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Determination of the thermal conductivity of graphite and high-temperature alloys by the laser-flash method
Determ!nation of the.thermal conductivity of graphite and high-temperature alloys by the laser-flash method Dr W. Neumann and K. Wallisch Department of Materials Science, Austrian Research Centre, Seibersdorf, Lenaugasse 10, A-1082 Vienna Thermal conductivity measurements at very high temperatures (above 1000°C) are difficult, particularly because of the heat loss by radiation which is hard to avoid when using all the steady-state methods. But, in many cases, the experimental problems can be overcome by measuring the thermal diffusivity and calculating the conductivity data after additional determinations of specific heat and density have been made. For some high-temperature materials (graphite and metallic alloys), this procedure was chosen to determine the thermal conductivities. Therefore an apparatus was designed based on the known method, but with some special adaptations. Standard materials were tested in this way to show its advantages. The laser-flash apparatus is described, and the results obtained are reported and discussed.
Introduction
Experimental apparatus and procedure
One of the recent trends in materials science is the development of materials for high-temperature application to meet certain requirements. One such need is to run processes at higher temperatures to increase efficiency, while another is to improve thermal isolation with respect to energy saving. The applicability of new or advanced materials, as well as of existing ones, strongly depends on their thermophysical properties. One of the most important of these properties is thermal conductivity. Many data can be found in the literature but most of the known values have been obtained at ambient or moderate temperatures. Any extrapolation of known data to higher temperatures may cause significant errors, so reliable data can only be obtained by experimental determination. However, to measure the thermal conductivity value itself (which could be done by a steady-state method) causes numerous problems at high temperatures, e g, the unavoidable heat loss by radiation. A possible solution of these problems is the determination of the thermal diffusivity by a transient method, followed by a calculation of the thermal conductivity according to the well-known formula :
The flash technique developed by Parker et al (1961)is very well described in the literature (Taylor, 1978). It is based on theoretical considerations made by Carslaw and Jaeger (1959), who derived the fornmla of tile temperature distribution as a function of time under these particular conditions. The specimen, a disc-shaped plate, is heated up to the measuring temperature. An energy flash on to one of its surfaces immediately causes an increase of temperature on this surface. After few milliseconds (the exact time depends on the specimen's diffusivity and thickness), the temperature on the rear surface increases and achieves its maxinmm value after a certain time. The temperature-time history of the rear surface (Fig 1) is significant for the specimen's thermal diffusivity. The absolute diffusivity value can be calculated by the use of the following equation:
)t = c t x
CpX p
where X is the thermal conductivity, c~ the thermal diffusivity, Cp the specific heat,
and p the density. The paper discusses this procedure with the aid of welldocumented materials, such as POCO graphite, graphite for nuclear applications, Armco Iron, and Inconel 702, using a laser-flash apparatus to measure the thermal diffusivity. 204
0.139 l 2 /1;2
where a is the thermal diffusivity, l the specimen thickness, and tl/2 the time, until half of the maximum temperature is achieved. This simple formula is only valid under certain conditions, of course, e g, parallel surfaces, negligible heat loss, homogeneous absorption of energy on the front surface, short pulse time related to tv2, homogeneous specimens, etc. If some of these requirements are not fulfilled, corrections developed for special cases can be applied, such as finitepulse effect (Larson and Koyama, 1963), heat-loss effect (Cowen, 1962), non-uniform heating (Taylor, 1975 ). Nevertheless, tile intention should be to design tile Measurement Vol 1 No 4, O c t - D e c 1983
Neumann and Wallisch
temperatureincrease
100%
50~
ff
•
T,
0,5Tmax
Trnax
V
'
6o
measuring device so that a minimum of correction is necessary. To meet these requirements, an apparatus was designed. It consists of three units (Fig 2): (i) an energy source for the pulse; (ii) a specimen chamber, with furnace; and (iii) control and recording equipment. The energy source is a high-energy neodym glass laser (Laser Optronic System 2000) with a pulse duration time of about 0.5 ms and a maximum pulse energy of 40 J, which produces the required very-rapid temperature increase on the surface. The laser runs in multi-mode conditions to guarantee a sufficient energy supply in a homogeneous laser beam. For alignment, a He-Ne laser is used (Fig 3). The specimen chamber was designed with a resistance heater of small heat capacity to enable very quick heating as well as cooling. This results in two advantages: first, reduction of the time of measuring the diffusivity in a certain temperature range; second, the possibility of getting diffusivity values of materials in a metastable state. The specimen chamber is gas tight and can be evacuated, so that tests can be carried out in vacuum or inert gas.
Pyrometer
- ,' . . -
time rn sec
Fig I Temperature-time history of the rear surface
The specimen, of cylindrical shape (10 mm in diameter and up to 4 mm high), is horizontally positioned within a tantalum tube, which acts as resistance heater. The resistance heater is supplied with high-stabilised DC (max 600A, - 1 0 V ) . Because of the horizontal position, an elaborate specimen holder is not necessary. The specimen is supported by three small ceramic tubes to minimise the heat loss by conduction along the specimen holder. Heat loss by convection can be avoided by evacuating the chamber, while heat loss by radiation is reduced by reflectors. Temperature measurement is undertaken by a Pt-PtRh thermocouple in contact with the rear surface of the specimen. Above 1700°C, a pyrometer can be used instead of the thermocouple. The temperature increase on the rear surface of the specimen, due to the laser pulse, is detected by either a germanium-photodiode or a silicon-photodiode. The temperature-time history of the rear surface is recorded by a transient recorder and can be seen on a screen or be plotted by an x - y recorder. The diagrams of the x - y recorder were graphically examined and the tz/2 was determined. The heat effect was taken into account according to Cowen's report (Cowen, 1962). An automatic digital data-acquisition system will be applied soon.
Photodetector
CAMAC~dier~s~aty~ ~urn°ce-~"-~ ~pec~rnen IK°mP.atrat°r!CAMAC
CAMACIcontr~ierl ~ ]
L~r~
I Disiay I Fig 2 Thermal diffusivity measurement equipment
Measurement Vol 1 No 4, Oct--Dec 1983
205
Neumann and Wallisch TABLE 1: Thermophysical data of POCO graphite Temperature T (K)
Thermal ] diffusivity c~(cm 2Is)
Specific 2 heat Cp(J/gK)
Density 2 p (g/cm ~ )
Thermal 3 conductivity X(W/m K)
390 420 450 615 728 736 865 999 1002 1186 1221 1260 1328 1473 1600 1739 1860
0.55 0.54 0.52 0.34 0.28 0.275 0.245 0.20 0.205 0.172 0.165 0.160 0.160 0.144 0.137 0.127 0.120
0.932 0.999 1.063 1.403 1.552 1.562 1.695 1.796 1.799 1.899 1.913 1.927 1.951 1.966 2,028 2.058 2.080
1.737 1.736 1.735 1.730 1.726 1.725 1.720 1.714 1.714 1.705 1.704 1.702 1.698 1.693 1.687 1.680 1.675
89.0 93.6 95.9 82.5 75.0 74.1 71.4 61.6 63.2 55.7 53.8 52.5 53.0 47.9 46.9 43.9 41.8
Measured by laser-flash method. Ref Taylor, 1980. a Calculated.
were listed. A comparison of the conductivity values obtained by the different methods is given in Fig 5. These experiments were only carried out at a temperature of 1273 K.
3 Ineonel
Fig 3
Laser-flashapparatus
Specific experiments 1 P O C O graphite
The experiments described were performed on a POCOAXM 5Q1 specimen. It was the same material as used in the investigation of R. E. Taylor (Taylor, 1980). POCO graphite is a much-researched material, which acts as a standard for thermal conductivity and thermal diffusivity measurements at high temperatures. Because of the excellent absorption of the laser energy, a special preparation of the surface was not necessary. The results obtained are listed in Table 1. Based on these results and applying the density and specific heat values shown in Table 1, the thermal conductivity was calculated. The calculated values are compared with conductivity data measured by the Kohlrausch method (Taylor, 1980) (Fig 4).
2 Graphite Besides POCO graphite, a graphite usually used in hightemperature nuclear reactor fuel fabrication was tested. This example was chosen because small specimens are particularly suitable for this purpose. Three types were investigated. Four specimens of each were prepared (10 mm in diameter, 2 mm high), two being parallel and two perpendicular to the direction of the pressure applied during the fabrication process. The results obtained are summarised in Table 2. In addition, the thermal conductivity data measured by a heat-flow method in another laboratory 206
Inconel 702 serves as a standard material for the comparative method. The chemical composition of this Nibased alloy is Cr 17, AI 2.5, C 0.066, Cu 0.25, Fe 0.36, Si 0.19, Ti0.59wt%. The specimens (10ram in diameter, 1.21 mm high) for the laser-flash apparatus were cut off a sample, which was delivered as reference material for steady-state comparative tests. The specimen's surfaces were grit-blasted to guarantee a sufficient and homogeneous heat absorption. The speci-
AX(W/mK)
100 T\,
,
\
\ N
80
N \
\
60 "-- ..~ x
x
60
---
aS reported
× calculated 500
10110
1500 T(K)
Fig 4
Thermal conductivit>' of POCO graphite Measurement Vol 1 No 4, Oct--Dec 1983
Neumann and Wallisch TABLE 2: Thermal conductivity of graphite Type 1
Type 3
Type 2
Parallel
Normal
Parallel
Normal
Parallel
Normal
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
Thermal diffusivity (cm2/s) at 1273 K
0.117
0.105
0.110
0.107
0.106
0.098
0.108
0.108
0.103
0.105
0.090
0.088
Density at 300 K (g/cm ~ )
1.708
1.713
1.703
1.704
1.708
1.714
1.699
1.705
1.672
1.680
1.697
1.696
0.357
0.334
0.342
0.296
0.290
0.4633
Specific heat (cal X g/grd) at 1273 K Thermal conductivity (W/cmgrd) at 1273 K
0.388
Thermal conductivity reported data (W/cm grd) at 1273 K
0.349
0.363
--0.39
0.354
0.326
0.351
--0.36
--0.39
~
(W/mK)
II 30
/
/1 //
J
" // ,~
/
/
/
;;/// /
/I
/
/
/// /
• type 1
• type2
.I I
:~///
, type 3
//
/ II
7t measured I
I
30
20
--0.32
~->-
///
/ //"
--0.37
accuracy of heat flow method
//
/,0
--0.31
Thermal diffusivity, specific heat and density are listed together with the conductivity data in Table 3. The latter values are graphically shown in Fig 6. The temperature dependence of the conductivity, measured by a longitudinal method and reported by Flynn (1962) is also shown in the diagram.
tic heat in a limited temperature range was experimentally determined by the use of a differential scanning calorimeter (DSC). The density values were calculated using the room temperature data, which were also experimentally determined, and the thermal expansion coefficient already published,
~ calculated
0.356
v
Fig 5 Thermalconductivity of graphitesamples
-'-"-(W/mR) I j
[
40
50
28 .~;~(W/mK)
TAB LE 3 : Thermophysical properties of I nconel 702
x Temperature T (K)
700 755 811 866 922 978 1033 1089 773 823 873
Thermal* diffuaivity ~(cm2/s)
Specifict heat cp(J/g K)
Dansity~ p (g/cm 3 )
0.042 0.043 0.044 0.046 0.048 0,047 0.046 0.047 0.044 0.045 0.046
0.569 0.569 0.599 0.620 0.620 0.649 0.712 0.720 0.511 ¶ 0.569 0.582
7.949 7.927 7.906 7.884 7.861 7.837 7.811 7.783 7.920 7.901 7.881
Thermal § conductivity 7,(W/m K)
19.3 19.8 21,3 23.1 24.1 24.7 26,5 27.4 18.2 20.7 21.7
* Measured by laser-flash method. t Ref Venturi and Seibel, 1959. ~: Geometric density measured at R T a n d calculated by the use of the thermal expansion coefficient. § Calculated. ¶ Measured with differential scanning calorimeter (DSC). Measurement Vol 1 No 4, O c t - D e c 1983
x
/ / /
x
24 /
/ /
20 f
/
--- as reported
5. /
x
/
I/
/
/ /
/
+ +
calculated calculated (cp m e a s u r e d
by D S C ) T(K)
I
7OO Fig 6
,
I
80O
,
!
9OO
,
I
IOO0
I
1100
Thermal conductivity of lnconel 702 207
Neumann and Wallisch
~
T A B L E 4: Thermophysical properties of Armco Iron Temperature T (K)
820 872 926 927 979 1021 1025 1083
Thermal ~ diffusivity c~(cm 2Is)
Specific 2 heat Cp(J/gK)
Density 3 p (g/era 3 )
0.062 0.054 0.049 0.047 0.039 0.033 0.030 0.043
0.858 0.862 0.875 0.875 0.917 0.996 1.507 1,214
7,434 7.417 7.399 7.399 7.382 7.369 7,368 7.351
;~ (W/mK)
Thermal 4 conductivity X(W/m K)
40.4 35.4 32.6 31.3 27.2 25.0 34.4 39.7
\
/,0
,',,\
30
Measured by laser-flash method. 2 Ref Venturi and Seibel, 1959. 3 Geometric density measured at R T a n d calculated by the use of the thermal expansion coefficient. 4 Calculated.
---
recommended
value s
x calculoted
20 J
4 Armco Iron Specimens of this standard reference material were handled as the lnconel specimens described above. The sample thickness was 1.01 mm. The related values are listed in Table 4. The thermal conductivity data obtained are graphically shown in Fig 7, together with the 'recommended values' reported by Touloukian (1970).
Discussion and conclusion The laser-flash method is an excellent technique to determine the thermal diffusivity because of the • • • •
very short measuring time (t < 1 s) feasibility to run it up to very high temperatures small and simple specimen geometry simple arithmetic.
In addition, a measurement of energy or heat flow is not necessary. All the materials tested absorbed the flash energy in a sufficient way. Therefore the increase of temperature on the rear surface was easily detectable. An error of the diffusivity results of about -+3 to -+5% was estimated. Based on the results, especially on the comparison of those experimentally obtained with those derived from diffusivity measurement, it can be concluded that: (i)
The conductivity of materials like graphite can be calculated with high accuracy. This can be seen in the excellent agreement of the POCO graphite results as well as in the results of the graphite for technical application. (ii) The accuracy of the conductivity data calculated strongly depends on the accuracy of the specific heat values. This could be significantly shown by the results of Inconel and (especially) of Armco Iron. (iii) The conductivity values of lnconel, derived from specific heat data measured on the same sample which was used for diffusivity measurement, are in better agreement with the expected values than those calculated by the use of literature data. (iv) The reason for the poor agreement between the conductivity results obtained by the approach described here and the recommended values is the very strong temperature dependence of the specific heat of Armco hon near the Curie point. Small errors in temperature
2Q8
800
Fig 7
,
l
,
900
I
1000
,
(
1100 - - D - - T(K)
Thermal conductivity o f Armco Iron
measurement cause great errors in specific heat and, therefore, in the conductivity data calculated. (v) The temperature dependence of the density usually does not influence the results in an important way. Nevertheless, special attention has to be paid to transfom~ation points because of their accompanying density changes. Finally, it could be experimentally shown that thermal conductivity data at high temperatures can be derived without major problems from thermal diffusivity data measured by the laser-flash method. The error obtained is within the range of errors usually resulting from the use of the steady-state method, provided that the specific heat and density are sufficiently known.
References Carslaw, H. S. and Jaeger, J. C. 1959. Conduction o f heat in solids, Clarendon Press, Oxford, 510. Cowen, R. D. 1962. 'Pulse method of measuring thermal diffusivity at high temperatures', JApplPhys, 34,926. Flynn, D. R. 1962. NBS-report 7740 in Touloukian (1970). Larson, K. B. and Koyama, K. 1963. 'Correction for finitepulse-time effects in very thin samples using the flash method of measuring thermal diffusivity', J Appl Phys, 34, 1909.
Parker, J., Jenkins, R. J., Butler, C. P. and Abbott, G. L. 1961. JApplPhys, 32, 1679. Taylor, R. E. 1975. 'Critical evaluation of flash method for measuring thermal diffusivity', Rev Int Hts Temp et Refract, 12, 141. Taylor, R. E. 1978. 'Heat-pulse thermal diffusivity measurements', PRL-143, Purdue Univ, Indiana. Taylor, R. E. 1980. 'Thermophysical properties of POCO graphite', High Te mp , High Press, 12, 147. Touloukian, J. S. 1970. 'Thermophysical properties of matter', Thermal conductivity o f metallic elements and alloys, Vol 1, Plenum, New York. Venturi, R. and Seibel, R. D. 1959. DRI-Rept 1023 in Touloukian (I 970). Measurement Vol 1 No 4, Oct--Dec 1983
Introduction
Experimental apparatus and procedure
One of the recent trends in materials science is the development of materials for high-temperature application to meet certain requirements. One such need is to run processes at higher temperatures to increase efficiency, while another is to improve thermal isolation with respect to energy saving. The applicability of new or advanced materials, as well as of existing ones, strongly depends on their thermophysical properties. One of the most important of these properties is thermal conductivity. Many data can be found in the literature but most of the known values have been obtained at ambient or moderate temperatures. Any extrapolation of known data to higher temperatures may cause significant errors, so reliable data can only be obtained by experimental determination. However, to measure the thermal conductivity value itself (which could be done by a steady-state method) causes numerous problems at high temperatures, e g, the unavoidable heat loss by radiation. A possible solution of these problems is the determination of the thermal diffusivity by a transient method, followed by a calculation of the thermal conductivity according to the well-known formula :
The flash technique developed by Parker et al (1961)is very well described in the literature (Taylor, 1978). It is based on theoretical considerations made by Carslaw and Jaeger (1959), who derived the fornmla of tile temperature distribution as a function of time under these particular conditions. The specimen, a disc-shaped plate, is heated up to the measuring temperature. An energy flash on to one of its surfaces immediately causes an increase of temperature on this surface. After few milliseconds (the exact time depends on the specimen's diffusivity and thickness), the temperature on the rear surface increases and achieves its maxinmm value after a certain time. The temperature-time history of the rear surface (Fig 1) is significant for the specimen's thermal diffusivity. The absolute diffusivity value can be calculated by the use of the following equation:
)t = c t x
CpX p
where X is the thermal conductivity, c~ the thermal diffusivity, Cp the specific heat,
and p the density. The paper discusses this procedure with the aid of welldocumented materials, such as POCO graphite, graphite for nuclear applications, Armco Iron, and Inconel 702, using a laser-flash apparatus to measure the thermal diffusivity. 204
0.139 l 2 /1;2
where a is the thermal diffusivity, l the specimen thickness, and tl/2 the time, until half of the maximum temperature is achieved. This simple formula is only valid under certain conditions, of course, e g, parallel surfaces, negligible heat loss, homogeneous absorption of energy on the front surface, short pulse time related to tv2, homogeneous specimens, etc. If some of these requirements are not fulfilled, corrections developed for special cases can be applied, such as finitepulse effect (Larson and Koyama, 1963), heat-loss effect (Cowen, 1962), non-uniform heating (Taylor, 1975 ). Nevertheless, tile intention should be to design tile Measurement Vol 1 No 4, O c t - D e c 1983
Neumann and Wallisch
temperatureincrease
100%
50~
ff
•
T,
0,5Tmax
Trnax
V
'
6o
measuring device so that a minimum of correction is necessary. To meet these requirements, an apparatus was designed. It consists of three units (Fig 2): (i) an energy source for the pulse; (ii) a specimen chamber, with furnace; and (iii) control and recording equipment. The energy source is a high-energy neodym glass laser (Laser Optronic System 2000) with a pulse duration time of about 0.5 ms and a maximum pulse energy of 40 J, which produces the required very-rapid temperature increase on the surface. The laser runs in multi-mode conditions to guarantee a sufficient energy supply in a homogeneous laser beam. For alignment, a He-Ne laser is used (Fig 3). The specimen chamber was designed with a resistance heater of small heat capacity to enable very quick heating as well as cooling. This results in two advantages: first, reduction of the time of measuring the diffusivity in a certain temperature range; second, the possibility of getting diffusivity values of materials in a metastable state. The specimen chamber is gas tight and can be evacuated, so that tests can be carried out in vacuum or inert gas.
Pyrometer
- ,' . . -
time rn sec
Fig I Temperature-time history of the rear surface
The specimen, of cylindrical shape (10 mm in diameter and up to 4 mm high), is horizontally positioned within a tantalum tube, which acts as resistance heater. The resistance heater is supplied with high-stabilised DC (max 600A, - 1 0 V ) . Because of the horizontal position, an elaborate specimen holder is not necessary. The specimen is supported by three small ceramic tubes to minimise the heat loss by conduction along the specimen holder. Heat loss by convection can be avoided by evacuating the chamber, while heat loss by radiation is reduced by reflectors. Temperature measurement is undertaken by a Pt-PtRh thermocouple in contact with the rear surface of the specimen. Above 1700°C, a pyrometer can be used instead of the thermocouple. The temperature increase on the rear surface of the specimen, due to the laser pulse, is detected by either a germanium-photodiode or a silicon-photodiode. The temperature-time history of the rear surface is recorded by a transient recorder and can be seen on a screen or be plotted by an x - y recorder. The diagrams of the x - y recorder were graphically examined and the tz/2 was determined. The heat effect was taken into account according to Cowen's report (Cowen, 1962). An automatic digital data-acquisition system will be applied soon.
Photodetector
CAMAC~dier~s~aty~ ~urn°ce-~"-~ ~pec~rnen IK°mP.atrat°r!CAMAC
CAMACIcontr~ierl ~ ]
L~r~
I Disiay I Fig 2 Thermal diffusivity measurement equipment
Measurement Vol 1 No 4, Oct--Dec 1983
205
Neumann and Wallisch TABLE 1: Thermophysical data of POCO graphite Temperature T (K)
Thermal ] diffusivity c~(cm 2Is)
Specific 2 heat Cp(J/gK)
Density 2 p (g/cm ~ )
Thermal 3 conductivity X(W/m K)
390 420 450 615 728 736 865 999 1002 1186 1221 1260 1328 1473 1600 1739 1860
0.55 0.54 0.52 0.34 0.28 0.275 0.245 0.20 0.205 0.172 0.165 0.160 0.160 0.144 0.137 0.127 0.120
0.932 0.999 1.063 1.403 1.552 1.562 1.695 1.796 1.799 1.899 1.913 1.927 1.951 1.966 2,028 2.058 2.080
1.737 1.736 1.735 1.730 1.726 1.725 1.720 1.714 1.714 1.705 1.704 1.702 1.698 1.693 1.687 1.680 1.675
89.0 93.6 95.9 82.5 75.0 74.1 71.4 61.6 63.2 55.7 53.8 52.5 53.0 47.9 46.9 43.9 41.8
Measured by laser-flash method. Ref Taylor, 1980. a Calculated.
were listed. A comparison of the conductivity values obtained by the different methods is given in Fig 5. These experiments were only carried out at a temperature of 1273 K.
3 Ineonel
Fig 3
Laser-flashapparatus
Specific experiments 1 P O C O graphite
The experiments described were performed on a POCOAXM 5Q1 specimen. It was the same material as used in the investigation of R. E. Taylor (Taylor, 1980). POCO graphite is a much-researched material, which acts as a standard for thermal conductivity and thermal diffusivity measurements at high temperatures. Because of the excellent absorption of the laser energy, a special preparation of the surface was not necessary. The results obtained are listed in Table 1. Based on these results and applying the density and specific heat values shown in Table 1, the thermal conductivity was calculated. The calculated values are compared with conductivity data measured by the Kohlrausch method (Taylor, 1980) (Fig 4).
2 Graphite Besides POCO graphite, a graphite usually used in hightemperature nuclear reactor fuel fabrication was tested. This example was chosen because small specimens are particularly suitable for this purpose. Three types were investigated. Four specimens of each were prepared (10 mm in diameter, 2 mm high), two being parallel and two perpendicular to the direction of the pressure applied during the fabrication process. The results obtained are summarised in Table 2. In addition, the thermal conductivity data measured by a heat-flow method in another laboratory 206
Inconel 702 serves as a standard material for the comparative method. The chemical composition of this Nibased alloy is Cr 17, AI 2.5, C 0.066, Cu 0.25, Fe 0.36, Si 0.19, Ti0.59wt%. The specimens (10ram in diameter, 1.21 mm high) for the laser-flash apparatus were cut off a sample, which was delivered as reference material for steady-state comparative tests. The specimen's surfaces were grit-blasted to guarantee a sufficient and homogeneous heat absorption. The speci-
AX(W/mK)
100 T\,
,
\
\ N
80
N \
\
60 "-- ..~ x
x
60
---
aS reported
× calculated 500
10110
1500 T(K)
Fig 4
Thermal conductivit>' of POCO graphite Measurement Vol 1 No 4, Oct--Dec 1983
Neumann and Wallisch TABLE 2: Thermal conductivity of graphite Type 1
Type 3
Type 2
Parallel
Normal
Parallel
Normal
Parallel
Normal
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
1Pr
2 Pr
Thermal diffusivity (cm2/s) at 1273 K
0.117
0.105
0.110
0.107
0.106
0.098
0.108
0.108
0.103
0.105
0.090
0.088
Density at 300 K (g/cm ~ )
1.708
1.713
1.703
1.704
1.708
1.714
1.699
1.705
1.672
1.680
1.697
1.696
0.357
0.334
0.342
0.296
0.290
0.4633
Specific heat (cal X g/grd) at 1273 K Thermal conductivity (W/cmgrd) at 1273 K
0.388
Thermal conductivity reported data (W/cm grd) at 1273 K
0.349
0.363
--0.39
0.354
0.326
0.351
--0.36
--0.39
~
(W/mK)
II 30
/
/1 //
J
" // ,~
/
/
/
;;/// /
/I
/
/
/// /
• type 1
• type2
.I I
:~///
, type 3
//
/ II
7t measured I
I
30
20
--0.32
~->-
///
/ //"
--0.37
accuracy of heat flow method
//
/,0
--0.31
Thermal diffusivity, specific heat and density are listed together with the conductivity data in Table 3. The latter values are graphically shown in Fig 6. The temperature dependence of the conductivity, measured by a longitudinal method and reported by Flynn (1962) is also shown in the diagram.
tic heat in a limited temperature range was experimentally determined by the use of a differential scanning calorimeter (DSC). The density values were calculated using the room temperature data, which were also experimentally determined, and the thermal expansion coefficient already published,
~ calculated
0.356
v
Fig 5 Thermalconductivity of graphitesamples
-'-"-(W/mR) I j
[
40
50
28 .~;~(W/mK)
TAB LE 3 : Thermophysical properties of I nconel 702
x Temperature T (K)
700 755 811 866 922 978 1033 1089 773 823 873
Thermal* diffuaivity ~(cm2/s)
Specifict heat cp(J/g K)
Dansity~ p (g/cm 3 )
0.042 0.043 0.044 0.046 0.048 0,047 0.046 0.047 0.044 0.045 0.046
0.569 0.569 0.599 0.620 0.620 0.649 0.712 0.720 0.511 ¶ 0.569 0.582
7.949 7.927 7.906 7.884 7.861 7.837 7.811 7.783 7.920 7.901 7.881
Thermal § conductivity 7,(W/m K)
19.3 19.8 21,3 23.1 24.1 24.7 26,5 27.4 18.2 20.7 21.7
* Measured by laser-flash method. t Ref Venturi and Seibel, 1959. ~: Geometric density measured at R T a n d calculated by the use of the thermal expansion coefficient. § Calculated. ¶ Measured with differential scanning calorimeter (DSC). Measurement Vol 1 No 4, O c t - D e c 1983
x
/ / /
x
24 /
/ /
20 f
/
--- as reported
5. /
x
/
I/
/
/ /
/
+ +
calculated calculated (cp m e a s u r e d
by D S C ) T(K)
I
7OO Fig 6
,
I
80O
,
!
9OO
,
I
IOO0
I
1100
Thermal conductivity of lnconel 702 207
Neumann and Wallisch
~
T A B L E 4: Thermophysical properties of Armco Iron Temperature T (K)
820 872 926 927 979 1021 1025 1083
Thermal ~ diffusivity c~(cm 2Is)
Specific 2 heat Cp(J/gK)
Density 3 p (g/era 3 )
0.062 0.054 0.049 0.047 0.039 0.033 0.030 0.043
0.858 0.862 0.875 0.875 0.917 0.996 1.507 1,214
7,434 7.417 7.399 7.399 7.382 7.369 7,368 7.351
;~ (W/mK)
Thermal 4 conductivity X(W/m K)
40.4 35.4 32.6 31.3 27.2 25.0 34.4 39.7
\
/,0
,',,\
30
Measured by laser-flash method. 2 Ref Venturi and Seibel, 1959. 3 Geometric density measured at R T a n d calculated by the use of the thermal expansion coefficient. 4 Calculated.
---
recommended
value s
x calculoted
20 J
4 Armco Iron Specimens of this standard reference material were handled as the lnconel specimens described above. The sample thickness was 1.01 mm. The related values are listed in Table 4. The thermal conductivity data obtained are graphically shown in Fig 7, together with the 'recommended values' reported by Touloukian (1970).
Discussion and conclusion The laser-flash method is an excellent technique to determine the thermal diffusivity because of the • • • •
very short measuring time (t < 1 s) feasibility to run it up to very high temperatures small and simple specimen geometry simple arithmetic.
In addition, a measurement of energy or heat flow is not necessary. All the materials tested absorbed the flash energy in a sufficient way. Therefore the increase of temperature on the rear surface was easily detectable. An error of the diffusivity results of about -+3 to -+5% was estimated. Based on the results, especially on the comparison of those experimentally obtained with those derived from diffusivity measurement, it can be concluded that: (i)
The conductivity of materials like graphite can be calculated with high accuracy. This can be seen in the excellent agreement of the POCO graphite results as well as in the results of the graphite for technical application. (ii) The accuracy of the conductivity data calculated strongly depends on the accuracy of the specific heat values. This could be significantly shown by the results of Inconel and (especially) of Armco Iron. (iii) The conductivity values of lnconel, derived from specific heat data measured on the same sample which was used for diffusivity measurement, are in better agreement with the expected values than those calculated by the use of literature data. (iv) The reason for the poor agreement between the conductivity results obtained by the approach described here and the recommended values is the very strong temperature dependence of the specific heat of Armco hon near the Curie point. Small errors in temperature
2Q8
800
Fig 7
,
l
,
900
I
1000
,
(
1100 - - D - - T(K)
Thermal conductivity o f Armco Iron
measurement cause great errors in specific heat and, therefore, in the conductivity data calculated. (v) The temperature dependence of the density usually does not influence the results in an important way. Nevertheless, special attention has to be paid to transfom~ation points because of their accompanying density changes. Finally, it could be experimentally shown that thermal conductivity data at high temperatures can be derived without major problems from thermal diffusivity data measured by the laser-flash method. The error obtained is within the range of errors usually resulting from the use of the steady-state method, provided that the specific heat and density are sufficiently known.
References Carslaw, H. S. and Jaeger, J. C. 1959. Conduction o f heat in solids, Clarendon Press, Oxford, 510. Cowen, R. D. 1962. 'Pulse method of measuring thermal diffusivity at high temperatures', JApplPhys, 34,926. Flynn, D. R. 1962. NBS-report 7740 in Touloukian (1970). Larson, K. B. and Koyama, K. 1963. 'Correction for finitepulse-time effects in very thin samples using the flash method of measuring thermal diffusivity', J Appl Phys, 34, 1909.
Parker, J., Jenkins, R. J., Butler, C. P. and Abbott, G. L. 1961. JApplPhys, 32, 1679. Taylor, R. E. 1975. 'Critical evaluation of flash method for measuring thermal diffusivity', Rev Int Hts Temp et Refract, 12, 141. Taylor, R. E. 1978. 'Heat-pulse thermal diffusivity measurements', PRL-143, Purdue Univ, Indiana. Taylor, R. E. 1980. 'Thermophysical properties of POCO graphite', High Te mp , High Press, 12, 147. Touloukian, J. S. 1970. 'Thermophysical properties of matter', Thermal conductivity o f metallic elements and alloys, Vol 1, Plenum, New York. Venturi, R. and Seibel, R. D. 1959. DRI-Rept 1023 in Touloukian (I 970). Measurement Vol 1 No 4, Oct--Dec 1983