Optical properties of amorphous and crystalline tris(8-hydroxyquinoline) indium films

Article abstract of DOI:10.1016/j.jallcom.2016.05.121

Tris(8-hydroxyquinoline) indium (Inq₃) films were physically deposited via thermal evaporation technique and were subsequently thermally annealed at different temperatures in air atmosphere. The effect of annealing on the structural and optical properties of the films was investigated. X-ray diffraction showed that the as-deposited and annealed films at 100 and 200 °C have amorphous structure, whereas the annealed films at 270 and 300 °C have crystalline structure in which a preferred orientation of growth is obtained. The evolution of the optical properties of the films due to annealing has been correlated with their structural properties. The optical properties were studied in terms of spectrophotometeric measurements of the transmittance and reflectance over the spectral range 200-2500 nm, from which the refractive and absorption indices were calculated using Murmann's exact equations. The single oscillator and Drude models were applied for determining the dispersion parameters of the films. Analysis of the absorption coefficient revealed that the films have direct allowed optical band gap of 2.77 eV, which is increased to 2.85 eV as a result of annealing. The thermal properties were studied by means of differential scanning calorimetry and thermogravimetric measurements.

Full text of DOI:10.1016/j.jallcom.2016.05.121

Accepted Manuscript
Optical properties of amorphous and crystalline tris(8-hydroxyquinoline) indium films
E.M. El-Menyawy
PII:
S0925-8388(16)31454-2
10.1016/j.jallcom.2016.05.121
JALCOM 37641
DOI:
Reference:
To appear in: Journal of Alloys and Compounds
Received Date: 12 December 2015
Revised Date: 26 April 2016
Accepted Date: 13 May 2016
Please cite this article as: E.M. El-Menyawy, Optical properties of amorphous and crystalline
tris(8-hydroxyquinoline) indium films, Journal of Alloys and Compounds (2016), doi: 10.1016/
j.jallcom.2016.05.121.
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ACCEPTED MANUSCRIPT
Optical properties of amorphous and crystalline tris(8-hydroxyquinoline)
indium films
E.M. El-Menyawy
Solid State Electronics Laboratory, Solid State Physics Department, Physical Research
Division, National Research Centre, 33 El-Bohouth St., Dokki, Giza 12622, Egypt.
Abstract
Tris(8-hydroxyquinoline) indium (Inq3) films were physically deposited
via thermal evaporation technique and were subsequently thermally annealed
at different temperatures in air atmosphere. The effect of annealing on the
structural and optical properties of the films was investigated. X-ray
diffraction showed that the as-deposited and annealed films at 100 and 200 ˚C
have amorphous structure, whereas the annealed films at 270 and 300 ˚C have
crystalline structure in which a preferred orientation of growth is obtained.
The evolution of the optical properties of the films due to annealing has been
correlated with their structural properties. The optical properties were studied
in terms of spectrophotometeric measurements of the transmittance and
reflectance over the spectral range 200-2500 nm, from which the refractive
and absorption indices were calculated using Murmann’s exact equations. The
single oscillator and Drude models were applied for determining the
dispersion parameters of the films. Analysis of the absorption coefficient
revealed that the films have direct allowed optical band gap of 2.77 eV, which
is increased to 2.85 eV as a result of annealing. The thermal properties were
studied by means of differential scanning calorimetry and thermogravimetric
measurements.
Keywords: Inq3 films; Structural properties; Optical constants; Annealing.
Corresponding author: Tel: +2 01006021326; Fax: +2 0233709310.
E-mail address: emad_elmenyawy@yahoo.com (E.M. El-Menyawy).

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1. Introduction
Organic semiconductors with promising optical and electrical properties
are recognized as an important class of interesting materials for applications in
advanced electronic and optoelectronic devices in which their physical
properties can be tuned by chemical modification on the molecular frame. The
domain of organic materials continues to be of great scientific and commercial
interest due to other advantages such as low cost and ease of processing. They
are currently used as active layers in large number of advanced electronic and
optoelectronic devices such as light emitting diodes [1], thin film transistors
[2] and solar cells [3], as alternatives to expensive inorganic materials.
Tris(8-hydroxyquinoline) aluminum (Alq3) is the first efficient material
in organic light emitting diode (OLED) devices, which was reported in 1987
by Tang and Vanslyke [4]. Since then, intense efforts have been dedicated to
develop and improve the efficiency of such diodes. Most of the recent studies
have been directed towards improving morphological stability [5], optimizing
the device characteristics [6], understanding the charge carrier transport
mechanisms [7] and tuning the emission spectrum of OLED [8]. Besides, Alq3
is used as a buffer electron transport layer [9] and dopant material in organic
solar cells [10]. Ever since the success of Alq3 in these devices, a lot of
attention has been paid to synthesize and investigate other counterparts. In this
regard, Inq3 has been introduced as promising candidate in OLEDs. Triggered
by its interesting properties, efforts have been paid for further material
analysis and characterization. The study of the optical behavior of such
materials in thin film form is a prerequisite for the successful device
fabrication. Shukla and Kumar [11] have been investigated the optical
properties of Inq3 and Alq3 films by using spectroscopic ellipsometry. The
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study showed that the refractive index of Inq3 films is higher than Alq3 films.
Thangaraju et al. [12] showed that the Inq3 films have less photoluminescence
intensity compared with that of Alq3 thin film. Thermal annealing was used as
an effective tool for influencing the structural and optical properties of Alq3
[13-15] and Gaq3 [16] films.
To the best of my knowledge, the effect of thermal annealing on the
structural and optical properties of Inq3 thin films has not been extensively
reported. The target of this work is to study the influence of thermal annealing
temperature on the structural properties and optical functions of thermally
evaporated Inq3 films over the spectral range 200-2500 nm. Thermal annealing
is a common used process in optical applications, which is helpful tool to
improve the film properties. For example, annealing has been used as a vital
process to improve the electrical conversion efficiency of solar cells. Thus, it
is important to find the optimum annealing temperature, at which the film
could possess better optical properties.
2. Experimental
2.1 Synthesis
Tris(8-hydroxyquinoline) indium was prepared according the procedure
given elsewhere [17]. In typical synthesis, 0.5 g of 8-hydroxyquinoline was
dissolved in a mixture of 10 ml double distilled water and 2.5 ml of glacial
acetic acid. The mixture was vigorously stirred until an orange transparent
solution was obtained. Then, 0.3 g of indium nitrate hydrate was dissolved in
20 ml of double distilled water and stirred until a clear solution was obtained.
The two solutions were mixed together and stirred for 5 min. After that,
ammonium hydroxide was added to the mixture solutions, drop by drop with
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continuous stirring to get maximum precipitation. A yellow-green precipitate
was filtered out and washed 15 times with double distilled water and dried at
80 ˚C under argon gas flow.
2.2 Films deposition and measurements
Inq3 films were deposited onto pre-cleaned glass and optically flat fused
quartz substrates using thermal evaporation technique under a base pressure of
about 10-4 Pa by using high vacuum coating unit (Edwards, E 306 A). Initially,
Inq3 powder was placed inside a quartz crucible that has been surrounded by a
tungsten coil capable of supplying sufficient heat to the materials upon
passing an electrical current through this coil. Current of about 40 A was
enough to start sublimating Inq3 powder. The rate of deposition and film
thickness were controlled during the evaporation by using a quartz crystal
thickness monitor. The rate of deposition was adjusted at 0.15 nm/s. The film
thickness was determined as 386 nm after deposition by spectrophotometeric
method. The substrates were kept at room temperature (25 ˚C) during the
deposition process. Prior to deposition, the substrates were cleaned
ultrasonically for 15 min with hot distilled water, followed by 10 min rinsing
in an ultrasonic bath in acetone, ethanol and distilled water, respectively.
Finally, the substrates were dried thoroughly under argon gas. Glass substrates
were used for structural analysis, whereas quartz substrates were used for
optical measurements.
Inq3 films were thermally annealed at temperatures of 100, 200, 270 and
300 ˚C in air atmosphere. Annealing was performed in dark condition and the
time of annealing was two hours. The temperature of the samples was
recorded by using NiCr-NiAl thermocouple with an accuracy of ±1 ˚C.
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The X-ray diffractometer (Philips X' pert) with Ni-filtered CuKα-
radiation was used to identify the structural characteristics of both powder and
films. The measurements were performed in the diffraction angle (2
4–80˚ with a step size of 0.02 (2 /s). Morphology of the films was studied by
field emission scanning electron microscope (Quanta FEG 250).
θ) range
θ
The optical transmittance and reflectance spectra of the films were
recorded over the wavelength range 200–2500 nm using double beam
spectrophotometer (JASCO V-570 UV–Vis–NIR). The measurements were
performed under ambient conditions. The absolute values of total measured
transmittance, Tm, after introducing corrections resulting from the absorbance
and reflectance of the substrate were calculated by [18]:
T = Tm
(
1− Rq
)
(1)
where Rq is the reflectance of reference quartz substrate. The
spectrophotometer was also provided with a reflection attachment to measure
the reflectance. The absolute values of the total measured reflectance, Rm, after
introducing corrections resulting from reflectance of the substrate and
reference mirror were calculated by:
R = Rm RAl
{
1+ (1− Rq )2
}
−T 2 Rq
(2)
where RAl is the reflectance of the reference aluminum mirror.
The thermogravimetric (TG) and differential scanning calorimetry
(DSC) measurements were performed at heating rate of 10 ˚C/min and in
nitrogen environment by thermogravimetric analyzer SDTQ 600 TA.
3. Results and discussion
3.1 Structural properties
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Fig. 1 depicts the X-ray diffraction patterns of Inq3 in both powder and
thin film conditions. It can be observed that the spectrum of the powder has
different peaks with different intensities implying polycrystalline structure.
Upon thermal deposition, no identified diffraction peaks are found which give
the ambiguous evidence of amorphous structure. The same behavior can also
be seen for annealed films at 100 and 200 ˚C. Upon rising annealing
temperature up to 270 ˚C, a preferred orientation of growth along the
diffraction peak centered at diffraction angle of 7.03˚ is obtained indicating
crystalline structure. The intensity of this peak is slightly increased by
annealing at 300 ˚C indicating slight improvement of films crystallinity. The
appearance of this diffraction peak at high annealing temperatures is attributed
to the sufficient increase in supply of thermal energy for crystallization, re-
crystallization and growth of grains in the films. As-deposited Alq3 [13] and
Gaq3 [16] films are also found to grow with amorphous structure. Thermal
annealing at 200 ˚C is found to crystallize Alq3 films and thermal annealing at
255 ˚C is found to crystallize Gaq3 films.
The surface morphology of films plays an important role for electronic
and optoelectronic device applications. Surface morphology of Inq3 films is
investigated by field emission scanning electron microscope (FESEM). Fig.
2(a,b) represents the FESEM images of as-deposited and annealed films at 270
˚C with the same value of magnification. The SEM image shows that the
particles of as-deposited amorphous films have granular shape with uniform of
distribution over the substrate surface. With annealing, some of irregular
shaped particles in the as-deposited film are transformed to a more rounded
structure resulting in more defined particles which can be attributed to
crystallization process.
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3.2 Optical properties
Inq3 films were thermally annealed at different temperatures (100, 200,
270 and 300 ˚C). The effect of thermal annealing at 100 and 200 ˚C on the
transmittance and reflectance spectra of the films was very weak. The attempt
for measuring the transmittance and reflectance of the annealed films at 300
˚C has failed, because that the annealing was resulted in a decrease in film
thickness and formation of rough surface. So, the influence of thermal
annealing on the optical properties of the films is achieved at only 270 ˚C.
Fig. 3 demonstrates the optical transmittance and reflectance spectra of
as-deposited and annealed Inq3 films. Inspection of this figure shows that the
spectra of as-deposited films can be simply divided into two regions. In
spectral range 200-550 nm, the total sum of T and R is less than unity
implying the existence of absorption. At wavelengths greater than 550 nm, the
total sum of T and R approaches unity value i.e transparent region. The
absorption region is separated from transparent one by sharp transmittance
edge. In the transparent region, the T and R spectra of the films exhibit many
peaks and valleys. These oscillations are due to the interference effect
originating from the multiple reflections which occur at the interface of the
air-film and film-substrate systems, constructive and destructive wave
interference occur periodically. On annealing, the transmittance edge is
slightly shifted towards shorter wavelengths. The value of T in transparent
region is also decreased and the corresponding value of R is increased. It can
be observed that the T and R spectra of as-deposited and annealed films have
nearly the same behavior in transparent region. This indicates that the as-
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deposited and annealed film have almost the same thickness, within the
experimental error.
The optical transmittance and reflectance spectra of Inq3 films were
used to estimate the refractive, n, and absorption, k, indices using Murmann′s
equations [19,20]. To get the optical constants, n and k, a computer program
comprising a modified search technique of Abèlès et al. technique [21] was
used. The idea of technique is based on minimizing |
∆
T|2 and |
∆
R|2
simultaneously, where
2
2
∆T = T(n,k) −T
(3)
(4)
∆R 2 = R(n,k) − R 2
where T and R are the experimental absolute values calculated from Eqs (1)
and (2), respectively. R(n,k) and T(n,k) are the proposed values of T, R using
Murmann′s equations. By applying such technique, values of n and k are
obtained. The details of these calculations are given in previous work [22].
The spectral distributions of the calculated refractive index, n, of as-
deposited and annealed Inq3 films are depicted in Fig. 4. It can be seen that the
spectrum of as-deposited films exhibits three peaks located at 280, 330 and
440 nm. These peaks represent the anomalous dispersion of the refractive
index which can be explained with the multi-oscillator model [23]. At
wavelength range 550-2500 nm, the refractive index decreases with increasing
the wavelength and shows non-dispersive behavior at higher wavelengths.
This behavior is the normal dispersion which can be interpreted by using
single oscillator model. The value of the refractive index for as-deposited
films is in the range of 1.9-2 which is slightly higher than that observed for
Alq3 [24]. With annealing, the refractive index increases over the whole
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spectral range and the peak located at 440 nm shifts slightly towards higher
wavelengths.
Fig. 5 illustrates the influence of annealing on the absorption index
spectra of Inq3. The spectrum of the as-deposited film is dominated by two
major bands in ultraviolet and visible spectral regions. Similar behavior is also
observed for Alq3 [25] and Gaq3 [26]. Muhammad et al. [26] have been
pointed that the band in the visible light region is attributed to the
optoelectronic transition across
π
-
π
* orbitals, whereas that the band in the
* orbital.
ultraviolet region is due to the optoelectronic transition from 4p to
π
Inspection of the absorption spectra shows that the intensity of the absorption
band in the visible light region is decreased by annealing, whereas the
intensity of the absorption band in the ultraviolet region is increased. In
addition, the visible light absorption band shifts towards higher energy, while
the ultraviolet absorption band shifts towards lower energy. From the
foregoing observations, it can be deduced that the changes in the optical
constants of Inq3 films as a result of annealing are attributed to corresponding
enhancement in both packing density and intermolecular interactions upon
crystallization or rearrangement [27].
In weak absorption region, the dispersion data of the refractive index
can be evaluated according to the single oscillator model proposed by Wemple
and Di Domenico [28,29]. According to this model, the real part of dielectric
function, ε1, is expressed by:
Ed Eo
ε1 = n2 − k 2 =
1
+
(5)
2
Eo −
(h
ν
)
where Ed and Eo are the dispersion and oscillator energies, respectively and h
ν
is the photon energy. The parameter Ed is a measure of the intensity of inter-
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band optical transitions and it does not depend significantly on the band gap,
while Eo can be considered as an average value of the energy gap of the
ν
material. Fig. 6 shows the relation between (n2-1)-1 and (h )2 for as-deposited
and annealed Inq3 films. The relation gives a straight line over a long range of
photon energy verifying Eq. 5. The deviation from linearity at low photon
energy is observed which can be ascribed to the negative contribution of
lattice vibration to the refractive index [29]. The values of Ed and Eo of as-
deposited and annealed Inq3 films are determined from the slope (1/EdEo) and
the intercept (Eo/Ed) of the straight lines. The values of Ed and Eo for as-
deposited films are estimated as 15.06 and 5.56 eV, respectively. With
annealing, these values are increased to 27.94 and 7.73 eV, respectively. The
2
dielectric constants at high frequency (
ε
∞=n∞ ) were determined from the
intercept of the straight line with the (n2-1)-1 axis at zero photon energy. The
value of ε∞ for as-deposited and annealed films was determined as 3.71 and
4.61, respectively.
The real part of the dielectric function can be analyzed to obtain
additional information concerning the contribution of the free carriers and the
lattice vibration modes to the dispersion. The dependence of the real part of
the dielectric function relation on the wavelength of the incident light is
expressed by [30]:
e2
π 2εoc2 m
N
ε1 = n2 − k 2 = ε L
−
λ2
(6)
4
where εL is the lattice dielectric constant, e is the charge of the electron, εo is
the dielectric constant of free space, c is the velocity of light in free space and
N/m* is the ratio of the carrier concentration to its effective mass. Fig. 7 shows
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the variation of n2 with λ2 for the as-deposited and annealed Inq3 films. The
relation shows linear behavior at higher wavelengths. Extrapolating the linear
portions to zero wavelength value gives the value of εL, whereas the ratio N/m*
is determined from the slope of the straight line portions. The value of εL is
estimated as 3.72 for as-deposited films and it is increased to 4.63 as a result
of annealing. The accordance between the values of εL and ε∞ indicates that
the contribution of the free carries is marginal for the films under investigation
[31]. Besides, the ratio N/m* is slightly increased from 1.35×1055 to 1.47×1055
Kg-1 m-3 by annealing. The value of N/m* is in the same order of that obtained
for Alq3 [13]. The increase in the ratio N/m* is due to the crystallinity
improvement of the films.
The absorption coefficient of the films was calculated by the well-
known relation;
α=4πk/λ. According to electronic inter-band absorption
theory, optical band gap of non metallic films can be evaluated using Tauc’s
relation [32]:
m
α
h
ν
= B
(
hν
− Eg
)
(7)
where B is the probability parameter for the transition, Eg is the optical band
gap of the material and m is the transition coefficient. The exponent m takes
the values 1/2 and 3/2 for direct allowed and forbidden transitions,
respectively, and takes the values 2 and 3 for indirect allowed and forbidden
transitions, respectively. The experimental data were fitted to different values
of m, and it was found that the m=1/2 provided the best fit to the data. This
indicates the existence of direct electronic transitions between the molecular
orbital energy bands. The relation between (αhν
)2 and photon energy is
represented in Fig. 8. The extrapolation of the straight line graphs (αhν
)2 =0
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gives the values of the optical band gap. The value of Eg is estimated as 2.77
and 2.85 eV for as-deposited and annealed films, respectively. The Eg value is
lower than that of Gaq3 (2.81 eV) and Alq3 (2.86 eV) films [33] which can be
attributed to the effect electrons number in the outer shell for the central metal
cation. The increase in the Eg value can be correlated with the improvement of
the films crystallinity. The value of the optical band gap of as-deposited and
annealed films verifies the relation; Eo≈2×Eg which is also observed to be
verified for Alq3 [34].
The behavior of the absorption coefficient in the low energy range was
found to follow the exponential law given by Urbach’s expression [35]:


h
ν




α
=
α o exp
for h
ν<Eg
(8)
EU


where αo is a constant, and EU is an empirical parameter, which has the
dimensions of energy and describes the width of the localized states in the
band gap. Fig. 9 gives ample evidence that the experimental data below the Eg
verifies Eq. 8. From the slopes of this linear relationship, the empirical
parameter EU for as-deposited and annealed films was estimated as 0.16 and
0.14 eV, respectively. These results indicate that as-deposited films have
higher values of localized states than the annealed films which are in
accordance with the X-ray studies.
Fig. 10 depicts the TG-DSC curves of as-prepared Inq3 powder. The TG
curve shows a weight loss starts at 39 up to about 49 ˚C which is accompanied
with endothermic peak in DSC curve. This peak is attributed to the
evaporation of the residual ammonium hydroxide. The curves show also that
the absorbed water molecules start to evaporate at 85 ˚C and continue to 109
˚C. The glass transition temperature, Tg, is observed at 198 ˚C and
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recrystallization temperature, Tc, is located at 261 ˚C. The endothermic peak
observed at 375 ˚C is corresponding to the melting point, Tm, whereas that
observed at 425 ˚C is corresponding to the degradation temperature, Td. The
values of Tg, Tc and Tm are reported as 177, 251 and 419 ˚C, respectively, for
Alq3 [36] and are determined as 182, 259 and 286 ˚C, respectively, for Gaq3
[16]. In comparison to Alq3 and Gaq3, Inq3 shows higher thermal stability
which can be ascribed to the stabilizing effect of cationic In+3 central metal
atom [26].
4. Conclusion
Inq3 powder has polycrystalline structure. As-deposited and thermally
annealed films at 100 and 200 ˚C have amorphous structure. Annealing at 270
and 300 ˚C results in crystalline films in which a preferred orientation of
growth is observed. Inq3 films are optically absorbing over the spectral range
200-550 nm, whereas they are optically transparent over the spectral range
550-2500 nm. The refractive index is found to increase with annealing at 270
˚C. The behavior of the refractive index is investigated in which some
important dispersion parameters; Ed, Eo, ε∞,
εL and N/m* are estimated for as-
deposited and annealed films. The absorption analysis of the as-deposited
films revealed the existence of direct allowed transition with optical energy
gap of 2.77 eV. This value is increased to 2.85 eV due to annealing. Using
Urbach’s relation, the width of the localized states in the band gap of the films
is found to decrease with annealing. Thermal properties analysis showed that
Inq3 has glass transition and recrystallization temperatures of 198 and 261 ˚C,
respectively. It could be concluded that the modification in optical properties
of the films by annealing is due to crystallization.
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[34] Z.Z. You, G.J. Hua, Vacuum 83 (2009) 984.
[35] F. Urbach, Phys. Rev. 92 (1953) 1324.
[36] L.S. Sapochak, A. Padmaperuma, N. Washton, F. Endrino, G.T. Schmett,
J. Marshall, D. Fogarty, P. E. Burrows, S. R. Forrest, J. Am. Chem. Soc. 123
(2001) 6300.
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Figure captions
Scheme 1 Molecular structure of Inq3 compound.
Fig. 1 X-ray diffraction spectra of Inq3: (a) powder, (b) as-deposited film, (c) annealed
films at 100 ˚C, (d) annealed films at 200 ˚C, (e) annealed film at 270 ˚C and (f)
annealed film at 300 ˚C.
Fig. 2 SEM images of Inq3 films: (a) as-deposited and (b) annealed at 270 ˚C.
Fig. 3 Optical transmittance and reflectance spectra of Inq3 thin films.
Fig. 4 Refractive index dispersion curve of Inq3 films.
Fig. 5 Spectral distribution of absorption index for Inq3 films.
Fig. 6 The relation between (n2-1)-1 and (hν)2 for as-deposited and annealed Inq3 films.
Fig. 7 The variation of n2 with λ2 for as-deposited and annealed Inq3 films.
Fig. 8 The relation between (αhν)2 and photon energy for Inq3 films.
Fig. 9 The relation between lnα and hν for as-deposited and annealed Inq3 films.
Fig. 10 TGA-DSC curves of Inq3 powder.
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N
O
O
N
In
O
N
Scheme 1
18

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(f)
(e)
(d)
(c)
(b)
(a)
4
8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
(2θ o
)
Fig. 1
19

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(a)
20

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(b)
Fig. 2
21

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1.0
0.8
0.6
0.4
0.2
0.0
T
as-deposited
annealed
R
200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
λ
(nm)
Fig. 3
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as-deposited
annealed
2.6
2.4
2.2
2.0
1.8
1.6
n
200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
λ
(nm)
Fig. 4
23

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0.56
0.48
0.40
0.32
0.24
0.16
0.08
0.00
as-deposited
annealed
k
200
300
400
500
λ
(nm)
Fig. 5
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0.44
0.40
0.36
0.32
0.28
0.24
0.20
as-deposited
annealed
0
1
2
3
4
5
(hν
)2 (eV)2
Fig. 6
25

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5.6
5.2
4.8
4.4
4.0
3.6
3.2
2.8
n2
as-deposited
annealed
0
1
2
3
4
5
6
7
λ2 m)2
(µ
Fig. 7
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2.0x1010
1.5x1010
1.0x1010
as-deposited
annealed
ν
α
5.0x109
0.0
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
hν (eV)
Fig. 8
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as-deposited
annealed
2980.95799
1096.63316
403.42879
α
2.3
2.4
2.5
2.6
2.7
2.8
hν (eV)
Fig. 9
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44
43
42
41
40
39
100
80
60
40
20
0
Td
Tm
Tc
Tg
100
200
300
400
500
t (oC)
Fig. 10
29