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At least 19 records

Phase transitions in HfO2 probed by first-principles computations

Ever since ferroelectricity was discovered in HfO2, the question of its origin remains controversial. Here, we probe this question using a combination of Landau theory of phase transitions and first-principles computations. In such an approach, the energy landscape associated with the phase transition between cubic and different experimentally demonstrated phases of HfO2 (tetragonal, monoclinic, orthorhombic Pbca, orthorhombic Pnma, and orthorhombic Pca21) is explored using density functional theory calculations. Computations revealed that stabilization of all but orthorhombic Pbca phase is driven by a single unstable zone-boundary antipolar mode X2−. When coupled with zone-center modes (Γ1+ and Γ3+), it stabilizes the tetragonal phase. Coupling with four additional modes (Γ5+, X3−, X5−, X5+) results in the monoclinic phase, which is the ground state of the material. If, however, Γ5+ mode is replaced with Γ4− mode, orthorhombic polar phase Pca21 is stabilized. The application of this framework to examine the effect of electric field on the ferroelectric phase of hafnia reveals that the field of 5 MV/cm is capable of stabilizing ferroelectric phase over the monoclinic one at 0 K.

Physics↗

Materials Data on HfO2 by Materials Project

HfO2 is Baddeleyite-like structured and crystallizes in the orthorhombic Pbca space group. The structure is three-dimensional. Hf4+ is bonded to seven O2- atoms to form a mixture of distorted edge and corner-sharing HfO7 pentagonal bipyramids. There are a spread of Hf–O bond distances ranging from 2.05–2.22 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of edge and corner-sharing OHf4 tetrahedra. In the second O2- site, O2- is bonded in a trigonal planar geometry to three equivalent Hf4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Baddeleyite structured and crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Hf4+ is bonded to seven O2- atoms to form a mixture of distorted corner and edge-sharing HfO7 pentagonal bipyramids. There are a spread of Hf–O bond distances ranging from 2.05–2.26 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three equivalent Hf4+ atoms. In the second O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of distorted corner and edge-sharing OHf4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Fluorite structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Hf4+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. All Hf–O bond lengths are 2.20 Å. O2- is bonded to four equivalent Hf4+ atoms to form a mixture of edge and corner-sharing OHf4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Baddeleyite-like structured and crystallizes in the orthorhombic Pca2_1 space group. The structure is three-dimensional. Hf4+ is bonded to seven O2- atoms to form a mixture of distorted edge and corner-sharing HfO7 pentagonal bipyramids. There are a spread of Hf–O bond distances ranging from 2.04–2.25 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a trigonal planar geometry to three equivalent Hf4+ atoms. In the second O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of edge and corner-sharing OHf4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Cotunnite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Hf4+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Hf–O bond distances ranging from 2.14–2.59 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of edge and corner-sharing OHf4 tetrahedra. In the second O2- site, O2- is bonded in a 3-coordinate geometry to five equivalent Hf4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Baddeleyite-like structured and crystallizes in the orthorhombic Pbca space group. The structure is three-dimensional. Hf4+ is bonded to seven O2- atoms to form a mixture of distorted corner and edge-sharing HfO7 pentagonal bipyramids. There are a spread of Hf–O bond distances ranging from 2.05–2.23 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three equivalent Hf4+ atoms. In the second O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of corner and edge-sharing OHf4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Hydrophilite-like structured and crystallizes in the orthorhombic Pbcn space group. The structure is three-dimensional. there are two inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing HfO6 octahedra. The corner-sharing octahedra tilt angles range from 50–53°. There are a spread of Hf–O bond distances ranging from 2.09–2.11 Å. In the second Hf4+ site, Hf4+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing HfO6 octahedra. The corner-sharing octahedra tilt angles range from 50–53°. There are a spread of Hf–O bond distances ranging from 2.04–2.16 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to three equivalent Hf4+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to three Hf4+ atoms. In the third O2- site, O2- is bonded in a trigonal planar geometry to three Hf4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Rutile structured and crystallizes in the tetragonal P4_2/mnm space group. The structure is three-dimensional. Hf4+ is bonded to six equivalent O2- atoms to form a mixture of edge and corner-sharing HfO6 octahedra. The corner-sharing octahedral tilt angles are 50°. All Hf–O bond lengths are 2.10 Å. O2- is bonded in a distorted trigonal planar geometry to three equivalent Hf4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 crystallizes in the tetragonal P4_2/nmc space group. The structure is three-dimensional. Hf4+ is bonded in a distorted body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.07 Å) and four longer (2.40 Å) Hf–O bond lengths. O2- is bonded to four equivalent Hf4+ atoms to form a mixture of distorted edge and corner-sharing OHf4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

HfO2 is Baddeleyite-like structured and crystallizes in the orthorhombic P2_12_12 space group. The structure is three-dimensional. Hf4+ is bonded to seven O2- atoms to form a mixture of distorted corner, edge, and face-sharing HfO7 pentagonal bipyramids. There are a spread of Hf–O bond distances ranging from 2.01–2.28 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a 3-coordinate geometry to three equivalent Hf4+ atoms. In the second O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of distorted corner and edge-sharing OHf4 trigonal pyramids. In the third O2- site, O2- is bonded to four equivalent Hf4+ atoms to form a mixture of corner and edge-sharing OHf4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗

Materials Data on HfO2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗