Determination of thermal diffusivity of opaque materials using the photothermal mirror method

Abstract

A pump-probe photothermal mirror (PTM) method has been developed to determine the thermal dif- fusivity of opaque solid samples. The method involves the detection of the distortion of a probe beam whose reflection profile is affected by the photoelastic deformation of a polished material surface induced by the absorp- tion of a focused pump field. We have measured the time dependence of the PTM signal of Ti, Al, Cu, Sn, Ag, and Ni samples. We show theoretically and experimentally that the time derivative of the signal in the first micro- seconds is proportional to the square root of the thermal diffusivity coefficient. The method affords a simple calibration and efficient interpretation of experimental data for a sensitive determination of the thermal diffusivity coefficient for materials. We demonstrate the applicability of the technique by measuring the thermal diffusivities of wadsleyite (β-Mg2SiO4) and diopside (MgCaSi2O6), two important minerals relevant to geophysical studies. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1.OE.53.12.127101) beams. 9-12 A useful signal can be generated by measuring the transmission of the reflected probe light through a small aperture located at some distance from the sample. The PTM signal is defined as the relative change of the probe light transmission through the aperture. In the continuous wave regime of excitation, the signal grows as the square root of time in the first microseconds after the start of illu- mination. The signal reaches a stationary value when thermal diffusivity equilibrates the intake of thermal energy, yielding stationary values for the induced thermal gradients. The steady state situation is reached within a few milliseconds for metals, whose thermal diffusivities based on the simul- taneous resolution of the thermoelastic equation for the sur- face deformations range from 10 −5 to 2 × 10 −4 m 2 s −1 . The theoretical model used to explain the PTM method is based on the simultaneous resolution of the thermoelastic equation for the surface deformations and the heat conduction equa- tion. The thermal surface deformation yields a phase shift of the reflected probe beam of light. Diffraction theory provides the value of the probe wavefront at the detector location. The method affords a simple nondestructive determination of the photothermal properties of the sample. In this work, we have developed a simple and practical PTM technique to measure the thermal diffusivity of opaque samples. Based on the developed theoretical model for the PTM effect, we numerically show that the time derivative for the first microseconds of growth of the PTM signal divided over its stationary value is linearly proportional to the square root of the thermal diffusivity coefficient. We have studied the time dependence of the PTM signal for six different met- als: Ag, Cu, Ni, Al, Sn, and Ti. By measuring the time deriv- atives of these dependences, we demonstrate the validity of the theoretical predictions. We provide a calibration curve of the values of the time derivatives of the PTM signal that we have subsequently used to determine the thermal diffusivities of wadsleyite (β-Mg2SiO4) and diopside (MgCaSi2O6), two important minerals relevant to geophysical studies.