Inspection of functionally graded coating materials using frequency domain photoacoustic microscopy

A frequency domain photoacoustic microscopy system has been developed for the inspection of functionally graded mullite coatings deposited on SiC substrates. Narrow-bandwidth surface acoustic waves (SAWs) are generated with an amplitude modulated laser source. A photorefractive crystal based interferometer coupled to a lock-in amplifier is used for the detection of the resulting surface displacements. The complex displacement field is mapped over a source-to-receiver distance of approximately 500mum in order to extract the wavelengths of SAWs at a given excitation frequency, from which the phase velocities are determined. SAW dispersion characteristics are sensitive to the elastic properties of the near surface region. The measured SAW dispersion is compared to a theoretical model in order to extract the elastic properties and thickness of the coatings. Frequency domain photoacoustic microscopy allows for the rapid, non-contact characterization of graded coatings and is potentially suitable for in-situ process control.; The velocities of SAWs propagating in graded materials are found using the reflectance function technique combined with a transfer matrix approach. Theoretical results demonstrate that SAW dispersion in micron-scale functionally graded coatings over the 100-200 MHz frequency range is most sensitive to the mean elastic modulus of the coating and the coating thickness. In addition, the dispersion behavior is also influenced by the form of the elastic property variation through the coating thickness and can, in some cases, be used to determine the elastic property distribution. The photoacoustic microscopy technique was used to measure SAW dispersion on as-grown mullite coatings, and a simplex optimization algorithm was used to determine the mean elastic modulus and thickness through minimization of the error between measured and calculated SAW velocities. The results show agreement with independent measurements of the mean elastic modulus and thickness of the coating measured using nanoindentation and optical microscopy, respectively. It is found that SAW velocity measurement error caused by local porosity and spatial inhomogeneities can be reduced by spatial averaging over the measurement region. Experimental measurements also confirm that photoacoustic microscopy can be used to gain insight into the form of elastic modulus distribution through the coating thickness in micron scale graded coatings.