2. Chapter 14

3. Area under curve

5. Relative dielectric constant …. Very important It is a measure of how much charge a solid can store relative to vacuum

6. D =    P In general where D is the displacement (C/m 2 ) E is the applied electric field, (V/m) and P is the polarization (C/m 2 ) of your material. In vacuum, P = 0 and D =   

7. Dielectric Properties

8. Something happens in the solid that allows the parallel plate capacitors to store more charge. That something is called polarization Thus understanding polarization is the key to understanding dielectric properties. P = qd

10. Dipolar or orientation polarization P dip Electronic polarization P e Ionic polarization PiPi Convince yourself that when E is applied the center -ve charge is no longer coincident with the center of +ve charge.

11. N = number of diploes/m 3  polarizability, which is an ionic/ atomic property. Only valid for dilute gases or when E applied = E local Only valid for cubic symmetry but used in many situations

12. Most Important Equation in This Chapter Why? Because it is link between micro and macro… Always recall that it is an approximate expression and if it agrees with experiment it is because you were born under a lucky star and your mother loves you....

13. 4 Fundamental Polarization Mechanisms in Solids Electronic Polarization Ionic Polarization Dipolar Polarization ( linear) is also referred to as orientational. Space charge - occurs at electrodes and is very important in electrochemistry… Not discussed in this class…

14. The Effect of Frequency When charges are in perfect sync with E app you have a perfect dielectric, with no losses. If charges are in phase what is the current doing? Hint: I = dq/dt In a perfect dielectric the current ?? the voltage by ?? Purple = V Red = q Blue = I

15. Ideal vs. Real Dielectric Charge in phase with voltage; since i = dQ/dt, then current, I chg, is 90° out of phase. This current is called a displacive current and does NOT lead to energy loss. In a real dielectric, there is energy loss. To take these into account: Power dissipation, W/m 3 G = 1/R =conductance

16. A digression on i It is a shorthand notation that - in the context of dielectric and optical properties you have two components.. a brilliant tool to solve DE and describe various physical phenomena.. When you see i, then your first thought should be: there must be some form of energy loss somewhere in this system… The last jewel:

17. Vectorial Sum I tot = I chg + I loss Tan  = I loss / I chg Some charges are in phase with V and result in a charging current - but no loss. Others are 90° out of phase and lead t energy dissipation.

18. Measuring Dielectric Properties If  is 90° then you have a perfect dielectric with no losses. If  is 0°, then you have a perfect conductor and no capacitance. You use a something called a lock-in analyzer..

19. How can you measure k’’ In principle, one way would be to simply measure the temperature change in the system… If k” is zero there is no energy loss in the system and thus no heat increase.

20. Electronic Polarization Assumptions: i) Applied field = local field…. ii) The electrons are collectively attached by a spring to the nucleus, with a natural frequency of vibration of  o and a spring constant = S o. iii) Recall:

21. Electronic Polarization Newton’s Law F = ma f is a friction factor, and is thus related to k’’ Z i = atomic number of atom/ion

23. Resonance; a thing of beauty Any examples from real life?

24. DC limit, viz.  = 0 and Near resonance:   =  and k e increases dramatically. and would go to infinity, if there was no friction, i.e. if f =0   <<  then charges cannot follow the field and drops out. Then k e goes to 1. Region 1 Region 2 Region 3

25. Compare:

26. What determines, k e ’ Radius of atom

27. 1- Size 2 - Charge 3 - Presence of d-electrons which are less shielding. Very important result… Electronic polarizability is Proportional to the volume of an atom or ion.

28. Very simple model. Assumed an electron jelly around a nucleus attached with a spring…. Life is more complicated. Quantum mechanics tells us: Other simplification that local E = Applied E, does not change the physics, but only resonant frequency.

29. Ionic Polarization

30. In DC limit  = 0 and k”= 0 then: N ion = number of ion pairs/m 3

31. What determines k ion What is r 0 ???

32. roro

33. ABO 3 -+-+ P Dipolar Polarization Teams teams… teams..

34. Dipolar Polarization Dipole moment = q 

36. In English: What determines k’ dip ?? charge on the dipole is a big one density of dipoles is another jump distance… another big one and finally, T ……. and here comes Mr. Entropy!

37. Debye Model At high frequency, As freq goes to 0,

38. Debye Equations For DC what is k’ dip?? How about at very high  For DC what is k’’ dip?? How about at very high  For DC what is  ?? How about at very high 

39. Relaxation

40. Temperature Dependence

41. Total polarization P = P e + P i + P o With increasing frequency you tend to lose the various mechanisms in order shown.

42. Dielectric Loss

43. Slight digression: What is P v for DC conditions? Does anybody recognize the expression?

44. Dielectric Breakdown Intrinsic: That’s when the electrons go ballistic or postal. :-) Thermal Breakdown: Lossy dielectric, leads to T increase - leads to more current - leads to more Heat - lead to more current leads to death of capacitor.

45. Worked Example Consider CsCl: Lattice parameter = 0.412 nm Cs+:  e = 3.35x10 -40 Fm 2 Cl - :  e = 3.4x10 -40 Fm 2 Mean ionic polarizability per ion pair = 6x10 -40 Fm 2 Estimate the dielectric constant of CsCl at low and optical frequencies. _______________________________________________________ If you solve for k’ you get 7.56. Note # of ion pairs is also equal to # of each ion individually

46. Insulators and Capacitors For capacitor functions: –k’ should be maximum of minimum?? –k” should be low or high?? For insulator functions: –k’ should be maximum of minimum?? –k” should be low or high??

47. How about at optical frequencies? Solving for k’ e gives: 2.71. Experimental values are: 7.2 and 2.62, respectively. Moral of the story: If you want to use CsCl as a window what is k’?? How about if you want to use it as a capacitor, then what?

51. Effect of dipolar polarization on k’. MP of compound

52. Material Dielectric constant Vacuum 1 (by definition) Air 1.00054 Polyethylene 2.25 Paper 3.5 PTFE (Teflon(TM)) 2.1 Polystyrene 2.4-2.7 Pyrex glass 4.7 Rubber 7 Silicon 11.68 Methanol 30 Water (20°) 80.4 Barium titanate 1200 Capacitors and Insulators

53. Summary of Linear Dielectrics Polarization - separation of charge - is key Electronic polarization = rapid, T indep., low k’ and occurs in ALL solids, liquids and gases. Ionic polarization = rapid, T indep.- low and need ions! Dipolar polarization: T dep. - intermediate k’; requires permanent dipole! k e and k ion examples of resonance; k dip e.g. of relaxation: difference is in restoring force. Charges in phase with voltage give rise to k’. Analogy with elastic loading Charges 90° out of phase with voltage give rise k” and dissipation of energy.

54. From here on optional… Have fun..

57. Effect of Frequency Total polarization P = P e + P i + P o With increasing frequency you tend to lose the various mechanisms in order shown.

58. Ferroelectric Ceramics Ferroelectric Ceramics are dipolar below Curie T C = 120ºC cooled below T c in strong electric field - make material with strong dipole moment Fig. 18.35, Callister 7e.

59. As BaTiO 3 is cooled below 120 °C it goes from cubic to tetragonal spontaneously. The tetragonal unit cell has a permanent dipole moment that is huge, which is why most capacitors today are made from BaTiO 3 or related compounds.

60. Piezoelectric Materials at rest compression induces voltage applied voltage induces expansion Piezoelectricity – application of pressure produces current Application of voltage produces dimensional changes

62. Solids that do not conduct electricity are called dielectric solids. The relative dielectric constant,  ’ is a measure of the charge storing capacity of a material relative to vacuum. The 3 most common polarization mechanisms are: Electronic: occur in all solids Ionic: Only occurs in ionically bonded solids Orientation: Where permanent dipoles orient in the applied electric field. The first two are rather small, the third one is the most important and includes ferroelectric solids. Piezoelectric solids can convert mechanical energy to electrical energy and vice versa. Summary II