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13TH Winter Workshop on PA & TWM, Wisła 2008

On the possibilities of application of thermal wave methods

for standardized measurement of thermal diffusivity

Silesian University of Technology, Institute of Physics

Jerzy Bodzenta, Jacek Mazur *, Barbara Pustelny

* e-mail:Jacek.Mazur@polsl.pl

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Outline■ Determination of thermal properties

■ Standardized methods – quick review

■ Methods for determination of thermal

diffusivity of plate Flash method (standardized)

Thermal wave methods Possible configurations of measurement set-up

Examples

Properties of Two-beam method

■ Conclusions

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Determination of thermal properties (1)

Description of thermal properties

thermal conductivity

specific heat

heat capacity

thermal diffusivity

thermal effusivity

thermal resistance

[ ]Wm Kκ

Jkg Kc

3J

m KC cρ=

2msC

κα =

2W sm K

Cε κ=2m K

WQ

dR

κ=

Basic laws

Fourier’s law

basic equation of constant-volume calorimetry

Fourier-Kirchhoff equation

Qj Tκ= −rr

dQ mcdT CVdT= =

2 1 T qT

tα κ= −

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Determination of thermal properties (2)

Steady flux methods Variable flux methods

Qj Tκ= −rr ( ) 2T T

T C q Tt t

ακ = − =r r r

Pulse WaveAbsolute Comparative

Flash method

TTG method

Ångström’s methods

3ω method

Comparativemethods

Interference methods

Guarded-Hot-PlateMethod

Heat-Flow-MeterTechnique

Guarded-Comparative-Longitudinal

Heat Flow Technique

Hot-wiremethod

Transient

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STEADY FLUX METHODS■ ABSOLUTE

Guarded-Hot-Plate Method ISO 22007-2: Plastics - Determination of thermal conductivity and

thermal diffusivity - Part 2: Transient plane heat source (hot disk) method ASTM: C177-04 Standard Test Method for Steady-State Heat Flux

Measurements and Thermal Transmission Properties by Means of the Guarded- Hot-Plate Apparatus

ISO: 8302:1991 Thermal Insulation – Determination of Steady-State Thermal Resistance and Related Properties – Guarded Hot Plate Apparatus

Heat-Flow-Meter Technique C518-04 Standard Test Method for Steady-State Thermal Transmission

Properties by Means of the Heat Flow Meter Technique ASTM: E1530-04 Standard Test Method for Evaluating the Resistance to

Thermal Transmission of Materials by the Guarded Heat Flow Meter Technique

■ COMPARATIVE Guarded-Comparative- Longitudinal Heat Flow Technique

ASTM: E1225-04 Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded-Comparative-Longitudinal Heat Flow Technique

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VARIABLE FLUX METHODS (1)

■ PULSE METHODS Laser Flash (Heat Pulse)

ASTM E1461-01 Standard Test Method For Thermal Diffusivity of Solids By The Flash Method

ISO 18755 Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics) - Determination Of Thermal Diffusivity Of Monolithic Ceramics By Laser Flash Method

ISO DIS 22007-4 Plastics - Determination Of Thermal Conductivity And Thermal Diffusivity - Part 4: Laser Flash Method

BS 7134 P4 S4.2 Testing Of Engineering Ceramics - Thermo-Mechanical Properties - Method For The Determination Of Thermal Diffusivity, By The Laser Flash (Or Heat Pulse) Method

BS EN 821-2 Advanced Technical Ceramics - Monolithic Ceramics - Thermo- Physical Properties - Part 2. Determination Of Thermal Diffusivityby The Laser Flash (Or Heat Pulse) Method

JIS R 1667 Determination Of Thermal Diffusivity Of Continuous Fiber- Reinforced Ceramic Matrix Composites By The Laser Flash Method

JIS R 1611 Test Methods Of Thermal Diffusivity, Specific Heat Capacity, And Thermal Conductivity For Fine Ceramics By Laser Flash Method

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VARIABLE FLUX METHODS (2)

■ PULSE METHODS Laser Flash (Heat Pulse) cont.

*PL, BS, DIN EN 821 P2 Monolithic Ceramics - Thermo-Physical Properties - Part 2. Determination Of Thermal Diffusivity By The Laser Flash (Or Heat Pulse) Method

*PL, DIN EN 1159-2 Advanced Technical Ceramics - Ceramic Composites; Thermophysical Properties - Part 2: Determination Of Thermal Diffusivity (Foreign Standard)

* Translated to Polish

■ TRANSIENT Hot-wire method

ISO 8894-2:2007 Refractory materials - Determination of Thermal Conductivity – Part 2: Hot-wire method

■ WAVE Ångström's Method

ISO/DIS 22007-3: Plastics - Determination of Thermal Conductivity and Diffusivity - Part 3: Temperature wave analysis methodUnder Development

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VARIABLE FLUX METHODS (3)

■ WAVE Thermal Wave Method

DIN 50992-2: Determination of the layer thicknessUnder Development ?

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Thermal diffusivity – flash (1)

■ Parker et al., Flash Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity, J. Appl. Phys., 32(9), 1961

Pulse Laser / Flash Lamp

OpticsSample

IR Detektor

( ) ( ) ( )

−−+== ∑

∞

=12

22

exp121,n

n

L

tn

cL

QtLTtT

απρ

limT T(L,t)

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Thermal diffusivity – flash (2)

■ Standardized method: EN 1159-2

100 2 4 6 80

0.2

0.4

0.6

0.8

1V

ω

5,02

2

38.1t

L

πα =

xt

L2

2

48.0π

α =

( ) ( )lim

,,

T

tLTtLV =

2

2

L

tαπω =

( ) ( ) ( )∑∞

=

−−+=1

2exp121,n

n ntLV ω

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Pulse, thermal wave – comparison (1)

■ Pulse

TimeAmplitude vs. time

Light pulsLaser / Flash Lamp

Thermocouple,IR radiometry,PA cell

■ Thermal wave

FrequencyPhase vs. frequency

Modulate light

IR radiometry,PA cell,Optical photodeflection,reflection

■ Method

Domain of measurement:

Generation ofheat source:

Temperature detection

Common characteristic time:

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Pulse, thermal wave – comparison (2)

■ A.I. Korobov, N.I. Odina, I.N. Kokshaysky and A.F. Asainov, Pulsed Photoacoustic Technique for Thermal Diffusivity Determination, IEEE Ultrasonic Symposium 1994, p. 785

Equivalence of two measurement techniques: CW laser with mechanical chopper Pulsed laser (25ns, 6.3mJ) + FFT

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TWM Set-up

Lightsource (Front)

Sample Detector (IR or PA)

Control Unit (PC)

Light Source (Back)

Measurement Data Acquisition

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TWM configurations■ Front illumination

Thermal wave interference

Comparative method – e.g. carbon black thermally

thick reference sample

■ Back illumination Flash method equivalent

Reference sample needed

■ Both sides illumination (Two-beam method) Self-normalized method

Simplified fitting procedure

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Two-beam method - examples (1)

■ T. Sheenu, I. Johney J. Philip, Thermal diffusivity of solids by photoacoustic cell rotation and phase lag measurement, Rev. Sci. Instrum., 66 (7), 1996, 3907

■ M. Aravind, P. C. W. Fung, S. Y. Tang, and H. L. Tam, Two-beam photoacoustic phase measurement of the thermal diffusivity of a Gd-doped bulk YBCO superconductor, Rev. Sci. Instrum., 67(4), 1996

■ J.A. Balderas-Lopez, Photothermal signal normalization method and its application to the measurement of the thermal diffusivity for opticaly opaque materials, Rev. Sci. Instrum., 77, 064902, 2006

■ O. Pessoa,Jr, C.L. Cesar, N.A. Patala, H. Vargas, C.C. Ghizoni andL.C.M. Miranda, Two beam photoacoustic phase measurement of the thermal diffusivity of solids, J. Appl. Phys. 59(4), 1986

■ J.A. Balderas-Lopez, A. Mandelis, Self-normalized photothermal techniquefor accurate thermal diffusivity measurement in thin metal films, Rev. Sci. Instrum., 74 (12), 2003

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Two-beam method - examples (2)

■ Investigated Materials: metals (Cu, Al, steel), semiconductors (Si, Ge, GaAs, InP), glass, superconductor (YBCuO), plastic (tape), paint layer

■ Detection method: PA, IR radiometry■ Temperature range: 100 – 370K

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Two-beam method - properties

■ Ratio of front and back independent on detection equipment

■ CW measurement

■ Reference sample not needed

■ Only 1 parameter for fitting

■ Simple mathematical description

10-4 – 10 -1 s

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Conclusions

■ Thermal wave methods are widely used for determination of thermal diffusivity

■ Methods are based on phase-sensitive

measurement

■ CW methods do not need expensive pulsed

light source

■ Elaboration of standard is important for

cooperation with industry

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Acknowledgment

This work is supported as part of project

Elaboration of System for Measurement of Thermal Diffusivity by Thermal Wave Methods

Multi-Year Programme PW-004 “Development of innovativeness systems of

manufacturing and maintenance 2004-2008”, established by a resolution of the Council of Ministers

of the Republic of Poland