If I refer to the US patent describing the application of the TSR method to diffusivity measurements and to subsequent papers on this topic, the diffusivity is inferred from a simple algebric relation involving the time corresponding to a singular point on a curve derived from a polynomial fit of temperature vs time (in log scales). This singular point is typically a peak on the curve of the 2nd derivative of the polynomial.

The algebraic relation stems from an oversimplified thermocinetic model : Dirac pulse, no heat losses, homogeneous heating, and so on. Most often, with metallic samples of only a few mm thickness (i.e. small through-thickness diffusion time), the pulse delivered by the flash lamp cannot be considered as negligibly short. In addition, the lamp is warm for a long time after the flash and the glass cover emits infrared radiation towards the sample which is then reflected in the direction of the infrared camera. This provides a contribution that adds to the IR signal emitted by the sample itself. In the end the resulting signal is far from the ideal signal considered in the TSR method.

Actually the TSR approach is from an old age when non-linear multiparameter fitting was too cumbersome. At present this task is easily done by dedicated software (refer to Matlab Optimization toolbox, for example). In adition, one can find thermocinetic models in the litterature that are far closer to the real conditions of your experiment (e.g. long pulse, heat losses...).

Refer for example to the papers from the "Nancy school" (e.g. Degiovanni, Maillet, Remy, Jannot)

Best regards

Jean-Claude

Have you coated your Aluminum or Titanium sample since they are highly reflective? And how evenly was your heating source distributed? Usually for the thermal diffusivity purpose, a flash lamp is used instead of halogen due to a more predictable power deposited to the sample surface than a halogen one and shorter duration of the pulse