The intermetallic compound Mg₂₁Zn₂₅

The crystal structure of the intermetallic compound henicosa­magnesium pentacosazinc, Mg₂₁Zn₂₅, has been determined by single-crystal X-ray diffraction. It is isomorphous with Zr₂₁Re₂₅ and deviates slightly from the rules that define the Frank-Kasper phases.

S1. Comment

The intermetallic phase with a composition close to MgZn has been reported several times in the literature [Tarschisch, 1933; Clark & Rhines, 1957; Clark et al., 1988; Khan 1989; International Centre for Diffraction Data, card 08–0206 (ICDD, 2001)], and its composition was reported as Zn-rich. The crystal structure of stoichiometric MgZn (P6₃/mmc, a = 10.66 and c = 17.16 Å) was given by Tarschisch (1933). It is derived from the hexagonal structure of the Frank-Kasper (Frank & Kasper, 1958, 1959) phase of MgZn₂ (Friauf, 1927) by a substitution of one Zn site by Mg and deformation of coordination icosahedra. It was recognized later (McKeehan, 1935) that the structure has orthorhombic symmetry (Imm2, a = 5.33, b = 17.16 and c = 9.23 Å). However, short interatomic Mg—Zn distances of 2.23 Å were present in the structural model.

The phase reported by Khan (1989) has the nominal composition MgZn, and its powder pattern was indexed with a hexagonal lattice (a = 25.69 and c = 18.104 Å) showing systematic extinctions corresponding to an R-centred cell. Another, very similar, powder pattern of a compound with the nominal composition MgZn was also reported in the PDF-2 database (ICCD, 2001).

The compound Mg₂₁Zn₂₅ presented here is isostructural with Zr₂₁Re₂₅ (Cenzual et al., 1986). It deviates slightly from the rules that define the Frank-Kasper phases; it does not precisely follow the equations given by Shoemaker & Shoemaker (1986) that account for the numbers of each Frank-Kasper coordination polyhedron in the structure. Atom Mg2 is coordinated by an Mg₄Zn₁₂ Frank-Kasper coordination polyhedron, atom Mg1 by Mg₇Zn₇, atom Mg3 by Mg₇Zn₈ and atom Mg4 by Mg₁₀Zn₄. Atoms Zn4 and Zn6 are coordinated by an Mg₆Zn₆ icosahedron, atoms Zn1, Zn2 and Zn3 by an Mg₇Zn₅ icosahedron, and Zn5 by an Mg₈Zn₄ icosahedron. The Zn—Zn distances are in the range 2.57–2.72 Å, Zn—Mg 2.95–3.18 Å and Mg—Mg 3.01–4.04 Å. The crystal structure of Mg₂₁Zn₂₅ can be constructed from (00 l) slabs (Fig. 1) and is repeated three times in the unit cell by the R-centring.

In Cenzual et al. (1986), the coordination of Zr4 (here Mg4) was described as a Zr₈Re₄ icosahedron. If two additional Mg atoms at distances of 4.032 Å from Mg4 are added to the Mg4 coordination icosahedron, we get an Mg₁₀Zn₄ coordination polyhedron, which is not of the Frank-Kasper type. However, we prefer this description, because it fills all the available space in the structure (Fig. 1).

The calculated powder pattern of Mg₂₁Zn₂₅ agrees better with that reported in the PDF-2 database (ICCD, 2001) than with that reported by Khan (1989). The cell parameters reported by Khan do not agree exactly with ours. The a parameter can be considered essentially the same as our value (no experimental errors are given by Khan). However, half the c parameter reported by Khan is significantly different from our value for the c parameter. No doubling of the c length was observed in our data. It is necessary to note that the experiment by Khan was performed on rapidly cooled ribbons that were then annealed at low temperature (450 K); therefore, intermediate phases that were not in equilibrium cannot be excluded.

S2. Experimental

A sample of nominal composition MgZn was melted by placing a compressed mixture of Mg powder (Strem Chemical, 99.8%) and Zn powder (Fluka, p.a. 99.0%) into a quartz ampoule, which was sealed under 0.3 bar (1 bar = 10 ⁵ Pa) of argon pressure and annealed at 573 K for 1 d. The ingot (1 g) was crushed into several pieces and powdered under a protective argon atmosphere. In spite of melting losses of about 2.3 wt.%, the X-ray powder pattern indicated mainly the presence of Mg₂₁Zn₂₅ with small amounts of Mg₅₁Zn₂₀ and MgZn₂ as minor impurities. Several single crystals of suitable size for X-ray analysis were found in the crushed sample and were examined by the Laue method.

S3. Refinement

Three non-coherent domains with the Mg₂₁Zn₂₅ cell parameters were identified in the crystal. The reflections of the domains were separated in the process of integration of the images. From 12063 measured reflections of the first domain, 2274 reflections were rejected because of the overlap with reflections of the second and third domains. Mean F²/σ(F²) = 7.9. In the second domain, 12090 reflections were measured, mean F²/σ(F²) = 4.0. In the third domain, 12064 reflections were measured, mean F²/σ(F²) = 3.1. Only the data of the first domain were used for the structure solution and refinement. The R-factor statistics show no systematic deviation of different reflection groups from the mean, whether dependent on hkl or on F_obs or on sin(θ)/λ.

Computing details

Data collection: EXPOSE in IPDS Software (Stoe & Cie, 1999); cell refinement: CELL in IPDS Software; data reduction: TWIN and X-RED in IPDS Software; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ATOMS (Dowty, 1993); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures

Fig. 1. One structural slab (00 l) of Mg21Zn25 at z ~0, composed of the Zn6Mg6Zn6 and Zn3Mg7Zn5 icosahedra (light grey) and the Mg4Mg10Zn4 Frank-Kasper polyhedron (dark grey).

henicosamagnesium pentacosazinc

Crystal data

Mg21Zn25	Dx = 4.238 Mg m^−3
Mr = 2144.72	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3c	Cell parameters from 2000 reflections
Hall symbol: -r 3 2"c	θ = 3–25°
a = 25.7758 (13) Å	µ = 17.85 mm^−1
c = 8.7624 (6) Å	T = 293 K
V = 5041.7 (5) Å^3	Irregular, metallic dark grey
Z = 6	0.09 × 0.07 × 0.04 mm
F(000) = 6012

Data collection

Stoe IPDS diffractometer	780 reflections with I > 2σ(I)
ϕ oscillation scans	Rint = 0.087
Absorption correction: analytical (X-RED in IPDS Software; Stoe & Cie, 1999)	θmax = 25.9°, θmin = 2.7°
Tmin = 0.363, Tmax = 0.455	h = −31→31
9789 measured reflections	k = −31→30
1097 independent reflections	l = −10→10

Refinement

Refinement on F^2	73 parameters
Least-squares matrix: full	0 restraints
R[F^2 > 2σ(F^2)] = 0.032	w = 1/[σ^2(Fo^2) + (0.0371P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.076	(Δ/σ)max < 0.001
S = 0.96	Δρmax = 0.78 e Å^−3
1097 reflections	Δρmin = −1.63 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.

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

	x	y	z	Uiso*/Ueq
Mg1	0.00136 (10)	0.23096 (11)	0.0463 (3)	0.0147 (5)
Mg2	0.11678 (11)	0.11725 (11)	0.0645 (3)	0.0167 (5)
Mg3	0.31341 (11)	0.10866 (11)	0.2501 (3)	0.0157 (5)
Mg4	0.69282 (13)	0.0	0.25	0.0170 (8)
Zn1	0.05762 (4)	0.17952 (4)	0.25065 (10)	0.0162 (2)
Zn2	0.23376 (4)	0.17517 (4)	0.24752 (9)	0.0141 (2)
Zn3	0.23687 (4)	0.11857 (4)	−0.00094 (9)	0.0142 (2)
Zn4	0.06084 (5)	0.0	0.25	0.0235 (3)
Zn5	0.44195 (5)	0.0	0.25	0.0133 (3)
Zn6	0.0	0.0	0.0	0.0154 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mg1	0.0126 (12)	0.0145 (12)	0.0184 (11)	0.0079 (11)	0.0000 (9)	0.0010 (9)
Mg2	0.0155 (12)	0.0142 (12)	0.0196 (12)	0.0067 (11)	−0.0007 (10)	0.0003 (10)
Mg3	0.0141 (12)	0.0153 (13)	0.0126 (12)	0.0035 (10)	0.0014 (9)	0.0010 (10)
Mg4	0.0145 (14)	0.0120 (17)	0.0235 (19)	0.0060 (8)	−0.0023 (7)	−0.0047 (14)
Zn1	0.0115 (5)	0.0155 (5)	0.0179 (4)	0.0040 (4)	0.0001 (3)	−0.0002 (3)
Zn2	0.0154 (4)	0.0127 (5)	0.0147 (4)	0.0074 (4)	−0.0016 (3)	−0.0004 (3)
Zn3	0.0152 (4)	0.0153 (5)	0.0131 (4)	0.0083 (4)	−0.0003 (3)	−0.0015 (3)
Zn4	0.0206 (5)	0.0266 (7)	0.0254 (7)	0.0133 (4)	−0.0001 (3)	−0.0003 (5)
Zn5	0.0133 (5)	0.0099 (6)	0.0157 (5)	0.0049 (3)	0.0003 (2)	0.0006 (5)
Zn6	0.0164 (7)	0.0164 (7)	0.0134 (9)	0.0082 (3)	0.0	0.0

Bond lengths (Å)

Mg1—Zn2^i	2.950 (2)	Zn1—Zn4^v	2.6495 (15)
Mg1—Zn3^i	2.968 (2)	Zn1—Zn3^i	2.6659 (12)
Mg1—Zn5^ii	2.983 (2)	Zn1—Zn3^vii	2.6722 (12)
Mg1—Zn1	2.998 (2)	Zn1—Mg3^vii	3.017 (3)
Mg1—Zn2^iii	3.015 (2)	Zn1—Mg1^iv	3.017 (3)
Mg1—Zn1^iv	3.017 (3)	Zn1—Mg2^xxviii	3.154 (2)
Mg1—Zn3^v	3.030 (2)	Zn1—Mg2^i	3.172 (2)
Mg1—Mg4^vi	3.073 (3)	Zn1—Mg2^vii	3.176 (3)
Mg1—Mg2^i	3.077 (4)	Zn2—Zn2^vii	2.6161 (17)
Mg1—Mg3^vii	3.078 (3)	Zn2—Zn1^vii	2.6266 (12)
Mg1—Mg3^v	3.126 (3)	Zn2—Zn3	2.6442 (11)
Mg1—Mg4^viii	3.267 (3)	Zn2—Zn3^xi	2.6702 (11)
Mg1—Mg3^ii	3.413 (3)	Zn2—Zn5^xiv	2.6716 (8)
Mg1—Mg1^iv	3.570 (5)	Zn2—Mg1^ix	2.950 (2)
Mg2—Zn2	3.064 (3)	Zn2—Mg4^xxix	2.953 (3)
Mg2—Zn6	3.069 (2)	Zn2—Mg1^xxviii	3.015 (2)
Mg2—Zn4^v	3.072 (2)	Zn2—Mg3^vi	3.043 (3)
Mg2—Mg1^ix	3.077 (4)	Zn2—Mg2^vii	3.079 (3)
Mg2—Zn2^vii	3.079 (3)	Zn3—Zn1^ix	2.6659 (12)
Mg2—Zn4	3.082 (2)	Zn3—Zn2^xxx	2.6702 (11)
Mg2—Zn4^i	3.113 (2)	Zn3—Zn1^vii	2.6722 (12)
Mg2—Zn3^i	3.114 (3)	Zn3—Zn5^x	2.7216 (10)
Mg2—Zn3	3.131 (3)	Zn3—Mg1^ix	2.968 (2)
Mg2—Zn1^iii	3.154 (2)	Zn3—Mg3^vi	2.970 (3)
Mg2—Zn1	3.164 (3)	Zn3—Mg1^xiii	3.030 (2)
Mg2—Zn1^ix	3.172 (2)	Zn3—Mg3^xxx	3.034 (2)
Mg2—Zn1^vii	3.176 (3)	Zn3—Mg2^ix	3.114 (3)
Mg2—Mg2^i	3.221 (3)	Zn4—Zn1^vii	2.6495 (15)
Mg2—Mg2^ix	3.221 (3)	Zn4—Zn1^xiii	2.6495 (15)
Mg2—Mg2^vii	3.251 (5)	Zn4—Zn6	2.6941 (8)
Mg3—Zn5^x	2.967 (2)	Zn4—Zn6^vii	2.6941 (8)
Mg3—Zn3^vi	2.970 (3)	Zn4—Zn4^xiii	2.716 (2)
Mg3—Mg3^vi	3.010 (5)	Zn4—Zn4^v	2.716 (2)
Mg3—Zn1^vii	3.017 (3)	Zn4—Mg2^xiii	3.072 (2)
Mg3—Zn3^xi	3.034 (2)	Zn4—Mg2^vii	3.072 (2)
Mg3—Zn2^vi	3.043 (3)	Zn4—Mg2^xxxi	3.082 (2)
Mg3—Zn3	3.049 (3)	Zn4—Mg2^xi	3.113 (2)
Mg3—Mg3^xii	3.052 (5)	Zn4—Mg2^ix	3.113 (2)
Mg3—Mg1^vii	3.078 (3)	Zn5—Zn2^xxvii	2.6716 (8)
Mg3—Mg1^xiii	3.126 (3)	Zn5—Zn2^xviii	2.6716 (8)
Mg3—Zn5^xiv	3.131 (3)	Zn5—Zn3^xxxii	2.7215 (10)
Mg3—Mg4^xv	3.255 (2)	Zn5—Zn3^xxxiii	2.7216 (10)
Mg3—Zn2	3.267 (3)	Zn5—Mg4^xiv	2.9220 (13)
Mg3—Mg1^xvi	3.412 (3)	Zn5—Mg4^xv	2.9221 (13)
Mg3—Mg4^xiv	4.032 (4)	Zn5—Mg3^xxxii	2.967 (2)
Mg4—Zn5^xvii	2.9220 (13)	Zn5—Mg3^xxxiii	2.967 (2)
Mg4—Zn5^xviii	2.9220 (13)	Zn5—Mg1^xxxiv	2.983 (2)
Mg4—Zn2^xix	2.953 (3)	Zn5—Mg1^xvi	2.983 (2)
Mg4—Zn2^xx	2.953 (3)	Zn5—Mg3^xxvii	3.131 (3)
Mg4—Mg1^xxi	3.073 (3)	Zn5—Mg3^xviii	3.131 (3)
Mg4—Mg1^vi	3.073 (3)	Zn6—Zn4^ix	2.6941 (8)
Mg4—Mg4^xxii	3.146 (2)	Zn6—Zn4^xxxv	2.6941 (8)
Mg4—Mg4^xxiii	3.146 (2)	Zn6—Zn4^v	2.6941 (8)
Mg4—Mg3^xvii	3.255 (2)	Zn6—Zn4^i	2.6941 (8)
Mg4—Mg3^xxiv	3.255 (2)	Zn6—Zn4^xiii	2.6941 (8)
Mg4—Mg1^xxv	3.267 (3)	Zn6—Mg2^xxxv	3.069 (2)
Mg4—Mg1^xxvi	3.267 (3)	Zn6—Mg2^i	3.069 (2)
Mg4—Mg3^xviii	4.032 (4)	Zn6—Mg2^ix	3.069 (2)
Mg4—Mg3^xxvii	4.032 (4)	Zn6—Mg2^xiii	3.069 (2)
Zn1—Zn1^iv	2.5724 (16)	Zn6—Mg2^v	3.069 (2)
Zn1—Zn2^vii	2.6266 (12)

Symmetry codes: (i) x−y, x, −z; (ii) −x+y+1/3, −x+2/3, z−1/3; (iii) −x+y, y, z−1/2; (iv) −x, −x+y, −z+1/2; (v) −y, x−y, z; (vi) −x+2/3, −y+1/3, −z+1/3; (vii) y, x, −z+1/2; (viii) y, −x+y+1, −z; (ix) y, −x+y, −z; (x) −y+1/3, x−y−1/3, z−1/3; (xi) x, x−y, z+1/2; (xii) −x+2/3, −x+y+1/3, −z+5/6; (xiii) −x+y, −x, z; (xiv) y+1/3, −x+y+2/3, −z+2/3; (xv) x−y−1/3, x−2/3, −z+1/3; (xvi) −y+2/3, x−y+1/3, z+1/3; (xvii) y+2/3, −x+y+1/3, −z+1/3; (xviii) x−y+1/3, x−1/3, −z+2/3; (xix) −x+1, −x+y, −z+1/2; (xx) −y+1, x−y, z; (xxi) −x+y+1/3, y−1/3, z+1/6; (xxii) −x+y+4/3, −x+2/3, z−1/3; (xxiii) −y+2/3, x−y−2/3, z+1/3; (xxiv) x+1/3, x−y−1/3, z+1/6; (xxv) −y+1, −x, z+1/2; (xxvi) x−y+1, x, −z; (xxvii) −y+2/3, −x+1/3, z−1/6; (xxviii) −x+y, y, z+1/2; (xxix) −x+y+1, −x+1, z; (xxx) x, x−y, z−1/2; (xxxi) x−y, −y, −z+1/2; (xxxii) −x+y+2/3, −x+1/3, z+1/3; (xxxiii) y+1/3, x−1/3, −z+1/6; (xxxiv) −x+1/3, −x+y−1/3, −z+1/6; (xxxv) −x, −y, −z.