AME 60634 Int. Heat Trans.
Thermal Conductivity Measurements
D. B. Go
Slide 1
Traditional Methods
Guarded Hot Plate and Cylinder Method The guarded hot plate method can be used for the determination of the thermal conductivity of nonmetals such as glasses, ceramics, polymers and thermal insulation materials but also for liquids and gases in the temperature range between about 80 K and 800 K. The geometry of the sample or sample chamber is a plate or a cylinder with axial heat flow. Depending on the thermal conductivityGuarded and homogeneity the material under investigaHotof Plate tion, the sample thickness varies between a few millimestate) ters and a (steady few decimeters. There are two different types
(U3 − U1 ) solid materials This is because # ! be investigated. ". λρel =can (8.8) of the 4 2T − + T (T ) Φ ln 2 1 3 influence of convection on thermal conductivity measλ= TheIn specific electrical resistivity can be determined from must 2πl (T1 − urements. order to avoid convection, the sample the length l and cross-sectional area A of the sample, be heated from the top. Because of its si heating current Ih and voltage drop Uh according to technique The cylinder method with axial heat flow can be have b Uh A mal conductivity . ρel = (8.9) % used for thermal Ihl conductivity measurements of met20 mW m−1 K− als with thermal conductivities up to 500 W m−1 temperatures K−1 bet Transient modific Pipe and Hot Wire Method in a temperature range between about 4 K and 1000 K. The characteristic of this class of methods is radial heat neous determinat Comparing principlesample of operation thel).mathediffusivity are of flow inthe a cylindrical (diameter d1and , length 8.3 the shows the principle of the pipe matical Figure model, cylinder method andmethod. the guarded hot A hole on agree. the central axismost of theimportant sample contains 8.1.2 Transien plate method fully The difference the core heater (diameter d2 ), which is a rod, tube or is the sample geometry, which is a flat or diskWith forthe availab wire. Depending on the temperature rangeplate of interest Pipe Method the sample is surrounded by and a liquid-cooled heat sink oracquisition syste the guarded hot plate method a long cylinder rod (steady state) or a combination of muffle heater and water jacket. creasingly popula for the cylinder method. This is due to the fact that the are that much less main difficulty for measurements of materials with that high various therm Muffle heater Specimen Temperature sensors same measureme thermal conductivity (e.g. metals) is the determination tion of one hour of the temperature difference. In this case the contact rea few minutes o sistances between the sample and the heater and between methods. In man two opposite the sample and the cold plate must be considered.atThe a temperature me minimization and determination of the resulting temperone position. Thi ature drop across these thermal contact resistances istransient the measur steady-state m most important criterion for the optimization of this totype of the results. of instrument. Therefore, guarded hot plate and cylinder method Transient Ho Most are realizations of the same measurement principle op- thermal co and powde timized for different ranges of thermal conductivity.gases sient hot wire me
Part C 8.1
methods of measuring the thermal conductivity are dis-
AME 60634 tinguished. Int. Heat Trans.
Traditional methods are typically based on a simple application of Fourier’s law to macroscopic samples
a)
b) Cold-plate Insulation Auxiliary heater Guarded heater “hot plate” Specimen
Fig. 8.1a,b Principle of the guarded hot plate method. (a) twospecimen apparatus. (b) single-specimen apparatus
k=
P⋅L Ac (T2 − T1 )
Water cooled cylindrical chamber
Muffle heater Core heater Insulation
Fig. 8.3 Principle of the pipe method
D. B. Go
“Thermal Properties, W. Buck, S. Rudtsch, Springer Handbook of Materials Measurement Methods
pipe method with radial heat flow. inum wire or nic solids the wire i equally sized spe the sample prepa mal contact resis heating wire. The (hot strip method come increasingl
Slide 2
The sample is placed in a vacuum chamber, clamped
AME 60634 very between Int. Heat Trans. two liquid-cooled heat sinks and heated by
plate ensor t the s and cular s. To mple uard
nts is upon on of both comheat d the Unpoint f the mple ature d the relmeter polyasses duc, the
Traditional Methods
a sufficiently high electrical current Ih to achieve sample temperatures in the range 400–3000 K. Temperatures and voltage drops are measured at three positions; one position is in the middle of the rod, while the others are placed symmetrically at equal distances from the middle
Direct Heating
Vacuum enclosure
Specimen 3
2
Cylindrical guard heater
Tguard
Run electric current through the sample to heat it by Joule heating: voltage drop (ΔU) and temperature difference (ΔT) across sample related to thermal conductivity and electrical resistivity
(U3 −U1 )2 k ρelec = 4 "#2T2 − (T1 + T3 )
%$1 T1, T2, T3 U3 – U1
Power supply
ΔU ⋅ Ac ρelec = i⋅L
Fig. 8.2 Principle of the direct heating method
D. B. Go
“Thermal Properties, W. Buck, S. Rudtsch, Springer Handbook of Materials Measurement Methods
Slide 3
AME 6acity 0634 is the Int. Heat Trans.
property of interest, a calorimetric method
of thermal conductivity and thermal diffusivity.
Table 8.1 Comparison of measurement methods for the determination of thermal conductivity and thermal diffusivity Method Guarded hot plate Cylinder
Temperature range 80–800 K
4–1000 K
Uncertainty Materials
Merit
2%
Insulation materials, High accuracy plastics, glasses
2%
Metals
Demerit Long measurement time, large specimen size, low conductivity materials Long measurement time
Temperature range, simultaneous determination of electrical conductivity and Seebeck-coefficient possible ◦ Heat flow meter −100–200 C 3–10% Insulation materials, Simple construction Measurement uncertainty, plastics, glasses, and operation relative measurement ceramics ◦ Comparative 20–1300 C 10–20% Metals, ceramics, Simple construction Measurement uncertainty, plastics, plastics and operation relative measurement Direct heating 400–3000 K 2–10% Metals Simple and fast measurements, only electrically (Kohlrausch) simultaneous determination conducting materials of electrical conductivity Pipe method 20–2500 ◦ C 3–20% Solids Temperature range Specimen preparation, long measurement time Hot wire, 20–2000 ◦ C 1–10% Liquids, gases, low Temperature range, Limited to low conductivity solids fast, accuracy conductivity materials hot strip Laser flash −100–3000 ◦ C 3–5% Solids, liquids Temperature range, most Expensive, not for solids, liquids and powders, insulation materials small specimen, fast, accuracy at high temperatures Photothermal 30–1500 K Not suffiSolids, liquids, Usable for thin films, Nonstandard, knowledge D. B. Go Slide 4 “Thermal Properties, W. Buck, S. Rudtsch, Springer Handbook of Materials Measurement Methods ciently gases, thin films liquids and gases about accuracy photoacoustic
AME 60634 Int. Heat Trans.
Periodic Heating Approaches
• Periodic heating approaches are often favored – Give rise to periodic thermal response – Minimize radiation losses (non-steady heating) – Solve heat equation to determine periodic component (fairly simple) – Lock-in measurement system to detect periodic component (fairly cheap)
Stanford Research SR830 Lock in Amplifiers D. B. Go
Slide 5
AME 60634 Int. Heat Trans.
3ω Method
Developed for measurement of thermal conductivity of thin films. - use thin metal strip as both heater and thermometer by applying AC signal
thin metal strip V
~
thin film substrate
D. B. Go
Slide 6
AME 60634 Int. Heat Trans.
D. B. Go
3ω Method
courtesy of Dr. Robert Sayer, Sandia National Lab
Slide 7
AME 60634 Int. Heat Trans.
Photoacoustic (PA) Thermal Measurements
microphone
laser beam
pressure waves
Sample
D. B. Go
sealed chamber
courtesy of Prof. Bara Cola, Ga. Tech.
Slide 8
AME 60634 Int. Heat Trans.
•
Photoacoustic (PA) Thermal Measurements
Heat equation for multilayer material with modulated incident light:
) N , ! 2" i (x,t) 1 !" i (x,t) %i I o %i ( x $li ) j' t = $ & 1 + e & e & exp $ % L ( m m . where, 2 + * m =i +1 !x #i !t 2ki
(
)
θ i = Ti − Tamb
Laser beam
Solution consist of three parts: Layer 3 (N+1)
He 80 nm Ti
θ i (x,t) = θ i,t + θ i,s + θi,s
x Layer 2 (N)
Steady
CNT array
RSi-Ag Layer 0
Transient
Ag foil
Layer 1
Si wafer
Steady periodic
Lock-in amplifier only senses the steady periodic solution thus the desired solution is:
θ i (x,t) = θi,s
D. B. Go
courtesy of Prof. Bara Cola, Ga. Tech.
Slide 9
AME 60634 Int. Heat Trans.
•
Photoacoustic (PA) Thermal Measurements
Applying B.C.’s, temperature change in gas layer: −σ N +1x jω t θ N +1,s = B N +1 e e
Phase:
φ = Arg(B N +1 ) − π / 4
Amplitude:
A=
pamb BN +1 2Tamb Lg ag
Least squares regression for q different laser frequencies: q
∑ "#φ
n=1
D. B. Go
2
Measured
− φTheoretical
%$Ideal gas relation:
pamb BN +1 j (ωt−π /4) p dp = < θ N +1,s >= e T 2Tamb Lg ag Uncertainty: Measured signal +/- 0.2° phase shift (more stable than amplitude) Thermal contact resistance
q < 0.1°
+/- 0.5 mm2K/W
courtesy of Prof. Bara Cola, Ga. Tech.
Slide 10
AME 60634 Int. Heat Trans.
Enhanced Resolution for CNT Interfaces
Thermal resistance (mm2K/W)
silicon/copper substrates at room temperature
12 1-D reference bar measurement Photoacoustic measurement
10 8 6 4 2 0 0.1
0.2
0.3 Pressure (MPa)
0.4
0.5
B.A. Cola et al., J. Appl. Phys. 101, 054313 (2007)
D. B. Go
courtesy of Prof. Bara Cola, Ga. Tech.
Slide 11
AME 60634 Int. Heat Trans.
Transient Thermoreflectance BS
EOM
BIBO crystal
Lock-‐in
Ti:Sapphire Oscillator
pump laser
delay stage
sample
sample
photo detector
Variable Delay
1.0
Normalized reflectance
BS
Probe (800nm) Pump (400nm)
Al:GaAs
0.8
metal layer D. B. Go
0.6 1
courtesy of Prof. Tengfei Luo, Notre Dame
3 Delay time (ns)
5
Slide 12 12
AME 60634 Int. Heat Trans.
Transient Thermoreflectance
D. B. Go
courtesy of Prof. Tengfei Luo, Notre Dame
Slide 13 13
AME 60634 Int. Heat Trans.
Bi-layer Pump-Probe Measurement Pump beam size: 20 – 100 um Probe beam size: 10 – 20 um
Al (Metal Transducer Layer)
Substrate (With Unknown ProperQes) D. B. Go
courtesy of Prof. Tengfei Luo, Notre Dame
Slide 14 14
AME 60634 Int. Heat Trans.
Tri-layer Pump-Probe Measurement
Liquid (With Unknown ProperQes) Al (Metal Transducer Layer)
Glass
D. B. Go
courtesy of Prof. Tengfei Luo, Notre Dame
Slide 15 15
AME 60634 Int. Heat Trans.
MEASURED AND REFERENCE THERMAL CONDUCTIVITY VALUES Silicon
Measured (W/mK)
100
Quartz
Sapphire
10
Fused Silica 1
Water Hexadecane
0.1 0.1
1
10
100
Reference values (W/mK)
D. B. Go
courtesy of Prof. Tengfei Luo, Notre Dame
Slide 16 16