Applied Mechanics and Materials
ISSN: 1662-7482, Vol. 420, pp 185-193
doi:10.4028/www.scientific.net/AMM.420.185
© 2013 Trans Tech Publications, Switzerland
Online: 2013-09-27
Determination of Specific Heat of EutecticIndium – Bismuth- Tin Liquid
Metal Alloys as a Test Material for Liquid Metal - Cooled Applications
Adam Lipchitz1,a, Glenn Harvel1,b, Takeyoshi Sunagawa2,c
1
Faculty of Energy Systems and Nuclear Sciences, University of Ontario Institute of Technology,
2000 Simcoe Street North, Oshawa, Ontario, Canada, L1H 7K4
2
Department of Applied Nuclear Technology, Fukui University of Technology, 3-6-1 Gakuen,
Fuku-shi, Fukui, 910-8505, Japan
a
[email protected], [email protected], [email protected]
Keywords:Liquid Metals, Liquid Metal Cooled Nuclear Reactors, Specific Heat, Eutectic Alloys
Abstract. Currently, Russia, India, China, France, South Korea, and Japan are actively pursuing
liquid metal cooled applications such as liquid cooled metal nuclear reactor concepts. The liquid
metal coolants being considered for these designs are sodium, lead and lead-bismuth eutectic; these
designs utilize reactive and toxic materials at temperatures up to 1073 K for nuclear power plant
operations and other similar applications. To simulate these systems with the actual coolant
material requires a high level of safety systems. Use of these materials in university experimental
laboratory settings is difficult due to the safety hazards and that lead (Pb) is a designated substance
requiring special permission to use. Therefore, a less toxic and less reactive liquid metal that can
be used to simulate liquid metal cooled flows will allow for a greater number of investigations and
experimentation of liquid metal flow with regards to the field of thermal hydraulics. Good
candidates for a liquid metal experimental fluid are alloys from the indium-bismuth-tin system such
as Field’s metal, which by weight percent is 51% indium, 32.5% bismuth and 16.5% tin and
possesses a melting temperature of 333 K. However, the thermodynamic properties of Field’s metal
and similar alloys in their liquid state are not well described in literature. This work experimentally
measures the specific heat of the eutectic alloys of theindium-bismuth-tin tertiary system using a
differential scanning calorimeter technique and analyzes the results to determine if the
thermodynamic properties of the system have sufficient scaling for experimental modeling
applications. The results verify the melting temperatures of the alloys and establish a relationship
between temperature and specific heat.
Introduction
Liquid metals have been used to cool advanced power generation systems such as nuclear power
plants and submarines since the 1970s[1,2]. Typically, the liquid metals are either a pure elemental
metal, such as lithium, lead or sodium or a eutectic alloy, for examplelead-bismuth or
sodium-potassium[3,4,5].
Currently, the international Generation IV Forum has selected liquid metal cooled reactors as one
of six concepts to explore for future nuclear power generation designs and technologies as these
systems can achieve thermal efficiencies on the order of 40%. The forum has selected three liquid
metals as the possible coolant for this type of reactor; sodium, lead and lead-bismuth[1].
Therefore, it is essential that the thermal-hydraulics of liquid metals and especially liquid metal
eutectic alloys be investigated and understood using modern techniques and methods. However, in
Canada; sodium, due to its chemical reactivity and lead (Pb) due to its toxicity, are difficult
materials to study inuniversity laboratory settings without special considerations to health and
safety[6,7].Despite this problem, it is still necessary to perform experiments at the University level
for education, training, and research on liquid metals to improve the overall understanding of their
use in a nuclear reactor environment.
Therefore, if a liquid metal could be developed as an experimental model then experimentation
in this field could be increased significantly. For water cooled reactors, Freons were commonly used
as a test fluid to simulate the fluid behaviour. Thus, the same methods can be applied here to liquid
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Recent Trends in Materials and Mechanical Engineering II
metals. In order to achieve this objective, the thermo-physical properties of a liquid metal
experimental fluid need to be characterized[8,9,10]. Unfortunately, the fluid properties of many
eutectic alloys have not been well documented in the liquid region in the public
literature[11,12,13,14]. This workutilizes a method to measure the specific heat of eutectic liquid
metal alloys in the indium-bismuth-tin system and compare the values to that of a lead-bismuth
eutectic. The compositions of the various alloys used in this study are described in Table 1 along
with their critical (melting) temperatures.
Table 1: Composition by weight percent of eutectic liquid metal alloys [11,13]
Indium-Bismuth-Tin Eutectic Alloys
Alloy Name (Weight Percent)
Field’s Metal (51 In /32.5 Bi/ 16.5 Sn)
Local Eutectic Reactions for In-Bi-Sn System
Indalloy 27 (54 Bi /29.7 In/ 16.3 Sn)
Indalloy 174 (57 Bi/26 In/17 Sn)
Other Eutectic Alloys
Bismuth-Tin (52 Bi/48 Sn)
Lead – Bismuth (45.5 Pb/55.5 Bi)
Critical Temperature/ Reaction
333 [K] Eutectic
354 [K]
352 [K]
415 [K] Eutectic
397 [K] Eutectic
The study investigates the eutectic alloys of the In-Bi-Snternary system;where there are three
different eutectic alloys. The primary eutectic alloy Field’s metal and two local eutectic alloys
whose compositions are presented in Table 1. Field’s metal is considered to be the primary eutectic
reaction occurring in the ternary system as it has the lowest critical temperature 333 K. Therefore,
Field’s metalalso has the highest potential for the easiest use in a laboratory setting of the three
eutectic alloys. Field’s metal also has several other advantageous properties; it is non-reactive with
air and water, responds to a magnetic field and is easily fabricated[8]. However, little is publicly
available about its thermo-physical properties in a liquid state or the other In-Bi-Sn alloys[12,15]
even though its material thermodynamic properties were recently determined and optimized[16].
This study examines the specific heat of all three In-Bi-Sn alloys. The property of specific heat
(Cp) is chosen as it is a fundamental parameter to thermal hydraulics and fluid dynamics
research.Specific heat is dependent on the material, its state of matter and the temperature. Specific
heat in this work is measured using a differential scanning calorimeter, which has been
demonstrated to effectively measure the specific heat of liquid metals[17,18,19].
Experimental Design
The In-Bi-Sn alloys tested and investigated are the same as those presented in Tables 1 and 2;
Field’s metal, Indalloy-27, and Indalloy 174. The alloys were fabricated at University of Ontario
Institute of Technology. The alloys are created in a carbon-rich environment and after formation are
filtered for oxides based on a method developed by Sunagawa et al. [20] . A reference sample of
Field’s metal was acquired from Fukui University of Technology created by Dr. Sungawais also
tested and compared to the UOIT fabricated sample of Field’s metal.The metal alloys’ specific heat
is measured using a TA instruments Q20 v.23.4 differential scanning calorimeter (DSC).
DSCs work by heating two materials, the sample and the reference, at a constant specified rate.
The calorimeter records the time-dependent temperature of each material using a thermocouple. As
the temperatures of two materials’ heat capacity are different the rate at which they heat and the
corresponding temperatures will also be different. This difference is innate to materials themselves
and can be used to calculate the specific heat. Figure 1 is a schematic of the type differential
scanning calorimeter employed.
Applied Mechanics and Materials Vol. 420
187
Figure 1: Schematic of a TA Q20 series differential scanning calorimeter [19]
There are several methods to calculate specific heat from a DSC. The method used in this work
is called the cell constant method[19]. The cell constant method uses the following equation:
C =
∗ ∗
∗
.
(1)
where, E is the cell constant, H is the heat flow, m is the mass and Hr is the heating rate. The
systems’ cell constant is determined using a built-in function of the DSC software. A pure sample of
Indium is required to run until it reaches its melting point as this is a known reference sample.Next
the background heat rate is determined by placing two empty pans into the DSC. The heat flow is
calculated by subtracting the background from the recorded data.
The TA instruments Q20 v.23.4 differential scanning calorimeter was used with nitrogen purge
gas and platinum reference pans. The samples are placed inside a reference pan and sealed.Each
sample is heated at a rate of 5◦C/min up to 150◦C except in the case of Sn-Bi, where it was heated to
180◦C due to its higher melting temperature.
Results and Discussions
The melting temperatures and specific heat of all three alloys were calculated and are presented in
this section. Figure 2 is a description of the heat flow curves presented in Figures 3-5. The heat
flow changes as energy is added or removed from the system. For metals a significant change in the
positive direction in heat flow is from the solidification or endothermic reaction of the liquid. A
significant change in the negative direction is an exothermic reaction. In the following figures the
exothermic reaction is the melting of the metal alloy. For the specific heat measurement the reaction
of interested is heating section of the curve where temperature is rising.
Figure 2: Description of heat flow vs. temperature curve for a differential scanning calorimeter with exothermic and
endothermic reactions
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The melting temperature occurs at the point where the tangent of the inflection point intersects
the base of the curve. In order to determine the melting temperature the point can be determined
from an examination of heat flow curve. A tie line is drawn from the beginning of the reaction
(across the valley) to the end of the reaction. From here a line is drawn from the inflection point
until it intersects with the tie line. The point where the lines intersect is the eutectic melting
temperature. The method is demonstrated in Figure 3 with Field’s metal. Field’s metal has a
double peak shape in its eutectic reaction. Therefore, two points of interest are determined. The first
point is the intersection of the tie line and inflection point, therefore the eutectic melting point. The
alloy then goes through a brief transition period before the melting reaction is concluded. A line is
drawn that is tangent to the larger curve. The second point is where this line intersects with the tie
line, which is the melting temperature.
Both samples of Field’s metal produced very similar heat curves with a double valley shape
during its melting reaction. The first smaller valley occurs at approximately 59.5 ◦C, while the
second valley occurs at 61 ◦C. The double valley suggests a transition period where the melting
reaction does not emit a linear amount of energy but rather a smaller initial release of energy and
then a larger secondary release. Figures 4 and 5 are the entire curves for the three fabricated alloys
and the reference sample of Field’s metal.
15
Heat Flow (mW)
10
5
0
-5
55
60
65
70
75
80
-10
-15
Temperature (°C)
Figure 3: Determination of melting temperature for a liquid metal based upon the experimentalcalorimetric data.The
melting point is determined at the intersection of the tangent to the slope and the baseline.
15
15
10
Heat Flow (mW)
Heat Flow (mW)
10
5
0
-5
0
50
100
150
a)
0
0
50
100
150
-5
-10
-15
5
-10
Temperature (°C)
Temperature (°C)
b)
Figure 4: Heat flow versus temperature for a) fabricated sample of Field's metal b) reference sample for the
determination of melting temperature and specific heat calculations
Applied Mechanics and Materials Vol. 420
80
40
30
60
Heat Flow (mW)
Heat Flow (mW)
60
50
189
20
10
0
-10 0
50
100
150
-20
-30
40
20
0
0
Temperature (°C)
a)
b)
-20
50
100
150
Temperature (°C)
Figure 5: Heat flow versus temperature for a) Indalloy-174 and b) Indalloy-127for the determination of melting
temperature and specific heat calculations
The other two alloys, Indalloy-174 and Indalloy-27, have a smooth single valley with a single
point where the melting reaction occurs. This shape allows for an easier determination of the
melting temperature with a single value of 79◦C and 80.5◦C for Indalloy-174 and Indalloy-27
respectively. Table 2 lists the melting temperatures and the percent difference between the reference
values and experimental data. The calculated melting temperatures are all within 1◦C of the
reference values, which are in the range of acceptable accuracy for the application of ± 2◦C[19].
Table 2: Measured melting temperatures of eutectic In-Bi-Sn alloys using a differential scanning calorimeter
Alloy
Field’s Metal
Indalloy 27
Indalloy 174
Recorded Melting Temperature
[K]
332.5, 334
353.5
352
Reference Melting Temperature
[K][13]
333
354
352
Percent Difference
[%]
1.67
0.6
0
The specific heat is calculated using the cell constant method, explained in Section 2, from the
heat curve experimental data. Figure 7 displays the specific heat and temperature data. The peaks
occur at the melting temperatures of the alloys and have the same shape of heat curve exothermic
reaction expect in the positive direction. The area of interest is the specific heat of the alloys in their
liquid state, which occurs to the right of the peak. Immediately, after the peak there is significant
variation of up to 25% from the median value. Therefore, the median value is used to calculate the
approximated specific heat in that region.
Table 3: Uncertainty of Specific Heat Calculation
Parameter
Indium [E]
Mass
Temperature
Heat Flow
Uncertainty
± 5 [%]
± 0.05 [mg]
± 1 [K]
±5E-8[mW]
Furthermore, it is important to note that the area between the curve and the tie-line or the area
within the exothermic reaction is representative of the heat generated in the experiment. Therefore,
this area can be used to calculate the heat of fusion (enthalpy of melting). However, this analysis
was not performed as it is not needed for the creation of the thermal hydraulic model.
Table 4 lists the calculated specific heat at 150 ◦C or 423 K. Field’s metal has the highest heat
capacity of the three alloys. At 423 KLead-Bismuth Eutectic (LBE) has a specific heat in the
range of 145-148 J/kg-K. Therefore, Indalloy-27 has a specific heat most similar to Lead-Bismuth
out of the alloys investigated. The result is not unexpected as Indalloy-27 has the highest bismuth
content and therefore should be closest physically to LBE. Field’s metal however is comprised of
nearly two-thirds a combination of indium and tin which have a significantly higher specific heat
than lead and bismuth.
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The experimental results are used to create an equation with the capability to approximate the
specific heat for the purpose of inclusion into a numerical model. The correlations are only an
approximation of the specific heat within a specified temperature. The calculated specific heats
based on the correlations are presented in Figure 7. The correlations are presented in Table 4. The
regions immediately before and after the spike in specific heat that occurs during melting have
significant variance and have been corrected for the determination of the correlations. In the
future a more detailed investigation of specific heat in this region may yield a more accurate
correlation if it is necessary to have accurate knowledge near phase transitions. However, the
correlations are considered sufficient for the approximation of specific heat in numerical models
with a7% variance from the experimental data.
Table 4: Experimentally determined specific heat of eutectic liquid metal alloys and reference values for other liquid
metals
Alloy
Cp [J/kg-K]
At 423[K]
Field’s Metal
250
Indalloy 27
170
Indalloy 174
200
Sn-Bi
263
Other Liquid Metals at T = 573 [K][11][21]
Indium
247
Tin
244
Lead
145
Bismuth
140
Lead-Bismuth
150
Sodium
1304
Lithium
4280
Table 5: Experimentally derived correlations for the approximation of specific heat for a numerical model
◦
Alloy
Correlation
Temperature Range [ C]
Field’s Metal – Fabrication
0.3661 – 1 x 10-3T + 3 x 10-6T2
60-150
Field’s Metal – Reference
0.347 – 9 x 10-4T + 2 x 10-6T2
60-150
Indalloy 27
0.1178 – 1.1 x 10-3T + 3 x 10-6T2
80-140
Indalloy 174
0.1343 – 1.9 x 10-3T + 2 x 10-6T2
85-150
18
54 Bi-29.7 In16.3 Sn
16
Cp (J/g-K)
14
12
57 Bi-26 In-17
Sn
10
58 Bi-42 Sn
8
6
4
2
0
0
50
100
Temperature (K)
150
200
Figure 6: Specific heat versus temperature for In-Bi-Sn eutectic alloys and eutectic Sn-Bi with error of ±25% in the
liquid region.
Applied Mechanics and Materials Vol. 420
191
0.35
Specific Heat (J/g◦K)
0.3
0.25
0.2
0.15
0.1
Field's Metal - Fabircated
Field's Metal - Reference
Indalloy 27
Indalloy 174
0.05
0
60
80
100
120
Temperature ( K)
140
Figure 7: Calculated heat capacity of In-Bi-Sn eutectic alloys based upon experimentally determined correlations with a
variance of ±7% from the experimental data
Concluding Remarks
The following concluding remarks were obtained from the completion of this study;
The specific heat of the three eutectic alloys of interest in the In-Bi-Sn ternary system was
experimentally determined. Field’s metal is observed to have a higher specific heat than the other
two alloys as expected due to the higher indium and tin content. Indalloy 27 has a specific heat
similar to lead-bismuth eutectic.
The melting temperatures of the In-Bi-Sn eutectic alloys have been confirmed and verified by
this work. The temperatures are in agreement with the published data from the Indium Corporation
as oppose to some critical temperatures of theses alloys published in literature. The heat rate curves
also determine there is a transition occurring during melting for Field’s metal that is undetermined
and warrants further investigation.
Correlations for the relationship between specific heat and temperaturehave been developed to
approximate the specific heat of the In-Bi-Sn eutectic alloys. The correlations are considered
suitable for anumerical model of a system utilizing these alloys as a liquid coolant. However, the
correlations require further investigation and verification if they need to be used beyond the
measured range of data or if more accuracy near the phase transition boundary is required.
The data collected in this work can now be used as inputs into a thermal-hydraulic model to
approximate the change in specific heat with temperature and establish the lower bound with
respect to temperature for the model.
Acknowledgments
The authors wish to acknowledge and thank TheophileImbert at UOIT and on loan from Universite
Joseph Fourier for his technical assistance and support.We also acknowledge Dr. Frank McCluskey,
Dr. Matthew Kaye, Dr. GhausRivzi and Dr. UsmanSaeedof the University of Ontario Institute of
Technology Materials Science Research Group for access to the equipment and support regarding
the differential scanning calorimeter and for valuable discussions. This work is supported by
NSERC of Canada Discovery Grants and Ontario Graduate Scholarships.
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Recent Trends in Materials and Mechanical Engineering II
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Recent Trends in Materials and Mechanical Engineering II
10.4028/www.scientific.net/AMM.420
Determination of Specific Heat of Eutectic Indium – Bismuth-Tin Liquid Metal Alloys as a Test
Material for Liquid Metal - Cooled Applications
10.4028/www.scientific.net/AMM.420.185