Thermal diffusivity measurements by photothermal laser beam deflection (PTD): data analysis using the Levenberg-Marquardt algorithm

Photothermal laser beam deflection (PTD) is a powerful tool used to obtain the thermal diffusivities of bulk solids and thin films. PTD is of special interest for non-destructuve evaluation of bulk, thin film and composite materials anticipated for use in future space missions. Polycrystalline diamond thin films are expected to be useful as heat sinks and thermal conductors in space applications, and measurement of thermal diffusivity in these films is very important. One of the major problems in applying the PTD technique for diffusivity measurements (and hence the thermal conductivity, since heat capacities and densities are not difficult to measure and are frequently known) is that a numerical regression analysis must be performed to simultaneously determine several unknown parameters. Regression is done by matching experimental data with calculations based on analytic models such that an error function is minimized. This paper describes the adaption of the Levenberg-Marquardt algorithm for regression analysis to the determination of thermal diffusivity of bulk and thin film solids by PTD. The analytic theory is reviewd and the numerical analysis method is described. Experimental equipment for high signal-to-noise ratio data is described and data on bulk aluminum taken over a range of frequencies are presented. Regression analysis fits to the theory (performed in an inverse space reference frame) yield values for parameters of the experiment, including the thermal diffusivity.