α-Quartz Crystal as Absolute Intensity and Phase Standard in Sum-Frequency Generation Vibrational Spectroscopy

Quartz crystal has been used as intensity and phase reference standard in sum-frequency generation (SFG) and other nonlinear spectroscopy measurements. In this report, we examined the issues regarding the most widely used z-cut α-quartz in SFG intensity and phase measurements, through systematic comparison of optical rotation, piezoelectric, and SFG vibrational spectroscopy (SFG-VS) measurement results. For quartz crystal used as SFG-VS intensity standard, we examined the issue on the spectroscopic flatness of quartz crystal and gold film in the broad range of 1000–4000 cm–1, and we concluded that, in the range of 2000–4000 cm–1, both quartz crystal and gold film are spectrally flat and are suitable for intensity reference in the SFG-VS measurement. For quartz crystal being used as an absolute phase standard, the determination of the absolute direction of the quartz crystal is crucial, and in the past this has been defined and determined using piezoelectric measurement. We found that the 1949 and 1945 IRE (Institute of Radio Engineers) standards of defining the coordinates system based on the piezoelectric measurement for the quartz unit cell and crystal are often inconvenient in the applications to the nonlinear spectroscopy measurement and may cause confusion. Therefore, we proposed a new SFG/SHG (second-harmonic generation) convention to consistently define the quartz crystal coordinates system. Then, we showed that the internal heterodyne phase-resolved (IHPR) SFG-VS measurement of adsorbed molecular layers, e.g., OTS (octadecyltrichlorosilane), on the quartz crystal surface can be used to self-consistently determine the absolute azimuthal orientation direction of the quartz crystal, independent from the use of the piezoelectric measurement. In the end, we also examined the issue regarding the absolute phase of the hyperpolarizability of various molecular groups, as well as quartz, under proper coordinates system. These results are useful for the future applications to the nonlinear spectroscopy, particularly the nonlinear spectroscopy for surface and interface studies.