[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES
OPTICAL PROPERTIES OF GLASS AND PLASTIC DOPED BY CU
Elharam Ali Eltahir Mohammed*1, Mubarak Dirar Abdallah2, Sawsan Ahmed Elhouri Ahmed3 &
Rawia A.Elgani4
*1&4
Sudan University of Science& Technology-College of Science-Department of Physics-KhartoumSudan
2
Sudan University of Science & Technology-College of Science-Department of Physics & International
University of Africa- College of Science-Department of Physics -Khartoum-Sudan
3
University of Bahri-College of Applied & Industrial Sciences-Department of Physics-Khartoum - Sudan
ABSTRACT
Glass and plastic samples are doped with Cu at different concentrations. The results obtained show that increasing
Cu concentration decreases absorption coefficient, refractive index, real and imaginary electric permittivity, where
as energy gap increases. These results surprisingly agree with the theoretical model that treats Cu as an electric
dipole.
Keywords: Glass, plastic, Cu, doping, absorption coefficient, Refractive index, energy gap.
I.
INTRODUCTION
Optical properties of materials play an important role in technology.
They are important for solar cells and light sensor [1]. The optical properties include absorption, refractive index,
reflection and transmission. The optical properties can be changed by doping or by physical techniques [2].The
emergence of nano science raises a hope in changing optical properties of materials by controlling the nano size and
concentration or geometry [3].Nano science shows that nano particles behavior is descended by the laws of quantum
mechanics [4].One of the importance materials used in doping is Cu .It was shown in literature that doping some
materials with Cu can change them to superconductivity this is encourages to try to see how Cu can change the
optical properties of glass and plastic this done in section 2,3,4,and 5 are devoted for results , discussion and
conclusion .
II.
THEORETICAL INTERPRETATION
The real and imaging permeability can be found from equation of Particle viscous medium of viscosity ƞ which is
given by
1
ƞ = mn0 L ν
2
𝑚 = particle mass
n0 = number density
L = free path length
𝜈 = velocity
(2.1)
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 𝜈
(2.2)
Where
𝛾 = 6𝜋 𝑎 ƞ 𝜈 = 3𝜋 𝑎 𝑚 𝐿 𝜈n0
49
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
= 𝛾0 n0
(2.3)
𝑎 = Radius of the particle
𝛾0 = 3𝜋 𝑎 𝑚 𝐿 𝜈
Consider now the solution
𝑥 = 𝑥0 𝑒 𝑤𝑡
ẋ = 𝑖𝑤𝑥 = 𝜈
ẍ = −𝑤 2 𝑥
(2.4)
Substituting (2.3) in (2.1) given
(𝑖𝛾 − 𝑚𝑤 2 )𝑥 = − 𝑒 𝐸
(2.5)
Thus
−𝑒
𝑥=
[𝑖𝛾−𝑚𝑤 2 ]
𝐸=
𝑝 = 𝑒 𝑛 𝑥 = 𝑒 2𝑛
= [𝑥1 + 𝑖𝑥2 ] 𝐸
𝑥1 =
𝑚𝑤2 𝑛𝑒 2
[𝑚2 𝑤2 +𝛾2 ]
[𝑚𝑤 2 +𝑖𝛾]𝑒𝐸
(2.6)
[𝑚2 𝑤 4 +𝛾2 ]
[𝑚𝑤 2 + 𝑖𝛾] 𝐸
[𝑚2 𝑤 2 + 𝛾 2 ]
(2.7)
𝑥2 =
𝛾𝑛𝑒 2
(2.8)
[𝑚2 𝑤 2 +𝛾2 ]
For very large friction coefficient
𝛾 ≫ 𝑚𝑤
(2.9)
Hence
𝑥1 =
𝑥2 =
𝑚𝑤2 𝑛𝑒 2
𝛾2
𝑛𝑒 2
𝛾
=
=
𝑛𝑒 2
𝛾0 𝑛0
𝑛𝑒 2 𝑚𝑤2
𝛾0 2 𝑛0 2
(2.10)
(2.11)
𝜎1 = 𝑤 𝜀2 = 𝑤𝜀0 𝑥2 (2.12)
𝜎
α= 1
𝑐n1
III.
(2.13)
MATERIALS& METHODS
Five samples plastics and glasses were doped by Cu with different concentration ranging from 28.9 𝝁g/cm2 to
1965.8𝝁g/cm2.
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.
50
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOIRESULTS
Absorption Coefficinent  ( cm-1 )
IV.
ISSN 2348 – 8034
Impact Factor- 4.022
28.9 g/cm2
136.8 g/cm2
687.9g/cm2
755.3 g/cm2
1965.8g/cm2
6.24x10-8
5.46x10-8
4.68x10-8
3.90x10-8
3.12x10-8
2.34x10-8
1.56x10-8
7.80x10-9
0.00
336
392
448
504
560
616
672
728
784
Wavelength  ( nm )
Fig (1) The relation between absorption coefficient and wavelength for glass doping by Cu with different concentration
28.9 g/cm2
136.8 g/cm2
687.9g/cm2
755.3 g/cm2
1965.8g/cm2
22.4
Refractive Index ( n )
19.6
16.8
14.0
11.2
8.4
5.6
2.8
0.0
336
392
448
504
560
616
672
728
784
Wavelength  ( nm )
Fig (2) The relation between refractive index and wavelength for glass doping by Cu with different concentration
51
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
4.23x10-14
28.9 g/cm2
136.8 g/cm2
687.9g/cm2
755.3 g/cm2
1965.8g/cm2
( h )2 ( eV.cm-1 )2
3.76x10-14
3.29x10-14
2.82x10-14
2.35x10-14
28.9 m Eg = 2.61 eV
1.88x10-14
1.41x10-14
1965.8m Eg = 2.633 eV
9.40x10-15
4.70x10-15
0.00
1.54 1.68 1.82 1.96 2.10 2.24 2.38 2.52 2.66 2.80
h ( eV )
Fig (3) The optical energy gap for glass doping by Cu with different concentration
28.9 g/cm2
136.8 g/cm2
687.9g/cm2
755.3 g/cm2
1965.8g/cm2
448
Real Dielectric Constant
392
336
280
224
168
112
56
0
336
392
448
504
560
616
672
728
784
Wavelength  ( nm )
Fig (4) The relation between real dielectric constant and wavelength for glass doping by Cu with different concentration
52
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
9x10-14
28.9 g/cm2
136.8 g/cm2
687.9g/cm2
755.3 g/cm2
1965.8g/cm2
Imaginary Dielectric Constant
8x10-14
7x10-14
6x10-14
5x10-14
4x10-14
3x10-14
2x10-14
1x10-14
0
336
392
448
504
560
616
672
728
784
wavelength  ( nm )
Fig (5) The relation between imaginary dielectric constant and wavelength for glass doping by Cu with different
concentration
Absorption Coefficient  ( cm-1 )
3.24x10-7
122.3 g/cm2
261.4 g/cm2
355.5g/cm2
393 g/cm2
624 g/cm2
2.88x10-7
2.52x10-7
2.16x10-7
1.80x10-7
1.44x10-7
1.08x10-7
7.20x10-8
3.60x10-8
0.00
336
392
448
504
560
616
672
728
784
Wavelength  ( nm )
Fig (6) The relation between absorption coefficient and wavelength forplastic doping by Cu with different
concentration
53
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
Fig (7) The relation between refractive index and wavelength forplastic doping by Cu with different concentration
1.26x10-13
122.3 g/cm2
261.4 g/cm2
355.5g/cm2
393 g/cm2
624 g/cm2
(h)(eV.cm-1 )2
1.12x10-13
9.80x10-14
8.40x10-14
7.00x10-14
5.60x10-14
122.3 m Eg = 2.65 eV
4.20x10-14
624 m Eg = 2.68 eV
2.80x10-14
1.40x10-14
0.00
1.50
1.65
1.80
1.95
2.10
2.25
2.40
2.55
2.70
2.85
h ( eV )
Fig (8) The optical energy gap forplastic doping by Cu with different concentration
54
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
549
122.3 m
261.4 m
355.5m
393 m
624 m
Real Dielectiric Conestant
488
427
366
305
244
183
122
61
0
336
392
448
504
560
616
672
728
784
Wavelength  ( nm )
Fig (9) The relation between real dielectric constant and wavelength forplastic doping by Cu with different concentration
4.5x10-13
122.3 g/m2
261.4 g/cm2
355.5g/cm2
393 g/cm2
624 g/cm2
Imaginary Dielectric Constant
4.0x10-13
3.5x10-13
3.0x10-13
2.5x10-13
2.0x10-13
1.5x10-13
1.0x10-13
5.0x10-14
0.0
336
392
448
504
560
616
672
728
784
Wavelength  ( nm )
Fig (10) The relation between imaginary dielectric constant and wavelength forplastic doping by Cu with different
concentration
V.
DISCUSSION
The behaviour of glass and plastic doped with Cu for some optical properties like absorption coefficient α ,
refractive index 𝑛1 , energy gap 𝐸𝑔 , real and imaginary permitavity inrelationto concentration of Cu 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
55
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
concentration of Cu on α, 𝑛1 ,𝜀1 ,𝜀2 ,shows inverse relation except for𝐸𝑔 which shown that 𝐸𝑔 is directly proportional
to concentration , i.e.
𝐸𝑔 ∝ 𝑛0
1
𝛼 ∝
𝑛0
1
𝑛1 ∝
𝑛0
1
𝜀1 ∝
𝑛0
1
𝜀2 ∝
(5.1)
𝑛0
Where 𝑛0 represent the number density of Cu atoms. This can forms with equations (2.9, 2.10, 2.11, and 2.12)
1
𝛼 ~𝜎1 ~
𝑛0
1
𝜀1 ~ 1 + 𝑥1 ~
(5.2)
𝑛0
This means that increasing Cu concentration increase into density. This increase frictional forcetoo. This increase of
friction increases absorption which is straight forward by physical intuition. The refractive index 𝑛1 is related to the
relaxation time 𝜏 throught the relation between speed of light ina medium 𝜈,and in vacuum c,beside the distance a
between two atoms . According to this relation
a
𝑐𝑡 = 𝜈(𝑡 + 𝜏) = 𝑎
𝑎
𝜈 ( + 𝜏) = 𝑎
𝑐
𝜈
(𝑎 + 𝑐𝜏) = 𝑎
𝑐
𝑐
𝑐
𝑎
𝜈
(1 + 𝜏) = = 𝑛1 (5.3)
But𝜏 decreases as particlesdensity no increase
𝑐0
𝜏=
𝑛0
𝑐𝑐
1
𝑛1 = (1 + 0 ) ~
(5.4)
𝑎𝑛0
𝑛0
This derivation agrees with the empirical relation between 𝑛1 and 𝑛0 shown in equation (1).
It is very interesting to note that the energy gap𝐸𝑔 , in all cases increases with 𝑛0 i.e
𝐸𝑔 ∝ 𝑛0
(5.5)
This empirical relation agrees with the theoretical one, where
𝑛𝑖 = 𝑁𝑣 𝑁𝑐 𝑒 −𝛽𝐸𝑔
1
𝑁 𝑁
𝐸𝑔 = 𝐿𝑛( 𝑐 2ⱱ)
(5.6)
𝛽
𝑛𝑖
56
(C)Global Journal Of Engineering Science And Researches
[Mohammed, 4(6): June 2017]
DOI-
ISSN 2348 – 8034
Impact Factor- 4.022
Where
𝑁𝑐 , 𝑁𝜈 are the average concentrations of carriers in the conduction and valence band respectively. The term 𝑛𝑖 stands
for free charges generated thermally. This means that increasing concentrations of Cu and Fe, increases
concentration of holes𝑁𝑣 and concentration of free conduction electrons 𝑁𝐶 without increasing thermally generated
carriers 𝑛𝑖 , i.e
𝑁𝑐 , 𝑁𝜈 ~ 𝑛0
Thus from (5.5)
𝐸𝑔 ~ 𝑛0
(5.7)
(5.8)
In agreement with the empirical relation
VI.
CONCLUSION
The absorption of light by glass can be changed by changing the concentration of Cu. The increase of Cu
concentration decrease absorption coefficient. This means that in the design of windows in homes one can enable
more light to pass into the room, by decreasing concentration of Cu. It can be also be used in designing sensor and
solar cells to improve their performance.
VII.
ACKNOWLEDGEMENT
The authors are thankful to Jawaharlal Dada Institute of Engineering and Technology, Yavatmal, for their valuable
support and providing facilities to carry out this research work.
REFERENCES
1.
2.
3.
4.
5.
6.
Lewis, Peter Rhys (2016-06-09). Forensic Polymer Engineering: Why Polymer Products Fail in Service.
Woodhead Publishing. ISBN 978-0-08-100728-0.
Klein, Hermann Joseph (1881-01-01). Land, sea and sky; or, Wonders of life and nature, tr. from the Germ.
[Die Erde und ihr organisches Leben] of H.J. Klein and dr. Thomé, by J. Minshull.
"Glass - Chemistry Encyclopedia". Retrieved 1 April 2015.
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.
"Borosilicate Glass vs. Soda Lime Glass? - Rayotek News". rayotek.com. Retrieved 2017-04-23.
Robertson, Gordon L. (2005-09-22). Food Packaging: Principles and Practice, Second Edition. CRC Press.
ISBN 978-0-8493-3775-8.
57
(C)Global Journal Of Engineering Science And Researches