Introduction

Laser Flash Analysis (LFA) is used for determining the thermal conductivity of the sample by measuring thermal diffusivity in respect of temperature. Thermal conductivity and diffusivity are important concepts needed for understanding the analysis method.[1] 

Thermal conductivity (symbol k or λ) is a property of the material that tells about how well heat move or conduct through the body of the material. Heat is moving through material by kinetic molecular activity. The thermal conductivity is used in Fourier's law that states the rate of flow of heat (dQ/dt) to be equal with negative thermal conductivity (-k) multiplied by area of surface (A) and temperature gradient (dT/dt). Fourier's Law also states that thermal conductivity is dependent of temperature.  The SI units for thermal conductivity are W*m-1*K-1. Thermal conductivity values varies depending of material and is high with metals and low with finely powdered materials. [2]

The thermal diffusivity (symbol α), which LFA is used to measure, tells the rate of material heat conducting from the hot to cold end. The thermal diffusivity can be calculated by dividing the thermal conductivity with specific heat capacity and density of the material. Metals have high thermal diffusivity and that means that they diffuse heat at faster rate than other materials with lower thermal diffusivity. The SI units of the thermal diffusivity are m2*s-1.[2]

Laser flash analysis method was developed by Parker et al. in 1960. Parker et al. defined the method's advantages to be a minimum need for specialized equipment, a relatively easy data reduction, small sample size, an option to test in different temperatures and an energy efficiency. The analysis method was first made and tested for metals but can be widely used for all kind of solid materials. In addition of mentioned advantages, the analysis method can be used for determine three thermal properties: diffusivity, thermal conductivity and heat capacity.[1]Later the method has been improved by many researchers by perfecting apparatuses, data processing and taking account factors like heat losses, finite pulse durations and uniformity of heating effect. Also, nowadays the laser flash analysis is used for measuring thermophysical properties of more advanced materials like for example anisotropic materials, layered structures, composites and thin films. [3]

Principle and apparatus

In the picture 1, a simplified picture of the LFA apparatus can be seen. Laser flash apparatus main parts include sample holder, laser system, sample chamber and detector. 

Picture 1. Simplified picture of LFA apparatus parts (Figure by Sami Patteri)[4]

Laser Flash Analysis is based on increasing sample’s temperature for short duration with a high intensity laser flash pulse from one side and detecting emitted heat waves from the other side. The heat waves are detected by the infrared measuring device. Atmospheric temperature during the analysis can be controlled by chamber with equipment like oven, cryostats or insulated chambers for ambient temperature needs. As a result, the thermal diffusivity in respect of temperature is measured. The Machine calculates thermal diffusivity by following equation. [5]


\[ α = (1,37 * L^2)/ (π^2 * t_{0.5}) \]


Where 

L = sample's thickness in millimetres,

t0.5 = seconds that take that the test sample reaches one half of its maximum temperature after flash pulse.[5]

For determining thermal conductivity with LFA, the specific heat capacity (Cp) and density of the sample material are needed. After acquiring the needed values, the thermal conductivity can be calculated by following equation. [6]

\[ k = ρ * C_p * α \]


Where

k = Thermal conductivity,

ρ = Density,

α = Thermal diffusivity,

Cp = Specific heat. [6]

Example of analysis

Park et al. researched the thermal conductivity of Li2TiO3 by utilizing the LFA. Analysis method was chosen over other measurement techniques due to its advantages, for example accuracy and repeatability.  During the measurements, the sample of Li2TiO3 was in the form of pebbles. Pebble bed was formed to sample holder and dimensions of the whole pebble bed was used in calculations. [6]Before analysing the thermal diffusivity of the material with the laser flash analysis, specific heat and density of the material had to be measured for calculation of thermal conductivity.[6]

Specific heat (Cp) was measured with a differential scanning calorimetry (DSC) method. At the DSC analysis temperature range up to 900 °C was used. As a result, researchers plotted Cp in respect with temperature and got following equation for Cp[6]

\[ Cp = 0.1278*lnT + 0.4836 (T≤ 700 °C) \]


Density (ρ) of individual sample pebbles (bulk density of the material) were determined with He pycnometer and Hg porosimeter. By taking factor dimensions and mass of the pebble bed they were able to determine the true density of the used sample bed in correlation of bulk density. The true density of pebble bed was calculated to be 57 % of the bulk density.[6]

\[ ρ = 1.75 g/cm^3 \]


With the LFA thermal diffusivity (α) of the sample was measured. According of results and how material reacted at high temperatures in the DSC analysis, temperature range for LFA analysis and for calculating the thermal conductivity was chosen to be up to 700 °C. LFA was done in flowing helium atmosphere. As a result, researchers plotted α in respect with temperature and got following equation for α.[6]

\[ α = -0.026*lnT + 0.7266 (T≤ 700 °C) \]


With all values the thermal conductivity was calculated and plotted in respect with temperature up to 700 °C. From the results Park et al. determined that the thermal conductivity of Li2TiO3 increased with temperature increase up to 500 °C and after that started to stabilize.[6]

References

1. 1 2

Parker W.J, Jenkins R.J., Butler C.P. & Abbot G.L. Flash method of determining thermal diffusivity, Heat Capacity, and Thermal Conductivity, Journal of applied physics, 1961, 32, 1679. (https://doi.org/10.1063/1.1728417).

2. 1 2

 Schaschke, C. (2014) A dictionary of chemical engineering. First edition. Oxford: Oxford University Press.

3. 1

Vozár L., Hohenauer W. Flash method of measuring the thermal diffusivity. A review, High Temp. Press., 2004, 36, 253-264. (http://dx.doi.org/10.1068/htjr119).

4. 1
Netzsch Group. Laser Flash Technique (LFA). (https://www.netzsch-thermal-analysis.com/en/contract-testing/methods/laser-flash-technique-lfa/). visited 27.02.2022.
5. 1 2

SFS-EN821-2. Advanced technical ceramics. Monolithic ceramics. Thermo-physical properties. Part2: Determination of thermal diffusivity by the laser flash (or heat pulse) method. 1997.

6. 1 2 3 4 5 6 7 8

Park Y.H., Ku D.Y., Ahn M.Y., Lee Y. & Cho S.  Measurement of thermal conductivity of Li2TiO3 pebble bed by laser flash method, Fusion Engineering and Design, 2019, 146, 950-954. (https://doi.org/10.1016/j.fusengdes.2019.01.122).

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