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The polar behavior of double perovskite (Bi,Pb)ZnNbO$_6$ and (Bi,Sr)ZnNbO$_6$was investigated using first principles density functional calculations withinthe local density approximation. These materials have both $A$-site sizedisorder and ions with sterochemical activity. We found a strong ferroelectricdistortion in both materials. The polarization of the Pb material is $>$80$\mu$C/cm$^2$ along the rhombohedral direction and the Sr based material isonly slightly inferior. The high polarization results mainly from a largeoff-centering of Bi and the large Born effective charge of Nb, which yields alarge contribution polarization although the Nb off-centers by a smalleramount. Neither of these materials favors a tetragonal state, and thereforesolid solutions with PbTiO$_3$ may show morphotoropic phase boundaries.

Polar behavior of double perovskite (Bi,Pb)ZnNbO6 and (Bi,Sr)ZnNbO6: Density functional calculations