In the present work, the nanocrystalline particles of hydroxyapatite (HAp) using an easy alkoxide-based sol-gel technique including triethyl phosphate [PO (OC2H5)(3)] and Ca (NO3)(2)center dot 4H(2)O as P and Ca precursors have been synthesized. The sample characterization was performed by X-ray diffraction, Fourier transform-infrared analysis, scanning electron microscopy, thermal analysis (thermogravimetric analysis/differential thermal analysis), and elemental analysis of energy-dispersive X-ray analysis. It is interesting that single phase of HAp was obtained at a low firing temperature of 500 degrees C. Modified Scherrer equation as the Williamson-Hall method was applied for the measurement of crystallite size distributions and micro-strain of the sample. The determined crystallite size by complementary technique of transmission electron microscopy has good consistency with those obtained from the Scherrer formula. Moreover, we reported the one-pot synthesis of 3,4-disubstituted isoxazole-5(4H)-ones through the aqueous solution reaction of three components of ethyl acetoacetate, hydroxylamine hydrochloride and various aromatic aldehydes at room temperature. This protocol offers several advantages, including a simple work-up procedure, very short reaction times (under 25 min), in accordance with the principles of green chemistry, recyclability, excellent yields (87-98%) and environmentally friendly.