHAPTER :1 CHAPTER :1 NO. OF SLIDES : 33 NO. OF SLIDES : 33

2 S.No.ModuleLectureNo. PPT Slide No. 1IntroductionL Dielectric constant L211 3 Electronic,Ionic,& orientational Polarizations L Internal fields in solids. Clausuis Mossoti relation L UNIT INDEX UNIT-I

3 5 Dielectrics in alternating fields. Dielectrics in alternating fields. Frequency dependence L Ferro and piezo electricity. Ferro and piezo electricity.L832-33

4 INTRODUCTION Dielectrics represent a class of materials which, although insulators, exhibit a number of effects when placed in an electric field. Dielectrics represent a class of materials which, although insulators, exhibit a number of effects when placed in an electric field. A good example is their effect on capacitors. A good example is their effect on capacitors. A capacitor has capacitance C 0 when the space between its two conductors is a vacuum, filling this space with a dielectric increases the capacitance to a new value Cm. The ratio Cm/C 0 = r is known as the relative permittivity of the dielectric. A capacitor has capacitance C 0 when the space between its two conductors is a vacuum, filling this space with a dielectric increases the capacitance to a new value Cm. The ratio Cm/C 0 = r is known as the relative permittivity of the dielectric. LECTURE-1

5 When the atoms or molecules of a dielectric are placed in an external electric field, the nuclei are pushed with the field resulting in an increased positive charge on one side while the electron clouds are pulled against it resulting in an increased negative charge on the other side. When the atoms or molecules of a dielectric are placed in an external electric field, the nuclei are pushed with the field resulting in an increased positive charge on one side while the electron clouds are pulled against it resulting in an increased negative charge on the other side.

6 This process is known as polarization and a dielectric material in such a state is said to be polarized. There are two principal methods by which a dielectric can be polarized: stretching and rotation. This process is known as polarization and a dielectric material in such a state is said to be polarized. There are two principal methods by which a dielectric can be polarized: stretching and rotation. Stretching an atom or molecule results in an induced dipole moment added to every atom or molecule. Stretching an atom or molecule results in an induced dipole moment added to every atom or molecule.

7 Polarizability It can be defined as induced dipole moment per unit electric field. It can be defined as induced dipole moment per unit electric field. i.e. µ= αE i.e. µ= αE Where α is the proportionality constant called Polarizability. Where α is the proportionality constant called Polarizability.

8 Polarization vector The dipole moment per unit volume of the dielectric material is called polarization vector. The dipole moment per unit volume of the dielectric material is called polarization vector. If µ is the average dipole moment per molecule and N is the number of molecules per unit volume then the Polarization vector P=N µ If µ is the average dipole moment per molecule and N is the number of molecules per unit volume then the Polarization vector P=N µ

9 Electric flux density (D) The flux density or electric displacement D at a point in a material is given by D=є r є 0 E. The flux density or electric displacement D at a point in a material is given by D=є r є 0 E. Where E is the electric field strength, є 0 is the dielectric constant and є r is relative permitivity of the material. Where E is the electric field strength, є 0 is the dielectric constant and є r is relative permitivity of the material. The 3 vectors D,E and P are related by the equation D= є 0 E+P The 3 vectors D,E and P are related by the equation D= є 0 E+P P= є 0 (є r -1)E P= є 0 (є r -1)E

10 Electric susceptibility( e ) The polarization vector can be written as P= є 0 e E The polarization vector can be written as P= є 0 e E Where the constant e is the electric susceptibility. Where the constant e is the electric susceptibility. e =(є r -1). e =(є r -1).

11 Dielectric constant (є r ) 2 Dielectric constant (є r ) Lecture- 2 Dielectric constant (є r ) is the ratio between the permitivity of the medium and the permitivity of free space. Dielectric constant (є r ) is the ratio between the permitivity of the medium and the permitivity of free space. i.e є r = є/ є 0. i.e є r = є/ є 0. Є r has no units. Є r has no units. є r =C 1 /C. є r =C 1 /C.

12 Electric Polarization 3 Electric Polarization Lecture- 3 If a material contains polar molecules, they will generally be in random orientations when no electric field is applied. If a material contains polar molecules, they will generally be in random orientations when no electric field is applied. An applied electric field will polarize the material by orienting the dipole moments of polar molecules. An applied electric field will polarize the material by orienting the dipole moments of polar molecules.dipole momentsdipole moments This decreases the effective electric field between the plates and will increase the capacitance of the parallel plate structure. This decreases the effective electric field between the plates and will increase the capacitance of the parallel plate structure.effective electric field capacitanceeffective electric field capacitance

13 The process of producing electric dipoles which are oriented along the field direction is called Polarization in dielectrics. The process of producing electric dipoles which are oriented along the field direction is called Polarization in dielectrics. P=NαE. P=NαE.

14 Polarization in dielectrics Electronic polarization. Electronic polarization. Ionic Polarization. Ionic Polarization. Orientational Polarization. Orientational Polarization.

15 Electronic polarization Electronic polarization represents the distortion of the electron distribution or motion about the nuclei in an electric field. Electronic polarization represents the distortion of the electron distribution or motion about the nuclei in an electric field. distortion The positive charge in the nucleus and the center of the negative charges from the electron "cloud" will thus experience forces in different direction and will become separated. We have the idealized situation shown in the image below. The positive charge in the nucleus and the center of the negative charges from the electron "cloud" will thus experience forces in different direction and will become separated. We have the idealized situation shown in the image below.

16 Electronic polarization

17 Electronic polarization The separation distance d will have a finite value because the separating force of the external field is exactly balanced by the attractive force between the centers of charge at the distance d. The separation distance d will have a finite value because the separating force of the external field is exactly balanced by the attractive force between the centers of charge at the distance d.

18 Ionic Polarization In the absence of electric field, In the absence of electric field, The polarization of a given volume, however, is exactly zero because for every dipole moment there is a neighboring one with exactly the same magnitude, but opposite sign. The polarization of a given volume, however, is exactly zero because for every dipole moment there is a neighboring one with exactly the same magnitude, but opposite sign.

19 The dipoles can not rotate; their direction is fixed.

20 When field is applied In an electric field, the ions feel forces in opposite directions. For a field acting as shown, the lattice distorts a little bit In an electric field, the ions feel forces in opposite directions. For a field acting as shown, the lattice distorts a little bit The Na+ ions moved a bit to the right, the Cl– ions to the left. The Na+ ions moved a bit to the right, the Cl– ions to the left. The dipole moments between adjacent NaCl - pairs in field direction are now different and there is a net dipole moment in a finite volume now. The dipole moments between adjacent NaCl - pairs in field direction are now different and there is a net dipole moment in a finite volume now.

21 The Na+ ions moved a bit to the right, the Cl– ions to the left

22 The distance between the ions increases by d

23 Orientational polarization. The polarization arising due to the allignment of already existing but randomly oriented dipoles in the polar substance is called the Orientational or dipolar polarization. The polarization arising due to the allignment of already existing but randomly oriented dipoles in the polar substance is called the Orientational or dipolar polarization. It is denoted by α o. It is denoted by α o.

24 It depends on temperature T It depends on temperature T It decreases with T. It decreases with T. α o (T)=µ m 2 /3K B T. α o (T)=µ m 2 /3K B T.

25 Orientational polarization ELECTRIC FIELD IS NOT APPLIED. MOLECULAR DIPOLES IN RAMDOM DIRECTIONS

26 Electric dipoles in Electric field ELECTRIC FIELD IS APPLIED E MOLECULAR DIPOLES ORIENTED IN FIELD DIRECTION.

27 Internal fields in solids. 4 Internal fields in solids. Lecture- 4 The total electric field at the site of the atom within the dielectric is called the local field or the internal field. The total electric field at the site of the atom within the dielectric is called the local field or the internal field. It is also called the Lorentz field. It is also called the Lorentz field. We have P=NαE i. We have P=NαE i. E i =[ є 0 (є r -1)E]/N α. E i =[ є 0 (є r -1)E]/N α. E i =E+(ГP/ є 0 ). E i =E+(ГP/ є 0 ).

28 Claussius-Mosotti relation Claussius-Mosotti relation Lecture-5 It gives the relation between the microscopic polarizability and the macroscopic dielectric constant. It gives the relation between the microscopic polarizability and the macroscopic dielectric constant. Clasius Mossotti equation is given by (є r - 1)/( єr +2)= N α/3 є 0. Clasius Mossotti equation is given by (є r - 1)/( єr +2)= N α/3 є 0.

29 Dielectrics in alternating fields Dielectrics in alternating fields Lecture-6 According to Maxwells theory of wave propagation V=1/ єµ. According to Maxwells theory of wave propagation V=1/ єµ. C= 1/ є 0 µ 0. C= 1/ є 0 µ 0. Hence C/V=n= є r µ r. Hence C/V=n= є r µ r. If the materials are non magnetic, µ r=1 If the materials are non magnetic, µ r=1

30 n= є r ( or) є r =n 2. n= є r ( or) є r =n 2. Then the Clasius Mossotti relation becomes (n 2 -1)/( n 2 +2)= N α/3 є 0. Then the Clasius Mossotti relation becomes (n 2 -1)/( n 2 +2)= N α/3 є 0. This is known as Lorentz-Lorentz relation. This is known as Lorentz-Lorentz relation.

31 Lecture-7 In case of the alternating fields, we write E=E (t) and P=P (t) to indicate that both E and P vary with time t. In case of the alternating fields, we write E=E (t) and P=P (t) to indicate that both E and P vary with time t. There will be some time lag between the response P (t) and the cause E (t). There will be some time lag between the response P (t) and the cause E (t). If the applied field E (t) is oscillatory, then P (t) is also oscillatory. If the applied field E (t) is oscillatory, then P (t) is also oscillatory. If E (t) is given by E (t)=E 0 coswt, then P (t)=P 0 cos(wt+δ). If E (t) is given by E (t)=E 0 coswt, then P (t)=P 0 cos(wt+δ).

32 The ferroelectricity 8 The ferroelectricity Lecture- 8 Some dielectrics become spontaneously polarized when their temperature is equal to critical temperature. Some dielectrics become spontaneously polarized when their temperature is equal to critical temperature. This phenomena is called the ferroelectricity.It is not because of it is possessed by the ferrous materials but because its origin and characteristics are same as those of ferro magnetism. This phenomena is called the ferroelectricity.It is not because of it is possessed by the ferrous materials but because its origin and characteristics are same as those of ferro magnetism. The critical temperature of the polar dielectrics is called the ferroelectric curie temperature. The critical temperature of the polar dielectrics is called the ferroelectric curie temperature.

33 PIEZOELECTRICITY When crystals are subjected to electric field, their geometrical dimensions are altered. This phenomenon is called electrostriction. When crystals are subjected to electric field, their geometrical dimensions are altered. This phenomenon is called electrostriction. If crystals are subjected to mechanical stress, electrical charges will be induced on the surfaces of the crystals. This phenomenon is called piezoelectricity. If crystals are subjected to mechanical stress, electrical charges will be induced on the surfaces of the crystals. This phenomenon is called piezoelectricity. When an electric stress (voltage) is applied, the material becomes strained. This phenomenon is known as inverse piezoelectric effect. When an electric stress (voltage) is applied, the material becomes strained. This phenomenon is known as inverse piezoelectric effect.