Ba8Ge43 revisited: A 2a′x2a′x2a′ superstructure of the clathrate-I type with full vacancy ordering

Article abstract of DOI:10.1002/zaac.200400268

The reinvestigation of the crystal structure of Ba₈Ge ₄₃□₃ (space group Ia3d, no. 230; a = 21.3123(5) A; Z = 8; Pearson symbol cI408) shows a full ordering of the vacancies (□) in the germanium framework. This ordered crystal structure can be considered as a derivative of an ideal Ba₈Ge₄₆ clathrate-I type structure (Pm3n, a′ = a/2) in which three Ge vacancies (per formula unit) are allowed to order in a cubic superstructure with a doubled unit cell parameter (□ at the 24c site, space group Ia3d). In the resulting Ge framework, each vacancy □ is surrounded by four three-bonded (3b)Ge ^- species. The ordering in crystals of as-cast samples (cooled in argon atmosphere, non-annealed) is partially disrupted. For the as-cast crystals, a short-range model is proposed based on the partial distribution of Ge on the 24c and 24d sites. From the electron balance, Ba₈Ge₄₃ can be considered as a metallic Zintl phase with four excess electrons per formula unit. The Ba₈Ge₄₃ phase is stable in the temperature range 770-810°C and exists in equilibrium with Ba₆Ge₂₅ and Ge. By decomposition of undercooled (metastable) Ba₈Ge₄₃, a new metastable binary BaGe _～5 phase is formed.

Full text of DOI:10.1002/zaac.200400268

Ba8Ge43 revisited: a 2aЈ؋2aЈ؋2aЈ Superstructure of the Clathrate-I Type with
Full Vacancy Ordering
Wilder Carrillo-Cabrera*, Serhij Budnyk, Yurii Prots, and Yuri Grin
Dresden, Max-Planck-Institut für Chemische Physik fester Stoffe
Received June 12th, 2004.
Professor Martin Jansen zum 60. Geburtstag gewidmet
Abstract. The reinvestigation of the crystal structure of Ba8Ge43ᮀ
“as-cast” crystals, a short-range model is proposed based on the
partial distribution of Ge on the 24c and 24d sites. From the elec-
tron balance, Ba8Ge43 can be considered as a metallic Zintl phase
with four excess electrons per formula unit. The Ba8Ge43 phase is
stable in the temperature range 770 Ϫ 810 °C and exists in equili-
brium with Ba6Ge25 and Ge. By decomposition of undercooled
(metastable) Ba8Ge43, a new metastable binary BaGeϳ5 phase is
formed.
3
˚
¯
(space group Ia3d, no. 230; a ϭ 21.3123(5) A; Z ϭ 8; Pearson sym-
bol cI408) shows a full ordering of the vacancies (ᮀ) in the germa-
nium framework. This ordered crystal structure can be considered
as a derivative of an ideal “Ba8Ge46” clathrate-I type structure
¯
(Pm3n, aЈ ϭ a/2) in which three Ge vacancies (per formula unit)
are allowed to order in a cubic superstructure with a doubled unit
¯
cell parameter (ᮀ at the 24c site, space group Ia3d). In the resulting
Ge framework, each vacancy ᮀ is surrounded by four three-bonded
(3b)GeϪ species. The ordering in crystals of as-cast samples (cooled
in argon atmosphere, non-annealed) is partially disrupted. For the
Keywords: Ba8Ge43; Clathrate-I; Superstructure; Lone pairs orde-
ring; BaϪGe Phase diagram
Ba8Ge43 erneut untersucht: eine 2aЈ؋2aЈ؋2aЈ Clathrat-I Überstruktur mit vollständig
geordneten Leerstellen
Inhaltsübersicht. Die erneute Untersuchung der Kristallstruktur
nicht-getemperter Proben wird gestört. Für die nicht-getemperten
Kristalle wurde ein Ordnungsmodell mit partieller Verteilung von
Ge auf den Lagen 24c und 24d vorgeschlagen. Die Elektronenbi-
lanz zeigt, dass Ba8Ge43 als metallische Zintl-Phase mit vier Über-
schusselektronen pro Formeleinheit beschrieben werden kann. Die
Phase Ba8Ge43 ist im Temperaturbereich von 770 °C bis 810 °C sta-
bil und steht im Gleichgewicht mit Ba6Ge25 und Ge. Durch Zerset-
zung von unterkühltem, metastabilen Ba8Ge43 bildet sich eine neue
˚
¯
von Ba8Ge43ᮀ (Raumgruppe Ia3d, Nr. 230; a ϭ 21.3123(5) A;
3
Z ϭ 8; Pearson-Symbol cI408) zeigt eine komplette Ordnung der
Defekte (ᮀ) innerhalb des Germaniumgerüstes. Diese geordnete
Struktur kann als ein Abkömmling des idealen “Ba8Ge46” Cla-
¯
thrat-I-Typs (Pm3n, aЈ ϭ a/2) beschrieben werden, in der drei De-
fekte pro Formeleinheit in einer kubischen Überstrukturzelle mit
verdoppeltem Gitterparameter (ᮀ auf der Lage 24c in der Raum-
Ϫ
¯
gruppe Ia3d) geordnet vorliegen mit vier dreibindigen (3b)Ge -
metastabile binäre Phase BaGeϳ5.
Spezies um jeden Defekt herum. Die Ordnung in Kristallen aus
Introduction
The structure refinement indicated that the Ge1 (6c) posi-
tion was occupied by 50.5(4) % Ge, and a split model was
applied to the surrounding Ge3 atoms (Ge3 Ǟ 0.5 Ge31 ϩ
0.5 Ge32). A short-range model with one Ge vacancy per
hexagonal Ge6 ring (two faces of the Ge24 tetrakaidecahe-
dron of Ba2 are hexagons) was anticipated. Based on the
Zintl concept [2, 3], the following charge balanced formula
was proposed for the title compound: (Ba2ϩ)8((3b)-
Ge1Ϫ)12((4b)Ge0)31(4eϪ), where (3b)Ge1Ϫ are three-bonded
and (4b)Ge0 are four-bonded Ge species. It is assumed that
lone electron pairs are attached to the (3b)Ge species in the
covalently bonded germanium framework. Nevertheless,
the question about the existence of an ordered superstruc-
ture in Ba8Ge43 remained open.
In our previous investigation [1], Ba8Ge43 was characterized
as a defect clathrate-I type structure with three missing Ge
atoms in the covalent germanium framework (aЈ ϭ
˚
¯
10.6565(2) A, space group Pm3n, Z ϭ 1). The single crystal
was extracted from an as-cast “Ba3Ge4C2” sample after
heat treatment at 850 °C (1h) under 40 Kbar pressure (coo-
led to room temperature under pressure in 5 min). Super-
structure reflections were not detected in this investigation.
* Wilder Carrillo-Cabrera
Max-Planck-Institut für Chemische Physik fester Stoffe
Nöthnitzer Str. 40
D-01187 Dresden/Germany
E-mail: carrillo@cpfs.mpg.de
Tel: 0049-351-4646-3325
In a more recent work on Ba8Ge43 [4], where the super-
structure was not observed either (arc-melted sample), the
¯
refined crystal structure (space group Pm3n) was the same
Fax: 0049-351-4646-3002
as in the first structure determination [1], but a split model
Z. Anorg. Allg. Chem. 2004, 630, 2267Ϫ2276
DOI: 10.1002/zaac.200400268
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W. Carrillo-Cabrera, S. Budnyk, Y. Prots, Y. Grin
To verify the ordered structure for Ba8Ge43 in the annealed bulk
material, the atomic parameters were refined from X-ray powder
diffraction data using the Rietveld method (STOE-STADI P dif-
fractometer, linear PSD detector; CuKα1 radiation; 10° Յ 2θ Յ
120°; 10990 points, step width ϭ 0.01°).
Several single crystals were extracted mechanically from an as-cast
batch and an annealed batch and tested by Laue photographs. The
best from each batch was chosen for single-crystal X-ray diffraction
experiments carried out on a Rigaku AFC7 four-circle diffractome-
ter equipped with a Mercury CCD area detector. For each crystal,
two measurements with short and long exposure times were perfor-
med to obtain accurate intensities for strong and weak reflections.
Both data sets were scaled and combined by using the program
XPREP [8].
The single-crystal structure refinements were carried out with the
SHELXL-97 program [9]. Details of the single-crystal data collec-
tion and the structure refinement for the ordered (annealed) and
the partially ordered (as-cast) Ba8Ge43 crystals are summarized in
Table 1.
Further details on the crystal structure investigations can be obtai-
ned from the Fachinformationszentrum Karlsruhe, D-76344 Eg-
genstein-Leopoldhafen, Germany, fax: (ϩ49)7247-808-666, e-mail:
crysdata@fiz.karlsruhe.de, on quoting the depositary numbers
CSD-no. 414162 (ordered) and CSD-no. 414163 (partially ordered).
was not applied. In an earlier report (high-frequency melted
material) [5], even when superstructure reflections were ob-
served by electron diffraction ([211] beam direction), a
model for an ordered crystal structure was not suggested.
In the present investigation, accurate single-crystal X-ray
diffraction intensity data were collected and the crystal
structure is re-determined and discussed in detail (two re-
presentative crystals were studied, namely one from an an-
nealed sample and one from an as-cast sample).
Experimental
Preparation and thermal analysis
To study the phase relationships of Ba8Ge43 and Ba6Ge25 [6] in the
BaϪGe system, samples (2Ϫ3 g) with compositions in the range
Ba0.33Ge0.67 to Ba0.10Ge0.90 were prepared from the elements in
open glassy carbon crucibles by high-frequency induction melting
(argon atmosphere). In particular, several samples with nominal
composition Ba0.157Ge0.843 ϵ Ba8Ge43 were synthesized. The star-
ting materials were handled in an argon-filled glove box (content
of O2 < 1 ppm, H2O < 1 ppm). The homogenization annealing was
performed in argon filled quartz ampoules with subsequent quen-
ching in water. The main heat treatments were done at 650 °C and
795 °C (7 Ϫ 42 d). For investigation of the metastable behaviour
of Ba8Ge43, some heat treatments were also carried out at lower
temperatures (450 Ϫ 600 °C) for hours or several days. In all experi-
ments, to avoid reaction with the quartz ampoule, each sample was
wrapped in molybdenum foil (for heat treatments at T Յ 650 °C) or
inserted in a glassy carbon crucible (for heat treatments at 795 °C).
The differential thermal analysis (DTA) was done on annealed
samples (60Ϫ120 mg) in an argon protective atmosphere with the
heating rate of 2 °C/min (Netzsch STA 409 EP). The DTA experi-
ments used for the phase diagram determination were performed
only on the series of BaxGe1Ϫx alloys (x ϭ 0.10 Ϫ 0.33) annealed
at 650 °C. The samples annealed at 795 °C (quenched in water)
were used to establish the phase relationships of the high-tempera-
ture phase Ba8Ge43.
Results and discussion
Phase relationships
To optimize the preparation conditions and to determine
the stability range of Ba8Ge43 and its phase relationships,
the germanium-rich part of the BaϪGe phase diagram [10]
was reinvestigated. A revised variant of the Ge-rich region
is proposed in Fig. 1 (T > 430 °C; 75Ϫ100 at.% Ge). The
temperature values taken for the phase diagram are the onset
points of the heat-flow peaks registered in the DTA curves.
The phase Ba8Ge43 is stable in the range 770 Ϫ 810 °C,
forming peritectically and decomposing eutectoidally into
Ba6Ge25 and Ge. According to metallographic and X-ray
powder diffraction data, the samples with compositions in
the range Ba0.19Ge0.81 Ϫ Ba0.10Ge0.90 and annealed at
650 °C contain Ba6Ge25 and Ge. By studying samples con-
taining Ba8Ge43 and Ba6Ge25, pre-annealed at temperatures
between 770 °C and 810 °C, it was found that, if the cooling
was not enough rapid, apart of the decomposition of
Ba8Ge43 into Ba6Ge25 and primary germanium at the grain
boundaries, a metastable phase BaGeϳ5 together with se-
condary germanium (very thin inclusions; difficult to be ob-
served even with SEM) were found to precipitate within the
Ba8Ge43 grains. The EDXS analysis of the metastable phase
gave the composition Ba0.99(1)Ge5.01(1). The BaGeϳ5 phase
is the only optically active one (suggesting a non-cubic
structure) of all four phases present in the samples, there-
fore, it can be easily identified using polarized light. E.g.
see the microstructure of the Ba0.17Ge0.83 sample annealed
at 795 °C for 20 days and fast cooled in water (Fig. 2). A
piece of the Ba0.17Ge0.83 sample (containing mostly Ba8Ge43
and Ba6Ge25) was used for a DSC experiment and the result
is shown in Fig. 3. There is an ’anomalous’ exothermic peak
with an onset at 458 °C, originating from the decomposi-
Differential scanning calorimetry (DSC; Netzsch STA 409C/CD)
was performed to establish the decomposition temperature of
Ba8Ge43 (ϳ 60 mg; argon atmosphere, heating rate 10 °C/min).
Metallographical examination
Because Ba8Ge43 and Ba6Ge25 are chemically stable enough outside
the argon box, the specimens for the metallographic investigations
were polished using standard methods without final etching. The
optical micrographs were obtained using differential interference
contrast and partially polarized light (ZEISS Axioplan2 optical
microscope). The chemical analyses were performed by the EDXS
method (Philips XL30 SEM).
X-ray diffractometry
The X-ray powder diffraction intensities were collected on a Huber
Guinier image plate camera G670 (CuKα1 radiation,
1.540598 A) at room temperature. The lattice parameters were refi-
ned from the powder data applying the program package STOE
λ ϭ
˚
WinXPOW [7]. LaB6 was used as internal standard (a
4.15695 A).
ϭ
˚
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Z. Anorg. Allg. Chem. 2004, 630, 2267Ϫ2276

Ba8Ge43: a 2aЈϫ2aЈϫ2aЈ Superstructure of the Clathrate-I Type
Table 1 Selected crystallographic data for ordered (annealed) and partially ordered (as-cast) Ba8Ge43.
ordered (annealed)
partially ordered (as-cast)
Crystal
grey metallic clump
grey metallic clump
Crystal size
Preparation
Space group; formula units
Pearson code
Unit cell dimensions
(powder data)
Density (calculated)
Absorption coefficient
F(000)
0.130 ϫ 0.070 ϫ 0.040 mm
HF melted; 795 °C / 42 d, fast cooled in water
0.080 ϫ 0.060 ϫ 0.040 mm
HF melted, cooled in argon atmosphere
¯
Ia3d (no. 230), Z ϭ 8
cI408
3
3
˚
˚
˚
˚
a ϭ 21.3123(5) A, V ϭ 9680.3(4) A
a ϭ 21.3123(6) A, V ϭ 9680.3(5) A
(107 reflections)
(71 reflections)
5.791 g·cmϪ3
32.61 mmϪ1
14592
˚
Data collection
Rigaku AFC7, Mercury CCD; λ(Mo Kα) ϭ 0.71073 A
4.6° < 2θ < 67.7°
Multi-scan method
0.180, 0.355
40
Absorption correction
Min. and max. transmission
Refined parameters
Goodness-of-fit on F2
∆ρmax, ∆ρmin
0.101, 0.356
1.605
1.621
ϩ1.9, Ϫ1.9 e·A
Ϫ3
Ϫ3
˚
˚
ϩ1.4, Ϫ2.4 e·A
N(hkl) measured
N(hkl) unique
42604
1585 [R(int) ϭ 0.053]
1452
0.050
0.090
47159
1590 [R(int) ϭ 0.061]
1412
0.057
0.089
NЈ(hkl) with I > 2σ(I)
Rgt(F)
wRall(F2)
3
Ba6Ge25 and Ge: /4 Ba8Ge40 Ǟ Ba6Ge25 ϩ 5 Ge. The se-
cond endothermic peak (onset at 780 °C) revels the reaction
back to Ba8Ge43 (Ba6Ge25 ϩ Ge Ǟ Ba8Ge43) and the third,
broader and highest endothermic peak (onset at 820 °C) re-
presents the peritectic decomposition of both, Ba8Ge43 and
the remaining Ba6Ge25 (cf. decomposition temperatures
810 °C and 815 °C, respectively, in Fig. 1). In the DSC
curve, the onset temperature values of the last two reactions
are shifted by about 10 °C as compared to those obtained
from the DTA curves (2 °C/min; samples pre-annealed at
650 °C) used for the determination of the BaϪGe phase
diagram in Fig. 1. The difference might be caused by the
different heating rate which was 5 times faster for DSC in
comparison with DTA. Thus, we estimated that for low
heating rates the two first reaction temperatures should be
shifted down by about 8 °C (to ϳ 450 °C and ϳ 608 °C,
respectively, in Fig. 1).
The DTA/DSC experiments and further low temperature
heat-treatments on samples pre-annealed at 795 °C suggest
that the BaGeϳ5 phase is a metastable phase that forms
readily at temperatures in the range 460 Ϫ 600 °C from its
high-temperature precursor Ba8Ge43 which is undercooled
well below its equilibrium eutectoid decomposition tempe-
rature. BaGeϳ5 is kinetically a very “sluggish” phase (even
after 3 months at 460 °C it is still present). Thus, the trans-
formation to the equilibrium phases (Ba6Ge25 ϩ Ge) needs
overheating. In Fig. 1, dashed lines indicate the metastable
behaviour for the undercooled Ba8Ge43.
Fig. 1 Revised phase diagram of the BaϪGe system in the germa-
nium-rich region. Dashed lines at temperatures below 650 °C show
the metastable behavior of Ba8Ge43.
The EDXS analysis for Ba8Ge43 resulted in the composi-
tion Ba8.0(1)Ge42.9(1). The Ba8Ge43 lattice parameter was
tion of the undercooled Ba8Ge43 phase into the intermedi-
ate BaGeϳ5 phase (Х Ba8Ge40) and germanium: Ba8Ge43
Ǟ Ba8Ge40 ϩ 3 Ge. The endothermic peak with an onset
at 616 °C represents the transformation of the metastable
phase BaGeϳ5 (Х Ba8Ge40) into the equilibrium phases
˚
found to be the same for annealed (21.3123(5) A) and as-
˚
cast (21.3123(6) A) samples, suggesting a phase with con-
stant composition. The symmetry and the lattice parame-
Z. Anorg. Allg. Chem. 2004, 630, 2267Ϫ2276
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W. Carrillo-Cabrera, S. Budnyk, Y. Prots, Y. Grin
Fig. 3 Thermal behavior of a Ba0.17Ge0.83 sample pre-annealed at
795 °C (DSC, heating rate 10 °C/min).
In an ordered crystal structure with a superstructure, se-
ven crystallographically independent atom sites are needed:
two Ba positions (Ba1 at the 16a site, Ba2 at the 48g site)
and five Ge positions (Ge1 at 24d, Ge2 at 32e, Ge2Ј at 96h,
Ge3 at 96h and Ge3Ј at 96h), as listed in Table 2. In contrast
to the number of Ba sites, which are equal (2) in both space
¯
groups, each Ge site in the space group Pm3n (parent struc-
¯
ture) splits into two sites in the space group Ia3d (super-
¯
Fig. 2 Microstructure of a Ba0.17Ge0.83 sample annealed at 795 °C
and fast cooled in water. (a) Precipitation of BaGeϳ5 and Ge in
the predominantly two-phase material (optical image, polarized
light). (b) Back-scattered electron image pointing up the different
kinds of germanium precipitation at the grain boundaries and in-
side the grains.
structure). In particular, the Ge1 site (6c, Pm3n) would split
¯
¯
into Ge1 (24d, Ia3d) and Ge1Ј (24c, Ia3d) sites, but the refi-
nement of the fully ordered structure for the annealed crys-
tal reveals that the Ge1Ј site is empty.
The structure refinement for the as-cast crystal indicated
that the Ge1 position is not fully occupied and that the
Ge1Ј site has a low occupancy parameter. The occupancies
of the Ge1 and Ge1Ј sites are complementary (Ge1 is the
major site and Ge1Ј is the minor site). The stronger elonga-
tion of the displacement ellipsoid of the Ge3 and Ge3Ј posi-
tions (average sites are not shown in Table 3) in the as-cast
crystal as compared to those in the annealed crystal (Table
2), confirms a partial order for these Ge neighbors of Ge1
and Ge1Ј, and split positions were introduced in the final
model for the as-cast crystal (Table 3). Also, the feature that
Ba2 effectively shifts towards the center point between two
vacancies at Ge1Ј (as compared to the average special posi-
ters of BaGeϳ5 could not be determined. The X-ray diffrac-
tion pattern is complex and rich in reflection peaks.
Crystal structure determination
Ideal atomic coordinates for Ba8Ge43 in the space group
¯
¯
Ia3d can be derived from those for the Pm3n parent struc-
¯
¯
ture, taking into account that a(Ia3d) ϭ 2 ϫ aЈ(Pm3n) and
the relationship between the crystallographic sites of both
space groups.
¯
tion for Ba2 in the Pm3n subcell) was also taken into ac-
count in the split model and a split position Ba2Ј (Table 3)
was introduced at a position shifted in a direction towards
the center between two vacancies at Ge1 which is opposite
to the shift of Ba2.
For a description of the Ba8Ge43 structure in the space
¯
group Pm3n (defect clathrate-I type structure, aЈ ϭ
˚
10.6565(2) A, Z ϭ 1), five crystallographically independent
atom positions were needed: two Ba positions (Ba1 at the
2a site, Ba2 at the 6d site) and three Ge positions (3 Ge1 at
6c, 16 Ge2 at 16i, 24 Ge3 at 24k) [1]. Because the Ge1 site
was only occupied by 50 %, a split model for the neighbo-
ring Ge3 sites (Ge3 Ǟ 0.50 Ge31 ϩ 0.50 Ge32) was refined,
and a short-range ordered model for the Ge environment
around Ba2 (with two well-distant Ge vacancies ᮀ) was
suggested [1].
Fully ordered crystal structure
As mentioned before, in the annealed (795 °C) and fast-coo-
led specimen the crystal structure is fully ordered (Table 2).
Thus, the Ge1 (24d) site is fully occupied and the comple-
mentary Ge1Ј (24c) site is totally empty. Fig. 4a shows a
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Z. Anorg. Allg. Chem. 2004, 630, 2267Ϫ2276

Ba8Ge43: a 2aЈϫ2aЈϫ2aЈ Superstructure of the Clathrate-I Type
Table 2 Atomic coordinates and displacement parameters (in pm2) for fully ordered Ba8Ge43. Standard deviations are given in parentheses.
Atom
Site
x
y
z
U11
U22
U33
U12
U13
U23
Ba1
Ba2
Ge1
Ge2
Ge2Ј
Ge3
Ge3Ј
16a
48g
24d
32e
96h
96h
96h
0
1/8
3/8
0.09144(3)
0.08999(3)
0.49942(3)
0.00111(3)
0
0
92(2)
U11
U11
U22
U22
U11
92(3)
116(3)
164(3)
2(2)
Ϫ22(2)
0
Ϫ15(2)
21(2)
Ϫ1(2)
Ϫ4(2)
U12
U12
0
U12
Ϫ13(2)
1(2)
U12
Ϫ17(2)
0
0.24720(2)
0
x
0.40513(3)
0.15332(3)
0.16667(3)
Ϫy ϩ 1/4
1/4
x
0.09097(3)
0.05629(3)
0.06549(3)
159(3)
113(5)
104(2)
103(3)
112(3)
128(3)
286(2)
100(3)
U11
103(3)
110(3)
153(3)
U12
10(2)
Ϫ2(2)
33(2)
8(2)
Table 3 Atomic coordinates and displacement parameters (in pm2) for partially ordered Ba8Ge43, split model. Standard deviations are given
in parentheses.
Atom
Site
x
y
z
U11(Uiso
)
U22
U33
U12
U13
U23
U12
Ba1
16a
48g
48g
24d
24c
32e
96h
96h
96h
96h
96h
0
1/8
1/8
3/8
0
0
104(2)
187(5)
235(35)
117(6)
176(28)
120(2)
119(3)
126(2)
126
U11
318(6)
U11
U22
3(2)
Ϫ19(2)
U12
U12
Ba2 a
Ba2Ј b
0.2470(1)
0.2540(8)
0
0
x
0.40565(3)
0.15315(5)
0.1644(4)
0.16690(6)
0.1540(4)
Ϫy ϩ 1/4
Ϫy ϩ 1/4
1/4
1/4
x
0.09110(3)
0.05621(5)
0.0642(4)
0.06554(5)
0.0554(4)
0(8)
a
Ge1
106(4)
U22
0
0
0
Ge1Ј b
Ge2
1/8
0.09147(3)
0.09028(3)
0.49957(5)
0.4990(4)
0.00090(5)
0.0009(4)
U11
119(3)
U11
109(3)
Ϫ18(2)
23(2)
U12
Ϫ16(2)
U12
15(2)
Ge2Ј
Ge3A a
Ge3B b
Ge3ЈA a
Ge3ЈB b
152(2)
152
a) Occ(Ba2) ϭ Occ(Ge1) ϭ Occ(Ge3A) ϭ Occ(Ge3ЈA) ϭ 0.880(4)
b) Occ(Ba2Ј) ϭ Occ(Ge1Ј) ϭ Occ(Ge3B) ϭ Occ(Ge3ЈB) ϭ 0.120
fragment of the superstructure equivalent to the unit cell of
the subcell in Pm3n. The Ba1 and Ba2 atoms are coordi-
Partially ordered crystal structure
¯
As stated before for the as-cast specimen, its crystal struc-
ture is not fully ordered and it was refined using a split
model (Table 3). Thus, the as-cast crystal (cooled in the
glove box, argon atmosphere) contains structural defects,
involving primarily the Ge1/Ge1Ј sites and their next neigh-
bors. Short-range ordered models for the germanium envi-
ronment around Ba2 (majority site) and Ba2Ј (minority
site) are proposed in Fig. 7. The environment of the major-
ity Ba2 site (associated with Ge vacancies at the 24c site;
Fig. 7a) is matching quit well with that of the fully ordered
structure (Fig. 6). The d(GeϪGe) bond lengths in the envi-
ronment of the minority Ba2Ј component (associated with
Ge vacancies at the 24d site) are somewhat different, but
nated by 20 and 22 Ge atoms, respectively (Figs. 4b, 4c).
The cage of Ba1 is a distorted Ge20 pentagondodecahedron
formed by 14 four-bonded (4b)Ge atoms and 6 three-
bonded (3b)Ge atoms. The Ge environment around Ba2 is
a 2-openings “nido” tetrakaidekahedron (Ge24Ϫ2) which
due to the missing Ge atoms is truncated at two corners,
resulting in a hexakaidecahedron with 10 pentagonal, 4
quadrangular, and 2 triangular faces. Thus, each Ba2 atom
is surrounded by 16 four-bonded (4b)Ge atoms and 6 three-
bonded (3b)Ge atoms. Particularly, the holes (ᮀ) at Ge1Ј
(24c) are arranged around a 41 four-fold screw axes to form
chiral helices along the {100} directions (Fig. 5). The Ba1
and Ba2 germanium environments are shown in Fig. 6 as
two condensed polyhedra with Ge labels and GeϪGe bond
lengths (see also Table 4).
˚
within a similar range (2.443 Ϫ 2.600 A).
For each Ba8Ge43 formula unit, 31 Ge atoms are four-
bonded (4b) and 12 Ge atoms (at Ge3Ј sites for the full
ordered structure) are three-bonded (3b). Assuming 2eϪ
GeϪGe bonds, the formal charge balance for the title
Superstructure in the X-ray powder data
Superstructure reflections in the X-ray powder diffraction
patterns of Ba8Ge43 were observed for the as-cast and the
annealed samples. Despite of cooling in water, the quen-
ching of Ba8Ge43 was not perfect, because the Ba8Ge43
samples contained minor amounts of its decomposition
products (the sealed quartz ampoule enclosing the sample
and crucible seems to be a relatively bad thermal conduc-
tor). The best annealed sample has about 97 wt-% Ba8Ge43
and the refinement of its X-ray powder diffraction data
using the Rietveld method (GSAS program [13]) confirms
the superstructure model for the bulk material (46 variables;
wR(P) ϭ 0.077, R(P) ϭ 0.059; R(F)Ge ϭ 0.048,
compound can be written as (Ba2ϩ)8((3b)Ge1Ϫ
)
12
((4b)Ge0)31(4eϪ). According to this, Ba8Ge43 is a metallic
Zintl phase [11] with few conduction electrons. Metallic or
semimetallic properties are expected for this compound. We
assume in the following that in the germanium framework
each three-bonded (3b)Ge3Ј atom in Ba8Ge43 has attached
a lone pair of electrons. In contrast to the so-called dan-
gling bonds observed on the surface of semiconductors like
silicon [12], the lone pairs in Ba6Ge25 and Ba8Ge43 can be
considered as inner dangling bonds.
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Fig. 5 Three condensed Ge24Ϫ2 defect tetrakaidecahedra with their
missing atoms (small grey cubes) showing the spiral substructure
of the Ge vacancies along the {100} directions.
Table 4 Interatomic distances for fully ordered Ba8Ge43 (cf. Fig. 6).
˚
˚
Atoms
Distance, A
Atoms
Distance, A
Ba1 ϪGe2
ϪGe2Ј
ϪGe3
ϪGe3Ј
Ba2 ϪGe3Ј
ϪGe3Ј
ϪGe3
3.375(1) 2ϫ
3.395(1) 6ϫ
3.481(1) 6ϫ
3.817(1) 6ϫ
3.421(1) 2ϫ
3.518(1) 2ϫ
3.552(1) 2ϫ
3.639(1) 2ϫ
3.726 2ϫ
3.810(1) 2ϫ
3.886(1) 2ϫ
3.925(1) 2ϫ
3.926(1) 2ϫ
3.973(1) 2ϫ
4.111(1) 2ϫ
4.323(1) 2ϫ
Ge1 ϪGe3
Ge2 ϪGe2
ϪGe3Ј
Ge2Ј ϪGe2Ј
ϪGe3
ϪGe3
ϪGe3Ј
Ge3 ϪGe2Ј
ϪGe2Ј
ϪGe1
ϪGe3Ј
Ge3Ј ϪGe2Ј
ϪGe2
2.528(1) 4ϫ
2.477(2)
2.566(1) 3ϫ
2.441(1)
2.511(1)
2.514(1)
2.531(1)
2.511(1)
2.514(1)
2.528(1)
2.611(1)
2.531(1)
2.566(1)
2.611(1)
2.182 4ϫ
ϪGe3
Ϫᮀ
ϪGe1
ϪGe2
Fig. 4 Fragments of the crystal structure of Ba8Ge43. (a) Distorted
pentagondodecahedra (black) and hexakaidecahedra (Z defect te-
trakaidecahedra, grey) in the germanium framework. (b) Ge20 pen-
tagondodecahedron centered by Ba1 with three-bonded (3b)Ge and
four-bonded (4b)Ge germanium atoms. (c) Germanium environ-
ment around Ba2. Two Ge atoms are missing in the Ge24Ϫ2 defect
tetrakaidecahedron, producing three-bonded (3b)Ge species
around the defects.
ϪGe2Ј
ϪGe2Ј
ϪGe3Ј
ϪGe2Ј
ϪGe3
ϪGe3
Ϫᮀ
Further crystallographic remarks
Even if the unit cell of the 2aЈϫ2aЈϫ2aЈ superstructure of
Ba8Ge43 is relative large, the arrangement of the structural
building units and their connectivity nets can be described
with few characteristic graphs or diagrams. The point con-
figuration for Ba1 (16a) and for the ideal position of Ba2
R(F)Ba8Ge43 ϭ 0.058; ϳ3 wt-% Ge). The strongest super-
structure reflections of Ba8Ge43 are outlined in Fig. 8,
where a relevant part of the X-ray diffraction pattern is
shown.
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Ba8Ge43: a 2aЈϫ2aЈϫ2aЈ Superstructure of the Clathrate-I Type
Fig. 6 Coordination polyhedra of Ba1 and Ba2 sharing a penta-
gonal face with the lengths of the GeϪGe bonds for the fully orde-
red structure.
Fig. 8 The observed X-ray powder diffraction pattern of an an-
nealed Ba8Ge43 sample in the range 26° < 2θ < 41°. The Bragg
peak positions (vertical bars) and the difference profile plot (solid
line, bottom part) are shown. The strongest superstructure reflec-
tions of Ba8Ge43 are indexed. A peak of the minority phase (Ge)
is highlighted.
the shortest distance), the I2 and W2 graphs (called “frame-
works” in [14]) are obtained.
One feature of great interest for us is the graph related to
the holes at Ge1Ј (24c) in the fully ordered structure. For
the as-cast specimens, the minority vacancies at Ge1 (24d)
site may also be ordered, and the corresponding graph is
also considered here. The inspection of the point configura-
tions reveals that the related Ge1 (24d) and Ge1Ј (24c) sites
are far from being “equivalent“. The point configuration
for the Ge1Ј (24c) site is V* (three-connected nodes) and
for the Ge1 (24d) site it is S* (four-connected nodes). While,
the V* graph consists of two interpenetrating enantio-
morphic graphs, namely the VϪ and the Vϩ graphs (Fig 9a,
orange and blue nets, respectively) [14Ϫ17], the S* graph is
only one net (yellow, Fig. 9b) [14, 17]. Each vacancy (ᮀ) is
represented by its surrounding Ge4 tetrahedron (orange or
blue) of Ge3Ј atoms for V* graph in Fig. 9a (or yellow
tetrahedra of Ge3B atoms for the S* graph in Fig. 9b). The
¯
periodic nodal surfaces (PNS) [18] I2ϪY** (also called Ia3d
1
1
¯
< (211)0(220)0> Ia3d, with the notation used in [19]) and
the complementary one C(I2ϪY**), also called Ia3d <
(211)π(220)0> Ia3d, envelope the V* and S* graphs, respec-
¯
1
1
¯
tively [15, 17] (Figs. 9a and 9b).
Additional inspection reveals that periodic surfaces deri-
1
¯
¯
ved from the PNS Ia3d < (211)π> Ia3d [17, 20] with isovalue
Fig. 7 Short-range ordered models with corresponding GeϪGe
bond lengths for the partially ordered (as-cast) crystal. (a) Germa-
nium environment around the majority Ba2 site. (b) Ge24Ϫ2 poly-
hedron of the minority Ba2Ј site.
1
¯
¯
f(x,y,z) ϭ 0.63 (further denoted as ΗIa3d < (211)π> Ia3dΗf ϭ
0.63) envelopes very closely the (ᮀ)Ge4 tetrahedra. Thus, for
the description of the V* tetrahedral arrangement the iso-
surface ΗIa3d < (211)π> Ia3dΗf ϭ 0.63 is the adequate one, and
for the S* tetrahedral array the isosurface ΗIa3d < (211)π>
1
¯
¯
1
¯
(48g with y ϭ 1/4) are I2 and W2, respectively. By connec-
ting all the positions of these point configurations (using
¯
Ia3dΗf ϭ Ϫ0.63 is sufficient. Fig. 9c illustrates the ordered
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W. Carrillo-Cabrera, S. Budnyk, Y. Prots, Y. Grin
Fig. 9 Topology of the Ba8Ge43 structure. (a) I2ϪY** periodical nodal surface with the V* graph of the Ge1Ј sites. (b) Complementary
C(I2ϪY**) periodical nodal surface with the S* graph of the Ge1 sites. The V* graph is composed of the interpenetrating VϪ (orange net)
and Vϩ (blue net) partial graphs. (c) Ordered Ba8Ge43 structure (blue Ge20 pentagondodecahedra, beige Ge24Ϫ2 defect tetrakaidecahedra)
1
¯
¯
with the isosurface ΗIa3d < (211)π > Ia3dΗf ϭ 0.63 as a space partitioner. The white 3(b)Ge3Ј atoms lie at the isosurface. The dark green
labyrinths contain the lone pairs of the 3(b)Ge3Ј species, as well as the Ge2ϪGe2 dumbbells.
1
¯
¯
Ba8Ge43 structure together with the ΗIa3d < (211)π> Ia3dΗf ϭ
0.63
the 3ϱ[RhBi8/2] polyhedral framework in RhBi4 structure
with a hyperbolic lone-pair structure in the double channels
of the Y** gyroide (the I2ϪY** nodal surface is comple-
mentary to the Y** gyroide) [15].
isosurface, revealing the labyrinth organization. The
(3b)Ge3Ј atoms are located on the isosurface and the lone
pairs are directed into the green labyrinths. The neighboring
Ge2ϪGe2 dumbbells are also located in the green laby-
rinths.
The symmetry of the defect-free structure of the cla-
¯
thrate-I type belongs to the space group Pm3n. Our deter-
It is interesting that the lone pairs in the full ordered
Ba8Ge43 structure occupy a part of the double channels of
the I2ϪY** PNS (blue in Fig. 9a). The same PNS envelopes
mination of the fully disordered variant of the Ba8Ge43
structure [1], resulted in exactly a half-occupied position
Ge1. Consulting the International Tables for Crystallogra-
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Ba8Ge43: a 2aЈϫ2aЈϫ2aЈ Superstructure of the Clathrate-I Type
Fig. 10 Group-subgroup relationship between the fully disordered and fully ordered Ba8Ge43 structures, using the formalism [22]. The table
shows the corresponding atomic positions (rounded numbers) with Wyckoff symbols. By ordering of the vacancies (ᮀ) at the 24c sites,
only the initial positions Ge2 and Ge3 subdivide into two independent positions each.
phy [21], one can easily deduce that the real structure of
Note added in proof: A similar 2 ϫ 2 ϫ 2 superstructure
was found independently for the rubidium-tin clathrate
Rb8Sn44ᮀ2 [23]. In this crystal structure, the superstructure
is caused by a partial ordering of the vacancies.
Ba8Ge43 described here represents a maximal non-iso-
¯
morphic subgroup of the space group Pm3n namely the va-
¯
riant IIb: Ia3d (aЈ ϭ 2a, bЈ ϭ 2b, cЈ ϭ 2c).This group-sub-
group relationship leads to a ’klassengleich’ [22] (class-equi-
Acknowledgments. Prof. Dr. H. G. von Schnering and Dr. M. Baitin-
ger are gratefully acknowledged for valuable comments. The au-
thors thank Dr. R. Ramlau and Mrs. P. Scheppan for the SEM/
EDXS study, Dr. R. Niewa and Mrs. S. Müller for the DTA/DSC
measurements, and Dr. R. Cardoso Gil and Mr. S. Hückmann for
recording the X-ray diffraction patterns.
valent) symmetry reduction of index 4 with enlarged cell,
¯
¯
¯
i.e. Pm3n (P 42/m 3 2/n) Ϫ k4 (2a1, 2a2, 2a3) Ǟ Ia3d (I 41/a
¯
3 2/d). The group-subgroup and atomic positions relations-
hips are summarized in Fig. 10.
The adoption of the 24c site for the ᮀ vacancies (24 per
unit cell) in fully ordered Ba8Ge43 crystals means that the
four lone electron pairs associated with each Ge vacancy
prefer, for spatial reasons, to surround a site of lower sym-
metry, i.e. 24c (site symmetry 222) instead of the alternative
References
[1] W. Carrillo-Cabrera, J. Curda, K. Peters, S. Paschen, M.
Baenitz, Yu. Grin, H. G. von Schnering, Z. Kristallogr. NCS
2000, 215, 321.
¯
site 24d (site symmetry 4).
[2] E. Zintl, G. Brauer, Z. Phys. Chem. 1933, B20, 245.
[3] H. Schäfer, Annu. Rev. Mater. Sci. 1985, 15, 1.
[4] H. Fukuoka, J. Kiyoto, S. Yamanaka, J. Solid State Chem.
2003, 175, 237.
[5] R. F. W. Herrmann, K. Tanigaki, T. Kawaguchi, S. Kuros-
hima, O. Zhou, Phys. Rev. 1999, B60, 13245.
[6] W. Carrillo-Cabrera, J. Curda, H. G. von Schnering, S. Pa-
schen, Yu. Grin, Z. Kristallogr. NCS 2000, 215, 207.
[7] STOE & Cie GmbH, STOE WinXPOW, Version 1.06, Hil-
pertstr. 10, D-64295 Darmstadt, 2001.
[8] Bruker Analytical X-ray Systems, XPREP-data preparation
and reciprocal space exploration, Ver. 5.1, 1997.
[9] G. M. Sheldrick, SHELXL-97. Program for the refining of
crystal structures, University of Göttingen, Germany 1997.
[10] Th. B. Massalski (Ed. in Chief), H. Okamoto, P. R. Subra-
mian, L. Kacprzak (Eds.), Binary Alloy Phase Diagrams (2nd
Edition), Vol. 1, ASM International 1996.
4 Conclusions
The Ba8Ge43 phase is stable between 770 °C and 810 °C,
and contains defects in its Ge network which are fully orde-
¯
¯
red in a superstructure (Ia3d) of the clathrate-I type (Pm3n)
˚
¯
¯
with a(Ia3d) ϭ 21.3123 A ϭ 2 ϫ aЈ(Pm3n). The vacancy
ordering can be disrupted if the samples are not annealed
or after annealing they are cooled slowly.
The space group of the defect-free clathrate-I structure
¯
¯
is Pm3n. The real structure of Ba8Ge43 (Ia3d) represents a
maximal non-isomorphic subgroup for the space group
¯
Pm3n in the case of ordering. This group-subgroup rela-
tionship produces a ’klassengleich’ symmetry reduction of
index 4.
Z. Anorg. Allg. Chem. 2004, 630, 2267Ϫ2276
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 2004 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
2275

W. Carrillo-Cabrera, S. Budnyk, Y. Prots, Y. Grin
[11] J. T. Zhao, J. D. Corbett, Inorg. Chem. 1995, 34, 374.
[12] G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Phys. Rev. Lett.
1983, 50, 120.
[13] R. B. Von Dreele, A. C. Larson, GSAS generalized structure
analysis system. M. Lujan Jr. Neutron Scattering Center,
MS-H805, Los Alamos National Laboratory, Los Alamos,
NM 87545, USA 2000.
[14] E. Hellner, E. Koch, A. Reinhardt, The homogeneous Frame-
works of the Cubic Crystal Structures, Physik Daten, Fachin-
formationszentrum Karlsruhe Nr. 16-2, 1981.
[16] W. Carrillo-Cabrera, M. Somer, K. Peters, H. G. von Schne-
ring, Chem. Ber. 1996, 129, 1015.
[17] A. Zürn, Dissertation, Universität Stuttgart 1998.
[18] H. G. von Schnering, R. Nesper, Z. Phys. 1991, B83, 407.
[19] Yu. Grin, U. Wedig, F. Wagner, H. G. von Schnering, A.
Savin, J. Alloys Compd. 1997, 255, 203.
[20] H. G. von Schnering, Private communication.
[21] T. Hahn (Ed.), International Tables for Crystallography, Vol.
A, Chapter 7, Kluver Academic, Dordrecht, The Nether-
lands 1989, p. 672.
[15] Yu. Grin, U. Wedig, H. G. von Schnering, Angew. Chem.
1995, 107, 1318; Angew. Chem. Int. Ed. Engl. 1995, 34, 1204.
[22] H. Bärnighausen, MATCH-Commun.Math. Chem. 1980, 9, 139.
[23] F. Dubois, T. F. Fässler, Z. Anorg. Allg. Chem. 2004, 630, 1718.
2276
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