W. Carrillo-Cabrera, R. Cardoso Gil, M. Somer, Ö. Persil, H. G. von Schnering
Table 1 Selected crystallographic data (293 K).
hafen (Germany), on quoting the depository number CSD-
412932, the name of the author(s), and the citation paper.
Compound; molar mass
Crystal
Na12Ge17; 1510.25 amu
dark grey fragment
(0.14ϫ0.13ϫ0.11 mm)
Space group; Pearson code
Unit cell; formula units
P21/c (No. 12); mP464
3 Results and Discussion
˚
˚
a ϭ 22.117(3) A, b ϭ 12.803(3) A,
˚
˚
c ϭ 41.557(6) A, β ϭ 91.31(2)°,
3.1 Crystal Structure
3
V ϭ 11764(4) A ; Z ϭ 16
dcalc
Data collection
3.411 g·cmϪ3
˚
As mentioned in section 2, the present X-ray reinvestigation
on Na12Ge17 reveals that the unit cell (I) is two times larger
than the one previously reported [5]. Furthermore, weak
reflections (I < 8σ(I)) indicate an even larger C-centred
STOE-IPDS, λ(AgKα) ϭ 0.56087 A, 450
exposures, ∆φ ϭ 0.4°; 2.1° < 2θ < 29.2°
Numerical absorption correction [9, 10].
µ ϭ 90.5 cmϪ1; transmission:
0.331Ϫ0.419
Data correction
˚
˚
Structure solution
Direct methods, SHELXLS-97 [11]
Refinement on F2, SHELXL-97 [12]
(513 variable parameters)
31115; 8953
3064; 4119
monoclinic unit cell II (aЈ ϭ 44.23 A, bЈ ϭ 25.60 A, cЈϭ
˚
46.63 A, βЈ ϭ 117.0°). This indicates a further orientational
N(hkl): measured; unique
NЈ(hkl) with I > 3·σ(I);
I > 2·σ(I)
ordering of those Ge9 clusters, which show some dis-
ordering in the unit cell I, as presented below.
Rgt(F), wRgt(F2)
0.095, 0.144 (I > 3·σ (I))
0.118, 0.153 (I > 2·σ (I))
0.167
The crystal structure of Na12Ge17 (non-split average mo-
del) contains four and eight crystallographically indepen-
dent [Ge9]4Ϫ and [Ge4]4Ϫ cluster ions, respectively.
wRall(F2)
Regarding only the packing of the Zintl anions [Ge9]4Ϫ
and [Ge4]4Ϫ, the structure can be described as a hierarchical
cluster replacement derivative [13] of the hexagonal MgZn2
structure (basic structure or hierarchy initiator). As shown
in Fig. 1, the Ge9 and Ge4 units substitute the Mg and Zn
atoms, respectively, and the Na atoms occupy 12 of the 17
tetrahedral holes of the pseudo-hexagonal packing (most of
the Na atoms are off-centre and several of them are signifi-
cantly relaxed towards the empty ᮀ sites). The formula can
ation of all measured reflections revealed a larger C-centred
˚
˚
monoclinic unit cell II (aЈϭ 44.23 A, bЈ ϭ 25.60 A, cЈ ϭ
˚
46.63 A, βЈ ϭ 117.0°; the relation between unit cell II and
ជ
ជ
unit cell I is: aជЈ ϭ 2aជ, bЈ ϭ Ϫ2b, cជЈ ϭ ϪaជϪcជ). But, the
intensity data were very poor (only 14 % of the measured
reflections had I > 2·σ(I)) and the structure solution with
direct methods failed. In detail, the reflections which were
necessary to chose the larger unit cell II instead of a smaller
one were comparatively weak (I < 8σ(I), representing 19 %
of the observed reflections). Neglecting these reflections,
the data could be indexed for a smaller primitive mono-
clinic unit cell (I) and the space group was determined to
be P21/c (No. 14).
be written as: Na12Ge17 ϭ (Naϩ)12ᮀ5[Ge49Ϫ][Ge44Ϫ
ᮀ17[Mg][Zn]2.
]
Z
2
In this description, the quasi-hexagonal axis of Na12Ge17,
chЈ ϭ c ϭ 2·c(MgZn2), is two times larger than that of an
equivalent MgZn2 arrangement. Apart of the effect of the
unfilled ᮀ tetrahedral holes, the deformation of the for-
mally hexagonal unit cell to a monoclinic one is mainly a
result of the site colouring due to the different orientations
of the ’non-spherical’ Ge9 clusters for a better packing in
the crystal. Further cluster site colouring of this kind might
causes the additional enlargement of the unit cell. The
doubling of chЈ also results from this colouring and not
from a change in the layer stacking sequence as in MgNi2.
Because of the hierarchical relationship of Na12Ge17 with
MgZn2, the characteristic topological features are un-
Direct methods (ΗEΗ > 1.1) were used to solve the crystal
structure. The E map of the best solution yielded the lo-
cation of all the germanium atoms and most of the sodium
atoms. The positions of the remaining Na atoms were re-
vealed through difference Fourier syntheses (calculations
were performed using the programs listed in Table 1, see
also section 4). The refinement of the structure converged
rapidly and a conventional Rgt value of 0.142 (for I > 2 ·
σ(I)) was obtained for a model with isotropic displacement
parameters (the number of observed reflections is not large
enough for a reliable refinement with anisotropic displace-
ment parameters). The Fourier syntheses and the large dis-
placement parameters for several Ge positions indicated
splitting of each one of those sites into two sites, both with
SOF ϭ 0.50 (a similar solution model with split positions
resulted in the non-centrosymmetric space group P21). The
final refinement for the split-model converged to a Rgt value
of 0.118 for I > 2·σ(I) (a Rgt value of 0.095 was obtained
for I > 3·σ(I)).
´
changed. Thus, as illustrated in Fig. 1b, 2D 3.6.3.6 Kagome
nets parallel to the (001) plane are formed by connecting
the centres of the Ge4 tetrahedral anions. By further con-
´
necting the nodes of these Kagome nets with intermediate
sites along the c-axis, a 3D framework with tetrahedral and
truncated tetrahedral holes is formed. One tetrahedron of
Ge4 tetrahedra (a supertetrahedron) centred by a Naϩ cation
is shown in Fig. 2b. Also, one truncated tetrahedron of Ge4
tetrahedra (a trucated supertetrahedron) centred by a
[Ge9]4Ϫ anion is illustrated in Fig. 2a. Thus, each Ge9 clus-
ter is coordinated by 12 Ge4 units and 4 Ge9 units (the latter
not shown in Fig. 2a), forming a CN-16 Frank-Kasper or
Friauf superpolyhedron.
The crystallographic data, the positional and isotropic
displacement parameters, and the important distances
d(GeϪGe) are listed in Table 1, Table 2 and Table 3, respec-
tively. Further details are available from the Fachinforma-
tionszentrum Karlsruhe, D-76344 Eggenstein-Leopolds-
To easy the recognition of the atoms belonging to a Gen
cluster, they were labelled as Ge(iY), where i ϭ 1Ϫ4 (for
602
Z. Anorg. Allg. Chem. 2003, 629, 601Ϫ608
Carrillo-Cabrera
