Effective medium formulation for phonon transport analysis of nanograined polycrystals J. Appl. Phys. 111, 014307 (2012) Negative refraction of elastic waves in 2D phononic crystals: Contribution of resonant transmissions to the construction of the image of a point source AIP Advances 1, 041405 (2011) Thermal energy transport model for macro-to-nanograin polycrystalline semiconductors J. Appl. Phys. 110, 114310 (2011) Nanostructure model of thermal conductivity for high thermoelectric performance J. Appl. Phys. 110, 114306 (2011) Additional information on J. Appl. Phys. In this paper we report phonon dynamics in chemically synthesized Zn 1−x Mg x O ͑0 Յ x Յ 0.07͒ and Zn 1−y Cd y O ͑0 Յ y Յ 0.03͒ alloy nanostructures of sizes ϳ10 nm using nonresonant Raman and Fourier transformed infrared spectroscopy. Substitution by Mg makes the unit cell compact while Cd substitution leads to unit cell expansion. On alloying, both A 1 ͑LO͒ and E 1 ͑LO͒ mode of wurtzite ZnO show blueshift for Zn 1−x Mg x O and redshift for Zn 1−y Cd y O alloy nanostructures due to mass defect and volume change induced by the impurity atoms. Significant shift has been observed in E 1 ͑LO͒ mode for Zn 1−x Mg x O ͑73 cm −1 for x = 0.07͒ and Zn 1−y Cd y O ͑17 cm −1 for y = 0.03͒ nanostructures. The variation in Zn͑Mg,Cd͒-O bond length determined from the blue-͑red-͒ shift of IR bands on alloying with Mg ͑Cd͒ is consistent with their respective ionic sizes and the structural changes predicted by x-ray diffraction study. However, on progressive alloying one can detect phase segregation ͑due to presence of interstitial Mg and Cd ions͒ in the alloy nanostructures for relatively higher Mg and Cd concentrations. This is confirmed by the gradual absence of the characteristic IR and Raman bands of wurtzite ZnO near 400-600 cm −1 as well as by x-ray and TEM studies.