MgAuGa and MgAu₂Ga: first representatives of the Mg-Au-Ga system

MgAuGa (magnesium gold gallium), the first ternary representative of the Mg-Au-Ga system, crystallizes in the space group P2m and adopts the Fe₂P structure type (Pearson symbol hP9). Various phases with the general composition AB₂ have been reported in the surrounding binary systems, viz. Mg₂Ga (hP18), MgGa₂ (hP6; CaIn₂ type), AuGa₂ (cF12; CaF₂ type), Au₂Ga (oS24; Pd₂As type) and Mg₂Au (oP12; Co₂Si type). In principle, MgAuGa can be obtained from each of them by partial replacement of the major element with the missing element. In fact, the structure of MgAuGa closely resembles hexa­gonal Mg₂Ga through a direct group-subgroup relationship. MgAu₂Ga (magnesium digold gallium) also crystallizes hexa­gonally in the space group P6₃/mmc and is isotypic with Na₃As. It adopts the structure of another binary compound, viz. Mg₃Au (hP8), but shows an unexpected distribution of Mg, Au, and Ga among the atomic positions of the asymmetric unit. Both MgAuGa and MgAu₂Ga can be described as formally anionic Au/Ga frameworks, with pseudo-hexa­gonal tunnels around Mg in MgAuGa or cages in MgAu₂Ga.

S1. Introduction

Extensive synthetic explorations focusing on alkali/alkaline-earth–late transition–post transition systems have revealed a variety of compounds with novel structural motifs and bonding features (Corbett, 2010). Among these combinations, systems with active metals, Au and Ga, have been our focus over the last five years, resulting in quite fruitful outcomes (Smetana et al., 2012 [Ambiguous. Smetana, Corbett & Miller 2012, Smetana, Lin et al., 2012 or Smetana, Miller & Corbett, 2012 ?]; Smetana et al., 2013). These compounds exhibit polyanionic frameworks and clusters with encapsulated cations forming one-dimensional chains (A_0.55Au₂Ga₂ and AAu₂Ga₄; A = Na–Cs), two-dimensional sheets (AAu₃Ga₂; A = K–Cs) and three-dimensional cages (Na₁₃Au₉Ga₁₈ and Na₁₇Au_5.9Ga_46.6). However, the last case is better described as two inter­penetrating polyanionic and polycationic networks. Moreover, the Na-containing phases, which are quasicrystalline or its approximant, indicate significant polar–covalent Na—Au bonding.

Along these lines, Li and Mg occupy special places among the active alkali and alkaline-earth metals in their inter­metallic chemistry. Their especially high electronegativities and small sizes allow these elements to be incorpotated into polyanionic networks with more electronegative metals and semimetals (Tillard-Charbonnel et al., 1990; Li & Corbett, 2005). Since the Mg–Au, Mg–Ga and Au–Ga systems contain significant numbers of binary compounds (Villars, 2013), there is an excellent opportunity to discover new ternary phases. Moreover, a large homogeneity region has been reported for MgAu (Schubert, 1966) and a maximum solubility of 13 at.% Ga in Au at around 673 K (Cooke & Hume-Rothery, 1966). In spite of these reports, no compound has been reported, as yet, in the ternary Mg–Au–Ga system, so we decided to conduct a preliminary exploration.

Our initial investigations have revealed that two ternary compounds in the Mg–Au–Ga system, in particular, are derivatives of the corresponding binaries. MgAu₂Ga adopts the structure of Mg₃Au (Schubert & Anderko, 1951), with partial redistribution of all positions in the asymmetric unit and the presence of Au–Au dimers, whereas MgAuGa shows a group–subgroup relation with Mg₂Ga (Frank & Schubert, 1970).

S2. Experimental

S2.1. Synthesis and crystallization

The starting materials were Mg pieces (99.98%, Alfa Aesar), Au particles (99.999%, BASF) and Ga ingots (99.999%, Alfa Aesar). Mixtures of 300–400 mg total were weighed in an N₂-filled glove-box (H₂O < 0.1 p.p.m.v.), loaded into 9 mm Ta ampoules, sealed by arc-welding under Ar and then enclosed in evacuated SiO₂ jackets. The samples were heated at 1073 K for 8 h, cooled to 623 K at a rate of 10 K h^-1, then annealed at this temperature for 7 d and finally cooled to room temperature by switching off the furnace. Single crystals of MgAuGa and MgAu₂Ga were obtained from several samples with loaded compositions of `MgAuGa', `MgAuGa₃' and `MgAu₂Ga₂'. No homogeneity ranges were observed, in spite of frequent Au/Ga mixing in related compounds. The title compounds have a metallic luster and are stable against exposure to air or water at room temperature. Phase analyses were performed using monochromatic Cu Kα₁ radiation on a Stoe STADI P diffractometer.

S2.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Analysis of the systematic absences for the single-crystal data of MgAuGa led to the possible space groups P3 (No. 143), P3 (No. 147), P3m1 (No. 164), P321 (No. 150), P31m (No. 157), P6₃/m (No. 176), P6₃ (No. 173), P62m (No. 176) and P6₃22 (No. 166). The space group P62m was found to be correct during the structure refinement. The starting atomic parameters were derived via direct methods and the structure was refined successfully using anisotropic atomic displacement parameters for all atoms. All crystallographic positions are fully occupied. Difference Fourier synthesis exhibits almost identical residual peaks and holes of about 2.5 e Å^-3, which might result from insufficient data quality. However, all of these peaks and holes were found in the direct vicinity of Au atoms (~1.5 Å) and could not be assigned to any new atom.

S3. Results and discussion

The crystal structure of MgAuGa is best described as a ternary representative of the Fe₂P structure type (Hendricks & Kosting, 1930). Au atoms occupy the P-atom positions, whereas Mg and Ga each occupy one of two inequivalent Fe positons. No Mg/Au or Au/Ga mixing was observed in this compound. A projection of the MgAuGa polyatomic framework along the c axis is shown in Fig. 1. The Mg atoms are formally cationic in this combination, so the compounds can also be represented in terms of tunnel structures. Penta­gonal Au-capped Au₅Ga₅ prisms (Fig. 2a) stack together, forming channels around Mg and along the c axis. The Mg—Mg distances in the chain are equivalent to the length of the axis. The Ga and Au atoms have somewhat lower coordination numbers, viz. 10 and 9, respectively. The coordination polyhedra of Au are two similar equatorially capped trigonal prisms with inverted locations of Ga and Mg, i.e. either [Au1Ga₆Mg₃] or [Au2Mg₆Ga₃] (Figs. 2c and 2d). All vertical Ga—Ga and Mg—Mg bonds are equivalent to the length of the c axis. All Mg—Ga connections within the first polyhedron are identical [3.051 (4) Å], whereas those in the second form two groups [2.981 (5) and 3.051 (4) Å]. These polyhedra reveal the similar roles of Ga and Mg in this crystal structure. The coordination polyhedra of Ga consist of inter­penetrating Mg₆ trigonal prisms and Au₄ tetra­hedra (Fig. 2b), although this description is rather formal because of one short [3.3738 (3) Å] and five quite long [4.2536 (3) and 4.5759 (2) Å] Au—Au distances. Mg—Mg and Mg—Au distances are in the ranges 3.3738 (3)–3.967 (7) and 2.835 (7)–2.844 (3) Å, respectively. This resembles the polyhedra of Au with one small exception, i.e. one of the equatorial capping atoms is split into two along the c axis.

The crystal structure of MgAu₂Ga (Fig. 3), together with that of the binary compound Mg₃Au, belong to the hexagonal Na₃As structure type, although the distributions of elements in each of them are different. In Mg₃Au, the Mg and Au atoms occupy the positions of Na and As, respectively, in accordance with their electronegativities. However, the situation is slightly different in MgAu₂Ga, in which two Mg atoms are formally replaced by Au atoms (the 4f position) and Ga replaces Au at the 2a position (the sites of the As atoms in Na₃As). At first glance, this substitution pattern does not follow the relative electronegativities of Mg, Au and Ga. However, the atomic distribution results in Au–Au dimers [2.761 (1) Å] oriented along the c axis and bridged by Mg atoms [Mg—Au = 2.8896 (6) Å]. Preliminary electronic structure calculations on MgAu₂Ga suggest optimum Au—Au bonding in these dimers, but further theoretical analysis is underway to identify the nature of these bonds. In fact, the three-dimensional [Au₂Ga] polyanionic network involves four-bonded Au atoms, by a distorted tetra­hedron of three Ga and one Au, and six-bonded Ga atoms, by a puckered six-membered ring of Au atoms to form a distorted close-packed environment. The Mg atoms are most closely coordinated by a trigonal prism of Ga atoms; likewise, each Ga atom is surrounded by a trigonal anti­prism (distorted o­cta­hedron) of Mg atoms.

The relationship between Mg₂Ga and MgAuGa is also structurally inter­esting. In spite of almost identical covalent radii for Au and Mg (Cordero et al., 2008), the Au atoms prefer to occupy the positions of the more electronegative Ga atoms than the geometrically closer Mg atoms. As mentioned above, the same crystallographic positions are occupied by P atoms in the Fe₂P prototype, showing strong site preference for the most electronegative element in each compound. However, Mg₂Ga deviates from the Fe₂P structure type by a doubling of the c axis, creating its own structure type with the space group P62c, which is a minimal non-isomorphic subgroup of P62m. MgAuGa has unit-cell parameters [a = 7.3682 (5) Å and c = 3.3738 (3) Å] that create a volume approximately one-half of that of Mg₂Ga [a = 7.794 (2) Å and c = 6.893 (1) Å]. The coordination polyhedra of Ga in Mg₂Ga remain the same tricapped trigonal prisms, but the polyhedra around the Mg atoms are significantly distorted tetra­gonal and penta­gonal prisms. Thus, replacing Mg with Au in the structure of Mg₂Ga stimulates atomic ordering and a slight increase in symmetry. Another comparison may also come from Au₂Ga (Puselj & Schubert, 1974), which crystallizes in the orthorhombic Pd₂As structure type (Baelz & Schubert, 1969). In spite of the different crystallographic symmetry and no direct relation between the space groups of Au₂Ga (Pbam) and MgAuGa (P62m), Au₂Ga contains an ordered packing of trigonal and penta­gonal prisms. Moreover, a polymorphic modification of Pd₂As (Schubert et al., 1963) includes the hexagonal Fe₂P structure type. This reveals potential similarities between the Mg–Ga and Au–Ga binary systems concerning a strong structural correlation along the 33 at.% Ga line, i.e. Mg₂Ga–MgAuGa–Au₂Ga.

[Please supply refinement instruction files]

Related literature

For related literature, see: Baelz & Schubert (1969); Cooke & Hume-Rothery (1966); Corbett (2010); Cordero et al. (2008); Frank & Schubert (1970); Hendricks & Kosting (1930); Li & Corbett (2005); Puselj & Schubert (1974); Schubert (1966); Schubert & Anderko (1951); Schubert et al. (1963); Smetana et al. (2013); Smetana, Corbett & Miller (2012); Smetana, Lin, Pratt, Kreyssig, Ramazanoglu, Corbett, Goldman & Miller (2012); Smetana, Miller & Corbett (2012); Tillard-Charbonnel, Belin & Soubeyroux (1990); Villars (2013).

Computing details

For both compounds, data collection: SMART (Bruker, 2001); cell refinement: SAINT (Bruker, 2001); data reduction: SAINT (Bruker, 2001); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures

	Fig. 1. A projection of the MgAuGa structure along the c axis.
	Fig. 2. The coordination polyhedra of Mg, Ga and Au in the crystal structure of MgAuGa. Au atoms are orange, Ga blue and Mg green. [What do the parts a/b/c/d specifically represent, e.g. (a) The pentagonal Au-capped Au5Ga5 prism. (b) The coordination polyhedron of Ga, consisting of interpenetrating Mg6 trigonal prisms and Au4 tetrahedra. (c) The [Au1Ga6Mg3] coordination polyhedron of Au, consisting of equatorially capped trigonal prisms. (d) The [Au2Mg6Ga3] coordination polyhedron of Au, consisting of equatorially capped trigonal prisms]
	Fig. 3. The crystal structure of MgAu2Ga, showing views of the unit cell along different directions.

(I) Magnesium gold gallium

Crystal data

MgAuGa	Dx = 9.139 Mg m^−3
Mr = 291.00	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P62m	Cell parameters from 2837 reflections
Hall symbol: P -6 -2	θ = 5.5–39.5°
a = 7.3682 (5) Å	µ = 81.83 mm^−1
c = 3.3738 (3) Å	T = 296 K
V = 158.63 (2) Å^3	Irregular fragment, colourless
Z = 3	0.12 × 0.10 × 0.09 mm
F(000) = 366

Data collection

Bruker SMART CCD area-detector diffractometer	388 independent reflections
Radiation source: fine-focus sealed tube	313 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.071
ω scans	θmax = 39.5°, θmin = 5.5°
Absorption correction: empirical (using intensity measurements) (Blessing, 1995)	h = −13→13
Tmin = 0.000, Tmax = 0.001	k = −12→13
2837 measured reflections	l = −5→6

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0308P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.032	(Δ/σ)max < 0.001
wR(F^2) = 0.069	Δρmax = 2.59 e Å^−3
S = 1.07	Δρmin = −2.06 e Å^−3
388 reflections	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
14 parameters	Extinction coefficient: 0.0086 (12)
0 restraints	Absolute structure: Flack (1983), with 163 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.02 (5)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Au1	0.0000	0.0000	0.0000	0.01147 (19)
Au2	0.3333	0.6667	0.5000	0.01267 (18)
Ga1	0.2816 (3)	0.0000	0.5000	0.0108 (3)
Mg1	0.6152 (9)	0.0000	0.0000	0.0121 (12)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Au1	0.0094 (2)	0.0094 (2)	0.0157 (4)	0.00468 (12)	0.000	0.000
Au2	0.00854 (18)	0.00854 (18)	0.0209 (4)	0.00427 (9)	0.000	0.000
Ga1	0.0080 (5)	0.0082 (7)	0.0161 (8)	0.0041 (4)	0.000	0.000
Mg1	0.010 (2)	0.014 (3)	0.014 (3)	0.0068 (13)	0.000	0.000

Geometric parameters (Å, º)

Au1—Ga1^i	2.6740 (15)	Au2—Au2^ix	3.3738 (3)
Au1—Ga1	2.6740 (15)	Ga1—Au2^xiv	2.6672 (12)
Au1—Ga1^ii	2.6740 (15)	Ga1—Au2^xv	2.6672 (12)
Au1—Ga1^iii	2.6740 (15)	Ga1—Au1^ix	2.6740 (15)
Au1—Ga1^iv	2.6740 (15)	Ga1—Mg1^ix	2.981 (5)
Au1—Ga1^v	2.6740 (15)	Ga1—Mg1	2.981 (5)
Au1—Mg1^vi	2.835 (6)	Ga1—Mg1^viii	3.051 (4)
Au1—Mg1^vii	2.835 (6)	Ga1—Mg1^xiii	3.051 (4)
Au1—Mg1^viii	2.835 (6)	Ga1—Mg1^xvi	3.051 (4)
Au1—Au1^v	3.3738 (3)	Ga1—Mg1^vi	3.051 (4)
Au1—Au1^ix	3.3738 (3)	Mg1—Au1^xvii	2.835 (6)
Au2—Ga1^x	2.6672 (12)	Mg1—Au2^xv	2.8443 (19)
Au2—Ga1^ii	2.6672 (12)	Mg1—Au2^xviii	2.8443 (19)
Au2—Ga1^vi	2.6672 (12)	Mg1—Au2^xix	2.8443 (19)
Au2—Mg1^ii	2.844 (5)	Mg1—Au2^xiv	2.8443 (19)
Au2—Mg1^xi	2.844 (5)	Mg1—Ga1^v	2.981 (5)
Au2—Mg1^xii	2.844 (5)	Mg1—Ga1^xx	3.051 (4)
Au2—Mg1^x	2.844 (5)	Mg1—Ga1^xxi	3.051 (4)
Au2—Mg1^vi	2.844 (5)	Mg1—Ga1^xxii	3.051 (4)
Au2—Mg1^xiii	2.844 (5)	Mg1—Ga1^xxiii	3.051 (4)
Au2—Au2^v	3.3738 (3)	Mg1—Mg1^ix	3.3738 (3)
Ga1^i—Au1—Ga1	134.346 (18)	Au2^xiv—Ga1—Au1	117.915 (12)
Ga1^i—Au1—Ga1^ii	134.346 (18)	Au2^xv—Ga1—Au1	117.915 (12)
Ga1—Au1—Ga1^ii	84.44 (4)	Au2^xiv—Ga1—Au1^ix	117.915 (12)
Ga1^i—Au1—Ga1^iii	78.23 (5)	Au2^xv—Ga1—Au1^ix	117.915 (12)
Ga1—Au1—Ga1^iii	84.44 (4)	Au1—Ga1—Au1^ix	78.23 (5)
Ga1^ii—Au1—Ga1^iii	84.44 (4)	Au2^xiv—Ga1—Mg1^ix	60.17 (4)
Ga1^i—Au1—Ga1^iv	84.44 (4)	Au2^xv—Ga1—Mg1^ix	60.17 (4)
Ga1—Au1—Ga1^iv	134.346 (18)	Au1—Ga1—Mg1^ix	175.35 (8)
Ga1^ii—Au1—Ga1^iv	78.23 (5)	Au1^ix—Ga1—Mg1^ix	106.43 (7)
Ga1^iii—Au1—Ga1^iv	134.346 (18)	Au2^xiv—Ga1—Mg1	60.17 (4)
Ga1^i—Au1—Ga1^v	84.44 (4)	Au2^xv—Ga1—Mg1	60.17 (4)
Ga1—Au1—Ga1^v	78.23 (5)	Au1—Ga1—Mg1	106.43 (7)
Ga1^ii—Au1—Ga1^v	134.346 (18)	Au1^ix—Ga1—Mg1	175.35 (8)
Ga1^iii—Au1—Ga1^v	134.346 (18)	Mg1^ix—Ga1—Mg1	68.92 (14)
Ga1^iv—Au1—Ga1^v	84.44 (4)	Au2^xiv—Ga1—Mg1^viii	59.21 (10)
Ga1^i—Au1—Mg1^vi	140.89 (3)	Au2^xv—Ga1—Mg1^viii	140.52 (4)
Ga1—Au1—Mg1^vi	67.173 (9)	Au1—Ga1—Mg1^viii	58.94 (10)
Ga1^ii—Au1—Mg1^vi	67.173 (9)	Au1^ix—Ga1—Mg1^viii	100.47 (6)
Ga1^iii—Au1—Mg1^vi	140.89 (3)	Mg1^ix—Ga1—Mg1^viii	119.37 (8)
Ga1^iv—Au1—Mg1^vi	67.173 (9)	Mg1—Ga1—Mg1^viii	82.23 (8)
Ga1^v—Au1—Mg1^vi	67.173 (9)	Au2^xiv—Ga1—Mg1^xiii	140.52 (4)
Ga1^i—Au1—Mg1^vii	67.173 (9)	Au2^xv—Ga1—Mg1^xiii	59.21 (10)
Ga1—Au1—Mg1^vii	140.89 (3)	Au1—Ga1—Mg1^xiii	100.47 (6)
Ga1^ii—Au1—Mg1^vii	67.173 (9)	Au1^ix—Ga1—Mg1^xiii	58.94 (10)
Ga1^iii—Au1—Mg1^vii	67.173 (9)	Mg1^ix—Ga1—Mg1^xiii	82.23 (8)
Ga1^iv—Au1—Mg1^vii	67.173 (9)	Mg1—Ga1—Mg1^xiii	119.37 (8)
Ga1^v—Au1—Mg1^vii	140.89 (3)	Mg1^viii—Ga1—Mg1^xiii	155.12 (17)
Mg1^vi—Au1—Mg1^vii	120.0	Au2^xiv—Ga1—Mg1^xvi	59.21 (10)
Ga1^i—Au1—Mg1^viii	67.173 (9)	Au2^xv—Ga1—Mg1^xvi	140.52 (4)
Ga1—Au1—Mg1^viii	67.173 (9)	Au1—Ga1—Mg1^xvi	100.47 (6)
Ga1^ii—Au1—Mg1^viii	140.89 (3)	Au1^ix—Ga1—Mg1^xvi	58.94 (10)
Ga1^iii—Au1—Mg1^viii	67.173 (9)	Mg1^ix—Ga1—Mg1^xvi	82.23 (8)
Ga1^iv—Au1—Mg1^viii	140.89 (3)	Mg1—Ga1—Mg1^xvi	119.37 (8)
Ga1^v—Au1—Mg1^viii	67.173 (9)	Mg1^viii—Ga1—Mg1^xvi	67.14 (9)
Mg1^vi—Au1—Mg1^viii	120.0	Mg1^xiii—Ga1—Mg1^xvi	107.20 (16)
Mg1^vii—Au1—Mg1^viii	120.0	Au2^xiv—Ga1—Mg1^vi	140.52 (4)
Ga1^i—Au1—Au1^v	50.89 (3)	Au2^xv—Ga1—Mg1^vi	59.21 (10)
Ga1—Au1—Au1^v	129.11 (3)	Au1—Ga1—Mg1^vi	58.94 (10)
Ga1^ii—Au1—Au1^v	129.11 (3)	Au1^ix—Ga1—Mg1^vi	100.47 (6)
Ga1^iii—Au1—Au1^v	129.11 (3)	Mg1^ix—Ga1—Mg1^vi	119.37 (8)
Ga1^iv—Au1—Au1^v	50.89 (3)	Mg1—Ga1—Mg1^vi	82.23 (8)
Ga1^v—Au1—Au1^v	50.89 (3)	Mg1^viii—Ga1—Mg1^vi	107.20 (16)
Mg1^vi—Au1—Au1^v	90.000 (1)	Mg1^xiii—Ga1—Mg1^vi	67.14 (9)
Mg1^vii—Au1—Au1^v	90.0	Mg1^xvi—Ga1—Mg1^vi	155.12 (17)
Mg1^viii—Au1—Au1^v	90.0	Au1^xvii—Mg1—Au2^xv	107.36 (12)
Ga1^i—Au1—Au1^ix	129.11 (3)	Au1^xvii—Mg1—Au2^xviii	107.36 (12)
Ga1—Au1—Au1^ix	50.89 (3)	Au2^xv—Mg1—Au2^xviii	145.3 (2)
Ga1^ii—Au1—Au1^ix	50.89 (3)	Au1^xvii—Mg1—Au2^xix	107.36 (12)
Ga1^iii—Au1—Au1^ix	50.89 (3)	Au2^xv—Mg1—Au2^xix	72.75 (6)
Ga1^iv—Au1—Au1^ix	129.11 (3)	Au2^xviii—Mg1—Au2^xix	96.80 (9)
Ga1^v—Au1—Au1^ix	129.11 (3)	Au1^xvii—Mg1—Au2^xiv	107.36 (12)
Mg1^vi—Au1—Au1^ix	90.000 (1)	Au2^xv—Mg1—Au2^xiv	96.80 (9)
Mg1^vii—Au1—Au1^ix	90.0	Au2^xviii—Mg1—Au2^xiv	72.75 (6)
Mg1^viii—Au1—Au1^ix	90.0	Au2^xix—Mg1—Au2^xiv	145.3 (2)
Au1^v—Au1—Au1^ix	180.0	Au1^xvii—Mg1—Ga1^v	145.54 (7)
Ga1^x—Au2—Ga1^ii	120.0	Au2^xv—Mg1—Ga1^v	95.14 (16)
Ga1^x—Au2—Ga1^vi	120.0	Au2^xviii—Mg1—Ga1^v	54.43 (8)
Ga1^ii—Au2—Ga1^vi	120.0	Au2^xix—Mg1—Ga1^v	54.43 (8)
Ga1^x—Au2—Mg1^ii	67.13 (12)	Au2^xiv—Mg1—Ga1^v	95.14 (16)
Ga1^ii—Au2—Mg1^ii	65.40 (11)	Au1^xvii—Mg1—Ga1	145.54 (7)
Ga1^vi—Au2—Mg1^ii	143.61 (3)	Au2^xv—Mg1—Ga1	54.43 (8)
Ga1^x—Au2—Mg1^xi	65.40 (11)	Au2^xviii—Mg1—Ga1	95.14 (16)
Ga1^ii—Au2—Mg1^xi	143.61 (3)	Au2^xix—Mg1—Ga1	95.14 (16)
Ga1^vi—Au2—Mg1^xi	67.13 (12)	Au2^xiv—Mg1—Ga1	54.43 (8)
Mg1^ii—Au2—Mg1^xi	132.522 (18)	Ga1^v—Mg1—Ga1	68.92 (14)
Ga1^x—Au2—Mg1^xii	67.13 (12)	Au1^xvii—Mg1—Ga1^xx	53.89 (10)
Ga1^ii—Au2—Mg1^xii	65.40 (11)	Au2^xv—Mg1—Ga1^xx	53.66 (4)
Ga1^vi—Au2—Mg1^xii	143.61 (3)	Au2^xviii—Mg1—Ga1^xx	160.8 (2)
Mg1^ii—Au2—Mg1^xii	72.75 (6)	Au2^xix—Mg1—Ga1^xx	93.63 (5)
Mg1^xi—Au2—Mg1^xii	88.42 (4)	Au2^xiv—Mg1—Ga1^xx	106.76 (5)
Ga1^x—Au2—Mg1^x	65.40 (11)	Ga1^v—Mg1—Ga1^xx	143.02 (9)
Ga1^ii—Au2—Mg1^x	143.61 (3)	Ga1—Mg1—Ga1^xx	99.96 (5)
Ga1^vi—Au2—Mg1^x	67.13 (12)	Au1^xvii—Mg1—Ga1^xxi	53.89 (10)
Mg1^ii—Au2—Mg1^x	88.42 (4)	Au2^xv—Mg1—Ga1^xxi	160.8 (2)
Mg1^xi—Au2—Mg1^x	72.75 (6)	Au2^xviii—Mg1—Ga1^xxi	53.66 (4)
Mg1^xii—Au2—Mg1^x	132.522 (18)	Au2^xix—Mg1—Ga1^xxi	106.76 (5)
Ga1^x—Au2—Mg1^vi	143.61 (3)	Au2^xiv—Mg1—Ga1^xxi	93.63 (5)
Ga1^ii—Au2—Mg1^vi	67.13 (12)	Ga1^v—Mg1—Ga1^xxi	99.96 (5)
Ga1^vi—Au2—Mg1^vi	65.40 (11)	Ga1—Mg1—Ga1^xxi	143.02 (9)
Mg1^ii—Au2—Mg1^vi	88.42 (4)	Ga1^xx—Mg1—Ga1^xxi	107.8 (2)
Mg1^xi—Au2—Mg1^vi	132.521 (19)	Au1^xvii—Mg1—Ga1^xxii	53.89 (10)
Mg1^xii—Au2—Mg1^vi	132.521 (19)	Au2^xv—Mg1—Ga1^xxii	106.76 (5)
Mg1^x—Au2—Mg1^vi	88.42 (4)	Au2^xviii—Mg1—Ga1^xxii	93.63 (5)
Ga1^x—Au2—Mg1^xiii	143.61 (3)	Au2^xix—Mg1—Ga1^xxii	160.8 (2)
Ga1^ii—Au2—Mg1^xiii	67.13 (12)	Au2^xiv—Mg1—Ga1^xxii	53.66 (4)
Ga1^vi—Au2—Mg1^xiii	65.40 (11)	Ga1^v—Mg1—Ga1^xxii	143.02 (9)
Mg1^ii—Au2—Mg1^xiii	132.52 (2)	Ga1—Mg1—Ga1^xxii	99.96 (5)
Mg1^xi—Au2—Mg1^xiii	88.42 (4)	Ga1^xx—Mg1—Ga1^xxii	72.17 (12)
Mg1^xii—Au2—Mg1^xiii	88.42 (4)	Ga1^xxi—Mg1—Ga1^xxii	67.14 (9)
Mg1^x—Au2—Mg1^xiii	132.521 (19)	Au1^xvii—Mg1—Ga1^xxiii	53.89 (10)
Mg1^vi—Au2—Mg1^xiii	72.75 (6)	Au2^xv—Mg1—Ga1^xxiii	93.63 (5)
Ga1^x—Au2—Au2^v	90.0	Au2^xviii—Mg1—Ga1^xxiii	106.76 (5)
Ga1^ii—Au2—Au2^v	90.0	Au2^xix—Mg1—Ga1^xxiii	53.66 (4)
Ga1^vi—Au2—Au2^v	90.0	Au2^xiv—Mg1—Ga1^xxiii	160.8 (2)
Mg1^ii—Au2—Au2^v	53.62 (3)	Ga1^v—Mg1—Ga1^xxiii	99.96 (5)
Mg1^xi—Au2—Au2^v	126.38 (3)	Ga1—Mg1—Ga1^xxiii	143.02 (9)
Mg1^xii—Au2—Au2^v	126.38 (3)	Ga1^xx—Mg1—Ga1^xxiii	67.14 (9)
Mg1^x—Au2—Au2^v	53.62 (3)	Ga1^xxi—Mg1—Ga1^xxiii	72.17 (12)
Mg1^vi—Au2—Au2^v	53.62 (3)	Ga1^xxii—Mg1—Ga1^xxiii	107.8 (2)
Mg1^xiii—Au2—Au2^v	126.38 (3)	Au1^xvii—Mg1—Mg1^ix	90.0
Ga1^x—Au2—Au2^ix	90.0	Au2^xv—Mg1—Mg1^ix	53.62 (3)
Ga1^ii—Au2—Au2^ix	90.0	Au2^xviii—Mg1—Mg1^ix	126.38 (3)
Ga1^vi—Au2—Au2^ix	90.0	Au2^xix—Mg1—Mg1^ix	126.38 (3)
Mg1^ii—Au2—Au2^ix	126.38 (3)	Au2^xiv—Mg1—Mg1^ix	53.62 (3)
Mg1^xi—Au2—Au2^ix	53.62 (3)	Ga1^v—Mg1—Mg1^ix	124.46 (7)
Mg1^xii—Au2—Au2^ix	53.62 (3)	Ga1—Mg1—Mg1^ix	55.54 (7)
Mg1^x—Au2—Au2^ix	126.38 (3)	Ga1^xx—Mg1—Mg1^ix	56.43 (5)
Mg1^vi—Au2—Au2^ix	126.38 (3)	Ga1^xxi—Mg1—Mg1^ix	123.57 (5)
Mg1^xiii—Au2—Au2^ix	53.62 (3)	Ga1^xxii—Mg1—Mg1^ix	56.43 (5)
Au2^v—Au2—Au2^ix	180.0	Ga1^xxiii—Mg1—Mg1^ix	123.57 (5)
Au2^xiv—Ga1—Au2^xv	105.78 (7)

Symmetry codes: (i) −x+y, −x, z−1; (ii) −y, x−y, z; (iii) −x+y, −x, z; (iv) −y, x−y, z−1; (v) x, y, z−1; (vi) −x+y+1, −x+1, z; (vii) x−1, y, z; (viii) −y, x−y−1, z; (ix) x, y, z+1; (x) x, y+1, z; (xi) x, y+1, z+1; (xii) −y, x−y, z+1; (xiii) −x+y+1, −x+1, z+1; (xiv) x, y−1, z; (xv) y, x, −z+1; (xvi) −y, x−y−1, z+1; (xvii) x+1, y, z; (xviii) x, y−1, z−1; (xix) y, x, −z; (xx) −y+1, x−y, z; (xxi) −x+y+1, −x, z−1; (xxii) −x+y+1, −x, z; (xxiii) −y+1, x−y, z−1.

(II) Magnesium digold gallium

Crystal data

MgAu2Ga	Dx = 11.311 Mg m^−3
Mr = 487.96	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63/mmc	Cell parameters from 1404 reflections
Hall symbol: -P 6c 2c	θ = 4.8–33.0°
a = 4.4015 (3) Å	µ = 111.34 mm^−1
c = 8.5398 (7) Å	T = 297 K
V = 143.28 (3) Å^3	Irregular fragment, colourless
Z = 2	0.12 × 0.11 × 0.11 mm
F(000) = 402

Data collection

Bruker SMART CCD area-detector diffractometer	129 independent reflections
Radiation source: fine-focus sealed tube	111 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.041
ω scans	θmax = 33.0°, θmin = 4.8°
Absorption correction: empirical (using intensity measurements) (Blessing, 1995)	h = −5→6
Tmin = 0.02, Tmax = 0.06	k = −4→6
1404 measured reflections	l = −12→12

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.023	Secondary atom site location: difference Fourier map
wR(F^2) = 0.054	w = 1/[σ^2(Fo^2) + (0.0275P)^2 + 1.7138P] where P = (Fo^2 + 2Fc^2)/3
S = 1.19	(Δ/σ)max < 0.001
129 reflections	Δρmax = 2.00 e Å^−3
9 parameters	Δρmin = −2.97 e Å^−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Au1	0.3333	0.6667	0.08837 (7)	0.0069 (2)
Mg2	0.6667	0.3333	0.2500	0.016 (2)
Ga3	0.0000	0.0000	0.0000	0.0105 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Au1	0.0063 (2)	0.0063 (2)	0.0082 (3)	0.00314 (12)	0.000	0.000
Mg2	0.019 (3)	0.019 (3)	0.009 (4)	0.0097 (16)	0.000	0.000
Ga3	0.0047 (7)	0.0047 (7)	0.0221 (12)	0.0023 (4)	0.000	0.000

Geometric parameters (Å, º)

Au1—Ga3^i	2.6509 (2)	Mg2—Au1^xii	2.8919 (3)
Au1—Ga3	2.6509 (2)	Mg2—Au1^iii	2.8919 (3)
Au1—Ga3^ii	2.6509 (2)	Mg2—Ga3^viii	3.3190 (2)
Au1—Au1^iii	2.7606 (12)	Mg2—Ga3	3.3190 (2)
Au1—Mg2^iv	2.8896 (6)	Mg2—Ga3^xi	3.3190 (2)
Au1—Mg2^i	2.8919 (3)	Mg2—Ga3^xiii	3.3190 (2)
Au1—Mg2^v	2.8919 (3)	Ga3—Au1^vi	2.6509 (2)
Au1—Mg2	2.8919 (3)	Ga3—Au1^x	2.6509 (2)
Au1—Au1^vi	2.9556 (6)	Ga3—Au1^xiv	2.6509 (2)
Au1—Au1^vii	2.9556 (6)	Ga3—Au1^iv	2.6509 (2)
Au1—Au1^iv	2.9556 (6)	Ga3—Au1^xv	2.6509 (2)
Mg2—Au1^viii	2.8896 (6)	Ga3—Mg2^xiv	3.3190 (2)
Mg2—Au1^iv	2.8896 (6)	Ga3—Mg2^xvi	3.3190 (2)
Mg2—Au1^ix	2.8919 (3)	Ga3—Mg2^v	3.3190 (2)
Mg2—Au1^x	2.8919 (3)	Ga3—Mg2^iv	3.3190 (2)
Mg2—Au1^xi	2.8919 (3)	Ga3—Mg2^xv	3.3190 (2)
Ga3^i—Au1—Ga3	112.237 (10)	Au1^x—Mg2—Ga3	49.952 (5)
Ga3^i—Au1—Ga3^ii	112.237 (10)	Au1^xi—Mg2—Ga3	111.456 (11)
Ga3—Au1—Ga3^ii	112.237 (10)	Au1^xii—Mg2—Ga3	88.316 (8)
Ga3^i—Au1—Au1^iii	106.540 (12)	Au1^iii—Mg2—Ga3	88.316 (8)
Ga3—Au1—Au1^iii	106.540 (12)	Au1—Mg2—Ga3	49.952 (5)
Ga3^ii—Au1—Au1^iii	106.540 (12)	Ga3^viii—Mg2—Ga3	134.982 (2)
Ga3^i—Au1—Mg2^iv	73.460 (12)	Au1^viii—Mg2—Ga3^xi	130.035 (3)
Ga3—Au1—Mg2^iv	73.460 (12)	Au1^iv—Mg2—Ga3^xi	49.965 (3)
Ga3^ii—Au1—Mg2^iv	73.460 (12)	Au1^ix—Mg2—Ga3^xi	88.316 (8)
Au1^iii—Au1—Mg2^iv	180.0	Au1^x—Mg2—Ga3^xi	49.952 (5)
Ga3^i—Au1—Mg2^i	73.422 (3)	Au1^xi—Mg2—Ga3^xi	49.952 (5)
Ga3—Au1—Mg2^i	168.03 (2)	Au1^xii—Mg2—Ga3^xi	88.316 (8)
Ga3^ii—Au1—Mg2^i	73.422 (3)	Au1^iii—Mg2—Ga3^xi	168.475 (10)
Au1^iii—Au1—Mg2^i	61.491 (10)	Au1—Mg2—Ga3^xi	111.456 (11)
Mg2^iv—Au1—Mg2^i	118.509 (10)	Ga3^viii—Mg2—Ga3^xi	134.982 (2)
Ga3^i—Au1—Mg2^v	73.422 (3)	Ga3—Mg2—Ga3^xi	83.070 (5)
Ga3—Au1—Mg2^v	73.422 (3)	Au1^viii—Mg2—Ga3^xiii	49.965 (3)
Ga3^ii—Au1—Mg2^v	168.03 (2)	Au1^iv—Mg2—Ga3^xiii	130.035 (3)
Au1^iii—Au1—Mg2^v	61.491 (10)	Au1^ix—Mg2—Ga3^xiii	49.952 (5)
Mg2^iv—Au1—Mg2^v	118.509 (10)	Au1^x—Mg2—Ga3^xiii	88.316 (8)
Mg2^i—Au1—Mg2^v	99.107 (13)	Au1^xi—Mg2—Ga3^xiii	88.316 (8)
Ga3^i—Au1—Mg2	168.03 (2)	Au1^xii—Mg2—Ga3^xiii	49.952 (5)
Ga3—Au1—Mg2	73.422 (3)	Au1^iii—Mg2—Ga3^xiii	111.456 (11)
Ga3^ii—Au1—Mg2	73.422 (3)	Au1—Mg2—Ga3^xiii	168.475 (10)
Au1^iii—Au1—Mg2	61.491 (10)	Ga3^viii—Mg2—Ga3^xiii	83.070 (4)
Mg2^iv—Au1—Mg2	118.509 (10)	Ga3—Mg2—Ga3^xiii	134.982 (2)
Mg2^i—Au1—Mg2	99.107 (13)	Ga3^xi—Mg2—Ga3^xiii	80.069 (6)
Mg2^v—Au1—Mg2	99.107 (13)	Au1^vi—Ga3—Au1^x	180.00 (2)
Ga3^i—Au1—Au1^vi	56.118 (5)	Au1^vi—Ga3—Au1	67.763 (10)
Ga3—Au1—Au1^vi	56.118 (5)	Au1^x—Ga3—Au1	112.237 (10)
Ga3^ii—Au1—Au1^vi	132.75 (3)	Au1^vi—Ga3—Au1^xiv	112.237 (10)
Au1^iii—Au1—Au1^vi	120.707 (19)	Au1^x—Ga3—Au1^xiv	67.763 (10)
Mg2^iv—Au1—Au1^vi	59.293 (19)	Au1—Ga3—Au1^xiv	180.00 (2)
Mg2^i—Au1—Au1^vi	128.426 (2)	Au1^vi—Ga3—Au1^iv	112.237 (10)
Mg2^v—Au1—Au1^vi	59.217 (10)	Au1^x—Ga3—Au1^iv	67.763 (10)
Mg2—Au1—Au1^vi	128.426 (2)	Au1—Ga3—Au1^iv	67.763 (10)
Ga3^i—Au1—Au1^vii	56.118 (5)	Au1^xiv—Ga3—Au1^iv	112.237 (10)
Ga3—Au1—Au1^vii	132.75 (3)	Au1^vi—Ga3—Au1^xv	67.763 (10)
Ga3^ii—Au1—Au1^vii	56.118 (5)	Au1^x—Ga3—Au1^xv	112.237 (10)
Au1^iii—Au1—Au1^vii	120.707 (19)	Au1—Ga3—Au1^xv	112.237 (10)
Mg2^iv—Au1—Au1^vii	59.293 (19)	Au1^xiv—Ga3—Au1^xv	67.763 (10)
Mg2^i—Au1—Au1^vii	59.217 (10)	Au1^iv—Ga3—Au1^xv	180.00 (2)
Mg2^v—Au1—Au1^vii	128.426 (2)	Au1^vi—Ga3—Mg2^xiv	56.626 (7)
Mg2—Au1—Au1^vii	128.426 (2)	Au1^x—Ga3—Mg2^xiv	123.374 (7)
Au1^vi—Au1—Au1^vii	96.25 (3)	Au1—Ga3—Mg2^xiv	123.374 (7)
Ga3^i—Au1—Au1^iv	132.75 (3)	Au1^xiv—Ga3—Mg2^xiv	56.626 (7)
Ga3—Au1—Au1^iv	56.118 (5)	Au1^iv—Ga3—Mg2^xiv	123.426 (13)
Ga3^ii—Au1—Au1^iv	56.118 (5)	Au1^xv—Ga3—Mg2^xiv	56.574 (13)
Au1^iii—Au1—Au1^iv	120.707 (19)	Au1^vi—Ga3—Mg2	123.374 (7)
Mg2^iv—Au1—Au1^iv	59.293 (19)	Au1^x—Ga3—Mg2	56.626 (7)
Mg2^i—Au1—Au1^iv	128.426 (2)	Au1—Ga3—Mg2	56.626 (7)
Mg2^v—Au1—Au1^iv	128.426 (2)	Au1^xiv—Ga3—Mg2	123.374 (7)
Mg2—Au1—Au1^iv	59.217 (10)	Au1^iv—Ga3—Mg2	56.574 (13)
Au1^vi—Au1—Au1^iv	96.25 (3)	Au1^xv—Ga3—Mg2	123.426 (13)
Au1^vii—Au1—Au1^iv	96.25 (3)	Mg2^xiv—Ga3—Mg2	180.0
Au1^viii—Mg2—Au1^iv	180.0	Au1^vi—Ga3—Mg2^xvi	123.426 (13)
Au1^viii—Mg2—Au1^ix	61.491 (10)	Au1^x—Ga3—Mg2^xvi	56.574 (13)
Au1^iv—Mg2—Au1^ix	118.509 (10)	Au1—Ga3—Mg2^xvi	123.374 (7)
Au1^viii—Mg2—Au1^x	118.509 (10)	Au1^xiv—Ga3—Mg2^xvi	56.626 (7)
Au1^iv—Mg2—Au1^x	61.491 (10)	Au1^iv—Ga3—Mg2^xvi	56.626 (7)
Au1^ix—Mg2—Au1^x	127.873 (5)	Au1^xv—Ga3—Mg2^xvi	123.374 (7)
Au1^viii—Mg2—Au1^xi	118.509 (10)	Mg2^xiv—Ga3—Mg2^xvi	83.070 (5)
Au1^iv—Mg2—Au1^xi	61.491 (10)	Mg2—Ga3—Mg2^xvi	96.930 (4)
Au1^ix—Mg2—Au1^xi	57.02 (2)	Au1^vi—Ga3—Mg2^v	56.574 (13)
Au1^x—Mg2—Au1^xi	99.107 (13)	Au1^x—Ga3—Mg2^v	123.426 (13)
Au1^viii—Mg2—Au1^xii	61.491 (10)	Au1—Ga3—Mg2^v	56.626 (7)
Au1^iv—Mg2—Au1^xii	118.509 (10)	Au1^xiv—Ga3—Mg2^v	123.374 (7)
Au1^ix—Mg2—Au1^xii	99.107 (13)	Au1^iv—Ga3—Mg2^v	123.374 (7)
Au1^x—Mg2—Au1^xii	57.02 (2)	Au1^xv—Ga3—Mg2^v	56.626 (7)
Au1^xi—Mg2—Au1^xii	127.873 (5)	Mg2^xiv—Ga3—Mg2^v	96.930 (4)
Au1^viii—Mg2—Au1^iii	61.491 (10)	Mg2—Ga3—Mg2^v	83.070 (5)
Au1^iv—Mg2—Au1^iii	118.509 (10)	Mg2^xvi—Ga3—Mg2^v	180.0
Au1^ix—Mg2—Au1^iii	99.107 (13)	Au1^vi—Ga3—Mg2^iv	56.626 (7)
Au1^x—Mg2—Au1^iii	127.873 (5)	Au1^x—Ga3—Mg2^iv	123.374 (7)
Au1^xi—Mg2—Au1^iii	127.873 (5)	Au1—Ga3—Mg2^iv	56.574 (13)
Au1^xii—Mg2—Au1^iii	99.107 (13)	Au1^xiv—Ga3—Mg2^iv	123.426 (13)
Au1^viii—Mg2—Au1	118.509 (10)	Au1^iv—Ga3—Mg2^iv	56.626 (7)
Au1^iv—Mg2—Au1	61.491 (10)	Au1^xv—Ga3—Mg2^iv	123.374 (7)
Au1^ix—Mg2—Au1	127.873 (5)	Mg2^xiv—Ga3—Mg2^iv	83.070 (5)
Au1^x—Mg2—Au1	99.107 (13)	Mg2—Ga3—Mg2^iv	96.930 (4)
Au1^xi—Mg2—Au1	99.107 (13)	Mg2^xvi—Ga3—Mg2^iv	83.070 (4)
Au1^xii—Mg2—Au1	127.873 (5)	Mg2^v—Ga3—Mg2^iv	96.930 (4)
Au1^iii—Mg2—Au1	57.02 (2)	Au1^vi—Ga3—Mg2^xv	123.374 (7)
Au1^viii—Mg2—Ga3^viii	49.965 (3)	Au1^x—Ga3—Mg2^xv	56.626 (7)
Au1^iv—Mg2—Ga3^viii	130.035 (3)	Au1—Ga3—Mg2^xv	123.426 (13)
Au1^ix—Mg2—Ga3^viii	49.952 (5)	Au1^xiv—Ga3—Mg2^xv	56.574 (13)
Au1^x—Mg2—Ga3^viii	168.475 (10)	Au1^iv—Ga3—Mg2^xv	123.374 (7)
Au1^xi—Mg2—Ga3^viii	88.316 (8)	Au1^xv—Ga3—Mg2^xv	56.626 (7)
Au1^xii—Mg2—Ga3^viii	111.456 (11)	Mg2^xiv—Ga3—Mg2^xv	96.930 (4)
Au1^iii—Mg2—Ga3^viii	49.952 (5)	Mg2—Ga3—Mg2^xv	83.070 (5)
Au1—Mg2—Ga3^viii	88.316 (8)	Mg2^xvi—Ga3—Mg2^xv	96.930 (4)
Au1^viii—Mg2—Ga3	130.035 (3)	Mg2^v—Ga3—Mg2^xv	83.070 (4)
Au1^iv—Mg2—Ga3	49.965 (3)	Mg2^iv—Ga3—Mg2^xv	180.0
Au1^ix—Mg2—Ga3	168.475 (10)

Symmetry codes: (i) x, y+1, z; (ii) x+1, y+1, z; (iii) x, y, −z+1/2; (iv) −x+1, −y+1, −z; (v) x−1, y, z; (vi) −x, −y+1, −z; (vii) −x+1, −y+2, −z; (viii) −x+1, −y+1, z+1/2; (ix) x+1, y, −z+1/2; (x) x, y−1, z; (xi) x+1, y, z; (xii) x, y−1, −z+1/2; (xiii) −x+1, −y, z+1/2; (xiv) −x, −y, −z; (xv) x−1, y−1, z; (xvi) −x+1, −y, −z.