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Screening effect. Look at homogeneous crystal; We inserted a point charge in this model Inhomogeneous crystal Answer 1: = +. Jelly model. Poisson equ. :. +. Point charge. Prob1 : point charge field at position ?. homogeneous crystal.

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Presentation Transcript
slide1

Screening effect

Look at homogeneous crystal; We inserted a point charge in this model Inhomogeneous crystal

Answer 1: = +

Jelly model

Poisson equ. :

+

Point charge

Prob1: point charge field at position ?

homogeneous crystal

slide4

contents

Screening Effect :

Thomas-Fermi method

Lind hard method

slide5

Screening effect

We consider all other charges presence in medium on our calculations, as this causes some reductions in our quantities then we recall it as a screen.

slide6

Screening effect

D free charges

E total charges = free charges + induced charges

Linear relation between E & D:

E is decreased in the presence of dielectric

nonlocal

slide7

Screening effect

a.

= 0

Potential is Zero

Basic Principle in Hartree Model

slide8

Jelly model without free charges

Screening effect

Answer a:

Jelly model with free charges

slide9

0

Hartree method for Jelly model

Screening effect

&

= ?

1- Tomas-Fermi method (classic)

Solution :

2- Lindhard method (quantum mechanical)

slide10

Tomas-Fermi dielectric constant

Screening effect

1- Tomas- Fermi method: our hypothesis is slow varying

Semi classic

classical

Quantum mechanical

Homogeneous gas

&

Inhomogeneous gas

slide11

Tomas-Fermi dielectric constant

Screening effect

is chemical potential

In presence of free charges, density become a function of r

Basic Tomas-Fermi Relation

slide12

As is small we can expand it:

Tomas-Fermi dielectric constant

r

2

(

)

k

e

= +

0

q

1

2

q

In cavity

Now we have screening effect on Tomas-Fermi method

Tomas-Fermi method

Screening effect

slide13

Prob2: charge distribution field at position ?

Tomas-Fermi method

Screening effect

Answer 2:

Jelly model

Charge distribution

=

slide14

Tomas-Fermi dielectric constant

Screening effect

Fourier Transform

slide15

Potential energy

Potential energy

potential shows the screening effect

Tomas-Fermi dielectric constant

Screening effect

slide16

Without screening effect

Considering screening effect

Potential energy of one electron

Tomas-Fermi dielectric constant

Screening effect

We plot potentials in reciprocal lattice:

slide17

&

First perturbation term

Lind hard method

Screening effect

2- Lind hard method : First principle; we can use time independent perturbation theory (quantum model)

;

slide18

j

j

Screening effect on Ion-Ion Interaction

Screening effect

Direct interaction: coulomb inter.

Ion-Ion interaction :

Indirect interaction: screening inter.

&

Atomic form factor

Structure factor

slide20

Screening effect on Ion-Ion Interaction

Screening effect

Potential is a real quantity

&

slide21

Is q independent on Tomas-Fermi

Screening effect on Ion-Ion Interaction

Screening effect

&

Lind hard method

slide22

1

1/2

q

1

Screening effect on Ion-Ion Interaction

Screening effect

When q 0 Lind Hard model tends to Tomas-Fermi model

slide23

Lind hard dielectric constant

Screening effect

Lind hard relation

Lind hard model

slide24

Lind hard dielectric constant

Screening effect

It has Bessel behavior & we can see Friedel Oscillation

Lind hard model

It is classical yukawa potential by considering screening effect

Tomas-Fermi model

slide25

Lind hard method

Screening effect

slide26

R

Lind hard method

Screening effect

Attraction & repulsion

slide27

Screening effect

Screening effect

Screening effect on e-e interaction

Screening effect

Fourier Transpose

e-e interaction becomes weak

Conclusion :

slide28

Thanks for your attention

Thanks for your attention