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MgCu2 is Cubic Laves structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Mg is bonded in a 12-coordinate geometry to twelve equivalent Cu atoms. All Mg–Cu bond lengths are 2.91 Å. Cu is bonded to six equivalent Mg and six equivalent Cu atoms to form a mixture of face, edge, and corner-sharing CuMg6Cu6 cuboctahedra. All Cu–Cu bond lengths are 2.48 Å.
MgCu2(SiO3)4 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six SiO4 tetrahedra. There are a spread of Mg–O bond distances ranging from 2.02–2.30 Å. Cu3+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.82–1.89 Å. There are two inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one MgO6 octahedra and corners with two equivalent SiO4 tetrahedra. The corner-sharing octahedral tilt angles are 56°. There are a spread of Si–O bond distances ranging from 1.62–1.66 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MgO6 octahedra and corners with two equivalent SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 41–55°. There are a spread of Si–O bond distances ranging from 1.63–1.66 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to one Mg2+, one Cu3+, and one Si4+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Mg2+, one Cu3+, and one Si4+ atom. In the third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Cu3+ and one Si4+ atom. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to two Si4+ atoms. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to one Mg2+, one Cu3+, and one Si4+ atom. In the sixth O2- site, O2- is bonded in a bent 150 degrees geometry to two Si4+ atoms.
MgCu2(MoO4)2 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MoO4 tetrahedra, an edgeedge with one MgO6 octahedra, and edges with two equivalent CuO5 trigonal bipyramids. There are a spread of Mg–O bond distances ranging from 2.10–2.29 Å. There are two inequivalent Mo6+ sites. In the first Mo6+ site, Mo6+ is bonded to four O2- atoms to form MoO4 tetrahedra that share corners with three equivalent MgO6 octahedra and corners with two equivalent CuO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 29–49°. There are a spread of Mo–O bond distances ranging from 1.79–1.84 Å. In the second Mo6+ site, Mo6+ is bonded to four O2- atoms to form MoO4 tetrahedra that share corners with three equivalent MgO6 octahedra and corners with three equivalent CuO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 50–60°. There are a spread of Mo–O bond distances ranging from 1.77–1.88 Å. There are two inequivalent Cu1+ sites. In the first Cu1+ site, Cu1+ is bonded to five O2- atoms to form CuO5 trigonal bipyramids that share corners with five MoO4 tetrahedra and edges with two equivalent MgO6 octahedra. There are a spread of Cu–O bond distances ranging from 1.96–2.24 Å. In the second Cu1+ site, Cu1+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.97–2.12 Å. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a 3-coordinate geometry to one Mg2+, one Mo6+, and one Cu1+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Mg2+, one Mo6+, and one Cu1+ atom. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to one Mg2+, one Mo6+, and one Cu1+ atom. In the fourth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Mo6+ and one Cu1+ atom. In the fifth O2- site, O2- is bonded in a rectangular see-saw-like geometry to two equivalent Mg2+, one Mo6+, and one Cu1+ atom. In the sixth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Mg2+, one Mo6+, and one Cu1+ atom. In the seventh O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Mo6+ and one Cu1+ atom. In the eighth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Mo6+ and two Cu1+ atoms.
MgCu2(PO4)2 crystallizes in the triclinic P1 space group. The structure is three-dimensional. Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with five PO4 tetrahedra and an edgeedge with one CuO5 trigonal bipyramid. There are a spread of Mg–O bond distances ranging from 2.00–2.13 Å. There are two inequivalent Cu2+ sites. In the first Cu2+ site, Cu2+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.94–2.05 Å. In the second Cu2+ site, Cu2+ is bonded to five O2- atoms to form CuO5 trigonal bipyramids that share corners with five PO4 tetrahedra and an edgeedge with one MgO5 trigonal bipyramid. There are a spread of Cu–O bond distances ranging from 2.00–2.26 Å. There are two inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two equivalent CuO5 trigonal bipyramids and corners with three equivalent MgO5 trigonal bipyramids. There are a spread of P–O bond distances ranging from 1.52–1.59 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two equivalent MgO5 trigonal bipyramids and corners with three equivalent CuO5 trigonal bipyramids. There is one shorter (1.53 Å) and three longer (1.56 Å) P–O bond length. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to one Mg2+, one Cu2+, and one P5+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Mg2+, one Cu2+, and one P5+ atom. In the third O2- site, O2- is bonded in a trigonal planar geometry to one Mg2+, one Cu2+, and one P5+ atom. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to two Cu2+ and one P5+ atom. In the fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to two Cu2+ and one P5+ atom. In the sixth O2- site, O2- is bonded in a trigonal planar geometry to one Mg2+, one Cu2+, and one P5+ atom. In the seventh O2- site, O2- is bonded in a bent 120 degrees geometry to one Mg2+ and one P5+ atom. In the eighth O2- site, O2- is bonded in a bent 120 degrees geometry to one Cu2+ and one P5+ atom.
The tight atomic packing generally exhibited by alloys and intermetallics can create the impression of their being composed of hard spheres arranged to maximize their density. As such, the atomic size factor has historically been central to explanations of the structural chemistry of these systems. However, the role atomic size plays structurally has traditionally been inferred from empirical considerations. The recently developed DFT-Chemical Pressure (CP) analysis has opened a path to investigating these effects with theory. In this article, we provide a step-by-step tutorial on the DFT-CP method for non-specialists, along with advances in the approach that broaden its applicability. A new version of the CP software package is introduced, which features an interactive system that guides the user in preparing the necessary electronic structure data and generating the CP scheme, with the results being readily visualized with a web browser (and easily incorporated into websites). For demonstration purposes, we investigate the origins of the crystal structure of K3Au5Tl, which represents an intergrowth of Laves and Zintl phase domains. Here, CP analysis reveals that the intergrowth is supported by complementary CP features of NaTl-type KTl and MgCu2-type KAu2 phases. In this way, K3Au5Tl exemplifies how CP effects can drive the merging for geometrical motifs derived from different families of intermetallics through a mechanism referred to as epitaxial stabilization.