Thermal Analysis Application
Thermal Analysis Application No. UC 271
Application published in METTLER TOLEDO Thermal Analysis UserCom 27
Heat capacity determination at high temperatures
by TGA/DSC Part 1: DSC standard procedures
Introduction
Several different standardized DSC measurement procedures are currently
used for the determination of the specific
heat capacity (cp). These have been described in earlier publications [1, 2].
The introduction of the TOPEM® technique [3, 4] provides another interesting new method.
In DSC, the measured heat flow is directly proportional to the specific heat
capacity. This allows cp to be calculated
directly from the DSC signal (Fmeas). To
do this, the DSC curve must be corrected
by subtracting a blank curve and the
masses of the crucibles should be as close
as possible.
The isothermal baselines measured before and after the temperature increase
should be long enough for the system to
stabilize and reach stationary conditions.
The results are evaluated according to
standards such as ISO 11357, DIN 53765,
DIN 51007 or ASTM E1269 [5–8].
Temperature/
Literature ref.
500
550
600
1250
1300
1350
°C
Material
platinum
9
0.144
0.145
0.147
0.16
0.1672
0.168
J/gK
nickel
10, 11
0.529 0.534
0.54
0.62
0.616
0.629 J/gK
sapphire
MT
1.171
1.185
1.197
1.29
1.295
1.299 J/gK
quartz
12, 13
0.777
0.789
0.732
0.79
0.793
0.798
quartz
11
1.24
1.14
J/gK
J/gK
Table 1. Values of specific heat capacities at different temperatures. (MT: Data taken from
the STARe software).
dH/dT: change in enthalpy with temperature,
Cp:
heat capacity,
cp:
specific heat capacity,
m:
mass, which should remain constant during the measurement,
bs:
heating rate (change of the sample temperature with time),
F:
heat flow,
dH/dt is the change in enthalpy with time
and in this case is called the sensible
heat flow (Fsens).
The measured heat flow (Fmeas) is the
sum of the sensible and latent heat flows
plus the heat flow (Fbl) of the blank
curve. The latent heat flow (Flat) is the
sum of thermal events such as transitions or reactions.
where Cp = mcp
Measurement of Fsens to calculate the
heat capacity assumes that Flat and Fbl
are known. In c p determination, this
means that other overlapping thermal
events must not occur. Usually, the following two methods are employed:
The Direct method uses eq 3 to calculate
the specific heat capacity.
The Sapphire method is carried out according to the standard methods given
above and eq 4:
where m sap, c p,sap and Fsap are obtained
from the sapphire measurement.
Thermal Analysis Application
Both methods take the influence of different crucible masses into account.
Details and information on the use of
the different methods are given in UserCom 7 [1]. This present article discusses methods for the determination of
the specific heat capacity at temperatures
above 500 °C and shows suitable examples.
Table 1 summarizes different cp reference
values taken from the literature to check
the results. The values for quartz are relatively uncertain because the literature
values differ by up to 40%.
Experimental details
The experiments to determine specific
heat capacity at high temperatures were
carried out using stable materials that
could be repeatedly measured and that
differed in cp, thermal conductivity, and
color. Platinum and nickel were measured as pure metal disks. Different types
of aluminum oxide, i.e. pieces of sapphire, powder and disks (sintered alumina) were also compared. The specific
heat capacity of all three forms of aluminum oxide was assumed to be the same.
The measurements were performed with
a TGA/DSC 1 equipped with the large
furnace for temperatures to 1600 °C and
the HSS2 sensor. The furnace was purged
with nitrogen at 80 mL/min to prevent
long-term oxidation of nickel.
Calibration
The TGA/DSC 1 was first adjusted according to the standard procedures using pure
metals (Zn, Al, Au and Pd) in a 70-µL
alumina crucible. If the direct method is
used, the heat flow must be properly adjusted for the desired temperature range
and crucibles. Since the calibration metals form alloys with platinum crucibles,
the following procedure was adopted: a
30-µL alumina crucible was placed inside
a 150-µL Pt crucible and the reference
Figure 1. The upper diagram (black curve) shows the sample temperature. The DSC curves
of sapphire, platinum and nickel are displayed in the lower diagram (with blank curve
subtraction). The dashed curves refer to alumina crucibles. The curves were not recorded
during heating from 650 °C to 1200 °C and stabilization.
Figure 2. The upper diagram shows the heat flow curves of sapphire and platinum. The
lower curves show the cp curves of platinum together with three numerical values (rounded). The values were used to calculate the results presented in Table 2.
sample weighed into the alumina crucible. A separate crucible was used for each
metal. The crucibles could be repeatedly
used for calibration and adjustment. Zinc
and aluminum however slowly oxidize so
these samples could only used about ten
times. In the case of palladium, a small
amount of vaporization has to be taken
into account. This was done by checking
the sample weight each time.
Crucibles and sample mass
A series of measurements was first performed to decide which type of crucible
would be best for cp determinations.
Figure 1 shows the sample temperature
curve and the heat flow curves of sapphire, platinum and nickel samples, each
sample measured once in a platinum
crucible and once in an alumina crucible
METTLER TOLEDO
TA Application No. UC 271
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Thermal Analysis Application
using crucible lids. Comparison of the
results of the two 150-µl crucibles (typical
masses are noted in the figure) showed
that the influence of the type of sample
(e.g. color, thermal conductivity) was
much more apparent in the alumina crucible than in the platinum crucible. This
affects not only the magnitude of the
heat flow but also the repeatability and
accuracy of the cp measurement. Further
determinations were therefore performed
only using the platinum crucible.
The results showed that measurements
must be performed using a lid. Platinum
lids however tend to weld to platinum
crucibles at temperatures above 1000 °C,
especially when new crucibles are used.
This can be prevented by coating the lid
with a very thin film of inert material.
In the measurements performed here, a
thin film of Ceramabond™ (ME-71302)
was applied to the underside of the lid.
Accurate cp measurements require the use
of a large sample masses in order to obtain a large heat flow signals. The reproducibility of the signal must also be very
good. This is the reason why the 150-µL
crucibles were used because they allow
a large amount of sample to be used in
comparison with the mass of the crucible. The optimum amount of sample for
a cp determination is when the crucible is
about three-quarters full. Furthermore,
the mass of sample should be chosen so
that heat capacity of the sample matches
the heat capacity of the sapphire reference and thus produces a similar heat
flow signal. This is, however, not always
possible because it depends on the density
of the material (e.g. with alumina powder).
The sapphire reference consisted of several sapphire disks (4.8 mm diameter,
ME-00017758).
Temperature program
°C
500
550
600
1250
1300
1350
Platinum
918.81 mg
cp
s
Dcp
J/gK
%
%
0.16
0.0
11.1
0.16
0.0
10.3
0.16
0.0
8.8
0.19
5.3
13.3
0.18
6.0
8.0
0.18
5.6
7.4
Nickel
523.77 mg
cp
s
Dcp
J/gK
%
%
0.57
3.0
7.8
0.57
4.1
6.1
0.57
3.0
5.6
0.68
6.0
9.0
0.68
7.4
8.1
0.68
7.4
8.6
cp
s
Dcp
J/gK
%
%
1.13
2.2
–3.8
1.14
2.2
–4.1
1.15
2.2
–4.2
1.18
2.13
–8.3
1.20
1.67
–7.3
1.19
1.75
–8.7
Alumina lid
229.63 mg
cp
s
Dcp
J/gK
%
%
1.16
0.9
–0.9
1.17
1.7
–1.3
1.18
2.6
–1.7
1.29
8.89
0.3
1.25
5.34
–3.7
1.20
6.45
–7.4
Quartz
169.83 mg
cp
s
Dcp
J/gK
%
%
1.23
2.2
–0.8
1.28
2.2
–
1.24
2.9
8.8
1.30
4.0
–
1.30
4.9
–
1.31
5.9
–
Aluminum
oxide powder
218.17 mg
Table 2. Results using the sapphire method. Crucible: Pt 150-µL with lid. Here, cp is the
mean value, s the standard deviation of the three values, and Dcp the deviation from the
literature value.
°C
500
550
600
1250
1300
1350
0.08
0.81
–50.08
Platinum
918.81 mg
cp
s
Dcp
J/gK
%
%
0.18
1.12
23.61
0.17
3.20
20.00
0.17
2.06
14.29
0.11
0.41
–31.40
0.09
1.33
–46.10
Sapphire
232.12 mg
cp
s
Dcp
J/gK
%
%
1.29
0.72
10.22
1.27
1.43
7.14
1.25
1.50
4.29
0.75
15.14
–41.86
0.71
0.69
15.63
17.81
–44.92 –46.88
Table 3. Results using the direct method. Pt 150-µL crucible with lid. Here, cp, s, and Dcp
are as given in Table 2.
In general, a heating rate of 20 K/min
was used. This is a compromise between
a large heat flow signal, good temperature homogeneity within the sample, and
the time for the system to reach a steady
state in the dynamic segment.
Optimum measurement reproducibility
was achieved by performing the experiments one after the other at equal intervals. With alumina crucibles, the sample
robot can ideally be used.
The method included a low and a high
temperature range. This involved heating from 450 to 650 °C at 20 K/min with
10-minute isothermal phases before and
after heating. This was followed by a
jump to 1200 °C, an isothermal phase
of 10 min, heating to 1400 °C, and another 10-minute isothermal phase (see
Figure 1). The system was allowed to
stabilize at 450 °C and 1200 °C before
starting the measurement. The isother-
mal phases must be long enough for the
DSC signal to stabilize before the next
heating ramp begins.
Results
Sapphire method
Figure 2 shows the curves obtained for a
typical evaluation. The upper diagram
displays the heat flow curves of platinum
and sapphire. Both curves were evaluated
using the “Cp with Sapphire...” DSC function of the STARe software. The lower
diagrams show the resulting curves for
the specific heat capacity of platinum
separately for the lower and higher temperature ranges. Three values were automatically evaluated from the curves and
are presented in the table.
Table 2 summarizes the results of the cp
determinations of different materials ob-
METTLER TOLEDO
TA Application No. UC 271
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Thermal Analysis Application
tained using the sapphire method. Three
separate measurements of each sample
were performed in the lower and higher
temperature ranges. Each measurement
of the same material was performed with
the same single sample. The samples were
re-inserted into the furnace each time
prior to measurement. The table presents
the mean values and the standard deviation of three individual values as well as
the deviation from the literature values
given in Table 1. The reference value
for aluminum oxide was assumed to be
same as that of sapphire.
The mean values of the specific heat
capacities of different materials show a
maximum deviation of about 10% from
the corresponding reference values. The
smaller values (e.g. of Pt) vary more
strongly than the larger values (e.g. aluminum oxide). The results for the metals
tend to deviate to larger values and for
the oxides to lower values. The deviations
also tend to be greater at higher temperatures than at lower temperatures. The repeatability (standard deviation) is rather
better at low temperatures than at high
temperatures. Comparison of the results
for aluminum oxide powder and aluminum oxide lids show that the influence of
packing density is hardly noticeable. In
summary, a platinum crucible used with
a lid gives very good results for quantitative cp determinations at high (and low)
temperatures. An accuracy of ± 10% can
be expected.
Mettler-Toledo AG, Analytical
CH-8603 Schwerzenbach, Switzerland
Phone +41-44-806 77 11
Fax
+41-44-806 72 60
Internet www.mt.com
Direct method
The measurements obtained for the sapphire method can also be used to directly
determine c p values according to eq 3.
The results are shown in Table 3. The
large deviations indicate that this method is not suitable for cp determination.
Conclusions
Two standard DSC methods were used
to determine c p at temperatures up to
1600 °C. In general, results from the
direct method show that repeatability
and absolute accuracy are strongly temperature dependent. The method cannot
therefore be recommended. In contrast,
the sapphire method has the great advantage that no additional calibrations are
needed for special crucibles or gases. The
best way to minimize the influence of the
thermal conductivity of the sample and
other effects is to use platinum crucibles
with lids. Depending on the temperature
range, measurements of pure substances
are accurate to ± 5% to ± 10% in comparison with literature values. To achieve
high reproducibility and accuracy, measurements of a series should be performed
directly one after the other at constant
time intervals. This is most easily done
using the sample robot. Furthermore,
one or two blank measurements should
be performed at the beginning of a series
but not used for subtraction.
Literature
[1] Measuring specific heat capacity,
UserCom 7, 1–5
[2] G. W. H. Höhne, W. Hemminger
and H.-J. Flammersheim:
Differential Scanning Calorimetry,
Springer Verlag, 1996, 118
[3] J. Schawe, The separation of sensible
and latent heat flow using TOPEM®,
UserCom 22, 16–19
[4] J. Schawe et. al., Stochastic temperature modulation: A new technique
in temperature modulated DSC, Thermochimica Acta, 446 (2006) 147
[5] ISO 11357-4, Plastics – Differential
scanning calorimetry (DSC), Determination of Specific Heat Capacity
[6] DIN 53765, Testing of plastics and
elastomers; thermal analysis, DSC
method, Deutsches Institut für
Normung / German Institute for Standardization
[7] DIN 51007 Thermische Analyse (TA);
Differenzthermoanalyse (DTA);
Grundlagen, Deutsches Institut für
Normung / German Institute for Standardization
[8] ASTM E1269, Determining specific
heat capacity by DSC, ASTM International Westconshohocken, USA
[9] J.W. Arblaster, the thermodynamic
properties of platinum in ITS-90,
Platinum Metals Review, 38, 1994,
119–125.
[10] American Institute of Physics Handbook, 2nd edition, McGraw-Hill,
New York
[11] D’Ans . Lax, Taschenbuch für Chemie
and Physik, Band 1, Makroskopische
physikalisch-chemische Eigenschaften, 1967, Springer Berlin
[12] Handbook of Chemistry and Physics,
70th edition, 1989–1990, CRC Press
Inc., Boca Raton, Florida
[13] I. Barin, O. Knacke, Thermochemical
properties of inorganic substances,
1973, Springer Berlin
Publishing Note:
This application has been published in
the METTLER TOLEDO Thermal Analysis
UserCom No. 27.
See www.mt.com/ta-usercoms
www.mt.com/ta
For more information
Subject to technical changes
©01/2010 Mettler-Toledo AG
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METTLER TOLEDO
TA Application No. UC 271
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