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A density functional theory plus Hubbard U method is used to investigate how the incorporation of Pu waste into Gd₂Zr₂O₇ pyrochlore influences its thermo-physical properties. It is found that immobilization of Pu at Gd-site of Gd₂Zr₂O₇ has minor effects on the mechanical and thermal properties, whereas substitution of Pu for Zr-site results in remarkable influences on the structural parameters, elastic moduli, elastic isotropy, Debye temperature and electronic structure. The discrepancy in thermo-physical properties between Gd_2−yPu_yZr₂O₇ and Gd₂Zr_2−yPu_yO₇ may be a result of their different structural and electronic structures. This study provides a direct insight into the thermo-physical properties of Pu-containing Gd₂Zr₂O₇, which will be important for further investigation of nuclear waste immobilization by pyrochlores.