Optical Properties Of Glass And Plastic Doped By Fe

174

P

1

P

Mubarak Dirar Abdallah, P

2

P

Elharam Ali Eltahir Mohammed

P

3

P

Sawsan Ahmed Elhouri Ahmed & P

4

P

Rawia A.Elgani

P

1

P

International University of Africa- College of Science-Department of Physics & Sudan University of Science& Technology-College of Science-Department of

Physics-Khartoum-Sudan

P

2, 4

P

Sudan University of Science& Technology-College of Science-Department of Physics-Khartoum-Sudan

P

3

P

University of Bahri-College of Applied & Industrial Sciences-Department of Physics Khartoum - Sudan

Abstract:

Fe material with different concentrations was used to dope glass and plastic samples. The absorption coefficient, refractive index, real and imaginary electric constants decreases as Fe concentration increases. These results agree with theoretical relations.

Keywords: Glass, plastic, Fe, doping, absorption coefficient, refractive

index, energy gap.

Introduction:

175

2. Theoretical interpretation

The real and imaging permeability can be found from equation of Particle viscous medium of viscosity ƞ which is given by

ƞ = 1

2mnR0 RL ν(2.1)

𝑚 = particle mass nR0R = number density

L = free path length

𝜈𝜈 = velocity

The equation of motion under the effect of electric field of strength E is giving by

𝑚ẍ = 𝑒 𝐸 −6𝜋 𝑎 ƞ ⱱ =𝑒 𝐸 − 𝛾 𝜈𝜈 (2.2) Where

𝛾 = 6𝜋 𝑎 ƞ 𝜈𝜈 = 3𝜋 𝑎 𝑚 𝐿 𝜈𝜈nR0

= 𝛾0nR0R (2.3)

𝑎 = Radius of the particle

𝛾0 = 3𝜋 𝑎 𝑚 𝐿 𝜈𝜈

Consider now the solution

𝑥 = 𝑥0𝑒𝑤𝑡 ẋ =𝑖𝑤𝑥 =𝜈𝜈

ẍ =−𝑤2_{𝑥 (2.4)}

Substituting (2.3) in (2.1) given

(𝑖𝛾 − 𝑚𝑤2_{)𝑥 =− 𝑒 𝐸 (2.5)}

Thus

𝑥 =_{[𝑖𝛾−𝑚𝑤}−𝑒 _2]𝐸 = [_[𝑚𝑤_𝑚2𝑤2+𝑖𝛾_4+𝛾]𝑒𝐸_2] (2.6)

𝑝 = 𝑒 𝑛 𝑥 =𝑒2_𝑛 [𝑚𝑤2+𝑖𝛾] 𝐸 [𝑚2_𝑤2_+𝛾2_]

= [𝑥₁ +𝑖𝑥₂] 𝐸 (2.7)

𝑥1 = 𝑚𝑤

2_𝑛𝑒2

[𝑚2_𝑤2_+𝛾2_]𝑥2 =

𝛾𝑛𝑒2

[𝑚2_𝑤2_+𝛾2_] (2.8)

For very large friction coefficient

𝛾 ≫ 𝑚𝑤 (2.9) Hence

𝑥1 =𝑚𝑤

2_𝑛𝑒2

𝛾2 =

𝑛𝑒2𝑚𝑤2

𝛾02𝑛02 (2.10)

𝑥2 = 𝑛𝑒 2

𝛾 =

𝑛𝑒2

𝛾0𝑛0 (2.11)

𝜎1 =𝑤𝑥2 = 𝑤𝜀0𝑥2 (2.12)

α = 𝜎1

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Five samples plastics and glasses were doped by Fewith different concentration ranging from 29.3 𝝁𝝁g/cmP

2

P

to2623𝝁𝝁g/cmP

2

P

.

The optical properties of samples were studied by using the following devices with the following specification.

a. Spin coater

A thin film is made by the spin coating method, the number of round proportional increases with the voltage, then the thickness decreases with an increase in the number of round

b. Ultra violet (UV) spectrometer

The visible spectra obtained in shimadzo mini 1240 spectrophotometer scanning between 200 -1200 nm.The spectrophotometer measures how much of the light is absorbed by the sample.

4. Results:

Fig(1)The relation between absorption coefficient and wavelength for glass doping by Fe with different concentration

560 588 616 644 672 700 728 756 784 0.00

2.20x10-9 4.40x10-9 6.60x10-9 8.80x10-9 1.10x10-8 1.32x10-8 1.54x10-8 1.76x10-8 1.98x10-8

A

bs

orpt

ion C

oef

fic

inent

α

(

c

m

-1 )

Wavelength λ ( nm )

177

Fig(2)The relation between refractive index and wavelength for glass doping by Fe with different concentration

Fig (3) The optical energy gap for glass doping by Fe with different concentration

560 588 616 644 672 700 728 756 784 3.9

5.2 6.5 7.8 9.1 10.4 11.7 13.0 14.3

R

ef

ac

tiv

e I

ndex

(

n )

Wavelength λ ( nm )

29.3 µm 75.1 µm 115.2 µm 120.7 µm 205.8 µm

1.408 1.452 1.496 1.540 1.584 1.628 1.672 1.716 1.760 3.30x10-17

6.60x10-17 9.90x10-17 1.32x10-16 1.65x10-16 1.98x10-16 2.31x10-16 2.64x10-16 2.97x10-16

(

α

h

υ

)

2 (

e

V

.c

m

-1 )

hυ ( eV )

29.3 µm 75.1 µm 115.2 µm 120.7 µm 205.8 µm

29.3 µmE_g = 1.759 eV

178

Fig (4) The relation between real dielectric constant and wavelength for glass doping by Fe with different concentration

Fig (5) The relation between imaginary dielectric constant and wavelength for glass doping by Fe with different concentration

560 588 616 644 672 700 728 756 784 0

23 46 69 92 115 138 161 184 207

R

eal

D

iel

ec

tri

c C

ons

tant

Wavelength λ ( nm ) 29.3 µm

75.1 µm 115.2 µm 120.7 µm 205.8 µm

560 588 616 644 672 700 728 756 784 8.30x10-15

1.66x10-14 2.49x10-14 3.32x10-14 4.15x10-14 4.98x10-14 5.81x10-14 6.64x10-14 7.47x10-14

I

m

agi

narny

D

iel

ec

tr

ic

C

ons

tant

Wavelength λ ( nm )

179

Fig (6) The relation between absorption coefficient and wavelength forplastic doping by Fe with different concentration

Fig (7) The relation between refractive index and wavelength forplastic doping by Fe with different concentration

560 588 616 644 672 700 728 756 784 0.00

1.10x10-9 2.20x10-9 3.30x10-9 4.40x10-9 5.50x10-9 6.60x10-9 7.70x10-9 8.80x10-9

A

bs

or

pt

ion C

oef

fi

c

inet

α

( c

m

-1 )

Wavelength λ ( nm )

51.1 µg/cm2

106.8 µg/cm2

260.4 µg/cm2

275 µg/cm2

2623 µg/cm2

560 588 616 644 672 700 728 756 784 1.050

1.071 1.092 1.113 1.134 1.155 1.176 1.197 1.218

R

ef

rac

ti

v

e I

ndex

( n )

Wavelength λ ( nm )

180

Fig (8) The optical energy gap forplastic doping by Fe with different concentration

Fig (9) The relation between real dielectric constant and wavelength forplastic doping by Fe with different concentration

Fig (10) The relation between imaginary dielectric constant and wavelength forplastic doping by Fe with different concentration

1.7532 1.7568 1.7604 1.7640 1.7676 1.7712 1.7748 0.156 0.234 0.312 0.390 0.468 0.546 0.624 0.702 0.780 ( α h υ )

2 (

e

V

.c

m

-1 )

2

hυ ( eV ) 51.1 µm 106.8 µm 260.4 µm 275 µm 2623 µm

2623 µm E_g= 1.763 eV

51.1 µm E_g = 1.764 eV

560 588 616 644 672 700 728 756 784 1.08 1.20 1.32 1.44 1.56 1.68 1.80 1.92 2.04 R eal D iel ec tic C ons tant

Wavelength λ ( nm )

51.1 µm 106.8 µm 260.4 µm 275 µm 2623 µm

560 588 616 644 672 700 728 756 784 0.00 2.20x10-15 4.40x10-15 6.60x10-15 8.80x10-15 1.10x10-14 I m agi nry D iel ec tr ic C ons tant

Wavelength λ ( nm )

181

5. Discussion

The behaviour of glass and plastic doped with Fe for some optical properties like absorption coefficient α , refractive index 𝑛1, energy gap 𝐸𝑔 , real and

imaginary permitavity inrelationto concentration of Fe is shown in figures (1,2,3,4,5) for glass and figurers (6,7,8,9,10) for plastic respectively . The effect of increasing doping concentration of Fe on α, 𝑛1,𝜀1,𝜀2,shows inverse

relation except for𝐸_𝑔 which shown that 𝐸_𝑔 is directly proportional to concentration , i.e.

𝐸𝑔 ∝ 𝑛0

𝛼 ∝ _𝑛1 0 𝑛1 ∝_𝑛1₀

𝜀₁ ∝_𝑛1 0

𝜀2 ∝ _𝑛1₀ (1)

Where 𝑛₀ represent the number density of Fe atoms. This can forms with equations (2.9, 2.10, 2.11, and 2.12)

𝛼 ~𝜎₁~_𝑛1 0 𝜀1~ 1 +𝑥1 ~ _𝑛1

0 𝜀2~ 𝑥2 ~ _𝑛1₀ (2)

This means that increasing Fe concentration increase into density. This increase frictional force too. This increase of friction increases absorption which is straight forward by physical intuition.

The refractive index 𝑛₁is related to the relaxation time 𝜏 throught the relation between speed of light in a medium𝜈𝜈, and in vacuumc, beside the distance a between two atoms. According to this relation

a

𝑐𝑡 =𝜈𝜈(𝑡+𝜏) = 𝑎 𝜈𝜈 �𝑎_𝑐 +𝜏�= 𝑎 𝜈𝜈

𝑐(𝑎+𝑐𝜏) = 𝑎

�1 +𝑐_𝑎𝜏�= 𝑐_𝜈 =𝑛1 (3)

182 𝜏 =_𝑛

0

𝑛1 =�1 +_𝑎𝑛𝑐𝑐0₀�~_𝑛1₀ (4)

This derivation agrees with the empirical relation between 𝑛₁ and 𝑛₀ shown in equation (5.1).

For plastic doped with Fe the empirical relation between 𝜀₁ ,𝑛₁is similar to that of Fe with glass. However the relations of α,αl,ε₂shows that

𝛼 ,𝛼𝑙 ,𝜀2 ~ 𝑛 (5)

Where n is the concentration of free charge carriers which also increases when 𝑛₀ increase.

These empirical relations agrees also with the theoretical relations (2.8, 2.12, 2, 13) where

𝛼,𝛼𝑙 ~ 𝜎₁~ 𝑛

𝜀2~𝑥2~𝑛 (6)

This indicates that the effect of free carriers becomes important than the effect of friction in the absorption process.

It is very interesting to note that the energy gap𝐸_𝑔, in all cases increases with 𝑛₀ i.e

𝐸𝑔 ∝ 𝑛0 (7)

This empirical relation agrees with the theoretical one, where

𝑛𝑖 = 𝑁𝑣𝑁𝑐𝑒−𝛽𝐸𝑔

𝐸𝑔 = _𝛽1𝐿𝑛(𝑁_𝑛𝑖𝑐𝑁ⱱ2 ) (8)

Where

𝑁𝑐 ,𝑁𝜈are the average concentrations of carriers in the conduction and

valence band respectively. The term 𝑛_𝑖 stands for free charges generated thermally. This means that increasing concentrations of Fe and Fe, increases concentration of holes𝑁_𝑣 and concentration of free conduction electrons 𝑁_𝐶 without increasing thermally generated carriers 𝑛_𝑖 , i.e

𝑁𝑐,𝑁𝜈 ~ 𝑛0 (8)

Thus from (5)

𝐸𝑔 ~ 𝑛0 (9)

In agreement with the empirical relation

6. Conclusion

183

into the room, by decreasing concentration of Fe. It can be also be used in designing sensor and solar cells to improve their performance.

7. Reference:

1. Glass - Chemistry Encyclopedia". Retrieved 1 April 2015.

2. B. H. W. S. de Jong, "Glass"; in "Ullmann's Encyclopedia of Industrial Chemistry"; 5th edition, vol. A12, VCH Publishers, Weinheim, Germany, 1989, ISBN 978-3-527-20112-9, pp. 365– 432.

3. Pfaender, Heinz G. (1996). Schott guide to glass. Springer. pp. 135, 186. ISBN 978-0-412-62060-7. Retrieved 8 February 2011.

4. Corning, Inc. Pyrex data sheet. (PDF). Retrieved 2012-05-15. 5. AR-GLAS Schott, N.A., Inc data sheet