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PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 10: Complete reading of Chapter 4 Microscopic macroscopic polarizability Clausius-Mossotti equation Electrostatic energy in dielectric media 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Focus on dipolar fields: 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

E +q Microscopic origin of dipole moments Polarizable isotropic atoms/molecules Charge anisotropic molecules Polarizable isotropic atoms/molecules E +q k=mw02 x 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

+q E Polarizable isotropic atoms/molecules – continued: k=mw02 dx 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

E Alignment of molecules with permanent dipoles p0: + p0 - 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Field due to collection of induced dipoles 1 7 3 2 5 4 6 9 8 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Field due to collection of induced dipoles -- continued 1 7 3 2 5 4 6 9 8 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Field due to collection of induced dipoles -- continued 1 7 3 2 5 4 6 9 8 Claussius-Mossotti equation 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Example of the Clausius-Mossotti equation – Pentane (C5H12) at various densities Density (g/cm3) Mol/m3 e/e0 3V*(e/e0-1)/(e/e0+2) 0.613 5.12536E+27 1.82 1.25646E-28 0.701 5.86114E+27 1.96 1.24084E-28 0.796 6.65544E+27 2.12 1.22536E-28 0.865 7.23236E+27 2.24 1.2131E-28 0.907 7.58353E+27 2.33 1.2151E-28 gmol = 1.2 x 10-28 m3= 0.12 nm3 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Re-examination of electrostatic energy in dielectric media 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Comment on the “Modern Theory of Polarization” Some references: R. D.King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993) R. Resta, Rev. Mod. Physics 66, 699 (1994) R. Resta, J. Phys. Condens. Matter 23, 123201 (2010) N. A. Spaldin, J. Solid State Chem. 195, 2 (2012) Note: In general P is highly dependent on the boundary values; often it is more convenient/meaningful to calculate DP. 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

Comment on the “Modern Theory of Polarization” -- continued By contrast, the concept of the polarization of a periodic solid is not unique: 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

DP example 02/03/2017 PHY 712 Spring 2017 -- Lecture 10

DP example -- linear visualization Effects on the electronic distribution Na Cl 02/03/2017 PHY 712 Spring 2017 -- Lecture 10