### What is the laser flash analysis?

The laser flash analysis (LFA)is a transient method for determining the thermal properties of solids and powders. The laser flash analysis directly measures thermal diffusivity, and then uses the temperature rise from the performed measurement, the heat from the laser, and the intensity of the beam to determine specific heat. With these two values, the thermal conductivity of the sample can be calculated indirectly, within the ranges of 0.1 to 4000 W/mK. Additionally, thermal effusivity can also be determined when thermal conductivity and specific heat are known.

### Measurements with the laser flash method

The laser flash apparatus at its core consists of a laser, a temperature detector of some sort, and the sample material. The laser emits a very brief pulse onto one side of the material, and the temperature detector at the other side detects the change in temperature over time. Modern methods also involve calibrating the conditions around the sample to remove the effect of convection, as well as coating the sample in a layer of graphite, or gold, to increase the emissivity of the sample.

### Mathematical considerations of the laser flash method

The laser pulse is designed to simulate a Dirac delta function as closely as possible. In theory, the pulse is converted to thermal energy in an instant, and is equally distributed across the sample to a certain depth, \( g \). For this theory to work, the penetration depth must be smaller than the total depth of the sample, \( {L} \), and narrower than the width of the laser beam. The temperature distribution across the sample is then,

\[ T(x,0)=\begin{cases}\frac{Q}{\rho c g}\textit{ for }0<x<g\\0 \textit{ for }g < x < L \end{cases} \]

Where \( Q \) is the heat flux from the laser, and \( \rho c \) is the volumetric heat capacity. For a thermally insulated slab of material, where initial temperature conditions are known and represented by \( T(x,0) \), the solution can be found. For this initial condition, the temperature distribution at time \( t \) will be,

\[ T(x,t)=\frac{Q}{\rho c L}\Bigg [ 1+2 \sum_{n=1}^\infty \cos \Big(\frac{n \pi x}{L}\Big )\frac{\sin(n \pi g/L)}{n \pi g/L}e^{-\frac{n^{2}\pi^{2}}{L^{2}}\kappa t}\Bigg ] \]

Where \( \kappa \) is the thermal diffusivity. Here, since \( {n} \pi {g} \) is so small, \( \sin (n \pi g / L) \) is approximately \( n \pi g / L \) . At the rear end of the slab, ie \( x = L \) , the temperature follows

\[ T(x,t)=\frac{Q}{\rho c L}\Bigg [ 1+2 \sum_{n=1}^\infty (-1)^{n}e^{-\frac{n^{2}\pi^{2}}{L^{2}}\kappa t}\Bigg ] \]

By comparing \( T(L,t) \) to the maximum of \( T(L,t) \) , an expression for thermal diffusivity can be derived:

\[ \kappa = \frac{1.38 L^{2}}{\pi^{2}t_{1/2}} \]

Where \( t_{1/2} \) is the time taken to reach half the maximum temperature. Experimentally, the maximum temperature measured may not be the theoretical maximum temperature; this is due to heat losses from radiation, convection, and conduction, to other parts of the apparatus, but care is taken to minimize these factors. Notice that the expression for diffusivity does not depend on the heat from the laser, or the heat capacity. For volumetric heat capacity to be calculated, the heat from the laser must be known.

### Instrument calibration

The laser flash method is a transient, absolute method that does not require calibration. The laser flash method does not need to be calibrated because the user is able to manually remove the effect of contact resistance with the computer software after the tests have been performed. Measurements made by the laser flash method take longer than other transient methods, but the thermal diffusivity results are highly accurate, achieving results of better than 3%.

### Internationally recognized standards

The laser flash apparatus follows internationally recognized standards: ASTM Standard E1461 for determining thermal diffusivity, the ISO Standard 22007-4 for measuring the thermal conductivity and thermal diffusivity of plastics, the DIN EN Standard 821-2, for finding the thermal diffusivity of ceramics, and finally, DIN 30905, for determining the thermal diffusivity of hard metals.

### Additional literature

The laser flash method is explained in depth by Parker and his colleagues in, “Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity”. Although written in 1961, this paper remains relevant as it explains the most commonly used method to measure thermal diffusivity to this day. For more information on experimental applications of the laser flash analysis, the following articles may be useful.

- Thermal Conductivity Measurements Using the Flash Method. Authors: P.S. Gall, M.A. Thermitus, and D.E. Stroe (2004).
*Journal of Thermal Analysis and Calorimetry.*78(1). - Novel Laser Flash Technique to Measure Thermal Effusivity of Highly Viscous Liquids at High Temperature. Authors: Hiromichi Ohta, Hiroyuki Shibata, Atsushi Suzuki, and Yoshio Waseda (2001).
*Review of Scientific Instruments*72(3). - Improvement of the Laser Flash Method to Reduce Uncertainty in Thermal Diffusivity Measurements. Authors: T. Baba, A. Ono (2001).
*Measurement Science and Technology*12(12). - A Laser Flash Apparatus for Thermal Diffusivity and Specific Heat Capacity Measurements. Authors: K. Shinzato, T. Baba (2001).
*Journal of Thermal Analysis and Calorimetry*64(1):413-422