Transient Plane Source Techniques for measuring Thermal Conductivity of Various Materials Evitherm September 15, 2003 Dr. Lars Hälldahl Hot Disk AB

Hot Disk … or Transient Plane Source, TPS… or Gustafsson Probe… or G-Probe

The technique is based around : -A unique sensor -A new mathematical model for thermal conductivity A Transient Plane Source in infinite material - Special electronics to collect data Designed for accuracy and precision

The Sensor A double spiral made of Nickel metal foil, cladded by Kapton or Mica to provide electrical insulation from the sample. The diameter varies from 1 mm up to 60 mm. It connects to the electronics, which sends out a current during a selected time, while the voltage drop is recorded See in the following four slides the historical development of Hot Disk from Hot Wire – Hot Strip !

Hot Wire About 1960-ties Metal wire in contact with the sample OK for liquids, but not for solids contact resistance problems…

Hot Strip Development of Hot Wire the wire….flattened out better contact on sample

From a Strip… …..to a spiral covers larger area on smaller sample

So….the story is … from Hot Wire to Hot strip and next step… Transient Plane Source This is Hot Disk

Sensor embedded in the sample. Heat can spread in all directions

A transient recording Power Time Voltage =resistance =temperature Send in power.. ….and measure at the same time For good conductors:high power, short time For good insulators: low power, long time

Ideally, the sensor is surrounded by infinite sample in all direction. Can’t see the edge, the temperature increase doesn’t reach the edges. Both Conductivity and Diffusivity are measured, and from them Heat Capacity is calculated Heat dissipation in infinite sample

Sample Parameters of importance: POWER, TIME SENSOR SIZE The relation between Diffusivity, Time for measurement and radius of sensor is called Total to Characteristic Time  x t r x r Sample Sensor =1 This value between 0.3 – 1.0 satisfies the basic assumption done for the Heat Conductivity equation: A Plane Source in Infinite Material

Variants of the TPS method By varying sensor size, power and time in the basic method, thermal conductivity over more than 4 orders of magnitude can be covered. To cover more applications, some variants have been developed……

Thin Film Method Samples like paper, textile, cloth, polymer films, etc. Background material Sample Sensor Sample Background material Thickness from ~ 10μm ~ 500μm Conductivity from ~ 0.01W/mK ~ 10W/mK Background material is good conductor, experiment parameters as if this is the sample: high power, short time

Thin Film often uses a square, naked Ni-sensor which is most sensitive,but also cladded sensors can be used

Slab Method Insulator Sample Sensor Sample Insulator For good conductors, >10 W/mK - Ceramic, metals, Si-wafer, SiC. Etc. Relation between Sample Thickness/Sensor radius 0.03 < t/R < Different radii to match different samples

Developing Slab Method -Air is very insulating

Anisotropic samples Radial direction Conductvity Diffusivity Axial direction Conductivity Diffusivity To solve the heat conductivity equation in this case: Heat Capacity Cp must be known!

Anisotropic sampels Tensile testing bars, polymer matrix with fiber reinforcement in the plan. Thickness 2 mm.

λ radial W/mK λ axial W/mK χ radial mm2/s χ axial mm2/s χ mm2/s λ W/mK

Single sided method If you do not want to cut your precious sample… put the sensor on the surface… …..and back it up with a known sample. Tell the software the properties of the known, and run the analysis as before. In principal, the more similar, the better

In Transient Methods, like Hot Disk, the contact resistance does not cause any problem. This is not the case with Steady State Methods, where this is a limitation for the use. The following slides explains how Contact resistance is dealt with, and gives an illustrative example.

Ideally, the sensor is surrounded by infinite sample in all direction. Contact area Temp C Time s Cut off here!

Ideally, the sensor is surrounded by infinite sample in all direction…. If this should occur, the later part of the raw data are removed Cut off here! Temp C Time s

Measuring coated and uncoated ceramics Varistors made of ZnO ceramics uncoated surface surface coated by Al-metal, 60μm thick Measuring with same conditions – sensor, time, power,temperature

It seems like the Al-metal coating was insulating? A metal like Al ? In this case the sprayed metal was very porous. The conductivity was about 0.5 W/mK 60μm of porous metal added to the kapton coating increases the temperture about 4 times!

Some results Green Metal Coated W/mK std % W/mk std% 23 C (0.2) (0.8) 300 C (2.2) (0.8) Sensor radius mm Sensor radius mm 23 C (0.8) (1.0) 300 C (1.3) (0.4) Mica sensor Kapton sensor Mica sensor

Measuring liquids -vertical sensor -low power -short time …to avoid convection Put it in a heating/cooling bath, and run at different temperatures - liquids with a viscosity as low as water and methanol can be measured

Pure water: Temperature Time Conductivity std Diffusivity std Heat Capacity std C s W/mK % mm2/s % MJ/m3K % see A see B

Measuring at high temperatures Sample Muffle furnace from RT to 700 C Mica cladded sensor

How accurate is Hot Disk ? An article by professor Torbjorn Log* compares results from 5 different materials, measured with different techniques, with Hot Disk measurements. * T.Log, S.E.Gustafsson, Transient Plane Source (TPS) Technique for Measuring Thermal Transport Properties of Building Materials, Fire and Materials 19, (1995)

These are the samples…….. …with properties found with different techniques. Almost 4 orders of magnitude

Results for diffusivity. Small deviations – but who is right?

Results on Conductivity – almost perfect agreement

Measuring on a NIST Standard Extruded Polystyrene, cert. No 1453 Values given for a range of density and temperatures for a thickness of 13.4mm Density from 38 kg/m3 to 46 kg/m3 at 295 K, the given Thermal Resistance (m2K/W), converted to Thermal Conductivity by using the thickness gives a range W/mK

13.4 mm 100 mm Density 43.8 kg/m kg/m3 4 possible combinations to place the sensor Side combinations Results (W/mK) Std %

So….what Hot Disk can do in Evitherm.. measure most materials from to 500 W/mK.. develop new applications… provide consultancy, measurements and equipment, as well as training, courses, seminars In Uppsala – development electronics, manufacturing, applications, testing service In Göteborg – development sensors/software applications, testing

That’s all folks ! Thank you for your attention.

Metal insert Vacuum feed through Sample holder and sensor

Outer lid with vacuum connection, gas valves, pressure valve and cables