Impedance Spectros 3fj1p

Impedance Spectroscopy and Material Science

Dr. Muhammad Idrees Department of Physics, CIIT, Lahore, Pakistan

Importance  Electronic, Ionic , Mixed Conductor and Even Insulators  Alloys, Ceramics, Polymeric, Superconductors  Dynamic behavior of bound and mobile charges  Isolate Electrical Response of Different Phases  Grain boundaries can be Characterized and Interpreted

Principle Sinwave input

Sinwave output

Linear System

V( i) = Vo sin t

• Excite a system with AC voltage

V()  Vo exp(it )

I( i) = Iosin (t

• System responds with an AC current

I ( )  Io exp i (t   )

• The ratio output / input signal determines the Impedance for the corresponding frequency: Z( )  Zo exp( i ) The impedance also includes the Phase Shift

Z (i )  R  iX

resistive part

capacitative part

Other Formalisms of the Impedance Data  Complex permittivity

ε* = ε/ + j ε//

 Complex ittance

Y* = Y/ + j Y//

 Complex Modulus

M* = M/ + j M//

Data Presentation and Interpretation Bode and Plane Plots Bode Plots 1. At low frequencies the applied signal behaves like a dc signal (Phase shift is zero) and the corresponding quantity is equivalent to dc counterpart ……. 2. At low frequencies the, the larger polarization is due to presence of response from all type of polarizations 3. As the frequency increases the phase shift increases and the carriers lag behind the applied frequency and the polarization seizes….. 4. The fr indicated by dotted lines is the frequency beyond which the carriers or dipoles are not mobile enough to follow the applied ac signal

Plane Plots 1. Real quantity is plotted against imaginary part as a parametric function of frequency…. 2. Higher intercept (low frequency) at real axis is the total impedance of the system…… and is equal to the dc resistance 3. As the frequency increases, the phase shift (δ or θ) increases and the   R impedance is given Z *   by the  phasor Z   jZ   1  jRC  diagram…..

  R Z/   2 1  (  RC )   

RC  2  1  (  RC )  

Z //  R 

Systems with Multiple Relaxations

Larger the product RC, larger will be fr

 Relaxation frequency of different phases is different

carriers

at

 Difference in fr depends upon the relative resistances and capacitances.  Grain boundaries are generally more resistive and capacitive, Hence, the carriers relax at relatively lower frequencies  In some cases the electrode polarization effect is also present and it usually appears at very low frequencies

Other Formalisms of the Impedance Data  Complex permittivity

ε* = ε/ + j ε//

 Complex ittance

Y* = Y/ + j Y//

 Complex Modulus

M* = M/ + j M//

Advantages of Other Formulism For Example 

C M   Cg

M  

C Cg

(Rg C g ) 2 



C    2  1  (Rg C g )  C gb



M* = jwCoZ* = M/ + j M//



(RgbC gb ) 2



2  1  (RgbC gb ) 

Rg C g  RgbC gb  C     2 2 1  (  R C ) C 1  (  R C )  g g gb  gb gb  

Disorder in a System

Data Modeling

The brick layer model

S.M. Haile, D.L. West, J. Campbell, Journal of Materials Research 13 (1998) 1

NorFERM-2008, Gol

10000

/

8000 6000 4000 2000

LaFe0.9Ni0.1O3

0 0

2

10

3

10

10

4

5

10

6

10

10

4

10

7

10

Frequency (Hz)

-10000

202K 218K 226K 234k 246K

-8000

b

-6000

If ∆fr/∆T > 0

-4000

-2000

0

Ionic or electronic conductivity?

0

10

2

10

3

10

10

5

6

10

7

10

g

1E-3

gb 1E-4

1E-5 -1

 (s )

τ = 2πfr

1

10

Frequency (Hz)

(activation energy for migration)

τ = τoexp(Er/kT)

1

10

//

∆fr/∆T > 0 in oxide (localized)

12000

Z ( )

Localized or delocalized nature of the electrical charge carriers ∆fr/∆T < 0 (metals and Si, Ge)

218K 226K 238K 250K 268K 288K

14000

Z ( )

Applications Electrical Investigations

b

16000

1E-6

1E-7

1E-8 0.0032

0.0036

0.0040

0.0044 -1

-1

T (K )

0.0048

0.0052

Microstructure and Defect Chemistry at G.Bs Electron Phonon Interactions Polaron Formations

Impedance spectroscopy continued..

LaFeO3 Two types of thermal activations In case of the elemental semiconductors On the other hand, in oxide semiconductors where charge carriers are localized SPH σ = (σo/T) exp(-Ec/kBT) Ec = WH+Wb/2 τ = τoexp(WH/kBT) T xQuant tan(δmax ) α ndEexpW(-W /2k T) E (g) (g)b WB c

c

ity

H

(gb)

Wb/2

Wb/2

(gb)

(g)

(gb)

H

Resistan

0.475

0.541

----

----

----

----

ce Tan(δ)

0.477

0.553

0.448

0.514

0.029

0.039

Modulus

----

----

0.438

0.554

----

----

Idrees et. (M ) al. //

Acta Materialia 59 (2011) 1338.

14

On Adding Ni in LaFeO3 LaFe0.9Ni0.1O3

LaFe0.7Ni0.3O3

LaFe0.5Ni0.5O3

Relaxation frequency increases in accord to the increase in the Fe4+ content or band ‘L’ Activation energy for carrier hopping also decreases with doping Ni in accordance to the increase in band ‘L’

15

Now we make a qualitative analysis of the localized and itinerant behavior Jonscher Power Law

(d(σ/ac)/dω > 0)

Peminov et. al.

16

Impedance spectroscopy continued..

Origin of colossal dielectric response in LaFeO3 hd = (2ε/ZNd(Vb-Va))1/2 Ce α 1/hd

dgb α nt/nf Cgb = εgb Agb/dgb

M. Idrees et. al.

Acta Materialia 59 (2011) 1338.

17

Thanks

?