An Analysis of Thermal Properties
Experiment 4
Alex High
MatSE 462, Section 4
27 April 2015
Abstract
Thermal analysis is important in the determination of the thermal properties of a material.
This experiment involved performing thermal gravimetric analysis (TGA), differential thermal
analysis (DTA), dilatometry, creep beam viscometry, and thermal diffusivity (TD) tests.
TGA, DTA, dilatometry, and creep beam viscometry were performed on glass, while TD was
performed on aluminum. The tests all provided data on the thermal properties of the materials,
which is useful in subsequent applications.
Introduction
These experiments were performed with the objective of determining the thermal
properties of the studied alkaline earth aluminosilicate glass and of the aluminum. For the
alkaline earth aluminosilicate glass, TGA, DTA, dilatometry, and thermal diffusivity were
performed. For the aluminum, TD was performed.
Thermal gravimetric analysis by measuring the weight change of the sample. Differential
Thermal Analysis measures the temperature difference between the test sample and a reference
sample. Dilatometry measures the expansion or contraction of a sample. Creep beam viscometry
heats glass which is then bent under an applied load; the deflection of the sample is then
measured. Thermal diffusivity measures the conduction of heat through a material.
The TGA/DTA analyses allowed for the glass transition temperature to be identified, as
does the dilatometry analysis. The creep beam viscometry allows for the annealing deflection
rate and the strain deflection rate to be identified. The annealing deflection rate is calculated as:
Eq.1
𝑎𝑑𝑟 =
(2.67∗10−11 )∗L3 ∗M
I𝑐
where L (cm) is the support span, M (g) is the centrally applied load, and Ic (cm4) is the cross
section moment of inertia of the test beam. The moment of inertia, Ic, is calculated as:
Eq. 2
I𝑐 =
b∗c3
12
where b (cm) is the longer cross section length of the beam and c (cm) is the shorter cross section
length of the rectangle.
The strain deflection rate is calculated as:
Eq. 3 𝑠𝑑𝑟 =
𝑎𝑑𝑟
31.6
where adr is the annealing deflection rate from Eq. 1.
The TD analysis allows for the thermal diffusivity of the material to be calculated.
Thermal diffusivity is formulated as 𝛼 =
𝜅
𝜌∙𝐶𝑃
, where α (m2/s) is the thermal diffusivity, κ
(W/(m·K)) is the thermal conductivity, ρ (kg/m3) is the density, and Cp (J/(kg·K)).
Alkaline earth aluminosilicate glasses have important uses. These glasses can be used in
high temperature applications in electrical engineering and in bulb and exhaust tubes for halogen
lamps for lighting applications1. Aluminum is used as a base alloy and as a product in many
industry applications.
Experimental Procedures
I. Thermal Gravimetric Analysis/Differential Thermal Analysis
These analyses were both performed on a SDT Q600 from TA Instruments in New
Castle, Delaware. The samples were alkaline earth aluminosilicate glasses. The experiment
proceeded as follows. The furnace was tared to accommodate the sample and reference crucibles.
Once the machine was tared, the test sample and reference samples were loaded into the
appropriate crucibles for testing. The TA Instruments software was run and the directions within
the software were followed. Once the gas flow rate was entered (typically 100 ml/min), the test
was run.
II. Dilatometry
The dilatometry was performed on a Dilatometer 1200C from Theta Industries in Port
Washington, New York. The samples were alkaline earth aluminosilicate glasses. The input data
is listed in Table 1.
Table 1. – Dilatometer User-Input Data
Sampling rate
2 sec
Data logging rate
Initial temperature
Heating time
Cooling time
% softening
20 sec
23 °C
5 hrs
7 hrs
5
Min. softening temp.
300 °C
Once this data was inputted, the sample was loaded. This was achieved by sliding back
the cover over the linear variable differential transducer (LVDT) and placing the sample into
position on the back rod. The cover was replaced and the test was run.
III. Creep Beam Viscometry
The viscometry was performed on a Beam-Bending Viscometer 1200C from Theta
Industries in Port Washington, New York. The samples were alkaline earth aluminosilicate
glasses. The experiment proceeded as follows. The weights were loaded onto the stage in the
correct amounts. The weight used was 1090 g. The sample was placed onto the stage and the
furnace was lowered around it and care was taken so that the furnace did not contact the sample
while lowering. The data found in Table 2 was then inputted into the computer.
Table 2. – Viscometer User-Input Data
Sample width
0.341 cm
Sample thickness 0.337 cm
Cooling rate
4 °C/min
Sample rate
1 sec
Data logging rate 60 sec
Then the viscometry test was run.
Note: The bolded terms in Table 2 represent the values from the tests in this experiment.
These values should be properly amended for the measurements of a sample used in a
subsequent test.
IV. Thermal Diffusivity
The thermal diffusivity tests were performed on cylindrical aluminum rods. The end of
the rods were attached to a thermocouple with the intent of measuring the temperature at each
end. The rod was placed vertically (with only an end contacting the hot plate). Over 10 minutes,
the temperature of the rod, at both the end contacting the hot plate and at the end opposite the hot
plate, was measured3.
Results and Discussion
I. Thermal Gravimetric Analysis/Differential Thermal Analysis
The TGA was plotted on a graph of percent initial weight, % W0 (mg), vs. temperature
(°C). The DTA was plotted on the same graph, but with axes of temperature difference (°C) vs.
temperature (°C). These plots are seen in Fig. 1.
Initially, in the TGA plot, the percent initial weight is linearly constant. The % W0
remains above 99.97 % of the original sample until immediately before the temperature reaches
700 °C. At this point, the plot loses it linear form.
The DTA exhibits sharp changes in its plot. The peak at ~1050 °C is the cold
crystallization of the glass, i.e. where crystals form (during cooling) but the glass remains
rubbery because it is above the glass transition temperature. The dip at ~1275 °C is the
traditional melting temperature of the glass. For cooling, the plot falls sharply at ~700 °C. This
marks the glass transition temperature.
Fig. 1. – TGA/DTA Plot for Aluminosilicate Glass
TGA/DTA of Alkaline Earth Aluminosilicate Glass
100.05
0
100
99.95
-2
% W0 (mg)
99.9
99.85
-3
99.8
-4
99.75
-5
99.7
-6
99.65
99.6
0
200
400
600
800
T (°C)
TGA
DTA
1000
1200
-7
1400
Temperature Difference (°C)
-1
II. Dilatometry
The dilatometry data was plotted on a graph of sample expansion (ppm) vs.
temperature (°C). The temperatures did not follow a total linear progression as seen in Fig 2. The
equations of the lines of the two different sections were determined, and the intersection between
these lines was solved for. This value is where two sections meet and is known as the glass
transition temperature, Tg. From the dilatometry data, this temperature is calculated as
Tg =
756.13 °C.
The coefficient of thermal expansion (CTE) is calculated as the slope of the linear
sections of the graph. For the material below the glass transition temperature (Tg > T), the CTE is
measured to be 9.627 ppm/°C. For the material above the glass transition temperature (Tg < T),
the CTE is measured to be 31.065 ppm/°C.
At the glass transition temperature (when going from a lower to a higher temperature),
the glass takes on a rubbery characteristic, which is a departure from its uniformly solid previous
state. The coefficient of thermal expansion increases here because of the ability of the molecules
to move more, relative to the glassy state. This movement allows for the rubbery glass to be
more flexible will respond more to heat.
Fig. 2. – Dilatometry Plot for Aluminosilicate Glass
Dilatometry of an Alkaline Earth Aluminosilicate Glass
10000
y = 31.065x - 16609
9000
Sample Expansion (ppm)
8000
T=756.13 °C
7000
6000
5000
y = 9.6268x - 398.93
4000
3000
2000
1000
0
-1000
0
100
200
300
400
500
T (°C)
600
700
800
900
III. Creep Beam Viscometry
The viscometry data was plotted on a graph of the natural logarithm of the deflection
rate (cm/sec), vs. temperature (°C). The data is divided into two linear sections. These sections
can be seen in Fig. 3.
Fig. 3. – Creep Beam Viscometry
Creep Beam Viscometry
0
0
100
200
300
400
500
600
700
800
900
-2
ln(DR) (cm/sec)
-4
-6
-8
-10
y = 0.0002x - 13.558
-12
y = 0.0734x - 64.798
-14
-16
T (°C)
ln(Annealing Deflection Rate) (cm/min)
ln(Strain Deflection Rate) (cm/min)
The point where the plot slopes linearly upwards is the glass transition temperature. This is at
700 °C.
The annealing deflection rate was calculated from Eq. 1 using the values found in
Table 2. In addition, L = 7.75 cm and M = 1090 g. This rate was calculated to be
4.78E-5 cm/min. The strain deflecting rate, calculated from Eq. 3, was found to be
1.51E-6 cm/min. The natural logarithms of these two values were plotted on the viscometry data
in the form of a horizontal line. These lines intersected the upward sloping linear section, and the
points of intersection offer the temperatures for the annealing deflection rate and the strain
deflection rate. The annealing deflection rate corresponds to 750 °C, and the strain deflection rate
corresponds to 700 °C.
The annealing point is the temperature at which internal stresses within a glass are
substantially relieved within minutes3. The strain point is the temperature at which internal
stresses in a glass are substantially relieved in the timeframe of hours3.
These temperatures are vital to recognize when working with glass because of the brittle
nature of glass in its glassy state. As seen from the TGA/DTA and dilatometry data, the Tg is
approximately 700 °C, which is also seen as the strain deflection rate from this viscometry data.
If the glass was strained below this corresponding temperature, the material would be in its
glassy state and would be brittle. However, if the glass needs to be strained, this can be achieved
by raising the temperature of the glass to over 700 °C, which will be effective in annealing,
rather than breaking, the glass.
Additionally, flame-working the glass requires the knowledge of the temperatures.
Effectively molding the glass requires that glass is relieved of many internal stresses, which is
the characterization of both the annealing and strain points.
IV. Thermal Diffusivity
The aluminum rod offered the data found in Fig. 4. T1 was the temperature where the rod
contacted the hot plate. T2 was the temperature of the end of the rod that was completely free
from any heating source. At the free end of the rod, the temperature progression was linear. This
is due to the thermal diffusivity of the material. At the end of the rod that contacted the hot plate,
the temperature progression followed a nonlinear path.
Fig. 4. – Temperature data for a heated aluminum rod.
Temperature vs. Time for Aluminum
100
y = 3E-12x6 - 3E-09x5 + 1E-06x4 - 0.0002x3 + 0.0111x2 + 0.3608x +
22.802
90
80
70
T (°C)
60
50
T1
y = 0.0458x + 22
40
T2
30
20
10
0
0
50
100
150
200
250
300
350
Time (sec)
As time increases, T1 continually increased but with a decreasing rate. Through ~75 sec, the rate
of temperature increase was steep, but as the time approached ~100 sec, the rate of temperature
increase had lessened. The difference between T1 and T2 can be seen in Fig. 5.
Fig. 5. – Temperature differential plot
Temperature Differential Plot
60
50
ΔT (°C)
40
30
20
y = 4E-12x6 - 4E-09x5 + 1E-06x4 - 0.0002x3 + 0.0144x2 + 0.2373x - 0.0631
10
0
0
-10
50
100
150
200
Time (sec)
250
300
350
Thermal diffusivity is the measure of a material’s ability to store thermal energy vs. its ability to
conduct heat. Through ~75 sec, the aluminum rod was storing the thermal energy, but following
this time, the rod tended to conduct more through its bulk than to store the thermal energy. This
reason explains why after ~100 sec, the T1 plot becomes almost linear with possibly a similar
slope to the linear T2 plot.
From literature, alkaline-aluminosilicates have Tg values of 800-1000 K, which
corresponds to the ~700 °C calculated Tg. The alkaline aluminosilicates are represented in Fig. 6
by the open circles4.
Fig. 6. – Tg of silicates4
Conclusions
The TGA/DTA and dilatometry all provided a Tg of ~700 °C which corresponds to the
literature values of ~1000 K. The strain point also corresponds to ~700 °C which is where the
glass can be strained to relieve internal stresses. Overall, the thermal analyses provided data that
corresponded with literature, which reinforces its importance for testing materials.
References
1. MatWeb, Schott Glass 8253 Alkaline Earth Aluminosilicate Glass. 4/26/15.
<http://www.matweb.com/search/datasheettext.aspx?matguid=863cb3ed7395450bb6f
cc86680ff63f9>
2. ASTM, Standard Test Method for Annealing Point and Strain Point of Glass by Beam
Bending. 4/27/15.
<https://cms.psu.edu/Merge/2009/MRG-150103-132958ERB105/_assoc/B961FE6F878544D19A252509EDC4ABD0/ASTM_Std_C59893__Reapproved_2013__Creep.pdf>
3. ASTM, Standard Test Method for Linear Expansion of Solid Materials With a PushRod Dilatometer. 4/27/15.
<https://cms.psu.edu/Merge/2009/MRG-150103-132958ERB105/_assoc/68A8D09BEAF84C43A3F466D6B02D12F0/E228.29361.pdf>
4. I. Avramov, Ts. Vassilev, I. Penkov. The glass transition temperature of silicate and
borate glasses. Journal of Non-Crystalline Solids, 2005, 351, 472-476.