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We report first principles density functional studies using plane wave basissets and pseudopotentials and all electron linear augmented plane wave (LAPW)of the relative stability of various ferroelectric and antiferroelectricsupercells of PMN for 1:2 chemical ordering along [111] and [001]. We usedlinear response with density functional perturbation theory (DFPT) asimplemented in the code ABINIT to compute the Born effective charges,electronic dielectric tensors, long wavelength phonon frequencies and LO-TOsplittings. The polar response is different for supercells ordered along [111]and [001]. Several polar phonon modes show significant coupling with themacroscopic electric field giving giant LO-TO splittings. For [111] ordering, apolar transverse optic (TO) mode with E symmetry is found to be unstable in theferroelectric P3m1 structure and the ground state is found to be triclinic.Multiple phonon instabilities of polar modes and their mode couplings providethe pathway for polarization rotation. The Born effective charges in PMN arehighly anisotropic and this anisotropy contributes to the observed hugeelectromechanical coupling in PMN solid solutions.Comment: 34 pages, 6 figures. to appear in PR

physical review. b, condensed matter and materials physics

<i>Ab initio</i>linear response and frozen phonons for the relaxor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Pb</mml:mi><mml:msub><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">Nb</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>∕</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal…

Ab initiolinear response and frozen phonons for the relaxorPbMg1∕3Nb2∕3