Thermodynamics of glass/crystal transformation in Se58Ge 42-xPbx (9 ≤ x ≤ 20) glasses

Article abstract of DOI:10.1021/jp9066845

This article reports the thermodynamics of Se₅₈Ge _42-xPb_x (9 ≤ x ≤ 20) glassy alloys determined from the heat of fusion and specific heat capacity measurements. A differential scanning calorimetry method has been employed for the determination of thermodynamic quantities such as entropy, enthalpy, and Gibbs free energy differences between the glassy and crystalline phase of these alloys as a function of temperature. An effort has also been made to determine the stability of these glasses using the data obtained from different thermodynamic quantities. This study reveals that stability of the samples increases with the increase of lead (Pb) content in the glassy alloys.

Full text of DOI:10.1021/jp9066845

28
J. Phys. Chem. B 2010, 114, 28–35
Thermodynamics of Glass/Crystal Transformation in Se58Ge42-xPbx (9 e x e 20) Glasses
Deepika* and Narendra S. Saxena
Semi-conductor & Polymer Science Laboratory, 5-6, Vigyan Bhawan, UniVersity of Rajasthan,
Jaipur - 302004, India
ReceiVed: July 15, 2009; ReVised Manuscript ReceiVed: October 2, 2009
This article reports the thermodynamics of Se58Ge42-xPbx (9 e x e 20) glassy alloys determined from the
heat of fusion and specific heat capacity measurements. A differential scanning calorimetry method has been
employed for the determination of thermodynamic quantities such as entropy, enthalpy, and Gibbs free energy
differences between the glassy and crystalline phase of these alloys as a function of temperature. An effort
has also been made to determine the stability of these glasses using the data obtained from different
thermodynamic quantities. This study reveals that stability of the samples increases with the increase of lead
(Pb) content in the glassy alloys.
Introduction
metallic glasses has been studied by Isabella Gallino et al. They
investigated that the residual enthalpy of frozen-in glass is found
to relax with stretching exponents approaching unity, which
indicates rather strong glass behavior, reflected also by the high
value of the fragility parameter and the small driving force of
crystallization.3 Jean A. Tangeman et al. have studied the
thermodynamics and structure of single- and two-phase
yttria-alumina glasses. Various quantities like heat capacities
(Cp) of the glasses and supercooled liquids, glass transition
temperatures (Tg), configurational heat capacities at Tg (Cp(Tg)),
and glass structures were investigated using differential scanning
calorimetry (DSC) and 27Al MAS NMR spectroscopy. It was
found that the Tg increases slightly with alumina content, from
1146 to 1156 K and Cp increases 60% at Tg to form a highly
fragile supercooled liquid.4 G. Shao et al. have studied the role
of thermodynamics and transformation kinetics on phase selec-
tion in the nonequilibrium processing of materials. They
demonstrated that the microstructural development of materials
processed in nonequilibrium condition is controlled by the
inteplay between thermodynamic and transformation kinetics.5
Xiulin Ji et al. have studied the Gibbs free energy difference in
Thermodynamic properties of matter in the crystalline and
liquid state have been well investigated and known for a long
time, whereas amorphous substances and undercooled liquids
are not so well studied yet. Glasses are amorphous solids that
exhibit a more or less sudden change in the derivative
thermodynamic properties, such as heat capacity and expansion
coefficient, from crystal-like to liquid-like values.1 One of the
most significant feature of the glassy state is its deviation from
thermodynamic equilibrium. Glasses are thermodynamically
unstable relative to an (metastable) equilibrium liquid so that
they tend to approach the latter state. This process, called
stabilization, proceeds so slowly below the glass transition
region that all properties of glasses seem to be almost fixed.
To predict these transformations, when a system is driven away
from equilibrium to a nonequilibrium state, the knowledge of
thermodynamic properties of the undercooled liquid is essential.
Glass formation entails slowing down continuously the particles
in a liquid to such an extent that the structure of the liquid no
longer changes over the duration of the macroscopic experiment.
Such a situation is commonly achieved by cooling or compress-
ing so as to avoid crystallization. It is well-known that the
crystallization of glasses and undercooled melts occurs by a
heterogeneous process of nucleation and growth of crystals.
Glass transition is a phenomena that may easily be observed in
most glasses by, for instance, differential scanning calorimetry
(DSC). This is primarily due to the fact that, on heating, the
heat capacity, Cp, of a glass increases suddenly by at least about
half its original value in a very small temperature interval as
the glass changes to a liquid. Usually, a characteristic temper-
ature called glass transition temperature (Tg) is defined at the
inflection point in the Cp versus temperature curve.
metallic glass forming liquids and proposed a hyperbolic
l-s
variation of heat capacity difference of liquid and solid (∆Cp
)
with temperature.6 M. M. A Imran et al. have studied the
thermodynamic properties of ternary Se80Te20-xInx (x ) 2, 4, 6,
8, and 10) chalcogenide glasses and their experimental observa-
tions and theoretical calculation showed that Se80Te10In10 is the
most stable glass.7
In the present article, an effort has been made to determine
the stability of Se58Ge42-xPbx (9 e x e 20) glassy alloys through
the study of various thermodynamic properties like entropy,
enthalpy, and Gibbs free energy between the glassy and
crystalline state.
Some effort have been made by the researchers to study the
thermodynamics of glassy systems in the past decade. Z.
Cernosˇek et al. have studied the enthalpic relaxation of As2Se3
Experimental Methods
ˇ
Glassy alloys of Se58Ge42-xPbx (9 e x e 20) were prepared
by melt-quenching technique. High purity (99.999%) of all
constituent materials in appropriate atomic weight proportions
were weighed into a quartz ampule. The content (4 g) of the
ampule was sealed in a vacuum of 10-5 Torr. The ampules are
heated in two stages to avoid the sudden evaporation and
deposition of the selenium to the inner wall of the quartz tube.
glass and they found that enthalpies of metastable equilibria at
temperatures below glass transition temperatures are higher than
the ones obtained at the same temperatures by linear extrapola-
tion of H(T) of a supercooled liquid.2 Thermodynamics of
* To whom correspondence should be addressed. E-mail: deepika.spsl@
gmail.com.
10.1021/jp9066845  2010 American Chemical Society
Published on Web 12/10/2009

Thermodynamics of Se58Ge42-xPbx (9 e x e 20) Glasses
J. Phys. Chem. B, Vol. 114, No. 1, 2010 29
Figure 1. X-ray diffraction pattern of the as-prepared samples of
Se58Ge42-xPbx (9 e x e 20) glassy alloys.
The ampules are heated slowly and maintained at 600 °C for
about 6 h with continuous rotation. The temperature is then
subsequently raised to 900 °C and kept under constant rotation
for 30 h to facilitate the homogenization of the sample. The
molten sample was rapidly quenched in ice-cooled water to get
a glassy state. The ingot of so produced glassy sample was taken
out of the ampule by breaking the ampule and then grinded
gently in mortar and pestle to obtain powder form. The
amorphous nature of the alloy was ascertained through X-ray
diffraction pattern of the samples using Bragg-Brentanno
geometry on Panalytical X’pert Pro differactometer in 2θ range
of 20-90° with Cu KR radiation source (λ) 1.5406 Å). The
X-ray tube was operated at 45 kV and 40 mA.
Differential scanning calorimetry (DSC) Rigaku Model 8230
is used to measure the caloric manifestation of the phase
transformation under nonisothermal condition. The accuracy of
heat flow measurement is (0.01 mW and the temperature
precision as determined by the microprocessor of the thermal
analyzer is (0.1K. The DSC runs have been taken at a heating
rate of 20 K/min on accurately weighed samples taken in
aluminum pans. The temperature range covered in DSC was
from room temperature (300 K) to 753 K.
Figure 2. DSC thermograms of all the as-prepared samples at a heating
rate of 20 K/min.
TABLE 1: Values of the Characteristic Temperatures
(Tg, Tc1, Tc1, Tp1, and Tp2) of All of the Samples of
Se58Ge42-xPbx (9 e x e 20) Glassy Alloys at a Heating Rate
of 20 K/min
Tp1
Tp2 Ta
sample
Tg (K)
Tc1 (K)
(K)
Tc2 (K)
(K) (K)
Se58Ge33Pb9 522.3 ( 0.6 620.7 ( 0.9 633.7 661.3 ( 0.7 685.5 640
Se58Ge30Pb12 507.6 ( 0.8 601.6 ( 0.8 620.7 653.8 ( 0.6 696.2 643
Se58Ge27Pb15 503.1 ( 0.6 599.4 ( 0.6 614.3 674.7 ( 0.9 693.4 648
Se58Ge24Pb18 492.6 ( 0.7 556.8 ( 0.7 603.8 666.5 ( 1.0 691.1 650
Se58Ge22Pb20 478.3 ( 0.8 547.2 ( 0.9 586.8 671.3 ( 0.8 694.2 655
between the first and second crystallization peaks. These
intermediate temperatures (Ta) for all of the samples of
Se58Ge42-xPbx (9 e x e 20) glassy alloys have been given in
Table 1. The annealed samples were then subjected to XRD.
Figure 3 shows the XRD pattern of annealed samples. The XRD
pattern of annealed samples show sharp peaks at various
diffraction angles. The d values corresponding to these peaks
were matched with standard d values obtained from JCPDS card.
Results and Discussion
Structural and Thermal Analysis. Figure 1 shows the X-ray
diffraction patterns of as-prepared Se58Ge42-xPbx (9 e x e 20)
glassy alloys. The absence of any sharp peak confirms the
amorphous nature of these samples. Figure 2 shows the DSC
curves of all of the as-prepared samples at a heating rate 20
K/min as a representative case. The characteristic features of
the investigated thermal curves were as follows: first, the glassy
alloys under consideration shows an endothermic step corre-
sponding to its glass transition temperature (Tg). Second, the
crystallization process of the considered glassy alloys shows
two exothermic crystallization peaks. The two exothermic peak
represents the glass-crystal transformation. The glass crystallizes
partially at the first crystallization and, when the temperature
is further increased in DSC, it gets completely crystallized at
the second crystallization. The appearance of double crystal-
lization peak indicates phase separation occurring in these glassy
alloys. The values of the glass transition temperature (Tg), onset
temperature of first crystallization (Tc1), onset temperature of
second crystallization (Tc2), peak temperature for first crystal-
lization (Tp1), and peak temperature for second crystallization
(Tp2) are mentioned in Table 1.
For the confirmations of the reminant crystallization and
identification of crystalline phases present in the samples, the
samples were annealed at 2 h at temperature intermediate
Figure 3. XRD pattern of annealed samples.

30 J. Phys. Chem. B, Vol. 114, No. 1, 2010
Deepika and Saxena
of the glass toward the lower temperature side on annealing is
due to the fact that the annealing of glass will enhance the
crystallization phenomenon of the glass and hence the crystal-
lization of the glass will set at earlier or nucleation will start at
lower temperature as compared to the as-prepared glasses.
Consequently, on annealing, the glassy matrix will become less
stable and hence amorphous to glass transition process is peaked
out at a lower temperature.8
Thermodynamic Properties.
Specific Heat. Determination of specific heat, Cp, as a
function of temperature provides an easy method for detection
of glass transition under different compositions and heating rates.
The sudden change in the specific heat at the glass transition
temperature is one of the characteristics of all glassy materials.14
Specific heat (Cp) of the samples could be easily evaluated using
the DSC data from the following relation:
Figure 4. DSC thermogram of Se58Ge42-xPbx (9 e x e 20) glassy
alloys annealed at intermeadiate\temperatures.
Cp ) [mr∆s/ms∆r]Cr
where ms and mr are the masses of the sample and reference
material respectively and ∆s and ∆r are the shifts for sample
and reference materials with respect to baseline respectively and
Cr is the specific heat of the reference material, which was taken
from the standard literature. All of the measurements of shifts
and baseline for the determination of specific heats of different
samples at different temperatures have been made at a heating
rate of 20 K/min. Figure 7 shows the specific heat of
Se58Ge42-xPbx (9 e x e 20) glassy alloys in the entire range of
temperature from 350 to 750 K. Figure 7 also shows Cp versus
T plot within glass transition region in the insert.
From Figure 7, it is observed that, the specific heat below
the glass transition temperature (Tg) is weekly temperature
dependent for all the compositions. However, specific heats of
the glassy samples show a compositional dependence in the
entire range of temperature. At Tg, the glass becomes liquid
and the abrupt jump in the specific heat is due to the additional
configurational degrees of freedom of motion of the atoms so
that the complete short-range order is formulated in the liquid
state. The excess of specific heat above Tg is attributed to the
fact that the supercooled liquid resembles that of the glass.
Above crystallization temperature (Tc), the specific heat de-
creases abruptly and attains its minimum value at approximately
the peak temperature of crystallization (Tp). This may be due
to the vestiges of short-range order still remains above Tc, which
may disappear when the temperature is further raised.15
Composition Dependence of the Enthalpy Released During
Transformation from Glass to Crystalline State. The enthalpy
released during phase transformation from glass to crystalline
state (∆Hgc) is important parameter for the determination of
stability of glasses. The enthalpy released during transformation
from glass to crystalline state is given by:
It was found that the all the samples except Se58Ge33Pb9
crystallize in GeSe2 and PbSe phases, while Se58Ge33Pb9
crystallizes in GeSe2 and Se phases. The absence of Pbse phase
at 9 at wt % is due to the fact that at 9 at wt % of Pb, the lead
atoms goes into the interstitial sites and does not contribute to
the structure of the glass, whereas at Pb concentration beyond
9 at wt %, the Pb atoms starts occupying the lattice sites and
results in two phases, viz. GeSe2 and PbSe. Therefore, at 9 at
wt % of Pb, only GeSe2 and Se phases are observed in the
system, whereas at Pb concentration beyond 9 at wt %, GeSe2
and PbSe phases are found in the system. The GeSe2 phase is
found to crystallize in the monoclinic structure with a unit cell
defined by a ) 7.016 Å, b ) 16.79 Å, and c ) 11.83 Å. The
PbSe phase crystallizes in the cubic structure with unit cell of
a ) 6.128 Å, whereas the Se phase crystallizes in the monoclinic
structure with a unit cell defined by a ) 15.01 Å, b ) 14.71 Å,
and c ) 8.789 Å.
Figure 4 shows the DSC thermogram of Se58Ge42-xPbx (9 e
x e 20) glassy alloys annealed at a temperature intermediate
between first and second crystallization at a heating rate of 20
K/min. The thermogram shows an endothermic peak (glass
transition region) and a exothermic peak (crystallization region).
The occurrence of glass transition is due to the presence of some
amorphous matrix in the annealed sample, whereas the exo-
thermic peak observed is broader and seems to be a combination
of the two peaks that were observed in the as-prepared sample.
The appearance of a single exothermic peak confirms the fact
that glass crystallizes completely at temperatures closer to
second crystallization. This fact has also been confirmed by
annealing the samples (obtained after annealing at intermediate
temperatures) of Se58Ge33Pb9 and Se58Ge22Pb20 glasses beyond
second crystallization temperature. The DSC scans (Figure 5)
again shows a single broader exothermic peak representing a
mixed phase. This phase also crystallizes around temperatures
closer to second phase of as-prepared sample. Therefore, it is
suggested that the samples partially crystallizes at first crystal-
lization, whereas the reminant crystallization is completed on
further heating the samples up to second crystallization
temperature.
∆Hgc ) ∆Hg - ∆Hc
(1)
where ∆Hg and ∆Hc represent the enthalpy released during
relaxation process and crystallization process, respectively.
The relaxation enthalpy ∆Hg has been evaluated by determin-
ing the area under the curve of the specific heat versus
temperature that is
The phases obtained in XRD (Figure 6) of these samples is
same as obtained before on annealing at intermediate temper-
atures with a small increase in the number of peaks of phases
present in the samples. From Figures 4 and 5, it is also observed
that the glass transition and crystallization temperatures shift
toward the lower temperature side after annealing. A shift in
the glass transition temperature and crystallization temperature
∆H )
C dT
(2)
∫
g
p
whereas the crystallization enthalpy ∆Hc has been calculated
by measuring the area under the crystallization peak. The overall
enthalpy released during transformation from glassy to crystal-
line phase is obtained using eq 1. Variation of ∆Hgc as a function
of Pb composition for phase transformation between glass and

Thermodynamics of Se58Ge42-xPbx (9 e x e 20) Glasses
J. Phys. Chem. B, Vol. 114, No. 1, 2010 31
Figure 5. DSC thermogram of Se58Ge33Pb9 and Se58Ge22Pb20 glassy alloys annealed at the end of second crystallization temperature.
released, ∆Hgc, is associated with the stability of the glasses. A
glass being in the metastable state tries to minimize its enthalpy
as well as Gibbs free energy at every temperature by elementary
atomic motions to gain stability. The most stable glass will
release the least energy to gain stability as it already possesses
a stable atomic configuration. Therefore, the most stable glass
will have the least value of ∆Hgc. Also, the least stable glasses,
that is the glasses with maximum value of ∆Hgc, will have the
lowest value of (Tc - Tg).9–11 Therefore, it may be inferred that
Se58Ge22Pb20 is the most stable glass among all of the samples
of the series. Further, it is also observed that decrease of enthalpy
(∆Hgc2) is sharp in case of second phase, whereas ∆Hgc1 assumes
an almost constant value in the case of first phase, which
indicates the higher stability of second phase.
Figure 9 shows the trends of values of ∆T1(Tc1 - Tg) and
∆T2(Tc2 - Tg) with lead composition for the two phases of all
of the samples of the series at a heating rate of 20 K/min. It
has been observed that the values of ∆T1 do not follow any
trend (increase or decrease with lead composition) and hence
cannot be taken as measure of determination of stability of the
Figure 6. XRD pattern of Se58Ge33Pb9 and Se58Ge22Pb20 glassy alloys
annealed at the end of second crystallization temperature.
glasses. In view of this, the second phase that follows an
increasing trend of ∆T2 values is used for the determination of
stability in terms of lead content in the glassy alloys. From the
plot Tc - Tg against Pb composition, it is observed that
Se58Ge22Pb20 glass has higher values of (Tc - Tg) and therefore
it is most stable among all of the other studied samples. Plots
of Tc - Tg against Pb composition confirm the results obtained
from plots of ∆Hgc against Pb composition.
This can also be explained on the basis of the bond energy
of the system. In Se58Ge42-xPbx (9 e x e 20) system, substitution
of Ge with Pb atoms results in the reduction of Ge-Se bonds
and an increase in Pb-Se bonds. The single-bond energy
values12 of Ge-Ge, Pb-Pb, and Se-Se bonds are 205.2, 85.7,
and 206.1 kJ/mol respectively, whereas the single covalent bond
energies of Ge-Se and Pb-Se bonds are 234.9 and 231.2 kJ/
mol, respectively. With the increase in Pb content in Se-Ge
system, more Pb-Se bonds are formed, resulting in reduction
of total bond energy of the system13 and ultimately leading to
increase in the stability of system, hence the Se58Ge22Pb20 glassy
alloy is found to be most stable among other samples of the
series.
Entropy Difference between Metastable States in Glassy
Region. The entropy difference, ∆S, between metastable states
in glassy region in a certain temperature range (i.e increase in
temperature), can be obtained using the following relation:
Figure 7. Plot of Specific heat (Cp) vs T for Se58Ge42-xPbx (9 e x e
20) glassy alloys. (The figure in the insert shows Cp vs T plot within
glass transition region.)
first crystallization (∆Hgc1) and glass and second crystallization
(∆Hgc2) has been shown in Figure 8. It is evident from Figure
8 that enthalpy released during phase transformation, ∆Hgc,
decreases with increase in Pb concentration. This enthalpy
∆S ) ∆Q/T
(4)
where ∆Q is the amount of thermal energy absorbed by the
glass in the glass transition region. Experimentally, the amount

32 J. Phys. Chem. B, Vol. 114, No. 1, 2010
Deepika and Saxena
Figure 8. Plot of ∆Hgc1 and ∆Hgc2 against Pb composition of Se58Ge42-xPbx (9 e x e 20) glassy system.
Figure 9. Plot of ∆T1(Tc1 - Tg) and ∆T2 (Tc2 - Tg) against Pb composition at a heating rate of 20 K/min.
Figure 10. Plot of ∆S as a function of temperature.
of thermal energy absorbed by the system is calculated by
measuring the area under the endothermic peak. Figure 10 shows
the plot of ∆S as a function of temperature.
From Figure 10, it is observed that entropy of the system
increases with the increase in Pb concentration. Entropy of the
system is highest for Se58Ge22Pb20, which indicates higher
disorderness and hence more stability of this glassy composition.
This is because of the fact that glass is a disordered solid and
the addition of another element in the matrix increases the
disorderness and hence the stability of the sample. When Pb is

Thermodynamics of Se58Ge42-xPbx (9 e x e 20) Glasses
J. Phys. Chem. B, Vol. 114, No. 1, 2010 33
introduced in Se-Ge system, it creates a compositional and
configurational disorder in the glassy system and hence increases
the stability of the glassy system. Thus, entropy, which
represents the disorderness, is found to increase with the increase
in lead (Pb) concentration in the Se-Ge glassy alloys.
The main characteristics of these plots is the sudden jump at
Tg and a decreasing trend at a temperature where crystallization
process begins. The jump in ∆S near Tg is due to increase in
number of atomic arrays, which leads to increase in topological
disorder in the system.
Gibbs Free Energy. Gibbs free energy for the crystallization
of undercooled liquid, ∆G, is an important parameter in the
study of crystallization kinetics. It is well-known that the exact
temperature dependence of ∆G can be calculated if the heat
capacities of the liquid and crystalline solid are known as a
function temperature. However, the heat capacity data of
undercooled liquid is not available easily due to its metastable
nature. Therefore, in the case of nonavailability of the specific
heat data in the undercooled region, the functional dependence
of ∆G on undercooling must be estimated theoretically. Various
expressions for ∆G are available in the literature.16–21 These
expressions depend on some kind of assumption for the
temperature dependence of the heat capacity.
The Gibbs free energy difference (∆G) between crystal and
liquid means the driving force of crystallization and is a vital
parameter in the nucleation ratio and crystal growth. In an
alloying system, the less ∆G means the less driving force of
crystallization, the more stable is the supercooled liquid and
the better the glass forming ability (GFA). So, estimation of
∆G plays an important role in appraising the GFA of glassy
systems.
Figure 11. Plot of ∆Ggc1 and ∆Ggc2 against Pb composition of
Se58Ge42-xPbx (9 e x e 20) glassy alloys.
nucleation and growth process occurs sluggishly. Hence, one
can infer that stability of the samples increases with an increase
in Pb concentration in these glassy alloys. Further, it can also
be concluded that the decrease in Gibbs free energy is more in
the case of the second phase, and therefore the second phase is
more stable than the first phase. The values of Tc - Tg and
∆Hgc for both the phases also confirm the same fact.
Entropy Difference between the Glass and the Crystalline
States (∆Sgc). The entropy difference between the glass and
crystalline states is given by the following relation:
∆Sgc ) ∆Sg - ∆Sc
(8)
where ∆Sg and ∆Sc are the entropies of the glassy and crystalline
states, respectively.
Gibbs free energy difference between the glass and the
corresponding crystalline phase is given by:
The entropy of the glassy state Sg is given by the following
thermodynamical relation:22
∆Ggc ) ∆Gg - ∆Gc
(5)
Cp
where ∆Gg and ∆Gc represent the Gibbs free energy in the
glassy and crystalline state, respectively.
The Gibbs free energy difference in the glassy region is
obtained using the following relation:
T
Sg ) Sconf
+
dT
(9)
∫
[ ]
0
T
where Sconf is the configurational entropy and is defined as
Sconf ) -k ln W
∆Gg ) ∆Hg - T∆S
(6)
where W denotes the total number of different ways in which
atoms can arrange themselves in a particular fashion and is given
by:23
where ∆Hg denotes the heat released by the sample in the
relaxation process and T∆S ) ∆Q is the amount of thermal
energy absorbed by the sample in the glassy region. However,
when a transformation from glassy to crystalline state is
considered, then ∆H represents the energy released by the glass
during the crystallization process and is denoted by ∆Hc. The
Gibbs free energy difference in this case is calculated using the
relation:
W ) N!/{(ASeN)!(BGeN)!(CPbN)!}
where N is the total number of atoms present in the system. ASe
is the fraction of Se atoms, BGe is the fraction of Ge atoms, and
CPb is the number of Pb atoms. For the calculation of the entropy
of the crystalline state, we have taken the configuration entropy
to be zero. This is because there is only one way to arrange the
atoms in the correct ordered array (W ) 1).22 Therefore, the
entropy of the crystalline state can be written as:
∆Gc ) ∆Hc - T∆S
(7)
and the Gibbs free energy difference between the glassy and
crystalline phases (∆Ggc) is calculated using eq 5. Figure 11
shows the plot of ∆Ggc against Pb composition for phase
Cp
T
transformation between glass and first crystallization (∆Ggc1
)
S )
dT
(10)
∫
C
[ ]
0
T
and phase transformation between glass and second crystalliza-
tion (∆Ggc2) of Se58Ge42-xPbx (9 e x e 20) glassy alloys.
It is evident from Figure 11 that the values of the Gibbs free
energy difference between the glass and crystalline states of
both first and second crystallization phases decrease with the
increase in Pb concentration in the samples. Because the number
of nuclei available at any temperature decreases exponentially
with the decrease of the free energy, therefore it is reasonable
to suggest that at the composition of minimum free energy
Figures 12 and 13 show the plot of entropy difference ∆Sgc
against temperature difference (∆T) for phase transformation
between glass and first and second crystallization of
Se58Ge27Pb15 glass respectively as a representative case. ∆T is
the difference of temperatures of the two crystallization regions
and the glass transition region. It can be noted that the entropy
shows its maximum in the vicinity of the glass transition peak
beyond, which it decreases until the crystallization is completed.

34 J. Phys. Chem. B, Vol. 114, No. 1, 2010
Deepika and Saxena
Figure 12. Plot of entropy difference ∆Sgc against temperature difference ∆T for phase transformation between glass and first crystallization of
Se58Ge27Pb15 glass.
Figure 13. Plot of entropy difference ∆Sgc against temperature difference ∆T for phase transformation between glass and second crystallization
of Se58Ge27Pb15 glass.
The values of ∆Sgc that is (∆Sg - ∆Sc) for phase transforma-
tion between glass and first crystallization for Se58Ge33Pb9,
Se58Ge30Pb12, Se58Ge27Pb15, Se58Ge24Pb18, and Se58Ge22Pb20
glasses were found to be 0.586, 0.588, 0.638, 0.642, and 0.699
J/gK respectively, whereas the values of Sgc for phase trans-
formation between glass and second crystallization for
Se58Ge33Pb9, Se58Ge30Pb12, Se58Ge27Pb15, Se58Ge24Pb18, and
Se58Ge22Pb20 glasses were found to be 0.584, 0.585, 0.631,
0.634, and 0.689 J/gK, respectively. The values of ∆Sgc for all
of the compositions show that the entropy difference between
the glassy and crystalline states increases with the increase in
Pb concentration. The maximum value of ∆Sgc ) ∆Sg - ∆Sc is
found to be for x ) 20 at wt % of Pb indicating that entropy is
maximum in the glassy state. Meanwhile, in the crystalline state
around Tc ordering is minimum for this glass in comparison to
other samples. Further, the difference in entropy goes on
increasing up to certain temperature (around Tp) and after that
attains approximately stable values. The highest value of Sgc
for Se58Ge22Pb20 glass again confirms that this glass is the most
stable among the whole series.
1. The Se58Ge42-xPbx (9 e x e 20) glassy systems exhibit
single glass transition and double crystallization on heating,
which is attributed to the phase separation during crystallization.
The XRD study reveals that the Se58Ge33Pb9 glassy alloy
crystallizes into GeSe2 and Se phases with monoclinic structures,
whereas all other glasses (Se58Ge42-xPbx (12 e x e 20)) in the
series crystallizes into GeSe2 and PbSe phases with monoclinic
and cubic structures, respectively.
2. The most stable glass (Se58Ge22Pb20) is found to have
maximum entropy in the glassy region. This maximum value
of entropy is found to persist even in the crystalline region,
indicating that growth and nucleation processes occur sluggishly.
3. Gibbs free energy difference between the glass and the
corresponding crystalline phase ∆Ggc is found to be highest for
9 at wt % of Pb and lowest for 20 at wt % of Pb, which suggests
that stability of sample increases with the increase of Pb content
in the glasses under investigation. The enthalpy released during
transformation from glassy to crystalline phase and the values
of Tc - Tg also favor the same fact.
Conclusions
Acknowledgment. One of the authors (Deepika) is grateful
to the DSA program of UGC in the department for providing
financial support in the form of fellowship during this work.
The authors are also thankful to Mr. Kuldeep S. Rathore, Ms.
Investigation of various thermodynamic properties of
Se58Ge42-xPbx (9 e x e 20) alloys leads to the following
conclusions:

Thermodynamics of Se58Ge42-xPbx (9 e x e 20) Glasses
J. Phys. Chem. B, Vol. 114, No. 1, 2010 35
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Manasvi Dixit, and Mrs. Sandhya Gupta for their help in various
ways during the course of this work.
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