Excess thermochemical properties and local structure in the entropy stabilized (Hf-Zr)TiO4 system
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Rosenberg, William (ORCID:0000000178532136)↗
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HfZr_BCC_SolidSolution_128atoms_VASP6
We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-zirconium (Hf-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions.
36 MATERIALS SCIENCE↗
Materials Data on HfZr by Materials Project
HfZr is Magnesium-derived structured and crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. Hf is bonded to six equivalent Hf and six equivalent Zr atoms to form HfHf6Zr6 cuboctahedra that share corners with eighteen equivalent HfHf6Zr6 cuboctahedra, edges with six equivalent HfHf6Zr6 cuboctahedra, edges with twelve equivalent ZrHf6Zr6 cuboctahedra, faces with eight equivalent HfHf6Zr6 cuboctahedra, and faces with twelve equivalent ZrHf6Zr6 cuboctahedra. All Hf–Hf bond lengths are 3.22 Å. All Hf–Zr bond lengths are 3.17 Å. Zr is bonded to six equivalent Hf and six equivalent Zr atoms to form ZrHf6Zr6 cuboctahedra that share corners with eighteen equivalent ZrHf6Zr6 cuboctahedra, edges with six equivalent ZrHf6Zr6 cuboctahedra, edges with twelve equivalent HfHf6Zr6 cuboctahedra, faces with eight equivalent ZrHf6Zr6 cuboctahedra, and faces with twelve equivalent HfHf6Zr6 cuboctahedra. All Zr–Zr bond lengths are 3.22 Å.
36 MATERIALS SCIENCE↗
Materials Data on HfZr3 by Materials Project
HfZr3 is Magnesium-derived structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Hf is bonded to twelve equivalent Zr atoms to form HfZr12 cuboctahedra that share corners with six equivalent HfZr12 cuboctahedra, corners with twelve equivalent ZrHf4Zr8 cuboctahedra, edges with eighteen equivalent ZrHf4Zr8 cuboctahedra, faces with eight equivalent HfZr12 cuboctahedra, and faces with twelve equivalent ZrHf4Zr8 cuboctahedra. There are six shorter (3.18 Å) and six longer (3.23 Å) Hf–Zr bond lengths. Zr is bonded to four equivalent Hf and eight equivalent Zr atoms to form ZrHf4Zr8 cuboctahedra that share corners with four equivalent HfZr12 cuboctahedra, corners with fourteen equivalent ZrHf4Zr8 cuboctahedra, edges with six equivalent HfZr12 cuboctahedra, edges with twelve equivalent ZrHf4Zr8 cuboctahedra, faces with four equivalent HfZr12 cuboctahedra, and faces with sixteen equivalent ZrHf4Zr8 cuboctahedra. There are a spread of Zr–Zr bond distances ranging from 3.19–3.23 Å.
36 MATERIALS SCIENCE↗