Polar behavior of double perovskite (Bi,Pb)ZnNbO$_{6}$ and (Bi,Sr)ZnNbO$_{6}$: Density functional calculations Shigeyuki Takagi 1 , $^{2}$, Alaska Subedi1 , $^{2}$, David J. Singh$^{1}$, and Valentino R. Cooper1 $^{1}$Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114 $^{2}$Department of Physics, University of Tennessee, Knoxville, TN 37996 (Dated: November 1, 2018) The polar behavior of double perovskite (Bi,Pb)ZnNbO 6 and (Bi,Sr)ZnNbO 6 was investigated using first principles density functional calculations within the local density approximation. These materials have both A -site size disorder and ions with sterochemical activity. We found a strong ferroelectric distortion in both materials. The polarization of the Pb material is > 80 µ C/cm 2 along the rhombohedral direction and the Sr based material is only slightly inferior. The high polarization results mainly from a large off-centering of Bi and the large Born effective charge of Nb, which yields a large contribution polarization although the Nb off-centers by a smaller amount. Neither of these materials favors a tetragonal state, and therefore solid solutions with PbTiO 3 may show morphotoropic phase boundaries. PACS numbers: 77.84.Ek,71.20.Ps a substantial ferroelectric instability of the ideal cubic structure, but now the tilt instability is stronger, and so ferroelectricity does not occur. 7–9 However, accord- ing to first principles calculations, if the octahedra are prevented from tilting by mixing large and small A -site ions they may become ferroelectrics. 10 There is exper- imental support for this. For example, ferroelectricity in the (Ba,Ca)TiO$_{3}$ solid solution is strongly enhanced compared to what would be expected interpolating be- tween the properties of the end-point compounds. 11 Im- portantly, this leads to new compositions that have high piezoelectric coefficients. 11,12 Perovskite ferroelectrics and relaxor ferroelectrics are widely used in applications including electromechanical transducers, actuators, passive electronic components, memory devices and microwave technology. There is strong interest in obtaining improvements in materials performance, such as high polarization, high Curie tem- perature, improved electromechanical coupling and lower loss. One approach is through the exploration of new ma- terials. Besides this technological motivation, these ma- terials have been the focus of considerable fundamental interest, particularly in unraveling the complex interplay between crystal chemistry and lattice distortions and in understanding the range of polar behaviors that can be produced by strain and chemical substitutions. Much has been learned over the past several years. Generally, high piezoelectric coefficients and elec- tromechanical coupling are found near phase boundaries. In particular, the electromechanical coupling in per- ovskite piezoelectrics is associated with polarization ro- tation near morphotropic phase boundaries (MPBs). 13,14 These are generally boundaries between ferroelectric states differing in the direction of their ground state polarization. Therefore one strategy for finding new piezoelectric compositions is to search for solid solutions with MPBs. A particular emphasis has been in solid solutions with PbTiO$_{3}$ (PT) as one end-point, follow- ing the commonly used Pb(Zr,Ti)O$_{3}$ (PZT) system and the PbMg$_{1}$$_{/}$$_{3}$Nb$_{2}$$_{/}$$_{3}$O$_{3}$ (PMN) - PT and PbZn$_{1}$$_{/}$$_{3}$Nb$_{2}$$_{/}$$_{3}$O$_{3}$ (PZN) - PT piezocrystal systems. 15 PT is tetragonal with a substantial tetragonality. There is considerable inter- est in finding materials that can be alloyed with PT and which have strong ferroelectricity with rhombohe- dral or related ground states to produce an MPB perhaps with high Curie temperature, high polarization and high tetragonality on the tetragonal side of the MPB. A development of potential importance is the realiza- tion that Bi based perovskites can be very useful ferro- electrics, as exemplified by progress in BiFeO$_{3}$. In partic- ular, the small ionic radius and stereochemical activity of Bi $^{3+}$, leads to large displacements in a low volume unit cell, and its high charge (3+ vs. 2+ for Pb) and hybridization of Bi 6 p states with O 2 p states leads to a The lattice instabilities of perovskite oxides, AB O$_{3}$ are often understood using the tolerance factor t = ( r$_{O}$ + r$_{A}$ ) $_{/}$√$_{2(}$$_{r}$$_{O}$$_{+}$$_{r}$$_{B}$$_{), where}$$_{r}$$_{O}$$_{,}$$_{r}$$_{A}$ and r$_{B}$ are the ionic radii for the O, A -site and B -site ions, respectively. 1–3 These materials are classed in two groups according to whether the tolerance factor is less than unity or not. Several t > 1 ferroelectrics are known, including the pro- totypical materials, BaTiO$_{3}$ and KNbO$_{3}$. In these mate- rials there is a tendency towards lattice distortions where the too-small B -site ion off-centers. This is strongly en- hanced by covalency involving O 2 p states and nomi- nally unoccupied B -site d states. This then leads to enhanced Born effective charges and large longitudinal optic - transverse optic splittings. 4,5 In the majority of t < 1 materials the B O$_{6}$ octahedra are tilted and they are not ferroelectrics. 6 The exceptions are generally per- ovskites with lone-pair A -sites such as Pb and Bi. In these cases, the ideal cubic perovskite structure is often unstable against octahedral tilting, but the ferroelectric instability, which is enhanced by the stereochemical ac- tivity of the A -site, is stronger. In materials with t < 1 but no stereochemically active A -site ion, there is often arXiv:1001.2227v1 [cond-mat.mtrl-sci] 13 Jan 2010 I. INTRODUCTION