Thermal diffusivity and conductivity - an introduction to theory and practice

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1 Thermal diffusivity and conductivity - an introduction to theory and practice Utrecht, 02 October 2014 Dr. Hans-W. Marx Linseis Messgeräte GmbH Vielitzer Str. 43 D Selb / GERMANY Phone: Fax: France:

2 Linseis Messgeräte GmbH Linseis Messgeräte GmbH is a german medium sized company specialized in the production of instruments for thermal analysis since the 1950s. Product range: - Thermogravimetry TGA (under pressure; corrosive atmosphere) - Differential thermal analysis DTA - Dynamic scanning calorimetry DSC - Simultanous thermal analysis STA (TGA-DTA-DSC) - Dilatometry (piston or optical; with our without contact) - Thermomechanical analysis TMA - Couplings for evolved gas analysis (EGA: MS FTIR) - Analysis for thermoelectrics (electrical resistivity and Seebeck coefficient) - Thermal diffusivity and thermal conductivity

3 Applications I - Low thermal conductivity: insulations - Building industry, instruments: thermal isolators (refrigerators, hot water tanks, heating pipes, brand protection ) - Thermoelectrics: increasing figure of merit by decreasing thermal conductivity

4 Applications II - High thermal conductivity: - Brake discs - High performance alloys for tools: fast cooling of friction heat for longer lifetime and better performance (drills, tools for hot presses etc.) - Electronics: dissipation of local heat avoiding overheating - Knowledge of thermal conductivity: - Simulation of casting and solidification processes - Management of solidification and control of material properties

5 Thermal diffusivity thermal conductivity - Thermal diffusivity area/time (m²/s) - : propagation of a temperature difference in a material how fast a temperature difference in a material is levelled out (German: Temperaturleitfähigkeit temperature conductivity ) - Thermal conductivity power/(length * Kelvin) (W/m K) : propagation of a heat difference in a material how good heat energy is conducted through a material (German: Wärmeleitfähigkeit heat conductivity ) Heat (W) passing by a sample of 1 m thickness and a surface of 1 m² for a temperature gradient of 1 K during 1 sec

6 Thermal diffusivity thermal conductivity Thermal diffusivity and thermal conductivity are related through the following equation: = Cp * density * Thermal conductivity = heat capacity * density * thermal diffusivity Transmitted heat = heat capacity * mass * temperature difference All those properties (Cp, density ) are temperature-dependent!

7 Thermal diffusivity thermal conductivity Material Thermal diffusivity in 10-6 m²/s Thermal conductivity in W/m*K Water 0,15 0,56 Air 20 0,026 Wood 0,1-0,2 0,1-0,2 Glass 0,35-0,5 0,75-0,9 Iron Steel 3, Copper Diamond Graphit "Plexiglass PMMA 0,1 0,19 EPS 0,35-1,55 0,035-0,05

8 Methods Stationary methods: - A stable temperature gradient is installed through the material to be tested - Achieved when the heat flux in the sample equals the heat flux out of the sample - Advantage: simple theory and simple experimental set-up - Disadvantage: long measuring times Transient (time dependant) methods: - Sample is subjected by a thermal disturbance; this disturbance is observed as a function of time - Advantage: rapid and simple measurement, small samples, measurement at different temperatures - Disadvantage: complicated theory; homogenous samples needed

9 Stationary methods Heat Flow Meter Guarded Hot Plate Hot Plate Heat flux sensor Sample Guard Ring Guard Cold Plate Guard Sample Insulation Hot Plate Guard Ring Heat flux Cold sensor Plate Cold Plate Sample Cold Plate Typical sample size: 30 x 30 x 10 cm Typical range: ca 0,001 to 1 W/mK

10 Transient methods hot wire method Hot wire thermocouple T T 1 T 2 t 1 t 2 ln(t) Typical signal Thermal conductivity is inversely proportional to temperature increase. Thermal diffusivity is calculated from the time needed for maximum temperature rise Typical range: to W/mK Typical sample size: some cm x some cm x cm

11 Transient methods THB THB Transient Hot Bridge: improved hot wire method (compensation of end effects)

12 Application example THB Investigations of the PTB (National Metrology Institute of Germany) on the thermal conductivity of soils and sediments

13 Laser Flash Method - ASTM E 1461 Standard Test Method for Thermal Diffusivity by the Flash Method A small, thin disc specimen is subjected to a high intensity short duration radiant energy pulse. The energy of the pulse is absorbed on the front surface of the specimen and the resulting temperature rise at the rear face is recorded. The thermal diffusivity value is calculated from the specimen thickness and the time required for the rear face temperature rise to reach half of its maximum value.

14 The Laser Flash Method d IR radiation laser 1 ms IR-detector sample lens T T Norm (t) Zeit time

15 Calculation of thermal diffusivity Calculation - Determination of the baseline and the maximum temperature rise => T max - Determination of the time required to reach half maximum height T ½ ; this is the half time, t ½ - Calculation of thermal diffusivity from sample thickness L and half time t ½ : = L 2 /t ½

16 Calculation of thermal diffusivity Calculation - Determine the baseline and maximum rise to give the temperature difference, T max - Determine the time required from the initiation of the pulse for the rear face temperature to reach T ½. This is the half time, t ½. - Calculate the thermal diffusivity, a, from the specimen thickness, L squared and the half time t ½, as follows: Α = L 2 /t ½

17 LFA and XFA instrument Detector Detektor Iris Iris Ofen Furnace Sample holder Probenhalter Laser Xenonlampe

18 LFA and XFA instrument Detector furnace Pulse source Laser or Xenon Typical range: 0.1 up to 1000 W/mK Typical sample size: ca. 2 cm diameter, thickness ca 2 mm

19 The Laser Flash Method limits Minimal sample thickness depends: 1. on acquisition rate of the instrument/detector: (limited number of measurement points) 2. On the duration of the laser pulse (overlay of temperature rise through the sample and laser pulse):

20 Sample holder for thin films in-plane-adapter Sample holder for thin films of < 0,1 mm (depending on thermal diffusivity of the sample) Effective in-plane heat path approx. 6 mm

21 Thermal conductivity measurement A suitable method for nano structured materials: Time Domain Thermoreflectance (TDTR)

22 TDTR example ZnO Z.X. Huang et. al. Physica B 406 (2011) thickness d 2 (nm) k 2 (W/(m*K)) Bulk ZnO: k 2 ~ 100 W/m K

23 Time domain thermoreflectance (TDTR) measurement principle Optical properties depend on temperature - e.g. reflectance of electromagnetic radiation: R 1 R R R T = T = C TR T Reflectance can be used as an indicator for temperature variation and thermal conductivity

24 TDTR experimental set-up Z.X. Huang et. al. Physica B 406 (2011)

25 TDTR measurement principle High speed laser flash method Rear heating / front detection Conventional Nanosecond thermoreflectance method Front heating / front detection T. Baba, Japanese Journal of Applied Physics 48 (2009) 05EB04

26 Choice of measurement method HFM heat flow meter: plates 30 x 30 cm; thickness up to 10 cm THB transient hot bridge: solids, liquids, powders, pastes; 4 x 8 x < 1 cm XFA and LFA - Xenon and Laser Flash Analyzer; solids and liquids; diameter 25,4 mm; thickness: some mm TFA: thin films on substrates, thickness in the sub- m range

27 Choice of measurement method Heat Flow Meter ( C) Guarded Hot Plate ( C) Guarded Heat Flow Meter ( C) Hot Wire (RT 1500 C) Flash ( C) Thermal Conductivity (W/m-K)

28 Anaspec Solutions Anaspec Solutions BV Coenecoop 3C PG Waddinxveen Bezoek onze stand 8D065 anaspec.eu

29 Thank you for your kind attention! Any questions or remarks?

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