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THERMAL PROPERTIES OF SOLIDSMeasurement Techniques

March 22nd, 2001

Presented by:Ileana ConstantinescuJamshid Sulaymonov

MatE 210, Experimental Methods in Mat. Eng., Spring 2001

In partial fullfillment of requirements for MatE 210Professor G. Selvaduray

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THERMAL PROPERTIES - SOLIDS

• Introduction • Classification• Measurement Techniques • Thermal Conductivity• Axial Heat Flow Method - AHF• Calibration/Errors/Limitations of AHF• Conclusion

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kkTo-Conductivity

SSTTThermal

Shock

ααTo-Diffusivity

CCppHeat

Capacity

ββvvThermal

Expansion

TECHNIQUES

INTRODUCTION/ BACKGROUNDINTRODUCTION/ BACKGROUND

Steady-State Non Steady-State

Hot WireHW

Radial HeatFlowRHF

GuardedHot Plate

GHP

Axial HeatFlowAHF

Laser Pulse(Flash)

ElectronBombardment

Heat Input

MonotonicHeating

Thermal Wave

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INTRODUCTION

• THERMAL PROPERTIES OF SOLIDS– Interaction and propagation of thermal energy quanta (phonons)

through solid materials

• HEAT FLOW THROUGH SOLIDS– Initiated by ∆T across two sides of a solid

• HEAT CONDUCTION LAWS

First Order Fourier-Biot Equation Second Order Fourier-Biot Equation

dxAdTkq*

−=

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Significance of Thermal Properties

• Design Applications– Material selection criteria– Thermo-mechanical

analysis for structural component design for extreme temperatures

– Prediction of alloy properties based on unalloyed metal properties (law of mixtures)

• Failure Analysis– Evaluation of thermally

induced stresses and degree of thermal cycling that led to material fracture (thermal shock resistance)

Fig. 1 – Orbiter Surface Isotherms (Solomon Musikant,"What Every Engineer Should Know about Ceramics", 1991, p. 148)

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Heat Capacity

Fig.2 - Temperature Dependence of the MolarHeat Capacity (after Rolf E. Hummel, "ElectronicProperties of Materials”, 1985, p.269, fig. 19.1)

• Heat capacity,

• Specific heat,

• Molar heat capacity,

• Temperature dependence

• Dulong-petit value

• Cp ~ Cv

CvdQdT v

cv

Cv

m

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• Debye temperature

• Total heat capacity

Ctot Cel Cph

Concept of Heat Capacity

Fig. 3 – Temperature Dependence of the Molar Heat Capacity; Experimental Values vs. Model predictions (Rolf E. Hummel, "Electronic Properties of Materials", 1985, p. 264)

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1-10All100 – 1000 SCLim. In high temps.

Fast and EconomicalDifferential Scanning

2-10Electrical Conductor (Wire, rod, tube)

1000 - 7000EC Complex Instrumentation

SLSHigh Temps. MPM

Pulse

2-5All80 - 3000Solid SpecimenMulti-Property Measurement (MPM)

Modulation

2-5Electrical Conductor (sphere)

1000 - 2500Specimen:Electric Conductor (EC)ED

Solid & Liquid Specimen

Levitation

1-3All300 - 2000SCTime consumingED

Solid & Liquid Specimen

Drop

1-3All4 - 1300Specimen in Container (SC)Limitation in high temps. Based on enthalpy data (ED)

Very VersatileHigh SensitivitySolid and Liquid Specimen (SLS)

Adiabatic

Uncertainty (%)

Principal Specimen Materials

Temperature Range (K)

DisadvantagesAdvantagesMeasurement Technique

Table 1 - Specific Heat Measurement Techniques (after K.D. Maglic, “Compendium of ThermophysicalProperty Measurement Methods”, 1984, Volume 1, p.459)

Specific Heat Measurement Techniques

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Thermal Expansion• Volumetric Expansion,

• Linear Expansion,

• Temperature Dependence

βm1

K

αm1

K

Fig. 4 - Thermal Expansion of Al and Pt from 0 Kto their melting temperature, from K.D. Maglic,“Compendium of Thermophysical PropertyMeasurement Methods”, 1992, Vol.2, p.551 fig2.)

βm

V2 V1

V1

T2

T1

.

αm

L2 L1

L1

T2

T1

.

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Thermal Expansion of Materials

Fig. 5 - Coefficients of thermal expansion at roomtemperature for various materials (from N.E. Dowling,Mechanical Behavior of Materials", 1999, p. 187)

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Thermal Expansion Measurement Techniques

Accuracy(%)

Min. Coefficient of Thermal ExpansionTemperature

Range (C)CharacteristicsMeasurement

Techniques

3-12above 5-120 - 600Inconsistent precision

Thermomechanical Analysis

1-3below 5-150 - 700High accuracy Optical

Interference Techniques

5-7above 5-150 -2000Medium precision

Mechanical Dilatometer

αmµmmC.

Table 2 - Comparison of thermal expansion measurement techniques (ASTM Standards E831, E228, E-289)

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• Thermal Conductivity, (Fourier’s Law)

• Principal Carriers of Heat

κJ

m s. K.

Fig. 6 - Heat flow in a solid state material (S. O.Kasap, "Principles of Electrical Engineering Materials And Devices”, 1997, p.137)

Fig. 7 - Heat flow in a metal rod heated at one end (after S.O. Kasap, “Principles of ElectricalEngineering Materials and Devices”, 1997, p.137)

Thermal Conductivity

dQdT

A κ.δTδx

.

κtot κel κph

Jq κdTdx

. J

m2 K.

• Fourier’s Law

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• Thermal conduction in metals and alloys

Fig. 8 - Thermal Conductivity vs. temperature for two puremetals (Cu and Al) and two alloys (brass and Al-14%Mg)(S.O. Kasap, “Principles of Electrical EngineeringMaterials and Devices”, 1997, p.139)

Fig. 9 - Thermal Conductivity vs. electrical conductivity forvarious metals at 20C (after (after S.O. Kasap, “Principles ofElectrical Engineering Materials and Devices”, 1997, p.139)

Thermal Conductivity Mechanism

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Thermal Conductivity Measurement Techniques

150.05 – 15Refractory Materials

600 – 1600 High temp. gradients Slow

SimplicityPanel Test

5 - 150.02 – 2Refractory Materials

RT – 1800Low conductivity materials

Small Temperature Drop in specimen

Hot Wire Method

2 - 5<1.0Thermal Insulators

80 – 1500ComplexCostly

Slow (3 – 12 h)

Wide Range of MaterialsHigh Accuracy

Guarded Hot Plate

2 - 510 – 200Wires, rods, tubes of elec. Conductors

400 – 3000Complex Equipment

High Temps.FastElect.Properties

Direct Electrical Heating

3 - 150.01- 200Solids and powders in cylindrical form

RT – 2600Large specimensAccuracy High Temps.

Radial Heat Flow

0.5 - 2.010 – 500Metals & Alloys, Cylindrical Shape

90 – 1300heat losses above ~ 500K

High AccuracyElectrical Resistivity

Axial Heat Flow

Uncertainty (%)

Conductivity Range,

Principal Specimen Materials

Temperature Range (K)

DisadvantagesAdvantagesMeasurement Technique

Table 3 - Specific Heat Measurement Techniques (K.D. Maglic, “Compendium of Thermophysical Property Measurement Methods”, 1984, Volume 1, p.6)

Wm K.

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Thermal Diffusivity

• Definition– Rate at which a temperature

disturbance on one side of the body travels to another part of the body

• Classical Measurement Techniques:– Pulse Method (Laser)– Temperature Wave– Electron bombardment– Monotonic heating

2nd Order Fourrier Law:

k = α * cp * ρ

k – thermal conductivityα – thermal diffusivityCp – heat capacityρ - density

α

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THERMAL DIFFUSIVITY MEASUREMENT TECHNIQUES

2 – 1210-8 – 10-5Ceramics, plastics, composites

4.2 - 3000Inappropriate for good thermal conductors Low precision

Simple ApparatusSimple MeasurementWide T Range

Monotonic Heating Regime Method

2 – 1010-7 – 10-5Metals, nonmetals, liquid metals

330 – 3200High Vacuum;Complex Experimental apparatus

High T coverageSmall specimenAC techniques applicable

Electron Bombardment Heat Input Method

1 – 910-7 – 10-4

Solids, liquid metals, gasesSpecimens: rods, cylinders

60 – 1300Complex Math AnalysisComplex Error Analysis

Wide Materials RangeMulti-property Measurement

Temperature Wave Method

1.5 – 5 10-7 – 10-3

solids, liquid metalsSpecimen disks 6- 16 mm in diameter

100 – 3300Not convenient for translucent materialsComplex Error Analysis

Wide T rangesSimple, rapidmeasurement

Pulse Method

Uncertainty%

Diffusivity Range

Principal Specimen Material

Temperature Range (K)

DisadvantagesAdvantagesMeasurement Technique

Table 4 – Thermal Diffusivity Measurement Techniques (K.D. Maglic, “Compendium of Thermophysical Property MeasurementMethods”, 1984, Volume 1, p.302)

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Thermal Shock

The tendency of ceramicmaterials to fracture as a resultof rapid temperature changeduring rapid cooling:

σ * dxST = -------------

Q

σ = stress developed (psi)Q = unit flux of heat (J)dx = solid thickness (in)

The thermal shock coefficient, ST, can be calculated from CTE and thermal conductivity measurements:

β * EST = -------------

k

β − coefficient of thermal expansion (CTE)E - Young's Modulusk – thermal conductivity

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Heating Method Advantages Disadvantages Materials Studied

Induction (5-40 kW capacity)

rapid heating; complex sample geometries

coil design experience;electric noise due to high magnetic field; high cost

Al, Cu, Steels, Ni-superalloys

Quartz Lamp (radiation)

inexpensive; uniform T; screening materials

slow cooling rates; enforced cooling needed

Ni, Co alloys, metallic composites

Fluidized Bed good for screening TF resistance

surface oxidation, calculation of σ-ε T transients

Ni-base superalloys

Burner Heating (Flame)

screening of TF; surface corrosion representative of service

oxidation, T transients

Ni-superalloys, steels

Dynamometer (friction heating)

very high T on surface reached; representative of service

oxides are wedged into cracks; friction changes with time

0.5 to 0.7% C steels

THERMAL SHOCK / THERMO-MECHANICAL METHODS

Table 5 – Thermal Shock, Thermo-mechanical Measurement Techniques (ASM Metals Handbook, vol. 19, "Fatigue and Fracture", 1996, p. 529)

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Guarded Hot PlateSummary of the Test Method

Fig. 10a - Components of the Guarded-Hot-Plate Apparatus Fig. 10b – Measurement Principle for a Guarded Hot Plate

(ASTM Standard C-177, 2000, p.21)

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Hot Wire MethodSummary of the Test Method

Fig.11a - Components of the Hot Wire Apparatus Fig. 11b - Hot Wire Sample Setup

(ASTM Standard C 177, 2000, p.21)

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Axial Heat Flow – Comparative Method

• Summary

• Requirements – Meter bars (standards)– Insulation materials– Temperature sensors– Guard cylinder– Sampling

• Calculation

Fig. 12 (Axial Heat Flow Apparatus - http://www.umr.edu/)

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Summary

± 5% to ± 10%depending on sample and

conductivityAccuracy

± 2% Reproducibility

Customized size Sample Size

-180 to 600°CMean Sample Temp. Range

0.02 to 250 W/(m*K) Thermal Conductivity Range

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Requirementsλ M T( )

λMtop

λMbm

λ S T( )

λ S 1( ) T( )

λ I T( )

-Conductivity of meter bars as a function of T

- Conductivity of top bar

- Conductivity of bottom bar

- Conductivity of specimen

- Conductivity of specimen

- Conductivity of insulation

rA

rB

• Specimen radius

• Guard cylinder inner radius

•Guard temperature as a function of position

Tg z( )Fig. 13 - Schematic of a Comparative-Guarded-Axial Heat

Flow System. (ASTM Standards 1999, E 1225, p.437)

rA rB

T1

T2

T3

T4T5

T6

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Reference Materials for Use As Meter Bars

NISTNIST specification2To 1000Electrolytic Iron SRM 734

Manufacturer……90 to 1200Pyroceram Code 9606

ManufacturerDependent on T (K)< 8 up to 900(K)1300Fused Silica

Manufacturer6 90 to 600Pyrex 7740

ManufacturerDependent on T (K)< 290 to 1250Copper

…Dependent on T (K)2 80 to 1200Iron

NISTCalculated from measured values

< 54 to 1200Austenitic SS SRM 735

NISTDependent on T (K)2 to 84 to >2000Tungsten SRM 730

Material Source Percent Uncertainty in λ

(%)

Temperature Range (K)

Material λm

Wm K.

Table 6 - Reference Materials for Use as Meter Bars (ASTM Standards 1999, E 1225, p. 420)

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0.250.090.039Zirconia 60 – 90 (kg/m3)

0.330.130.044Aluminosilicate 60 – 120 (kg/m3)

…0.170.05Perlite

…0.160.07Vermiculite

0.370.330.19Bubbled Zirconia

0.410.370.21Bubbled Alumina

1300K800K300K

Typical Thermal Conductivity, Material

λmW

m K.

Table 7 - Suitable Thermal Insulation Materials (ASTM Standards 1999, E 1225, p. 420)

Suitable Thermal Insulation Materials

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Thermocouple Attachments

Fig. 14 - Thermocouple Attachments (ASTM Standards 1999, E 1225, p. 421)

1 2

3 4

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Calculations

qtop

λ M T2 T1

.

Z2

Z1

qbottom

λ M T6

T5

.

Z6

Z5

λs

qtop qbottom Z4

Z3

.

2 T4

T3

.

Fig. 15 - Schematic of a Comparative-Guarded-AxialHeat Flow System. (ASTM Standards 1999, E 1225, p.437)

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AXIAL HEAT FLOW TECHNIQUESources of Error

• Equipment• Operator• Material Tested• Experimental Plan

– Absolute or Comparative Technique– Need for NIST traceable standards– Number of samples tested– Number of readings per sample– Precision/ Accuracy of Method

(matching desired value?)– Propagation of Errors

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AHF - Equipment Design to Minimize Measurement Errors

• Selection of suitable low 'k' insulation material to prevent lateral heat losses

• Determination of optimum attachment method of to-probe to sample surface to reduce the interfacial thermal resistance

• Selection of appropriate thermocouple temperature probes

– 'T' (Copper-Constantan)– 'K' (Chromega-Alomega)– 'J' (Iron-Constantan)– 'E' (Chromega-Constantan)

• Fit the equipment with heated guards to achieve better temperature control along bars in the axial direction

Fig. 16 - Schematic of a Comparative-Guarded-AxialHeat Flow System. Use of Guard Heaters and Insulation to Minimize Lateral Heat Losses (ASTM Standards 1999, E 1225, p.437)

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AHF - Instrumentation

• Sensor Measurement Precision– combination of T sensor and instrument used for measuring sensor output

should ensure a T measurement precision of +/- 0.04 K and an absolute error less than +/- 0.5%

• Temperature Control– instrumentation should be adequate to maintain required T control and

measure all output voltages with accuracy comparable with the system capability (reported in the OEM manual)

• Calibration and Verification Required:– if ratio of meter bar to sample ‘k’ values is below 0.3 or above 3.0, and

thermal conductance match is not possible to attain – if specimen geometry is complex– if unusual test conditions or modifications of the setup are required

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SAMPLE INFORMATION

• Chemical composition (impurity, alloying element content) • Crystal structure• Porosity (concentration of voids)• Processing history• Sample preparation (e.g. mechanical polishing)

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?Which Is The Best Technique ??

Fig. 17 – Thermal Conductivity Measurement Techniques for Titanium (L- Longitudinal Heat Flow Method, C- Comparative Method, E- Direct Electrical Heating Method. Y.S. Touloukian, "THERMAL CONDUCTIVITY- Metallic Elements and Alloys", vol. 1, 1970, p. 410)

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CONCLUSION

• Knowledge of materials' thermal properties allows their correct evaluation and selection as thermal conductors or insulators for a specific application

• Selection of the optimum measurement technique must be done based on:– Previous knowledge of expected TC value for that material– Desired accuracy– Temperature of interest

• The AHF Comparative method (steady-state) – Advantages:

• Relatively simple equipment• Precise method for TC measurements of good conductors (e.g. metals, alloys)• Flexible geometries of specimen and standard• High accuracy at temperatures between 298 and 400 K

– Disadvantages:• Slow measurement times (requires thermal equilibrium)• ~ 10 % Uncertainty in TC values at temperatures > 400 K• Requires standards (meter bars) with TC values similar to that of specimen

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List of References

• ASTM Standards 1999, C 1113, E 1225, E 831, E 228, E 289• ASTM Standards 2000, C 177• N. E. Dowling “Mechanical Behavior of Materials”, 1999• R. E. Hummel, “Electronic Properties of Materials”, 1985• S.O. Kasap “Principles of Electrical Engineering Materials

and Devices”, 1997• K.D. Maglic “Compendium of Thermophysical Property Measurement

Methods”, Vol1. and Vol2., 1984• S. Musikant "What Every Engineer Should Know About Ceramics",

1991• Y. S. Touloukian "Thermal Conductivity – Metallic Elements and

Alloys", vol. 1, 1970• L. H. Van Vlack “ Materials Science for Engineers”, 1975