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Development of a multiphase equation of state for gallium with experiments and ab initio free-energy calculations

Here, we present a five-phase equation of state (EOS) for elemental gallium (Ga) that is developed using both experimental data and new theoretical predictions. Four experimentally observed solid phases (Ga-I, Ga-II, Ga-III, and Ga-IV) and one liquid phase are included. To improve our understanding of the thermal behavior of Ga and its phase boundaries under compression, we have performed ab initio density functional theory (DFT) free-energy calculations for the Ga-III and liquid phases, which enables us to determine the melt temperature to be 2214 ± 100 K at 110 GPa, extending significantly beyond the existing experimental melt data, which are limited to 25 GPa. In order to best describe the electron-thermal contribution, which dominates the liquid free energy at high temperatures, we have carried out averaged-atom-in-jellium DFT calculations to cover the entire temperature and density range of the EOS. The resulting multiphase Ga EOS is able to accurately reproduce a diverse variety of data, including known phase boundaries, the principal Hugoniot, low-pressure liquid isobars, and diamond-anvil-cell isotherm measurements at high pressures. It agrees more closely with key experimentally measured properties than other Ga EOS models targeted for high-pressure applications.

Wu, Christine J. [Lawrence Livermore National Labo↗

Materials Data on YGa by Materials Project

GaY crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Y is bonded in a 7-coordinate geometry to seven equivalent Ga atoms. There are a spread of Y–Ga bond distances ranging from 3.06–3.20 Å. Ga is bonded in a 9-coordinate geometry to seven equivalent Y and two equivalent Ga atoms. Both Ga–Ga bond lengths are 2.63 Å.

36 MATERIALS SCIENCE↗

Materials Data on YGa2 by Materials Project

YGa2 is hexagonal omega structure structured and crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Y is bonded to twelve equivalent Ga atoms to form a mixture of edge and face-sharing YGa12 cuboctahedra. All Y–Ga bond lengths are 3.19 Å. Ga is bonded in a 9-coordinate geometry to six equivalent Y and three equivalent Ga atoms. All Ga–Ga bond lengths are 2.43 Å.

36 MATERIALS SCIENCE↗

Materials Data on YGa6 by Materials Project

YGa6 crystallizes in the tetragonal P4/nbm space group. The structure is three-dimensional. Y is bonded to twelve Ga atoms to form a mixture of edge and face-sharing YGa12 cuboctahedra. There are four shorter (3.08 Å) and eight longer (3.23 Å) Y–Ga bond lengths. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a 9-coordinate geometry to four equivalent Y and five Ga atoms. There are one shorter (2.44 Å) and four longer (2.62 Å) Ga–Ga bond lengths. In the second Ga site, Ga is bonded in a 4-coordinate geometry to one Y and three Ga atoms. The Ga–Ga bond length is 2.56 Å.

36 MATERIALS SCIENCE↗

Materials Data on GaI3 by Materials Project

GaI3 crystallizes in the monoclinic P2_1/c space group. The structure is zero-dimensional and consists of two GaI3 clusters. Ga3+ is bonded to four I1- atoms to form edge-sharing GaI4 tetrahedra. There are a spread of Ga–I bond distances ranging from 2.52–2.72 Å. There are three inequivalent I1- sites. In the first I1- site, I1- is bonded in a single-bond geometry to one Ga3+ atom. In the second I1- site, I1- is bonded in a single-bond geometry to one Ga3+ atom. In the third I1- site, I1- is bonded in an L-shaped geometry to two equivalent Ga3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ga2I3 by Materials Project

Ga2I3 crystallizes in the monoclinic P2_1/c space group. The structure is zero-dimensional and consists of four gallium molecules and two GaI3 clusters. In each GaI3 cluster, Ga is bonded in a distorted tetrahedral geometry to one Ga and three I atoms. The Ga–Ga bond length is 2.43 Å. There are two shorter (2.64 Å) and one longer (2.65 Å) Ga–I bond lengths. There are three inequivalent I sites. In the first I site, I is bonded in a distorted single-bond geometry to one Ga atom. In the second I site, I is bonded in a single-bond geometry to one Ga atom. In the third I site, I is bonded in a single-bond geometry to one Ga atom.

36 MATERIALS SCIENCE↗

Materials Data on Y5Ga3 by Materials Project

Y5Ga3 crystallizes in the tetragonal P4/ncc space group. The structure is three-dimensional. there are two inequivalent Y sites. In the first Y site, Y is bonded to five Ga atoms to form a mixture of distorted face, edge, and corner-sharing YGa5 trigonal bipyramids. There are a spread of Y–Ga bond distances ranging from 3.07–3.21 Å. In the second Y site, Y is bonded in a 4-coordinate geometry to six Ga atoms. There are a spread of Y–Ga bond distances ranging from 3.04–3.65 Å. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a 9-coordinate geometry to eight Y and one Ga atom. The Ga–Ga bond length is 2.66 Å. In the second Ga site, Ga is bonded in a 10-coordinate geometry to ten Y atoms.

36 MATERIALS SCIENCE↗

Materials Data on YGa3 by Materials Project

YGa3 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Y is bonded to twelve equivalent Ga atoms to form a mixture of distorted face and corner-sharing YGa12 cuboctahedra. There are six shorter (3.06 Å) and six longer (3.16 Å) Y–Ga bond lengths. Ga is bonded in a 10-coordinate geometry to four equivalent Y and six equivalent Ga atoms. There are two shorter (2.79 Å) and four longer (2.80 Å) Ga–Ga bond lengths.

36 MATERIALS SCIENCE↗

Materials Data on YGa3 by Materials Project

YGa3 is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Y is bonded to twelve equivalent Ga atoms to form YGa12 cuboctahedra that share corners with twelve equivalent YGa12 cuboctahedra, edges with twenty-four equivalent GaY4Ga8 cuboctahedra, faces with six equivalent YGa12 cuboctahedra, and faces with twelve equivalent GaY4Ga8 cuboctahedra. All Y–Ga bond lengths are 3.03 Å. Ga is bonded to four equivalent Y and eight equivalent Ga atoms to form distorted GaY4Ga8 cuboctahedra that share corners with twelve equivalent GaY4Ga8 cuboctahedra, edges with eight equivalent YGa12 cuboctahedra, edges with sixteen equivalent GaY4Ga8 cuboctahedra, faces with four equivalent YGa12 cuboctahedra, and faces with fourteen equivalent GaY4Ga8 cuboctahedra. All Ga–Ga bond lengths are 3.03 Å.

36 MATERIALS SCIENCE↗