Thermal Conductivity & Thermal Effusivity Calibration of the C-Therm TCi (MTPS) and TC-30

Calibration Material Characteristics Isotropic- should be isotropic, free of directional thermal properties. Homogenous- should be highly homogenous. Surface- testing surface smooth and parallel. Stable- moisture resistant and non-degrading over calibration period. Temperature- the temperature dependent relationship with temperature should be the same for all calibration materials. i.e. If the thermal conductivity increases with increase in temperature, the same should be true for all calibration materials.

Calibration Material Selection Thermal Conductivity or thermal effusivity- Three or more materials should be used which span the thermal conductivity of your unknown sample i.e. for a range of 0.1 to 4 W/mK, which covers mostly polymers, the following standards could be used: Lexan: 0.25 W/mK Pyrex: 1.14 W/mK Steatite: 2.23 W/mK Pyroceram: 3.97 W/mK The larger the calibrated range of thermal conductivity / thermal effusivity, the more materials required. C-Therm TCi Manual

Measurement of Calibration Materials- Thermal Conductivity Thermal Conductivity- for highest accuracy, the calibration materials should be measured by absolute method (non-comparative). These include: Laserflash Apparatus (LFA), measures thermal diffusivity. Thermal Conductivity can be calculated with known density and specific heat. Range: 0.1 to 2000 W/mK. Accuracy: < 7% Hot Disk Transient Plane Source (TPS), measures thermal conductivity and thermal diffusivity. Range: 0.001 to 1800 W/mK. Accuracy: < 5% Guarded Hot Plate (GHP), measures thermal conductivity. Range 0.001 to 2 W/mK. Accuracy: < 3% *Measurement Accuracy: The accuracy of your MTPS or MTHW measured values is dependent on accuracy of calibration materials!

Measurement of Calibration Materials- Thermal Effusivity Thermal Effusivity- This is the square root of the product of thermal conductivity (W/mK), Specific Heat (J/kg-K) and Density (kg/m3). Thermal Conductivity- for highest accuracy, the calibration materials should be measured by absolute methods (non-comparative). These include: LFA, TPS and GHP. Accuracy: 3% to 7% Specific Heat- this property can be measured by a differential scanning calorimeter (DSC) or the Hot Disk TPS Specific Heat Testing Module. Accuracy: <3% Density- method would depend on material type and desired accuracy. *Measurement Accuracy: The accuracy of your MTPS or MTHW measured thermal effusivity values is dependent on composite accuracy of calibration materials: 10% to 15%. C-Therm / Mathis TC-30 Manual

MTPS Calibrating For the desired range, each calibration material is measured to generate a calibration graph of 1/m vs calibration material. It is important the calibration incorporate all parameters: Power, test time & start-time Contact agent & testing temperature. Any changes to these parameters would require re- calibration. Needs to be repeated at multiple temperature points to complete calibration process. TCi C-Therm TCi Manual

MTPS Calibrating con’t C-Therm TCi vs TC-30 predecessor to the TCi (MTPS), the TC-30 (MTHW) is calibrated in a similar manner. Calibration Graphs: Thermal Effusivity: 1/m vs calibration material < ~2000 Effusivity- linear fit. > ~2000 Effusivity- Polynomial fit. Thermal Conductivity: 1/m-m* vs calibration material- straight line fit.

MTPS Measurement If testing conditions are the same as the calibration, testing of unknown materials may begin for materials with-in the calibrated range. Raw data of 1/m (slope) C-Therm TCi Manual

MTPS Measurement Con’t Thermal Effusivity: Using the test slope (1/m), the result can be calculated using the created calibration. Straight-line fit for low effusivity materials Polynomial fit for high effusivity materials C-Therm TCi Manual

MTPS Measurement Con’t Thermal Conductivity Algorithm to calibrate and calculate k is the m*, it uses an iterative process to calibrate the sensor against measured materials with known thermal conductivity. The calibration process generates a value called m*. Using the test slope (1/m), the result can be calculated using the created calibration. C-Therm TCi Manual

MTPS Calibration Materials Here is list of OEM calibration materials, more can be found / tested at added to calibration for expanded ranges. C-Therm TCi Manual

MTPS Additional Reading http://www.google.com/patents/US6676287 http://www.ndt.net/article/ecndt2010/reports/1_05_11.pdf C-Therm TCi Manual (Can be found online) Mathis Instrument TC-30 Manual (Can be found online)