1 / 61

Chapter 14

Chapter 14. Linear Dielectric Properties. Area under curve. Relative dielectric constant …. Very important. It is a measure of how much charge a solid can store relative to vacuum. In general. D =    P. where D is the displacement (C/m 2 ) E is the applied electric

cerise
Download Presentation

Chapter 14

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 14 Linear Dielectric Properties

  2. Area under curve

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

  4. In general D = P where D is the displacement (C/m2) E is the applied electric field, (V/m) and P is the polarization (C/m2) of your material. In vacuum, P = 0 and D = 

  5. Dielectric Properties

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

  7. Electronic polarization Pe Ionic polarization Pi Dipolar or orientation polarization Pdip Convince yourself that when E is applied the center -ve charge is no longer coincident with the center of +ve charge.

  8. N = number of diploes/m3 polarizability, which is an ionic/ atomic property. Only valid for dilute gases or when Eapplied = Elocal Only valid for cubic symmetry but used in many situations

  9. 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 ....

  10. 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…

  11. The Effect of Frequency Purple = V Red = q Blue = I When charges are in perfect sync with Eapp 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 ??

  12. Ideal vs. Real Dielectric • Charge in phase with voltage; since i = dQ/dt, then current, Ichg, 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: G = 1/R =conductance Power dissipation, W/m3

  13. 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:

  14. Vectorial Sum 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. Itot = Ichg + I loss Tan = I loss/Ichg

  15. 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 ..

  16. 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.

  17. 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 = So. iii) Recall:

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

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

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

  21. Compare:

  22. What determines, ke’ Radius of atom

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

  24. 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.

  25. Ionic Polarization

  26. In DC limit  = 0 and k”= 0 then: Nion = number of ion pairs/m3

  27. What determines kion What is r0???

  28. ro

  29. - + P ABO3 Dipolar Polarization Teams teams… teams ..

  30. Dipolar Polarization Dipole moment = q

  31. 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!

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

  33. 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 

  34. Relaxation

  35. Temperature Dependence

  36. Total polarization P = Pe + Pi + Po With increasing frequency you tend to lose the various mechanisms in order shown.

  37. Dielectric Loss

  38. Slight digression:What is Pv for DC conditions?Does anybody recognize theexpression?

  39. 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.

  40. Worked Example Note # of ion pairs is also equal to # of each ion individually Consider CsCl: Lattice parameter = 0.412 nm Cs+: e = 3.35x10-40 Fm2 Cl-: e = 3.4x10-40 Fm2 Mean ionic polarizability per ion pair = 6x10-40 Fm2 Estimate the dielectric constant of CsCl at low and optical frequencies. _______________________________________________________ If you solve for k’ you get 7.56.

  41. 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??

  42. 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?

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

More Related