The metallic Zintl phase Ba3Si4 - Synthesis, crystal structure, chemical bonding, and physical properties

Article abstract of DOI:10.1002/zaac.200800116

The Zintl phase Ba₃Si₄ has been synthesized from the elements at 1273 K as a single phase. No homogeneity range has been found. The compound decomposes peritectically at 1307(5) K to BaSi₂ and melt. The butterfly-shaped Si₄^6- Zintl anion in the crystal structure of Ba₃Si₄ (Pearson symbol tP28, space group P4₂/mnm, a = 8.5233(3) A, c = 11.8322(6) A) shows only slightly different Si-Si bond lengths of d(Si-Si) = 2.4183(6) A (1x) and 2.4254(3) A (4x). The compound is diamagnetic with χ ≈ -50 × 10^-6 cm³ mol^-1. DC resistivity measurements show a high electrical resistivity (ρ(300 K) ≈ 1.2 × 10 ^-3 Ω m) with positive temperature gradient dρ/dT. The temperature dependence of the isotropic signal shift and the spin-lattice relaxation times in ²⁹Si NMR spectroscopy confirms the metallic behavior. The experimental results are in accordance with the calculated electronic band structure, which indicates a metal with a low density of states at the Fermi level. The electron localization function (ELF) is used for analysis of chemical bonding. The reaction of solid Ba₃Si₄ with gaseous HCl leads to the oxidation of the Si₄^6- Zintl anion and yields nanoporous silicon.

Full text of DOI:10.1002/zaac.200800116

Articles
DOI: 10.1002/zaac.200800116
The Metallic Zintl Phase Ba3Si4 ؊ Synthesis, Crystal Structure, Chemical
Bonding, and Physical Properties
Umut Aydemira, Alim Ormecia, Horst Borrmanna, Bodo Böhmea, Fabio Zürcherb, Burcu Uslud,
Thorsten Goebela, Walter Schnellea, Paul Simona, Wilder Carrillo-Cabreraa, Frank Haarmanna,
Michael Baitingera, Reinhard Nesperb, Hans Georg von Schneringc, and Yuri Grina,*
a Dresden, Max-Planck-Institut für Chemische Physik fester Stoffe
b Zürich / Switzerland, ETH, Laboratorium für Anorganische Chemie
c Stuttgart, Max-Planck-Institut für Festkörperforschung
d Istanbul / Turkey, Koc¸ University, Chemistry Department
Received March 26th, 2008.
Abstract. The Zintl phase Ba3Si4 has been synthesized from the
elements at 1273 K as a single phase. No homogeneity range has
been found. The compound decomposes peritectically at 1307(5) K
NMR spectroscopy confirms the metallic behavior. The experimen-
tal results are in accordance with the calculated electronic band
structure, which indicates a metal with a low density of states at
the Fermi level. The electron localization function (ELF) is used
for analysis of chemical bonding. The reaction of solid Ba3Si4 with
6Ϫ
to BaSi2 and melt. The butterfly-shaped Si4 Zintl anion in the
crystal structure of Ba3Si4 (Pearson symbol tP28, space group
6Ϫ
˚
˚
P42/mnm, a ϭ 8.5233(3) A, c ϭ 11.8322(6) A) shows only slightly
gaseous HCl leads to the oxidation of the Si4 Zintl anion and
yields nanoporous silicon.
˚
different Si-Si bond lengths of d(SiϪSi) ϭ 2.4183(6) A (1ϫ)
and 2.4254(3) A (4ϫ). The compound is diamagnetic with
˚
χ ഠ Ϫ50 ϫ 10Ϫ6 cm3 molϪ1. DC resistivity measurements show a
high electrical resistivity (ρ(300 K) ഠ 1.2 ϫ 10Ϫ3 Ω m) with positive
temperature gradient dρ/dT. The temperature dependence of the
isotropic signal shift and the spin-lattice relaxation times in 29Si
Keywords: Barium; Tribariumtetrasilicide; Zintl phases; Phase
diagrams; Electronic structure; Chemical bonding; Nanoporous
silicon; Crystal structures
1 Introduction
[Ba2ϩ]3[(3b)Si1Ϫ]2[(2b)Si2Ϫ]2, being in agreement with the
Zintl concept [4, 5]. Investigations on the oxidation be-
havior of binary compounds with alkali metals and main
group elements led to the preparation of new phases with
framework structures [6Ϫ8]. The extension of these studies
to the compounds of alkaline earth metals was the next
logical step, thus attracting our attention to Ba3Si4.
In the present study, the crystal structure was re-deter-
mined to higher accuracy. The binary system BaϪSi was
reinvestigated in the range of 50Ϫ60 at-% Si and the syn-
thesis of Ba3Si4 was optimized. Electrical and magnetic
properties were measured on single-phase samples and
compared with the results of quantum mechanical calcu-
lations. The electronic transport properties were confirmed
by extensive 29Si NMR spectroscopy experiments, which are
independent from grain boundaries and contact problems.
Finally, the chemical reactivity of Ba3Si4 and its reaction
with gaseous HCl were investigated.
Intermetallic compounds of alkali metals and earth alkali
metals with group 14 elements form crystal structures with
a broad variety of polyanions with covalent bonds, which
follow the Zintl-Klemm concept [1]. Numerous crystal
structures of Zintl phases were determined, but only little
is known about their physical properties due to their high
reactivity against oxygen and moisture. It is expected that
Zintl phases of closed shell cations and polyanions should
be in general diamagnetic semiconductors. However, atomic
interactions in solid phases influence the electronic struc-
ture, which may result in a nonzero density of states (DOS)
at the Fermi energy EF [2, 3]. Therefore, more precise pre-
dictions of physical properties need quantum mechanical
calculations as demonstrated, e.g., by the unexpected
metallic behavior of single phase Ba3Si4. This compound
contains quasi-isolated Si4
1969 by Eisenmann et al. [4]. The butterfly shaped anion
6Ϫ
anion, as first reported in
was explained with the formal charge distribution
2 Experimental Details
2.1 Preparation
* Prof. Dr. Yu. Grin
Max-Planck-Institut für Chemische Physik fester Stoffe
Nöthnitzer Straße 40
01187 Dresden/Germany
E-mail: grin@cpfs.mpg.de
Ba3Si4 Ϫ 0.7858 g (5.7 mmol) Ba (ChemPur, 99.9 %) and 0.2143 g
(7.6 mmol) Si (ChemPur, 99.999 %) were sealed under argon in a
Ta container. The container was further fused under argon in a
silica ampoule and placed vertically in a tube furnace. In the first
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Y. Grin et al.
step of the reaction, the sample was heated in 3 hours to 1473 K,
annealed for 1 h at this temperature, and then quenched to room
temperature. Alternatively, induction heating was used as the first
step. The heating was performed slowly enough to prevent the
evaporation of Ba. In the second step, the sample was annealed for
3 days at 1273 K. The reaction product consists of metallic shining,
brittle, well-shaped crystals and is a single phase according to
XRPD and SEM (Fig. 1). It is very sensitive to air and moisture;
therefore all sample manipulations were carried out in an argon-
filled glove box. EDXS analysis on three different pieces revealed
the chemical composition Ba3.0(1)Si4.1(1). A reaction under same
conditions in open glassy carbon crucibles, welded in tantalum am-
poules, lead always to the formation of small amounts of BaSi2 as
a by-product. Evaporation of Ba was not observed at this tempera-
ture.
Table 1 Crystallographic data of Ba3Si4.
Formula; molar mass
Ba3Si4; 524.323 g molϪ1
tetragonal; P42/mnm (no. 136)
8.5233(3); 11.8322(6)
Crystal system; space group
˚
˚
a / A; c / A
3
˚
Unit cell volume
859.57(6) A
4; 4.0516(3)
Z; ρcalc/(g cmϪ3
)
Diffractometer
Wave length λ / A; monochromator
Crystal size
T / K
RIGAKU Spider
0.56087; multilayer-optics
40 ϫ 50 ϫ 70 μm
295
˚
θ range
Indexes ranges
2.67° to 40.00°
Ϫ19 Յ h Յ 13, Ϫ18 Յ k Յ 10,
Ϫ26 Յ l Յ 20
μ / mmϪ1
7.424
F(000) / e
896
Multi-scan
Absorption correction
Reflections collected; independent
Refinement method
Refined parameters
Residuals [I > 2σ(I)]
Residuals (all data)
Goodness-of-fit on F2
Extinction coefficient
Largest diff. peak and hole
24327; 2931 [Rint ϭ 0.017]
Full-matrix least-squares on F2
24
R1 ϭ 0.015, wR2 ϭ 0.023
R1 ϭ 0.021, wR2 ϭ 0.024
1.212
0.00471(12)
1.372 and Ϫ0.973 e / A
3
˚
2.2 Characterization
X-Ray powder diffraction: The samples were finely ground under
argon in an agate mortar and placed on a sample holder between
two polyimide X-Ray films (d ϭ 7.5 μm, Chemplex). The X-ray
films were sealed with vacuum grease (Lithelen, Leybold), which
protected the samples from oxidation during the measurement.
Phase analysis on powder was performed with X-ray Guinier dif-
fraction technique (Huber G670 camera, Cu Kα1 radiation, λ ϭ
Fig. 1 SEM images of Ba3Si4. The lamellar structure is an indica-
tion of the formation from the melt. The sample is homogeneous
according to EDXS.
Ba329Si4: A sample for NMR experiments was synthesized with the
same reaction conditions from 98.70 % enriched 29Si (Isoflex). No
silicon-containing impurity phases were detected in the 29Si NMR
experiment. XRPD shows single-phase Ba3Si4.
˚
1.540598 A, graphite monochromator, 5° Յ 2θ Յ 100°, Δ2θ ϭ
˚
0.005°, LaB6, NIST standard, a ϭ 4.1569162(97) A at 295.5 K).
The reflection positions were determined by a single profile fit and
the unit cell parameters were calculated from a least-square refine-
ment [9].
BaSi: 0.8302 g (6.05 mmol) Ba and 0.1698 g (6.05 mmol) Si were
sealed under argon in a Ta ampoule. The sample was heated in
24 h to 1473 K and then annealed for 2 h at this temperature. The
ampoule was quenched in water to room temperature and then
annealed for 3 more days at 1073 K. The reaction product is met-
allic shining, brittle, and very sensitive to air and moisture. XRPD
did not show any by-products.
X-ray single crystal diffraction: Single crystals were selected from
the sample under argon and sealed in Mark-tubes (borosilicate
glass, л ϭ 0.2 mm, d ϭ 0.01 mm, Hilgenberg). The measurements
were performed with a rotating anode diffractometer (RIGAKU
˚
Spider, Varimax optical system, Ag Kα radiation λ ϭ 0.56087 A).
Absorption correction was performed with a multi-scan procedure
and the crystal structure refinement by employing a full-matrix le-
ast-squares procedure [10]. Details concerning the data collection
and structure refinement are given in Table 1.
BaSi2: 0.7097 g (5.17 mmol) Ba and 0.2903 g (10.34 mmol) Si were
placed in a glassy carbon crucible. The sample was melted under
argon with an induction furnace and cooled down within few mi-
nutes to room temperature. No Ba evaporation was observed. The
fine crystalline powder is sensitive to air and moisture and did not
contain any by-product according to XRPD. Larger crystals were
obtained by subsequent annealing at 1273 K for 2 d.
Differential scanning calorimetry: DSC measurements were per-
formed on a Netzsch DSC 404 C calorimeter from room tempera-
ture up to 1573 K with 10 K minϪ1 heating rate. About 50 mg of
substance were measured in closed Nb ampoules (л 5 mm, 600 mg)
under argon atmosphere.
Nanoporous silicon: Fine powder of Ba3Si4 (13 mg, 0.025 mmol)
and dry NH4Cl (40 mg, 0.75 mmol) were placed into separate
aluminum oxide crucibles and were sealed together into a quartz
ampoule under Ar atmosphere. Subsequently, the ampoule was an-
nealed in a tube furnace at 873 K for 2.5 hours. XRPD of the
reaction product shows the reflections of BaCl2. The product was
washed with distilled water to dissolve BaCl2. Brownish powder
was obtained which is amorphous according to XRPD. All par-
ticles which were investigated by EDXS with high-resolution SEM
consist only of silicon. According to EDXS the overall sample con-
tains less than 1 wt-% Ba.
Magnetic susceptibility: A polycrystalline sample of Ba3Si4 (m ഠ
108 mg) was sealed under He (ഠ 400 mbar) in a quartz ampoule
and measured in a SQUID magnetometer (MPMS-XL7, Quantum
Design) in fields μ0H from 2 mT to 7 T and a temperature range
from 1.8 K to 400 K. The contribution of the sample holder was
subtracted.
Electrical resistivity: Electrical resistance was measured with a four-
point dc method on an irregular crystalline piece (ca. 3.5 ϫ 2.1 ϫ
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The Metallic Zintl Phase Ba3Si4
2
˚
Table 2 Atomic coordinates and displacement parameters (in A )
for Ba3Si4.
Atom
Site
x
y
z
Ueq
Ba(1)
Ba(2)
Ba(3)
Si(1)
4f
4e
4d
8i
0.33515(1)
0
0
0.90055(3)
0.20077(3)
x
0
0.01466(2)
0.01031(1)
0.01212(1)
0.01134(4)
0.01359(5)
0
0.16963(1)
1/4
0
1
/
2
0.30007(3)
x
Si(2)
8j
0.35403(3)
Atom
U11
U22
U33
U23 ϭ U13
U12
Ba(1)
Ba(2)
Ba(3)
Si(1)
0.01296(2)
0.01111(2)
0.01186(2)
0.01005(9)
0.01303(6)
U11
U11
U11
0.01263(10)
U11
0.01805(3)
0.00871(2)
0.01264(3)
0.01135(9)
0
0
0
0
Ϫ0.00047(2)
0.00067(2)
0
Ϫ0.00111(8)
0.00064(8)
Si(2)
0.01472(11) Ϫ0.00326(6)
Ueq is defined as one third of the trace of the orthogonalized Uij tensor, which is exp
(Ϫ2π2 [h2a*2U11 ϩ ··· ϩ 2 h k a* b* U12])
1.7 mm3). The undefined contact geometry leads to a large inaccur-
acy (ഠ 50 %) of the absolute resistivity.
NMR: For NMR measurements, fine powder of Ba3Si4 was diluted
in the volume ratio of about 1:5 with dry GeO2 (Chempur,
99.999 %) to avoid a skin effect of the electric-conducting material
and eddy currents during MAS experiments. The mixture was en-
closed under Ar into a ZrO2 rotor (л ϭ 4 mm). The spectra were
recorded using a Bruker AVANCE spectrometer (B0 ϭ 11.74 T, ν ϭ
99.364 MHz for 29Si); MAS and static wide line experiments were
performed with a 4 mm standard triple resonance probe (Bruker).
The spectral parameters of the MAS signals (νrot ϭ 2.65 kHz) were
determined by a single pulse sequence with 1.5 μs pulse duration.
A Hahn-echo pulse sequence with 1.5 μs and 3.0 μs pulse duration
and a inter-pulse delay of ν ϭ 60 μs was used for the static measure-
ment. A saturation recovery pulse sequence was used for spin-lat-
tice relaxation (T1) experiments applying a sample rotation fre-
quency of 7.5 kHz. 30 relaxation delays equally spaced on logarith-
mic time scale were measured to determine T1 for each of seven
measurement temperatures between 170 K to 298 K. All experi-
ments were performed by eight-fold phase cycling of the pulse se-
quences. The spectral parameters of the signals were determined
from the line shapes by least-squares analysis with the program
SIMPSON [11]. The definitions from Bak et al. are used for the
isotropic signal shift, the anisotropic signal shift and the asymmetry
parameter [11]. The signal shifts are referred to tetramethyl-
silane (TMS).
Fig. 2 Phase diagram of the system Ba/Si in the range of
45Ϫ67 at-% Si. Grey circles show thermal effects of the liquidus
curve. Half-filled circles indicate the phases observed by XRPD
(without annealing).
functions are obtained by solving an effective Schrödinger equation
applying a spherically averaged crystal potential and a confining
potential [13]. The confining potential forces the basis functions to
be more localized than the genuine atomic orbitals. The presented
calculations were performed within the density functional theory
[14] in the local density approximation (LDA) [15]. The Perdew-
Wang parameterization [16] was chosen for the exchange-corre-
lation potential. The basis sets for Si and Ba consisted of 2s, 2p /
3s, 3p, 3d and 5s, 5p / 6s, 6p, 5d, respectively. Convergence with
respect to k point number was carefully checked. The atomic par-
ameters from single-crystal diffraction data (Tab. 2) were used in
the calculations. The electron localization function (ELF) [17, 18]
was calculated using a module recently implemented in the FPLO
method [19]. Topological analysis of the electron density (ED) and
ELF was performed using the program Basin [20].
SEM: The microstructure of the Ba3Si4 samples was investigated
with a Philips XL 30 Scanning Electron Microscope (LaB6 cath-
ode). Energy dispersive X-ray spectroscopy (EDXS) was performed
with an attached EDAX Si (Li) detector. The composition of nano-
porous silicon particles was determined using a high resolution
scanning electron microscope, Quanta 200 FEG ESEM (FEI),
which was equipped with a Schottky field emission gun (FEG) and
an EDAX Si (Li) detector.
3 Results and Discussion
3.1 Phase relations
In the only former report of the binary system BaϪSi [21],
two phases BaSi and BaSi2 were evaluated. Meanwhile, the
crystal structures of the phases Ba2Si [22, 23], Ba5Si3 [24,
25], BaSi [26, 27], Ba3Si4 [4] and BaSi2 [28Ϫ29] are known.
Furthermore, Ba6Si25 [30] and Ba8ϪxSi46 [31] have been ob-
tained by high pressure experiments. We reinvestigated the
region 45 Ϫ 66.7 at-% Si by XRPD, DSC and microstruc-
ture analysis. The compositions of the samples and the
phase equilibria are shown in Figure 2, the lattice param-
eters are listed in Table 3. Due to the high sensitivity of
TEM: Fine powder of the sample was deposited on a holey-carbon
film supported by a copper grid and studied using a Technai 10
electron microscope (FEI).
Calculation procedure
The all-electron full-potential local orbital minimal basis method,
FPLO [12], was used in this study. The atomic orbital-like basis
Z. Anorg. Allg. Chem. 2008, 1651Ϫ1661
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1653

Y. Grin et al.
Table 3 Lattice parameters of selected compounds in the system
BaϪSi.
Table 4 Interatomic distances for Ba3Si4.
˚
d / A
Atoms
Compound Space group Lattice parameters Method
Reference
˚
Ba(1)
Ba(2)
Ϫ Si(2)
Ϫ Si(1)
Ϫ Si(1)
Ϫ Si(2)
Ϫ Si(1)
Ϫ Si(2)
Ϫ Si(2)
Ϫ Si(1)
Ϫ Si(1)
Ϫ Si(2)
Ϫ Ba(2)
Ϫ Ba(3)
Ϫ Ba(1)
Ϫ Ba(1)
Ϫ Si(1)
Ϫ Ba(2)
Ϫ Ba(3)
Ϫ Ba(1)
4 ϫ
2 ϫ
2 ϫ
2 ϫ
4 ϫ
2 ϫ
4 ϫ
4 ϫ
1 ϫ
2 ϫ
2 ϫ
2 ϫ
1 ϫ
1 ϫ
2 ϫ
2 ϫ
2 ϫ
2 ϫ
3.5761(3)
3.7017(3)
3.7163(3)
3.2584(3)
3.3598(3)
3.6177(3)
3.3088(2)
3.5174(2)
2.4183(6)
2.4254(3)
3.3598(3)
3.5174(2)
3.7017(3)
3.7163(3)
2.4254(3)
3.2584(3)
3.3088(2)
3.5761(3)
in A
Ba3Si4
Ba3Si4
P42/mnm
P42/mnm
a ϭ 8.5233(3)
c ϭ 11.8322(6)
Powder; Cu Kα1 This work
2θmax ϭ 100°;
115 hkl
LaB6 standard
Ba(3)
Si(1)
a ϭ 8.5223(4)
c ϭ 11.830(1)
Powder; Cr Kα1 This work
2θmax ϭ 100°;
42 hkl
LaB6 standard
Ba3Si4
BaSi
P42/mnm
a ϭ 8.52(2)
c ϭ 11.84(2)
Single crystal,
Mo KͰ1
[4]
Cmcm
a ϭ 5.0404(8)
b ϭ 11.937(2)
c ϭ 4.1389(7)
Powder; Cu Kα1 This work
2θmax ϭ 100°;
51 hkl
Si(2)
LaB6 standard
BaSi
Cmcm
Pnma
a ϭ 5.0430(8)
b ϭ 11.933(2)
c ϭ 4.1395(8)
Single crystal,
Mo Kα1
[27]
decomposes peritectically at 1216(5) K to Ba3Si4 and a Ba-
rich melt. The lattice parameters of single phase Ba3Si4 are
identical within e.s.d. with all equilibrium samples in the
two-phase regions with BaSi2 and BaSi. Thus the com-
pound exists at a constant composition.
BaSi2
a ϭ 8.9314(3)
b ϭ 6.7271(2)
c ϭ 11.5345(3)
Powder; Cu Kα1 This work
2θmax ϭ 100°;
105 hkl LaB6
standard
BaSi2
Pnma
a ϭ 8.92(6)
b ϭ 6.75(6)
c ϭ 11.57(6)
Single crystal,
Mo Kα1
[29]
3.2 Crystal structure
BaSi, Ba3Si4 and BaSi2 to oxygen and moisture, and to en-
sure the equilibrium pressure, DSC measurements were per-
formed in welded Nb crucibles. However, the metal cru-
cibles react rapidly with all silicon containing melts and,
therefore, the liquidus line could only be approximated. To
investigate, which phases are formed from the melt, the
samples were melted by induction heating in open glassy
carbon crucibles under Ar and cooled down within few mi-
nutes to room temperature.
The first structure determination [4] resulted in unexpec-
tedly short and different SiϪSi bond lengths of about
6Ϫ
˚
˚
2.29 A (1ϫ) and 2.34 A (4ϫ) in the Si4
polyanion
(Weißenberg-film data). Assuming an average oxidation
number of 1.5Ϫ on the silicon atoms [5], the average dis-
¯
tance d (SiϪSi) within the polyanion is expected to be be-
tween the average distances in BaSi2 (2.40 A, Si1Ϫ) and BaSi
˚
2Ϫ
˚
¯
(2.50 A, Si ). The previously observed average distance d
˚
(SiϪSi) ϭ 2.33 A is significantly smaller. The present crys-
BaSi2 (66.7 at-% Si) is formed congruently from the melt.
The melting point was determined to be 1447(5) K, which
is in accordance with the reported phase diagram [21]. Be-
tween 57 and 66.7 at-% Si, a mixture of Ba3Si4 (57.1 at-%
Si) and BaSi2 is always formed after cooling from the melt,
indicating a peritectic formation of Ba3Si4. The peritectic
temperature of Ba3Si4 was determined to be 1307(5) K.
DSC measurements in Nb ampoules on single-phase
samples of Ba3Si4 can be misleading, because a sufficient
amount of Si reacts always with the Nb crucible, which
might give the wrong impression of a congruent instead of
a peritectic formation of Ba3Si4. Nevertheless, SEM pic-
tures of Ba3Si4 samples, which were cooled from the melt
within few minutes, show that the phase was directly crys-
tallized from the melt and not formed by diffusion in solid
state (Fig. 1). This might also explain why the synthesis of
a single phase was only possible in Ta with short annealing
times and not in inert glassy carbon crucibles. In the molten
state, a part of Si reacts with the crucible wall and therefore
Ba3Si4 instead of BaSi2 crystallizes from the melt. Towards
higher Ba content, Ba3Si4 is in equilibrium with BaSi, which
tal structure data resolve this discrepancy. In agreement
with the previous data, Ba3Si4 crystallizes in the space
group P42/mnm (no. 136) with four formula units in the
tetragonal unit cell (Tab. 1Ϫ4). Silicon atoms in two crystal-
lographically independent positions form quasi-isolated,
butterfly-shaped, Si46Ϫ anions (Fig. 3a) with the point sym-
metry mm2 Ϫ C2ν around the position 4g (x,x¯,0 with x ϭ
0.2505). The bond length between the threefold bonded Si
˚
atoms (3b)Si of 2.4183(6) A is smaller than the distance
˚
d((3b)Si Ϫ (2b)Si) ϭ 2.4254(3) A. The differences to the
previous data can be understood taking in account that the
atomic parameters in [4] were not least-square refined.
Now, as expected from the average oxidation number of the
¯
silicon atoms in the polyanion, the average bond length d
˚
(SiϪSi) ϭ 2.424(3) A in Ba3Si4 is smaller than in BaSi and
larger than in BaSi2 (Tab. 5). The reduction of the tetrahed-
4Ϫ
6Ϫ
ranide Si4 to the Si4 anion results in the break of one
bond, so that the (2b)Si atoms are now at a distance of
˚
3.4543(6) A.
6Ϫ
The Si4 anions are surrounded by 12 Ba cations and
each Ba cation by 4 Si46Ϫ anions: (Si4)Ba12/4. Each Ba atom
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The Metallic Zintl Phase Ba3Si4
Table 5 Average bond lengths and formal charges of the silicon
anions.
˚
¯
d (Si-Si) / A Reference
Compound Connectivity
symbols
Average Si
charge
Ba5Si3
(1b)Si3Ϫ, (0b)Si4Ϫ Ϫ 3.333
2.437(7)
2.74
[25]
[24]
BaSi
(2b)Si2Ϫ
(2b)Si2Ϫ, (3b)Si1Ϫ Ϫ 1.5
Ϫ 2
2.502(3)
2.424(3)
2.404(2)
2.385(3)
2.351776(4)
[27]
Ba3Si4
This work
[48]
BaSi2
(3b)Si1Ϫ
Ϫ 1
Na2Ba6Si46 (4b) Si0.3Ϫ
Ϫ 0.304
0
[8]
Fig. 4 Coordination of the Ba atoms in Ba3Si4 (Si: red spheres).
Si
(4b)Si0
[58]
6Ϫ
Fig. 3 The Si4 anions (a) are condensed via Ba atoms to 1D
infinite polymers (red and blue) along [110] resulting in a twofold
rod packing (b, c).
is eightfold coordinated by Si atoms. The cations act as
single bonded ligands or as μ2-, and μ3-bridging ligands.
Four μ3 Ba-bridges of Ba1 and Ba2 complete the Si4 cluster
to a distorted tetrahedron star (stella quadrangula), similar
to those in K4Si4 [32] and Na4Pb4 [33]. The Ba1 and Ba2
atoms act as μ3 bridging ligands for two Si4 clusters, which
results in infinite one dimensional polymers 1ϱ[Ba4Si8] along
[110]. The polymers form a simple twofold rod packing, in
which each neighboring layer is turned by 90° (Fig. 3b, c).
˚
The shortest distance d(Ba1 Ϫ Si) ϭ 3.5761(3) A is
much longer than the shortest distances d(Ba2 Ϫ Si) ϭ
Fig. 5 (a, b): Unit cell of Ba3Si4 with displacement ellipsoids at
99 % probability (Si: red; Ba: blue). The relation to the Al3Ti struc-
ture type is indicated in (b) by the smaller red cell in the projection
along the c-axis. c: Averaged Ba3Si4 crystal structure, resulting from
the shifts of all equivalent atomic positions into a smaller Al3Ti
segments shown in (b). The centers of the Si4 anions are repre-
sented by large red spheres. d: Unit cell of the Al3Ti structure (Al:
blue; Ti: red; aЈ ϭ a √2 / 2)
˚
˚
3.2584(3) A and d(Ba3 Ϫ Si) ϭ 3.3088(2) A. This may ex-
plain that only the Ba2 and Ba3, but not the Ba1 atoms can
be substituted by Sr atoms (Ba3ϪxSrxSi4, 0 Յ x Յ 2 [34]),
and that Sr3Si4 does not exist (Fig. 4).
The centers of the [Si4] clusters at positions xx¯0 (x ϭ
1/4) form the non-characteristic Wyckoff position I4/mmm
(2a, 2b) [35] in the reduced cell aЈ ϭ a √2 / 2, cЈ ϭ c and
cЈ / aЈ ϭ 1.963. This leads directly to the Al3Ti structure-
type and to the structures of a series of complex fluorides
like Na3[UF7], which are hierarchical replacement deriva-
tives [36] of the Al3Ti type (c/a ϭ 2.01Ϫ2.23 for the Al3Ti
6Ϫ
members; c/a ϭ 1.97Ϫ2.00 for the Na3[UF7] members).
Figure 5 shows the structures of Al3Ti and Ba3[Si4] with the
6Ϫ
replacement of Ti (and [UF7]) by the Si4 cluster anion.
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Y. Grin et al.
Due to the local mm2 symmetry of Si46Ϫ, the Ba cations
show small shifts from the ideal Al (or Na) positions.
3.3 Electronic structure
The validity of the Zintl-Klemm concept is sometimes as-
sociated with physical property measurements, and es-
pecially the metallic state is then believed to be in conflict
with the concept. In fact, Zintl phases can be expected to
show a low electrical conductivity but they may show me-
tal-like temperature dependence of the conductivity as well.
The Zintl-Klemm concept implies an electron transfer to
the atoms with the highest electronegativity and this way
the covalent bonds of the Zintl anions are derived. The real
charges are reduced with ion-to-ion interactions (e.g.,
0.75 Ϫ 0.80 in NaCl [37]), but this does not change the
count for the covalent bonds. Applying the concept of
‘polar covalency’ of Sanderson [38], the effective charges in
an isolated Ba3Si4 molecule are estimated to be q(Ba) ϭ
ϩ1/2 and q(Si) ϭ Ϫ3/8. However, detailed predictions for
the physical properties can only be obtained from quantum
mechanical methods.
The total electronic density of states (DOS) reveals met-
allic behavior for Ba3Si4 with N(EF) ϭ 4.8 states eVϪ1 per
cell at Fermi energy (Fig. 6). The states between Ϫ3.6 eV
and Fermi energy are made up of mainly Si 3p and Ba 5d
basis functions. The occupancies of the Ba 5d states
(1.22Ϫ1.36 eϪ) are much larger than those of the 6s states
(0.30Ϫ0.44 eϪ) and 6p states (0.26Ϫ0.53 eϪ) and the strong
Si 3p Ϫ Ba 5d hybridization is responsible for the non-zero
DOS at the Fermi level.
The states forming the Fermi surface can be analyzed
from the band structure (Fig. 7). Starting from the ΓϪX
line, there is one band (red colored) occupied at Γ but unoc-
cupied at X with a large upward dispersion (bandwidth of
0.7 eV). Along the MϪΓ line, this band crosses the Fermi
energy near Γ, along Γ and Z it becomes unoccupied again
close to Z. This band is largely made up of Si(1) px, py,
2
2
2
2
Ba(2) dx Ϫy and Ba(3) d3z Ϫr orbitals. A doubly degener-
ated band (blue colored) along the ΓϪX line is barely unoc-
cupied at Γ with a downward dispersion towards X (band-
width of ഠ 0.3 eV). This band crosses the Fermi energy
between M and Γ close to Γ. Between Γ and Z it stays
unoccupied, flat and doubly degenerate and gets occupied
again between Z and R close to Z. Major contributors to
this band are Si(2) pz and Ba(1) dxz, dyz orbitals, together
2
2
with a very weak Ba(3) d3z Ϫr orbital participation. The
topology of the Fermi surface shows no pronounced aniso-
tropy for the metallic conductivity.
A topological analysis of the electron density calculated
by FPLO shows that only 3.4 instead of 6 electrons are
transferred from the three Ba atoms to the butterfly. There-
fore the difference between the total atomic basin charges
of the (3b)Si1 atoms (14.7 electrons; Si0.7Ϫ) and the (2b)Si2
atoms (15 electrons; Si1Ϫ) is smaller than expected. Bond
distances in Zintl anions are usually related to the charge
6Ϫ
Fig. 6 Total and atom resolved electronic density of states for Ba3Si4.
of the atoms (Table 5) as for the Si4 anion d(Si1ϪSi1) is
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The Metallic Zintl Phase Ba3Si4
ELF for free atoms are usually within ഠ 0.1 electrons of
the corresponding integer value [41]. In Ba3Si4, the large
deviation of the Ba ELF core basin populations from the
expected value of 54.0 is due to the influence of Ba 5d or-
bitals. In the crystalline environment of Ba3Si4, the Ba 5d
energy levels go down significantly in energy and become
occupied. They contribute to the charge density in the core
region, thereby increasing the total ELF core basin popu-
lation by amounts up to almost half-an-electron.
3.4 Electrical resistivity and magnetism
Fig. 7 The electronic band structure between Ϫ1 and 1 eV. For
colors see text.
The temperature-dependent resistivity measurement (Fig. 9)
on a polycrystalline bulk sample of Ba3Si4 revealed a high
resistivity at room temperature but a typical metal-like in-
crease of the resistivity with the temperature (ρ(300 K) ഠ
1.2 ϫ 10Ϫ3 Ωm; ρ0 ഠ 0.4 ϫ 10Ϫ3 Ωm). Ba3Si4 is therefore
a “bad metal” with low charge carrier concentration, in
agreement with the result of the band structure calculation.
A small upturn below 20 K may indicate a metal-to-semi-
conductor transition.
smaller than d(Si1ϪSi2). The atomic charges for the Ba
atoms with different site symmetries are similar (ϳ54.9 elec-
trons; Ba1ϩ).
Topological analysis of the ELF yields two bond attrac-
tors (Si1ϪSi1, Si1ϪSi2) and three lone-pair attractors (one
for Si1 and two for Si2) in the valence region (Fig. 8). Both
bond attractors, Si1ϪSi1 and Si1ϪSi2, are off the direct
connection line between the Si atoms. With bent SiϪSi
bonds, the bond angles of the Si atoms become closer to
tetrahedral angles, as shown e.g. for carbosilanes [39]. The
electron counts in the basins of the Si1ϪSi1 and Si1ϪSi2
bonds are 1.0 and 1.6, respectively. The basin of the lone-
pair attractor at Si1 contains 2.5 electrons, while the lone
pairs at Si2 contain 1.9 and 2.0 electrons. The total electron
count of the (Si1)2 fragment is therefore in agreement with
the expected value of six electrons, but the distribution be-
tween the bond and the lone-pairs is different from the ex-
pected one (similar examples were reported by Chestnut
[40]).
Fig. 9 Electrical resistivity between 3.8 and 320 K.
Magnetization measurements revealed a weakly tempera-
ture-dependent diamagnetism of the bulk phase at elevated
temperatures with the susceptibility χ ഠ Ϫ50(20) ϫ 10Ϫ6
cm3 molϪ1 (cgs system) (Fig. 10). With the diamagnetic in-
crements of Ba2ϩ and silicon atoms [42], a distinctly lower
susceptibility of about χcalc ഠ Ϫ120 ϫ 10Ϫ6 cm3 molϪ1 is
expected (the value would be even lower for anionic silicon
increments). The difference between the measured and cal-
culated values indicates the presence of Pauli paramagnet-
ism. In a free electron model [43] the difference of about
70 ϫ 10Ϫ6 cm3 molϪ1 would correspond to a density of
states of N(EF) ഠ 8 states eVϪ1 per cell, which is on the
order of magnitude as the calculated DOS value N(EF) ϭ
4.8 states eVϪ1 per cell.
6Ϫ
Fig. 8 ELF isosurfaces for the isolated Si4 anion. The ELF
values are 0.82 for the silver (a), and 0.76 for the golden (b) iso-
surfaces.
According to the topological analysis of the ELF in the
core region, the average of the electron counts in the Ba
and Si core basins is 54.4 and 10.1 electrons, respectively.
Generally, the individual core shell occupancies as calcu-
lated by ELF analysis are never exactly equal to the integer
values as required by the Aufbau principle, but the total
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Y. Grin et al.
Fig. 10 Magnetic susceptibility between 1.8 and 400 K at μ0H ϭ
0.1, 3.5 and 7 T.
Below 50 K, the susceptibility rises slightly and in terms
of paramagnetic defects this increase would be equivalent
to 0.1 % of S ϭ 1/2 species. No superconductivity was
found above 1.8 K in fields as low as μ0H ϭ 2 mT.
3.5 29Si NMR investigations
The static 29Si NMR experiment on an isotope-enriched
Ba3Si4 sample showed a broad signal, indicating a super-
position of different signal contributions (Fig. 11). Magic
angle spinning (MAS) at a low rotation frequency of
2.65 kHz already allowed the separation of two signal con-
tributions (Fig. 11), which is in accordance with two crys-
tallographic sites for the Si atoms (Tab. 2). The spectral par-
ameters (Tab. 6) were determined by a least-squares fit. The
isotropic shift positions Kiso were confirmed in a series of
MAS experiments at different rotation frequencies. The iso-
tropic shift of both 29Si signals is positive and outside of
the expected range of Ϫ350 ppm Յ δ Յ 50 ppm for diamag-
netic, non-metallic materials [44]. The large positive signal
shift indicates an interaction of the nuclear spins with the
electron spins of conduction electrons (e.g. Knight shift)
[45, 46]. For metallic conductors, the isotropic shift of a
signal is related to the s-orbital contribution of an atom to
the density of states at the Fermi energy. Assuming metallic
conductivity for Ba3Si4, Si1 (0.0005 states eVϪ1 per atom)
is assigned to the signal with the lower isotropic shift and
Si2 (0.001 states eVϪ1 per atom) to the signal with the
higher isotropic shift.
Fig. 11 29Si NMR signals of enriched Ba3Si4. (top) Static experi-
ment; experimental data are represented by a black dashed line.
Grey lines represent simulated signal contributions, the black line
the sum of the calculated signal conributions. The simulations are
based on the spectral parameters obtained by least-squares fitting
of the MAS signals. (bottom) Magic angle spinning (MAS) at
2.45 KHz. Full lines represent the sum of the simulated signal con-
tributions, dashed lines the experimental results. The difference bet-
ween the simulated and experimental signals is shown at the bot-
tom. The simulations of the signals are based on the parameters
from Table 6. Isotropic shift positions of the MAS signals are mar-
ked by arrows.
Table 6 Spectral parameters of the 29Si NMR signals of enriched
Ba3Si4 determined by least-squares analysis [11]. Kiso corresponds
to the isotropic Knight shift, Δ to the anisotropy parameter and η
to the asymmetry parameter.
The electrical transport properties of Ba3Si4 were investi-
gated with respect to the temperature dependence of the
isotropic signal shift (Fig. 12) and of the spin-lattice relax-
ation times (T1). The isotropic shift for Si2 is temperature
independent, as it is expected for a metal, but the isotropic
shift of Si1 slightly increases with temperature, which is fre-
quently observed for semiconductors. A semi logarithmic
plot of Kiso/T1/2 versus TϪ1 shows a positive gradient, which
is a clear evidence that Ba3Si4 is not a semiconductor
Atoms
Kiso / ppm
Δ / ppm
η
Si1
Si2
82.4(1)
281.8(1)
120.1(3)
348.3(1)
0.22(5)
0.10(5)
(Fig. 13). For semiconductors, a negative gradient is ex-
pected [47].
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The Metallic Zintl Phase Ba3Si4
Fig. 12 Isotropic shift of 29Si NMR signals at various temperatu-
res: Si1 (circles), Si2 (triangles), least-squares fit (dotted lines).
Fig. 14 Spin lattice relaxation times (T1) of the 29Si NMR signals
for various temperatures (Si1 (circles), Si2 (triangles)).
The line shape of the signals results from the charge dis-
tribution in the vicinity of the Si atoms. The large aniso-
tropy parameter Δ of the signals is due to the chemical
shielding, which is caused by orbital contributions of lo-
calized electrons. It is about 3 times larger for Si2 than for
Si1 (Tab. 6). The anisotropy parameter of Si1 is similar to
those observed for the (3b)Si1Ϫ anions in M4Si4 (M ϭ Na,
K, Rb, Cs) [48, 49].
The asymmetry parameter η of the Si2 signal is smaller
than that of Si1 (Tab. 6) and they are similar to those ob-
served for Si atoms in M4Si4 [48, 49]. An asymmetry param-
eter different from zero indicates that the symmetry of the
charge distribution is reduced compared to an ideal tetra-
hedranide anion. The charge distribution around the E14
atoms is less distorted for the silicides M4Si4 than for the
monostannides M4Sn4 (0.26 Յ η Յ 0.45) [50].
Fig. 13 Semi-logarithmic representation of the 29Si NMR iso-
Ϫ1/2
tropic signal shift K
T
as a function of TϪ1 (Si1 (circles), Si2
iso
(triangles)).
The spin-lattice relaxation times T1 differ for both sig-
nals. At ambient temperature, the values for Si1 (1.1 s) and
Si2 (10.9 s) are large in comparison with well conducting
metals, but they are at least two orders of magnitude
shorter than observed for the semiconducting alkali metal
monosilicides M4Si4 (M ϭ Na, K, Rb, Cs) [48]. For semi-
conductors, a positive gradient of the plot log(1/(T1 T2)) /
TϪ1 is expected [47], which is not observed for Ba3Si4. In
general, T1 for metals decreases linearly with increasing
temperature [45, 46], as it is observed for Si1. T1 for Si2
shows a non-linear temperature dependence (Fig. 14), indi-
cating another relaxation mechanism, which becomes more
relevant at higher temperatures. The reason might be that
the charge distribution around Si2 with 2 lone pairs is more
anisotropic than for Si1 with 1 lone pair. The higher aniso-
tropy leads to an enhanced spin lattice relaxation, which is
due to the interaction of the fluctuating electric field in-
duced by phonons with the charge distribution around the
atoms.
3.6 Oxidation of Ba3Si4 with gaseous HCl
A new application for reactive intermetallic phases has
arisen from their oxidation behavior as it was demonstrated
by the oxidation of Na4Ge4 or Na12Ge17 to a new element
modification of Ge (cF136) [6] or the oxidation of Mg2Ge
to mesoporous Ge [51]. In this work, nanoporous silicon
was obtained from the oxidation of Ba3Si4 with HCl. Gase-
ous HCl was evolved from the quantitative dissociation of
NH4Cl into NH3, N2, H2 and HCl at 873 K [52, 53]. Ba3Si4
reacted to a fine, brown powder, which is a mixture of nan-
oporous Si and BaCl2. The reaction is driven by the forma-
tion of solid BaCl2. The evolution of gaseous H2 might sup-
press the formation of crystalline α-Si and promote the for-
mation of nanoporous Si. The product is stable on air and
BaCl2 was removed by water. Similar techniques were pre-
viously applied for the syntheses of Na6.2Si46 [7], K7.0Si46
[7] and Na2Ba6Si46 [8].
Z. Anorg. Allg. Chem. 2008, 1651Ϫ1661
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Y. Grin et al.
ored silicon or germanium morphologies by oxidation of
different precursors under adapted reaction conditions.
Amorphous silicon is currently used for solar cells, which
are easier to manufacture, but less efficient than solar cells
based on crystalline silicon.
Remark on Ba3Ge4
In our theoretical calculations we find evidence for Ba 5d
contributions to the occupied states both for HT-Ba3Ge4,
which is isotypic to Ba3Si4, and for LT-Ba3Ge4 [56]. The
DOS, based on FPLO calculations, for HT-Ba3Ge4 is very
similar to that of Ba3Si4 with N(EF) ϭ 7.3 eVϪ1 per cell.
The DOS of LT-Ba3Ge4 is of semi-metallic type with
N(EF) ϭ 0.7 eVϪ1 per cell. As in the case of Ba3Si4, a strong
hybridization between Ge 4p and Ba 5d states is responsible
for the (semi-) metallic behavior of both modifications.
Contrary to previous results [56] our present TB-LMTO-
ASA [57] calculations did not show any band gap for either
modification and are in good agreement with the FPLO re-
sults.
Weitere Einzelheiten zur Kristallstrukturuntersuchung können
beim Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leo-
poldshafen (Fax: (ϩ49) 7247-808-666, E-mail@fiz-karlsruhe.de)
unter der Hinterlegungsnummer CSD-419308 angefordert werden.
Acknowledgment. The authors would like to thank Dr. S.
Hoffmann, P. Scheppan, R. Koban, S. Müller and S. Hückmann
for their support and technical assistance.
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