# Effect of Sn Addition on Thermal and Optical Properties ofPb

Authors: Vivek Modgil; V. S. Rangra
Journal: Journal of Materials
 (2014)

---

## Abstract

Study of thermal and optical parameters ofPb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
) glass has been undertaken. Crystallization and glass transition kinetics has been investigated under nonisothermal conditions by DSC technique. Phase separation has been observed in the material and is investigated by taking the XRD of annealed bulk samples. The material possesses good glass forming ability, high value of glass transition temperature about 420 K, and glass stability. Optical band gap and other optical constants such as refractive index and extinction coefficient have been determined. The isoelectronic substitution of Ge with Sn in the glassy system reduces the optical band gap and enhances the thermal properties.


---

## Body

## 1. Introduction

In amorphous semiconductors, among inorganic glassy materials, chalcogenide glasses occupy a unique place in material science towards advancement of technology. Generally these materials are weakly bonded materials than oxide glasses. But in comparison with amorphous silicon, halide glasses, and other group IV tetrahedral bonded semiconductors these materials exhibit the superior properties which can be tailored by varying the composition. The physical properties such as optical band gap, dielectric behavior, and conductivity of chalcogenide glasses mark their strong dependency on lone pair electrons and density of defect states in the band tails [1, 2]. The disorder in amorphous semiconductors causes perturbation in density of state functions resulting in band tails at the edges of the bottom of the conduction band and the top of the valence band [3]. The lone pair orbits have higher energy than the bonding states and hence occupy the top of the valence band. Interactions between lone pair electrons with their local environment and different atoms result in localized states in the band tails [4]. These localized states play crucial role in deciding optical properties of the materials.The better optical and thermal properties of these materials make them of potential use in the technological applications such as in photonics and phase change memories because of higher values of refractive index and lower value of phonon energy of these glasses [5, 6]. The present Investigation on phase change memories (PCM) shows the possibility of obtaining multistate behavior, enhanced ability to withstand thermal cycling, and use of lower voltages for achieving desired phase change response by using the bilayers of Ge-chalcogenide and Sn-chalcogenide [7].Germanium is a good glass former and has good glass forming region with Se but has the disadvantage that the Ge compositions have the wide optical band gap which results in the intrinsic optical loss and causes problem in long distance fiber communication. In order to remove such discrepancies chalcogen elements are added with heavy elements. Many researchers have carried out their work on this type of compositions such as Ge-Sb-Se, Ge-Sn-Se [8, 9], and Ge-Sn-Sb-Se [10] to improve the optical properties. These materials can be used in the photonic crystal applications due to their higher value of refractive index. Photonic crystals are the materials which are used in photonic applications, such as optical band gap devices and omnidirectional reflectors [6].It is necessary to have the knowledge of thermal stability and glass-forming ability (GFA) of material to know its suitability for the particular technological application before crystallization takes place. The addition of elemental impurity such as Ge, Sn, In, and Pb has a pronounced effect on structural, optical, electronic, and thermal properties of material [11–15]. The addition of Sn may expand and create compositional and configurational disorder in material and accordingly modifies the properties. The Sn has been added in Pb-Se-Ge system to see the effect of Sn incorporation on thermal and optical behaviors of this material.


## 2. Experimental Details

### 2.1. Material Synthesis and Characterization

The chalcogenide materialsPb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
at
.
%
)  are prepared by the melt quenching technique. Granules of Pb and powder of Sn, Ge, and Se having 99.999% purity are used. The material is then sealed in evacuated (~10−5 Torr) quartz ampoule (length ~15 cm and internal diameter ~8 mm). The ampoules containing material are heated to 1000°C and held at that temperature for 10 hours. The temperature of the furnace is raised slowly at a rate of 3-4°C per minute. During heating, the ampoule is constantly rocked. The obtained melt is quenched in ice cool water. The nature of the material is ascertained by powder X-ray diffraction technique. For this, X-ray diffraction (XRD) patterns of sample are taken at room temperature by using an X-ray diffractometer PANalytical X’pert Pro (PW 3050/60, Cu
K
α
1
λ
=
1.54
Å) shown in Figure 1.Figure 1
X-ray diffractograms of the chalcogenide glassPb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
).The thermal behavior of the material has been studied using differential scanning calorimetry (DSC) under nonisothermal conditions using DSC instrument Mettler Star SW 9.01 model. Approximately 15–20 mg quantity of each powdered sample is used for DSC analysis. Each sample is heated at different heating rates 10, 15, 20, and 25°k/minute. We have found that material’s samples atx
=
11,12 have double crystallization peaks which are due to the phase separation in the material. We have annealed the bulk sample x
=
11 at temperatures 507 K and 550 K for 3 hours to detect the phases separated in the material. Then XRDs of samples have been taken. Figure 4 shows the XRD patterns of the annealed samples (
x
=
11
). To find out the band gap and other optical constants, thin films of chalcogenide glasses have been deposited by vacuum evaporation technique on thoroughly cleaned microscope glass substrate. The room-temperature optical transmission and absorption spectra (not shown here) at normal incidence, of the samples, are recorded over the 200 nm to 2500 nm spectral region, by a double-beam UV/Vis/NIR spectrophotometer (Perkin-Elmer, model Lambda-750).


## 2.1. Material Synthesis and Characterization

The chalcogenide materialsPb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
at
.
%
)  are prepared by the melt quenching technique. Granules of Pb and powder of Sn, Ge, and Se having 99.999% purity are used. The material is then sealed in evacuated (~10−5 Torr) quartz ampoule (length ~15 cm and internal diameter ~8 mm). The ampoules containing material are heated to 1000°C and held at that temperature for 10 hours. The temperature of the furnace is raised slowly at a rate of 3-4°C per minute. During heating, the ampoule is constantly rocked. The obtained melt is quenched in ice cool water. The nature of the material is ascertained by powder X-ray diffraction technique. For this, X-ray diffraction (XRD) patterns of sample are taken at room temperature by using an X-ray diffractometer PANalytical X’pert Pro (PW 3050/60, Cu
K
α
1
λ
=
1.54
Å) shown in Figure 1.Figure 1
X-ray diffractograms of the chalcogenide glassPb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
).The thermal behavior of the material has been studied using differential scanning calorimetry (DSC) under nonisothermal conditions using DSC instrument Mettler Star SW 9.01 model. Approximately 15–20 mg quantity of each powdered sample is used for DSC analysis. Each sample is heated at different heating rates 10, 15, 20, and 25°k/minute. We have found that material’s samples atx
=
11,12 have double crystallization peaks which are due to the phase separation in the material. We have annealed the bulk sample x
=
11 at temperatures 507 K and 550 K for 3 hours to detect the phases separated in the material. Then XRDs of samples have been taken. Figure 4 shows the XRD patterns of the annealed samples (
x
=
11
). To find out the band gap and other optical constants, thin films of chalcogenide glasses have been deposited by vacuum evaporation technique on thoroughly cleaned microscope glass substrate. The room-temperature optical transmission and absorption spectra (not shown here) at normal incidence, of the samples, are recorded over the 200 nm to 2500 nm spectral region, by a double-beam UV/Vis/NIR spectrophotometer (Perkin-Elmer, model Lambda-750).


## 3. Results and Discussions

### 3.1. Structural and Thermal Analysis

XRD diffractograms of thePb
9
Se
71
Ge
20
-
x
Sn
x  (
x
=
8,9
,
10,11,12
at
.
%
) compositions are shown in Figure 1 which confirm the amorphous nature of material. In the diffractograms of glasses there are two types of halos, one big halo in 2
θ range 25°–35°, confirming the polymeric nature and the short range order of the material and appearing predominately in all the diffractograms. The second small halo is between 45° and 55°; this halo appears slightly at x
=
10 but appears significantly for samples x
=
11,12. That is because of partial phase separation in the material caused due to increasing concentration of Sn in the material.When the material is heated under nonisothermal conditions at constant heating rate in DSC experiment, glass undergoes the structural variations and crystallizes. The variation of glass transition temperature, crystallization temperature, with varying Sn concentration can be studied by comparing the DSC thermograms of all samples at the same heating rate. Figure2 shows the DSC thermograms of Pb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
at
.
%
) material at a heating rate of 10 K min−1. To know the thermodynamics of the material such as phase transformation, activation energy of glass transition, and crystallization, each sample is heated at four different heating rates. Figure 3 shows the DSC thermograms of x
=
12 at different heating rates. Similar variation in the thermograms of other samples has been observed at different heating rates.Figure 2
DSC thermograms of the samples at heating rate of 10 K/min.Figure 3
DSC thermograms ofPb
9
Se
71
Ge
8
Sn
12 at different heating rate.X-ray diffractograms of samplePb
9
Se
71
Ge
9
Sn
11 annealed at (a) 550 K and (b) 507 K.
(a)
(b)The glass up to atomic percentagex
=
10 of Sn shows the single crystallization peak and at x
=
11,12 shows the double crystallization peaks. This appearance of double crystallization is because of partial phase separation in material. Phase separation is the unmixing of the initially homogeneous multicomponent material in to two or more amorphous phases. The driving potential for unmixing process is the reduction in the system free energy. Phase separation occurs when the free energy of another phase or polyphase is less than that of initially homogeneous single phase composition. In order to identify the phases in material, the initial glassy sample Pb9Se71Ge9Sn11 is annealed at 507 K and 550 K for 3hours, which lies before the primary and secondary crystallization, respectively. The annealed samples are then passed through XRD.Figure4 shows the XRD patterns of the annealed samples. After annealing the samples for 3 hours, we have observed the two major phases SnSe2 and GeSe2 and minor phase PbSe as marked in XRD diffractograms. GeSe2 has monoclinic structure and lattice parameters a
=
7.231
Å,  b
=
16.748
Å, and  c
=
11.79
Å [JCPDS file card no. 30-0595]. The SnSe2 structure is formed in such a way that Sn layer is sandwiched between the two Se layers facing towards each other. The SnSe2 has the hexagonal structure having a
=
3.84
Å,  b
=
1.61
Å, and c
=
6.18
Å [JCPDS file card no. 38-1055] and Pb-Se phase has the cubic structure whose lattice parameter is a
=
6.089
Å. When the sample is annealed at temperature 550 K, mainly GeSe2 phase remains and other phases reduce to a large extent.On the basis of chemical bond approach [16], with increase of Sn content, glass transition temperature decreases because Ge-Se bonds are replaced by the Sn-Se bonds. From Figure 4 it is clear that glass at x
=
11,12 has been phase separated into two main phases, one Ge-rich and the other Sn-rich. The higher and lower T
c may be due to Ge-rich and Sn-rich phase, respectively.


### 3.2. Kinetics of Phase Transformations

#### 3.2.1. Glass Transition Region

The variations of glass transition temperature, activation energy of glass transition (E
g) with composition have been studied. The dependence of T
g on heating rate (α) is hereby discussed on the basis of two approaches. The first approach is the empirical relation suggested by Lasocka [17]:
(1)
T
g
=
A
+
B
ln
⁡
⁡
α
,
where A and B are constants for a given glass composition. The value of A indicates the glass transition temperature for the heating rate of 1 K min−1, while the value of B determines the time response of configurational changes within the glass transition region to the heating rate, shown in Table 1. This equation is found to hold well for all samples. Figure 5 depicts the plots of T
g versus ln
⁡
(
α
) for the investigated Pb
9
Se
71
Ge
20
-
x
Sn
x glassy system.Table 1
The values of glass transition temperature,A and B constants from Lasocka formulation, and activation energy of samples by Kissinger and Moynihan approach.
x
T
g
Lasocka approach
Kissinger
Moynihan
A
B (min)
E
g
(kJ/mol)
E
g (kJ/mol)
8
426.34
412.920
5.700
254.062
261.183
9
425.72
413.505
4.918
224.536
231.656
10
423.72
413.840
4.212
338.300
345.364
11
421.21
411.550
4.034
314.118
321.182
12
419.10
407.556
4.918
285.947
293.011Figure 5
Plot ofln
⁡
α against  T
g.The second approach Kissinger equation shows the dependence ofT
g on heating rate [18, 19]. This equation is used to find out the activation energy of glass transition. Kissinger equation is basically used to find activation energy of crystallization process; it can also be used for the determination of the activation energy of glass transition using the peak glass transition temperatures under nonisothermal conditions, if similar shift observed in the glass transition peaks and crystallization peaks with heating rate. As thermal mechanism varies with temperature, the position of peaks also varies with the heating rate. This temperature shift, in turn, can be used for the determination of kinetic parameters of crystallization [20]. Hence Kissinger equation relating the peak glass transition temperature and heating rate is given by
(2)
ln
⁡
(
α
T
g
2
)
=
-
E
g
R
T
g
+
constant
,
where T
g is the peak glass transition temperature and R is the gas constant.A graph is plotted betweenln
⁡
(
α
/
T
g
2
) and 1000/T
g shown in Figure 6, which yields a straight line. The slope (
-
E
g
/
R
) of the straight line gives the activation energy of glass transition. The one more approach used for calculation of activation energy of glass transition is Moynihan’s relation [21] Moynihan has found in his derivation of the dependence of T
g on heating rate |
α
|. Accordingly for a given heating rate
(3)
d
ln
⁡
|
α
|
d
(
1
/
T
g
)
≈
-
E
g
R
.
Plots of ln α against 1000/T
g are plotted for various glassy alloys shown in Figure 7. The values of activation energies found by Kissinger and Moynihan approaches are tabulated in Table 2.Table 2
The values of activation energies of crystallization calculated by Kissinger and Augis and Bennett approaches.
x
Activation energies of crystallization (KJ/mol)
Kissinger
Augis and Bennett
Peak 1
Peak 2
Peak 1
Peak 2
8
205.074
209.794
9
249.723
254.394
10
118.924
126.432
11
204.919
313.630
211.39
324.525
12
173.512
189.093
178.315
196.375Figure 6
Plot betweenln
⁡
(
α
/
T
g
2
) and 1000/T
g from Kissinger equation.Figure 7
Plots of lnα against 1000/T
g glassy alloys from Moynihan equation.Activation energy of glass transition decreases asx varies from 8 to 9. This is due to entrance of Sn in Pb-Se-Ge network, which weakens the network and decrease the activation energy of glass transition. Thenafter at x
=
10 this activation energy increases which might be due to replacement of Se-Se bonds by Sn-Se bonds (having large bond energy). The further addition of Sn to the glass matrix replaces mostly the Ge-Se bonds by Sn-Se bonds. So it results in decrease in cohesive energy and mean bond energy of the glassy matrix as well as the activation energy of glass transition.


#### 3.2.2. Activation Energy of Crystallization

For the determination of crystallization kinetics, the established Kissinger and Augis-Bennett models are applied.(a) Kissinger Model. The activation energy for crystallization, E
c, can be obtained from the dependence of peak crystallization temperature T
p on heating rate, using the equation derived by Kissinger [18, 19]:
(4)
ln
⁡
(
α
T
p
2
)
=
-
E
c
R
T
p
+
constant
.
The plot of ln
⁡
(
α
/
T
p
2
) versus 1000/T
p is shown in Figure 8. The activation energy of crystallization is calculated from slope of the straight lines in Figure 8 and tabulated in Table 3.Table 3
Values of refractive index (n), extinction coefficient (k), optical energy gap (E
g
opt), and real part (ε
r) and imaginary part (ε
i) of dielectric constant.
x
n
k
E
g
opt(eV)
ε
i
ε
r
8
2.21
0.0185
2.76
0.0817
4.8837
9
2.94
0.0219
2.71
0.1287
8.6431
10
3.19
0.0384
2.62
0.2449
10.1746
11
3.58
0.0515
2.56
0.3687
12.8137
12
3.71
0.0606
2.48
0.4496
13.7604Figure 8
The plot ofln
⁡
(
α
/
T
p
2
) versus 1000/T
p for Kissinger approach.(b) Augis and Bennett Method. The activation energy for crystallization, E
c, can be evaluated using the formula suggested by Augis and Bennett [22] which is given as follows:
(5)
ln
⁡
(
α
T
p
)
=
-
(
E
c
R
T
p
)
+
constant
.
The plot of ln
⁡
(
α
/
T
p
) versus 1000/T
p is shown in Figure 9. The calculated activation energies of crystallization are tabulated in Table 3.Figure 9
The plot ofln
⁡
(
α
/
T
p
) versus 1000/T
p for Augis and Bennett approach.The addition of Sn causes the structural disorder in the glassy  matrix; beyondx
=
10 phase separation in the material has been found. Mainly two phases GeSe2 and SnSe2 appear in the material which causes phase splitting and double crystallization peaks. The peak at high crystallization temperature is due to GeSe2 phase and at lower temperature due to SnSe2 phase. We analyze from Table 2 that activation energies obtained from Augis and Bennett method is approximately around the activation energies obtained from the Kissinger’s approach. However, this slight difference in the activation energies obtained by these approaches may be attributed to the different formalism of the equations in these models based on approximations. The addition of Sn has caused the structural disorder or configurational changes in the material. Beyond x
=
10 phase separation in the material has been observed. The double crystallization peaks in the material are due to phase splitting into two amorphous phases GeSe2 and SnSe2. In double crystallization peaks, the high crystallization temperature peak is due to Ge-rich phase and peak at lower crystallization temperature is due to Sn-rich phase.


### 3.3. Optical and Dielectric Parameters

Generally the optical band gap and refractive index (n) are the basic parameters to know the material’s optical behavior. The refractive index changes under the influence of light. The optical constants are calculated using Swanepoel’s method. According to Swanepoel’s method [23, 24], the value of the refractive index of film in the spectral region of medium and weak absorption can be calculated by the expression
(6)
n
=
[
N
+
(
N
2
-
s
2
)
1
/
2
]
1
/
2
,
where
(7)
N
=
2
s
T
M
-
T
m
T
M
T
m
+
s
2
+
1
2
,
where T
M and T
m are the transmission maximum and the corresponding minimum at a certain wavelength λ. The transmission spectra of material are shown in Figure 10.Figure 10
The transmission spectrum and variation of extinction coefficient with wavelength of chalcogenide glass thin films ofPb
9
Se
71
Ge
20
-
x
Sn
x.The spectra forx
=
8 is different than that for others. This might be due to some foreign element introduction at the time of bulk or thin film preparation; this has created some compositional disorder in material. The value of extinction coefficient (k) has been calculated using the relation
(8)
k
=
α
λ
4
π
,
where α  is the absorption coefficient [24] and is given by
(9)
α
=
1
d
ln
⁡
(
1
x
)
,
where x is the absorbance. The variations of the extinction coefficient with the wavelength are shown in Figure 10 inset.The optical absorption spectrum is the important tool for studying the band gap of materials. The absorption coefficient of an amorphous semiconductor in the high absorption region can be calculated by using Tauc’s relation [25] α
h
ν
=
B
(
h
ν
-
E
g
opt
)
m where B is a constant, E
g
opt is the optical energy gap of the material, and m determines the type of transition (m
=
1
/
2 for the direct transition and m
=
2 for the indirect allowed transition).The values of the optical energy gap(
E
g
opt
) obtained for indirect allowed transition for thin films of Pb
9
Se
71
Ge
20
-
x
Sn
x by making (
α
h
ν
)
0.5
→
0 are given in Table 3 and shown in Figure 11. The optical parameters refractive index (n) and extinction coefficient k have the compositional dependence as both increase with increasing Sn content. In covalent solids, variation in charge density results change in bond polarizability and hence permittivity; this variation alters the refractive index and the extinction coefficient of the material [26]. Optical constants (
n
,
k
) in anisotropic media depend on electronic polarization of atoms, ions, or molecules of the material when subjected to an electric field. The polarization does not respond instantly to an applied field and results in dielectric loss expressed as permittivity (
ε
), which is complex and frequency dependent and is given as ε
=
ε
r
+
i
ε
i, where (
ε
r
) and (
ε
i
) are real and imaginary parts of permittivity, respectively. The complex dielectric constant is a fundamental intrinsic property of material. The real (
ε
r
) and imaginary (
ε
i
) parts of the dielectric constant of thin films were also calculated by using the value of n and k in the following relations [27]:
(10)
ε
r
=
n
2
-
k
2
,
(11)
ε
i
=
2
n
k
.
It is evident from Table 3 that the values of ε
r and ε
i increase on incorporating Sn into the Pb-Se-Ge system. Sn may cause the more defect states in the chalcogenide glasses. These defect states in turn can increase the density of localized states which reduces the optical band gap.Figure 11
Plots of(
α
h
ν
)
0.5 versus (h
ν) for thin films of Pb
9
Se
71
Ge
20
-
x
Sn
x.


## 3.1. Structural and Thermal Analysis

XRD diffractograms of thePb
9
Se
71
Ge
20
-
x
Sn
x  (
x
=
8,9
,
10,11,12
at
.
%
) compositions are shown in Figure 1 which confirm the amorphous nature of material. In the diffractograms of glasses there are two types of halos, one big halo in 2
θ range 25°–35°, confirming the polymeric nature and the short range order of the material and appearing predominately in all the diffractograms. The second small halo is between 45° and 55°; this halo appears slightly at x
=
10 but appears significantly for samples x
=
11,12. That is because of partial phase separation in the material caused due to increasing concentration of Sn in the material.When the material is heated under nonisothermal conditions at constant heating rate in DSC experiment, glass undergoes the structural variations and crystallizes. The variation of glass transition temperature, crystallization temperature, with varying Sn concentration can be studied by comparing the DSC thermograms of all samples at the same heating rate. Figure2 shows the DSC thermograms of Pb
9
Se
71
Ge
20
-
x
Sn
x  (
8
≤
x
≤
12
at
.
%
) material at a heating rate of 10 K min−1. To know the thermodynamics of the material such as phase transformation, activation energy of glass transition, and crystallization, each sample is heated at four different heating rates. Figure 3 shows the DSC thermograms of x
=
12 at different heating rates. Similar variation in the thermograms of other samples has been observed at different heating rates.Figure 2
DSC thermograms of the samples at heating rate of 10 K/min.Figure 3
DSC thermograms ofPb
9
Se
71
Ge
8
Sn
12 at different heating rate.X-ray diffractograms of samplePb
9
Se
71
Ge
9
Sn
11 annealed at (a) 550 K and (b) 507 K.
(a)
(b)The glass up to atomic percentagex
=
10 of Sn shows the single crystallization peak and at x
=
11,12 shows the double crystallization peaks. This appearance of double crystallization is because of partial phase separation in material. Phase separation is the unmixing of the initially homogeneous multicomponent material in to two or more amorphous phases. The driving potential for unmixing process is the reduction in the system free energy. Phase separation occurs when the free energy of another phase or polyphase is less than that of initially homogeneous single phase composition. In order to identify the phases in material, the initial glassy sample Pb9Se71Ge9Sn11 is annealed at 507 K and 550 K for 3hours, which lies before the primary and secondary crystallization, respectively. The annealed samples are then passed through XRD.Figure4 shows the XRD patterns of the annealed samples. After annealing the samples for 3 hours, we have observed the two major phases SnSe2 and GeSe2 and minor phase PbSe as marked in XRD diffractograms. GeSe2 has monoclinic structure and lattice parameters a
=
7.231
Å,  b
=
16.748
Å, and  c
=
11.79
Å [JCPDS file card no. 30-0595]. The SnSe2 structure is formed in such a way that Sn layer is sandwiched between the two Se layers facing towards each other. The SnSe2 has the hexagonal structure having a
=
3.84
Å,  b
=
1.61
Å, and c
=
6.18
Å [JCPDS file card no. 38-1055] and Pb-Se phase has the cubic structure whose lattice parameter is a
=
6.089
Å. When the sample is annealed at temperature 550 K, mainly GeSe2 phase remains and other phases reduce to a large extent.On the basis of chemical bond approach [16], with increase of Sn content, glass transition temperature decreases because Ge-Se bonds are replaced by the Sn-Se bonds. From Figure 4 it is clear that glass at x
=
11,12 has been phase separated into two main phases, one Ge-rich and the other Sn-rich. The higher and lower T
c may be due to Ge-rich and Sn-rich phase, respectively.


## 3.2. Kinetics of Phase Transformations

### 3.2.1. Glass Transition Region

The variations of glass transition temperature, activation energy of glass transition (E
g) with composition have been studied. The dependence of T
g on heating rate (α) is hereby discussed on the basis of two approaches. The first approach is the empirical relation suggested by Lasocka [17]:
(1)
T
g
=
A
+
B
ln
⁡
⁡
α
,
where A and B are constants for a given glass composition. The value of A indicates the glass transition temperature for the heating rate of 1 K min−1, while the value of B determines the time response of configurational changes within the glass transition region to the heating rate, shown in Table 1. This equation is found to hold well for all samples. Figure 5 depicts the plots of T
g versus ln
⁡
(
α
) for the investigated Pb
9
Se
71
Ge
20
-
x
Sn
x glassy system.Table 1
The values of glass transition temperature,A and B constants from Lasocka formulation, and activation energy of samples by Kissinger and Moynihan approach.
x
T
g
Lasocka approach
Kissinger
Moynihan
A
B (min)
E
g
(kJ/mol)
E
g (kJ/mol)
8
426.34
412.920
5.700
254.062
261.183
9
425.72
413.505
4.918
224.536
231.656
10
423.72
413.840
4.212
338.300
345.364
11
421.21
411.550
4.034
314.118
321.182
12
419.10
407.556
4.918
285.947
293.011Figure 5
Plot ofln
⁡
α against  T
g.The second approach Kissinger equation shows the dependence ofT
g on heating rate [18, 19]. This equation is used to find out the activation energy of glass transition. Kissinger equation is basically used to find activation energy of crystallization process; it can also be used for the determination of the activation energy of glass transition using the peak glass transition temperatures under nonisothermal conditions, if similar shift observed in the glass transition peaks and crystallization peaks with heating rate. As thermal mechanism varies with temperature, the position of peaks also varies with the heating rate. This temperature shift, in turn, can be used for the determination of kinetic parameters of crystallization [20]. Hence Kissinger equation relating the peak glass transition temperature and heating rate is given by
(2)
ln
⁡
(
α
T
g
2
)
=
-
E
g
R
T
g
+
constant
,
where T
g is the peak glass transition temperature and R is the gas constant.A graph is plotted betweenln
⁡
(
α
/
T
g
2
) and 1000/T
g shown in Figure 6, which yields a straight line. The slope (
-
E
g
/
R
) of the straight line gives the activation energy of glass transition. The one more approach used for calculation of activation energy of glass transition is Moynihan’s relation [21] Moynihan has found in his derivation of the dependence of T
g on heating rate |
α
|. Accordingly for a given heating rate
(3)
d
ln
⁡
|
α
|
d
(
1
/
T
g
)
≈
-
E
g
R
.
Plots of ln α against 1000/T
g are plotted for various glassy alloys shown in Figure 7. The values of activation energies found by Kissinger and Moynihan approaches are tabulated in Table 2.Table 2
The values of activation energies of crystallization calculated by Kissinger and Augis and Bennett approaches.
x
Activation energies of crystallization (KJ/mol)
Kissinger
Augis and Bennett
Peak 1
Peak 2
Peak 1
Peak 2
8
205.074
209.794
9
249.723
254.394
10
118.924
126.432
11
204.919
313.630
211.39
324.525
12
173.512
189.093
178.315
196.375Figure 6
Plot betweenln
⁡
(
α
/
T
g
2
) and 1000/T
g from Kissinger equation.Figure 7
Plots of lnα against 1000/T
g glassy alloys from Moynihan equation.Activation energy of glass transition decreases asx varies from 8 to 9. This is due to entrance of Sn in Pb-Se-Ge network, which weakens the network and decrease the activation energy of glass transition. Thenafter at x
=
10 this activation energy increases which might be due to replacement of Se-Se bonds by Sn-Se bonds (having large bond energy). The further addition of Sn to the glass matrix replaces mostly the Ge-Se bonds by Sn-Se bonds. So it results in decrease in cohesive energy and mean bond energy of the glassy matrix as well as the activation energy of glass transition.


### 3.2.2. Activation Energy of Crystallization

For the determination of crystallization kinetics, the established Kissinger and Augis-Bennett models are applied.(a) Kissinger Model. The activation energy for crystallization, E
c, can be obtained from the dependence of peak crystallization temperature T
p on heating rate, using the equation derived by Kissinger [18, 19]:
(4)
ln
⁡
(
α
T
p
2
)
=
-
E
c
R
T
p
+
constant
.
The plot of ln
⁡
(
α
/
T
p
2
) versus 1000/T
p is shown in Figure 8. The activation energy of crystallization is calculated from slope of the straight lines in Figure 8 and tabulated in Table 3.Table 3
Values of refractive index (n), extinction coefficient (k), optical energy gap (E
g
opt), and real part (ε
r) and imaginary part (ε
i) of dielectric constant.
x
n
k
E
g
opt(eV)
ε
i
ε
r
8
2.21
0.0185
2.76
0.0817
4.8837
9
2.94
0.0219
2.71
0.1287
8.6431
10
3.19
0.0384
2.62
0.2449
10.1746
11
3.58
0.0515
2.56
0.3687
12.8137
12
3.71
0.0606
2.48
0.4496
13.7604Figure 8
The plot ofln
⁡
(
α
/
T
p
2
) versus 1000/T
p for Kissinger approach.(b) Augis and Bennett Method. The activation energy for crystallization, E
c, can be evaluated using the formula suggested by Augis and Bennett [22] which is given as follows:
(5)
ln
⁡
(
α
T
p
)
=
-
(
E
c
R
T
p
)
+
constant
.
The plot of ln
⁡
(
α
/
T
p
) versus 1000/T
p is shown in Figure 9. The calculated activation energies of crystallization are tabulated in Table 3.Figure 9
The plot ofln
⁡
(
α
/
T
p
) versus 1000/T
p for Augis and Bennett approach.The addition of Sn causes the structural disorder in the glassy  matrix; beyondx
=
10 phase separation in the material has been found. Mainly two phases GeSe2 and SnSe2 appear in the material which causes phase splitting and double crystallization peaks. The peak at high crystallization temperature is due to GeSe2 phase and at lower temperature due to SnSe2 phase. We analyze from Table 2 that activation energies obtained from Augis and Bennett method is approximately around the activation energies obtained from the Kissinger’s approach. However, this slight difference in the activation energies obtained by these approaches may be attributed to the different formalism of the equations in these models based on approximations. The addition of Sn has caused the structural disorder or configurational changes in the material. Beyond x
=
10 phase separation in the material has been observed. The double crystallization peaks in the material are due to phase splitting into two amorphous phases GeSe2 and SnSe2. In double crystallization peaks, the high crystallization temperature peak is due to Ge-rich phase and peak at lower crystallization temperature is due to Sn-rich phase.


## 3.2.1. Glass Transition Region

The variations of glass transition temperature, activation energy of glass transition (E
g) with composition have been studied. The dependence of T
g on heating rate (α) is hereby discussed on the basis of two approaches. The first approach is the empirical relation suggested by Lasocka [17]:
(1)
T
g
=
A
+
B
ln
⁡
⁡
α
,
where A and B are constants for a given glass composition. The value of A indicates the glass transition temperature for the heating rate of 1 K min−1, while the value of B determines the time response of configurational changes within the glass transition region to the heating rate, shown in Table 1. This equation is found to hold well for all samples. Figure 5 depicts the plots of T
g versus ln
⁡
(
α
) for the investigated Pb
9
Se
71
Ge
20
-
x
Sn
x glassy system.Table 1
The values of glass transition temperature,A and B constants from Lasocka formulation, and activation energy of samples by Kissinger and Moynihan approach.
x
T
g
Lasocka approach
Kissinger
Moynihan
A
B (min)
E
g
(kJ/mol)
E
g (kJ/mol)
8
426.34
412.920
5.700
254.062
261.183
9
425.72
413.505
4.918
224.536
231.656
10
423.72
413.840
4.212
338.300
345.364
11
421.21
411.550
4.034
314.118
321.182
12
419.10
407.556
4.918
285.947
293.011Figure 5
Plot ofln
⁡
α against  T
g.The second approach Kissinger equation shows the dependence ofT
g on heating rate [18, 19]. This equation is used to find out the activation energy of glass transition. Kissinger equation is basically used to find activation energy of crystallization process; it can also be used for the determination of the activation energy of glass transition using the peak glass transition temperatures under nonisothermal conditions, if similar shift observed in the glass transition peaks and crystallization peaks with heating rate. As thermal mechanism varies with temperature, the position of peaks also varies with the heating rate. This temperature shift, in turn, can be used for the determination of kinetic parameters of crystallization [20]. Hence Kissinger equation relating the peak glass transition temperature and heating rate is given by
(2)
ln
⁡
(
α
T
g
2
)
=
-
E
g
R
T
g
+
constant
,
where T
g is the peak glass transition temperature and R is the gas constant.A graph is plotted betweenln
⁡
(
α
/
T
g
2
) and 1000/T
g shown in Figure 6, which yields a straight line. The slope (
-
E
g
/
R
) of the straight line gives the activation energy of glass transition. The one more approach used for calculation of activation energy of glass transition is Moynihan’s relation [21] Moynihan has found in his derivation of the dependence of T
g on heating rate |
α
|. Accordingly for a given heating rate
(3)
d
ln
⁡
|
α
|
d
(
1
/
T
g
)
≈
-
E
g
R
.
Plots of ln α against 1000/T
g are plotted for various glassy alloys shown in Figure 7. The values of activation energies found by Kissinger and Moynihan approaches are tabulated in Table 2.Table 2
The values of activation energies of crystallization calculated by Kissinger and Augis and Bennett approaches.
x
Activation energies of crystallization (KJ/mol)
Kissinger
Augis and Bennett
Peak 1
Peak 2
Peak 1
Peak 2
8
205.074
209.794
9
249.723
254.394
10
118.924
126.432
11
204.919
313.630
211.39
324.525
12
173.512
189.093
178.315
196.375Figure 6
Plot betweenln
⁡
(
α
/
T
g
2
) and 1000/T
g from Kissinger equation.Figure 7
Plots of lnα against 1000/T
g glassy alloys from Moynihan equation.Activation energy of glass transition decreases asx varies from 8 to 9. This is due to entrance of Sn in Pb-Se-Ge network, which weakens the network and decrease the activation energy of glass transition. Thenafter at x
=
10 this activation energy increases which might be due to replacement of Se-Se bonds by Sn-Se bonds (having large bond energy). The further addition of Sn to the glass matrix replaces mostly the Ge-Se bonds by Sn-Se bonds. So it results in decrease in cohesive energy and mean bond energy of the glassy matrix as well as the activation energy of glass transition.


## 3.2.2. Activation Energy of Crystallization

For the determination of crystallization kinetics, the established Kissinger and Augis-Bennett models are applied.(a) Kissinger Model. The activation energy for crystallization, E
c, can be obtained from the dependence of peak crystallization temperature T
p on heating rate, using the equation derived by Kissinger [18, 19]:
(4)
ln
⁡
(
α
T
p
2
)
=
-
E
c
R
T
p
+
constant
.
The plot of ln
⁡
(
α
/
T
p
2
) versus 1000/T
p is shown in Figure 8. The activation energy of crystallization is calculated from slope of the straight lines in Figure 8 and tabulated in Table 3.Table 3
Values of refractive index (n), extinction coefficient (k), optical energy gap (E
g
opt), and real part (ε
r) and imaginary part (ε
i) of dielectric constant.
x
n
k
E
g
opt(eV)
ε
i
ε
r
8
2.21
0.0185
2.76
0.0817
4.8837
9
2.94
0.0219
2.71
0.1287
8.6431
10
3.19
0.0384
2.62
0.2449
10.1746
11
3.58
0.0515
2.56
0.3687
12.8137
12
3.71
0.0606
2.48
0.4496
13.7604Figure 8
The plot ofln
⁡
(
α
/
T
p
2
) versus 1000/T
p for Kissinger approach.(b) Augis and Bennett Method. The activation energy for crystallization, E
c, can be evaluated using the formula suggested by Augis and Bennett [22] which is given as follows:
(5)
ln
⁡
(
α
T
p
)
=
-
(
E
c
R
T
p
)
+
constant
.
The plot of ln
⁡
(
α
/
T
p
) versus 1000/T
p is shown in Figure 9. The calculated activation energies of crystallization are tabulated in Table 3.Figure 9
The plot ofln
⁡
(
α
/
T
p
) versus 1000/T
p for Augis and Bennett approach.The addition of Sn causes the structural disorder in the glassy  matrix; beyondx
=
10 phase separation in the material has been found. Mainly two phases GeSe2 and SnSe2 appear in the material which causes phase splitting and double crystallization peaks. The peak at high crystallization temperature is due to GeSe2 phase and at lower temperature due to SnSe2 phase. We analyze from Table 2 that activation energies obtained from Augis and Bennett method is approximately around the activation energies obtained from the Kissinger’s approach. However, this slight difference in the activation energies obtained by these approaches may be attributed to the different formalism of the equations in these models based on approximations. The addition of Sn has caused the structural disorder or configurational changes in the material. Beyond x
=
10 phase separation in the material has been observed. The double crystallization peaks in the material are due to phase splitting into two amorphous phases GeSe2 and SnSe2. In double crystallization peaks, the high crystallization temperature peak is due to Ge-rich phase and peak at lower crystallization temperature is due to Sn-rich phase.


## 3.3. Optical and Dielectric Parameters

Generally the optical band gap and refractive index (n) are the basic parameters to know the material’s optical behavior. The refractive index changes under the influence of light. The optical constants are calculated using Swanepoel’s method. According to Swanepoel’s method [23, 24], the value of the refractive index of film in the spectral region of medium and weak absorption can be calculated by the expression
(6)
n
=
[
N
+
(
N
2
-
s
2
)
1
/
2
]
1
/
2
,
where
(7)
N
=
2
s
T
M
-
T
m
T
M
T
m
+
s
2
+
1
2
,
where T
M and T
m are the transmission maximum and the corresponding minimum at a certain wavelength λ. The transmission spectra of material are shown in Figure 10.Figure 10
The transmission spectrum and variation of extinction coefficient with wavelength of chalcogenide glass thin films ofPb
9
Se
71
Ge
20
-
x
Sn
x.The spectra forx
=
8 is different than that for others. This might be due to some foreign element introduction at the time of bulk or thin film preparation; this has created some compositional disorder in material. The value of extinction coefficient (k) has been calculated using the relation
(8)
k
=
α
λ
4
π
,
where α  is the absorption coefficient [24] and is given by
(9)
α
=
1
d
ln
⁡
(
1
x
)
,
where x is the absorbance. The variations of the extinction coefficient with the wavelength are shown in Figure 10 inset.The optical absorption spectrum is the important tool for studying the band gap of materials. The absorption coefficient of an amorphous semiconductor in the high absorption region can be calculated by using Tauc’s relation [25] α
h
ν
=
B
(
h
ν
-
E
g
opt
)
m where B is a constant, E
g
opt is the optical energy gap of the material, and m determines the type of transition (m
=
1
/
2 for the direct transition and m
=
2 for the indirect allowed transition).The values of the optical energy gap(
E
g
opt
) obtained for indirect allowed transition for thin films of Pb
9
Se
71
Ge
20
-
x
Sn
x by making (
α
h
ν
)
0.5
→
0 are given in Table 3 and shown in Figure 11. The optical parameters refractive index (n) and extinction coefficient k have the compositional dependence as both increase with increasing Sn content. In covalent solids, variation in charge density results change in bond polarizability and hence permittivity; this variation alters the refractive index and the extinction coefficient of the material [26]. Optical constants (
n
,
k
) in anisotropic media depend on electronic polarization of atoms, ions, or molecules of the material when subjected to an electric field. The polarization does not respond instantly to an applied field and results in dielectric loss expressed as permittivity (
ε
), which is complex and frequency dependent and is given as ε
=
ε
r
+
i
ε
i, where (
ε
r
) and (
ε
i
) are real and imaginary parts of permittivity, respectively. The complex dielectric constant is a fundamental intrinsic property of material. The real (
ε
r
) and imaginary (
ε
i
) parts of the dielectric constant of thin films were also calculated by using the value of n and k in the following relations [27]:
(10)
ε
r
=
n
2
-
k
2
,
(11)
ε
i
=
2
n
k
.
It is evident from Table 3 that the values of ε
r and ε
i increase on incorporating Sn into the Pb-Se-Ge system. Sn may cause the more defect states in the chalcogenide glasses. These defect states in turn can increase the density of localized states which reduces the optical band gap.Figure 11
Plots of(
α
h
ν
)
0.5 versus (h
ν) for thin films of Pb
9
Se
71
Ge
20
-
x
Sn
x.


## 4. Conclusion

The thermal and optical properties of thePb-Ge-Se system have been greatly influenced by Sn addition. The phase transformation kinetics of Pb
9
Se
71
Ge
20
-
x
Sn
x glasses has been studied using Kissinger, Moynihan, and Augis approaches. The glassy alloys under investigation (except x
=
11,12) show a single glass transition and crystallization region, confirming the homogeneity of the samples. Samples (
x
=
11,12
) show a single glass transition and double crystallization peaks corresponding to SnSe2 and GeSe2 rich phases. It is observed that glass transition temperature decreases with increasing Sn concentration. The glassy material has high value of refractive index and decreasing optical band gap with increasing content of Sn in the glassy matrix.



---

*Source: 318262-2014-03-27.xml*