Thermal Conductivity Measurements

AME  60634     Int.  Heat  Trans.   Thermal Conductivity Measurements D.  B.  Go   Slide  1     Traditional Methods Guarded Hot Plate and Cylind...
Author: Jerome Weaver
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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

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“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

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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

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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 + θi,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) = θi,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)

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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

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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

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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  

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