PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 10:
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02/07/2014 PHY 712 Spring 2014 -- Lecture 10 1 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 10: Complete reading of Chapter 4 A.Microscopic macroscopic polarizability B.Clausius-Mossotti equation C.Electrostic energy in dielectric media
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PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 10: Complete reading of Chapter 4 Microscopic macroscopic polarizability Clausius-Mossotti equation Electrostic energy in dielectric media. Focus on dipolar fields:. Microscopic origin of dipole moments - PowerPoint PPT Presentation
Transcript of PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 10:
PHY 712 Spring 2014 -- Lecture 10 102/07/2014
PHY 712 Electrodynamics10-10:50 AM MWF Olin 107
Plan for Lecture 10:Complete reading of Chapter 4
A. Microscopic macroscopic polarizability
B. Clausius-Mossotti equationC. Electrostic energy in dielectric
media
PHY 712 Spring 2014 -- Lecture 10 202/07/2014
PHY 712 Spring 2014 -- Lecture 10 302/07/2014
rpprprrE
rpr
r
rrp
p
35
2
0
30
3
34 3
41
:dipole single from field ticElectrosta4
1
:dipole single from potential ticElectrosta: ofextent theoutside For
'' '
:moment Dipole
rr
r
r
)ρ(rd
Focus on dipolar fields:
PHY 712 Spring 2014 -- Lecture 10 402/07/2014
Microscopic origin of dipole moments Polarizable isotropic atoms/molecules Charge anisotropic molecules
Polarizable isotropic atoms/molecules
+q
x
E
k=mw02
0
:mequilibriuAt
20
20
w
w
mq
mqEx
xE
PHY 712 Spring 2014 -- Lecture 10 502/07/2014
E+q
xk=mw0
2
EEx
Ex
xE
molmqq p
mq
mq
w
w
w
020
2
20
20
:moment dipole Induced
0
:mequilibriuAt
Polarizable isotropic atoms/molecules – continued:
PHY 712 Spring 2014 -- Lecture 10 602/07/2014
Alignment of molecules with permanent dipoles p0:
+
-
Ep0
EE
Ep
mol
kTpE
kTEp
mol
kTp
ed
epd
0
20
/cos
/cos0
31
cos
:ondistributiBoltzmann a assuming estimatedfield, electrican in moment average its dipole rotatingfreely aFor
0
PHY 712 Spring 2014 -- Lecture 10 702/07/2014
Field due to collection of induced dipoles
17
32
5
4
6
98
0
0)(
0
itot
ijextjisite
exti
itot
EE
EEE
EEE
rpprprrE 3
5
2
0 34 3
41
:dipole single from field ticElectrosta
r
r
PHY 712 Spring 2014 -- Lecture 10 802/07/2014
Field due to collection of induced dipoles -- continued
173
2
54
6
98
PEpEE
Eprpr
rE
ErpprprrE
00)(
5
2
0)(
35
2
0
31
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34 3
41
tottotisite
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jjisite
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iii
tot
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0
0)(
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itot
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EEE
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PHY 712 Spring 2014 -- Lecture 10 902/07/2014
Field due to collection of induced dipoles -- continued
173
2
54
6
98
totemol
totmol
totmol
sitemol
totisite
VV
VV
EE
P
PEpP
Ep
PEE
00
0
0
0
0)(
1
311
31
2/1/3
31 0
0
V
V
Vmol
mol
mol
e
Claussius-Mossotti equation
PHY 712 Spring 2014 -- Lecture 10 1002/07/2014
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
PHY 712 Spring 2014 -- Lecture 10 1102/07/2014
Re-examination of electrostatic energy in dielectric media
)()( 21
)()( 21 0
)()( 21)( )(
21)(
21
)(:fieldnt displaceme of In terms
)()(21
3
3
333
3
rErD
rErD
rrDrrDrD
rD
rr
rdW
rd
rdrdrdW
rdW
mono
mono
PHY 712 Spring 2014 -- Lecture 10 1202/07/2014
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)
PDEDPE
0
0
:equations Basic
mono
bound
monoboundtot
Note: In general P is highly dependent on the boundary values; often it is more convenient/meaningful to calculate DP.
PHY 712 Spring 2014 -- Lecture 10 1302/07/2014
Comment on the “Modern Theory of Polarization” -- continued
D
DDDD
nnn
crystal
electronic
electronicnuclearbound
wwV
eboundbound
00 rP
P
