Direct integrals and spectral averaging

A one parameter family of selfadjoint operators gives rise to a corresponding direct integral. We show how to use the Putnam Kato theorem to obtain a new method for the proof of a spectral averaging result

The social and political philosophy of Sri Aurobundo

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Structural, optical and nanomechanical properties of (1 1 1) oriented nanocrystalline ZnTe thin films

Structural, optical and nanomechanical properties of nanocrystalline Zinc Telluride (ZnTe) films of thickness upto 10 microns deposited at room temperature on borosilicate glass substrates are reported. X-ray diffraction patterns reveal that the films were preferentially oriented along the (1 1 1) direction. The maximum refractive index of the films was 2.74 at a wavelength of 2000 nm. The optical band gap showed strong thickness dependence. The average film hardness and Young’s modulus obtained from loaddisplacement curves and analyzed by Oliver-Pharr method were 4 and 70 GPa respectively. Hardness of (1 1 1) oriented ZnTe thin films exhibited almost 5 times higher value than bulk. The studies show clearly that the hardness increases with decreasing indentation size, for indents between 30 and 300 nm in depth indicating the existence of indentation size effect. The coefficient of friction for these films as obtained from the nanoscratch test was ∼0.4.Financial support in the form of fellowships to MSRNK and SK from the ACRHEM project of DRDO is acknowledged